Elementi di Astronomia e Astrofisica per il Corso di Ingegneria Aerospaziale VI settimana

21/02/05 C.Barbieri Elementi_AA_2004_05 Sesta settimana

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Elementi di Astronomia e Astrofisica per il Corso di Ingegneria Aerospaziale

VI settimana

L'Atmosfera terrestre


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The terrestrial atmosphere - 1This chapter is devoted to the examination of the influence of the Earth’s atmosphere on the apparent coordinates of the stars and on the shape of their images; the discussion will be limited essentially to the visual band. The discussion of the effects of the atmosphere on photometry and spectrophotometry are deferred to a later chapter.

The figure gives a schematic representation of the vertical structure of the atmosphere; the visual band is mostly affected by what happens in the troposphere, namely in the first 15 km or so of height, where some 90% of the total mass of the atmosphere is contained.


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The terrestrial atmosphere -2

Na Layer


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The terrestrial atmosphere - 3The temperature profile in the troposphere is actually more complicated than shown in the Figure. The height of the tropopause (a layer of almost constant temperature) from the ground ranges from 8 km at high latitudes to 18 km above the equator; it is also highest in summer and lowest in winter. The average temperature gradient is approximately –6 C/km, but often, above a critical layer situated in the first few km, the temperature gradient is inverted, with beneficial effects on astronomical observations, thanks to the intrinsic stability of all layers with temperature inversion (such as the stratosphere and the thermosphere), essentially because convection cannot develop. This is the case for instance of the Observatory of the Roque de los Muchachos (Canary Islands, height 2400 m a.s.l.), where the inversion layer is usually few hundred meters below the telescopes at the top of the mountain.


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Chemical composition and structure

The chemical composition of the troposphere is mostly molecular Nitrogen N2

and molecular Oxygen O2 (approximately 3:4 and 1:4 respectively), with traces

of the noble gas Argon and of water vapor (the water vapor concentration may be as high as 3% at the equator, and decreases toward the poles). Above the tropopause, at higher heights in the stratosphere, the temperature raises considerably thanks to the solar UV absorption by the Ozone (O3)

molecule with the process:

UV photon + O3 = O2+O+heat.

The mesosphere ranges from 50 to 80 km; in this region, concentrations of O3

and H2O vapor are negligible, hence the temperature is lower than in the

stratosphere. The chemical composition of the air becomes strongly height-dependent, with heavier gases stratified in the lower layers. In this region, meteors and spacecraft entering the atmosphere start to warm up.


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The ozone O3

Most atmospheric ozone is concentrated in a layer in the stratosphere, about 15-30 kilometers above the Earth's surface. Even this small amount of ozone plays a key role in the atmosphere, absorbing the UVB portion of the radiation from the sun, preventing it from reaching the planet's surface.

O3 is a molecule containing 3 O atoms. It is blue in color and has a strong odor. Normal molecular O2, has 2 oxygen atoms and is colorless and odorless. Ozone is much less common than normal oxygen. Out of each 10 million air molecules, about 2 million are normal oxygen, but only 3 are ozone.


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Water vapor nomenclature - 1Water vapor is water in the gaseous phase. The actual amount is the concentration of water vapor in the air, the relative concentration is the ratio between the actual amount to the amount that would saturate the air. Air is said to be saturated when it contains the maximum possible amount of water vapor without bringing on condensation. At that point, the rate at which water molecules enter the air by evaporation exactly balances the rate at which they leave by condensation. The partial pressure of a given sample of moist air that is attributable to the water vapor is called the vapor pressure. The vapor pressure necessary to saturate the air is the saturation vapor pressure. Its value depends only on the temperature of the air. (The Clausius-Clapeyron equation gives the saturation vapor pressure over a flat surface of pure water as a function of temperature.) Saturation vapor pressure increases rapidly with temperature: the value at 32°C is about double the value at 21°C. The saturation vapor pressure over a curved surface, such as a cloud droplet, is greater than that over a flat surface, and the saturation vapor pressure over pure water is greater than that over water with a dissolved solute.


