Infrared Spatial Interferometer...C.H. Townesa, M. Beste?, W.C. Danchia, D.D.S. Halea, J.D. Monnie?, E.A. Lipmana, P.G. Tuthilla, M.A. JOhflSOflb, and D. Wa1ters' aSpace Sciences Laboratory,

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Infrared Spatial Interferometer

Townes, Charles, Bester, Manfred, Danchi, William, Hale,David, Monnier, John, et al.

Charles H. Townes, Manfred Bester, William C. Danchi, David D. SnyderHale, John D. Monnier, Everett A. Lipman, Peter G. Tuthill, Mark A. Johnson,Donald L. Walters, "Infrared Spatial Interferometer," Proc. SPIE 3350,Astronomical Interferometry, (24 July 1998); doi: 10.1117/12.317159

Event: Astronomical Telescopes and Instrumentation, 1998, Kona, HI, UnitedStates

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invited Paper


C.H. Townesa, M. Beste?, W.C. Danchia, D.D.S. Halea, J.D. Monnie?, E.A. Lipmana,

P.G. Tuthilla, M.A. Johnson", and D. Waltersc

aSpace Sciences Laboratory, University of California, Berkeley, CA 94720"Lawrence Livermore National Laboratory, Livermore, CA

cNaval Postgraduate School, Monterey, CA

ABSTRACT

The Infrared Spatial Interferometer (ISI) is an interferometer installed on Mt. Wilson and operating in the 10 tmwavelength region, using heterodyne detection and two movable 1.65 m telescopes. Its general technology andcharacteristics, recent changes, and observational results are broadly discussed. Some compensation for atmosphericpath length fluctuations is demonstrated. Stellar observations show, among other characteristics, that many starsemit gas and dust episodically with times of 10 - 100 years between events, and that stellar diameters measured inthe mid-infrared region are about 10% larger than those measured with interferometry using visible light.

Keywords: stellar interferometry, infrared interferometry

1. INTRODUCTION

Since the Berkeley Infrared Spatial Interferometer (ISI) appears to be the only astronomical interferometer operatingin the mid-infrared at present, we shall not only describe the instrument and some of its results but discuss the fieldsomewhat broadly. Most interferometry has been done in the radio and visible regions, although there is increasingattention to the near infrared for interferometric work on stars. The mid-infrared allows one to look at ratherdifferent objects than do these shorter wavelengths. It detects not only stars and hot dust, but also the mildly warmdust surrounding stars. Mid-infrared wavelengths can also penetrate clouds and see stars which, due to interveningdust, may not be intense enough at shorter wavelengths to study. The longer wavelengths change seeing problems;atmospheric fluctuations of importance vary more slowly and also correlate over much larger distances than thosefor visible light. The mid-infrared is quite sensitive to changes in temperature of dust clouds which are relativelycool and is useful in detecting such changes, but not very sensitive to changes in the temperatures of starsthemselves. For example, a star at 3000K will change its visible luminosity by a factor of about 2 if the temperatureis changed only 250K, while wavelengths in the 10 I.tm region change intensity by only about 10%. This means thatstars which have a nonuniform surface temperature or a changing one can give a very nonuniform intensity or achanging one in the visible region, while being relatively constant in the infrared. Interferometry at visiblewavelengths and in the mid-jR are thus mutually complementary.

2. DESCRIPTION AND CHARACTERISTICS OF TIlE ISI EQUIPMENT

The ISI has been operating on Mt. Wilson, using two telescopes of effective aperture 1.65 m. It has been previouslydescribed,' but will be summarized briefly here. The telescopes are in trailers, and hence can be moved to vary theirbaseline, at present between 4 m and 35 m. An extension to about 75 m is planned soon. The two telescopes can beseen in Fig. 1 with a separation of 16.1 m. The design is sometimes called a "Pfund" telescope. It involves a flat 80"mirror in an alt-azimuth mount and a 65" parabola fixed in position. The flat mirror can be regarded as a coelostat,sending radiation into the parabola which then focuses the radiation through a hole in the flat mirror and onto anoptics table. These telescopes are illustrated schematically by Fig. 2. The dashed lines in this figure represent HeNelaser beams which are distance interferometers. They measure path lengths within the telescope. Once the trailer ispositioned, it can be lowered, allowing the two larger mirrors and their mounts, as well as the optics table, to sit onkinematic motmts which in turn are supported by concrete blocks laid into the ground. Thus, the two mirrors and

Part of the SPIE Conference on Astronomical lnterferometrv Kona, Hawaii March 1998908 SPIE Vol. 3350 0277-786)(1981$10.00

Invited Paper


C.H. Townesa, M. Beste?, W.C. Danchia, D.D.S. Halea, J.D. Monnie?, E.A. Lipmana,

P.G. Tuthilla, M.A. JOhflSOflb, and D. Wa1ters'

aSpace Sciences Laboratory, University of California, Berkeley, CA 94720bLaence Livermore National Laboratory, Livermore, CA

CNaval Postgraduate School, Monterey, CA

ABSTRACT

The Infrared Spatial Interferometer (151) is an mterferometer installed on Mt. Wilson and operating in the 10 tmwavelength region, using heterodyne detection and two movable 1 .65 m telescopes. Its general technology andcharacteristics, recent changes, and observational results are broadly discussed. Some compensation for atmosphericpath length fluctuations is demonstrated. Stellar observations show, among other characteristics, that many starsemit gas and dust episodically with times of 10 - 100 years between events, and that stellar diameters measured inthe mid-infrared region are about 10% larger than those measured with interferometry using visible light.

Keywords: stellar interferometry, infrared interferometry

1. INTRODUCTION

Since the Berkeley infrared Spatial Interferometer (IS!) appears to be the only astronomical interferometer operatingin the mid-infrared at present, we shall not only describe the instrument and some of its results but discuss the fieldsomewhat broadly. Most interferometry has been done in the radio and visible regions, although there is increasingattention to the near infrared for interferometric work on stars. The mid-infrared allows one to look at ratherdifferent objects than do these shorter wavelengths. It detects not only stars and hot dust, but also the mildly warmdust surrounding stars. Mid-infrared wavelengths can also penetrate clouds and see stars which, due to interveningdust, may not be intense enough at shorter wavelengths to study. The longer wavelengths change seeing problems;atmospheric fluctuations of importance vary more slowly and also correlate over much larger distances than thosefor visible light. The mid-infrared is quite sensitive to changes in temperature of dust clouds which are relativelycool and is useful in detecting such changes, but not very sensitive to changes in the temperatures of starsthemselves. For example, a star at 3000K will change its visible luminosity by a factor of about 2 ifthe temperatureis changed only 250K, while wavelengths in the 10 tm region change intensity by only about 10%. This means thatstars which have a nonuniform surface temperature or a changing one can give a very nonuniform intensity or achanging one in the visible region, while being relatively constant in the infrared. Interferometry at visiblewavelengths and in the mid-IR are thus mutually complementary.

2. DESCRIPTION AND CHARACTERISTICS OF THE ISI EQUIPMENT

The ISI has been operating on Mt. Wilson, using two telescopes of effective aperture 1 .65 m. It has been previouslydescribed,' but will be summarized briefly here. The telescopes are in trailers, and hence can be moved to vary theirbaseline, at present between 4 m and 35m. An extension to about 75 m is planned soon. The two telescopes can beseen in Fig. 1 with a separation of 16.1 m. The design is sometimes called a "Pfund" telescope. It involves a flat 80"mirror in an alt-azimuth mount and a 65"parabola fixed in position. The flat mirror can be regarded as a coelostat,sending radiation into the parabola which then focuses the radiation through a hole in the flat mirror and onto anoptics table. These telescopes are illustrated schematically by Fig. 2. The dashed lines in this figure represent HeNelaser beams which are distance interferometers. They measure path lengths within the telescope. Once the trailer ispositioned, it can be lowered, allowing the two larger mirrors and their mounts, as well as the optics table, to sit onkinematic mounts which in turn are supported by concrete blocks laid into the ground. Thus, the two mirrors and

Part of the SPE Conference on Astronomical Interferometry • Kona, Hawaii • March 1998908 SPIE Vol. 3350 • 0277-786X198/$1O.OO

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optics table are freed from touching the trailer, and movements of operators inside the trailer do not shake thenisubstantially.

Fig. I. The two 1.65 m Pfund telescopes of the IS!. deployed on Mt. Wilson.

909

UCB INFRARED SPATIAI INTERFEROMETER I urrFp

SEMI-TRAILER OUTLINE

Fig. 2. A schematic of an IS! telescope, with a 65" stationary parabolic mirror and an 80" flat mirror on an alt-azimuth mount.The optics and instrument table is behind the flat mirror. Dashed lines indicate the beams of the HcNe laser distanceinterferometers.

optics table are freed from touching the trailer, and movements of operators inside the trailer do not shake thenisubstantially.

SEMI-TRAILER OUTLINE

Fig. 2. A schematic of an ISI telescope, with a 65" stationary parabolic mirror and an 80" flat mirror on an alt-azimuth mount.The optics and instrument table is behind the flat mirror. Dashed lines indicate the beams of the l4eNe laser distanceinterferometers.

909

Fig. I. The two 1.65 m Pfund telescopes of the IS!, deployed on Mt. Wilson.

MOB INFRARED SPATIAL INTERFEROMETER .


910

A schematic of the interferometer operation is shown in Fig. 3. Heterodyne detection is used with a CO2 laser asa local oscillator. The local oscillator power is mixed with the incoming infrared astronomical signal in a detectorwhich provides a beat frequency between the two with an IF bandwidth of about 3 GHz. Both sidebands, each 3GHz wide, are then transmitted by RF cable and mixed with a similar signal from the other telescope, providing abeat between the two signals or an interference fringe. Each telescope has its own local oscillator, and a beam sentfrom the CO2 laser in one telescope to the second telescope allows the second CO2 laser to be locked in phase to thefirst. However, the phase lock is done with a frequency difference of about 1 MHz frequency, which is varied insuch a way as to give what is known as lobe rotation. This provides a fringe signal of fixed frequency as theobserved object moves across the sky. This type of heterodyne detection and lobe rotation is commonly used inradio astronomy. In fact the whole system is in principle essentially like a radio interferometer.

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Fig. 3. A schematic of the ISI interferometer. showing the local oscillators (LO) and the semiconductor detector-mixers which provideheterodyne detection. The two LOs are locked together in phase by the phase lock loop (PLL) which responds to their beat signal in anotherdetector-mixer. The IF signals from the two telescopes, of bandwidth 3 GHz, are beat together to form a "fringe."

The laser beam sent from the first telescope to the second one is reflected back along the same path and beatwith the outgoing signal in the first telescope. This allows automatic pathlength adjustment to produce a path lengthwhich is an exact multiple of the wavelength, thus assuring that the phase of the local oscillator in the secondtelescope is uniquely related to that in the first.

The interference fringe produced by mixing the signals from the two telescopes is initially at a frequency ofabout 1 MHz, but it is mixed with a signal which differs from it by about 100 Hz, and the fmal fringe is observed attheir beat frequency near 100 Hz. This frequency varies slightly with time depending on fluctuations in the relativeatmospheric pathlengths.

A power spectrum of an interference fringe for the star a Orionis is shown in Fig. 4. This represents a signalrecorded over a time of 512 seconds. The width of the central spike is about 1/500 Hz, the width produced by thefmite time of observation. Small spikes on either side of the central fringe represent additional frequencies of thefringe spectrum produced by atmospheric fluctuations. This particular fringe was taken during excellent seeing withthe two telescopes separated by 4 m, and provided remarkably small phase fluctuations due to a very constantatmosphere. Fig. 5 shows a contrasting example, with a very wide fringe produced by large and rapid atmosphericfluctuations. As can be seen, the width of this fringe is about 15 Hz, indicating that the phase of the fringe changessubstantially on a timescale of about 1/15 of a second. This is very poor seeing. The timescale for changes of anoptical fringe is shorter than that for wavelengths of 11 sm, which is our normal working wavelength, by a factorsomewhat greater than the ratio of the two wavelengths. Thus, this particular fringe was taken when an opticalfringe would have been changing on a timescale somewhat shorter than 1/300 of a second. Nevertheless, the total

910

A schematic ofthe interferometer operation is shown in Fig. 3. Heterodyne detection is used with a CO2 laser asa local oscillator. The local oscillator power is mixed with the incoming infrared astronomical signal in a detectorwhich provides a beat frequency between the two with an IF bandwidth of about 3 GHz. Both sidebands, each 3GHz wide, are then transmitted by RF cable and mixed with a similar signal from the other telescope, providing abeat between the two signals or an interference fringe. Each telescope has its own local oscillator, and a beam sentfrom the CO2 laser in one telescope to the second telescope allows the second CO2 laser to be locked in phase to thefirst. However, the phase lock is done with a frequency difference of about 1 MHz frequency, which is varied insuch a way as to give what is known as lobe rotation. This provides a fringe signal of fixed frequency as theobserved object moves across the sky. This type of heterodyne detection and lobe rotation is commonly used inradio astronomy. In fact the whole system is in principle essentially like a radio interferometer.

