PHYS 3650 Observational Astronomy Astronomical Spectroscopy Learning Objectives

PHYS 3650: Observational Astronomy Astronomical Spectroscopy

Learning Objectives u Spectroscopy: - spectrum - spectrograph or spectrometer u Spectral Lines: - electron orbits and energy levels in atoms - emission and absorption of photons - energy levels and spectrum of hydrogen atoms and hydrogen-like ions - naming spectral lines - permitted and forbidden transitions - other ways for atoms/molecules/ions to produce spectral lines u Continuum and Spectral Line Formation: - Kirchoff’s laws - absorption lines - emission lines - continuous emission

Learning Objectives u Spectrometers or Spectrographs: - objective prism - slit spectroscopy - diffraction grating - line grating - blazed grating - spectral resolution - echelle grating - multi-object spectrographs - integral field spectrographs u Spectral Line Profiles and Shifts: - natural broadening - pressure broadening - Doppler effect - thermal or Doppler broadening

Learning Objectives u Slit Spectroscopy: - setup and observations - data reduction - extracting spectrum - wavelength calibration - extinction correction - flux calibration - removing sky lines

Learning Objectives u Spectroscopy: - spectrum - spectrograph or spectrometer u Spectral Lines: - electron orbits and energy levels in atoms - emission and absorption of photons - energy levels and spectrum of hydrogen atoms and hydrogen-like ions - naming spectral lines - permitted and forbidden transitions - other ways for atoms/molecules/ions to produce spectral lines u Continuum and Spectral Line Formation: - Kirchoff’s laws - absorption lines - emission lines - continuous emission

Spectroscopy and Spectrum Spectroscopy is the act of measuring the energy output rate (flux density) from a (celestial) object as a function of wavelength or frequency so as to study its spectral lines. u Plot of the flux density vs wavelength or frequency is the spectrum of the object. u What can we learn from measuring the spectra of celestial objects? Flux Density (10 -8 erg cm-2 s-1 Å-1) u

Spectroscopy and Spectrum Spectroscopy is the act of measuring the energy output rate (flux density) from a (celestial) object as a function of wavelength or frequency so as to study its spectral lines. u Plot of the flux density vs wavelength or frequency is the spectrum of the object. u What can we learn from measuring the spectra of celestial objects? - chemical properties – composition, relative abundance Requires knowledge of excitation mechanism - physical properties – density, temperature - bulk motions Flux Density (10 -8 erg cm-2 s-1 Å-1) u

Spectrograph or Spectrometer u Conversion between expressing flux density in wavelength and frequency Fλ = (ν 2/c) Fν u To measure spectra, we use a spectrograph or spectrometer to separate the incoming radiation into its component wavelengths. u Common wavelength separator: prism, diffraction grating, grism (grating + prism).

Learning Objectives u Spectroscopy: - spectrum - spectrograph or spectrometer u Spectral Lines: - electron orbits and energy levels in atoms - emission and absorption of photons - energy levels and spectrum of hydrogen atoms and hydrogen-like ions - naming spectral lines - permitted and forbidden transitions - other ways for atoms/molecules/ions to produce spectral lines u Continuum and Spectral Line Formation: - Kirchoff’s laws - absorption lines - emission lines - continuous emission

Electron Orbits and Energy Levels u In atoms, electrons can only prescribe certain orbits around the atomic nucleus. Electrons in different orbits can have the same or entirely different energies. u Each electronic orbit therefore defines an energy level of the atom. A given energy level can be degenerate (i. e. , comprising different orbital configurations. )

Electron Orbits and Energy Levels u Figure below shows the energy level diagram for the hydrogen atom. At n = ∞, the electron has the highest potential energy (defined to be 0) but no kinetic energy. At n < ∞, the energy of the electron is a sum of its potential and kinetic energy.

Emission of Photons u An electron in an atom can make a transition from a higher to lower energy level, emitting a photon with an energy equal to the energy difference between the two energy levels. An emission line is produced.

Absorption of Photons u A photon with the appropriate energy can be absorbed by and therefore excite an electron in an atom to make a transition from a lower to higher energy level. An absorption line is produced. u A photon with a sufficiently high energy can excite an electron from a bound to free state, thus ionizing an atom. What is the energy required to ionize the hydrogen atom in the ground state?