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Water vapor nomenclature - 2Relative humidity is the ratio of the actual vapor pressure to the saturation vapor pressure at the air temperature, expressed as a percentage. Because of the temperature dependence of the saturation vapor pressure, for a given value of relative humidity, warm air has more water vapor than cooler air. The dew point temperature is the temperature the air would have if it were cooled, at constant pressure and water vapor content, until saturation (or condensation) occurred. The difference between the actual temperature and the dew point is called the dew point depression. The wet-bulb temperature is the temperature an air parcel would have if it were cooled to saturation at constant pressure by evaporating water into the parcel. (The term comes from the operation of a psychrometer, a widely used instrument for measuring humidity, in which a pair of thermometers, one of which has a wetted piece of cotton on the bulb, is ventilated. The difference between the temperatures of the two thermometers is a measure of the humidity.) The wet-bulb temperature is the lowest air temperature that can be achieved by evaporation. At saturation, the wet-bulb, dew point, and air temperatures are all equal; otherwise the dew point temperature is less than the wet-bulb temperature, which is less than the air temperature.


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Water Vapor Mixing ratioSpecific humidity is the ratio of the mass of water vapor in a sample to the total mass, including both the dry air and the water vapor. The mixing ratio is the ratio of the mass of water vapor to the mass of only the dry air in the sample. As ratios of masses, both specific humidity and mixing ratio are dimensionless numbers. However, because atmospheric concentrations of water vapor tend to be at most only a few percent of the amount of air (and usually much lower), they are both often expressed in units of grams of water vapor per kilogram of (moist or dry) air. Absolute humidity is the same as the water vapor density, defined as the mass of water vapor divided by the volume of associated moist air and generally expressed in grams per cubic meter. The term is not much in use now.


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Water reservoir Water vapor is constantly cycling through the atmosphere, evaporating from the surface, condensing to form clouds blown by the winds, and subsequently returning to the Earth as precipitation. Heat from the Sun is used to evaporate water, and this heat is put into the air when the water condenses into clouds and precipitates. This evaporation - condensation cycle is an important mechanism for transferring heat energy from the Earth's surface to its atmosphere and in moving heat around the Earth.

Water vapor is the most abundant of the greenhouse gases in the atmosphere and the most important in establishing the Earth's climate. Greenhouse gases allow much of the Sun's shortwave radiation to pass through them but absorb the infrared radiation emitted by the Earth's surface. Without water vapor and other greenhouse gases in the air, surface air temperatures would be well below freezing.


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Aerospace devicesA multitude of systems exist for observing water vapor on a global scale and at high altitudes, supplementing the instruments on the ground, that measure in special sites and at ground level. Each has different characteristics and advantages. To date, most large-scale water vapor climatological studies have relied on analysis of radiosonde data, which have good resolution in the lower troposphere in populated regions but are of limited value at high altitude and are lacking over remote oceanic regions.


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The Water Vapor content in 1992

NASA Water Vapor Project (NVAP) Total Column Water Vapor 1992The mean distribution of precipitable water, or total atmospheric water vapor above the Earth's surface, for 1992. This depiction includes data from both satellite and radiosonde observations.


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Cloud effects on Earth Radiation


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The outer layers

Following the smooth decrease in the mesosphere, the temperature raises again in the thermosphere, because the solar UV and X-rays, and the energetic electrons from the magnetosphere can partly ionize the very thin gases of the thermosphere. The weakly ionized region which conducts electricity, and reflects radio frequencies below about 30 MHz is called ionosphere; it is divided into the regions D (60-90 km), E (90-140 km), and F (140-1000 km), based on features in the electron density profile. Finally, above 1000 km, the gas composition is dominated by atomic Hydrogen escaping the Earth’s gravity, which is seen by satellites as a bright geocorona in the resonance line Ly- at = 1216 Å.


