stellar rotation: a probe of star-forming modes and initial conditions? sidney c. wolff and stephen...
TRANSCRIPT
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Stellar Rotation:
A Probe of Star-Forming Modes and Initial Conditions?
Sidney C. Wolff and Stephen E. StromNational Optical Astronomy Observatory
(With collaborators Luisa Rebull, Kim Venn, and REU students David Dror and Laura Kushner)
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Motivation
• Address two key questions:– Do high and low mass stars form in the same way?
– What role do initial conditions and environment play in determining
outcome stellar properties?
• Why do we care:– Answering these questions is fundamental to developing a predictive
understanding of star-formation
– Knowing what kinds of stars form under what kinds of conditions is
key to understanding galactic evolution
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Roadmap
• Summary of the current star-formation paradigm
– Magnetospherically-mediated accretion (MMA)
• What accounts for the distribution of stellar masses?
– Can formation via MMA explain how stars of all mass form?
– What about the role of environment?
• Confronting MMA assumptions with observations
• Can observations of stellar rotation provide insight?
– Explaining observed trends in J/M vs M
– Exploring effects of environment on initial angular momenta
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The Current Paradigm
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Infalling envelope
Forming the Star-Disk System
Stellar seedAccretion Disk
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Solving the Angular Momentum Crisis
Wind/JetRotating accretion disk
Accreting material Forming star
Infalling gas/d
ustremoves angular momentum
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What Accounts for the Distribution of Stellar Masses?
1. Stellar mass reflects initial core mass
2. Stellar mass reflects core sound speed
3. Hybrid scenarios that invoke environment: Low M stars form from cores spanning a range in initial conditions
High M stars form via mergers or competitive accretion
Possibilities:
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What Accounts for the Distribution of Stellar Masses?
1. Stellar mass reflects initial core mass Test: Compare core mass distribution with IMF
Question: How do clumps spanning the full range of potential outcome masses all form stars within ~ 1 Myr ?
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What Accounts for the Distribution of Stellar Masses?
2. Stellar Mass Reflects Core Sound Speed
– M* ~ dM/dt x t
– dM/dt ~ a3 / G; a = sound speed
– Resulting stellar mass depends on a ~ (vth2 + vturb
2)1/2
– Implicit assumption: core accretion halted by outflow
– NB: In higher density environments, theory predicts
higher turbulent speeds, thus higher core accretion rates
• Does this lead to a higher proportion of high mass stars?
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What Accounts for the Distribution of Stellar Masses?
2. Stellar Mass Reflects Core Sound Speed
Tests:
— Compare core dM/dt with mass of the embedded star
— Use the location of the stellar birthline to search for
mass-dependent core accretion rate
— Search for differences among emerging IMFs in
differing star-forming environments
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Testing M* ~ Core Sound Speed:Direct Observations
• Select Class I sources showing a range in Lbol
• Determine dM/dt ~(a3/G) from high resolution (R ~ 105) spectroscopy
of molecular absorption features observed against star-disk system
• Determine spectral type of embedded forming star via R ~ 103
spectroscopy of scattered light emerging from walls of wind-driven
cavity
• Determine whether there is an M* vs dM/dt correlation
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Example: The BN Object
• Scoville et al. (1983) used CO (1-0) to probe T[r], [r], v[r] along the line of site to the BN object (Lbol ~ 104 Lsun)
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Testing M* ~ Core Sound Speed:Location of Birthline
-0.5
0.5
1.5
2.5
3.5
4.5
5.5
6.5
3.53.73.94.14.34.54.7
log Teff
log L/Lsun
ZAMS
Birthline for 10^-5 Mo/yr
Birthline 10^-4 Mo/yr
Birthline: 10^-4 Msun/yr
Birthline: 10^-5 Msun/yr
ZAMS
Location of birthline reflects the accretion rate(Palla and Stahler)
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500,000 Yr Isochrones forDifferent Accretion Rates
-0.5
0.5
1.5
2.5
3.5
4.5
5.5
6.5
3.53.73.94.14.34.54.7
log Teff
log L/Lsun
ZAMS
Isochrone: 5x10^5 yrs
Isochrone: 5x10^5 yrs500,000 Year Isochrones
ZAMS
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Testing M* ~ Core Sound Speed:IMF vs Environment
• If higher density regions are characterized by higher sound speeds, they should form relatively more high mass stars
• No persuasive evidence to date
Miller-Scalo
ONC: Hillenbrand and Carpenter, 2000
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What Accounts for the Distribution of Stellar Masses?