Fig. 3 . A schematic of the IS! interferometer, showing the local oscillators (LO) and the semiconductor detector-mixers which provideheterodyne detection. The two LOs are locked together in phase by the phase lock loop (PLL) which responds to their beat signal in anotherdetector-mixer. The IF signals from the two telescopes, ofbandwidth 3 GHz, are beat together to form a "fringe."

The laser beam sent from the first telescope to the second one is reflected back along the same path and beatwith the outgoing signal in the first telescope. This allows automatic pathlength adjustment to produce a path lengthwhich is an exact multiple of the wavelength, thus assuring that the phase of the local oscillator in the secondtelescope is uniquely related to that in the first.

The interference fringe produced by mixing the signals from the two telescopes is initially at a frequency ofabout 1 MHz, but it is mixed with a signal which differs from it by about 100 Hz, and the fmal fringe is observed attheir beat frequency near 100 Hz. This frequency varies slightly with time depending on fluctuations in the relativeatmospheric pathlengths.

A power spectrum of an interference fringe for the star a Orionis is shown in Fig. 4. This represents a signalrecorded over a time of 512 seconds. The width of the central spike is about 1/500 Hz, the width produced by thefmite time of observation. Small spikes on either side of the central fringe represent additional frequencies of thefringe spectrum produced by atmospheric fluctuations. This particular fringe was taken during excellent seeing withthe two telescopes separated by 4 m, and provided remarkably small phase fluctuations due to a very constantatmosphere. Fig. 5 shows a contrasting example, with a very wide fringe produced by large and rapid atmosphericfluctuations. As can be seen, the width of this fringe is about 15 Hz, indicating that the phase of the fringe changessubstantially on a timescale of about 1/15 of a second. This is very poor seeing. The timescale for changes of anoptical fringe is shorter than that for wavelengths of 11 pm, which is our normal working wavelength, by a factorsomewhat greater than the ratio of the two wavelengths. Thus, this particular fringe was taken when an opticalfringe would have been changing on a timescale somewhat shorter than 1/300 of a second. Nevertheless, the total


power of the fringe and hence the visibility of a Orionis can be determined from this very wide fringe associatedwith very poor seeing simply by integrating the total power under the curve, which can be done with substantialaccuracy in spite of its breadth. Thus, while the signal to noise ratio of the fringe in Fig. 4 is obviously very high,the integrated signal to noise ratio with the very poor seeing shown in Fig. 5 is still fairly high.

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Fringe Frequency [Hz]Fig. 4. An interference fringe signal of a Orionis under exceptionally good seeing conditions. Atmospheric fluctuations are smallenough that only very weak sidebands over a small fraction of one Hertz are produced by their variations. The data were takenfor 512 seconds, and the very narrow resulting fringe has a width due primarily to this finite time of measurement.

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Fringe Frequency [Hz]Fig. 5. An interference fringe from a Orionis under very poor seeing conditions. In this case the atmospheric pathlength isfluctuating severely and on timescales comparable with the inverse width seen, or about 1/15 sec. This is fast for wavelengths aslong as 11 rim. In spite of such fluctuations, the fringe magnitude, or total power, can be rather accurately determined byintegrating the total power under the curve of this figure.

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power of the fringe and hence the visibility of a Orionis can be determined from this very wide fringe associatedwith very poor seeing simply by integrating the totalpower under the curve, which can be done with substantialaccuracy in spite of its breadth. Thus, while the signal to noise ratio of the fringe in Fig. 4 isobviously very high,the integrated signal to noise ratio with the verypoor seeing shown in Fig. 5 is still fairly high.

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Fringe Frequency [Hz]Fig. 4. An interference fringe signal of a Orionis under exceptionally good

seeing conditions. Atmospheric fluctuations are smallenough that only very weak sidebands over a small fraction of one Hertz are produced by their variations. The data were takenfor 512 seconds, and the very narrow resulting fringe has a width due primarily to this finite time of measurement.

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Fringe Frequency [Hz]Fig. 5. An interference fringe from a Orionis undervery poor seeing conditions. In this case the atmospheric pathlength isfluctuating severely and on timescales comparable with the inverse width seen, or about 1/15 sec. This is fast for wavelengths aslong as 1 1 .tm. In spite of such fluctuations, the fringe magnitude, or total power, can be rather accurately determined byintegrating the total power under the curve ofthis figure.

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912

3. SENSITIVITY CONSIDERATIONS

It is perhaps useful to make some comparison at this point between heterodyne detection and direct detectionfor the measurement of fringes or interferometric visibilities. In the radio region, essentially all detection is done byheterodyne methods, since no direct photon detection is normally practical. At optical wavelengths, direct photondetection is normal and generally advisable for interferometry. Heterodyne detection produces a detector noise of 1photon per second per unit bandwidth for one polarization. For optical photons, this would be indeed a great deal ofnoise. In the radio region, there is background radiation of many photons per second per unit bandwidth in any case,and heterodyne detection provides no substantial additional noise. The mid-infrared is a region where both types ofdetection are appropriate, depending on the exact purpose and usage of such detection.

It can be argued that direct detection is much more sensitive than heterodyne detection in the mid-infrared, andhence that it is most appropriately used for interferometry. The number of photons per second per spatial mode perunit bandwidth due to thermal radiation at room temperature is about 0.03. If transmission through the atmosphereand the optical system used is reasonably good, then not more than perhaps 60% or 0.02 photons per second are

received as background noise. This would imply that for a given bandwidth, the sensitivity is greater by or

about 7, for direct detection than for heterodyne. In addition, heterodyne detection covers a rather narrow frequencyrange, in our particular case about 0.2 cm1, and it is unlikely to be larger by more than a few factors of 2. For directdetection one can easily use a bandwidth 100 times greater, implying another factor of 10 advantage in sensitivityfor direct detection. However, in actual practice various phenomena or interferometer uses can substantially modifythe apparent advantage of direct detection.

If a number of telescopes are used in an interferometric system in order to produce images, the energy must bedivided up if direct detection is used for a number of baselines. Thus, for 10 telescopes, the energy from eachtelescope must be divided into 9 equal parts, which then makes a relative loss in the sensitivity of a factor of 9. Forheterodyne detection, the division produces no such loss, because amplification and division of the signal can bedone with no decrease in signal to noise ratio. In addition, optical delay lines are rather more complex andtroublesome than are the delay lines for the narrow bandwidths used in heterodyne detection. In our case, the delaylines are simply RF cables. Instead of tracking the atmospheric fluctuations, we need only to put in calculatedchanges in the delay line length associated with the geometry of the telescopes and the object observed. To vary thedelay, we switch in or out 1 cm lengths of delay line, thus providing an accuracy of 1/2 cm for the delay, which isadequate. Thus the arrangement of delay lines, particularly for use of many telescopes, is rather simpler and moreconvenient for the heterodyne case, and avoids losses in signal to noise ratio due to division.

If detection is attempted on a rather weak star with no stronger star near enough to be used for tracking thenecessary delay, then the apparent advantage of direct detection decreases substantially further. This is because theappropriate pathlength must be tracked on a timescale comparable with the time of change of phase due toatmospheric fluctuations, which can be as short as about 1/100 second. Thus, an adequate signal must be obtained in1/100 of a second, unless some other special tracking mechanism is used, such as search and averaging when thefringe cannot be locked on. In the case of heterodyne detection, the delay is not varied by tracking on the star, butby precalculation, so that the fringe signal can be accumulated for periods as long as an hour or more, possiblyaveraging over more than one night. This gives the possibility of averaging a weak signal for a much longer time. If,for example, some allowance is made for averaging a fringe signal even when it is not phase-tracked perfectly, onemight assume a time as long as 1 second for detecting a weak fringe with a direct detection system. Comparing thiswith an hour for a heterodyne system gives heterodyne detection a relative sensitivity gain of a factor of 60.However, this conclusion applies only in some cases. If there is a bright star sufficiently close to the sourceobserved, then this problem for direct detection can be eliminated.

A further helpful characteristic of heterodyne detection is that the detected radiation, from which the totalpower is determined, is only that component of the astronomical signal which is in a single spatial mode and thusoverlaps the laser radiation correctly. This is the same part of the power which can produce interference betweensignals from two telescopes, so that seeing has little effect on the visibility calibration. For direct detection, radiationin only a single mode is sometimes similarly obtained by passing the radiation through a single mode fiber, and a

912

3. SENSITIVITY CONSIDERATIONS

It is perhaps useful to make some comparison at this point between heterodyne detection and direct detectionfor the measurement of fringes or interferometric visibilities. In the radio region, essentially all detection is done byheterodyne methods, since no direct photon detection is normally practical. At optical wavelengths, direct photondetection is normal and generally advisable for interferometry. Heterodyne detection produces a detector noise of 1photon per second per unit bandwidth for one polarization. For optical photons, this would be indeed a great deal ofnoise. In the radio region, there is background radiation of many photons per second per unit bandwidth in any case,and heterodyne detection provides no substantial additional noise. The mid-infrared is a region where both types ofdetection are appropriate, depending on the exact purpose and usage of such detection.

It can be argued that direct detection is much more sensitive than heterodyne detection in the mid-infrared, andhence that it is most appropriately used for interferometry. The number of photons per second per spatial mode perunit bandwidth due to thermal radiation at room temperature is about 0.03. If transmission through the atmosphereand the optical system used is reasonably good, then not more than perhaps 60% or 0.02 photons per second are

received as background noise. This would imply that for a given bandwidth, the sensitivity is greater by j5 orabout 7, for direct detection than for heterodyne. In addition, heterodyne detection covers a rather narrow frequencyrange, in our particular case about 0.2 cm', and it is unlikely to be larger by more than a few factors of 2. For directdetection one can easily use a bandwidth 100 times greater, implying another factor of 10 advantage in sensitivityfor direct detection. However, in actual practice various phenomena or mterferometer uses can substantially modifythe apparent advantage of direct detection.

If a number of telescopes are used in an interferometric system in order to produce images, the energy must bedivided up if direct detection is used for a number of baselines. Thus, for 10 telescopes, the energy from eachtelescope must be divided into 9 equal parts, which then makes a relative loss in the sensitivity of a factor of 9. Forheterodyne detection, the division produces no such loss, because amplification and division of the signal can bedone with no decrease in signal to noise ratio. In addition, optical delay lines are rather more complex andtroublesome than are the delay lines for the narrow bandwidths used in heterodyne detection. In our case, the delaylines are simply RF cables. Instead of tracking the atmospheric fluctuations, we need only to put in calculatedchanges in the delay line length associated with the geometry of the telescopes and the object observed. To vary thedelay, we switch in or out 1 cm lengths of delay line, thus providing an accuracy of 1/2 cm for the delay, which isadequate. Thus the arrangement of delay lines, particularly for use of many telescopes, is rather simpler and moreconvenient for the heterodyne case, and avoids losses in signal to noise ratio due to division.

If detection is attempted on a rather weak star with no stronger star near enough to be used for tracking thenecessary delay, then the apparent advantage of direct detection decreases substantially further. This is because theappropriate pathlength must be tracked on a timescale comparable with the time of change of phase due toatmospheric fluctuations, which can be as short as about 1/100 second. Thus, an adequate signal must be obtained in1/100 of a second, unless some other special tracking mechanism is used, such as search and averaging when thefringe cannot be locked on. In the case of heterodyne detection, the delay is not varied by tracking on the star, butby precalculation, so that the fringe signal can be accumulated for periods as long as an hour or more, possiblyaveraging over more than one night. This gives the possibility of averaging a weak signal for a much longer time. If,for example, some allowance is made for averaging a fringe signal even when it is not phase-tracked perfectly, onemight assume a time as long as 1 second for detecting a weak fringe with a direct detection system. Comparing thiswith an hour for a heterodyne system gives heterodyne detection a relative sensitivity gain of a factor of 60.However, this conclusion applies only in some cases. If there is a bright star sufficiently close to the sourceobserved, then this problem for direct detection can be eliminated.

A further helpful characteristic of heterodyne detection is that the detected radiation, from which the totalpower is determined, is only that component of the astronomical signal which is in a single spatial mode and thusoverlaps the laser radiation correctly. This is the same part of the power which can produce interference betweensignals from two telescopes, so that seeing has little effect on the visibility calibration. For direct detection, radiationin only a single mode is sometimes similarly obtained by passing the radiation through a single mode fiber, and a


similar advantage in visibility measurement is achieved. However, this use of a fiber entails a loss, usually by afactor between 2 and 5, which is another factor reducing the relative sensitivity advantage of direct detection fromits theoretical ideal.

