Radiative Transfer Models Radiative Transfer Models of Dusty YSOsof 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)

t < 104 yrs

(Shu, Adams & Lizano 1987; Lada 1987)

Collapse -- Class 0

SED: T~30 K

t ~105 yrs

(Shu, Adams & Lizano 1987; Lada 1987)

Late Collapse -- Class I

SED slope, > 0, for2 < < 22 m

t ~106-107 yrs

Accretion Disk Stage -- Class II

SED slope, 0 > > -2

2 < < 22 m

t > 107 yrs

Debris or no Disk -- Class III

SED slope, < -22 < < 22 m

Massive Star Formation -- Competing theories

Analogous to low-mass (McKee & Tan 2003)

Mergers in dense clusters (Bonnell & Bate 2002)

0.5 pc 5 pc

Disk formation, collimated outlfows

Disk disruptionless 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 mnew project, MIPSGAL, will get 24, 70, 160 !(PI: Sean Carey)

• b=[-1,+1], |l|=10-65GLIMPSE II: |l|<10 !

• Angular resolution <2”PI: Ed Churchwellwww.astro.wisc.edu/glimpse

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+0.01-2-4

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

NIR 3-color (Padgett et al. 1999)

2-D RT models

Spitzer IRAC predictions

J-H-K [3.6]-]-[4.5]-[8.0] [24]-[70]-[160]

LateClass 0

Class I

(Whitney et al. 2003b)

IRAS 04368+2557

2MASS J-H-K Spitzer IRAC [3.6]-[4.5]-[8.0]

Low-mass

Analog?

Massive protostars

L*=40000T*=4000M*=17.5M=10-4

Md=1

Embedded Massive YSO

i Av

0 6

60 53

90 3e4

.

Embedded Low-Mass YSO

i Av

0 6

60 50

90 4e6

L*=1.1T*=4000M*=1M=10-5

Md=0.05

.

Massive Star+Disk

i Av

0 0

60 0.1

90 3e3

L*=40000T*=30000M*=17.5Md=0.1

Low-Mass Star + Disk

i Av

0 0

60 0.1

90 3e5

L*=40000T*=4000M*=17.5Md=0.01

Effect of Bipolar Cavity on Colors

• Models without cavities (e.g., 1-D) will underestimate evolutionary stage!

Near-IR IRAC

No cavity

cavity

Massive Stars: The need for 2-D, 3-D models

>100 m: no<100 m: yes

(van der Tak et al. 2000)

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)

Indebetouw et al. (2005)

IRAC MIPS

3-D clumpy modelsNIR

Clumpy model SEDs

Average Smooth (1-D) model

200 sightlines from 1 source (grey lines)

Fits to Data: G5.89-0.39

Best smooth modelBest clumpy modelGrey lines show other sight lines

Mid-IR data: Faison et al. (1998)

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

Smooth model

200 sightlines from 1 clumpy model

All the UCHII Observations

Grey lines: G5.89 best model

Mid-IR data: Faison et al. (1998)

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 Spectral Index (2-20 m)

I >0

II -2 - 0

III <-2

Stage Envelope Infall rate (Msun/yr/

M*1/2)

Disk mass

(M*)

I >2x10-6

II <2x10-6 >1x10-7

III 0 <1x10-7

Synthetic cluster Color-color plots -- IRAC

• D=4 kpc (RCW 49)

• GLIMPSE low/high sensitivity limits

• “Stage I”• Stage II• Stage III• allstars

Reddening line

• Classification spectral index was defined over wavelength range of 2-22 m (Lada 1987).

• What happens for 2-I?

Class vs Stage

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

RCW 49

• 96.6% of sources fit with stellar atmospheres

• 3% well-fit with YSO models

Class I source

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 FittedMass

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