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Refraction IndexAs is well known, the light propagates in a straight line in any medium of constant refraction index n, with a phase velocity v given by

1/ 2v / 1/( )c n where is the dielectric constant and the magnetic permeability of the medium. All these quantities are wavelength dependent. The group velocity u is instead:

v dv / du At the separation surface between two media of different refraction index (say vacuum/air), the ray changes direction, so that the observer immersed in the second medium sees the light coming from an apparent direction different from the ‘true’ one (see Figure):


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The atmospheric refraction - 1Suppose that the atmosphere can be treated as a succession of parallel planes (hypothesis of plane-parallel stratification), by virtue of its small vertical extension with respect to the Earth’s radius. According to Snell’s laws, when the ray coming from the region of index of refraction n0 encounters the separation

surface with a medium of refraction index n1> n0, part of the energy will be

reflected to the left, on the same hemi-space with the same angle r0 with respect

to the normal. This part will not be considered here, it only implies a dimming of the source. The remaining fraction will be refracted, in the same plane as the incident ray, to an angle r1 < r0. Indeed, in a clear atmosphere without clouds, no

sharp air-vacuum separation surface exists, the refraction index gradually increases from 1 to a final value nf near the ground, with typical scale lengths

much greater than the wavelength of light (as already said, we limit our considerations to the visual band), so that the continuously varying direction can be considered as a series of finite steps in the plane passing through the vertical and the direction to the star.


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The atmospheric refraction - 2

0 0 1 1sin sinn r n r

1 1 1sin sini i in r n r

1 1sin sinf f f fn r n r

where ni+1> ni, and ri+1< ri. By equating each term:

0 0sin sinf fn r n r

Therefore: in a plane-parallel atmosphere the total angular deviation only depends on the refraction index close to the ground, independent of the exact law with which it varies along the path.

By following each refraction in cascade we have:


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By virtue of

The net effect is as shown in the figure: the star is seen in direction z’ smaller than the true direction z, namely closer to the local Zenith, by an amount R which is the atmospheric refraction:

z’ = z – R

0 0sin sinf fn r n r and for small R’s (in practice, if z < 45°):

sin ' sin sin( ' ) sin 'cos cos 'sin sin ' cos 'fn z z z R z R z R z R z


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( 1) tan 'fR n z

In the visual band, for average values of temperature and pressure (T = 273 K, P = 760 mm Hg), nf 1.00029, so that in round numbers

R(15°) 16”, R(45°) 60”

Already for Zenith distances as small as 20°, the refraction is larger than the annual aberration, and of any of the effects discussed in previous chapters that alter the apparent direction of a star.

and finally:


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The atmospheric refraction - 5For zenith distances larger than 45°, the path of the ray inside the atmosphere is so long that the curvature of the Earth cannot be ignored, and the mathematical treatment becomes more intricate, even restricting it to successive refraction in the same plane with n decreasing outwards with continuity.

2 2 2 2 21

dsin '

sin '

fn

f

f

nR a n z

n d n a n z

3 3tan ' tan ' ( 1) (1 ) tan ' tan 'f

l lR A z B z n z z

a a

After several mathematical steps:


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Effect of the refraction on the coordinates

The main effect of refraction is to move the star closer to the Zenith in the vertical plane, thus raising its elevation h but leaving essentially unchanged its azimuth A.

XX’ = R = h PXX’ = PXZ = q

ZX = z, ZX’ = z’PX = 90-XU =

cos ( ' ) cos sin

' cos

HA R q

R q

cos cos sin cos cos sin cos

sin sin cos sin sin cos sin

q h h A

A h HA q HA q

For an object in meridian, the refraction is all in declination, and in particular this is true for the Sun at true noon.