For carrying out interferometry on spectral lines, it is necessary to use bandwidths somewhat narrower than theline widths. Doppler widths at 10 xm wavelength for material around stars are typically about 0.02 cm, Forbandwidths this small or smaller, non-fundamental noise in direct detectors such as leakage currents or leakageradiation limits their sensitivity. Heterodyne detection by contrast does not become less sensitive than its

fundamental limits as the bandwidth is narrowed. Thus for bandwidths as narrow as 0.02 cm1 or less, heterodynedetection can be more sensitive than direct detection even without allowing for the various special factors notedabove. For interferometry on spectral lines, this characteristic is an important one.

The above discussion illustrates why probably both direct and heterodyne detection systems should bedeveloped for mid-infrared interferometry. They will be competitive and may serve complementary functions.

4. ATMOSPHERIC PATH LENGTH FLUCTUATIONS

Atmospheric pathlength fluctuations, closely related to "seeing," represent an important problem for interferometryfrom the Earth's surface. For that reason we have paid some attention to their measurement, sources, and thepossibility of correction. Such studies have shown that there is a correlation between fluctuations measured withinthe telescope optics by the HeNe laser distance interferometers (LDI) and fluctuations along the pathlengths throughthe atmosphere above the telescopes. Furthermore, a substantial fraction of the atmospheric pathlength fluctuationsis concentrated near the surface.'2 At Mt. Wilson, under normal good seeing conditions about 60% of the seeingproblem is concentrated within about 30 m of the surface, and much of it is correlated with fluctuations which aremeasurable a modest distance above the ground. The ground layer of turbulence is well demonstrated bymeasurements with a pulsing acoustic radar. Fig. 6 shows the results of such measurements. The pulse length isabout 2.5 m, and pulses scattered by atmospheric turbulence are received at ground level. Fig. 6 represents therelative intensity of this received acoustic signal as a function of height in meters and of time in seconds. Pulses arereleased periodically with 1 second separation. The left-hand part of Fig. 6 shows the turbulence structure of theatmosphere at a particular time on Mt. Wilson in the middle of the day. It can be seen that strong turbulence extendsup to at least 140 m in this case. The right hand part shows the same type of measurement during relatively goodseeing in the evening. Here, the scattered radiation is fairly intense up to a distance of about 40 m and thendecreases, demonstrating the ground layer of turbulence.

40 60 80 40 28 00 68 80 280 20 40 60 80 20 20 40 64 60 2(4)

Fig. 6. Scattering of acoustic pulses from the ground by atmospheric turbulence at various heights. Pulses are repeated everysecond, and shown for a total time of 200 seconds (the horizontal axis). The strength of scattering as a function of height (inmeters) above the ground (the vertical axis) is indicated by brightness in this diagram. The left-hand figure represents resultsduring midday on Mt. Wilson, when seeing is poor. The right-hand figure represents results during relatively good seeingconditions during the evening. It demonstrates that atmospheric turbulence is most severe near the ground and up to a height ofabout 40 m.

913

similar advantage in visibility measurement is achieved. However, this use of a fiber entails a loss, usually by afactor between 2 and 5, which is another factor reducing the relative sensitivity advantage of direct detection fromits theoretical ideal.

For carrying out interferometry on spectral lines, it is necessary to use bandwidths somewhat narrower than theline widths. Doppler widths at 10 .tm wavelength for material around stars are typically about 0.02 cm'. Forbandwidths this small or smaller, non-fundamental noise in direct detectors such as leakage currents or leakageradiation limits their sensitivity. Heterodyne detection by contrast does not become less sensitive than itsfundamental limits as the bandwidth is narrowed. Thus for bandwidths as narrow as 0.02 cm' or less, heterodynedetection can be more sensitive than direct detection even without allowing for the various special factors notedabove. For interferometry on spectral lines, this characteristic is an important one.

The above discussion illustrates why probably both direct and heterodyne detection systems should bedeveloped for mid-infrared interferometry. They will be competitive and may serve complementary functions.

4. ATMOSPHERIC PATH LENGTH FLUCTUATIONS

Atmospheric pathlength fluctuations, closely related to "seeing," represent an important problem for interferometryfrom the Earth's surface. For that reason we have paid some attention to their measurement, sources, and thepossibility of correction. Such studies have shown that there is a correlation between fluctuations measured withinthe telescope optics by the HeNe laser distance interferometers (LDI) and fluctuations along the pathlengths throughthe atmosphere above the telescopes. Furthermore, a substantial fraction of the atmospheric pathlength fluctuationsis concentrated near the surface.'2 At Mt. Wilson, under normal good seeing conditions about 60% of the seeingproblem is concentrated within about 30 m of the surface, and much of it is correlated with fluctuations which aremeasurable a modest distance above the ground. The ground layer of turbulence is well demonstrated bymeasurements with a pulsing acoustic radar. Fig. 6 shows the results of such measurements. The pulse length isabout 2.5 m, and pulses scattered by atmospheric turbulence are received at ground level. Fig. 6 represents therelative intensity of this received acoustic signal as a function of height in meters and of time in seconds. Pulses arereleased periodically with I second separation. The left-hand part of Fig. 6 shows the turbulence structure of theatmosphere at a particular time on Mt. Wilson in the middle of the day. It can be seen that strong turbulence extendsup to at least 140 m in this case. The right hand part shows the same type of measurement during relatively goodseeing in the evening. Here, the scattered radiation is fairly intense up to a distance of about 40 m and thendecreases, demonstrating the ground layer of turbulence.

Fig. 6. Scattering of acoustic pulses from the ground by atmospheric turbulence at various heights. Pulses are repeated everysecond, and shown for a total time of 200 seconds (the horizontal axis). The strength of scattering as a function of height (inmeters) above the ground (the vertical axis) is indicated by brightness in this diagram. The left-hand figure represents resultsduring midday on Mt. Wilson, when seeing is poor. The right-hand figure represents results during relatively good seeingconditions during the evening. It demonstrates that atmospheric turbulence is most severe near the ground and up to a height ofabout 40 m.

913


914

0.4

0.2

-o.o

J-0.2

-0.4

0.4

HeNe LDI Phase in Telescope 1, 2 and 1-2

I . I

dab shifled by .0.0005 (+0 p0.6+)

mis deviabiorr 0.060 rev

I I .. .

1.76 1.80 1.84 1.55

dala shilled by -3.2505 (65 pmnbs)

errs devizrtiorr 0.055 rev

I I

1.76 1.80 1.84 1.88

UTC [h}

Fig. 7. Path length fluctuations measured by HeNe laser interferometers within the optical paths between the two large mirrors ofeach telescope. The top trace shows, for the first telescope, fluctuations in units of 11 J.Lm as a function of time (the horizontalaxis) over a period of 0.15 hours, or about 10 mins. The second from top trace shows the same measurements for the secondtelescope during the same period of time. The third from top trace represents the difference between fluctuations in the twotelescopes, showing a strong correlation between the two as can be seen visually from the upper two traces. The lowest tracerepresents the difference between fluctuations in the two telescopes with fluctuations in the first telescope shifted by 3.25seconds in time with respect to those in the second telescope. This indicates a still stronger correlation if time required for agiven volume of air to move from the first to the second telescope is allowed for.

0.4

0.2

-0.0

-0.2

-0.4

0.4

0.2

-0.0

-0.2

-0.4

uTc [h}

Fig. 7. Path length fluctuations measured by HeNe laser interferometers within the optical paths between the two large mirrors ofeach telescope. The top trace shows, for the first telescope, fluctuations in units of 1 1 p.tm as a function of time (the horizontalaxis) over a period of 0. 1 5 hours, or about 10 mins. The second from top trace shows the same measurements for the secondtelescope during the same period of time. The third from top trace represents the difference between fluctuations in the twotelescopes, showing a strong correlation between the two as can be seen visually from the upper two traces. The lowest tracerepresents the difference between fluctuations in the two telescopes with fluctuations in the first telescope shifted by 3.25seconds in time with respect to those in the second telescope. This indicates a still stronger correlation if time required for agiven volume of air to move from the first to the second telescope is allowed for.

HeNe LDI Phase in Telescope 1, 2 and 1-2

>ci)

a-J

>U)

cva-J

U)

cJ

a-J

data slulted by +0.000 5 (+0 pointS)

mis deviation 0.060 rev

O.410.2 -

0.0

-0.2

04 1176 180 1.84 1.00

data shitted by -3.250 S (-65 points)

tins deviation 0.055 rev

0.4

>. 0.2

0.0a-J 0.2

04

1.76 180 1.84 1.88

914


It is important to note that many of the larger path length variations are correlated over some distance bothlaterally on the ground and vertically into the atmosphere. Fig. 7 shows variations within the HeNe LDIinterferometers in two different telescopes spaced 4 m apart. The two top traces represent fluctuations measured inwavelengths in the two separate telescopes. The third diagram from the top shows the difference between these two.It can be seen that many of the larger fluctuations are closely similar for the two. The bottom trace represents thedifference between paths in the two telescopes when one of them is shifted in time by 3.25 seconds. This shows astill closer correlation between the two, indicating a time delay between fluctuations in the two telescopes. Since thedistance between the two is 4 m, this time delay corresponds to a wind of about 2.5 mph.

The correlation between fluctuations measured by the two HeNe LDIs within the optics of the telescope and thepathlength difference from the star to the two telescopes is shown in Fig. 8. Here, it can be seen that for the largerand slower fluctuations, the two sets are closely correlated. Those associated with the fringe, or relative pathlengthsfrom the star to the two telescopes, are about 2.5 times larger than what is measured in the 10 m distance within thetelescopes themselves. This directly indicates a correlation up to a distance of about 25 m.

"4

TIME. minuLes

Fig. 8. A comparison between optical path length difference fluctuations within the two telescopes (a distance of 10 m) andmeasured by the HeNe laser distance interferometers (LDI), and those from a star to the detectors. A strong correlation for thelarger and slower variations can be seen, with path length fluctuations for the star being about 2.5 times larger in size. Thisindicates a correlation of fluctuations within the telescope optics near the ground and in the atmosphere above the telescopes.

A relatively simple attempt to correct fringe phase fluctuations due to atmospheric pathlength changes is shownin Fig. 9. Here, the first figure shows a fringe and its many sidebands extending to about ± 1/2 Hz. The central plotin this figure shows the same fringe when the measured fluctuations within the two telescopes have been subtractedfrom the fringe's phase fluctuations. It is obviously somewhat stronger at the central frequency and narrower infrequency spread. The third illustration in Fig. 9 shows the fringe fluctuations if twice the fluctuations within thetelescopes have been subtracted. It can be seen there that many of the slower fluctuations corresponding to nearbysidebands have been canceled out, and that the central fringe peak has been relatively enhanced. This representsboth an increase in signal to noise and an improvement in the possibility of accurate phase measurements. Overall,we believe that substantial refmement and corrections of atmospheric seeing fluctuations can in the long run beachieved, and that this is particularly applicable to the longer infrared wavelengths where the important fluctuationsare both slower and of larger scale than those for visible light.

915

676 677 678 679 680 681 682 682

It is important to note that many of the larger path length variations are correlated over some distance bothlaterally on the ground and vertically into the atmosphere. Fig. 7 shows variations within the HeNe LDIinterferometers in two different telescopes spaced 4 m apart. The two top traces represent fluctuations measured inwavelengths in the two separate telescopes. The third diagram from the top shows the difference between these two.It can be seen that many of the larger fluctuations are closely similar for the two. The bottom trace represents thedifference between paths in the two telescopes when one of them is shifted in time by 3.25 seconds. This shows astill closer correlation between the two, indicating a time delay between fluctuations in the two telescopes. Since thedistance between the two is 4 m, this time delay corresponds to a wind of about 2.5mph.

The correlation between fluctuations measured by the two HeNe LDIs within the optics of the telescope and thepathlength difference from the star to the two telescopes is shown in Fig. 8. Here, it can be seen that for the largerand slower fluctuations, the two sets are closely correlated. Those associated with the fringe, or relative pathlengthsfrom the star to the two telescopes, are about 2.5 times larger than what is measured in the 10 m distance within thetelescopes themselves. This directly indicates a correlation up to a distance of about 25m.

c4

>0

0)Cl)

0U)

U)z

676 677 678 679 680 681 682 633

TIME, minutes

Fig. 8. A comparison between optical path length difference fluctuations within the two telescopes (a distance of 10 m) andmeasured by the HeNe laser distance interferometers (LDI), and those from a star to the detectors. A strong correlation for thelarger and slower variations can be seen, with path length fluctuations for the star being about 2.5 times larger in size. Thisindicates a correlation of fluctuations within the telescope optics near the ground and in the atmosphere above the telescopes.

A relatively simple attempt to correct fringe phase fluctuations due to atmospheric pathlength changes is shownin Fig. 9. Here, the first figure shows a fringe and its many sidebands extending to about 1/2 Hz. The central plotin this figure shows the same fringe when the measured fluctuations within the two telescopes have been subtractedfrom the fringe's phase fluctuations. It is obviously somewhat stronger at the central frequency and narrower infrequency spread. The third illustration in Fig. 9 shows the fringe fluctuations if twice the fluctuations within thetelescopes have been subtracted. It can be seen there that many of the slower fluctuations corresponding to nearbysidebands have been canceled out, and that the central fringe peak has been relatively enhanced. This representsboth an increase in signal to noise and an improvement in the possibility of accurate phase measurements. Overall,we believe that substantial refmement and corrections of atmospheric seeing fluctuations can in the long run beachieved, and that this is particularly applicable to the longer infrared wavelengths where the important fluctuationsare both slower and of larger scale than those for visible light.

