spectroscopy - rijksuniversiteit groningensctrager/teaching/oa/spectroscopy.pdfspectroscopy...

SpectroscopyObservational Astronomy 2019 Part 10 Prof. S.C. Trager

Spectroscopy is the measurement of the intensity of light at different wavelengths

Why would we want to do this?

The spectrum of an object can give a vast amount of physical information

E.g., composition, temperature, velocity, internal motions, magnetic field strength, ionization, etc.

Spectroscopy is a much more powerful tool than photometry!

12 Czekala et al.

Figure 9. Same as Fig. 7 for the Phoenix models. Note the increased vertical scale and local covariance structure for the residuals.

A moderate resolution (R ⇡ 2, 000) near-infrared spec-trum of Gl 51 was obtained on 2000 Nov 6 using theSPEX instrument (Rayner et al. 2003) on the 2.3 mNASA Infrared Telescope Facility (IRTF). SPEX is across-dispersed echelle spectrograph that covers the red-optical to thermal-infrared spectrum (0.7–5.5 µm) in twosettings. These data were obtained as part of the IRTFspectral standard library project (Cushing et al. 2005;Rayner et al. 2009), and were processed through the well-vetted Spextool reduction pipeline (Cushing et al. 2004;Vacca et al. 2003) to deliver a fully calibrated spectrum.At 2.1µm, the S/N is ⇠400 per resolution element.

Modeling late-type stellar atmosphere structures andtheir spectra is considerably more complex than for Sun-like stars, due to lingering uncertainties in the atmo-sphere physics and molecular opacities. Especially con-

�0.36

�0.32

�0.28

�0.24

[Fe/

H]

6280

6320

6360

6400

Te↵ [K]

4.80

4.95

5.10

5.25

vsi

ni[k

ms�

1]

�0.35

�0.30

�0.25

[Fe/H]

4.80

4.95

5.10

5.25

v sin i [km s�1]

Figure 10. Same as Fig. 8, but for the Phoenix models.

founding is the presence of complex condensates (clouds)at the coolest temperatures (Allard et al. 2013), mak-ing it considerably more challenging to determine (sub-)stellar properties (Rajpurohit et al. 2014). Various ap-proaches have been taken to infer the key parameters inthe face of these di�culties, including iteratively maskingregions with poor spectral agreement (e.g., Mann et al.2013). Astutely, Mann et al. note that such a schememay exclude regions of the spectrum that contain in-trinsically useful information for discriminating betweenphysical properties, and that a more sophisticated ap-proach would weight each spectral region based on itsconsistency with the data. The modeling framework thatwe have constructed here does exactly that.

As a point of reference, Rojas-Ayala et al. (2012) useda K-band spectrum at similar resolution to the SPEXdata to estimate the basic Gl 51 parameters using an in-dexing technique. They measured equivalent widths forthe 2.205 µm Na I doublet and 2.263 µm Ca I triplet,along with a pseudo-continuum index defined over threenarrow passbands, 2.070–2.090, 2.235–2.255, and 2.360–2.380 µm (see their Fig. 2 for a useful visualization), de-signed to probe the spectral curvature induced by H2Oabsorption bands. With reference to a custom grid of theBT-Settl modifications of the Phoenix library (Allardet al. 2012), Rojas-Ayala et al. infer Te↵ = 3039 ± 56 Kand [Fe/H] = 0.28 ± 0.17 for a fixed log g = 5.0.

By modeling the K-band region of the SPEX data withthe Phoenix library12 and a Gaussian prior on log g (at5.0 ± 0.05 dex), we infer parameters for Gl 51 that areconsistent with Rojas-Ayala et al. (2012). Figure 11 dis-plays the spectral modeling results, and Figure 12 showsthe marginal posterior distributions for the relevant stel-lar parameters. The best-fit parameter values and theirassociated uncertainties are compiled in Table 2.

We concur with Rojas-Ayala et al. (2012) that thePhoenix models manage to match the overall spectral

12 The di↵erences between the Husser et al. (2013) Phoenixlibrary and the BT-Settl modification of the Phoenix models atthese (relatively) high e↵ective temperatures are minor. Since theformer is defined over a well-sampled, more regular grid of stellarparameters, we prefer it here for computational simplicity.

