Spectroscopy Spectrographs Roy van Boekel Kees Dullemond Overview

Spectroscopy & Spectrographs Roy van Boekel & Kees Dullemond

Overview • Spectrum, spectral resolution • Dispersion (prism, grating) • Spectrographs – longslit – echelle – fourier transform • Multiple Object Spectroscopy

Spectroscopy: what do we measure? • Spectrum = the intensity (or flux) of radiation as a function of wavelength • “Continuous” sampling in wavelength (as opposed to imaging, where we integrate over some finite wavelength range) – Note: In practice, when using CCDs for spectroscopy, one also integrates over finite wavelength ranges – they are just very narrow compared to the wavelength itself: Pixel width Δν << ν • Sampling is continuous but the spectral resolution is limited by the design of the spectrograph • Spectrum in classical sense holds no direct spatial information. Many spectrographs allow retrieving spatial info in 1 dimension, some even in 2 (“integral field units”)

Spectral resolution • Smallest separation in wavelength that can still be distinguished by instrument, usually given as fraction of and denoted by R: or alternatively useful, though somewhat arbitrary working definition

Basic spectrograph layout • a means to isolate light from the source in the focal plane, usually a slit • “collimator” to make parallel beams on the dispersive element • dispersive element, e. g. a prism or grating. Reflection gratings much more frequently used than transmission gratings • “Camera”: imaging lens to focus beams in the (detector) focal plane + detector to record the signal

Dispersion Splitting up light in its spectral components achieved by one of two ways: • differential refraction� – prism • interference – reflection/transmission grating – fourier transform – (Farby-Perot) 6

Prism • general light path through prism: one can show that: • dispersion is maximum for a symmetrical light path • dispersion is maximum for grazing incidence. Corresponding top angle depends on refractive index of material. E. g. ~74° for heavy flint glass • However: most light is reflected instead of refracted for grazing incidence. In practice, smaller are used (60° and 30° are common choices)

Prism dispersion curve strongly non-linear, dispersion in blue much stronger than in red part of spectrum 8

Prism spectrograph layout 9 Credit: C. R. Kitchin “Astrophysical techniques” CRC Press, ISBN 13: 978 -1 -4200 -8243 -2

Young’s double slit experiment double slit lens incident wave θ d θ screen

Young’s double slit experiment double slit Optical path difference: Phase difference: incident wave d ΔP Add the two waves: Intensity is amplitude-squared: θ lens screen

Young’s double slit experiment N=2

Now a triple slit experiment. . . triple slit Optical path difference: Phase difference: incident wave d ΔP θ Add the three waves, and take the norm: lens screen

Now a triple slit experiment. . . N=3

Adding more slits. . . N=4

Adding more slits. . . N=5

Adding more slits. . . N=6

Adding more slits. . . 0 th order N=16 1 st order 2 nd order

Width of the peaks N=4 Peak width is therefore: For one has with (Later: Relevance for spectral resolution)

Now do 3 different wavelengths 0 th order 1 st order 2 nd order N=4 Green is here the reference wavelength λ. Blue/red is chosen such that its 1 st order peak lies in green’s first null on the left/right of the 1 st order.

Now do 3 different wavelengths 0 th order 1 st order N=8 Keeping 3 wavelengths fixed, but increasing N 2 nd order

Now do 3 different wavelengths 0 th order 1 st order N=16 Keeping 3 wavelengths fixed, but increasing N 2 nd order

Now do 3 different wavelengths 0 th order 1 st order 2 nd order N=4 Green is here the reference wavelength λ. Blue/red is chosen such that its 1 st order peak lies in green’s first null on the left/right of the 1 st order.

Now do 3 different wavelengths 0 th order 1 st order 2 nd order N=8 Green is here the reference wavelength λ. Blue/red is chosen such that its 1 st order peak lies in green’s first null on the left/right of the 1 st order. Spectral resolution:

Let’s look at the 2 nd order 0 th order 1 st order 2 nd order N=8 Green is here the reference wavelength λ. Blue/red is chosen such that its 1 st order peak lies in green’s first null on the left/right of the 1 st order. Spectral resolution:

Let’s look at the 2 nd order m=0 m=1 m=2 m=3 m=4 N=8 Green is here the reference wavelength λ. Blue/red is chosen such that its 1 st order peak lies in green’s first null on the left/right of the 1 st order.