915

o 13 Data

+ LI)! Data 9

8


916

000 It\

ti

0 /t I 1J_.

0.20

0. 5

1000 IOX 0(0

0.05

0 00

IXS.o97 00 O'i (*i 0 101) 100.x97 0(0 0(( (.70 101)I.2I0

'0-lou

to.'.,

.1 .0I0

Fig. 9. Correction of fringe phase fluctuations by measurement of atmospheric fluctuations near the ground. The first (left-hand)figure represents the fringe frequency power spectrum after interference of the two 11 p.sm beams from a star to the two telescopedetectors. The central figure is the spectrum after subtraction of fluctuations within the telescopes as measured by HeNe laserdistance interferometers (LDIs). The third (right-hand) figure represents the fringe spectrum after subtraction of twice theamount of fluctuation measured by the LDIs. This demonstrates the correlation between fluctuations within the telescopes andthose in the atmosphere above the telescopes, and that effective correction techniques may be applied to maintain optimumquality of fringes and their phase variations.

IRC +10216

° =1St Data 1993A = 1St Data 1997- Model (Star + Dust)

= Model (Dust Only)

Maximum Lurnmosity

0 (0 20

Spatial Frequency [10 5 rad

Fig. 10. The 11 im visibility curve of the star IRC +10216. Radiation from dust around the star is largely resolved when thespatial frequency of fringes is as high as 106 rad' (1/5 arc second), leaving only a visibility value due to the star itself, which isapproximately 0.005. Thus the star produces only 1/200 of the total 11 im radiation detected. At the lowest resolutions shown,about 75% of the 11 I.Lm radiation is already resolved (visibility - 0.25). This spatial frequency, about 2 x 1 5 rad4, correspondsto a resolution of about 0.6 arcseconds.

(OSoo9 0(0 .; (OX 10')"Ice

101.000.00(09,,

1

190

Fig. 9. Correction of fringe phase fluctuations by measurement of atmospheric fluctuations near the ground. The first (left-hand)figure represents the fringe frequency power spectrum after interference of the two 1 1 p.m beams from a star to the two telescopedetectors. The central figure is the spectrum after subtraction of fluctuations within the telescopes as measured by HeNe laserdistance interferometers (LDIs). The third (right-hand) figure represents the fringe spectrum after subtraction of twice theamount of fluctuation measured by the LDIs. This demonstrates the correlation between fluctuations within the telescopes andthose in the atmosphere above the telescopes, and that effective correction techniques may be applied to maintain optimumquality of fringes and their phase variations.

0.05

0

0O

Spatial Frequency [10 rad1]

Fig. 10. The 11 .tm visibility curve of the star IRC +10216. Radiation from dust around the star is largely resolved when thespatial frequency of fringes is as high as 106 rad' (1/5 arc second), leaving only a visibility value due to the star itself, which isapproximately 0.005. Thus the star produces only 1/200 of the total 1 1 &m radiation detected. At the lowest resolutions shown,

about 75% of the 11 .tm radiation is already resolved (visibility 0.25). This spatial frequency, about 2 x iO rad', correspondsto a resolution of about 0.6 arcseconds.

OSep97 e, o; (0 x t.0) - •_ 0Seo97 0.0 ( 0 10) . CSe97 oo o,i (+20 .Dt). .--, .

-I

0

1.00108

8.0.

4.0.l0 -

2o.'o:L1i

' 80.70'

100.0 101.0 900 95..

0.20

0. 5

0.10

..

t; S 0 =lSl Data 1993

- A

-. — = Model (Star + Dust)

= Model (Dust Only)

Maximum Luminosity

(I)>

20

916


The visibility curve for the bright IR star IRC +10216 is shown in Fig. iø. Visibility represents simply the ratio ofthe Fourier spatial transform of intensity across the sky due to the object being observed compared with what itwould be for a point source. Thus, at any given spatial frequency and for a simple, non-repetitive pattern, thevisibility represents approximately the fraction of the object's radiation which has not been resolved. In this case, alarge part of the 11 j.tm radiation has been resolved at our lowest resolutions shown, representing a spatial frequencyof about 2 x 1 rad', or a resolution of about 1/2 arcsec. At higher resolutions, additional radiation is resolveduntil, at a spatial frequency of about 106 rad', all the dust around the star has been resolved. At the highestresolution shown, corresponding to about 50 milliarcsec (mas), we can expect that only the stellar radiation itselfremains unresolved. Its visibility is only 0.005, representing a very small fraction of the total radiation. Usingaveraging times of the order of an hour or so, this small visibility can be measured to a precision of about 10%.Radiation at 11 .tm from the star itself is somewhat larger than this very low visibility would indicate; a model ofthe dust shell shows that the optical depth of the dust at 11 jim is between 1 and 2. At visible wavelengths, the starhas probably never been seen, although a small amount of visible light has been detected which is probablyscattered through a somewhat nonuniform dust shell.

Fig. 11 shows a somewhat more detailed picture of the visibility of IRC +10216. The two curves represent twodifferent phases in the luminosity of the star, which varies on a timescale of about 2 years. The visibility is higherduring minimum luminosity because the dust is sufficiently warm to emit 11 jim radiation only out to a smallerradius, so that the total radiation is less resolved. However, still another effect is necessary in order to explain thischange with phase of the stellar luminosity. This is that new dust must be formed sometime during the cooler periodof the star.3 The visibility curves indicate a formation of dust in the temperature range 1000 to 1500K, which isapproximately what is expected theoretically for carbonaceous or silicate materials.

5. STELLAR OBSERVATIONS

0.10

= Oct 88, Apr 89(Near Maximum L)

= Oct 89(Near Minimum L)

Spatial Frequency [1 05/rad]Fig. 11. A detailed plot of the visibility of IRC + 10216 showing the visibility curve near maximum and minimum luminosityduring the star's approximately 2-year luminosity cycle. Difference between the two curves is due in part to a change in the dusttemperature and in part to formation of new dust during the less luminous part of the cycle.

917

0.40

0.30

-o(I)

>0.20

II I 'ii ii Iir---_.2.0 3.0 4.0 5.01.0

5. STELLAR OBSERVATIONS

The visibility curve for the bright IR star IRC +10216 is shown in Fig. iO. Visibility represents simply the ratio ofthe Fourier spatial transform of intensity across the sky due to the object being observed compared with what itwould be for a point source. Thus, at any given spatial frequency and for a simple, non-repetitive pattern, thevisibility represents approximately the fraction of the object's radiation which has not been resolved. In this case, alarge part of the 1 1 im radiation has been resolved at our lowest resolutions shown, representing a spatial frequencyof about 2 x i05 rad', or a resolution of about 1/2 arcsec. At higher resolutions, additional radiation is resolveduntil, at a spatial frequency of about 106 rad', all the dust around the star has been resolved. At the highestresolution shown, corresponding to about 50 milliarcsec (mas), we can expect that only the stellar radiation itselfremains unresolved. Its visibility is only 0.005, representing a very small fraction of the total radiation. Usingaveraging times of the order of an hour or so, this small visibility can be measured to a precision of about 10%.Radiation at 1 1 im from the star itself is somewhat larger than this very low visibility would indicate; a model ofthe dust shell shows that the optical depth of the dust at 1 1 tm is between 1 and 2. At visible wavelengths, the starhas probably never been seen, although a small amount of visible light has been detected which is probablyscattered through a somewhat nonuniform dust shell.

Fig. 1 1 shows a somewhat more detailed picture of the visibility of IRC +10216. The two curves represent twodifferent phases in the luminosity of the star, which varies on a timescale of about 2 years. The visibility is higherduring minimum luminosity because the dust is sufficiently warm to emit 11 tm radiation only out to a smallerradius, so that the total radiation is less resolved. However, still another effect is necessary in order to explain thischange with phase of the stellar luminosity. This is that new dust must be formed sometime during the cooler periodof the star.3 The visibility curves indicate a formation of dust in the temperature range 1000 to 1500K, which isapproximately what is expected theoretically for carbonaceous or silicate materials.

-o(I)

>

0.40

0.30

0.20

0.10

Spatial Frequency [105/rad]Fig. 11. A detailed plot of the visibility of IRC +10216 showing the visibility curve near maximum and minimum luminosityduring the star's approximately 2-year luminosity cycle. Difference between the two curves is due in part to a change in the dusttemperature and in part to formation of new dust during the less luminous part of the cycle.

917

1.0 2.0 3.0 4.0 5.0


918

Another and perhaps simpler case of dust distribution is that around VY CMa, as shown in Fig. 12. Theluminosity of VY CMa varies somewhat irregularly and not as much as that of IRC + 10216. It can be seen in Fig.12 that two measurements, made several years apart, are rather close together. However, some deviation anddifference between the two is clear. In this case also, the star itself provides a very small fraction of the total 11 tmradiation.

VY CMa

= IS! Data, 1988, 1992

SI Data, 1993

A - IS! Data, 1994

= 1St Data, 1995

A - lSl Data, 1996

0 = IS! Data, 1997

= Model Fit

Maximum Luminosity

0 I0 20 30

Spatial Frequency [10 radl]

Fig. 12. The 11 i.Lm visibility curve for VY CMa, an irregular variable star. The points taken several years apart in time and atvarious phases of luminosity do not differ markedly, in part because the stellar luminosity does not vary greatly. The star itself,probably largely unresolved at the higher spatial frequencies, contributes only a small fraction of the total II .tm radiation.

It is important to note the complex nature of the dust distribution around such stars and its change with time,which require many measurements over a short period of time in order to describe them fully. If dust flowsuniformly from the star, which is frequently assumed, then the dust density should vary as hR2. where R is thedistance from the star. However, the curve fitting in Fig. 11 represents a dust density varying approximately as11R312, which indicates a nonuniform flow. In addition, the dust can vary strongly from spherical symmetry. This isshown clearly by masking-type interferometry in the near IR, which has been carried out on the Keck telescope, asdescribed by Peter Tuthill in a talk at this meeting. The left-hand part of Fig. 13 gives a diagram of the mask used.The right-hand part of Fig. 13 represents the uv plane with the many baselines provided by the mask. Fig. 14 mapsthe intensity distribution of VY CMa at 2.2 pm and 3.1 .Lm as determined by this interferometry. The distributioncan be seen to differ strongly from spherical symmetry. The visibility curve of Figs. 12 represents the visibility at 11pm through such a cloud in one dimension only. The dust shell is probably somewhat more symmetric at 11 pmthan at 2.2 pm and 3.1 pm since more distant dust is involved and the variations probably average out to someextent. It is clear, however, that at 11 pm it is also important to obtain two dimensional pictures in order tothoroughly study the dust distribution.

918

Another and perhaps simpler case of dust distribution is that around VY CMa, as shown in Fig. 12. Theluminosity of VY CMa varies somewhat irregularly and not as much as that of IRC +102 16. It can be seen in Fig.12 that two measurements, made several years apart, are rather close together. However, some deviation anddifference between the two is clear. In this case also, the star itself provides a very small fraction of the total 11 tmradiation.

-oC')

>

Spatial Frequency [10 rad-1]

30

Fig. 12. The 11 tm visibility curve for VY CMa, an irregular variable star. The points taken several years apart in time and atvarious phases of luminosity do not differ markedly, in part because the stellar luminosity does not vary greatly. The star itself,probably largely unresolved at the higher spatial frequencies, contributes only a small fraction ofthe total I 1 j.tm radiation.

It is important to note the complex nature of the dust distribution around such stars and its change with time,which require many measurements over a short period of time in order to describe them fully. If dust flowsuniformly from the star, which is frequently assumed, then the dust density should vary as hR2 where R is thedistance from the star. However, the curve fitting in Fig. I 1 represents a dust density varying approximately aslit3/2, which indicates a nonuniform flow. In addition, the dust can vary strongly from spherical symmetry. This isshown clearly by masking-type interferometry in the near IR, which has been carried out on the Keck telescope, asdescribed by Peter Tuthill in a talk at this meeting. The left-hand part of Fig. 13 gives a diagram of the mask used.The right-hand part of Fig. 13 represents the uv plane with the many baselines provided by the mask. Fig. 14 mapsthe intensity distribution of VY CMa at 2.2 tm and 3.1 .tm as determined by this interferometry. The distributioncan be seen to differ strongly from spherical symmetry. The visibility curve of Figs. 12 represents the visibility at 11tm through such a cloud in one dimension only. The dust shell is probably somewhat more symmetric at 1 1 .tmthan at 2.2 tm and 3.1 pm since more distant dust is involved and the variations probably average out to someextent. It is clear, however, that at 11 .tm it is also important to obtain two dimensional pictures in order tothoroughly study the dust distribution.