A small portion the spectrum of an F dwarf star hosting a giant planet

In fact, multi-band photometry can be seen (and is often used) as very-low-resolution spectroscopy

An important question is then, why don’t we take spectra of every object we’re interested in?

Ideal but expensive

as the resolution increases, the number of photons per pixel on the detector decreases to conserve energy, and so the signal-to-noise ratio per pixel decreases

Our desire for spectrographic information is what drives the current desire to build ever-larger telescopes at all wavelengths

Slitless spectrographs

Slit spectrographs

Integral-field spectrographs

Fourier-transform spectrographs

Fabry-Perot interferometers

Monochromators

Heterodyne spectrographs

... etc. ...

Type of UV/optical/IR spectrographs

Slit spectrographs

We’ll focus here on slit spectrographs, the basis of the spectrographs used for most optical and NIR studies of stars and galaxies

We’ll mention some of its variants — multislit and IFU spectrographs — along the way...

A slit spectrograph is schematically made up of five elements:

a slit: provides narrow beam and “line shape” a collimator: makes diverging beam parallel (“collimated”) a dispersing element: disperses light into component wavelengths a camera: brings dispersed light to focus on detector

a detector: collects dispersed light

A slit spectrograph is schematically made up of five elements: a slit: provides narrow beam and “line shape” a collimator: makes diverging beam parallel (“collimated”)

a dispersing element: disperses light into component wavelengths a camera: brings dispersed light to focus on detector a detector: collects dispersed light

collimator

dispersing element

camera

detectorslit

In ~2D, we can describe this optical system as above The telescope has a diameter D and a focal length f The slit has a width w, which subtends an angle ϕ on the sky and an angle δα on the collimator, and a height h, which subtends an angle ϕ′ on the sky and an angle δα′ on the collimator

slitimageof slit

disperser

collimator camera

telescope

Dw

d1 d2

A

f f1 f2

ϕ δα δβ w′

The collimator has a focal length f1 and puts a collimated beam of diameter d1 onto the disperser The disperser has angular dispersion

where dθ is the angular difference between two rays of wavelength difference dλ

The camera has focal length f2

slitimageof slit

disperser

collimator camera

telescope

Dw

d1 d2

A

f f1 f2

ϕ δα δβ w′

A =d✓

d�

Then

The disperser can magnify the image along the direction of the dispersion, an effect called anamorphic magnification r, where

slitimageof slit

disperser

collimator camera

telescope

Dw

d1 d2

A

f f1 f2

ϕ δα δβ w′

� = w/f , �0 = h/f , �↵ = w/f1, and �↵0 = h/f1.

r =�↵

��=

d1d2

Assuming the angles are small, which is usually a good assumption.

Then the reimaged slit has width

and height

where F2=f2/d1 (recall that D/f=d1/f1 by similar triangles)

slitimageof slit

disperser

collimator camera

telescope

Dw

d1 d2

A

f f1 f2

ϕ δα δβ w′

w0 = rw(f2/f1) = r�DF2

h0 = h(f2/f1) = �0DF2

If we want to critically sample (i.e., Nyquist sample) our reimaged slit with 2 pixels, each of size Δ, then we want

For a slit that subtends (say) 1″ on an 8-m telescope with a detector with 15 µm pixels, rF2≈0.8 This means that matching the slit size to the pixel size forces a necessary value of rF2 and therefore a specific value of the focal ratio f2/d2 (= rF2) of the camera

slitimageof slit

disperser

collimator camera

telescope

Dw

d1 d2

A

f f1 f2

ϕ δα δβ w′

2� = r�DF2

Now consider our slit to be illuminated by light of two wavelengths λ and λ+dλ

Then the separation between the centers of the two images of the slit (at the detector) is

slitimageof slit

disperser

collimator camera

telescope

Dw

d1 d2

A

f f1 f2

ϕ δα δβ w′

�l0 = f2A��

remember that A=dθ/dλ and dθ~dl′/f2 from the geometry of the figure – l′ is in the direction of the project slit width w′

Let’s define the spectral purity δλ as the wavelength difference for which Δl′=w′ and the spectral images are on the verge of being resolved

Then

where again we’ve used D/f=d1/f1

slitimageof slit

disperser

collimator camera

telescope

Dw

d1 d2

A

f f1 f2

ϕ δα δβ w′

�� =w0

f2A=

r�

A

D

d1

If two images are separated less than the (imaged) slit width on the detector, you can’t resolve them

