1. Stellar Rotation: A Probe of Star-Forming Modes and Initial Conditions? Sidney C. Wolff and Stephen E. Strom National Optical Astronomy Observatory (With collaborators Luisa Rebull, Kim Venn, and REU students David Dror and Laura Kushner)

2. 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

3. 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

4. The Current Paradigm

5. Infalling envelope Forming the Star-Disk System Stellar seedAccretion Disk

6. Building a Star from a Protostellar Core Gas and dust transported: envelope accretion disk stellar seed Stellar mass builds up over time (~ 1 Myr) Accreting mass transports angular momentum inward –Absent a loss mechanism, seed will reach breakup velocity Winds launched at the disk-magnetosphere boundary can solve the stellar angular momentum crisis

7. Solving the Angular Momentum Crisis Wind/Jet Rotating accretion disk Accreting material Forming star Infalling gas/dust removes angular momentum

8. 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:

9. 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 ?

10. What Accounts for the Distribution of Stellar Masses? 2. Stellar Mass Reflects Core Sound Speed –M * ~ dM/dt x t –dM/dt ~ a 3 / G; a = sound speed –Resulting stellar mass depends on a ~ (v th 2 + v turb 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?

11. 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

12. Testing M * ~ Core Sound Speed: Direct Observations Select Class I sources showing a range in L bol Determine dM/dt ~(a 3 /G) from high resolution (R ~ 10 5 ) spectroscopy of molecular absorption features observed against star-disk system Determine spectral type of embedded forming star via R ~ 10 3 spectroscopy of scattered light emerging from walls of wind-driven cavity Determine whether there is an M * vs dM/dt correlation

13. 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 (L bol ~ 10 4 L sun )

14. Example Pilot Program R ~ 10 5 spectroscopy of Class I objects in Ophiuchus R ~ 10 3 spectroscopy at 2  m to derive spectral type of the central source by observing scattered light envelopes Bontemps et al. 2001 Padgett et al. 1999

15. Testing M * ~ Core Sound Speed: Location of Birthline Location of birthline reflects the accretion rate (Palla and Stahler)

16. 500,000 Yr Isochrones for Different Accretion Rates

17. IC 1805: OB Association Age: ~1-3 Myr Derive lower limit for accretion rate: 10 -5 M Sun /yr

18. 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

19. 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?

20. Possible Feedback Mechanism

21. What Accounts for the Distribution of Stellar Masses? 3. Hybrid mechanism involving environment Stars with M < 20 M sun form via magnetospherically- mediated accretion Stars with M > 20 M sun may form via an alternative path –Mergers? Competitive accretion? –Possibly explains why high mass stars are found in dense regions Credit M. Bate 2004

22. 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

23. What Accounts for the Distribution of Stellar Masses? Summary –Evidence for M * ~ M core is circumstantial Arranging for rapid (t < 1 Myr) formation at all masses a problem –Testing M * ~ dM acc /dt Is possible from R ~ 10 5 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

24. Can Stellar Rotation Provide More Clues ? If stars of all mass are formed via magnetospherically- mediated accretion (MMA): –stellar rotation speed ~ core dM acc /dt If high M stars form from cores with higher dM acc /dt, then such stars should exhibit higher rotation speeds –If dM acc /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

25. Magnetospherically-Mediated Accretion (MMA) Star and disk ‘locked’ at the co-rotation radius where P dyn = P magnetic  disk =  star

26. High [ dM acc /dt ] or low BLow [ dM acc /dt] or high B Rapid Rotation Slow Rotation  GM 5/7 (dM acc /dt) 3/7 B -6/7 R -18/7 Dependence of Rotation on dM acc /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

27. 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

28. Testing MMA Assumptions Magnetic Field measurements: Zeeman Splitting –In solar-like (M < 2 M sun ) PMS stars, measurements yield B ~ 2 kG –In more massive stars, Zeeman splitting unobservable (rapid rotation) Johns-Krull et al. 1999

29. 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 M sun ) 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 M sun

30. Testing MMA Assumptions Alternative magnetic field indicator: coronal activity –Low mass (M < 1 M sun ) PMS stars all exhibit strong coronal x-ray emission L x / L bol ~ 10 -3 likely results from magnetic activity –X-ray emission also seen among higher mass stars (2-10 M sun ) Origin is likely similar to lower mass PMS stars

31. 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 M sun ) accreting PMS stars –Direct evidence of jets found among accreting stars as massive as M ~ 10 M sun –Energetic winds observed among more massive stars Samples are small and the estimated wind momenta subject to large uncertainty R Mon HH-39 HH 30

32. Testing MMA Assumptions Magnetospheric funnel flow indicators: –Inverse P Cygni profiles observed for PMS stars spanning 0.05 to 5 M sun –Modelled successfully as funnel flows having accretion rates consistent with observed excess uv emission produced at field footprint Muzerolle et al. 2001

33. 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 T eff and Lbol –Does IR excess correlate with rotation period?

