AST443 / PHY517

Spectroscopy

Spectroscopy

• The science of breaking the light up into its component wavelengths (or frequencies), generally through use of a dispersive element.

• The resolution R = λ/Δλ. R may range from as low as a few tens in grism spectra to millions.

• The spectrum: a number of adjacent measures of the brightness as a function of wavelength.

• Filter photometry with narrowband filters. It consists of observing a series of single points rather than a dispersed spectrum. A BVRcIc SED has R~4.

Comparing Resolutions

Black: 3.1AGreen: 17A

R= 3000R=78000

Resolution tradeoffslow dispersion, 1D

Astrophysics of Spectroscopy

• Continuua. Spectra of continuua can determine the spectral energy distribution (SED). – Filter photometry is appropriate for many kinds of continuua,

but spectra are needed to show the absence (or irrelevance) of lines.

• Lines. Emission or absorption lines (and edges) are formed by bound-bound or bound-free electronic transitions in ions, atoms, and molecules. Lines are useful for– Determining gas, excitation, and ionization temperatures, – Determining ionization and exitation states, – studying thermal equilibria, – measuring gas density and pressure, – measuring abundances of various species – measuring gas velocities.

Terrestrial H2O lines in N Del

Data smoothed

Na D region in a K star

Hα region in K star

Line Broadening

• Natural line broadening gives rise to Lorentzian-shaped lines, with width of order 10-4A. Lorentzians are of the general form I(Δλ) = A/(Δλ2+B), where A and B are constants.

• Pressure Broadening is due to pertubations of energy levels by nearby atoms, by the Stark effect, Zeeman broadening, etc. The line profile is Lorentzian when thin, and develops a saturated core when thick.

• Thermal Broadening. Due to thermal motions. Gaussian profile. I(λ) = I(λ0) exp(-mc2(Δλ)2/2kTλ2) . HWHM = (2kT loge2/mc2)0.5λ0.

• Turbulent Broadening is due to flows and convection. This includes macroturbulence and microturbulence. It produces a Gaussian profile with a half width = (V2 loge2/c2)0.5λ0.

• Combined line profile. A sum of Gaussians is a Gaussian. A sum of a Gaussian and a Lorentzian is a Voigt profile.

• Rotational broadening. Rotation of a uniform disk gives a profile I(λ) = I(λ0) [1-(c2Δλ2)/(V2λ02)]0.5 The extrema are at ± V sin i.

Center of Mass Motions• Double lines give away a double-lined

spectroscopic binary (SB2).

An Orbit

V471 Tau K2V + DA

Center of Mass Motions

• A single-lined spectroscopic binary (SB1) is given away by varying line velocities.

• Expansion velocities of nebulae. • Radial Velocities.

Δλ/λ = v/c

Spectroscopic Measurements

• Equivalent Widths. ∫dl(Fc - Fl)/Fc– Fc is the flux in the continuum – Fl is the flux in the line. – Units are wavelength. – Absorption lines are positive; emission lines are

negative. – The equivalent width is the width of a rectangular

black line with the same area as the observed line. • Line widths. – FWHM: full width at half maximum. – FWZI: full width at zero intenzity

Diffraction Fundamentals. I.

• Light passing through an aperture is diffracted.Light passing through 2 or more apertures interferes with itself.

• Reflection grating geometry. Each step acts as its own aperture.

Diffraction Fundamentals. II.

• first term: diffraction by a single slit. • second term: interference pattern of N

apertures

Diffraction

• I(θ)/I(0) = sin2(Δ)/Δ2 sin2(Nδ)/sin2(δ). • Let δ = mπ + P (P is the phase). In the limit that P →0, I(θ)/I(0) = N2

• The fringe pattern has zeros where Nδ = m'π, where m' ≠ mN (m, m' are integers). m is the order number (m=0 is the specular reflection, or the zero-order image). The places where m' = mN, the fringe maxima, occur at sin(θ)=(m'λ)/(Nd)

• The resolution R is the distance between successive zeros, or R = 2λ/N d cos(θ).

• A grating diffracts light into many overlapping orders. – The free spectral range, the wavelength difference between two overlapping

points, is sin-1(mλ1/d) = sin-1((m+1)λ2/d), or Σ = λ1 - λ2 = λ2/m. – For small m, orders can be separated with filters (short-pass, long-pass, or

order-sorting). Where m is large, as in an echelle system, care must be taken to separate the orders.

• The slit width does not degrade the resolution so long as the slit width S < λf/(Nd cos(θ)), where f is the focal length of the camera.

Why use a slit?