2. Stellar Mass Reflects Core Sound Speed
Issues and Questions:
— Accounting for N(M) this way requires a feedback
mechanism involving:
— An energetic outflow that disperses the envelope
— Outflow momentum proportional to infall rate
— Can this account for the final mass absent any
constraints on the initial core mass?
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Possible Feedback Mechanism
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What Accounts for the Distribution of Stellar Masses?
3. Hybrid mechanism involving environment• Stars with M < 20 Msun form via magnetospherically-
mediated accretion
• Stars with M > 20 Msun may form via an alternative path
– Mergers? Competitive accretion?
– Possibly explains why high mass stars are found in dense regions
Credit M. Bate 2004
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What Accounts for the Distribution of Stellar Masses?
Cha I Complex ONC
• Simulations (e.g. Bate; Bonnell) are promising
• No direct observational tests have been made
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What Accounts for the Distribution of Stellar Masses?
Summary
– Evidence for M* ~ Mcore is circumstantial
• Arranging for rapid (t < 1 Myr) formation at all masses a problem
– Testing M* ~ dMacc/dt
• Is possible from R ~ 105 mid-IR spectroscopy
• Is not possible from birthline observations
– Searching for effects of environment on emerging IMF
• Reveals no significant differences over the density range investigated
• Observations of much higher density clusters required
• Such observations await AO-corrected observations on large telescopes
– No direct test of whether high mass stars form differently
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Can Stellar Rotation Provide More Clues ?
• If stars of all mass are formed via magnetospherically-
mediated accretion (MMA):
– stellar rotation speed ~ core dMacc/dt
• If high M stars form from cores with higher dMacc/dt, then
such stars should exhibit higher rotation speeds
– If dMacc/dt is larger in higher density environments, rotation speeds
should be higher as a consequence
• If high M stars form via mergers or competitive accretion,
their rotation properties (J/M) could differ from low M stars
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Magnetospherically-Mediated Accretion (MMA)
Star and disk ‘locked’ at the co-rotation radius where Pdyn = Pmagnetic
disk = star
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High [dMacc/dt] or low B Low [dMacc/dt] or high B
Rapid Rotation Slow Rotation
GM 5/7 (dMacc/dt) 3/7 B -6/7 R -18/7
Dependence of Rotation on dMacc/dt: Basic Concepts (Konigl Model)
Shu + Najita model invokes wind to carry away stellar angular momentum
Dependence of on B, dM/dt and R is similar
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Testing MMA: Basic Processes and Consequences for Stellar Rotation
• Determine if MMA occurs for stars of all masses
– Search for evidence of magnetic fields
• Direct (Zeeman splitting; circular polarization measurements)
• Indirect (magnetically-driven stellar activity)
– Search for evidence of magnetospheric ‘funnel flows’
• Inverse P-Cygni profiles
• Rotationally-modulated emission at base of the funnel flow
– Search for evidence of ‘disk-locking’
– Determine whether observed rotation vs. mass pattern finds
straightforward interpretation in the context of MMA
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Testing MMA Assumptions
• Magnetic Field measurements: Zeeman Splitting
– In solar-like (M < 2 Msun) PMS stars, measurements yield B ~ 2 kG
– In more massive stars, Zeeman splitting unobservable (rapid rotation)
Johns-Krull et al. 1999
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Testing MMA Assumptions
• Magnetic Field measurements (higher mass stars): circular polarization
– Magnetic fields induce circular polarization in magnetically sensitive lines