Absorption of Photons u A photon with the appropriate energy can be absorbed by and therefore excite an electron in an atom to make a transition from a lower to higher energy level. An absorption line is produced. u A photon with a sufficiently high energy can excite an electron from a bound to free state, thus ionizing an atom. What is the energy required to ionize the hydrogen atom in the ground state? At least 13. 6 e. V (λ≤ 0. 091 μm).

Absorption of Photons u Only O and very early-B spectral type stars can ionize interstellar hydrogen gas, which is primarily in the ground state.

Electron Transitions u Every atom, ion, and molecule has a unique spectroscopic signature which depends on its electron orbital structure and possible electron transitions. u E. g. , Some possible transitions of excited hydrogen.

Electron Transitions u Spectral lines of atomic hydrogen.

Electron Transitions u Spectral lines at optical wavelengths produced by selected atoms.

Energy Levels of Hydrogen Atom u Energy levels of the hydrogen atom: where n = principle quantum number. (μ = reduced mass of the electron, e = electronic charge, ħ = h/2π where h = Planck’s constant. ) u Ground state: n = 1. u Excited states: n = 2, 3, … u n = ∞ and continuum states correspond ionized (free) states. u Transition of an electron from the mth to nth energy level will require a photon of wavelength: -1. 51 e. V where RH = Rydberg constant = 1. 10 x 107 m-1. -13. 6 e. V to -3. 4 e. V

Energy Levels of Hydrogen Atom u Energy levels of the hydrogen atom: where n = principle quantum number. (μ = reduced mass of the electron, e = electronic charge, ħ = h/2π where h = Planck’s constant. ) u Ground state: n = 1. u Excited states: n = 2, 3, … u n = ∞ and continuum states correspond ionized (free) states. u Transition of an electron from the nth to mth energy level will result in a photon of wavelength: -1. 51 e. V where RH = Rydberg constant = 1. 10 x 107 m-1. -13. 6 e. V to -3. 4 e. V

Spectral Lines of Hydrogen Atom u Emission lines are produced when electrons make transitions from higher to lower energy levels and emit photons. (A given transition by a single electron results in the emission of a single photon having an energy equal to the energy difference between the energy levels. ) u Absorption lines are produced when electrons absorb photons to make transitions from lower to higher energy levels. (A given transition by a single electron requires a single photon having an energy equal to the energy difference between the energy levels. )

Spectral Lines of Hydrogen Atom u Lyman series correspond to transitions from or to the ground (n = 1) state, requiring or emitting UV photons. u Balmer series correspond to transitions from the first excited (n = 2) to a higher state, or from a higher to the first excited state, requiring or emitting either optical or UV photons.

Spectral Lines of Hydrogen Atom u Paschen series correspond to transitions from the second excited (n = 3) to a higher state, or from a higher to the second excited state, requiring or emitting near-infrared photons. u Followed by the Brackett, Pfund, and Humphreys series in the near-infrared to mid-infrared.

Naming Spectral Lines of Hydrogen u Individual spectral lines of hydrogen are identified by the series to which they belong.

Naming Spectral Lines of Hydrogen u Wavelengths of Lyman series lines. Lyman limit corresponds to n = 1 → ∞.

Naming Spectral Lines of Hydrogen u Wavelengths of Balmer series lines. Balmer limit corresponds to n = 2 → ∞.

Naming Spectral Lines of Hydrogen u Balmer break especially strong at spectral type A.

Naming Spectral Lines of Hydrogen u Recall from the last chapter that the sharp drop-off at the Balmer limit (absorption by hydrogen gas in the interstellar medium) can be used to estimate the redshifts of galaxies. (Notice the shift in wavelength of the Balmer limit with increasing redshifts. )

Energy Levels of Hydrogen-like Ions u Atoms which are ionized to the stage where they only have one electron remaining – hydrogen-like or hydrogenic ions – have an energy-level pattern similar to that of hydrogen (but the energy levels do not have the same energies as those of hydrogen). Singly-ionized Helium Hydrogen

Naming Spectral Lines of Hydrogen-like Ions u Atoms which are ionized to the stage where they only have one electron remaining – hydrogen-like or hydrogenic ions – have an energy-level pattern similar to that of hydrogen (but the energy levels do not have the same energies as those of hydrogen). u Hydrogen-like ions therefore exhibit spectra that have a pattern similar to hydrogen (except that the lines are not at the same wavelengths as hydrogen). u The individual spectral lines of hydrogen-like ions are identified by the series to which they belong just like for hydrogen. u E. g. , Ly-α line of singly-ionized helium at a wavelength of 304 Å.