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Approximate formulae for refractionFor Zenith distance not greater than approximately 45°, after several passages we finally get:

2sec sin( 1)

cos tan tan

tan tan cos( 1)

cos tan tan

f

f

HAn

HA

HAn

HA

by means of which formulae we can derive the true (or the apparent, according to the sign) topocentric positions. Obviously no such correction is necessary for a telescope in outer Space.


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The chromatism of the refractionThe refraction index n depends from the wavelength, diminishing from the blue to the red, and the same will be true for the refraction angle R: the image on the ground of the star is therefore a succession of monochromatic points aligned along the vertical circle; the blue ray will be below the red one, and thus the blue star will appear to the eye above the red one

The atmosphere behaves therefore like a prism producing a short spectrum in the vertical plane, whose length increases with the zenith distance, reaching several arc seconds at low elevations. The relationships n() can be expressed by the so-called Cauchy’s formula:

2 4

0.00566 0.000047( ) 0.00028 1n

( in micrometers), corresponding to a variation of about 2% over the visible range, namely to about 1”.2 at 45°.


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Density - temperature relationshipOnce we have fixed , the refraction index n depends from the density according to Gladstone-Dale’s law:

1n k and with the hypothesis of a perfect gas of pressure P, temperature T and

molecular weight :

R

P

T

(where R is now the gas universal constant)

1 'P

n kT

0

0 0

1

1

Tn P

n P T

61 78.7 10

Pn

T

( / 760)60".4 tan

( / 273)

PR z

T

(P in mm Hg, T in K)


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Vertical gradients of temperatureCalling H the height over the ground, we have:

1d ' d d

Pn k P T

T T 2 2

d 1 d d d d' '

d d d d d

n P P T P T P Tk k

H T H T H T P H H

The variation of pressure with the height is equal to the weight of the air in the

elementary volume having unitary base and height dH, d dP g H

so that:2

d d'

d R d

n P g Tk

q T H

where the constant g/R equals approximately 3.4 K/km, and is called adiabatic lapse. Hence the conclusion that the variations of the refraction index depend from the vertical gradients of the temperature. A practical consequence is that all effort must be made to control and minimize those gradients over the accessible volume of the telescope enclosure.


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Turbulence, Scintillation, SeeingThe Earth's atmosphere is turbulent and variations in the index of refraction cause the plane wavefront from distant objects to be distorted. This distortion introduces amplitude variations, positional shifts and image degradation. This causes two astronomical effects: •scintillation, which is amplitude variations, which typically varies over scales of few cm: generally very small for large aperture telescopes•seeing: positional changes and image quality changes. The effect of seeing depends on aperture size: for small apertures, one sees a diffraction pattern moving around, while for large apertures, one sees a set of diffraction patterns (speckles) moving around on scale of ~1 arcsec. These observations imply:

• wavefronts are flat on scales of small apertures• instantaneous slopes vary by ~ 1 arcsec.

The typical time scales are few milliseconds and up. The effect of seeing can be derived from theories of atmospheric turbulence, worked out originally by Kolmogorov, Tatarski, Fried.


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Structure functionThe structure of the refraction index n in a turbulent field can be described statistically by a structure function:

2( ) ( ) ( )nD x n r x n r

where x is separation of points, r is position. Kolmogorov turbulence gives:

2 21( )

3n nD x C x

where Cn is the refractive index structure constant. From this, one can derive

the phase structure function at the telescope aperture: 5/ 2

0

6.88x

Dr where the coherence length r0 (also

known as the Fried parameter) is:

3/56/5 3/5 2

0 00.185 cos dr z C h

where z is zenith angle, is wavelength. Using optics theory, one can convert D

into an image shape.


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The Fried parameterNotice that r0 increases with 6/5 = 1. 2.

