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Observing Protoplanetary Disks at Long Wavelengths Kobe International School of Planetary Sciences “Origins of Planetary Systems” 13 July 2005 Steven Beckwith Space Telescope Science Institute Outline • The signatures of disks in spectral energy distributions • Inferring the physical properties of disks from the radiation signatures – Unique & degenerate parameters – Addition of spatial information • Disk particles – Spectral signatures – Size and composition: dust “chemistry” • Disk dynamical properties – Orbital & infall signatures • Future observations – Spatial information (interferometry) – High resolution spectra (disk chemistry) 2 Spectral energy distributions Adams, Lada, & Shu 1988, Ap. J., 326, 865. Far IR optical depth: t ~ 1 at 100 mm t ~ 0.01 at 1 mm -16 -17 \ t 100 at 1 mm AV 300 nFn -19 -20 Observed AV ~ 3 Excess emission over photosphere -18 n3 blackbody XX Cha 1 \ clear line of sight to star and dust. 10 100 Wavelength (mm) 1000 3 Why does a disk dominate the infrared emission? Spectral Energy Distributions (SEDs) Thin, black disk: "standard theory" Lynden-Bell & Pringle 1974, MNRAS, 168, 603. Adams, Lada, & Shu 1988, Ap. J., 326, 865. Star luminosity, L* D L* angle q flat, black disk r Power/area absorbed ~ L* sin q 4pr2 L* D ~ 4pr 2 r Power/area emitted = sT4 ~ ~ L* r3 L* r3 (r >> D) T(r) ~ r Also true for accretion energy. -3/4 5 Spectral Energy Distribution (SED) Bn(T) 10 1 p nBn[T(r)] 2pr dr T(r) ~ r-3/4 nFn = C 1000 nFn r min L* 100 nFn = rmax Thin disk n4/3 T08/3 n4/3 area element surface emission x xmax X exp(x-3/4) -1 min nFn ~ n4/3 Planck n3 1 10 100 Wavelength (mm) 6 dx Thin disk SED: observations Adams, Lada, & Shu 1988, Ap. J., 326, 865. Beckwith et al. 1990, AJ, 99, 924 Thin disk nFn ~ n4/3 1000 XX Cha 100 nFn 10 n4/3 1 Planck n3 1 10 The SED from a theoretically thin black disk almost never fits the observations of young stars with excess infrared emission! • most SEDs flatter than n4/3 • some SEDs very flat, nFn ~ n0 100 Wavelength (mm) 7 Power law nFn power law T(r) Lynden-Bell & Pringle 1974, MNRAS, 168, 603. Adams, Lada, & Shu 1988, Ap. J., 326, 865. rmax T(r) = T0(r/r0) 1000 -q XX Cha r 10 na xmax min nFn = C T0 100 nFn nFn = pnBn[T(r)] 2pr dr 2/q a = 4-2/q na X x exp(x ) - 1 q dx min nFn ~ na ~ n4-2/q 1 n3 1 10 Wavelength (mm) q = 1/2 for a flat SED 100 • we can derive q from a • T(r) uniquely follows from a 8 How are disks really heated? • "Standard" flat, black disks with accretion: – Lynden-Bell & Pringle 1974, MNRAS, 168, 603. – Adams, Lada, & Shu 1987, Ap.J., 312, 788; & 1988, Ap.J., 326, 865. • Flaring: – Kenyon & Hartmann 1987, Ap.J., 323, 714. – Calvet et al. 1994, Ap.J., 434, 330. (w/ rad. trans. & envelope) – Chiang & Goldreich 1997, Ap.J., 490, 368. (w/ rad. trans., disk only) • Scattering halo: – Natta 1993, Ap.J., 412, 761. • Wave-driven accretion heating: – Shu et al. 1990, Ap.J., 358, 495. 