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Radiative Transfer Models of Dusty YSOs Barbara Whitney (Space Science Institute), Tom Robitaille & Kenny Wood (St. Andrews University), Jon Bjorkman (U. Toledo), Remy Indebetouw (U Va), Ed Churchwell (UW) Outline • Background and Motivation – Large Volumes of mid-IR data now available from Spitzer Space Telescope, ground-based observatories and future space-based • e.g., the GLIMPSE survey of the inner Galactic Plane – Unanswered questions • • • • 2-D Models 3-D Models (high mass) Model Grid & Fitter Answers to questions? A few, maybe Canonical View of Low-Mass Star Formation Dark cloud cores • Free-fall times short, yet star formation efficiency low (Zuckerman & Evans 1974) • Conditions for support/collapse – Magnetic fields/Ambipolar diffusion (Shu 1977; Mouschovias 1976; Nakano 1976) – Supersonic turbulence/local collapse (Mac Low & Klessen 2004) Collapse -- Class 0 t < 104 yrs SED: T~30 K (Shu, Adams & Lizano 1987; Lada 1987) Late Collapse -- Class I t ~105 yrs SED slope, > 0, for 2 < < 22 m (Shu, Adams & Lizano 1987; Lada 1987) Accretion Disk Stage -- Class II t ~106-107 yrs SED slope, 0 > > -2 2 < < 22 m Debris or no Disk -- Class III t > 107 yrs SED slope, < -2 2 < < 22 m Massive Star Formation -- Competing theories 0.5 pc 5 pc Analogous to low-mass (McKee & Tan 2003) Mergers in dense clusters (Bonnell & Bate 2002) Disk formation, collimated outlfows Disk disruption less collimated flows Questions • What are the global properties of star formation in the Galaxy? (GLIMPSE) – Star formation rate and efficiency – Timescales for evolution • How do massive stars form? – Do they form planets? – Do low-mass stars in the vicinity of massive stars form planets? • What supports clouds against collapse? Galactic Legacy Infrared Mid-Plane Survey Extraordinaire • One of five Spitzer Legacy programs – No proprietary period + enhanced data products • 4 wavelength bands: 3.6, 4.5, 5.8, 8 m new project, MIPSGAL, will get 24, 70, 160 ! (PI: Sean Carey) • b=[-1,+1], |l|=10-65 GLIMPSE II: |l|<10 ! PI: Ed Churchwell www.astro.wisc.edu/glimpse • Angular resolution <2” GLIMPSE Data Products* • GLIMPSE Point Source Catalog – Highly reliable (>99.5%) -- 31 million sources – Magnitude limits in 4 bands: 14.2, 14.1, 11.9, 9.5 • GLIMPSE Point Source Archive – Less reliable but more complete -- 48 million sources – Magnitude limits: 14.5, 14.0, 13.0, 11.5 • Cleaned mosaic images – 1.1x0.8 degrees (0.6” pixels) – 3x2 degrees (1.2” pixels) – Southern hemisphere available in Dec. (all Spitzer “BCD” images and mosaiced AORs are available) *Available at http://www.astro.wisc.edu/glimpse/glimpsedata.html Example of cluster formation? tens of pc Class 0 Source? 324.72+0.34 1-2-4 J-H-K 320.23-0.29 Ch 1,2,4 2MASS 332.73-0.61 317.35+0.0 1-2-4 3x2 deg Radiative Transfer Models • Monte Carlo method • 3-D spherical polar grid • Calculates radiative equilibrium of dust (Bjorkman & Wood 2001) • Non-isotropic scattering + polarization • Output: images + SEDs (+ polarization) • Not included: PAHs, stochastic heating of small grains, optically thick gas emission (Whitney et al. 2003a,b, 2004) 2-D YSO Model Geometry • Rotationally-flattened infalling envelope (Ulrich 1976) • Flared disk • Partially evacuated outflow cavity AV through Envelope & Disk Edge-on Pole-on Low-Mass Protostar: IRAS 04302+2247 L=0.5 Lsun 2-D RT models NIR 3-color (Padgett et al. 1999) Spitzer IRAC predictions J-H-K [3.6]-]-[4.5]-[8.0] [24]-[70]-[160] Late Class 0 Class I (Whitney et al. 2003b) IRAS 04368+2557 2MASS J-H-K Spitzer IRAC [3.6]-[4.5]-[8.0] Lowmass Analog? Massive protostars Embedded Massive YSO L*=40000 T*=4000 M . *=17.5 M=10-4 Md=1 i Av 0 6 60 53 90 3e4 Embedded Low-Mass YSO L*=1.1 T*=4000 M . *=1 -5 M=10 Md=0.05 i Av 0 6 60 50 90 4e6 Massive Star+Disk L*=40000 T*=30000 M*=17.5 Md=0.1 i Av 0 0 60 0.1 90 3e3 Low-Mass Star + Disk L*=40000 T*=4000 M*=17.5 Md=0.01 i Av 0 0 60 0.1 90 3e5 Effect of Bipolar Cavity on Colors Near-IR IRAC No cavity cavity • Models without cavities (e.g., 1-D) will underestimate evolutionary stage! Massive Stars: The need for 2-D, 3-D models (van der Tak et al. 2000) >100 m: no <100 m: yes 3-D models • Motivation – UCHII regions: Previous 1-D models of mid-IR spectra can’t fit full SED: give too deep 10 m absorption for a given FIR flux, and too steeply rising SED in NIR/MIR (Faison et al. 1998, van der Tak et al. 2000) Model Ingredients • O star in a molecular cloud (massive stars heat up large volumes) • Use fractal ISM structure, D=2.6 (Elmegreen 1997) • Average radial density profile is varied from r0 to r-2.5 • Smooth-to-clumpy ratio is varied from 3% to 100% (Indebetouw et al. 2005) 3-D clumpy models NIR IRAC MIPS Indebetouw et al. (2005) Clumpy model SEDs Average Smooth (1-D) model 200 sightlines from 1 source (grey lines) Fits to Data: G5.89-0.39 Mid-IR data: Faison et al. (1998) Best clumpy model Grey lines show other sight lines Best smooth model G5.89 Model parameters Tstar 41000 K L 2.54x105 Rin 0.0001 pc Rout 2.5 pc Menv 50000 Av_ave 131 Smooth/Clumpy 10% Radial density ave~r0 Fractal dimension 2.6 Color-color plots 200 sightlines from 1 clumpy model Smooth model All the UCHII Observations Mid-IR data: Faison et al. (1998) Grey lines: G5.89 best model 3-D Model summary • UCHII regions may be O-B stars still embedded in their natal molecular clouds but not surrounded by infalling envelopes. • Bolometric flux of clumpy models varies by a factor of 2 lower and higher than the true luminosity depending of viewing angle (Indebetouw et al. 2005) 2-D/3-D Model grid + Data fitter • Large Grid of YSO Models (20,000) x 10 inclinations = 200,000 SEDs! 6 weeks of cpu time on about 50 processors • Linear Regression Fitter to find best model to fit an observed SED – Models are convolved with any broadband filter of interest – First tries to find good fit from a grid of stellar atmosphere files – Simultaneously fits foreground AV – Can process the GLIMPSE survey in about a week (Robitaille et al. 2005) Grid Creation • Sample stellar mass and age (logarithmically) • calculate T* and R* from evolutionary tracks (Bernasconi & Maeder 1996; Siess et al. 2000) Grid Parameters 198,680 SEDs Relating Observed Class to Model “Stage” Class I Spectral Index (220 m) >0 II -2 - 0 III Stage Envelope Infall rate (Msun/yr/ M*1/2) I >2x10-6 Disk mass (M*) II <2x10-6 >1x10-7 III 0 <1x10-7 <-2 Synthetic cluster Color-color plots -IRAC Reddening line stars • D=4 kpc (RCW 49) • GLIMPSE low/high sensitivity limits • “Stage I” • Stage II • Stage III • all Class vs Stage • Classification spectral index was defined over wavelength range of 222 m (Lada 1987). • What happens for 2-I? Motivation for Fitter • Fit as many datapoints as available simultaneously • Unbiased (except for grid choices) -- shows all fits to a given dataset – Estimates uncertainties • Estimates foreground AV (Robitaille et al. 2005) Fitter results on a single source GLIMPSE Empty Field • 99.6% of sources fit with stellar atmospheres • 0.4% evolved stars, bad data or YSOs? RCW 49 Class I source RCW 49 • 96.6% of sources fit with stellar atmospheres • 3% well-fit with YSO models IC348 Mass histogram • “Known” IMF (using prior information on stellar parameters) • Data from Lada et al. (2005) IC348 Mass histogram • Based on Model Fitter Only RCW 49 Synthetic Mass histogram • Sampled masses from grid using Salpeter IMF (flatter slope below 0.5 Msun) • Sampled ages using Taurus ratios (Kenyon & Hartmann 1995) • Apply GLIMPSE sensitivy limits RCW 49 Fitted Mass histogram • Use model fitter to determine masses Applications of Grid & Fitter • Study Global properties of star formation in Galaxy – Star formation rate, lifetimes of evolutionary states, IMF – A high star formation efficiency argues for turbulent cloud support (vs. magnetic) • Search for disks around massive stars – Adds further credence to accretion model for high-mass star formation – Disks form planets …applications • Study low-mass star formation in vicinity of high-mass – May be more common mode of star formation (Hester & Desch 2004) – Disk lifetimes, sizes • 3-D extinction map • Galactic structure – 80% of stars are K giants – Fitter can distinguish gravity (I.e., giants/MS) Future Work • Radiative Transfer – Add PAHs, stochastic heating of small grains • Grid and fitter will be publicly available in 2006 • RT codes available at http://gemelli.spacescience.org/~bwhitney/codes