Naming Spectral Lines of other Atoms/Ions u For all other emission lines, they are identified by the species and its wavelength. u E. g. , neutral oxygen (O) is O I, singly-ionized oxygen (O+) is O II, doubly-ionized oxygen (O 2+) is O III, etc. u E. g. , a particular line of O I at 5577Å is referred to as O I λ 5577Å. u Furthermore, transitions between different energy levels have different probabilities of occurring. E. g. , for hydrogen, a transition between n = 3 → 1 has a factor of nearly 8 times higher probability than between n = 3→ 2. u Transitions that have a high probability of occurring are known as permitted transitions; i. e. , electrons spend relatively little time at the higher energy level before transitioning to the lower energy level.

Naming Spectral Lines of other Atoms/Ions u For all other emission lines, they are identified by the species and its wavelength. u E. g. , neutral oxygen (O) is O I, singly-ionized oxygen (O+) is O II, doubly-ionized oxygen (O 2+) is O III, etc. u E. g. , a particular line of O I at 5577Å is referred to as O I λ 5577Å. u Furthermore, transitions between different energy levels have different probabilities of occurring. E. g. , for hydrogen, a transition between n = 3 → 1 has a factor of nearly 8 times higher probability than between n = 3→ 2. u Transitions that have a low probability of occurring are known as forbidden transitions; i. e. , electrons spend a relatively long time at the higher energy level before transitioning to the lower energy level. Lines corresponding to forbidden transitions are denoted by []; e. g. , [O III] λ 5007Å. Lines from forbidden transitions are not seen from gases on the Earth but seen from gases in interstellar space. Why?

Naming Spectral Lines of other Atoms/Ions u Examples of permitted and forbidden lines in the spectrum of the Orion nebula.

Other Ways to Produce Spectral Lines u Transitions between different orbitals of an electron are not the only way to produce spectral lines. u E. g. , the 21 -cm line of atomic hydrogen is produced by transitions between different spin alignments of the electron and proton in the ground state of hydrogen.

Other Ways to Produce Spectral Lines u Transitions between different orbitals of an electron are not the only way to produce spectral lines. u Molecules can rotate at certain prescribed rotational frequencies, and vibrate at certain prescribed vibrational frequencies. Transitions between different rotation states at the same vibrational states are known as rotational transitions, and between the same or different rotational states at different vibrational states are known as rotational-vibrational transitions.

Learning Objectives u Spectroscopy: - spectrum - spectrograph or spectrometer u Spectral Lines: - electron orbits and energy levels in atoms - emission and absorption of photons - energy levels and spectrum of hydrogen atoms and hydrogen-like ions - naming spectral lines - permitted and forbidden transitions - other ways for atoms/molecules/ions to produce spectral lines u Continuum and Spectral Line Formation: - Kirchoff’s laws - absorption lines - emission lines - continuous emission

Kirchoff’s Laws u In the mid-19 th century, based on experiments Kirchoff summarized his three empirical laws under which spectral lines were produced:

Kirchoff’s Laws u To understand the physical basis of Kirchoff’s laws, know that an atom/ion/molecule can be excited either by the absorption of photons or collisions with another particle (which absorbs a part or all of kinetic energy of the colliding particle). u Similarly, an atom/ion/molecule can be de-excited either by the emission of photons or collisions with another particle (which excites the colliding particle or adds to its kinetic energy).

Absorption Lines u What is the physical explanation for the following Kirchoff’s law?

Absorption Lines u What is the physical explanation for the following Kirchoff’s law? In a cool and diffuse gas, low energy levels are strongly populated thus permitting strong absorption of photons to produce absorption lines.

