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 resolu'on 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 funcNon of wavelength. • Filter photometry with narrowband filters. It consists of observing a series of single points rather than a dispersed spectrum. Comparing ResoluNons Black: 3.1A Green: 17A ResoluNon tradeoffs Astrophysics of Spectroscopy • Con'nuua. Spectra of conNnuua can determine the spectral energy distribuNon (SED). – Filter photometry is appropriate for many kinds of conNnuua, but spectra are needed to show the absence (or irrelevance) of lines. • Lines. Emission or absorpNon lines (and edges) are formed by bound-­‐bound or bound-­‐free electronic transiNons in ions, atoms, and molecules. Lines are useful for – Determining gas, excitaNon, and ionizaNon temperatures, – Determining ionizaNon and exitaNon states, – studying thermal equilibria, – measuring gas density and pressure, – measuring abundances of various species – measuring gas velociNes. 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 pertubaNons 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 moNons. Gaussian profile. I(λ) = I(λ0) exp(-­‐mc2(Δλ)2/2kTλ2) . HWHM = (2kT loge2/mc2)0.5λ0. • Turbulent Broadening is due to flows and convecNon. 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 another Gaussian. A sum of a Gaussian and a Lorentzian is a Voigt profile. • Rota'onal broadening. RotaNon 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 MoNons • Double lines give away a double-­‐lined spectroscopic binary (SB2). Center of Mass MoNons • A single-­‐lined spectroscopic binary (SB1) is given away by varying line velociNes. • Expansion velociNes of nebulae. • Radial VelociNes. Δλ/λ = v/c Spectroscopic Measurements • Equivalent Widths. ∫(Fc -­‐ Fl)/Fc – Fc is the flux in the conNnuum – Fl is the flux in the line. – Units are wavelength. – AbsorpNon lines are posiNve; emission lines are negaNve. – 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 DiffracNon Fundamentals. I. • Light passing through an aperture is diffracted. Light passing through 2 or more apertures interferes with itself. • ReflecNon graNng geometry. Each step acts as its own aperture. DiffracNon Fundamentals. II. • first term: diffracNon by a single slit. • second term: interference papern of N apertures DiffracNon • 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 papern has zeros where Nδ = m'π, where m' ≠ mN (m, m' are integers). m is the order number (m=0 is the specular reflecNon, or the zero-­‐order image). The places where m' = mN, the fringe maxima, occur at sin(θ)=(m'λ)/(Nd) • The resoluNon R is the distance between successive zeros, or R = 2λ/N d cos(θ). • A graNng 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-­‐sorNng). Where m is large, as in an echelle system, care must be taken to separate the orders. • The slit width does not degrade the resoluNon 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 resoluNon (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 (graNng constant) • m=0: specular reflecNon • 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 graNng & plane of grooves Types of Spectrographs • Rowland Circle. Useful in the laboratory, but not compact enough for telescopes. Ebert Spectrograph • Uses flat graNngs. Liprow Spectrograph • Uses flat graNngs. Wadsworth Spectrograph • Curved graNngs permit compact design. HST/GHRS HST/STIS High Order Spectrographs • mλ = constant (graNng constant) • Used at high m • There will be contaminaNon of orders • Chiron: k ~ 565900 – m=100: λ = 5659 – m=101: λ = 5603 – m=102: λ = 5548 • Requires cross-­‐disperser or order-­‐sor'ng filters Echelles Echelle GraNng Chiron 4500-­‐8800A N Del 2013 130928
Cut Through Echelle STIS E140M 1100-­‐1700A RU Lup STIS E140 M 1100-­‐1700
A V471 Tau SpaNally-­‐Resolved Spectroscopy • Spectroscopy classically involves observing one object at a Nme, and so is inefficient, when compared to imaging photometry. Long Slit Spectroscopy Spectroscopy is o•en done through a long slit. • Permits spaNally-­‐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 opNcal (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 o•en be rotated to line up objects in the slit. Each point along the slit gives its own spectrum. Long Slit Example Sky SubtracNon • Long slits permit sky-­‐subtracNon. • This is very useful on moonlit nights. Long Slit Example MulN-­‐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 opNcal fibers to direct the light from many targets to the detector. • Example: WIYN-­‐HYDRA spectrograph at Kip Peak. • Hundreds of objects observable simultaneously. • Light losses in the fibers are more than offset by gains in observaNonal efficiency. WIYN HYDRA WIYN HYDRA WIYN Hydra WIYN/HYDRA Image Integral Field Spectroscopy • The IFU is similar in concept to the fiber-­‐fed mulN-­‐object spectrograph. • Goal: 2-­‐dimensional sampling of the spectra of an extended object. • A bundle of fibers covers the object, giving spaNal resoluNons of the projected size of the fibers. IFU schemaNcs Wavelength CalibraNon 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 posiNon of the line xarc in pixels. • Fit λarc(xarc) with an analyNcal funcNon • Determine λarc(xarc) Arc lamps Spectrophotometric CalibraNon • Spectrophotometry: the absolute flux as a funcNon of wavelength • Spectroscopic losses: – Slit loses (seeing; parallacNc angle – Fiber transmission – GraNng blaze • To correct these, observe a spectrophotometric standard star, with a well-­‐
determined SED (ergs cm-­‐2 s-­‐1 A-­‐1) as a funcNon of wavelength. • At each wavelength, measure the count rate (counts s-­‐1 A-­‐1). • The raNo 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, mulNply all spectra by Fcal to recover the true spectral flux. – If the night is not photometric, you can sNll use this conversion factor to recover the relaNve flux distribuNon, since clouds tend to be gray absorbers. What Makes a Good Standard? • A reasonably bright star – (why waste Nme doing calibraNons?) • A star with a smooth or featureless conNnuum. Spectrophotometric Standard Before and a•er