- The nature of light
- Optics - refraction and diffraction
- Radiation
- Classification of stellar spectra
- Effect of stellar movement on the spectrum
- Analysis of stellar atmospheres
- The following symbols for constants and quantities are used throughout this webpage:
Constants and quantities - light
Quantities - optics
Quantities - radiation and stars
- A brief history of spectroscopy
- References
Rainbows in Starlight
Astronomical Spectroscopy
Based on a talk given for "University Meets Public", Jan 9, 2001, Vienna
Local links are in blue,
External links are in green
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Overview
Light
The electromagnetic spectrum
(black areas: Transmissivity of the Earth's atmosphere)
The eye:
The sensitivity of the
cones and
rods
on the retina of the eye corresponds to the wavelength range of the "optical window", in which the transmissivity of the Earth's atmosphere is highest (see above).
Article on color vision by Ed Scott
Optics - refraction and diffraction
Newton was one of the first who conducted experiments with sunlight and prisms.
Huygens' principle is important for understanding the propagation of waves and related phenomena, e.g. refraction.
Derivation of the law of refraction - change of direction of a wave upon transition between two media (blue and red in the figure)
Optical path through a coplanar plate and a prism - this figure has been created using an applet by B.Surendranath Reddy.
Due to the dependence of the angle of refraction on wavelength, white light is transformed into a spectrum of colors.
The rainbow is also a result of
refraction:
Sunlight is reflected from the backside of rain drops
and refracted into different directions upon entry and exit.
At a certain angle, the "rainbow angle", the concentration of the scattered light rays reaches a maximum (central optical path in the figure).
This figure was created using the rainbow simulation of Frederick J. Wicklin and Paul Edelman (University of Minnesota).
Two articles on the formation of primary and secondary rainbows:
ACEPT, Arizona State University
Peter K. Kaiser, York University
When passing a narrow double slit, light waves change direction - the result is diffraction in several directions, so-called orders. The angle of diffraction depends on wavelength, order and the distance between the slits.
Diffraction also occurs at a grating (equivalent to many double slits next to each other).
Schematic design of an astronomical spectrograph (from Kaler, 1994) with reflection grating (from Gray, 1992)
The linear distance between two wavelength points on the detector is called dispersion. This quantity is required for the calculation of the theoretical resolving power, which depends only on the order (k) and the number of grating lines (N) (from Sexl, 1983).
For the actual resolving power of a spectrograph the projection of the slit (width b) has to be considered in addition.
A further effect which occurs due to the wave nature of light is the Doppler effect, a consequence of a movement of the light source relative to the observer.
Radiative processes
When an atom transits from a state of higher energy to a state of lower energy an electromagnetic wave with a certain frequency or wavelength is emitted.
The hydrogen atom with possible transitions and corresponding wavelengths in Ångström.
Emission line spectra of some elements (by John Talbot)
Spectral line broadening
Example for pressure broadening
To first approximation, radiation from solid bodies and hot gases depends only on temperature.
The Planck function for various temperatures
Characteristics of the Planck function
Kirchhoff's law states that for a certain temperature, absorptivity equals emissivity.
When an atom absorbs an electromagnetic wave with a certain frequency or wavelength, a transition from a state of lower energy to a state of higher energy takes place.
Absorption line spectra of some elements (by David Caley)
Types of transitions
Classification of stellar spectra
The light which we receive from stars originates from a very thin (in comparison to the radius) outermost layer, the so-called photosphere. In this schematic representation of the Sun this layer is thinner than the outermost black line. The core region, where nuclear fusion takes place, is shown in yellow, and the area in red represents the convection zone.
Fraunhofer was one of the first scientists who studied the absorption lines in the solar spectrum, and he assigned letters to the strongest lines.
The simplest way of obtaining spectra of several stars in order to characterize them, is to install a prism in front of the objective of the telescope. The objective prism spectra of the Hyades show that this star cluster contains several different classes of stars: Some of them radiate very strongly in the yellow region of the spectrum, others only in the red and green regions (e.g. top right).
In spectra with higher resolution one can also detect different groups of absorption lines, which originate from different chemical elements. They form the basis for spectral classification, by which the stars are divided into spectral classes. These are designated with letters and form a temperature and color sequence.
The following diagram shows how the line strengths of various types of absorption lines depend on spectral type and temperature.
Color spectra of main sequence stars (by John Talbot)
Frequency of spectral types in the Milky Way, based on a table by J.C. Evans (George Mason University)
Larger and brighter stars have less dense atmospheres with lower gas pressure, and therefore narrower spectral lines. This enables an additional classification in terms of luminosity.