Let’s look at the 2 nd order m=2 N=8 Zoom-in around 2 nd order Green is here the reference wavelength λ. Blue/red is chosen such that its 1 st order peak lies in green’s first null on the left/right of the 1 st order.

Let’s look at the 2 nd order m=0 m=1 m=2 m=3 m=4 N=8 Green is here the reference wavelength λ. Blue/red is chosen such that its 1 st order peak lies in green’s first null on the left/right of the 1 st order.

Let’s look at the 2 nd order m=0 m=1 m=2 m=3 m=4 N=8 Green is here the reference wavelength λ. Blue/red is chosen such that its 2 nd order peak lies in green’s first null on the left/right of the 2 nd order. Spectral resolution:

Let’s look at the 3 rd order m=0 m=1 m=2 m=3 m=4 N=8 Green is here the reference wavelength λ. Blue/red is chosen such that its 3 rd order peak lies in green’s first null on the left/right of the 3 rd order. Spectral resolution:

General formula m=0 m=1 m=2 m=3 m=4 N=8 Green is here the reference wavelength λ. Blue/red is chosen such that its mth order peak lies in green’s first null on the left/right of the mth order. Spectral resolution:

Building a spectrograph from this Place a CCD chip here Make sure to have small enough pixel size to resolve the individual peaks.

Overlapping orders m=0 m=1 m=2 m=3 m=4 N=8 Going to higher orders means higher spectral resolution. But it also means: a smaller spectral range, because the “red” wavelengths of order m start overlapping with the “blue” wavelengths of order m+1

Effect of slit width triple slit incident wave d w lens screen

Effect of slit width single slit incident wave As we know from the chapter on diffraction: This gives the sinc function squared: w lens screen

Effect of slit width N=16 d/w=8

Grating • many parallel “slits” called “grooves” • Transmission gratings and reflection gratings • width of principal maximum (distance between peak and first zeros on either side): Credit: C. R. Kitchin “Astrophysical techniques” CRC Press, ISBN 13: 978 -1 -4200 -8243 -2 • “Blazing”: tilt groove surfaces to concentrate light towards certain direction controls in which order m light of given gets concentrated blazed reflection grating

Grating, spectral resolution • resolution in wavelength: blazed transmission grating

Reflection grating with groove width w and groove spacing d w -i d

Basic grating spectrograph layout 40 Credit: C. R. Kitchin “Astrophysical techniques” CRC Press, ISBN 13: 978 -1 -4200 -8243 -2

Basic grating spectrograph layout Note: The word “slit” is here meant with a different meaning: Not a dispersive element, but a method to isolate a source on the image plane for spectroscopy. From here onward, “slit” will have this meaning. Dispersive slit = groove on a grating. 41 Credit: C. R. Kitchin “Astrophysical techniques” CRC Press, ISBN 13: 978 -1 -4200 -8243 -2

Longslit spectrum spatial direction • Very basic setup: entrance slit in focal plane, with dispersive element oriented parallel to slit (e. g. grooves of grating aligned with slit) • 1 spatial dimension (along slit) and 1 spectral dimension (perpendicular to slit) on the detector • Spectral resolution set by dispersive element, e. g. Nm for grating. • Spectrum can be regarded as infinite number of monochromatic images of entrance slit • projected width of entrance slit on detector must be smaller than projected size of resolution element on detector, e. g. for grating: where s is the physical slit width and 1 is the collimator focal length • slit width often expressed in arcseconds: where F is the effective focal length of the telescope beam entering the slit

spatial direction Example longslit spectrum wavelength • high spectral resolution longslit spectrum of galaxy • Continuum emission from stars, several emission lines from star forming regions in galaxy