We can now define the spectral resolution R, a dimensionless measure of the spectral purity:

note that most people take δλ to be the FWHM of a spectral image, but this isn’t actually the definition of spectral purity — however, it’s what astronomers expect, so we’ll keep that definition in mind

slitimageof slit

disperser

collimator camera

telescope

Dw

d1 d2

A

f f1 f2

ϕ δα δβ w′

R =�

��=

�Ad1r�D


To keep R constant, a bigger telescope requires a bigger beam on the collimator for a given A

slitimageof slit

disperser

collimator camera

telescope

Dw

d1 d2

A

f f1 f2

ϕ δα δβ w′

R =�

��=

�Ad1r�D


Alternatively, to achieve a higher resolution requires either a smaller slit, a faster collimator, a higher dispersion, or a bigger beam (or a smaller anamorphic magnification)

slitimageof slit

disperser

collimator camera

telescope

Dw

d1 d2

A

f f1 f2

ϕ δα δβ w′

R =�

��=

�Ad1r�D


Note that this is not the resolution limit set by diffraction of the light: that’s R0=Ad2 (because λ➝ϕD in this case)

slitimageof slit

disperser

collimator camera

telescope

Dw

d1 d2

A

f f1 f2

ϕ δα δβ w′

R =�

��=

�Ad1r�D

The slit:

Light from the telescope enters the slit at the focal plane of the telescope

We use a narrow slit in most cases to provide

high resolution

a “line shape”, useful for determining the profile of a spectral line due to, e.g., Doppler broadening, rotation, etc.

Elements of a (slit) spectrograph

The slit:

The slit can often be widened or narrowed using movable “slit jaws”, which allows for a continuous change in slit width, or a “decker”, which has different fixed slit widths


The slit:

The slit can often be widened or narrowed using movable “slit jaws”, which allows for a continuous change in slit width, or a “decker”, which has different fixed slit widths


The slit:

Often the slit is reflective on the side facing the telescope, so that slit-viewing optics can be used to guide the telescope


The slit:

Because we often want to recover spatial information on our objects, or we want to recover the light lost from a narrow slit, we use integral field spectrographs (IFS or IFUs, integral field units)


These devices “slice” the image plane a feed the light into a spectrograph

SAURON: lenslets, reimaged on the spectrograph (top)

PMAS: lenslets feed fibers, which are placed on a single long slit (middle)

HARMONI: image slicer, where mirrors “slice” the image into portions of a long slit (bottom)


SparsePak, PPAK, WEAVE: fibers sparsely sample image and feed a long slit


SparsePak, PPAK, WEAVE: fibers sparsely sample image and feed a long slit


Of course, many individual objects can be targeted by individual fibers, like in the Two-Degree Field (2dF) spectrograph system at the Anglo-Australian Telescope, the Sloan Digital Sky Survey (SDSS) spectrograph, and WEAVE’s multi-object spectroscopy (MOS) mode


Another way of “slicing” the image plane is to use several (non-overlapping) non-colinear “slitlets” in a multislit spectrograph

Most modern low-to-moderate-resolution spectrographs on big telescopes are multislit spectrographs, like LRIS & DEIMOS on Keck, FORS2 and VIMOS on VLT


The collimator:

As discussed above, the collimator brings the diverging beam from the slit into a parallel (collimated) beam

A couple of important points about the collimator:

“Underfilling” the collimator — i.e., using a beam with a smaller d1 than designed — results in a lower resolution

“Overfilling” the collimator results in a loss of light, as the disperser can’t intercept all of the beam

Always desirable to match the focal ratio of the collimator to that of the telescope, so that D/f=d1/f1


The dispersing element:

Recall from our lectures on optics that a prism has

where t is the length of the base of the prism, a is the beam width into and out of the prism, and

(for optical glass, roughly) is the change of the index of refraction with wavelength


A =d✓

d�=

t

a

dn

d�

dn

d�/ ��3

α1 α2A

n(λ)

θ(λ)

L L

t

s1 s2

a1 a2


Note that since a is the same into and out of the prism, a prism has r=1 and therefore no anamorphic magnification

The resolution of a prism is (with a=d2 and assuming a square beam)


α1 α2A

n(λ)

θ(λ)