Photospheric Absorption Lines u Spectral lines from stellar photospheres are seen in absorption. Why?

Photospheric Absorption Lines u Spectral lines from stellar photospheres are seen in absorption. Why? Light is emitted from a thin layer of the atmosphere known as the photosphere (the solar photosphere is about 400 km thick). The temperature decreases with height in the photosphere.

Emission Lines u What is the physical explanation for the following Kirchoff’s law?

Emission Lines u What is the physical explanation for the following Kirchoff’s law? In a hot and diffuse gas, high energy levels are well populated by collisions. De-excitation due to spontaneous emission dominates over that due to collisions, producing emission lines.

Emission Lines u What is the physical explanation for the following Kirchoff’s law? In a hot and diffuse gas, high energy levels are well populated by collisions. De-excitation due to spontaneous emission dominates over that due to collisions, producing emission lines. Some of the emission lines in the Orion Nebula are excited primarily by absorption of radiation (e. g. , many permitted lines), whereas others are excited primarily by collisions (e. g. , many forbidden lines).

Emission Lines

Continuous Emission u What is the physical explanation for the following Kirchoff’s law.

Continuous Emission u What is the physical explanation for the following Kirchoff’s law? In a hot and dense gas or solid, de-excitation due to collisions dominates over spontaneous emission, and thus no emission lines are produced.

Forbidden Lines u Forbidden lines are not seen from gases on the Earth, but seen from gases in interstellar space. Forbidden lines can be just as bright if not brighter than permitted lines. u Recall that forbidden lines have low transition probabilities; i. e. , electrons spend a relatively long time at the higher energy level before transitioning to the lower energy level. Why are forbidden transitions not seen from gases on the Earth but seen from gases in interstellar space?

Forbidden Lines u Forbidden lines are not seen from gases on the Earth, but seen from gases in interstellar space. Forbidden lines can be just as bright if not brighter than permitted lines. u Recall that forbidden lines have low transition probabilities; i. e. , electrons spend a relatively long time at the higher energy level before transitioning to the lower energy level. Why are forbidden transitions not seen from gases on the Earth but seen from gases in interstellar space? In dense gas on the Earth, collisional deexcitation dominates over spontaneous emission in forbidden lines, and so forbidden lines are not produced. In diffuse gas, spontaneous emission dominates over collisional de-excitation even in forbidden lines, and so forbidden lines can be produced.

Continuous Emission u In astronomy, continuous emission at optical wavelengths usually produced by: - thermal motions of atoms (e. g. , stellar photospheres)

Continuous Emission u In astronomy, continuous emission at optical wavelengths usually produced by: - thermal motions of atoms (e. g. , stellar photospheres) - recombination (electrons recombining with ions) in ionized gas

Learning Objectives u Spectrometers or Spectrographs: - objective prism - slit spectroscopy - diffraction grating - line grating - blazed grating - spectral resolution - echelle grating - multi-object spectrographs - integral field spectrographs u Spectral Line Profiles and Shifts: - natural broadening - pressure broadening - Doppler effect - thermal or Doppler broadening

Measuring Spectra u There a number of ways in which the spectra of celestial objects can be measured. u One way is to place a prism just in front of the telescope objective, known as an objective prism.

Measuring Spectra u An example of objective prism spectra of the Hyades open star cluster. u What are the advantages and disadvantages of objective prism surveys?

Measuring Spectra u An example of objective prism spectra of the Hyades open star cluster. u What are the advantages and disadvantages of objective prism surveys? - spectra of all objects can be measured in a single exposure - spectra of different objects can overlap u In this course, we consider spectrographs using diffraction gratings.

Spectrograph u Basic components of a spectrograph are: - entrance aperture, which can be a slit or circular apertures (optical fibers) - collimator, which is an optical element to make light parallel and hence have the same angle of incidence over the surface of the dispersing element - dispersing element (e. g. , prism), which separates light to different wavelengths - spectrum imager, which focuses the spectrum onto a detector - detector, which in modern times is a CCD

Spectrograph

Slit Spectroscopy u If you are measuring the spectrum of one object that is unresolved or in its entirety, it would not matter what shape aperture you use so long as the aperture only lets through light from that object. F ane l P l oca

Slit Spectroscopy What if you want to measure the spectrum as a function of position in an extended object? One way is to use a slit, which of course restricts the spectrum to just locations along the slit orientation position u λ

Diffraction Gratings u A diffraction grating is a collection of equally spaced transmitting or reflecting elements (grooves) separated by a distance comparable to the wavelength of light. u A simple diffraction grating consists of lines (opaque to light) scratched onto a glass surface, so that only the smooth surface transmits (transmission grating) or reflects (reflection grating) light.