– Observable even for lines in which rotational broadening >> Zeeman splitting
– However, the residual signals are small and require S/N ~ 1000 spectra
– Measurements provide net magnetic field
• Complex field geometries can produce small net signals despite high local B
– Studies of ~ 10 Herbig Ae/Be stars (accreting PMS stars with masses 2-10 Msun)
yield detections and upper limits of B < 200 G
• Smaller by a factor of 10 compared to T Tauri stars
• However, cTTS with observed B ~ 2 kG (Zeeman splitting) show B ~ 100 G from
circular polarization measurements
• Probably the result of complex surface field geometries
– Conclude: no reliable limits on surface fields for stars with M > 2 Msun
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Testing MMA Assumptions
• Alternative magnetic field indicator: coronal activity
– Low mass (M < 1 Msun) PMS stars all exhibit strong coronal x-ray emission
• Lx / Lbol ~ 10-3 likely results from magnetic activity
– X-ray emission also seen among higher mass stars (2-10 Msun)
• Origin is likely similar to lower mass PMS stars
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Testing MMA Assumptions
• Alternative magnetic field indicators: collimated jets and energetic winds
– Jets and winds are likely launched from the disk-magnetosphere boundary
– Such winds are ubiquitous among low mass (M < 2 Msun) accreting PMS stars
– Direct evidence of jets found among accreting stars as massive as M ~ 10 Msun
– Energetic winds observed among more massive stars
• Samples are small and the estimated wind momenta subject to large uncertainty
R Mon HH-39HH 30
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Testing MMA Assumptions
• Magnetospheric funnel flow indicators:
– Inverse P Cygni profiles observed for PMS stars spanning 0.05 to 5 Msun
– Modelled successfully as funnel flows having accretion rates consistent
with observed excess uv emission produced at field footprint
Muzerolle et al. 2001
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Testing MMA Assumptions:Disk Locking
• Disk locking predicts that
– Stars locked to circumstellar accretion disks will be locked to a fixed
rotation period even as they contract (= constant)
– Stars no longer locked to disks will spin up as they contract (~R-2)
• Stars surrounded by disks should rotate more slowly
• Two Observational tests
– Is constant or ~R-2 for a disk-dominated sample?
• Measure rotation periods from spot-modulated light curves
• Measure projected rotational velocities
• Obtain R from log Teff and Lbol
– Does IR excess correlate with rotation period?
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Testing Disk Locking: Rotational Evolution for Young, Disk-Dominated Populations
Stellar conserved: v ~ R
Stellar J conserved: v ~ R-1
Best Fit
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Stellar J conserved: P ~ R2
Best Fit
Stellar conserved: P ~ const
Testing Disk Locking: Rotational Evolution for Young, Disk-Dominated Populations
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Testing MMA Assumptions:Direct Test of Disk Locking - Initial Results
Disk-locking works !
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Testing MMA Assumptions:Direct Test of Disk Locking - Later Results
Disk-locking fails !
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Why is Evidence for Disk Locking Ambiguous?
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Possible Explanation?
• Sample sizes are not large enough to distinguish period distributions for
(disk)-regulated and unregulated stars
– Monte Carlo simulations suggest sample sizes of 500-1000 needed in order to
detect correlation between (unambiguous) disk indicators and period
• Near-IR excesses cannot identify disks unambiguously
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New Test: Can MMA Account for Observed Trends in Rotation vs Mass ?
