Where, Exactly, do Stars Form? (and how can SOFIA help with the answer) Alyssa A. Goodman Harvard University Astronomy Department photo credit: Alves, Lada & Lada
On a galactic scale Star Formation=Column Density Threshold + Schmidt Law Kennicutt 1989 Kennicutt 1998
Where, exactly, do stars form? Which Clouds form stars? The Spectral Correlation Function/Gravity What's required to form a star? Coherence in Dense Cores/Dissipation of Turbulence Connecting continuum & spectral line maps Help from SOFIA
Galaxy Star Formation Stars time Young Stellar Object +Outflow Which gas takes this step? "Velocity Coherent" Dense Core Self-Similar, Turbulent, "Larson's Law" Clouds (a.k.a. GMC or Cloud Complex)
Spectral-Line 1 Maps of Molecular Clouds Learning More from Too Much Data 1950 1960 1970 1980 1990 2000 10 8 Product 10 7 10 4 (S/N)*N pixels *N channels 10 6 10 5 10 4 10 3 N channels S/N N pixels 10 3 10 2 10 1 N channels, S/N in 1 hour, N pixels 10 2 10 0 1950 1960 1970 1980 1990 2000 Year 1 radio
The Spectral Correlation Function Figure from Falgarone et al. 1994 Simulation
How the SCF Works Measures similarity of neighboring spectra within a specified beam size lag & scaling adjustable signal-to-noise accounted for See: Rosolowsky, Goodman, Wilner & Williams 1999; Padoan, Rosolowsky & Goodman 1999.
Goals of SCF Project Develop sharp tool for statistical analysis of ISM, using as much data of a data cube as possible Compare information from this tool with other tools (e.g CLUMPFIND, GAUSSCLUMPS, ACF, Wavelets), applied to same cubes Incorporate continuum information Use best suite of tools to compare real & simulated ISM Adjust simulations to match, understanding physical inputs Develop a prescription for finding star-forming gas
Antenna Temperature Map greyscale: T A =0.04 to 0. 3 K Raw SCF Map Application of the SCF Data shown: C 18 O map of Rosette, courtesy M. Heyer et al. greyscale: while=low correlation; black=high Results: Rosolowsky, Padoan & Goodman 1999
Antenna Temperature Map greyscale: T A =0.04 to 0. 3 K Normalized SCF Map Application of the SCF Data shown: C 18 O map of Rosette, courtesy M. Heyer et al. greyscale: while=low correlation; black=high Results: Rosolowsky, Padoan & Goodman 1999
SCF Distributions Normalized C 18 O Data for Rosette Molecular Cloud Randomized Positions Original Data
Unbound High-Latitude Cloud Prelimary Insights from the SCF Rosolowsky, Goodman, Williams & Wilner 1999 Self-Gravitating, Star-Forming Region No gravity, No B field No gravity, Yes B field Yes gravity, Yes B field
Which one of these is not like the others? Change in Mean SCF with Randomization 1.0 0.8 0.6 0.4 0.2 0.0 0.0 Increasing Similarity of Spectra to Neighbors SNR H I Survey Rosette C 18 O Peaks G,O,S L134A 12 CO(2-1). MacLow et al. L1512 12 CO(2-1) Falgarone et al. 0.2 0.4 0.6 0.8 1.0 1.2 Mean SCF Value Rosette C 18 O Rosette 13 CO Rosette 13 CO Peaks HCl2 C 18 O L134A 13 CO(1-0) Pol. 13 CO(1-0) HCl2 C 18 O Peaks HLC Increasing Similarity of ALL Spectra in Map
Can the SCF describe gas physically? Change in Mean SCF with Randomization 1.0 0.8 0.6 0.4 0.2 0.0 0.0 Increasing Similarity of Spectra to Neighbors 0.2 0.4 G,O,S Falgarone et al. 0.6 Rosette C 18 O Peaks MacLow et al. Mean SCF Value 0.8 Rosette C 18 O Rosette 13 CO Rosette 13 CO Peaks HCl2 C 18 O HCl2 C 18 O Peaks 1.0 Increasing Similarity of ALL Spectra in Map 1.2
Q. Can the SCF find Star-Forming Gas? A. Empirically, but that s not good enough. Helping the SCF Physical training? Incorporate coherence ideas Add CONTINUUM information
Coherent Cores: Islands of Calm in a Turbulent Sea "Rolling Waves" by KanO Tsunenobu The Idemitsu Museum of Arts.
Types of Line width-size Relations Type 4: Single Cloud Observed in a Single Tracer Non-thermal Line Width Type 4 Type 4 Observed Size Gives information on power spectrum of velocity fluctuations. See Barranco & Goodman 1998; Goodman, Barranco, Heyer & Wilner 1998.