Gratings: characteristics • Light dispersed. If d ~ w most light goes into 1 or 2 orders at given . Light of (sufficiently) different gets mostly sent to different orders • Light from different orders may overlap (bad, need to deal with that!) • Spectral resolution scales with fringe order m and is nearly constant within a fringe order ~linear dispersion (in contrast to prism!) • Gratings are often tilted with respect to beam. Slightly different expression for positions of interference maxima: or equivalently i is the angle between the grating and the incoming beam. This expression is called the “grating equation”

“blaze function” The describes the transmittance of light transmitted or reflected into each order. It is the “envelope” of the interference pattern (i. e. diffraction due to finite width of single groove, D) long go into low m, short go into high m I m m m + i [deg]

Blaze function vs. wavelength I m m m

Order overlap in grating • • Each order gives its own spectrum. These can overlap in the focal plane: at a given pixel on the detector we can get light from several orders (with different ) We must reject light from the unwanted orders. Solution: 1) 2) For low orders m (low spectral resolution, large free spectral range) one can use a filter that blocks light from the other orders For high orders m (the free spectral range is very small), use “cross disperser”: a second dispersive element (usually a prism), mounted with the dispersion direction perpendicular to that of the grating. Causes different orders to be spatially offset on the chip. Advantage: multiple orders can be measured simultaneously. High spectral resolution and large coverage can be obtained simultaneously. “Echelle spectrograph”

Echelle grating • R m. For high spectral resolution, use high order. • Relatively large groove spacing (few grooves/mm) but very high blazing angle. Concentrate light in high orders. • Strong order overlap (solution: “cross-dispersion”, more later. . . ) Echelle grating Credit: C. R. Kitchin “Astrophysical techniques” CRC Press, ISBN 13: 978 -1 -4200 -8243 -2

Echelle grating: cross dispersion CCD m=103 m=102 m=101 m=100 m=99 m=98 m=97 m=96 Without cross dispersion: different wavelength ranges overlap. With cross dispersion: You get multiple short spectra. Note of caution: Above cartoon is not exact: colors should be sorted vertically; but it shows the principle of separating orders.

Echelle grating: cross dispersion CCD m=103 m=102 m=101 m=100 m=99 m=98 m=97 m=96 Strong blazing angle means that you focus the light on the part of the focal plane where the CCD is. Avoids waste of light.

optical layout Echelle spectrograph spectrum on detector order m • Cross dispersion with prism placed before grating • high blaze angle, grating used in very high orders (up to m~200) • coarse groove spacing (~20 to ~100 mm-1) at optical wavelengths w > few most light concentrated in 1 direction at given most light in 1 order • Each order covers small range, but many orders can be recorded simultaneously 51

Blaze function order= spectrum on detector order m • Blazing angle defines in which order light of given (mostly) ends up • If sum of angles of “incoming” and “exiting” rays equals m /d (d is groove spacing), all light goes into order m (assuming “perfect”, lossless grating) • For slightly smaller , part of the light goes into order m+1 optical layout Blaze function: “efficiency” of (an order of a) grating as a function of

prism dispersion Format of crossdispersed Echelle spetrogr. (Lick Observatory) echelle dispersion

Stellar spectrum

Spectroscopy & Spectrographs II Roy van Boekel & Kees Dullemond

Some applications of spectroscopy • Stellar spectroscopy: temperature, composition, surface gravity, rotation, micro-turbulence • Temperatures of interstellar medium, intergalactic medium • radial velocities, mass and internal structure of stars, exoplanets • Dynamics & masses of milky way and other galaxies (dark matter) • Cosmology / redshifts • spectro-astrometry (direct spatial information on scales << /D, relative between continuum emission and spectral lines) • composition of dust around young & evolved stars, ISM

Different Resolution for Different Scientific Applications • • Active galaxies, quasars, high-redshift objects: R ≈ 500 - 1, 000 Nearby galaxies (velocities 30… 300 km/s): R ≈ 3, 000 - 10, 000 Supernovae (expansion velocity ≈ 3, 000 km/s): R > 100 Stellar abundances: Hot stars: R ≈ 30, 000 Cool stars: R ≈ 60, 000 - 100, 000 • Exoplanet radial velocity measurements. E. g. R ≈ 115, 000 (HARPS). Best accuracy currently reached ~1 m/s, “effective” R ≈ 300, 000. How: centroid of a single line measured to much higher precision than spectral resolution + use many lines, precision scales like 1/sqrt(Nlines)

Exoplanet detection by radial velocity measurement Planet is very difficult to observe directly. But planet and star rotate around common center-of-mass Star wobbles: Measure radial velocity of star (doppler). Small effect: Need Δv=1 m/s effective spectral resolution This means: Reff=c/Δv=3 x 108 !