9 Geometrical changes: Flaring Kenyon & Hartmann 1987, Ap. J., 323, 714. Star luminosity, L* angle q' r • • • gravity (z/r)(GM/r2) ~ r-3 absorbed radiation ~ sinq' >> sinq Tflare(r) > Tflat(r), especially at large r h Flared, black disk h ~ r2/7 r Ti(r) ~ r-6/15 BUT cannot account for flat SEDs (6/15 < 1/2) still assumes “black” disk (no radiative transfer) 10 Radiative transfer Chiang & Goldreich 1997, Ap. J., 490, 368. Star luminosity, L* Surface t~ 1 in optical angle q' D Interior t> 1 in infrared r optical light absorbed tV ~ 1, tIR << 1 small grains "bare" => Tgrain > Tblackbody disk emission tIR < 1 (5 - 100 mm) Still cannot account for very flat SEDs but does fit majority. h r 0.9 r 209 AU Ti(r) 21 K ( ( r 209 AU Prediction: disk surface emission is optically thin ) ) 13 45 19 45 11 Radiative heating: isolated particle Distance r Particle radius a (spherical; rapidly spinning) Temperature T Absorbed radiative power: pa 2 L 4pr 2 Emitted radiative power: 4pa 2 sT 4 Luminosity L L T=( 16ps ) 1/4 r -1/2 Using en for small particles: T ~ r -2/5 cf L. Spitzer, Jr., Physical Processes in the Interstellar Medium, ch. 9.1 12 Disk Exercises • Calculate the “typical” disk radii (distance from the star) sampled by different wavelengths: – – – (µm) = 1, 2, 4, 10, 100 L* = 0.2, 1, 5 Lsun Vary assumptions about temperature (T~r-1/2, T~r-2/5, etc.) What areas of a disk do different search techniques sample? • Set up a model calculation of an SED using the tools of the last few slides and show how the SED varies with different model parameters (rmin, rmax, q) – Use MathCad, Mathematica, C, or a similar program to make numerical calculations easy – Vary disk inclination to the line-of-sight 13 Physical Modification: Holes L* “hole” rmin ~ R* rmin Disk rmax nFn = 2pn Bn[T(r)] r dr rmin ~ 5 R* r SED from continuous “flat-spectrum” disk 100 min 5 R* hole in center nFn Star SED rmin ~ 50 R* (0.5 AU) hole in center (large) 10 To produce an observable flux deficit, the hole must be large, ~10x larger than the star 1 10 Wavelength (mm) 100 14 Inner holes produce flux deficits 34 Superheated surface layer with small grains produces infrared light. 32 31 30 “Black” interior produces mm-wave emission. GM Aur Flux deficit from interior hole 33 Log nFn (erg s-1) Interior hole Flared equilibrium disk Stellar blackbody Disk surface t<1 Disk interior t>1 29 1 100 10 Wavelength (mm) 1000 15 n Fn(Jy)x10 11 Evolution of structure LKHa332-20 1000 PIA 7.2 100 10 As disks age, the hole sizes should increase 1 0.1 1 10 100 (mm) CS Cha 1000 PIA 7.2 HR4796 n Fn (Jy)x10 11 100 10 1 Weinberger et al. 1999, ApJ Let, 525, L53 0.1 0.1 1 10 (m m) 16 100 Fomalhaut: Ring Emission Holland et al. 2003, ApJ, 582, 1141 17 Kalas et al. 2005, Nature, 435, 1067 Vega-type stars: Fomalhaut Dent et al. 2000, MNRAS, 314, 702 1000 µm grain radius Note inner hole 300 100 30 T = 40 K BB “Ring” rmin = 100 AU rmax = 140 AU Mgrains = 1.4Mmoon Figure 1: Best fit 10 µm = 1.1 These results indicate a typical grain is ~100 µm in size. The models assume