• Assume that stars form via MMA
• Assume further that– Stars are locked to disks until they reach the stellar birthline
– Magnetic fields are ~ 2.5 kG (typical for T Tauri stars)
– Accretion rates are
• Constant at 10-5 Msun/yr
• Compare predicted trend in J/M with M* with observed trend
– Use sample of young stars spanning a range of masses (0.1-20 MSun)
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High [dMacc/dt] or low B Low [dMacc/dt] or high B
Rapid Rotation Slow Rotation
GM 5/7 (dMacc/dt) 3/7 B -6/7 R -18/7
Quick Reminder
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Observations of Specific Angular Momentum as a Function of Mass
Orion Stars plus OB Associations
Low mass stars on convective tracks; high mass stars on radiative tracks15.5
16
16.5
17
17.5
18
18.5
19
-1 -0.5 0 0.5 1 1.5
log M/Msun
log(Jsini/M)
Orion (WSH conv)
Orion (Rhode)
OB Associations
Orion ZAMS (WHS)
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MMA PredictionsJ/M vs. M
15.5
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-1 -0.5 0 0.5 1 1.5
log M/Msun
log(Jsini/M)
Orion (WSH conv)
Orion (Rhode)
OB Associations
Orion ZAMS (WHS)
Disk-locking (Mdot =10^-5)
Birthline=ZAMS
B = 2500 gauss
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MMA vs Observations: Summary
• Predicted J0/M vs M relationship fits the observed upper
envelope remarkably well for 0.1 < M/MSun < 20
• Scatter below the upper envelope power law may be due to – differerences in B or differences in accretion rates
– inclination effects
– loss of angular momentum as stars evolve down convective tracks
• Effectiveness of disk-locking questioned on theoretical grounds– Field topology complex; differential rotation opens closed field lines
• Prediction of J/M should become a test of alternative models (i.e., winds) for solving angular momentum problem
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MMA: Summary
• Overall: MMA appears plausible for stars with M < 20 Msun
– Continuity of J/M strong argument for single formation mechanism over this mass range
• Direct evidence of B fields for accreting PMS stars with 0.05< M/Msun< 3
– kG fields for stars with M < 1 Msun; Strength of B for higher mass stars uncertain
• Indirect evidence of B fields for accreting PMS stars up to M/Msun~ 10
– Collimated jets and molecular outflows, x-ray emission
• Rotation periods among disk-dominated populations appear to be ‘locked’
• Correlation between disks and periods weak or absent
• Disk indicators used to date are not robust
– Spitzer observations will yield robust disk indicators
• Sample sizes are too small (per Monte Carlo simulations)
– Ongoing studies of rotationally-modulated periods will yield larger samples
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What About Stars with M > 20 Msun ?
• Cannot extend J/M vs. M to M > 20 Msun
– Current sample sizes small
– Must find stars very near ZAMS since winds in massive stars may cause
significant loss of angular momentum on time scales of few times 106 yrs
– Masses also uncertain
• Open questions
– Do M > 20 Msun mass stars form differently?
– Are their initial angular momenta set by a different mechanism?
– Is rotation still a useful constraint on the star formation process?
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Can Stellar Rotation Probe Initial Conditions in Different Environments ?
• Dense stellar clusters form in regions of high gas surface density and
close packing of protostars.
• Gas turbulent velocities in these regions are likely to be high (e.g. McKee
and Tan, 2003) leading to:
– protostars of high initial density;
– rapid protostellar collapse times &
– high time-averaged accretion rates (dMacc/dt)
• Conditions in dense clusters should favor formation of
– (very) high mass stars
– Stars that rotate rapidly owing to high dMacc/dt
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B Stars Most Likely to Reflect Differences in Accretion Rates
Palla & Stahler
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Do B Stars in Dense Clusters Rotate More Rapidly Than Stars Formed in
Isolation?• Past observations hint at such a trend (Wolff et al. 1982)
– However, sample size is small (< 100 stars)
vsini (km/sec)
ONC Center
Orion Ia
Orion Ic
Orion Ib
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h and Per: A Laboratory for Probing the Effects of Initial Conditions?
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h and Per: A Laboratory for Probing the Effects of Initial Conditions?