Exoplanet detection by radial velocity measurement Beat the spectral resolution limit! Flux λ Shifts of line centroid can be measured even if they are much smaller than the line width. Need: High signal-to-noise ratio and/or many lines.

Fourier transform spectrometer • Incoming light is split 50: 50 into two beams, then reflected. Both beams are combined, then focused onto detector • one mirror is moveable, introduces path difference P • for monochromatic source the intensity on the detector is: • interference pattern, modulation with optical path difference (OPD) I(k) by wavenumber by OPD position I( P) k P

Fourier transform spectrometer • for a given position P the intensity modulation � due to light interfering from all wavelengths is: Typical FTS interferogram or, equivalently: I( P) Take I(-ν)=I(ν) so that we get: P (mm)

Fourier transform spectrometer • Thus, the output signal is the Fourier transform of the spectrum I( ) • Note: Fourier Transform of a symmetric function is real-valued, so the output signal is the complete Fourier transform (no imaginary part exists). • Inverse Fourier transform of the interferogram I( P) yields source spectrum I( ) • Spectral resolution scales directly with total length of OPD scan (say, x): • x can be up to ~2 m R can be several million in the optical example spectrum taken with an FTS

Multiple object spectroscopy • Often you want spectra of many objects in the same region on the sky • Doing them one by one with a longslit is very time consuming • When putting a slit on a source in the focal plane, the photons from all other sources are blocked and thus “wasted” • Wish to take spectra of many sources simultaneously! • Solution: “multiple object spectrograph”. Constructed to guide the light of >>1 objects through the dispersive optics and onto the detector(s), using: – a small slit over each source (“slitlets”) – a glass fiber positioned on each source – “integral field unit”

Multiple slit(lets) approach • A slitlet is a longslit, but of much shorter length than most “single” longslits • Normally done using focal plane “masks”: metal plates in which slitlets are cut, nowadays mostly done automatically by cutting devices using high-power lasers • Advantages: – (can do many objects simultaneously) – small longslits: sample object and sky background in each slitlet good sky correction in each spectrum – slits can be cut in almost any shape (useful for extended sources) • Disadvantages: – a new mask must be made for each field, often more than 1 mask/field – not complete freedom where to put slits (spectra should not overlap on detector)

Multi-object spectroscopy with slitlets CCD slit CCD Wasted CCD real estate

Multi-object spectroscopy with slitlets CCD • First do pre-imaging to find the stars/objects of interest + reference object • Create mask using computer program (mask is then cut in metal plate with laser) • Go back to telescope, do acquisition to center slits on objects • Do spectroscopic integration

Multi-object spectroscopy with slitlets CCD • But: Some slit combinations are forbidden: They would result in overlapping spectra

Credit: unknown near infrared multipleobject spectroscopy with SUBARU/MOIRCS

Slitlets approach, “peculiarities” • Optical layout essentially the same as with normal (single) longslit, but instead of single slit ~centered in focal plane, multiple slits distributed over focal plane. Consequences: – all slitlets have same dispersion direction all slitlets must have similar orientation ~perpendicular to dispersion direction (simple straight slits exactly perpendicular to dispersion direction in most cases) – wavelength scale is different for each slitlet, depending on its position – if chip size limits spectral range ( end - start) that fits on detector, then start and end depend on position of object (slit) on sky – if two slits are close together in spatial direction but far apart in dispersion direction, spectra can overlap due to optical distortions

Slit width issues • Spectral resolution is limited by R of the spectrograph. . . • . . . but also by the slit width. • Conversely: Slit width ~ brightness of the spectrum on the CCD Lower R Brighter on CCD, but also more background noise Higher R Weaker signal, but less background noise • Optimum slit width is balance between low slit losses (wide slit) versus low background and high spec. res. (narrow slit) • In general: Higher R requires longer exposure for same Signal-to-Noise ratio