0 10 20


200

I '°:0

-100

-200

250

200

150

100

50

0

---;}l'

:.ê

200

100

0U0

E< : =::

919

0 50 100 150 200 250

Fig. 13. A mask used for interferometry on the Keck telescope at 2.2 and 3.1 j.im wavelengths. The left figure shows the positionof holes in the mask projected onto the Keck primary mirror. The right figure provides a plot in the UV plane of the manyresulting baselines for which interferometiy can be obtained.

VY CMo at 2.2 tm VY CMo at 3.1

-200-100 0 100 200 -200-100 0 100 200Milliarcsecor,ds MIIiorcseconds

Fig. 14. The intensity distribution of near-IR radiation from VY CMa obtained from masking interferometry on the Keck telescope.The star itself is perhaps in the center of the patterns shown by intensity contours of 2.2 and 3.1 jim radiation, not at any one of theintensity peaks. Clearly for this near-IR radiation the intensity distribution deviates markedly from a spherical distribution.

An example in sharp contrast to IRC + 10216 and VY Cma is that of a Orionis, for which the visibility curve isshown in Fig. 15. At our lowest resolution of about 1 arcsec, 40% of the 11 jim radiation is already resolved. For thehigher resolutions in this curve, the visibility changes relatively little. This indicates that a dust shell external to thestar has been resolved at the lowest resolution, and that there is no further dust between that and the star itself,which is relatively unresolved at the resolutions shown in this figure. The bump near a spatial resolution of 2 x 1 5

radians' is believed to be due to the addition in phase of intensity from the star itself and the bright inner edge ofthe innermost dust shell. This then predicts a radius of about 1 arcsec for the dust shell, a size also indicated by othermeasurements.3

Fig. 13. A mask used for interferometry on the Keck telescope at 2.2 and 3.1 pm wavelengths. The left figure shows the positionof holes in the mask projected onto the Keck primary mirror. The right figure provides a plot in the UV plane of the manyresulting baselines for which interferometry can be obtained.

U)0c0UQ)U,00

Fig. 14. The intensity distribution ofnear-IR radiation from VY CMaobtained from masking interferometry on the Keck telescope.The star itselfis perhaps inthe center ofthe patterns shown by intensity contours of 2.2 and 3.1 pm radiation, not at any one of theintensity peaks. Clearly for this near-IR radiation the intensity distribution deviates markedly from a spherical distribution.

An example in sharp contrast to IRC +10216 and VY Cma is that of a Orionis, for which the visibility curve isshown in Fig. 15. At our lowest resolution of about 1 arcsec, 40% ofthe 1 1 pm radiation is already resolved. For thehigher resolutions in this curve, the visibility changes relatively little. This indicates that a dust shell external to thestar has been resolved at the lowest resolution, and that there is no further dust between that and the star itself,which is relatively unresolved at the resolutions shown in this figure. The bump near a spatial resolution of 2 x lOradians1 is believed to be due to the addition in phase of intensity from the star itself and the bright inner edge ofthe innermost dust shell. This then predicts a radius of about 1 arcsec for the dust shell, a size also indicated by othermeasurements.3

919

0 50 100 150 200 250

t( CMa at 3.1 m200

110:—100

—200

—200—100 0 100 200Milliarcseconds

.—200—100 0 100 200

Mifliorcseconds


920

1.0

0.8

0.2

0.0

k aOri= ISI Data 1988-1992 -= Model Fit -

0 2 4 6 8 10 12 14 16

Spatial Frequency [i05 rad1]

Fig. 15. Visibility curve for a. Orionis at 11 tm. The surrounding dust is rather completely resolved at the lowest resolutions ofthis curve, and contributes about 40% of the total 11 j.tm radiation. The slowly decreasing visibility at higher spatial frequenciesrepresents some resolution of the star itself. The bump near a spatial frequency of 2 x 1 rad' represents addition of the stellarradiation with that of the inner part of a dust shell, which produces spatial peaks in the visibility curve. This gives a distancefrom star to shell of about one arcsec.

We have recently measured several stars which are so faint in visible and near infrared radiation that we havenot previously been able to track them well. We can now do so thanks to a new near infrared camera which hasincreased sensitivity, and also to tip-tilt tracking, which allows very fast and relatively accurate tracking. These twonew improvements to our system are discussed in the paper given at this meeting by Everett Lipman. One set of datataken with the new camera is shown in Fig. 16, which is the visibility curve for CIT3. In this case, we used threedifferent baselines in a period of about 6 weeks, so that we have a snap shot of the dust distribution of CIT3 at aparticular phase of the star. It can be seen that the indicated uncertainties in each point are somewhat larger thanwhat might be guessed from their scatter. This is because part of the uncertainty represents systematic errors ratherthan random errors from point to point. Thus, the shape of the curve is somewhat more accurate than its absolutevalue. This visibility curve shows that even at our lowest resolution for this star, about 40% of the 11 jim radiationhas been resolved. As resolution is increased, the curve is flat and hence there is no additional dust over somedistance until a spatial frequency of about 4 x rad', where additional dust begins to be resolved. This indicatesan additional dust shell with a diameter of about 250 mas. At much higher resolutions, the curve flattens outindicating that all has been resolved excepting the star itself, and that the star provides a visibility less than about0.1. Fig. 17 shows a similar visibility curve taken for IRC + 10420. Here again, about half the total infrared radiationhas been resolved at our lowest resolution. There is no additional radiation for some short distance, and then dustbegins to be resolved at a spatial frequency of about 2.5 x iø rad, indicating that new dust begins again at adiameter of about 400 mas. In this case the star itself again provides a visibility of less than 0.1.

0(I)>

Fig. 15. Visibility curve for a Orionis at 11 tm. The surrounding dust is rather completely resolved at the lowest resolutions ofthis curve, and contributes about 40% of the total 1 1 .tm radiation. The slowly decreasing visibility at higher spatial frequenciesrepresents some resolution of the star itself. The bump near a spatial frequency of 2 x i€f raci' represents addition of the stellarradiation with that of the inner part of a dust shell, which produces spatial peaks in the visibility curve. This gives a distancefrom star to shell of about one arcsec.

We have recently measured several stars which are so faint in visible and near infrared radiation that we havenot previously been able to track them well. We can now do so thanks to a new near infrared camera which hasincreased sensitivity, and also to tip-tilt tracking, which allows very fast and relatively accurate tracking. These twonew improvements to our system are discussed in the paper given at this meeting by Everett Lipman. One set of datataken with the new camera is shown in Fig. 16, which is the visibility curve for CIT3. In this case, we used threedifferent baselines in a period of about 6 weeks, so that we have a snap shot of the dust distribution of CIT3 at aparticular phase of the star. It can be seen that the indicated uncertainties in each point are somewhat larger thanwhat might be guessed from their scatter. This is because part of the uncertainty represents systematic errors ratherthan random errors from point to point. Thus, the shape of the curve is somewhat more accurate than its absolutevalue. This visibility curve shows that even at our lowest resolution for this star, about 40% of the 1 1 tm radiationhas been resolved. As resolution is increased, the curve is flat and hence there is no additional dust over somedistance until a spatial frequency of about 4 x iO rad', where additional dust begins to be resolved. This indicatesan additional dust shell with a diameter of about 250 man. At much higher resolutions, the curve flattens outindicating that all has been resolved excepting the star itself, and that the star provides a visibility less than about0.1. Fig. 17 shows a similar visibility curve taken for IRC +10420. Here again, about half the total infrared radiationhas been resolved at our lowest resolution. There is no additional radiation for some short distance, and then dustbegins to be resolved at a spatial frequency of about 2.5 x i05 rad', indicating that new dust begins again at adiameter of about 400 mas. In this case the star itself again provides a visibility of less than 0.1.

1.0

0.8

0.6

0.4

0.2

0.0

0 2 4 6 8 10 12 14 16

Spatial Frequency [i05 rad1]

920


1

0.8---

0.4

0.2

0

921

1

0.8--O.6

C.)0.4

0.2

0

0 5 10 15

Baseline (in units of i05 A)

Fig. 16. The 11 jim visibility curve of CIT3, showing resolution of one dust shell at the lowest resolutions of the curve, noadditional dust resolution before a spatial frequency of about 4 x 10 rad1, and then resolution of another shell of dust. Theinner dust shell has a diameter of about 250 mas.

0 5 10 15

Baseline (in units of i05 A)

Fig. 17. The 11 jim visibility of IRC +10420, also showing a large outer dust shell, no dust for some distance towards the star,and then resolution of an additional dust shell which has a diameter of about 400 mas. The star itself provides a visibility ofabout 0.1, i.e. produces about 10% of the 11 jim radiation.uOuipi UXTI jj LfJJO %Øj noq s3npO1d i 'ç inoq

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922

Theoretical models of the dust which will fit the preliminary data of Figs. 16 and 17 have yet to be worked out.However, it is immediately clear what qualitative distribution of dust is present. Still another star which these newimprovements have allowed us to measure is R Cancri. It turned out to have a visibility of unity for all of ourresolutions up to the highest used during last Fall's observations. However, it is clear that there must be dust aroundthis star because of its infrared spectrum. Thus, one can conclude that R Cancri is surrounded by dust which all lieswithin a diameter less than about 90 mas. We will in time use higher resolution and measure its distribution moreprecisely.

Figure 18 shows additional measurements of the 11 j.tm visibility of a On. Two new results are obtained fromthis figure. First, we have used high enough resolution to resolve the star, which is why the curve steadily slopesdownward towards the higher resolutions. The theoretical fit for these points allows determination of the diameter ofa Orionis, which will be discussed somewhat later. The data also show that visibility at low resolution issubstantially different in 1994 from what it was in the period 19881992.2 The visibility at low resolution in 1994 issomewhat higher and a bit smoother than the earlier curve. This indicates that new dust has been emitted, and isgiving additional 11 .tm radiation fairly near the star. It is resolved at resolutions in the range 15-20 x l0 rad'. Thepresence of this new outburst of dust from a Orionis is also indicated by Fig. 19. Here, the visible magnitude and

1.0

0.8

0.6

-o(I)

>0.4

0.2

0.0

0

o = 1St Data 1988-1992 *= SI Data 1993

a = 1St Data 1994 == Model 1988-1992 -= Model 1993-1994 -

10 20

Spatial Frequency [10 rad1]30

Fig. 18. The 11 J.tm visibility curve of a Orionis. This shows resolution of the star at higher spatial frequencies, which allowsdetermination of its size. In addition, at the lower spatial frequencies the curves taken before and after 1994 differ substantially,indicating emission of a modest amount of additional dust in 1994. The solid and dashed curves represent theoretical fits for auniform disk of radiation from the star, an outer shell of dust at a radius of about I arcsec, and the dashed curve has the additionof some dust near the star, which was emitted in 1994.

11 .tm magnitude are compared over the same time period. It is notable that the visible magnitude varies by as muchas about ± 3/10 of a magnitude. This is partly because a relatively small change in temperature can vary the visiblelight substantially. The 11 im radiation during most of this period goes up and down a small amount synchronouslywith the visible radiation. It is much less sensitive to such a temperature change, and this behavior indicates thevisible intensity changes are primarily due to temperature changes rather than variation in the stellar diameter. In1994 and 1995 one can see that the visible magnitude increases sharply while the infrared magnitude by contrastdecreases slightly. This indicates that dust has been formed which is screening out some of the visible radiation. Wenow know that such outbursts or episodic emission of dust are rather typical, which is indicated in part by the distantshell of dust around a Orionis. Such phenomena are also found in many other stars.

Theoretical models of the dust which will fit the preliminary data of Figs. 16 and 17 have yet to be worked out.However, it is immediately clear what qualitative distribution of dust is present. Still another star which these newimprovements have allowed us to measure is R Cancri. It turned out to have a visibility of unity for all of ourresolutions up to the highest used during last Fall's observations. However, it is clear that there must be dust aroundthis star because of its infrared spectrum. Thus, one can conclude that R Cancri is surrounded by dust which all lieswithin a diameter less than about 90 mas. We will in time use higher resolution and measure its distribution more

precisely.

Figure 18 shows additional measurements of the 1 1 ptm visibility of a On. Two new results are obtained fromthis figure. First, we have used high enough resolution to resolve the star, which is why the curve steadily slopesdownward towards the higher resolutions. The theoretical fit for these points allows determination ofthe diameter ofa Orionis, which will be discussed somewhat later. The data also show that visibility at low resolution issubstantially different in 1994 from what it was in the period l988l992.2 The visibility at low resolution in 1994 issomewhat higher and a bit smoother than the earlier curve. This indicates that new dust has been emitted, and isgiving additional 1 1 im radiation fairly near the star. It is resolved at resolutions in the range 15-20 x iO rad'. Thepresence ofthis new outburst ofdust from a Orionis is also indicated by Fig. 19. Here, the visible magnitude and

Spatial Frequency [iO rad1]

Fig. 18. The 11 tm visibility curve of a Orionis. This shows resolution of the star at higher spatial frequencies, which allowsdetermination of its size. In addition, at the lower spatial frequencies the curves taken before and after 1994 differ substantially,indicating emission of a modest amount of additional dust in 1994. The solid and dashed curves represent theoretical fits for auniform disk of radiation from the star, an outer shell of dust at a radius of about 1 arcsec, and the dashed curve has the additionof some dust near the star, which was emitted in 1994.