The slit is generally useful because it :• Can be used to increase resolution (narrow slit) • Excludes sky, decreasing the background signal • Excludes other sources. • Fixes the zero-point. • Slitless spectrographs are used for surveying

emission line sources, or for emission line spectra of extended objects, such as the Sun

Low Order Spectrographs

• mλ = constant (grating constant)• m=0: specular reflection• m=1: first order• Note that long wavelength light may be

contaminated my high order short wavelength light (1x8000 = 2x4000 = 3x2667 = 4x2000)

• Blaze: angle between plane of grating & plane of grooves

Types of Spectrographs

• Rowland Circle. Useful in the laboratory, but not compact enough for telescopes.

Ebert Spectrograph

• Uses flat gratings.

Littrow Spectrograph

• Uses flat gratings.

Wadsworth Spectrograph

• Curved gratings permit compact design.

HST/GHRS

HST/STIS

High Order Spectrographs

• mλ = constant (grating constant)• Used at high m• There will be contamination of orders• Chiron: k ~ 565900– m=100: λ = 5659– m=101: λ = 5603– m=102: λ = 5548

• Requires cross-disperser or order-sorting filters

Echelles

Echelle Grating

Chiron

Tokovinin, A. et al. 2013 AJ 125, 1336

λ/Δλ: 27 400, 79 000, 95 000, 136 000Wavelength coverage: 415–880 nmSpectral orders: 138 to 66Collimator: F = 600 mm, beam diameter 130 mmGrating: 63.9° blaze, 31:6 l/mm, 130 x 260 mmCross-disperser: LF7 prism, apex 62°, one passCamera: oil triplet F = 1012 mm, D . 140 mmCCD: 4096 x 4112, 15 μm pixels, graded-ARFiber feed: 100 μm octagonal core, 2.7ʺ on the sky

ChironCTIO 1.5m

Bench-MountedFiber-FedTemperature-controlledVery stable

Chiron4500-8800AN Del 2013

130928

Cut Through Echelle

STISE140M

1100-1700ARU Lup

STISE140 M1100-1700A

V471 Tau

Spatially-Resolved Spectroscopy

• Spectroscopy classically involves observing one object at a time, and so is inefficient, when compared to imaging photometry.

Long Slit Spectroscopy

Spectroscopy is often done through a long slit.• Permits spatially-resolved spectroscopy in one dimension.• Slits lengths:

– set by the size of the detector and the plate scale– Typically cover a few arcminutes on ground-based

spectrographs. – The HST/STIS slit: 52" long in the optical (26" in the UV) in first

order. – To prevent order overlap, echelle spectrographs generally have

very short slits (0.06" on HST/STIS; a few arcsec on the ground). • Slits can often be rotated to line up objects in the slit. Each point along the slit gives its own spectrum.

Long Slit Example

Sky Subtraction

• Long slits permit sky-subtraction.• This is very useful on moonlit nights.

Long Slit Example

Multi-object Spectroscopy

• A way to take advantage of many objects in the field of view (e.g., a cluster of galaxies or a star cluster) is to use optical fibers to direct the light from many targets to the detector.

• Example: WIYN-HYDRA spectrograph at Kitt Peak. • Hundreds of objects observable simultaneously. • Light losses in the fibers are more than offset by

gains in observational efficiency.

WIYN HYDRA

WIYN HYDRA

WIYN Hydra

WIYN/HYDRA Image

Integral Field Spectroscopy

• The IFU is similar in concept to the fiber-fed multi-object spectrograph.

• Goal: 2-dimensional sampling of the spectra of an extended object.

• A bundle of fibers covers the object, giving spatial resolutions of the projected size of the fibers.

IFU schematics

Wavelength Calibration

You must observe a wavelength calibrator. • Generally an arc lamp– Neon produces strong lines in the red– He-Ar or Th-Ar is used in the blue.

• Each line has a known wavelength λarc

• Measure the position of the line xarc in pixels. • Fit λarc(xarc) with an analytical function • Determine λarc(xarc)

Arc lamps

Spectrophotometric Calibration• Spectrophotometry: the absolute flux as a function of wavelength• Spectroscopic losses:

– Slit loses (seeing; parallactic angle– Fiber transmission– Grating blaze

• To correct these, observe a spectrophotometric standard star, with a well-determined SED (ergs cm-2 s-1 A-1) as a function of wavelength.

• At each wavelength, measure the count rate (counts s-1 A-1). • The ratio of the true flux to the observed count rate gives a wavelength-

dependent conversion factor Fcal (ergs cm-2 / count). – If the night is photometric, and the guiding is good, multiply all spectra by Fcal

to recover the true spectral flux. – If the night is not photometric, you can still use this conversion factor to

recover the relative flux distribution, since clouds tend to be gray absorbers.

What Makes a Good Standard?

• A reasonably bright star – (why waste time doing calibrations?)

• A star with a smooth or featureless continuum.

Spectrophotometric Standard

Before and after