Physically, the image size d from seeing is (roughly) inversely proportional to r0

0/d ras compared with the image size from a diffraction-limited telescope of aperture D:

/d DSeeing dominates when r0 < D ; a larger r0 means better seeing. Seeing is more

important than diffraction at shorter wavelengths, diffraction more important at longer wavelengths; effect of diffraction and seeing cross over in the IR (at 5 microns for 4m); the crossover falls at a shorter wavelength for smaller telescope or better seeing. Fried’s parameter r0 varies from site to site and also in time. At

most sites, there seems to be three regimes called:surface layer (wind-surface interactions and manmade seeing), planetary boundary layer ( influenced by diurnal heating), free atmosphere (10 km is tropopause: high wind shears)


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An example of Cn2

A typical site has

r0 10 cm

at 5000Å , namely a seeing of 1". On rare occasions, in the best sites, the seeing can be as low as 0".3.


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The isoplanatic angleWe also have to consider the coherence of the same turbulence pattern over the sky: coherence angle call the isoplanatic angle:

00.314 /r H

where H is the average distance of the seeing layer:

For r0 10 cm, H = 5000 m , 1.3 arcsec.

In the infrared r0 70 cm, H = 5000 m , 9 arcsec.

Note however, that the ``isoplanatic patch for image motion" (not wavefront)

is 0.3D/H. For D = 4m, H = 5000 m, kin 50 arcsec.

- Another useful parameter is the correlation time 0, which is

approximately the dimension of the typical air bubble divided by the velocity of the wind. As r0, also 0 increases with 6/5.


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The seeing

Bubbles of air having slightly different temperatures, and therefore slightly different refractive indexes, are carried by the wind across the aperture of the telescope.

The Fried parameter r0 can be used to simplify the description of a very complex

rapidly varying medium, namely the typical size of the bubble. Values vary from

few centimeters (a poor site) to some 30 cm (a very good site).

r0 can be understood also as the effective diameter of the diffraction limited

telescope in that site (with respect to the angular resolution).


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Representation of the seeingThere are two main components of the seeing: •one coming from high altitudes (choice of site) •one due to ground layers (it can be actively controlled by shape of dome and proper thermalisation of structure) • The spectral power of the air turbulence is appreciable over a large interval of frequencies , say 1 to 1000 Hz, with a 1/f distribution.

The angles are exaggerated, actually AdOpt correction can be made over small fields of view. Another useful parameter is the maximum angle over which fluctuations are coherent (isoplanatic angle). Both Fried’s parameter and isoplanatic angle improve with increasing wavelength, the correction is better in the IR than in the Visible.


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A first remedy: Speckle Interferometry

• a very large number of short duration exposures are taken with very long focal length (say 100m) and narrow bandwidth (say 1 nm); in each exposure the seeing is frozen, each speckle represents the diffraction figure of the aperture

• Fourier Transforms allow the reconstruction of the true image;

• The technique works well for simple structures (e.g. double or multiple stars, disks).

Obtained with the Asiago 1.8 cm telescope


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A better remedy: Adaptive Optics

The fairly complex techniques that are nowadays implemented on the largest telescopes to contrast the seeing are known collectively as Adaptive Optics devices. • A suitable reference wavefront is also necessary. Suitably bright stars are rare. •An artificial laser star is a possible solution.


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The artificial laser star


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Before and after AdOpt

If one ‘freezes’ the image with short exposure times (say less than 0.01 sec) and a narrow filter, the seeing image breaks up in large number of ‘speckles’, each having dimension of the order of the diffraction figure of the telescope.

The number of speckles is of the order of :

(seeing diameter/diffraction figure)2


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The Galactic Center with the Keck AdOpt

Without AdOpt

With AdOpt


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Quality of the image -1The quality of an image can be described in many different ways. The overall shape of the distribution of light from a point source is specified by the point spread function (PSF). Diffraction gives a basic limit to the quality of the PSF, but any aberrations or image motion add to structure/broadening of the PSF. Another way of describing the quality of an image is to specify it's modulation transfer function (MTF). The MTF and PSF are a Fourier transform pair. Turbulence theory gives:

5 / 33.44( / )MTF ave where is the spatial frequency. Note that a Gaussian goes as 2, so this MTF is close to a Gaussian. The shape of seeing-limited images is roughly Gaussian in core but has more extended wings. This is relevant because the seeing is often described by fitting a Gaussian to a stellar profile.

