Technical Glossary to the

TLRBSE Solar Spectra Data Analysis

Package

March 2006

dark frame Thermal noise, dark current, and cosmic rays may alter the pixels in the CCD array. (Dark current is the response of a detector to radiation during periods when it is not exposed to light.) To counter such effects, astronomers take an average of several exposures with the CCD shutter closed and opened. The average of images taken with the shutter closed is necessary to lower the random noise. Once developed, the "dark frame" average image is then subtracted from the open-shutter image to remove the dark current and other systematic defects in the CCD (dead pixels, hot pixels, etc). Adapted from http://en.wikipedia.org/wiki/Charge-coupled_device.

dispersion The meaning of dispersion used in the context of our solar research is the pixel size in units of wavelength. The x-axis of the spectra are initially in units of pixels, but knowing the “dispersion” (the number of Angstroms per pixel), one can go from units of pixels to Angstroms. The number of pixels can be counted between two different spectral lines not under the influence of magnetic fields and those same two lines can be identified in a spectral atlas for their difference in Angstroms. Those two quantities ratioed can give the dispersion as defined here.

Doppler effect The Doppler effect for electromagnetic waves such as light, is of great use in astronomy, and results in either a so-called redshift or blueshift. It has been used to measure the speed at which stars and galaxies are approaching to, or receding from us, i.e. the radial velocity. This is used to detect that an apparently single star is, in fact, a close binary and even to measure the speed of rotation of stars and galaxies. The use of the Doppler effect for light in astronomy depends on the fact that the spectra of stars are not continuous. They show absorption lines at well defined frequencies that are correlated with the energies required to excite electrons in various elements from one level to another. The Doppler effect is recognizable in the fact that the absorption lines are not always at the frequencies that are obtained from the spectrum of a stationary light source. Since blue light has a higher frequency than red light, the spectral lines from an approaching astronomical light source show a blueshift and those of receding sources show a redshift. Among the nearby stars, the largest radial velocities with respect to the Sun are +308 km/s (BD-15°4041, also known as LHS 52, 81.7 light-years away) and -260 km/s (Woolley 9722, also known as Wolf 1106 and LHS 64, 78.2 light-years away). Positive radial velocity means the star is receding from the Sun, negative that it is approaching.

The redshift effect that shows remote galaxies seem to be moving away from us is not caused by the Doppler effect, although many laymen believe it is. This effect is caused by the expansion of the universe, which is subtly different, and can be used to estimate the age of the universe (see redshift and Hubble's Law). From http://en.wikipedia.org/wiki/Doppler_shift#Astronomy.

Dopplergram Dopplergram is a spatial map of the approaching and receding velocity of the solar surface. It is produced by measuring the change in the wavelength position of the central component of the spectral line.

Evershed effect The Evershed effect, named after the Britist astronomer John Evershed, is the radial flow of gas across the photospheric surface of the penumbra of sunspots from the inner border with the umbra towards the outer edge. The speed varies from around 1 km/second at the border between the umbra and the penumbra to a maximum of around double this in the middle of the penumbra and falls off to zero at the outer edge of the penumbra. Evershed first detected this phenomenon in January 1909, while working at the Kodaikanal Solar Observatory in India, when he found that the spectral lines of sunspots showed Doppler shift. From http://en.wikipedia.org/wiki/Evershed_effect.

Redshift of spectral lines in the optical spectrum of a supercluster of distant galaxies (right), as compared to that of the Sun (left).

flat frame

Image frames go through the basic reduction steps of subtracting the average dark frame from the spectral image and then dividing by the average flat frame. This removes the signature of the detector that recorded the data at the telescope.

helioseismology

Helioseisomology is the study of the propagation of pressure waves in the Sun. These waves are generated by the turbulence in the convection zone, near the surface of the sun, and certain frequencies are amplified by constructive interference. In other words, the turbulence "rings" the sun like a bell. The acoustic waves are transmitted to the outer photosphere of the sun, which is where the light emitted by the sun is generated. The acoustic oscillations are detectable on almost any time series of solar images, but are best observed by measuring the doppler shift of photospheric emission lines. Changes in the propagation of pressure waves through the Sun reveal inner structures and allows astrophysicists to develop extremely detailed profiles of the interior conditions of the Sun. From http://en.wikipedia.org/wiki/Solar_oscillation.

histogram A graphical representation of a frequency distribution in which the widths of the contiguous vertical bars are proportional to the class widths of the variable and the heights of the bars are proportional to the class frequencies (or number of occurrences). From “New College Edition of the American Heritage Dictionary of the English Language”

image frame Within the context of the solar research project, image frame typically refers to a spectrum from the solar database, but can also refer to an image of a magnetogram, dopplergram, line intensity map and Stokes V spectrum.