Line Gratings u A simple transmission (line-diffraction) grating. Only 2 grating apertures are shown in this example; in practice, there can be many thousands of grating apertures. u Maxima occur when the path difference between adjacent rays, d sin θ, is an integer multiple of the wavelength, λ, of light. m=2 m=1 m=0 m = -1 m = -2 mλ (m – ½ ) λ (m (m

Line Gratings u m is known as the order of the maxima in the diffracted pattern. E. g. , m = 0 is the zeroth order, |m| = 1 is the first order, etc. u Disadvantage of this type of grating is that much of the light falls at the zeroth order where no spectrum is produced, and the light intensity drops quickly towards higher orders. Note also that higher order maxima are more closely separated, so that high order maxima can overlap. m=2 m=1 m=0 m = -1 m = -2 mλ (m – ½ ) λ (m (m

Line Gratings u m is known as the order of the maxima in the diffracted pattern. E. g. , m = 0 is the zeroth order, |m| = 1 is the first order, etc. u Disadvantage of this type of grating is that much of the light falls at the zeroth order where no spectrum is produced, and the light intensity drops quickly towards higher orders. Note also that higher order maxima are more closely separated, so that high order maxima can overlap. m=3 m=2 m=1 m=0 m = -1 m = -2 m = -3

Line Gratings u A simple reflection (line-diffraction) grating. u Sign convention: angles on the side of the incident ray relative to the grating normal are defined to be positive, whereas angles on the side of the reflected ray relative to the grating normal are defined to be negative. u Maxima occur when the path difference between adjacent rays, (d sin θi + d sin θm), is an integer multiple of the wavelength, λ, of light; i. e. , d sin θi + d sin θm = mλ. d

Line Gratings u Is the any advantage of this design over a transmission grating? Hint: law of reflection states that -θm = θi (recall sign convention); at which order is most of the light concentrated? d

Line Gratings u Is the any advantage of this design over a transmission grating? Hint: law of reflection states that -θm = θi (recall sign convention). Most of the light is reflected to angles -θm = θi, such that d sin θi + d sin θm = mλ = 0; i. e. , m = 0. Light at all wavelengths interfere constructively at this angle, so no spectrum is produced at the zeroth order (just as in the example of the transmission grating). Light intensity drops quickly towards higher orders. Hence, same behavior as transmission grating. d

Blazed Gratings u In modern diffraction gratings, grooves are cut into the surface to give a regular geometrical shape. Such gratings are called blazed gratings, and have the advantage of causing most of the diffracted light energy to be concentrated in a certain direction away from the zeroth order.

Blazed Gratings u Definition of groove spacing and angles in a blazed diffraction grating. Note that most of light is now reflected not to m = 0 but instead to a higher m order.

Blazed Gratings u Ray 2 has to travel an extra distance d sin θi compared to ray 1 to reach their respective grooves. u On reflection, ray 2 travels a lesser distance d sin (θr) compared to ray 1. u Path difference between rays 2 and 1 is d sin θi + d sin (θr) = mλ for constructive interference. (Recall that θr is negative by the sign convention. ) θi θr

Blazed Gratings u d sin θi + d sin (θr) = mλ = 0 when θr = -θi. This is the zeroth order where no spectrum is produced. In a blazed grating, relatively little light is diffracted into the zeroth order. u Illuminate grating such that the angle of incidence θi and the blaze angle together gives rise to the highest light intensity at the desired order m. θi θr

Blazed Gratings u At progressively higher orders m, angular separation between adjacent orders decreases so that maxima at different wavelengths can overlap. u Use filter to restrict input wavelength range and thus prevent order overlap.