L L

t

s1 s2

a1 a2

R0 = tdn

d�


Prisms generally have much lower resolutions than desired (or possible) but are generally very efficient


α1 α2A

n(λ)

θ(λ)

L L

t

s1 s2

a1 a2


Because we’re often interested in higher resolutions than prisms can (easily) provide at the same beam size, we use diffraction gratings instead



The grating equation gives the wavelength λ in order m at diffraction angle β for light incident at angle α onto a grating with slits or grooves spaced evenly at distance σ:

Note that m is an integer


m� = �(sin� ± sin↵)


The grating equation gives the wavelength λ in order m at diffraction angle β for light incident at angle α onto a grating with slits or grooves spaced evenly at distance σ:

Note that m is an integer


Here read “σ” for “d”m� = �(sin� ± sin↵)


The plus sign applies to reflection gratings and the minus sign to transmission gratings

For a reflection grating, α=–β corresponds to m=0

For a transmission grating, α=β corresponds to m=0


αβ

Reflectiongrating

gratingnormal

α

Transmissiongrating

gratingnormal

β


The angular dispersion of a grating can be written

for any grating

or

for a reflection grating


αβ

Reflectiongrating

gratingnormal

α

Transmissiongrating

gratingnormal

β

A =d�

d↵=

m

� cos�

A =d�

d↵=

sin� + sin↵

� cos�


The first equation,

shows that at a given order m, the angular dispersion A is set by the groove spacing σ or the angle of diffraction β


αβ

Reflectiongrating

gratingnormal

α

Transmissiongrating

gratingnormal

β

A =d�

d↵=

m

� cos�


The second equation,

shows that at a fixed λ, A is set entirely by α and β and is completely independent of m and σ


αβ

Reflectiongrating

gratingnormal

α

Transmissiongrating

gratingnormal

β

A =d�

d↵=

sin� + sin↵

� cos�


Therefore many different combinations of m and σ give the same angular resolution for fixed α and β, provided that m/σ=constant



Coarsely-ruled gratings (large σ) used at high orders (large m) are called echelle gratings, and are used at high α and β

Echelles typically have 1/σ~300–30 (lines) mm–1 and m=10–100

First-order gratings (m=1) often have 1/σ~300–1200 (lines) mm–1



The anamorphic magnification of a grating is

Because a smaller r gives a higher resolution, it is desirable to have β<α

this means the grating normal is more nearly in the direction of the camera than the collimator


r =|d�||d↵| =

cos↵

cos�=

d1d2


If we want the grating to accept all the light from the collimator, then we require , where W is the width of the grating

The limiting spectral resolution of the grating (i.e., the diffraction limit) is

where N is the total number of grooves in the grating width W


W = d1/ cos↵

R0 =md2

� cos�=

mW

�= mN


In terms of angles,

In the seeing-limited case (i.e., a narrow-slit),

The free spectral range is the range over which spectral orders do not overlap, so that for λ and λ′, mλ′≠(m+1)λ:


R0 = W (sin� + sin↵)/�

R = W (sin� + sin↵)/(�D)

�� = �0 � � = �/m


Because of diffraction effects, we often want to maximize the efficiency of one particular wavelength

We due this by blazing — tilting — the facets (grooves) of the grating by some angle δ


δ


The peak wavelength is the blaze wavelength λb, given by

For small angles, the width of the blaze function is given by


δ

m�b = 2� sin � cos(↵� �)

�± =m�b

m⌥ 1/2


The blaze function has a characteristic shape

The intensity of the output spectrum is modulated by this blaze function

This allows us to choose an appropriate central wavelength:

choose a δ and change β by a small amount, while α is (normally) held fixed in a spectrograph


blaz

e fu

nctio

n

Acquisition and calibration of spectroscopic data

Along will all of the other calibrations required for CCD data reduction...

bias frames, dark frames, flat fields

...spectroscopic measurements taken with an optical spectrograph require a number of extra calibration frames

Wavelength calibration frames

These frames are known as arc lamp frames

because the light is produced by an electrical (arc) current through a single or a few element gas, like He or Ar or NeAr or HeNeAr (or sometimes ThAr)

A VI

MO

S IF

U ar

c lam

p fra

me


Because of possible focus or flexure changes in the spectrograph, or tilts of the grating, exposures of sources with known wavelengths (like He, Ne, Ar, Th, Cu lamps — or even the night sky) are required calibrate the wavelength scale of the spectrograph