Lande g-factor In atomic physics, it is a multiplicative term appearing in the expression for the energy levels of an atom in a weak magnetic field. The quantum states of electrons in atomic orbitals are normally degenerate in energy, with the degenerate states all sharing the same angular momentum. When the atom is placed in a weak magnetic field, the degeneracy is lifted. See Zeeman Effect (below). From http://en.wikipedia.org/wiki/Lande_g-factor.

latitude As used in the context of solar research, latitude is an angular measurement ranging from 0° at the Sun’s equator to 90° at the poles (90° N or 90° S).

line intensity images If you took a picture of the sunspot in terms of all the light from the iron line at the wavelength of 15648.5 Angstroms (or 1.56485 microns), you would see an image of a spatial map like:

longitude As used in the context of solar research, longitude is an angular measurement east and west within the Sun’s “surface” coordinate system. Unlike latitude, which has the equator as a natural starting position, there is no natural starting position for longitude. As a reference point, the longitude is defined relative to an agreed-upon value for the rotation of the Sun’s equator.

magnetic field A bar magnet is a seemingly ordinary piece of metal from which invisible magnetic field lines originate. These magnetic field lines affect any magnetic material in the vicinity of the magnet. Magnets have a north pole where, by convention, magnetic lines of force point outward and a south pole where they point inward. Opposite poles attract each other; while similar poles repel each other. A toy bar magnet has a magnetic field (~1000 Oersted) thousands of times larger than the Earth's surface magnetic field(~1/4 Oersted) and about the strength of the field found in sunspots on the solar surface. All magnetic fields are the result of moving electric charges. In the case of solid materials, the moving charges are the individual electrons rotating

about the atomic nuclei. However, that would not be sufficient to produce a magnetic field because the orbiting electrons are randomly oriented and their individual magnetic fields cancel out. In a permanent magnet, the fields of the individual atoms are all lined up so that they add rather than cancel each other out. Adapted from http://www.windows.ucar.edu/spaceweather/info_mag_fields.html.

magnetic field strength One way to picture magnetic field strength is as an intensity. Say two different bar magnets are equidistance from a third magnetic object and both bar magnets have the same pull. Both will then have the same magnetic field intensity. Magnetic field strength is measured in units of amps per centimeter, called Oersteds. It is related to magnetic flux density, measured in Gauss, but a multiplicative constant called magnetic

permeability or μ.

magnetogram It is a pictorial representation of the variations in strength of a magnetic field and polarity of sunspots on the “surface” of the Sun. The magnetic field strength and polarity are determined as follows. A “Stokes V” spectrum is created by subtracting the right-hand circularly polarized (RCP) spectrum from the left-hand circularly polarized spectrum (LCP) (at the same spatial position). (See figure below.) The magnetic field strength is determined by the wavelength separation of the minimum and maximum peaks in a pair of Zeeman split lines seen in the graphical representation of the Stokes V spectrum. (See figure below.) The larger the difference in wavelength is, the greater the magnetic field intensity. The polarity is seen as the black and white area representing the two senses of polarity.

The above figure is an example of a Stokes V spectrum, which is the difference between the LCP and RCP spectra. The alternating black and white areas show the effect of the magnetic field in a sunspot (the polarity). The wavelength separation of these areas is proportional to the magnetic field strength. The black & white areas in the figure above appear as downward and upward peaks in the graphical representation seen in the figure below.

magnetograph The magnetograph works by measuring the polarization of light at various wavelength positions within a solar spectral line. Circular polarization in the opposite sense on either side of a magnetically sensitive spectral line gives a measure of the longitudinal magnetic field (the strength of the field directed toward and away from the instrument). Linear polarization provides information on the strength and direction of the magnetic field transverse to the line of sight. From http://science.nasa.gov/ssl/pad/solar/maggraph.htm. See http://science.msfc.nasa.gov/ssl/pad/solar/magmore.htm for more detail.