Resolution used for classification
For the classification of stars of unknown spectral type the new spectrum is compared to those of well-known standard stars, until an agreement is found.
Spectral classification Exercise by Michael Briley, University of Wisconsin Oshkosh (shockwave)
Computer program for spectral classification
In order to facilitate the analysis of the stellar spectrum, a digital one-dimensional spectrum is extracted from the two-dimensional spectrum, i.e. the radiation intensity is plotted against wavelength.
Atlas of digital classification spectra by R. O. Gray (Appalachian State University)
Effect of stellar movement on the spectrum
Due to the Doppler effect, the absorption lines in the spectra of stars moving towards our Solar System are shifted towards the blue region, and towards the red for stars moving away from us.
The movement of spectroscopic binary stars around their common center of mass becomes apparent in the spectrum through the shift of the twofold absorption lines.
Digital spectrum of a spectroscopic binary star system
In the spectrum of beta Pictoris one can see up to four narrow lines in the cores of the broad absorption lines of the star, which change their position with time. These probably come from compact parts of the gas and dust disk that surrounds this star.
Because of the rotation of a star around an axis the spectral lines are additionally broadened. The width of the lines depends on the rotation velocity (v) and the inclination angle (i) of the axis to the line of sight.
Spectra of stars of similar spectral type and increasing rotational broadening v sin(i)
- Instrumental profiles for increasing resolution
- Rotational profiles for increasing rotational velocity
- Synthetic spectrum without instrumental and rotational broadening (connected circles: observations)
- Synthetic spectrum with instrumental broadening
- Synthetic spectrum with instrumental and rotational broadening
- Fe abundance too low and too high
- Correct Fe abundance
In this case there is more than a factor of 10 less Fe present than in the Sun.
Analysis of stellar atmospheres
In this figure depth, temperature, pressure and density are indicated for different layers of the Sun's photosphere.
In order to determine these values and the chemical composition of stars, one needs a model atmosphere, which is calculated using a set of assumptions, parameters and equations.
For the solution of the equation of radiative transport the wavelength dependent continuum absorption coefficient is needed. In the visible region of the spectrum, this quantity is mainly determined by the ionization of H--ions in cool stars, e.g. the Sun, and in hot stars by ionization of neutral hydrogen and helium (O and B stars) (from Unsöld & Baschek, 1988).
In addition the line absorption coefficient has to be calculated.
Calculation of the population numbers
Calculation of the line profile
Example for a line profile (from Unsöld & Baschek, 1988)
The atomic data that are needed in order to calculate the line absorption can be obtained e.g. from the Vienna atomic line database.
The model atmosphere equations given above are solved iteratively for a certain number of layers, and one obtains temperature, pressure and other quantities as a function of depth. As a starting model a simple analytic formula for the temperature as function of depth is usually used (so-called grey atmosphere).
Example for the calculation of the solar atmosphere (thick line: final result, thin lines: selected iterations)
Now the radiative flux at the surface of a star can be calculated and compared with observations.
Comparison of observed and calculated flux of the sun (red line in the lower figure: line absorption not taken into account, green line: Planck-function with a temperature of 5777 K)
Observed solar flux with higher resolution and line identification
For the detailed analysis of stellar atmospheres spectra with high resolution are used.
Example: Echelle spectrum of HD 84123
In order to be able to compare these observations with the calculations, the surface flux must be calculated with very high wavelength resolution ("synthetic spectrum") and convolved with the instrumental and rotational profile. The parameter FWHM needed for that is determined from the emission lines of the comparison light source.
Examples:
In order to be able to reproduce all the details of the observed spectrum, the abundance of the element that causes the line under consideration has to be adjusted (abundance = number of particles per cm3).
Example: Iron (Fe)
The following correlations can be used for main sequence stars of type A and F:
In order to determine the effective temperature of the stellar atmosphere,
lines with different excitation energies are considered.
The strength of lines with high excitation energy is almost independent of temperature, whereas the strength of lines with low excitation energy decreases with increasing temperature.
Example: high excitation energy - far left, low excitation energy - far right
In order to determine the gravitational acceleration - log(g) - in the stellar atmosphere, lines of different ionization stages are considered. The strength of lines from neutral elements is almost independent of log(g), whereas the strength of lines from singly ionized species decreases with increasing log(g).
Example: neutral element - Fe 1, singly ionized element - Fe 2
The complete procedure of an abundance analysis using many spectral lines (typically 100-1000) can be represented as a flow chart.
Chemical elements present in stellar atmospheres
Chemical composition of the Sun (number of particles; metals = all elements except for H and He)
Chemically peculiar stars: Am - metal rich A type stars, lambda Bootis: metal poor A type stars
© 2014 Ulrike Heiter