A VI

MO

S IF

U ar

c lam

p fra

me


Such frames can also calibrate the geometric distortions parallel to the dispersion caused by the grating itself

this is present for reflection and transmission gratings, even if the camera and collimator are aberration-free

A VI

MO

S IF

U ar

c lam

p fra

me

Geometric calibration frames

In slit spectrographs, distortions from the grating, spectrograph optics, and even the differential refraction of the atmosphere can cause objects to “bend” “along the slit” — perpendicular to the dispersion direction

An LMC star taken at twilight


This “s-distortion” (seen here for a star in a long-slit spectrum) can be removed by observing (e.g.) a star at multiple positions along the slit to map the distortions An LMC star taken at twilight


This “s-distortion” (seen here for a star in a long-slit spectrum) can be removed by observing (e.g.) a star at multiple positions along the slit to map the distortions An LMC star taken at twilight

Illumination correction frames

Generally dome flat fields (or flat fields from light sources inside the instrument) are used to flat-field long- and multi-slit data because the number of counts required is high, and the twilight sky has structure in the spectral direction: the Sun itself (see the spectrum on the previous slide!) Spatial coordinate

coun

ts

Illumination correction frames

However, twilight flat fields can be used to correct for the uneven illumination of the dome flats, as seen here

this is a cut through the direction along the slit: the spatial direction

Spatial coordinate

coun

ts

Flux standardsOften we want to put our spectroscopic standards on a uniform flux scale

For this, we take spectra of spectrophotometric standard stars, the spectral equivalent of photometric standard stars

also called “flux standards”

316 Bohlin

Figure 1. STIS or FOS fluxes below 1 µm and NICMOS above 0.8 µm.The noise level is evident in the fainter stars near the STIS long wavelengthlimit of 1 µm and in the NICMOS spectrum of the faint SNAP-1 beyond1.9 µm.

Following the establishment of the absolute SEDs for the primary stars, aflux distribution for another star is established by the response relative to theprimaries when observed by a linear spectrometer of constant sensitivity. Inpractice, no such instrumentation exists, especially for ground-based observa-tions through an atmosphere with a transparency that can vary on short timescales. Even in space, focus variations, sensitivity degradation with time, andnon-linear detectors limit the precision of the transfer of the calibration from theprimary standards to bright secondary standard stars. For fainter stars, photonstatistics also contributes to the uncertainties.

From its installation in 1997 until its death in 2004, the low-dispersion(R ∼ 1000) modes of STIS were the premier instrumentation for establishing fluxstandards from 1150–10200 A (Bohlin 2000; Bohlin, Dickinson, & Calzetti 2001).Considerable effort has been expended in tracking the STIS changes in sensitivitywith time (Stys, Bohlin, & Goudfrooij 2004 and unpublished updates) and incorrecting the CCD observations for loss of charge transfer efficiency (CTE;Goudfrooij & Bohlin 2006). In the 0.8–2.5 µm range, the NICMOS R ∼ 200grism spectrophotometry has been calibrated and the count rate dependent non-linearity has been characterized by Bohlin, Lindler, & Riess (2005) and Bohlin,Riess, & de Jong (2006).

Figures 1 and 2 include most of the SEDs of the stars with NICMOS

observations. Figure 1 shows the hotter WD stars, while Fig. 2 illustrates thesolar analog and cooler stars. The wavelength coverage, the spectral types, andthe dynamic range are typical of the standard observational capabilities of the

Bohlin (2007)

Flux standards

However, it is difficult to do absolute spectrophotometry, because the very wide slits required to intercept all of the flux of the flux standard or the object itself usually lower the resolution unacceptably

316 Bohlin






Bohlin (2007)

Flux standardsMoreover, recall from our discussion of the refraction of light by the atmosphere means that blue light can be “bent” out of the slit if one isn’t careful about the slit orientation or if one desires a specific slit orientation (say, to follow the major axis of a galaxy)

See Filippenko (1982) for more information

316 Bohlin






Bohlin (2007)

An observation may require

radial velocity standard stars to measure the systemic velocity of a target accurately

measurements of the line-spread function, tracing the linear (wavelength) resolution

absorption-line-strength standard stars Always make sure you know what you want to measure from your spectra, and take the appropriate calibrations!

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