Blazed Gratings u I will leave it as an exercise for you to show that the same mathematical relationship applies to a transmission (blazed) grating.

Blazed Gratings u Path difference between rays 2 and 1 is d sin θi + d sin (θr) = mλ for constructive interference. (Recall that θr is negative by the sign convention. ) u Path difference between rays 2 and 1 is d sin θi + d sin (θr) = m(λ/2) for destructive interference. u In between these extremes, we get partially constructive interference θi θr

Line Gratings u Maxima occur when the path difference between adjacent rays, d sin θ, is an integer multiple of the wavelength, λ, of light. u Minima occur when the path difference between adjacent rays, d sin θ, is an integer multiple of a half wavelength, λ/2, of light. u In between these extremes, we get partially constructive interference. m=2 m=1 m=0 m = -1 (m m = -2 mλ (m – ½ ) λ (m (m

Spectral Resolution u Even if incident spectral line has no width in wavelength, observed spectral line has a finite width in wavelength owing to properties of spectrograph. u Analogous to Rayleigh’s criterion for angular resolution, Rayleigh’s criterion for spectral resolution is defined as the minimum wavelength separation, Δλ, at the same order, m, such that an interference maximum at wavelength λ + Δλ falls on an interference minimum at wavelength λ. m=2 m=1 m=0 m = -1 m = -2

Dispersion and Resolving Power u The ability of a grating to produce spectra that permit precise measurement of wavelengths is determined by two intrinsic properties of the grating: - the width (or sharpness) of the lines, quantified as the resolving power of a grating R = / - the separation between spectral lines that differ by a small amount , quantified as the dispersion of a grating D = / θo+Δθo

Dispersion u u u To derive the dispersion, D = / , of a spectrograph, recall that maxima occur at: d sin θ = mλ (m = 0, 1, 2, …) Differentiating with and as variables gives d cos d = m d or d cos = m The dispersion D = / = m / (d cos ) With larger D implying higher dispersions, a spectrograph’s dispersion therefore depends on the separation, d, between slits and the order, m, used. It is independent of the number of rulings, N. In practice, there is a limit to how small d can be, and how large an order, m, that can be used due to overlap between adjacent orders.

Resolving Power u u Recall that for principal maxima, require d sin = m between adjacent slits, and therefore N d sin = Nm between first and last slit (altogether N + 1 slits). Thus for the minima just beyond the principal maxima, require N d sin( + ) = Nm + (m = 0, 1, 2, …) Notice that, for larger N and m, is smaller.

Resolving Power u Recall that for principal maxima, require d sin = m between adjacent slits, and therefore N d sin = Nm between first and last slit (altogether N + 1 slits). u Thus for the minima just beyond the principal maxima, require N d sin( + ) = Nm + (m = 0, 1, 2, …) u Expanding the sin term, sin( + ) = sin cos + cos sin = sin + cos for small angles u Solving or for , recalling that d sin = m , gives = / ( N d cos )

Resolving Power u Substituting the expression for the dispersion of a spectrograph (implicit in this substitution is that the principal maxima of one wavelength falls on a minima of an adjacent wavelength, known as Rayleigh’s resolution criterion) D = / = m / d cos gives the resolving power R = / = N m Larger R implies higher resolving power. Thus, the resolving power R = / of a spectrograph depends only on the number of rulings, N, and order used, m. (It is independent of the separation between rulings, d, although for gratings of equal dimensions smaller separations between rulings provide greater total number of rulings. ) θo+Δθo

Spectral Resolution u Using Rayleigh’s criterion for angular resolution, the resolving power of a diffraction grating (irrespective of its exact design) R = λ/Δλ = m. N, where m is the order and N the number of grating apertures. u To get higher spectral resolutions, use more grating apertures (there is practical limit) and higher order m (susceptible to order overlap; alternatively, restricted wavelength range of spectrum). u Recall that d sin θi + d sin (θr) = mλ. To use very high orders m, need very large θi and θr (close to 90 o). θr

Echelle Grating u An echelle grating is a particular type of blazed grating that has a very large blaze angle to allow very large θi and θr to be used, and hence achieve large R. u Recall that large m is suspectible to order overlap. To separate out different orders, a cross disperser (another grating) acts perpendicular to the echelle grating dispersion direction.