oscillation spectrum From looking at the shifts wavelength in spectral lines from the surface of the Sun can be used to determine frequency of acoustic waves. The spectrum of these acoustic waves provides insight into internal motions and structure of the Sun. An analogy would be a bell that from listening to the bell, one can infer how strong the clapper is striking and how often it strikes the inside of the bell. See the definition for helioseismology.

pixel A pixel (short for picture element, using the common abbreviation "pix" for "picture") is one of the many tiny dots that make up the representation of a picture in a computer's memory. Each such information element is not really a dot, nor a square, but an abstract sample. With care, pixels in an image can be reproduced at any size without the appearance of visible dots or squares; but in many contexts, they are reproduced as dots or squares and can be visibly distinct when not fine enough. The intensity of each pixel is variable. From http://en.wikipedia.org/wiki/Pixel.

polarization (linear, circular and elliptical)

The simplest manifestation of polarization to visualize is that of a plane wave, which is a good approximation to most light waves (a plane wave is a wave with infinitely long and wide wavefronts). Like all other propagating electromagnetic waves, a light wave has electric and magnetic fields perpendicular to the direction of propagation. Conventionally, when considering polarization the electric field vector is described, and the magnetic field is ignored since it is perpendicular to the electric field and proportional to it. Call the two components of the electric field vector x and y in two dimensional space (because we know the field is confined to two dimensions, since they are perpendicular to the light's direction of travel). For a simple harmonic wave, where the amplitude of the electric vector varies in a sinusoidal manner, the two components have exactly the same frequency. However, these components have two other defining characteristics that can differ. First, the two components may not have the

same amplitude. Second, the two components may not have the same phase, that is they may not reach their maxima and minima at the same time in the fixed plane we are talking about. By considering the shape traced out in a fixed plane by the electric vector as such a plane wave passes over it (a Lissajous figure), we obtain a description of the polarization state. The following figures show some examples of the evolution of the electric field vector (blue) with time (the vertical axes), along with its x and y components (red/left and green/right) and the path made by the vector in the plane (purple):

Consider first the special case (left) where the two orthogonal components are in phase. In this case the strength of the two components are always equal or related by a constant ratio, so the direction of the electric vector (the vector sum of these two components) will always fall on a single line in the plane. We call this special case linear polarization. The direction of this line will depend on the relative amplitude of the two components. This direction can be in any angle in the plane, but the direction never varies. Now consider another special case (center), where the two orthogonal components have exactly the same amplitude and are exactly ninety degrees out of phase. In this case one component is zero when the other component is at maximum or minimum amplitude. Notice that there are two possible phase relationships that satisfy this requirement. The x component can be ninety degrees ahead of the y component or it can be ninety degrees behind the y component. In this special case the electric vector in the plane formed by summing the two components will rotate in a

circle. We call this special case circular polarization. The direction of rotation will depend on which of the two phase relationships exists. We call these cases right-hand circular polarization and left-hand circular polarization, depending on which way the electric vector rotates. All the other cases, that is where the two components are not in phase and either do not have the same amplitude and/or are not ninety degrees out of phase (e.g. right) are called elliptical polarization because the sum electric vector in the plane will trace out an ellipse (the "polarization ellipse"). From http://en.wikipedia.org/wiki/Polarization#Basics_-_plane_waves.

region of interest Within an image, the region of interest (ROI) can help identify an area for analysis. Within a software program, the user can select the shape of an area to draw on, for example, a display window that shows a spectrum. By clicking on the display window and dragging the cursor to the desired area, the ROI is defined.

scatter plot A scatter plot or scatter graph is a graph used to visually display and compare two or more sets of related quantitative, or numerical, data by displaying many points, each having a coordinate on a horizontal and a vertical axis.

For example, if a statistician were studying the effects of lung capacity on the ability to hold one's breath, he would choose a group of people to study, and he would test each one's lung capacity (first data set) and how long that person could hold their breath (second data set). Then he would set up a scatter plot, assigning "lung capacity" to the horizontal axis, and "time holding breath" to the vertical axis. A person with a lung capacity of 400 cc who held their breath for 21.7 seconds would be represented by a single dot on the scatter plot at the point (400, 21.7) in Cartesian coordinates. The scatter plot of all the people in the study would enable the statistician to obtain a visual comparison of the two sets of data, and help him to determine what kind of relationship there might be between them.