MMT / Hectochelle MOS with fibers • instead of putting a slitlet on each source in the focal plane, position the head of a glass fiber on each source (movable) • fibers pass light of each object into the instrument • put the other end of all fibers in a row and feed light into spectrograph • result: one spectrum for each source, all spectra “nicely” aligned: wavelength scale the same for all spectra, and spectra regularly spaced in spatial direction • Disadvantage: no spatial info, background subtraction using “sky” fibers. fiber head close-up

Integral Field Units • • • A multiple object spectrograph is good at getting spectra of many sources in the same field Sometimes we would like to take a spectrum at every position of a spatially extended object (e. g. a galaxy). This can be done with an Integral field unit (IFU) We need to “catch” the light at each position, guide it through dispersive optics and project the spectrum of each position onto (a different part of) the detector. This can be done in two basic ways: 1) 2) • Using an “image slicer” Using “lenslets” and fibers NOTE: It will have low spatial resolution, because 2 D space + 1 D λ have to fit on a 2 D CCD. . .

JWST / MIRI Image Slicer • Many narrow (~spatial resolution element) long slits, each with slightly different tilt • effectively, do a large number of longslits simultaneously, send each slit into a different direction • slits imaged next to each other on detector Credit: unknown

Gemini / CIRPASS “Lenslets” & Fibers • Focal plane filled with “lenslets”. Each lenslet injects (nearly) all light falling onto it into a fiber • Fibers are fed into a spectrograph, in the same way as with the fiber Multiple Object Spectrograph 76

Spectroscopy: procedure • Recording the data – science observation – calibration observations: flatfield, “arcs” ( calibration), spectrophotometric standard stars • Data analysis/calibration – going from raw data to a calibrated spectrum in e. g. [erg/s/cm 2/Hz] • Interpretation of spectra, i. e. what do we learn about the object? – Use laws from your physics textbook or more elaborate numerical models of your science target to derive: • • Chemical composition of sources Thermal structure of objects Velocity structure of objects. . .

Spectroscopic flat field (Dome flat or twillight flat) slit “imperfections” spatial direction 78 dispersion direction

Wavelength calibration • We measure intensity I as a function of pixel position on a CCD Part of the CCD spectrum of target . . . but the CCD does not “see color”

Wavelength calibration • We measure intensity I as a function of pixel position on a CCD • How do we know which pixel corresponds to which wavelength? Part of the CCD spectrum of target Part of the CCD spectrum of lamp with known lines “arc” . . . the CCD sees this Illuminate spectrograph with a lamp with known lines before or after your observation.

spatial direction Wavelength calibration: “arc” 81 dispersion direction

Telluric + flux calibration • • Find nearby spectro-photometric standard star, which has known flux-calibrated spectrum Extract the spectrum of the standard star(s). If the standard was taken immediately before and/or after the science exposure you can get a science spectrum that is corrected for telluric absorption and is flux calibrated as follows: where Fstandard is the (known) spectrum of the standard star

Telluric + flux calibration More general approach if science target and standard star were not taken at (nearly) the same airmass: Possibility 1: observe standards at various airmasses and fit the instrument response R and the atmospheric extinction coefficient A (i. e. the same procedure as for photometry, but now at each wavelength instead of integrating over a filter). Calculate the calibrated science spectrum F from the raw science spectrum S observed at airmass am using F = S exp(A am) / R Possibility 2: Use a theoretical model for the Earth atmosphere and fit this to the calibrator observation and then extrapolate to the airmass of the science observation, or fit it to the science observation directly. Divide by synthetic spectrum to correct for Atmosphere. Use the standard star observation(s) for flux calibration.