fixed total grain mass. Figure 6: varying grain size 18 HD 4796 Modification 2: Gaps & Rings Weinberger et al. 1999 Gaps must be large to cause observable changes to the SEDs Fomalhaut rring ~ 130 AU ∆ring~ 25 AU 100 nFn r1 = 67, r2 = 150, Log(∆) = 0.35 Kalas, Graham, Clampin 2005 r1 = 50, r2 = 200, Log(∆) = 0.60 10 r2 ∆= r 1 1 r1 = 25, r2 = 400, Log(∆) = 1.20 10 Wavelength (mm) 100 19 Optically thin, dT/dr > 0 Emission features Chiang & Goldreich 1997, Ap. J., 490, 368. Superheated surface layer with small grains. Surface layer t1: dust emission features (face-on orientation). 33 log Ln (erg s-1) Optically thick interior cf Cohen & Witteborn 1985, Ap. J. 32 Stellar 31 Surface 30 29 Interior 1 10 100 Wavelength (mm) 1000 20 Silicate emission confirms t<1 atmospheres Fits: 1.2 µm pyroxene grains, CG97 model Top of atmosphere t11µm~1 t9µm~1 r, T(r) increasing Emission features indicate optically thin emission from in an atmosphere with vertically increasing temperature gradients Natta, Meyer, & Beckwith 2000, ApJ, 534, 838 21 10 mm emission: Mineralogy Natta, Meyer, & Beckwith 2000, ApJ, 534, 828. Grain sizes ~ 1 mm (from e) Some evidence for features at 8.5 and 11.3 mm: crystalline silicates e s10/smix DL silicates e= 0.84-2.2 1 mm 0.5:0.5 olivine/pyroxene 0.1 mm 0.3:0.7 olivine/pyrox. e= 10-21 e= 0.6-1.2 1.2 mm pyroxene 0.1 mm pyroxene 1.2 mm olivine 0.1 mm olivine Waelkens et al. 1996, A&A, 315, L245. 200 Comet Hale-Bopp 6 Oct 1996 Fn(Jy) 100 0 Foresterite is a "primordial" constituent of Solar dust HD 100546 200 Fn(Jy) Foresterite Mg2SiO4 100 PAH 0 10 20 30 Wavelength (mm) 40 24 HD 100546 - SWS and LWS : all components PAH PAH (7.8 µm) PAH (8.6 µm) PAH (6.2 µm) PAH (11.3 µm) 8 Hot & cold continuum Total 0 Crystalline forsterite Amorphous olivine -50 10 Malfait et al. 1998, A&A, 332, L25 [ OII ] (157.7 µm) Pf g Br a 6 4 Wavelength (µm) [ OI ] (63.2 µm) 2 H2O - ice (43.8 µm) PAH Crystalline pyroxene (40 µm) HD 100546 Stellar photosphere Hot continuum Cold continuum Total PAH 5 0 PAH (3.3-3.4-3.5 µm) Flux (Jy) 50 H2O - ice 10 150 100 Short wavelength part - SWS Br d FLUX (Jy) 200 15 Pf d 250 FeO Wavelength (µm) 100 25 Near- IR Disk Lifetimes Haisch, Lada, Lada 2001, ApJL, 553, L153. – 900 K – ≥1020 gm of dust – Inner disk (TBD) • Disk lifetime ~6 Myr • Principal uncertainty driven by NGC 2362 • Are outer and inner disk lifetimes the same? 100 Systematic NGC 2024 Trapezium 80 Fraction of JHKL Excess (%) • L-band (3.4 µm) light used as disk proxy Taurus IC 348 60 Cham I 40 tdisk ~ 6 Myr 20 0 NGC 2264 NGC 2362 0 2 4 6 Age (Myr) 8 10 26 How do we observe disk mass? Beckwith et al. 1990, AJ, 99, 924 Beckwith 1999, “OSPS”, p. 579. Fn ~ k0n2+ Td Md We want to observe where the disk is transparent (to see all the material) For long enough wavelengths ( > 200 mm), the dust t < 1. Fn ~ (Ad/D2) Bn(Td) (1 - e-t) Ad disk projected area D distance to source Td disk particle temperature tn optical depth at n Md mass of disk kn mass opacity (cm2 g-1) ~ (Ad/D2) kTdn2 tn ~ (Ad/D2) Tdn2 kn (Md/Ad) ~ D-2 Td n2 kn Md kn ~ k0 (n/n0) Md = 0.03 Msun Fn 1 Jy ( 2 D 100 pc ) ( 3 50 K 1.3 mm T ) 0.02 cm2 gm-1 k1.3mm 27 mm-wave continuum is easily seen 13CO 2-1 4.4-5.8 km s-1 HL Tau 1.3mm Continuum SII “ FWHM 1.4 Mundt et al. 1990, A&A, 232, 37. Koerner & Sargent 1995, Ap.SS., 223, 169 and unpublished data. 28 T(r) & S(r) govern where Fn originates Temperature: T(r) r rout rout Fn ~ D-2 Bn[T(r)] (1-e-t(r)) 2pr dr r in rin Fn ~ D-2 { Surface density: S(r) rout tn(r) k T(r) n2 knS(r) 2pr dr r in T(r) ~ r-q 3/4 < q < 1/2 S(r) ~ r-p 0<p<2 kn ~ ~2 n p = 3/2, q = 3/4 p = 1, q = 1/2 rout Fn ~ n2+k r1-q-p dr r ~ k0n2+r2-q-p in Fn(1 mm) ~ rin-1/4 Fn(1 mm) ~ rout1/2 29 Inner Parts May Have t >> 1 rout r1 rout Fn ~ Bn[T(r)] (1-e-t(r)) 2pr dr r in rin r1 Fn ~ k T(r) n2 2pr dr r (t > 1) in The radius at which the disk appears optically thick is a function of kn, hence wavelength. The changing ratio of optically thick/optically thin regions with wavelength offsets the changes from kn itself, thus causing a degeneracy of parameters (makes it difficult to derive uniquely.) rout + k T(r) n2 knS(r) 2pr dr r (t < 1) 1 Fn ~ T(r1) n2 pr12 + kn S(rout)T(rout) n2 prout2 30 Optical depth effects Andrews & Williams 2005, astro-ph 0506187 (June 2005) 1.0 0.8 Md(tn>1) Md 450 µm 850 µm 1.3 mm 0.6 0.4 0.2 10-5 10-4 10-3 10-2 0.1 1 Md (Msun) 31 Degeneracy of Parameters: mm-waves • Compare mm-wave spectral indices, , for opaque (t>> 1) and transparent (t«1) disks at ~ 1 mm – What are the limiting cases? • Estimate the relative contributions of optically thick and optically thin parts of a disk to mm-wave light – Assume a surface density law: S(r)~ r-p – Find the radius, rt(), where t() = 1 – What happens to relative contributions of thick/thin emission as wavelength varies? – Show how this degeneracy makes it impossible to derive the dust spectral index, , uniquely from an SED – How can one use spatial resolution to overcome this problem? 32 Disks can build planets Limit Solar Nebula 14 Taurus 12 Ophiuchus 10 Beckwith & Sargent Andre & Montemerle 8 6 4 2 0 0.0001 assumes gas/dust = 100 0.001 0.01 0.1 1 Mdisk (M) similar mass distribution for NGC 2071 by E. Lada 1998 but not Orion HST disks (E. Lada et al., Bally et al., unpublished) 33 Mass Evolution of Young Disks BSCG 1990, AJ., 99, 924. 1 0.1 MD M "Minimum" Solar nebula 0.01 0.001 Solar System planets 0.1 1 Age (Myr) 10 34 Disk Mass Andrews & Williams 2005, astro-ph 0506187 35 Distribution of Disk Radii: Orion Vicente & Alves 2005, astro-ph 0506585 (2005) 150 135 bright proplyds 14 pure silhouettes 100 a = -1.9 +/- 0.3 50 100 N N 20 50 10 5 0 218-354 0 400 800 Diameter (AU) 114-426 1200 100 200 400 Diameter (AU) 36 MM-waves interact with all atoms Particle size << wavelength coupling ~ - 1st order: size independent, wave sees every atom Conductors: “antenna” growth, absorption by free electrons Insulators: absorption by lattice resonances kn ~ n2 ~ -2 Lorentz “tail” kn ~ n2 ~ -2 plasma