6232

1 2 54 5

( )1

py px p

I pp p

A potentially better empirical fitting function is a Moffat function:


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Quality of the image -2Probably the most common way of describing the seeing is by specifying the full-width-half-maximum (FWHM) of the image, which may be estimated either by direct inspection or by fitting a function (usually a Gaussian); note the correspondence of FWHM to of a Gaussian: FWHM = 2.355 .

The FWHM doesn't fully specify a PSF, and one should always consider how applicable the quantity is. Another way of characterizing the PSF is by giving the encircled energy as a function of radius, or at some specified radius. A final way of characterizing the image quality, more commonly used in adaptive optics applications, is the Strehl ratio SR. The Strehl ratio is the ratio between the peak amplitude of the PSF and the peak amplitude expected in the presence of diffraction only. In practice, in the visible it is already very good reaching SR = 0.1 .


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The EE of the Rosetta WAC

The WAC is in space, so there is no seeing to worry about, only the vibrations of the spacecraft or thermal distortions of the jitter of the attitude.


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Effects of the atmosphere at radiofrequencies - 1The ionosphere will introduce a delay on the arrival time of the wave, given by:

2

40.3de

I

T N sc

seconds, being I the path along the line of sight and Ne the electron

density (cm-3). This density will vary with the night and day cycle, with the season and also with the solar cycle.


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Effects of the atmosphere at radiofrequencies -2

The tropospheric delay can be resolved in two components, a dry one and a wet one. The dry component amounts to about 7 ns at the Zenith, and varies with the ‘modified cosec z’ we have discussed for the optical observations:

0.00147(cos ) ns

0.0445 cott z

z

The wet component depends on the amount of water vapour, and amounts to about 10% of the dry one, but it varies rapidly and in unpredictable way.

Finally, two other mediums affect the propagation of the radio waves, namely the solar corona and the ionized interstellar medium.


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Extinction and spontaneous emission by the atmosphere

In addition to chaotic refraction effects, the atmosphere absorbs a fraction of the incident light, both in the continuum and inside atomic and molecular lines and bands.

Furthermore, the atmosphere spontaneously emits in particular atomic and molecular bands (this is in addition to scattering of artificial lights, see later).

The molecular oxygen O2 in particular is so effective at blocking radiation around 6800A and 7600A that Fraunhofer could detect by eye two dark absorption bands in the far red of the solar spectrum, bands he called respectively B and A (he examined the spectra from red to blue, the current astronomical practice is from blue to red).


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ExtinctionLet us consider the absorption due to a thin layer of atmosphere at height between h and h+dh in the usual simple model of a plane-parallel atmosphere. The light beam from the star makes an angle z with the Zenith, so that the traversed path is dh/cosz = seczdh. If I(h) is the intensity at the top of the layer, at the exit it will be reduced by

the quantity:

d ( ) ( )sec dI I h k h z h In total, if I() is the intensity outside the atmosphere, at the elevation h0 of

the Observatory the intensity will be reduced to:

00

sec ( ) d( ) sec( ) ( ) ( )h

z k h hzI h I e I e


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Optical Depthwhere we have introduced the a-dimensional quantity called optical depth :

d ( ) dk h h 0

( ) dh

k h h

The variable k (dimensionally, cm-1) represents the absorption per unit

length of the atmosphere at that wavelength. Astronomers use a particular measure of the apparent intensity, namely the

magnitude, defined by m = m0 -2.5logI (see in a later lecture), so that:

ground d 2.5 ( ) secoutsi em m D z

D is called the optical density of the atmosphere, while the variable X(z) = secz

is called air-mass. The minimum value of the airmass is 1 at the Zenith, and 2 at z = 60° (the limit of validity of the present approximate discussion).