• Stellar Density is high: 104 pc-3
– exceeds that of the ONC by a factor of 10
• Upper main sequence (M > 3 MSun) accessible to high resolution spectroscopy
using multi-object spectroscopy on 4-m telescopes
• Age t ~ 13 Myr
– Late B stars unevolved
– Early B stars are evolved well away from the ZAMS
• Compare with field stars
– Majority of field stars must have formed in lower density regions than the stars in h
and , which are still bound clusters
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The h and Rotation Sample
-6
-5
-4
-3
-2
-1
0
1
4.054.14.154.24.254.34.354.44.454.5Log Teff
Mv
15 Mo
12 Mo
9 Mo
7 Mo
5 Mo
4 Mo
3 Mo
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h and Per: Observations
• Sample of 200 stars with M > 3 MSun selected from recent
study by Slesnick, Hillenbrand, and Massey (2002)
• R = 20000 spectra obtained with WIYN-Hydra
• Rotational velocities derived via comparison with artificially
broadened spectra spanning B0 –B9
• Spectroscopic binary candidates identified via:– Spectra spanning multiple nights
– Comparison with cluster mean
• Binaries eliminated from sample
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h and Per: Comparison with Field
• Rotation can evolve with time:– Change of stellar structure
– Surface-interior mixing
– Angular momentum loss via winds
• Proper comparison of cluster with field requires selecting samples with exactly comparable ages
• Accurate ages can be derived from Stromgren , co
– Field & cluster samples span the same ranges in , co
• Sample divided into 3 bins:– 3 < M/M < 4.5
– 4.5 < M/M < 8
– 8 < M/M < 11
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h and Persei Compared with Field Stars:3 < M/M < 4.5
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
1 to 50 51-100 101-150 151-200 201-250 251-300 301-350 351-400
h and Persei
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
1 to 50 51-100 101-150 151-200 201-250 251-300 301-350 351-400
Field Stars
vsini (km/s)
Fra
ctio
n of
Tot
al
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0
0.1
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0.7
0.8
0.9
1
0 50 100 150 200 250 300 350 400
vsini (km/sec)
Fraction of Total
h and Persei Compared with Field Stars:3 < M/M < 4.5
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0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
1 to 50 51-100 101-150 151-200 201-250 251-300 301-350 351-400
h and Persei
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
1 to 50 51-100 101-150 151-200 201-250 251-300 301-350 351-400
Field Stars
vsini (km/s)
Fra
ctio
n of
Tot
al
h and Persei Compared with Field Stars:4.5 < M/M < 8
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0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
-50 0 50 100 150 200 250 300 350 400
vsini (km/sec)
Fraction of Total
h and Persei Compared with Field Stars:4.5 < M/M < 8
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0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
1 to 50 51-100 101-150 151-200 201-250 251-300 301-350 351-400
h and Persei
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
1 to 50 51-100 101-150 151-200 201-250 251-300 301-350 351-400
Field Stars
vsini (km/s)
Fra
ctio
n of
Tot
al
h and Persei Compared with Field Stars:8 < M/M < 11
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0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
-50 0 50 100 150 200 250 300 350
vsini (km/sec)
Fraction of Total
h and Persei Compared with Field Stars:8 < M/M < 11
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Conclusions
• Primary differences between h and Per stars and field
stars are:– Higher percentage of slow rotators in field all masses
– Unevolved stars (3 < M/M < 4.5) in h and Per rotate on average
nearly twice as fast as their field counterparts
• Maximum rotations similar for field and h and Per stars – But line widths insensitive to rotation for vsini > ~400 km/sec
• Average rotation of more massive, more evolved stars
early B stars more closely matches field counterparts– But excess of slow rotators persists
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Conclusions
• Observations of PMS stars surrounded by accretion disks consistent
with MMA for 0.1 < M/Msun < 20
– MMA + simple assumptions predict J/M vs M over this mass range
• Primary formation path for higher mass stars (M/Msun > 20) not yet
established; rotation may provide important clues
• Rotation properties appear to reflect environment
– May be first observational link between initial conditions and outcomes of
star formation
– Question: What is the physical connection between the rapid rotation of B
stars in clusters initial conditions (e.g., turbulence?)
– Are there also differences in the emergent IMF?