] Evidence for Coherence 1 1 1 9 8 IRAM 30-m C 17 O (1-0) 9 8 IRAM 30-m C 18 O (2-1) 9 8 IRAM 30-m C 34 S (2-1) 7 7 7 6 6 6 v [km s -1 ] 5 4 v [km s -1 ] 5 4 v [km s -1 ] 5 4 v [km s -1 ] 3 3 3 Type 4 slope 2 2 2 2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 9 1 4x10 1 T A [K] appears 0 5 6 T A [K] to T A [K] 1 1 1 9 9 9 17 18 8 FCRAO C O (1-0) decrease with O (1-0) 8 FCRAO C O (1-0) 8 FCRAO C 34 S S (2-1) (2-1) 7 density, 7 7 as predicted. 6 6 6 5 5 5 4 4 4 v [km s -1 ] v [km s -1 ] 3 3 3 2 2 2 2x10-1 3 4 5 6 6 7 8 9 0.1 2 3 4 5 6 7 8 9 1 2 0.1 2x10-1 3 4 T A [K] T A [K] T A [K] 10 1 9 "Radius" from Peak [pc] 1 0.1 0.01 1 9 3 2 "Radius" from Peak [pc] 0.1 9 8 7 6 5 TMC-1C, NH 3 (1, 1) 4 3 "Radius" from Peak [pc] 8 7 8 7 v NT =(0.20±0.02)T -0.11±0.07 A 6 6 v NT [km s -1 5 4 v NT [km s -1 ] 5 4 v NT [km s -1 ] 3 TMC-1C, OH 1667 MHz -0.7±0.2 v NT =(0.64±0.05)T A 3 2 2 2 3 4 5 6 7 8 9 T A [K] 1 2 3 6 7 8 9 0.1 Goodman, Barranco, Heyer & Wilner 1998 2 3 4 5 6 7 8 9 T A [K] 1 T A [K]
The Latest Evidence for Coherence N 2 H + : Coherence in the Ionized Gas TMC-1C 0.7 200 0.6 N 2 H + FCRAO 0.35 0.4 100 0.5 0.3 0.5 0.4 0.45 0.35 v [km s -1 ] 0.5 0.4 0.45 0 0.5 0.3 0.4 0.35 0.3 0.2-100 0.1 0.1 N 2 H + Thermal Width 0.2 0.3 0.4 0.5 0.6 0.7 100 0-100 -200-300 T A [K] Goodman, Arce, Caselli, Heyer, Williams & Wilner 1999
Coherent Dense Core ~0.1 pc (in Taurus) Coherent Core; N~R 0.9 Chaff ; N~R 0.1
Much molecular cloud material is chaff Bertoldi & McKee 1992
The Cause of Coherence? Most likely suspect: Loss of magnetic support due to low ionization fraction in core. (Scale gives clues.) Interesting question raised: Interesting question raised: What causes residual non-thermal line width? 3D MHD simulation of Ostriker, Gammie & Stone (1998) No ambipolar diffusion yet...
Connecting "Continuum" & "Spectral-line" Maps "Continuum"=no velocity information extinction maps, far-ir and sub-mm dust emission (SOFIA/HAWC) "Spectral Line"=velocity information primarily mm- and sub-mm maps with high (<<1 km/s) velocity resolution (Note: far-ir velocity resolution still coarse ~10 km/s)
IRAS 100-micron Image "Continuum" Information 1.3 mm map from Motte, André & Neri 1998
"Continuum" Information 1.3 mm map from Motte, André & Neri 1998
Keep in Mind...Warm Dust DOMINATES at 100 µm Wavelength [cm] 10-8 10-10 100 10 1 0.1 1 mm 0.01 100 µm 0.001 ] -1 B ν [erg sec -1 cm -2 Hz -1 ster 10-12 10-14 10-16 10-18 Pure Blackbodies 5e-16 1e-16 2e-17 30 K 100 K 7e-13 2e-14 7e-19 10-20 Emissivity-Weighted β=1.5 Normalized @ 10 14 Hz 10 K 10 8 10 9 10 10 10 11 10 12 10 13 10 14 Frequency [Hz]
"Continuum" Information Clumps w/in Cores have stellar-like IMF. Motte, André & Neri 1998
Connecting "continuum" & spectral line maps: Help from SOFIA =single pixel =array 50 K Dust 10 K Dust =mid-high resl n. spectroscopy 158 µm
Connecting "continuum" & spectral line maps: Help from SOFIA = Resolution SOFIA SOFIA Resolution at 100 µm >10x better than IRAS >3x better than SIRTF µ Wavelength (µm) SOFIA Sensitivity at 100 µm >10x better than IRAS >10x worse than SIRTF SOFIA Wavelength (µm)
Connecting "continuum" & spectral line maps: Help from SOFIA High-resolution of HAWC observations will enable best-yet far-ir column-density maps, with dust temperatures--and will NOT be superseded by SIRTF Spectral and/or SED-style observations with ~all other instruments will allow for unprecedented sensitivity in young stellar censuses (masses, temperatures, ages)
Connecting "continuum" & spectral line maps: The Dream Column Density information further constrains SCF-like observation/simulation matching Refined Models can predict stellar IMF output, and propagate it in time, for comparison with YSO census
What should you do now? Go talk to this guy, and he ll tell you all about great new maps of really big outflows, and what the flows do to the ISM... Héctor Arce