Echelle Grating

Echelle Grating u Spectrum of the Sun produced by an echelle spectrum.

Multi-Object Spectrographs u In modern astronomy, we are often interested in taking spectra of hundreds to thousands of objects (e. g. , stars, galaxies) at the same time. u We use a multi-object spectrograph, which directs light from the focal plane of the telescope using optical fibers (having circular apertures) to spectrographs. u E. g. , the LAMOST multi-object spectrograph employs 4000 fibers at the focal plane that can be individually moved, and a bank of sixteen spectrographs.

Integral Field Spectrographs u What if you want to measure the spectrum of an extended object at all positions at the same time? Use an integral field spectrograph. u Several designs have been employed. A simple design is a matrix of optical fibers analogous to a multi-object spectrograph. u E. g. , PPAK on the 3. 5 -m telescope on Calar Alto has 331 target fibers surrounded by 36 sky fibers.

Learning Objectives u Spectrometers or Spectrographs: - prism - diffraction grating - line grating - blazed grating - spectral resolution - echelle grating - multi-object spectrographs - integral field spectrographs u Spectral Line Profiles and Shifts: - natural broadening - pressure broadening - Doppler effect - thermal or Doppler broadening

Natural Broadening u The Heisenberg uncertainty principle dictates that we cannot know the position and velocity of particles (objects) to arbitrarily high precision (foundation of quantum physics). u Instead of orbits being at precise radii from the nucleus, orbits are “fuzzy; ” i. e. , decreasing probability of finding an electron away from the most probable radius. Precise orbits Fuzzy orbits

Natural Broadening u Transitions between the same two energy levels in different atoms can produce photons with slightly different energies.

Natural Broadening u Transitions between the same two energy levels in different atoms can produce photons with slightly different energies. u The resultant is that spectral lines are not infinitely sharp in wavelength or frequency, but has a spread in wavelength/frequency described by a Lorentzian profile.

Pressure Broadening u In describing atoms/ions/molecules so far, we have not considered electrostatic forces between adjacent atoms/ions/molecules. Such forces perturb electron orbits. The resulting broadening of spectral lines is known as pressure broadening. u Pressure broadening also gives rise to a Lorentzian profile. u Pressure broadening can be important in stellar atmospheres (e. g. , mainsequence stars), but typically not important in the interstellar medium.

Doppler Effect u Doppler effect of sound due to an approaching or receding source can be expressed in terms of: 1) the speed of the source relative to the wave-carrying medium (air); and 2) the speed of the observer relative to the wave-carrying medium. u Equation for Doppler effect of sound: where ν is the speed of sound waves in air, νs is the speed of the source relative to air (+ away from observer), and νo is the speed of the observer relative to air (+ towards source).

Doppler Effect u The speed of light is a constant, c, for all observers. Doppler effect of light is cased by a combination of: 1) geometrical effects (just like the Doppler effect of sound); and 2) time dilation (an effect of special relativity). u Equation for Doppler effect of light: where ν is the speed of the source relative to the observer (+ away from observer). u Because of the expansion of the Universe, distant galaxies are receding away from us. The recession velocity of galaxy is expressed in terms of redshift, z:

Thermal or Doppler Broadening u Motion of particles due to their thermal energy result in collisions that produce a particular distribution of speeds. More particles are traveling at lower than higher speeds. Furthermore, roughly equal number of particles are traveling towards as away from us.

Thermal or Doppler Broadening u The distribution of speeds along the line of sight is a Gaussian (or normal) distribution, giving rise to a spectrum with a Gaussian profile. u Full-width half-maximum (FWHM) of thermal or Doppler broadening:

Thermal or Doppler Broadening u The addition of a Lorentzian to a Gaussian profile is a Voigt profile. u In general, spectral lines have Voigt profiles.

Learning Objectives u Slit Spectroscopy: - setup and observations - data reduction - extracting spectrum - wavelength calibration - extinction correction - flux calibration - removing sky lines

Slit Spectroscopy u Steps for doing slit spectroscopy using a CCD: 1. Center the object within slit and take spectrum. 2. Reduce CCD frames with bias, dark, and flat (previously covered) 3. Extract spectrum of object 4. Take a spectrum of the standard lamp for wavelength calibration 5. Correct for Earth’s atmospheric extinction and interstellar extinction (previously covered) 6. Flux density calibration with standard stars 7. Remove sky lines.