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The Bouguer lineSuppose we start observing the star at its upper transit, and then keep observing it while its Hour Angle (and therefore also its Zenith distance) increases: we would notice a linear increase of its magnitude in agreement with the previous equation, namely a straight line with slope 2.5D in a graph (m, secz).

It is common practice to plot the m-axis pointing down. This straight line is known as Bouguer line, from the name of the XVIII century French astronomer who introduced it. The extrapolation of this line to X = 0 (a mathematical absurdity) gives the so-called loss of magnitude at the Zenith, or else the magnitude outside atmosphere.According to the formulae of the first lectures we have:

1sec ( )

sin sin cos cos cosz X z

HA

where is the latitude of the site, and HA the coordinates of the star.


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The least continuous extinctionThe Table shows the continuous extinction of the atmosphere above Mauna Kea, whose elevation above sea level (4300 m) is higher than that of most observatories so that the transparency of the sky is at its best, in the extended visible region.

Wavelength (nm)Extinction

(mag / air mass)Wavelength (nm)

Extinction(mag / air mass)

310 1.37 500 0.13

320 0.82 550 0.12

340 0.51 600 0.11

360 0.37 650 0.11

380 0.30 700 0.10

400 0.25 800 0.07

450 0.17 900 0.05


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Figures of the extinction from the visible to the near IR

The figure on the left gives the optical depth, the one on the right the transmission (one is the reverse of the other). In the violet region, the transparency quickly goes to zero, essentially because of the ozone O3 molecular

absorption; at the other end of the spectrum the transparency is reasonably good until about 2.4 micrometers, when the H2O and CO2 molecules heavily absorb

the light. The astronomical photometric wide bands (U,B,V, R, I, J, H, …) are indicated.


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Spontaneous and artificial emissionsTo complete these considerations about the influence of the atmosphere on the photometry (and also on the spectroscopy) of the celestial bodies, we must add that the atmosphere contributes radiation, by spontaneous emission and by scattering of natural and artificial lights. If the Observatory is close to populated areas, bright emission lines of Mercury and Sodium from street lamps are observed: Hg at 4046.6, 4358.3, 5461.0, 5769.5, 5790.7; Na at 5683.5, 5890/96 (the yellow D-doublet), 6154.6; Ne at 6506, and so on. Natural lines come from the atomic Oxygen in forbidden transitions (designated with [OI]) at 5577.4, 6300 and 6367, and especially from the molecular radical OH who provides a wealth of spectral lines and bands filling the near-IR region above 6800A. The OH comes from the dissociation of the water vapor molecule under the action of the solar UV radiation. Therefore, the atmosphere is a diffuse source of radiation, whose intensity strongly depends on the Observatory site; to set an indicative value in the visual band, a luminosity equivalent to one star of 20th mag per square arcsec at the Zenith can be assumed.


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The visible spectrum of the night sky

The night sky is calibrated (see ordinate) in surface brightness, given as mag/(arcsec)2. Mt. Boyun is in Korea.


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The Near-IR sky emission - 2

A very detailed section of the near-IR night sky OH-emission obtained at ESO Paranal with UVES.

http://www.eso.org/observing/dfo/quality/UVES/uvessky/sky_8600U_1.html


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A second limit of the terrestrial atmosphere: the artificial lights

The full Moon has difficulties in competing with the spectrum of artificial lights.


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The situation in Italy

1998 2025

If the extrapolation is correct, in 2025 no Italian will be able to see the Milky Way


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Planetary light pollution

From a paper by Cinzano, Falchi e Elvidge (2001)

Documents

Elementi di Astronomia e Astrofisica per il Corso di Ingegneria Aerospaziale VI settimana