skin depth Fe, graphite Olivines (silicates): Mg2SiO4, [Mg,Fe]Si2O5 37 Absorption in Insulators Lattice resonances np2 g n e” = (n 2 - n2)2 + g2n2 0 log(e”) 0 Vibrational modes ~ 1 – 30 mm -2 s~ -4 8pa Im(e'') ~ n2 kn ~ s(n) / mp ~ n2 -6 2 1 0 log (n) -1 -2 long wavelengths 38 Particle Emissivity in Disks Beckwith & Sargent 1991, Ap. J., 381, 250. Mannings & Emerson 1994, MNRAS, 267, 361 DG Tau 10-12 nFn (W/m2) 10-14 10-16 0.01 nFn ~ n3 nFn ~ n5 Interstellar Dust 0.1 1.0 Wavelength (mm) Pebbles 10 39 Spectral Index: Fn ~ kn (Mdust/A) Bn(T) kn = k0 (n/n0) = -0.5 RY Tau =0 = 1 – Interstellar dust: = 2 – Planetesimals: = 0 – Observed: -0.5 < < 2 Later work by: Lay et al. 1994 (0.85 mm CSO-JCMT) Wilner et al. 2000, 2005 DL Tau = -0.2 • Opacity index Adams et al. 1990 Beckwith & Sargent 1991 Mannings & Emerson 1994 (Fn/ n2) x C = 1.8 0.1 GW Ori 0.01 "Galactic" 10-3 =1 Planck = 0 0.5 1 DG Tau HK Tau =2 10 2 1 Wavelength (mm) 40 Radio Wavelength Emissivity Natta et al. 2004, AA, 416, 179 See also: Andrews & Williams 2005, astro-ph 0506187 41 TW Hydra: 3.5cm dust emission • Very long wavelengths sensitive to centimeter-size grains • Must rule out synchrotron & free-free (plasma) emission • Large grains out to tens of AU • Assumed disk mass ~0.1Msun Wilner et al. 2005, ApJL, 626, L109 42 Spatially Resolved Spectra: TW Hydra Roberge et al. 2005, ApJ, 622, 1121 The scattered light from the disk is essentially gray from ~50 AU to ~150 AU. This result argues for relatively large (>1 µm) scattering particles 43 Numerical Models: TW Hydra star inner disk outer disk edge outer disk Calvet et al. 2002, ApJ, 568, 1008 44 Grain size does alter opacity Miyake & Nakagawa 1993, Icarus, 106, 20. amax n(a) ~ a-p kn (cm2 g-1) kn (cm2 g-1) p=4 1 p=3.5 p=3 p=2.5 p=2 100 mm Wavelength 10-2 10-4 compact spheres n(a) ~ a-3.5 1 mm 102 compact sphere amax = 1 cm 1 cm 1 mm 100 mm 10-6 1 cm Wavelength 45 Interstellar opacities are uncertain Henning, Michel, & Stognienko 1995, Plan. & Sp. Sci. 100 kn (cm2 g-1) 10 =1 1 0.1 Draine & Lee (1984) dense regions =2 diffuse regions circumstellar 0.05 0.1 0.2 0.5 1 2 Wavelength (mm) 46 Particles grow quickly Coagulation times (yr) Weidenschilling, S. J. 1988, Meteorites & Early Solar Sys. Chokshi et al. 1993, Ap. J., 407, 806, Blum et al. 1999, EM&P, 80, 285 (lab experiments) 105 z/z• Turbulence M=0.01 104 Radial Drift z=0 103 Settling d=fr z=c/W d=fr 102 10 a/a• Turbulence M=1/3 Radial Drift z=0 1 ISM grain sizes YSO ages 10-4 10-2 1 102 Particle size (cm) Calculations for 1 AU orbits 104 106 47 Disk dynamics: what is the velocity field? Keplerian velocity field is clear signature. Velocity gradients & gravity Pure Keplerian rotation r q Circular disk viewed at high inclination angle v(r) Pure radial infall v f(r) = GM r -1/2 vr(r) =2GM r -1/2 vr(r) = 0 Major axis Dx vf(r) = 0 Minor axis Dx v(r) velocity gradient Dutrey et al. 1994, A&A, 286, 149. Saito et al. 1995, Ap. J., 453, 384 velocity gradient Hayashi et al. 1993, Ap. J. Lett., 418, L71. 