Setup and Exposure 1. Center the object within slit and take spectrum. u For a point source (e. g. , a star), a slit of width smaller than the FWHM of the seeing is chosen (i. e. , the narrower the better). u What is the disadvantage of using such a narrow slit?

Setup and Exposure 1. Center the object within slit and take spectrum. u For a point source (e. g. , a star), a slit of width smaller than the FWHM of the seeing is chosen (i. e. , the narrower the better). u What is the disadvantage of using such a narrow slit? Not all the light available from the source is directed into the spectrograph, resulting in a lower S/N than would otherwise be possible.

Setup and Exposure 1. Center the object within slit and take spectrum. u For a point source (e. g. , a star), a slit of width smaller than the FWHM of the seeing is chosen (i. e. , the narrower the better). u What is the advantage of using such a narrow slit?

Setup and Exposure 1. Center the object within slit and take spectrum. u For a point source (e. g. , a star), a slit of width smaller than the FWHM of the seeing is chosen (i. e. , the narrower the better). u What is the advantage of using such a narrow slit? Higher spectral resolution, as light from the point source is incident on the diffraction grating over a smaller range of angles and hence the interference maximum in a particular order at a given wavelength narrower in width. Highest spectral resolution possible limited according to Rayleigh’s criterion. θr

Setup and Exposure 1. Also take spectrum of standard lamp for wavelength calibration. u In optical astronomy, arc lamps containing gas of one or more elements (e. g. , Hg, C, Zn, Th. AR) are usually used for wavelength calibration. The gas is ionized by an electrical arc, and produces a rich spectrum.

Setup and Exposure 1. Also take spectrum of standard lamp for wavelength calibration. u In optical astronomy, arc lamps containing gas of one or more elements (e. g. , Hg, C, Zn, Th. AR) are usually used for wavelength calibration. The gas is ionized by an electrical arc, and produces a rich spectrum.

Setup and Exposure 1. Also take spectrum of standard lamp for wavelength calibration. u Of course, the wavelength of each line from the standard lamp has previously been measured in the laboratory to high precision.

Setup and Exposure 1. Finally, observe spectrophotometric standard star for flux density calibration. u Spectrophotometric standards are bright stars with accurate measurements of their spectra: flux density as a function of wavelength HR 9087

Spectral Extraction 3. Extract spectrum of object. u The spectrum of a point source recorded on CCD is a strip extending along the dispersion/spectral direction. Ideally the strip should be a rectangle aligned with the CCD rows/columns, but in practice the strip is curved depending on optics. u Obtain spectrum of the object by integrating few pixels near source along the spatial direction (over gwidth) and subtracting background. Need to correct for “missing light” arising from integrating only a finite width (similar to aperture correction in photometry). Spatial direction u CCD frame Dispersion/Spectral direction

Wavelength Calibration 4. Use standard lamp spectrum for wavelength calibration. u After extracting a spectrum, we need to put the data on a wavelength scale. u From the standard lamp spectrum, create a mapping of the spectral direction pixel number and wavelength. u A good diffraction grating will generate an almost linear mapping. Arc lamp frame Target frame

Flux Density Calibration 6. Flux density calibration. u At this point, spectrum is in units of photon-counts sec-1 Å-1. u Compare with photon-counts sec-1 Å-1 from spectrophotometric standard to convert to ergs-1 sec-1 cm 2 Å-1. Standard star frame Target frame

Sky Lines 7. Remove sky lines (including lines from artificial man-made source). u Apart from spectral lines from target star in the slit, spectral lines produced by Earth’s atmosphere, or scattered by the Earth’s atmosphere from man-made light sources, also are imprinted on the spectrum of the source. u Flux density of sky lines generally vary in position and with time. u Removed by fitting a profile to the sky lines in the background spectrum and subtracting from the target spectrum, or as a final resort blanking out affected parts of the target spectrum. From artificial light source