stellar rotation: a probe of star-forming modes and initial conditions?

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

The Current Paradigm

Infalling envelope

Forming the Star-Disk System

Stellar seedAccretion Disk

Solving the Angular Momentum Crisis

Wind/JetRotating accretion disk

Accreting material Forming star

Infalling gas/d

ustremoves angular momentum

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:


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 ?


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?



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], v[r] along the line of site to the BN object (Lbol ~ 104 Lsun)

Testing M* ~ Core Sound Speed:Location of Birthline

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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)

500,000 Yr Isochrones forDifferent Accretion Rates

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Isochrone: 5x10^5 yrs

Isochrone: 5x10^5 yrs500,000 Year Isochrones

ZAMS

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



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?

Possible Feedback Mechanism


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

• Simulations (e.g. Bate; Bonnell) are promising

• No direct observational tests have been made


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

disk = star

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

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


• 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


• 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


• 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


• 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 (= 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?

Testing Disk Locking: Rotational Evolution for Young, Disk-Dominated Populations

Stellar conserved: v ~ R

Stellar J conserved: v ~ R-1

Best Fit

Stellar J conserved: P ~ R2

Best Fit

Stellar conserved: P ~ const

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 !

Why is Evidence for Disk Locking Ambiguous?

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)

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

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

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Orion (Rhode)

OB Associations

Orion ZAMS (WHS)

MMA PredictionsJ/M vs. M

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Disk-locking (Mdot =10^-5)

Birthline=ZAMS

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

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

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

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

The h and Rotation Sample

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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

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

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

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h and Persei Compared with Field Stars:8 < M/M < 11

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

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?

stellar rotation: a probe of star-forming modes and initial conditions?

Documents

core mass distribution

mass form

distribution of stellar

stellar birthline

initial core massstellar

initial core mass test

low mass stars

core dmdt