49 Gas Dynamics in HL Tau: mostly infall 4.4 – 5.8 km s-1 HL Tau HL Tau shows an infalling disk. Hayashi et al. 1993, Ap. J. Lett., 418, L71. Koerner & Sargent 1995, Ap.SS., 223, 169 and unpublished data. 6.2 – 7.6 km s-1 13CO 8.0 – 9.4 km s-1 2-1 HST image 64" 1.4” FWHM 2000 AU 50 GG Tau system: a rotating disk Dutrey et al. 1994, A&A, 286, 149 13CO J=1-0 6.5 6.93 6.29 6.07 7.14 6.71 5.86 5.44 5.22 7.35 5.65 7.56 5.01 4.8 8.20 7.78 7.99 Model calculation 7.19 6.77 6.55 6.34 6.13 4.85 5.49 6.98 5.07 5.70 5.28 5.92 7.40 7.83 8.25 8.04 7.62 Observed velocity map 51 To see real* disks, need high resolution HL Tau 13CO Koerner & Sargent 1998 McCaughrean & O’Dell 1996 183-405 Solar System 114-426: "Largest disk" 400 AU *according to Shu (1998, ASI, public communication) HH 30 Burrows et al. 1996 52 Future Observations • Use high spatial resolution to break degeneracies – ALMA: resolution of mm-wave emission to tens of AU – VLT/Keck/LBTI: resolution of thermal IR emission to ~1 AU • Use spectral resolution to analyze disk atmospheres and grain/gas composition – Spitzer spectra of disks – SOFIA spectra in far infrared – ALMA for molecular abundances in disk interiors on few x 10 AU scales 53 van den Ancker 2000, astro-ph 0005060 H2 0-0 S(5) H2 0-0 S(3) H2 0-0 S(4) Ground-based spectroscopy call some of these detections into question (envelope/ISM emission?) 54 H2 in the GG Tau Disk Thi et al. 1999, Ap.J.Lett., 521, L63 55 Disk boundaries appear to be sharp O’Dell & Wen 1992, Ap.J., 387, 229. 0.55 µm 1.10 µm 1.7" Inner S(r) flat (~r-1) Sharp outer boundary 2.9" 1.60 µm 2.0 µm POL McCaughrean et al. 1998, ApJL, 492, L157. 56 114-426 Achromatic extinction 114-426 Interpretation: the particles have grown to pebbles or rocks. Throop et al., Science, April, 2001 Keck interferometer observations at 2 µm Eisner et al. 2005, ApJ, 623, 952 For AS 207A, V2508 Oph, and PX Vul, simple flat accretion disk models suggest much smaller sizes (when fitted to SEDs) than those determined interferometrically. Models incorporating puffed-up inner walls and flared outer disks provide better fits to our V2 and SED data than the simple flat disk models. This is consistent with previous studies of more massive Herbig Ae stars (Eisner et al. 2004; Leinert et al. 2004) and suggests that truncated disks with puffed-up inner walls describe lower mass T Tauri 59 stars in addition to more massive objects. Summary Lessons • Our understanding of disk atmospheres is compatible with observed SEDs • We can measure sizes, temperature distributions, masses, and some features (holes, gaps) with reasonable certainty • Parameter degeneracies that affect interpretations may be resolved with high angular resolution – ALMA for mm-wave disk “interiors” – IR-interferometry for inner disks, holes, and surfaces • Spectra and SEDs show good evidence for: – – – – Grain growth leading to small rocks Constituents similar to proto-Solar nebula Gas entrained with dust Disks bound to stars 60