Choosing standard stars A “good” standard star has the following properties: • • it is comparatively bright (so we don’t need much time for calibration) its intrinsic spectrum is known perfectly it has as little spectral structure as possible, i. e. a “smooth” spectrum it is close to your science target on the sky The “best choice” depends on the application and regime: • Hot stars (spectral type B, the hotter the better) are much used because: – they have relatively little spectral structure: H lines, weak lines of He and ionized metals, weak Balmer discontinuity • If we study H lines in science target, calibrator should have no H lines – G stars have relatively weak, narrow H lines (but many other lines, careful!) • For mid-IR applications, we need mid-IR bright calibrators – often limited to K and M type giant stars, + nearest hot stars

A note on telluric calibration Optical regime: • in most of the optical regime (~350 to ~1000 nm) the Earth atmosphere has no “structure” in its absorption spectrum, i. e. no atomic/molecular absorption lines. In the “red” part there are some lines (mainly O 2 and H 2 O). There is, of course, scattering off molecules and aerosols causing substantial but smooth extinction. • For work requiring no absolute calibration, e. g. measuring equivalent widths of lines in astronomical sources, no telluric calibration is required Infrared regime: • Strong spectral structure in the atmospheric absorption spectrum (and in its emission spectrum!) • Very careful telluric calibration needed, even if no absolute flux calibration is required.

Very high R work: peculiarities • For accurate calibration, need to take Earth motion into account (orbital motion up to 30 km/s corresponding to R = 104, daily rotation up to 460 m/s corresponding to R = 6. 5 105) • In the infrared, at high resolution the atmospheric opacity breaks up into very many narrow absorption lines. A specific spectral line you wish to measure may coincide with a telluric line and not be measurable at some instant, but due to the Earth’s orbital motion it may have red- or blue shifted out of the telluric absorption line later in the year. “Best time of year” depends on position of source w. r. t. ecliptic and the source radial velocity • When calibration must be extremely good (e. g. for Exoplanet radial velocity measurements) we cannot use separate calibration frames, calibration must be done simultaneously with science observation. Use gas absorption cell or telluric lines

Quantifying “line strength” The term “line strength” is not uniquely defined. Various ways of quantifying it exist: 1) Peak intensity – Problem with low spectral resolution, because each “pixel” is an integral over the pixel width: Flux λ

Quantifying “line strength” The term “line strength” is not uniquely defined. Various ways of quantifying it exist: 1) Peak intensity – Problem with low spectral resolution, because each “pixel” is an integral over the pixel width: Flux Peak strength is underestimated λ

Quantifying “line strength” The term “line strength” is not uniquely defined. Various ways of quantifying it exist: 2) Frequency-integrated flux in the line Advantage: Can also be measured with low-resolution spectrographs (if no continuum is present) Flux λ

Quantifying “line strength” The term “line strength” is not uniquely defined. Various ways of quantifying it exist: 3) Equivalent width Only when a continuum is present Flux continuum absorption line λ

Quantifying “line strength” The term “line strength” is not uniquely defined. Various ways of quantifying it exist: 3) Equivalent width Only when a continuum is present EW Flux continuum absorption line λ

Spectro-astrometry Beat the spatial resolution limit! Flux x [“] • At each velocity channel the emission might be slightly shifted in space. • Plot spatial shift as a function of velocity

Spectro-astrometry Offset [AU at 160 pc] Beat the spatial resolution limit! SR 21 0. 006” 0. 003” 0. 000” -0. 003” -0. 006” From: Pontoppidan et al. 2008 Diffraction limited resolution of VLT at 4. 7 μm is 1. 22λ/D=0. 15”

Spectro-astrometry Beat the spatial resolution limit! 1000 x higher resolution than this radio image! Brown et al. 2009

P Cygni line profiles: Stellar winds wind star Flux Star emits emission line. Wind is cooler at large radii. So the wind makes absorption line. But blue-shifted! blue red v [km/s]

P Cygni line profiles: Stellar winds λ [Å] Gemini Observatory/AURA, Travis Rector Aspin et al. 2009 • Mc. Neal’s nebula is a reflection of light from a just-born star. • This reflection appears only nowand-then: when the star has a “hickup” (outburst). • The P Cyg Hα profile shows: mass is ejected during this outburst!

Example of low-R Infrared spectroscopy - Origin of dust species in disk around young stars, solar system comets, and building blocks of planets - Young star undergoes accretion outburst - Amorphous dust turns into crystals Credit: Spitzer Science Center Abraham et al. 2009