1 1 p.tm magnitude are compared over the same time period. It is notable that the visible magnitude varies by as muchas about 3/10 of a magnitude. This is partly because a relatively small change in temperature can vary the visiblelight substantially. The 1 1 im radiation during most of this period goes up and down a small amount synchronouslywith the visible radiation. It is much less sensitive to such a temperature change, and this behavior indicates thevisible intensity changes are primarily due to temperature changes rather than variation in the stellar diameter. In1994 and 1995 one can see that the visible magnitude increases sharply while the infrared magnitude by contrastdecreases slightly. This indicates that dust has been formed which is screening out some of the visible radiation. Wenow know that such outbursts or episodic emission of dust are rather typical, which is indicated in part by the distantshell of dust around a Ononis. Such phenomena are also found in many other stars.

0(I)

>

1.0

0.8

0.6

0.4

0.2

0.0

0 10 20 30

922


a) 6.0C

0 5.5E

- 5.0

a)0 0.0

C

0 0.5a)n(I)

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0.8

0.6>'

0.4

0.2

0.00

I I I

Visible Data

.1S.

'S- .- S

- I i

I 1 I I I

K,cno, (1990. 1992. 1994)_o (1995)

I i i I I 1 I I -

2

Dyck & Benson (1992) 10.4 jim11.4/im

0 Fix & Cobb (1 988) N bandISl 11.15 jim

Double Shell ModelsT.-2500 K L=L. MeanT.2670 K L=1.3 x L. MaximumT.=2370 K L=L. / 1.3 Minimum

6Spatial Frequency (10' rodions)

Fig. 20. The 11 .tm visibility curve of NML Cygni, indicating discrete shells of dust.

923

7000 8000 9000 10000

Julian Date - 2440000

Fig. 19. Variations in the visible and 11 pm magnitudes of a Orionis over a period of years. Before 1994, the JR luminosityvaries synchronously with that of visible light, but by much smaller amounts. Beginning in 1994, the IR luminosity becomesslightly greater while that of visible light decreases markedly, indicating an emission of gas and dust.2

Another example of episodic emission of dust is demonstrated by the visibility curve of NML Cygni, shown inFig. 20.'° Here the lower resolution points come from Dyck and Benson,4 and from Fix and Cobb.5 The higherresolution points were obtained more recently with the IS! system. What is notable is that the curve does notcontinue downwards smoothly but has a substantial bump. This indicates an irregularity in the distribution of dust.Fig. 21 shows a theoretical fit for this visibility curve. It plots the 11 tm flux as a function of distance from the star,and shows peaks at about 90 mas and 340 mas. The solid curve represents a maximum entropy fit to the visibilitydata points. The other curves are somewhat idealized models, for example of two shells which are Gaussian in form.Measurement of the velocity of molecular gas around the star combined with its presumed distance allows one tocalculate the separation in time between emission of the two shells, which is about 80 years.

- II I I I I

a Cr1Infrared Data

2S S

S .

-1 I L I i i t I i

.1 ..

Julian Date — 2440000

Fig. 19. Variations in the visible and 1 1 pm magnitudes of a Orionis over a period of years. Before 1994, the 1R luminosityvaries synchronously with that of visible light, but by much smaller amounts. Beginning in 1994, the JR luminosity becomesslightly greater while that ofvisible light decreases markedly, indicating an emission ofgas and dust.2

Another example of episodic emission of dust is demonstrated by the visibility curve of NML Cygni, shown inFig. 20.10 Here the lower resolution points come from Dyck and Benson,4 and from Fix and Cobb.5 The higherresolution points were obtained more recently with the IS! system. What is notable is that the curve does notcontinue downwards smoothly but has a substantial bump. This indicates an irregularity in the distribution of dust.Fig. 21 shows a theoretical fit for this visibility curve. It plots the 1 1 tm flux as a function of distance from the star,and shows peaks at about 90 mas and 340 mas. The solid curve represents a maximum entropy fit to the visibilitydata points. The other curves are somewhat idealized models, for example oftwo shells which are Gaussian in form.Measurement ofthe velocity ofmolecular gas around the star combined with its presumed distance allows one tocalculate the separation in time between emission of the two shells, which is about 80 years.

0 2 6

Ii)

1.0

1I I I I

aOriInfrared Data

1 1 1 11

I 1 1 I

,

.

. .I

.

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— Double Shell IT.=2500 K L=L. Mean 'T.=2670 K L=1.3 x L. Maximum

, T=2370 K L=L. I 1.3 Minimum I.

.

. I . . I .8 10

spotaI Frequency ( 1 0 radions)

Fig. 20. The 1 1 m visibility curve ofNML Cygni, indicating discrete shells of dust.

923


924

1.0

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x

.2: 0.6U)CU)

C

0.4

00

0.2

000

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9 0.4>

0.20.0

2 Shells (Exp+Causs)2 Shells (Couss+Gauss

MEM Fit to 11 m VsibiIity Doto

2 4 6 8Spatial Frequency (10' rod)

100 200 300 400Distance from Star (Milliarcseconds)

10

41S1 -

Dyck & Benson (1992) i

500

Fig. 21. Radial intensity distributions which give theoretical fits to the 11 tm visibility curve of NML Cygni. These show twomore or less discrete dust shells at distances of about 90 and 340 mas from the star. The solid curve is a maximum entropy fit tothe visibility measurements. The other curves, which provide approximate fits, use somewhat different dust shell models.

Another case of episodic emission is 1K Tau, for which the visibility curve is shown in Fig. 22.6 This visibilitycurve not only has some bumps, it changed noticeably over one year's time, between the fall of 1992 and the Fall of1993. A maximum entropy fit for the intensity distribution as a function of distance from the star is shown in Fig.23. It can be seen that the outer two peaks in intensity, corresponding to shells surrounding the stars, increased indistance between 1992 and 1993. If velocity measured for OH masers and CO gas around the star give the correctvelocity of expansion of these shells, then the amount of expansion in one year's time allows an evaluation of thedistance to the star, which is 265 parsec.6 This corresponds rather well to previous estimates of distance, which were270 and 220 parsec. With this distance and velocity, we can also determine the time between emission of the threesuccessive shells indicated in this figure. That time is about 12 years. In the case of 1K Tau, masking interferometryin the near infrared on the Keck telescope shows that the dust shell is rather spherical, at least close to the star.Hence in this case a spherical model for the outer shells is probably justified.

The visibility curves of o Ceti, shown in Fig. 24, are quite complex.8 The visibility changes not only with phase,but it does not repeat with successive cycles. This can be seen by comparing the top and bottom figures for visibilityof o Ceti, both of which are near a minimum of luminosity but are taken at different cycles. The central diagram inthis figure gives the visibility at maximum luminosity, which is also different from the other two. A detailedanalysis and discussion of the case of o Ceti has been given by Lopez.8 This is too complex to discuss briefly here.However, it is found that there are nonsphericities in the distribution, and not only creation of new dust during thecool part of the star cycle, but probably evaporation of dust already formed during some of its higher luminosityphases.

It is clear that for a reasonably complete picture of the dust emission and distribution around many stars, a two-dimensional interferometric picture must be made on a relatively short timescale, that is, a timescale of less than afew months, substantially shorter than the stellar period for variable stars. Fig. 25 shows a series of visibilitymeasurements made on R Aqr. Since these include measurements made at a number of different times, the points donot fit on any simple single curve. Furthermore, they differ with each other even when the phases are the same.Thus, measurements taken in this way over a long period of time can only show the broad characteristics of the dustdistribution, and not many of its intricate details. This makes it important for such measurements to have availablemultiple telescopes and baselines in the future.

200 300Distance from Star (MIIarcseconds)

Fig. 21. Radial intensity distributions which give theoretical fits to the 11 pm visibility curve of NML Cygni. These show twomore or less discrete dust shells at distances of about 90 and 340 mas from the star. The solid curve is a maximum entropy fit tothe visibility measurements. The other curves, which provide approximate fits, use somewhat different dust shell models.

Another case of episodic emission is 1K Tau, for which the visibility curve is shown in Fig. 22.6 This visibilitycurve not only has some bumps, it changed noticeably over one year's time, between the fall of 1992 and the Fall of1993. A maximum entropy fit for the intensity distribution as a function of distance from the star is shown in Fig.23 . It can be seen that the outer two peaks in intensity, corresponding to shells surrounding the stars, increased indistance between 1992 and 1993. If velocity measured for OH masers and CO gas around the star give the correctvelocity of expansion of these shells, then the amount of expansion in one year's time allows an evaluation of thedistance to the star, which is 265 parsec.6 This corresponds rather well to previous estimates of distance, which were270 and 220 parsec. With this distance and velocity, we can also determine the time between emission of the threesuccessive shells indicated in this figure. That time is about 12 years. In the case of 1K Tau, masking interferometryin the near infrared on the Keck telescope shows that the dust shell is rather spherical, at least close to the star.Hence in this case a spherical model for the outer shells is probably justified.

The visibility curves of o Ceti, shown in Fig. 24, are quite complex.8 The visibility changes not only with phase,but it does not repeat with successive cycles. This can be seen by comparing the top and bottom figures for visibilityof o Ceti, both of which are near a minimum of luminosity but are taken at different cycles. The central diagram inthis figure gives the visibility at maximum luminosity, which is also different from the other two. A detailedanalysis and discussion of the case of o Ceti has been given by Lopez.8 This is too complex to discuss briefly here.However, it is found that there are nonsphericities in the distribution, and not only creation of new dust during thecool part of the star cycle, but probably evaporation of dust already formed during some of its higher luminosityphases.

It is clear that for a reasonably complete picture of the dust emission and distribution around many stars, a two-dimensional interferometric picture must be made on a relatively short timescale, that is, a timescale of less than afew months, substantially shorter than the stellar period for variable stars. Fig. 25 shows a series of visibilitymeasurements made on R Aqr. Since these include measurements made at a number of different times, the points donot fit on any simple single curve. Furthermore, they differ with each other even when the phases are the same.Thus, measurements taken in this way over a long period of time can only show the broad characteristics of the dustdistribution, and not many of its intricate details. This makes it important for such measurements to have availablemultiple telescopes and baselines in the future.

U)

-a0

x>'(I)C

C

xU-

0:3CC

1 .0

0.8

0.6

0.4

0.2

0.0

MEM ReconstrucOon 2 Shells (Exp+Gauss)Uniform Outflow Model --•-•-- 2 Shells (Gauss+Gauss)

-I!;' ') MEM Fit to 11 m Visibility Data —

,!,' 4 SI. /1 :' • Dyck & Benson (1992). 1, ;-

....,L,. %

... 1

,./I ... l% 0 2 4 6 8 10- : Spatial Frequency (10' rad);

II . .... .,•1 I . I/ . I .. .— —.

1 •/ ..— .—

I . .

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0 100 400 500

924


-D01

0.6>'

>0.4

0.2

000

Fig. 22. Visibility curves of 1K Tau for 11 tm radiation. Two maximum entropy fits to the data of 1992 and of 1993 respectivelyare shown, since a distinct change appeared between these two years for spatial frequencies in the 5 - 7 x i05 rad1 range.

0.00

'.1993

1992

o 1992 MeasurementsA 1993 Meosurements

1994/1995 Measurements1996 Measurements

5 10 15Spotiol Frequency (100 rod')

925

0 200 400 600 800 1000Radius (milliorcseconds)

Fig. 23. The radial intensity distribution of 11 .im radiation from dust around 1K Tau. The two curves are maximumentropy fitsof the two sets of points for 1992 and 1993. They show an outward motion of the outer two dust shells during one year's time.This allows a determination of the distance to the star (265 pc) and the elapsed time between shells (12 years).

1.0

0.8

20 25

>

>

Fig. 22. Visibility curves of 1K Tau for 11 .tm radiation. Two maximum entropy fits to the data of 1992 and of 1993 respectivelyare shown, since a distinct change appeared between these two years for spatial frequencies in the 5 - 7 x i05 rad' range.

c00-o0

E

0

a

800 1000

Fig. 23. The radial intensity distribution of 11 tm radiation from dust around 1K Tau. The two curves are maximum entropy fitsof the two sets of points for 1992 and 1993. They show an outward motion of the outer two dust shells during one year's time.This allows a determination of the distance to the star (265 pc) and the elapsed time between shells (12 years).

