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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)
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
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
Accretion Disk Stellar seed Infalling envelope Forming the Star-Disk System
Wind/Jet Rotating accretion disk Infalling gas/dust Forming star Accreting material Solving the Angular Momentum Crisis removes angular momentum
What Accounts for the Distribution of Stellar Masses? Possibilities: • Stellar mass reflects initial core mass • Stellar mass reflects core sound speed • 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
What Accounts for the Distribution of Stellar Masses? • 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 ?
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 + vturb2)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?
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
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
Example: The BN Object • Scoville et al. (1983) used CO (1-0) to probe T[r], r[r], v[r] along the line of site to the BN object (Lbol ~ 104 Lsun)
Testing M* ~ Core Sound Speed:Location of Birthline Location of birthline reflects the accretion rate (Palla and Stahler)
ONC: Hillenbrand and Carpenter, 2000 Miller-Scalo 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
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?
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
Cha I Complex ONC What Accounts for the Distribution of Stellar Masses? • Simulations (e.g. Bate; Bonnell) are promising • No direct observational tests have been made
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
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
Magnetospherically-Mediated Accretion (MMA) Star and disk ‘locked’ at the co-rotation radius where Pdyn = Pmagnetic Wdisk = Wstar
Slow Rotation Rapid Rotation Dependence of Rotation on dMacc/dt: Basic Concepts (Konigl Model) High [dMacc/dt] or low B Low [dMacc/dt] or high B W ~ eGM 5/7 (dMacc/dt) 3/7 B -6/7 R -18/7 Shu + Najita model invokes wind to carry away stellar angular momentum Dependence of W on B, dM/dt and R is similar
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
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
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
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
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 30 HH-39
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
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 (W = constant) • Stars no longer locked to disks will spin up as they contract (W~R-2) • Stars surrounded by disks should rotate more slowly • Two Observational tests • Is W 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?
Best Fit Stellar W conserved: v ~ R Stellar J conserved: v ~ R-1 Testing Disk Locking: Rotational Evolution for Young, Disk-Dominated Populations
Best Fit Stellar W conserved: P ~ const Stellar J conserved: P ~ R2 Testing Disk Locking: Rotational Evolution for Young, Disk-Dominated Populations
Testing MMA Assumptions:Direct Test of Disk Locking - Initial Results Disk-locking works !
Testing MMA Assumptions:Direct Test of Disk Locking - Later Results Disk-locking fails !
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
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)
Slow Rotation Rapid Rotation Quick Reminder High [dMacc/dt] or low B Low [dMacc/dt] or high B W ~ eGM 5/7 (dMacc/dt) 3/7 B -6/7 R -18/7
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 tracks
MMA PredictionsJ/M vs. M B = 2500 gauss
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
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
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?
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
B Stars Most Likely to Reflect Differences in Accretion Rates Palla & Stahler
Orion Ib Orion Ia Orion Ic ONC Center vsini (km/sec) 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)
h and c 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
The h and c Rotation Sample 15 Mo 12 Mo 9 Mo 7 Mo 5 Mo 4 Mo 3 Mo
h and c 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