Scatter Plot (or scatter diagram) shows the position of all of the cases in typically an x-y coordinate system. The relationship between interval variables can be identified from scatter graph. A dot in the body of the chart represents the intersection of the data on the x and y axis. One advantage of a scatter plot is that it does not require a user to specify dependent or independent variables. Either type of variable can be plotted on either axes. Scatterplots represents the association (not causation) between two variables. Adapted from http://en.wikipedia.org/wiki/Scatter_plot.

spectral line wavelength

A wave of light can be thought of as having troughs and crests. The wavelength is the distance from crest to crest. Waves in the electromagnetic spectrum vary in size from very long radio waves the size of buildings, to very short gamma-rays smaller than the size of the nucleus of an atom. Frequency has an inverse relationship to the concept of wavelength. The frequency of a wave is its rate of oscillation and is measured in hertz, the SI unit of frequency, equal to one oscillation per second. Light usually comprises a spectrum of frequencies which sum to form the resultant wave. Adapted from http://en.wikipedia.org/wiki/Electromagnetic_radiation.

spectral line wavenumber In spectroscopy, the wavenumber of electromagnetic radiation is defined as inversely related to wavelength, , where as a length in the SI-system is measured in meters (m) and commonly quantified in centimeters (cm = 10 2 m) refers to the wavelength in vacuum. The unit of this quantity is cm 1, pronounced as "inverse centimeter". The historical reason for using this quantity is that it is proportional to energy, but not dependent on the speed of light or Planck's constant, which were not known with sufficient accuracy (or rather not at all known). Adapted from http://en.wikipedia.org/wiki/Wavenumber.

spectroheliogram A spectroheliogram is an image of the solar surface viewed in a specific wavelength of light. The spectral data used by TLRBSE are two-dimensional images of the solar spectrum, with the horizontal axis as wavelength and the vertical axis as spatial position in one direction along the solar surface, defined by the spectrograph slit. The telescope is then moved slightly to a new position perpendicular to the slit and another spectrum is recorded. This builds up a three-dimensional “cube” of data, which can be sliced in two directions, as seen in the figure below. A spectroheliogram is a slice of this cube perpendicular to the spectrum.

Explanation of a spectroheliogram,

which is a slice of a “data cube” constructed from a set of spectra.

Stokes V parameter or diagram It is common to describe unpolarized, partially polarized, or fully polarized light or polarized radiation in terms of its total intensity (I), (fractional) degree of polarization, and the shape parameters of the “polarization ellipse”. A mathematical description is given by the Stokes parameters, introduced by George Gabriel Stokes in 1852. The relationship of the Stokes parameters to intensity and polarization ellipse parameters is described through four elements I, Q, U, and V , of which the Stokes V parameter describes right- or left-hand circularly polarized light. Adapted from http://en.wikipedia.org/wiki/Stokes_parameter and http://en.wikipedia.org/wiki/Stokes_vector.

time series or time cadence The use of the term time cadence in the context of instrumentation for solar research is the time step size in seconds; 0 means no time series.

x-scale The use of the term x-scale in the context of instrumentation used for our solar research is the spatial scale along slit in arcseconds per pixel.

y-scale The use of the term y-scale in the context of instrumentation used for our solar research is the scan step size in arcseconds per pixel.

Zeeman Effect or Zeeman-splitting of spectral lines The Zeeman effect (pronounced z 'män) is the splitting of a spectral line into several components in the presence of a magnetic field. It is analogous to the Stark effect, the splitting of a spectral line into several components in the presence of an electric field. In most atoms, there exist several electronic configurations that have the same energy, so that transitions between different pairs of configurations correspond to a single line. The presence of a magnetic field breaks the degeneracy, since it interacts in a different way with electrons with different quantum numbers, slightly modifying their energies. The result is that, where there were several configurations with the same energy, now there are different energies, which give rise to several very close spectral lines.

Without a magnetic field, configurations a, b and c have the same energy, as do d, e and f. The presence of a magnetic field splits the energy levels. A line produced by a transition from a, b or c to d, e or f now will be several lines between different combinations of a, b, c and d, e, f. Not all transitions will be possible. Since the distance between the Zeeman sub-levels is proportional with the magnetic field, this effect is used by astronomers to measure the magnetic field of the Sun and other stars. From http://en.wikipedia.org/wiki/Zeeman_effect.