925

0 5 10 15 20 25Spatial Frequency (1 O rod)

0 200 400 600Radius (milliarcseconds)


926

0.2

0.0

1.0

0.8

1.0

0.8

> 0.6

.0(0

5 0.4

0.2

0.0

0.2 -

0.0 -

0 Cet= SI Data 1990

0.8 o = SI Data 1995

= Model FitsMinimum Luminosity

I I I

o Cet- = SI Data 1992

= Model FitsMaximum Luminosity

o CetSI Data 1993-94= 0.21-0.48

o = SI Data 1995= 0.57-0.62

= Model Fits

10 20 30

Spatial Frequency [iO rod]

FIG. 7b

I I

0 10 20 3D

Spatial Frequency [1O rad']

Fig. 24. Three 11 .tm visibility curves for o Ceti, showing both a variation with phase of this variable star and a variation in dustdistributions at the same phase but during different cycles.

0 10 20 30

Spatial Frequency [iO rad1]

FIG. 7a

III I

Spatial Frequency [iOn rad1]

Fig. 24. Three 11 j.tm visibility curves for o Ceti, showing both a variation with phase of this variable star and a variation in dustdistributions at the same phase but during different cycles.

0 10 20

Spatial Frequency [i05 rad1]FIG. 7a

30

1.0

0.8

>.. 0.6

(I)

5 0.4

0.2

0.0

1.0

0.8

>. 0.6

n(I)5 0.4

0.2

0.0

0

-aU)

>

10 20

Spatial Frequency [iO rad1]FIG. 7b

30

0 10 20

926

30


0 10 20 30

Spatial Frequency [10 rad-1 I

Fig. 25. A series of visibility measurements at 11 tm of R Aquarii at different phases and different cycles. This shows variationsin visibility which are often encountered, even at similar phases. It illustrates that, while such measurements can provide a grosspicture of dust distribution around a star, an accurate measure requires a number of more or less simultaneous measurements inthe UV plane. Such rapid and complete measurements are required to provide a detailed map of dust distribution and behaviorfor a number of stars which are variable and do not repeat a fixed pattern as they valy.

6. STELLAR DIAMETERS

The diameters of stars have been measured for some time by interferometry in the visible region; the first was ofcourse the measurement of a Orionis by Michelson and Pease in 1921. The diameter of this star has been measuredmany times since then. A plot of various values obtained is shown in Fig. 26. Here, the probable errors given areclearly substantially less than variations in the results. White'4 has made this plot in order to examine whether thesize of a Orionis varied with its luminosity phase, and claimed that there was such evidence. However, it seemsclear now that these measurements have probably been misleading due to nonuniformities and changes iii intensitydistribution over the star.

Visibility curves for stars at visible wavelengths have characteristically been fitted to a uniformly intense disk,and stellar diameters thereby assigned. It has been recognized for some time that these disks are not uniform but aredarkened on the outer edges by what is called "limb darkening," and that furthermore this limb darkening typicallyreduces the apparent size of the star in the visible region by about 10%." This 10% estimate comes from theoreticalcalculations in the past, rather than actual measurements. There is now experimental evidence, however, for suchlimb darkening.27 Recently, it has been recognized that older stars in particular can vary in intensity over the diskby having hot spots, somewhat similar to solar sunspots but very much larger in magnitude. Certain of these hotspots can produce a substantial fraction of the total intensity, and thereby decrease the apparent size of the star if asimple fit to a limited number of points on the visibility curve is made, and a uniform disk is assumed. There havealso been claims that stars vary in shape, with some substantially elongated as well as changing in size. We believethese results may be questionable and need to be checked with infrared measurements. The infrared intensity ismuch less sensitive to changes in temperature on the surface of the star, as pointed out above, and hence generallywill represent a rather uniform disk. In addition, the limb darkening is much reduced in the infrared region. At 10

927

1.0

R Aqr

o =1St Data 1997

0.8 o = 1St Data 1994

= 1St Data 1993

= 1St Data 1992

0.6

Cl)

>0.4

0.2

0.0

1.0

R Aqr

0 = Data 1997

0.8 0 SI Data 1994

I = Data 1993. =ISI Data 1992

0.6>

-cD(I)>

: f I

0.0

0 10 20 30

Spatial Frequency [1 0 5 rad1]

Fig. 25. A series of visibility measurements at 1 1 tm of R Aquarii at different phases and different cycles. This shows variationsin visibility which are often encountered, even at similar phases. It illustrates that, while such measurements can provide a grosspicture of dust distribution around a star, an accurate measure requires a number of more or less simultaneous measurements inthe UV plane. Such rapid and complete measurements are required to provide a detailed map of dust distribution and behaviorfor a number of stars which are variable and do not repeat a fixed pattern as they vary.

6. STELLAR DIAMETERS

The diameters of stars have been measured for some time by interferometry in the visible region; the first was ofcourse the measurement of a Orionis by Michelson and Pease in 192 1 .The diameter of this star has been measuredmany times since then. A plot of various values obtained is shown in Fig. 26. Here, the probable errors given areclearly substantially less than variations in the results. White'4 has made this plot in order to examine whether thesize of a Orionis varied with its luminosity phase, and claimed that there was such evidence. However, it seemsclear now that these measurements have probably been misleading due to nonuniformities and changes in intensitydistribution over the star.

Visibility curves for stars at visible wavelengths have characteristically been fitted to a uniformly intense disk,and stellar diameters thereby assigned. It has been recognized for some time that these disks are not uniform but aredarkened on the outer edges by what is called "limb darkening," and that furthermore this limb darkening typicallyreduces the apparent size of the star in the visible region by about 10%•tlThis 10% estimate comes from theoreticalcalculations in the past, rather than actual measurements. There is now experimental evidence, however, for suchlimb darkening.2'7 Recently, it has been recognized that older stars in particular can vary in intensity over the diskby having hot spots, somewhat similar to solar sunspots but very much larger in magnitude. Certain of these hotspots can produce a substantial fraction of the total intensity, and thereby decrease the apparent size of the star if asimple fit to a limited number of points on the visibility curve is made, and a uniform disk is assumed. There havealso been claims that stars vary in shape, with some substantially elongated as well as changing in size. We believethese results may be questionable and need to be checked with infrared measurements. The infrared intensity ismuch less sensitive to changes in temperature on the surface of the star, as pointed out above, and hence generallywill represent a rather uniform disk. In addition, the limb darkening is much reduced in the infrared region. At 10

927


928

jim, calculations indicate that it represents only about a 1% decrease in the apparent size. In addition, if there is dustaround a star or certain types of gas, then obscuration or scattering can substantially affect the apparent size of thestar in the visible region, while not affecting it very much at the longer IR wavelengths. One can already deduce,from Fig. 19, that, as the visible luminosity changes, the change is primarily due to a change in temperature ratherthan a change in size of a Orionis, since the visible changes in luminosity are very much greater than those in theinfrared. Hence, it seems likely that the large changes in the size of a Orionis indicated by Fig. 26 are quitemisleading. Stellar size measurements at IR wavelengths can also be misleading if a star's atmosphere containsmolecular gas which absorbs infrared wavelengths, and such effects need exploration.

We have measured the size of a Orionis at 11 jim from the visibility curve shown in Fig. 18. The size of a Scohas also been measured.2 These sizes are shown in Table 1. The table also shows a measurement of the visible sizeof a On. This is a measurement which used phase closure and high resolution to take into account a spot on thestar.13 We believe this is the most reliable measurement of the size of a Onionis in the visible region. Our ownmeasurements at 11 jim give a result of 56 ± 1 mas, which is close to the theoretically estimated 9% increase in sizeto be expected from the visible to 11 jim wavelengths. Similar results were found for a Sco, as shown in Table 1.Although these results appear to fit limb darkening expectations, further measurements of stellar sizes at a variety ofwavelengths is needed in order to examine details of limb darkening and of the transparency of stellar atmospheres.

60

CD

z0UwU,

50

CD 40

-J

CDz

r

1

'1

Fig. 26. Various measurements of the diameter of a Orionis by interferometry at visible wavelengths. These have been arrangedby White'4 in accordance with the apparent phase of a On's somewhat irregular variations in luminosity. It is clear that theapparent size variation is substantially larger than the stated probable errors of measurement. This now appears to be primarilydue to non-uniformity and change of intensity distributions over the stellar surface.

0 .2 .4 .6 .8 0

PHASE.4 .6 .8 0

928

rim, calculations indicate that it represents only about a 1% decrease in the apparent size. In addition, if there is dustaround a star or certain types of gas, then obscuration or scattering can substantially affect the apparent size of thestar in the visible region, while not affecting it very much at the longer IR wavelengths. One can already deduce,from Fig. 19, that, as the visible luminosity changes, the change is primarily due to a change in temperature ratherthan a change in size of a Orionis, since the visible changes in luminosity are very much greater than those in theinfrared. Hence, it seems likely that the large changes in the size of a Orionis indicated by Fig. 26 are quitemisleading. Stellar size measurements at IR wavelengths can also be misleading if a star's atmosphere containsmolecular gas which absorbs infrared wavelengths, and such effects need exploration.

We have measured the size of a Orionis at 1 1 ptm from the visibility curve shown in Fig. 18. The size of a Scohas also been measured.2 These sizes are shown in Table 1 .The table also shows a measurement of the visible sizeof a On. This is a measurement which used phase closure and high resolution to take into account a spot on the

13 We believe this is the most reliable measurement of the size of a Orionis in the visible region. Our ownmeasurements at 1 1 im give a result of 56 1 mas, which is close to the theoretically estimated 9% increase in sizeto be expected from the visible to 1 1 tm wavelengths. Similar results were found for a Sco, as shown in Table 1.Although these results appear to fit limb darkening expectations, further measurements of stellar sizes at a variety ofwavelengths is needed in order to examine details of limb darkening and of the transparency of stellar atmospheres.

U)az00wU)

0

00

aa:

-J

0z

Fig. 26. Various measurements of the diameter of cx Orionis by interferometry at visible wavelengths. These have been arrangedby White'4 in accordance with the apparent phase of a On's somewhat irregular variations in luminosity. It is clear that theapparent size variation is substantially larger than the stated probable errors of measurement. This now appears to be primarilydue to non-uniformity and change of intensity distributions over the stellar surface.

PHASE


Objects

a On

a Sco

Diameter at visiblewavelengths withoutlimb darkening correction

52.7± 1.3 mas

40.0 ± 0.6 mas

Table 1

Measured diameters of a On and a Sco

Diameter at 11 mwavelength without limbdarkening correction

56.0±lmas

44.0±2mas

DActual diameterestimated from 11 jsmvalue with 1% correctionfor limb darkening

56.6 mas

44.4 mas

With the infrared size measurements comes an additional interpretation of stellar temperatures. The temperatureis of course not constant in all parts of the star, and hence can depend on characteristics of stellar atmospheres andhow such temperatures are defmed. Table 2 shows a collection of temperatures, some using the diameters measuredat 11 .tm. We believe these represent useful and representative values of the temperature.

Table 2

Temperatures of a On and a Sco

Objects

a On

a Sco

T1,Effective temperature fromluminosity andassuming

3290

3670

T11

Effective temperaturefrom luminosity andassuming D11

3190

3500

TTemperature calculatedfrom 11 jsm flux andD11

2850

2675

929

Table 1

Measured diameters of a On and a Sco

D11, DActual diameter

Diameter at visible Diameter at 1 1 tm estimated from 1 1 .tmwavelengths without wavelength without limb value with 1% correction

Objects limb darkening correction darkening correction for limb darkening

a On 52.7 1.3 mas 56.0 1 mas 56.6 mas

aSco 40.O±O.6mas 44.O±2mas 44.4mas

With the infrared size measurements comes an additional interpretation of stellar temperatures. The temperatureis of course not constant in all parts of the star, and hence can depend on characteristics of stellar atmospheres andhow such temperatures are defmed. Table 2 shows a collection of temperatures, some using the diameters measuredat 11 tm. We believe these represent useful and representative values of the temperature.

Table 2

Temperatures of a On and a Sco

T11,, TEffective temperature from Effective temperature Temperature calculatedluminosity and from luminosity and from 11 tm flux and

Objects assuming assuming D11 D11

aOri 3290 3190 2850

aSco 3670 3500 2675

929


930

7. CONCLUSION

A broad examination of the results of IS! observations of a number of stars leads to the following conclusions:

Dust is formed around the stars at temperatures between 1,000 and 1,500K, approximately as expectedtheoretically.About half of the stars observed emit dust episodically rather than continually or on each luminosity cycle.The time between episodic emissions varies from about 10 years to about 100 years. A few stars around whichseveral shells can be seen appear to have shells approximately equally separated, indicating perhaps aperiodicity. However, this conclusion is not a secure one. What we do know is that these times are long, andvary substantially between the stars. There seems to be no current theory which can produce timescales of thisgeneral magnitude.Cycles of variable stars clearly do not repeat very precisely. This has been known previously for some starsbecause of a lack of repetition of the visible magnitude as a function of the phase of a cycle. However, we cannow see that this is also associated with variations in the amount of dust emitted or surrounding the star at anyone time.Clearly many stars emit dust in patterns which are not spherically symmetric. It is not yet clear whether thisnonsymmetry can be directly associated with certain types of stars only, and further study will be needed toexamine this question.It appears important and fruitful to measure the diameter of stars in the infrared, perhaps in the near infrared aswell as the mid-infrared. This should produce a more reliable and accurate picture of whether the stars arechanging size and shape as well as give more representative diameters and additional insight into theiratmospheres and temperatures.It is important to make rapid interferometric measurements and over a substantial part of the UV plane in orderto get reasonably complete pictures of the distribution and behavior of dust. The distributions are not spherical,they can change rather rapidly with time, and are not completely periodic. This emphasizes the importance ofour building a third telescope so that we can obtain somewhat more rapid and more complete visibilitymeasurements.