34. Testing Disk Locking: Rotational Evolution for Young, Disk-Dominated Populations Stellar  conserved: v ~ R Stellar J conserved: v ~ R -1 Best Fit

35. Stellar J conserved: P ~ R 2 Best Fit Stellar  conserved: P ~ const Testing Disk Locking: Rotational Evolution for Young, Disk-Dominated Populations

36. Testing MMA Assumptions: Direct Test of Disk Locking - Initial Results Disk-locking works !

37. Testing MMA Assumptions: Direct Test of Disk Locking - Later Results Disk-locking fails !

38. Why is Evidence for Disk Locking Ambiguous?

39. 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

40. 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 M sun /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 M Sun )

41. High [ dM acc /dt ] or low BLow [ dM acc /dt] or high B Rapid Rotation Slow Rotation  GM 5/7 (dM acc /dt) 3/7 B -6/7 R -18/7 Quick Reminder

42. 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

43. MMA Predictions J/M vs. M B = 2500 gauss

44. MMA vs Observations: Summary Predicted J 0 /M vs M relationship fits the observed upper envelope remarkably well for 0.1 < M/M Sun < 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

45. MMA: Summary Overall: MMA appears plausible for stars with M < 20 M sun –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/M sun < 3 –kG fields for stars with M < 1 M sun ; Strength of B for higher mass stars uncertain Indirect evidence of B fields for accreting PMS stars up to M/M sun ~ 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

46. What About Stars with M > 20 M sun ? Cannot extend J/M vs. M to M > 20 M sun –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 10 6 yrs –Masses also uncertain Open questions –Do M > 20 M sun 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?

47. 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 (dM acc /dt) Conditions in dense clusters should favor formation of –(very) high mass stars –Stars that rotate rapidly owing to high dM acc /dt

48. B Stars Most Likely to Reflect Differences in Accretion Rates Palla & Stahler

49. 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

50. h and  Per: A Laboratory for Probing the Effects of Initial Conditions?

51. Stellar Density is high: 10 4 pc -3 –exceeds that of the ONC by a factor of 10 Upper main sequence (M > 3 M Sun ) 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

52. The h and  Rotation Sample 15 M o 12 M o 9 M o 7 M o 5 M o 4 M o 3 M o

53. h and  Per: Observations Sample of 200 stars with M > 3 M Sun 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

54. 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 , c o –Field & cluster samples span the same ranges in , c o Sample divided into 3 bins: –3 < M/M < 4.5 –4.5 < M/M < 8 –8 < M/M < 11

55. h and  Persei Compared with Field Stars: 3 < M/M < 4.5 h and  Persei Field Stars vsini (km/s) Fraction of Total

56. h and  Persei Compared with Field Stars: 3 < M/M < 4.5

57. h and  Persei Field Stars vsini (km/s) Fraction of Total h and  Persei Compared with Field Stars: 4.5 < M/M < 8

59. h and  Persei Field Stars vsini (km/s) Fraction of Total h and  Persei Compared with Field Stars: 8 < M/M < 11

61. 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

62. Questions Nature vs. Nurture for early B stars –Do early B stars in clusters start out with rates of rotation similar to those of field stars (i.e., independent of environment?) –Or do B stars in clusters initially rotate more rapidly and do rapid rotators lose angular momentum more quickly through winds in order to converge to a common value? –Is the deficiency of stars with vsini < 50 km/sec typical of OB associations?

63. New Sample: OB Associations 6 Associations –Similar density (lower than h and  Per) Ages –1-6 Myr Search for –Evolutionary effects –Cosmic dispersion –Comparison with field stars

64. Predicted Change in Angular Momentum 12 M sun Maeder et al.

65. NGC 6611 + IC 1805 B1-B3; 1.5-2Myr

66. NGC 2244, 6823, 7235, Cyg OB2 B1-B3; ~ 5Myr

67. Cumulative Distribution of vsini OB Associations (B1-B3 Stars) Models predict that rotation changes by constant percentage

68. OB Associations vs. Age OB Assns. In Order of Age IC 1805 NGC 6611 Cyg OB2 NGC 6823 NGC 2244 NGC 7235

69. vs. Age for OB Associations plus h and  Per OB Assns. In Order of Age IC 1805 NGC 6611 Cyg OB2 NGC 6823 NGC 2244 NGC 7235 h and  Per

70. Field Stars

71. Cumulative Distributions of vsini

72. Early B Stars: Evolution or Environment? Other studies also find deficiency of very slow rotators in clusters, associations relative to field stars throughout B star domain –Unevolved stars in h and  –Keller: LMC, older stars spin up –Gies and Huang: MW, stars spin down with age –Martin: Runaway stars deficient in slow rotators Environment not evolution may be unifying theme

73. Next Steps Does MMA paradigm extend to higher masses? –Establish J/M vs M * for individual clusters over the entire mass range 3< M/M Sun < 100 –Clusters such as NGC 6611; IC 1805 are ideal –~400-500 PMS stars and young ZAMS O & B stars –Avoid comparing J/M values drawn from different environments Evaluate effects of evolution, cosmic dispersion –Sample older clusters Observe more extreme environment –R136 in LMC is extremely dense, age ~1-2 Myr, somewhat more metal poor

74. Conclusions Observations of PMS stars surrounded by accretion disks consistent with MMA for 0.1 < M/M sun < 20 –MMA + simple assumptions predict J/M vs M over this mass range Primary formation path for higher mass stars (M/M sun > 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?