As we look to the future, we expect soon to do interferometry on spectral lines. Fig. 27 shows absorption linesof silane in IRC + 10216 and of ammonia in NML Cygni. Interferometry on their line frequencies can help establishwhere these molecules are formed. This may be particularly interesting because circumstellar material representsone of the few cases where the circumstances under which molecules are formed can be known. Material emergesfrom the star in more or less atomic form and becomes molecular as it cools off and material condenses into dust.Thus the timing, mechanisms, and nature of the formation can probably be examined in some detail. We have builtfilters for our heterodyne interferometry system so that visibility measurements can be made in narrow bands bothon and off a line. The filters are somewhat narrower in frequency range than are the lines, so that various parts ofthese lines can be examined. This should allow determination of the distribution of molecular material and thedistribution of excitation and velocity. We hope and expect that in the future this too will provide interesting andrevealing information.

930

7. CONCLUSION

A broad examination of the results of ISI observations of a number of stars leads to the following conclusions:

1) Dust is formed around the stars at temperatures between 1,000 and 1,500K, approximately as expectedtheoretically.

2) About half ofthe stars observed emit dust episodically rather than continually or on each luminosity cycle.3) The time between episodic emissions varies from about 10 years to about 100 years. A few stars around which

several shells can be seen appear to have shells approximately equally separated, indicating perhaps aperiodicity. However, this conclusion is not a secure one. What we do know is that these times are long, andvary substantially between the stars. There seems to be no current theory which can produce timescales of this

general magnitude.4) Cycles of variable stars clearly do not repeat very precisely. This has been known previously for some stars

because of a lack of repetition of the visible magnitude as a function of the phase of a cycle. However, we cannow see that this is also associated with variations in the amount of dust emitted or surrounding the star at anyone time.

5) Clearly many stars emit dust in patterns which are not spherically symmetric. It is not yet clear whether thisnonsymmetry can be directly associated with certain types of stars only, and further study will be needed toexamine this question.

6) It appears important and fruitful to measure the diameter of stars in the infrared, perhaps in the near infrared aswell as the mid-infrared. This should produce a more reliable and accurate picture of whether the stars arechanging size and shape as well as give more representative diameters and additional insight into theiratmospheres and temperatures.

7) It is important to make rapid mterferometric measurements and over a substantial part of the UV plane in orderto get reasonably complete pictures ofthe distribution and behavior of dust. The distributions are not spherical,they can change rather rapidly with time, and are not completely periodic. This emphasizes the importance ofour building a third telescope so that we can obtain somewhat more rapid and more complete visibilitymeasurements.

As we look to the future, we expect soon to do interferometry on spectral lines. Fig. 27 shows absorption linesof silane in IRC +10216 and of ammonia in NML Cygni. Interferometry on their line frequencies can help establishwhere these molecules are formed. This may be particularly interesting because circumstellar material representsone of the few cases where the circumstances under which molecules are formed can be known. Material emergesfrom the star in more or less atomic form and becomes molecular as it cools off and material condenses into dust.Thus the timing, mechanisms, and nature of the formation can probably be examined in some detail. We have builtfilters for our heterodyne interferometry system so that visibility measurements can be made in narrow bands bothon and off a line. The filters are somewhat narrower in frequency range than are the lines, so that various parts ofthese lines can be examined. This should allow determination of the distribution of molecular material and thedistribution of excitation and velocity. We hope and expect that in the future this too will provide interesting andrevealing information.


SIH4IRC ±10216

10

0.9

0.8

0.7

0.6

0.50

-3V) 0.9

n)0.6

1 0

0.71.0 _-_

0.9[

0.9F35

a(0.0)

R(1.1)

P(4,3)

!P(1.0)

NH3

N}L Cyg

aQ(9,9)

30 25LSR Velocity (km

20 15 10

Fig. 27. Spectral lines of SiH4 and NH4 due to formation of such molecules in material emitted by stars such as IRC + 10216 andNMI Cyg. The fractional intensity is plotted here as a function of Doppler shift due to a velocity with respect to the localstandard of rest (LSR). It is expected that high angular resolution by interferometry in the mid-IR region will help determine theplaces of appearance of various excitation states of these molecules, and allow some quantitative tests of theories of formation.

931

50 45 40 35 30LSR Velocity (km s')

Fig. 27. Spectral lines of SiH4 and NH4 due to formation of such molecules in material emitted by stars such as IRC +102 16 andNML Cyg. The fractional intensity is plotted here as a function of Doppler shift due to a velocity with respect to the localstandard of rest (LSR). It is expected that high angular resolution by interferometry in the mid-IR region will help determine theplaces of appearance of various excitation states of these molecules, and allow some quantitative tests of theories of formation.

931

SIH4IRC +10216

NH3N}IL Cyg

C)

C)

C)

a)

C)

0.9

0.71.0

0.9

Th-------

—50 —45 —40 —35

LSR Velocity (kna _1)

5P(10) j—30 —30 —25 —20 —15 —10

LSR Velocity (km s')


932

8. ACKNOWLEDGMENTS

This work was supported by grants from the Office of Naval Research (grants N000 14-96-073 7 and N000 14-97-1 -0743), and from the National Science Foundation (grants AST 9321289, AST 9321384, and AST 9500525). M.J.was supported under the auspices of the U.S. Department of Energy, contract W-7405-ENG-48. D.W. wassupported under the auspices of the U.S. Department of the Navy.

9. REFERENCES

M. Bester, W.C. Danchi, and C.H. Townes, "Long baseline interferometer for the mid-infrared," Amplitudeand Intensity Spatial Interferometry, J.B. Breckinridge (ed.), Proc. SPIE 1237, pp. 40-48, 1990.

M. Bester, W.C. Danchi, D. Hale, C.H. Townes, C.G. Degiacomi, D. Mékarnia, and T.R. Geballe,"Measurement at 11 micron wavelengths of the diameters of a Orionis and a Scorpii; and changes in effectivetemperature of a Orionis and very recent dust emission," Api 463, pp. 336-343, 1996.

W.C. Danchi, M. Bester, C.G. Degiacomi, and L.J. Greenhill, and C.H. Townes, "Characteristics of dust shellsaround 13 late-type stars," AJ 107, pp. 1469-1513, 1994.

M.M. Dyck and J.A. Benson, "Variations in the 8-13 sm visibility functions of shells around oxygen richstars," Ai 104, pp. 377-385, 1992.

J.D. Fix and M.L. Cobb, "The structure of circumstellar shells," Api 329, pp. 290-298, 1988.

David D.S. Hale, M. Bester, W.C.Danchi, S. Hoss, E. Lipman, J.D. Monnier, P.G. Tuthill, C.H. Townes, M.Johnson, B. Lopez, and T.R. Geballe, "Multiple dust shells and motions around 1K Tauri as seen by infraredinterferometry," Api 490, pp. 407-411, 1997.

A.R. Hajian, J.T. Armstrong, C.A. Hummel, J.A. Benson, D. Mozurkevich, T.A. Pauls, D.J. Hutter, N.M. EliasII, K.J. Johnston, L.J. Richard, and N.M. White, "Direct confirmation of stellar limb darkening with the Navyprototype optical interferometer," Api 496, pp. 484-489, 1998.

B. Lopez, et al, "Nonspherical structures and temporal variations in the dust shell of o Ceti observed with along baseline interferometer at 11 microns," Api 488, pp. 807-826, 1997.

A.A. Michelson and PG. Pease, "Measurement of the diameter of a Orionis with the interferometer," Api 53,pp. 249-259, 1921.

iD. Monnier, M. Bester, W.C. Danchi, M.A. Johnson, E.A. Lipman, C.H. Townes, P.G. Tuthill, T.R.Geballe, D. Nishimoto, and P.W. Kervin, "Nonuniform dust outflow observed around the infrared object NMLCygni," Api 481, pp. 420-432, 1997.

S.T. Ridgway, D.C. Wells, and R.R. Joyce, "Angular diameters for 11 late-type stars by the lunar occultationtechnique," Ai82, pp. 4 14-430, 1977.

R.N. Treuhaft, S.T. Lowe, M. Bester, and W.C. Danchi, and C.H. Townes, "Vertical scales of turbulence at theMount Wilson Observatory," Api453, pp. 522-531, 1995.

P.G. Tuthill, "Imaging stars through the atmosphere," Ph.D. thesis, Cambridge Univ., 1994.

N.M. White, "The occultation of 119 Tauri and the effective temperatures of three M supergiants," Api 242,646, 1980.

932

8. ACKNOWLEDGMENTS

This work was supported by grants from the Office of Naval Research (grants N000 14-96-0737 and N000 14-97-1-0743), and from the National Science Foundation (grants AST 9321289, AST 9321384, and AST 9500525). Mi.was supported under the auspices of the U.S. Department of Energy, contract W-7405-ENG-48. D.W. wassupported under the auspices ofthe U.S. Department ofthe Navy.

9. REFERENCES

1. M. Bester, W.C. Danchi, and C.H. Townes, "Long baseline mterferometer for the mid-infrared," Amplitudeandlntensity Spatial Interferometiy, J.B. Breckmridge (ed.), Proc. SPIE 1237, pp. 40-48, 1990.

2. M. Bester, W.C. Danchi, D. Hale, C.H. Townes, C.G. Degiacomi, D. Mékamia, and T.R. Geballe,"Measurement at 1 1 micron wavelengths of the diameters of a Orionis and a Scorpii; and changes in effectivetemperature ofa Orionis and very recent dust emission," ApJ463, pp. 336-343, 1996.

3. W.C. Danchi, M. Bester, C.G. Degiacomi, and L.J. Greenhill, and C.H. Townes, "Characteristics of dust shellsaround 13 late-type stars," AJ 107, pp. 1469-15 13, 1994.

4. M.M. Dyck and J.A. Benson, "Variations in the 8-13 .tm visibility functions of shells around oxygen richstars," AJ 104, pp. 377-385, 1992.

5. J.D. Fix and M.L. Cobb, "The structure ofcircumstellar shells," ApJ329, pp. 290-298, 1988.

6. David D.S. Hale, M. Bester, W.C.Danchi, S. Hoss, E. Lipman, J.D. Monnier, P.G. Tuthill, C.H. Townes, M.Johnson, B. Lopez, and T.R. Geballe, "Multiple dust shells and motions around 1K Tauri as seen by infraredinterferometry," ApJ 490, pp. 407-41 1 , 1997.

7. A.R. Hajian, J.T. Armstrong, C.A. Hummel, J.A. Benson, D. Mozurkevich, T.A. Pauls, D.J. Huller, N.M. EliasII, K.J. Johnston, Li. Richard, and N.M. White, "Direct confirmation of stellar limb darkening with the Navyprototype optical interferometer," ApJ496, pp. 484-489, 1998.

8. B. Lopez, et al, "Nonspherical structures and temporal variations in the dust shell of o Ceti observed with along baseline interferometer at 1 1 microns," ApJ488, pp. 807-826, 1997.

9. A.A. Michelson and PG. Pease, "Measurement of the diameter of a Orionis with the interferometer," ApJ 53,pp. 249-259, 1921.

10. J.D. Monnier, M. Bester, W.C. Danchi, M.A. Johnson, E.A. Lipman, C.H. Townes, P.G. Tuthill, T.R.Geballe, D. Nishimoto, and P.W. Kervin, "Nonuniform dust outflow observed around the infrared object NMLCygni," ApJ481, pp. 420-432, 1997.

11. S.T. Ridgway, D.C. Wells, and R.R. Joyce, "Angular diameters for 11 late-type stars by the lunar occultationtechnique," AJ82, pp. 4 14-430, 1977.

12. R.N. Treuhaft, S.T. Lowe, M. Bester, and W.C. Danchi, and C.H. Townes, "Vertical scales of turbulence at theMount Wilson Observatory," ApJ 453, pp. 522-531, 1995.

13. P.G. Tuthill, "Imaging stars through the atmosphere," Ph.D. thesis, Cambridge Univ., 1994.

14. N.M. White, "The occultation of 119 Tauri and the effective temperatures of three M supergiants," Api 242,646, 1980.


Documents

Infrared Spatial Interferometer...C.H. Townesa, M. Beste?, W.C. Danchia, D.D.S. Halea, J.D. Monnie?, E.A. Lipmana, P.G. Tuthilla, M.A. JOhflSOflb, and D. Wa1ters' aSpace Sciences Laboratory,