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)
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
Forming the Star-Disk System
Accretion Disk
Infalling envelope
Stellar seed
Solving the Angular Momentum Crisis
Rotating accretion disk
Accreting material
Wind/Jet
removes angular momentum
Forming star
What Accounts for the Distribution of
Stellar Masses?
Possibilities:
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
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 ?
What Accounts for the Distribution of
Stellar Masses?
2. Stellar Mass Reflects Core Sound Speed
–
M* ~ dM/dt x t
–
dM/dt ~ a3 / G;
–
Resulting stellar mass depends on
–
Implicit assumption: core accretion halted by outflow
–
NB: In higher density environments, theory predicts
a = sound speed
a ~ (vth2 + vturb2)1/2
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)
6 .5
5 .5
log L/Lsun
4 .5
Birthline: 10^-4 Msun/y r
ZAMS
3 .5
ZA M S
Birthline for 1 0 ^-5 M o/yr
Birthline 1 0 ^- 4 M o/yr
2 .5
Birthline: 10^-5 Msun/y r
1 .5
0 .5
- 0 .5
4 .7
4 .5
4 .3
4 .1
log Tef f
3 .9
3 .7
3 .5
500,000 Yr Isochrones for
Different Accretion Rates
6 .5
5 .5
log L/Lsun
4 .5
ZAMS
3 .5
ZA M S
I s oc hrone: 5 x1 0 ^5 yrs
I s oc hrone: 5 x1 0 ^5 yrs
500,000 Year
Isochrones
2 .5
1 .5
0 .5
- 0 .5
4 .7
4 .5
4 .3
4 .1
log Tef f
3 .9
3 .7
3 .5
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
ONC: Hillenbrand and Carpenter, 2000
Miller-Scalo
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?
Possible Feedback Mechanism
What Accounts for the Distribution of
Stellar Masses?
3. Hybrid mechanism involving environment
•
Stars with M < 20 Msun form via magnetosphericallymediated 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
What Accounts for the Distribution of
Stellar Masses?
•
Simulations (e.g. Bate; Bonnell) are promising
•
No direct observational tests have been made
Cha I Complex
ONC
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 magnetosphericallymediated 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
Dependence of Rotation on dMacc/dt:
Basic Concepts (Konigl Model)
Rapid Rotation
High [dMacc/dt] or low B
Slow Rotation
Low [dMacc/dt] or high B
W ~ e GM 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
HH 30
R Mon
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?
Testing Disk Locking: Rotational Evolution
for Young, Disk-Dominated Populations
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 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)
Quick Reminder
Rapid Rotation
High [dMacc/dt] or low B
Slow Rotation
Low [dMacc/dt] or high B
W ~ e GM 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
19
1 8 .5
log(Jsini/M)
18
1 7 .5
O rion (WSH c onv)
O rion (R hode)
O B A s s oc iations
O rion ZA M S (WH S)
17
Low mass stars
on convective
tracks; high
mass stars on
radiative tracks
1 6 .5
16
1 5 .5
-1
- 0 .5
0
0 .5
log M/Msun
1
1 .5
MMA Predictions
J/M vs. M
19
1 8 .5
log(Jsini/M)
18
O rion (WSH c onv)
O rion (R hode)
O B A s s oc iations
O rion ZA M S (WH S)
D is k-loc king (M dot =1 0 ^- 5 )
Birthline=ZA M S
1 7 .5
17
1 6 .5
B = 2500
gauss
16
1 5 .5
-1
- 0 .5
0
0 .5
log M/Msun
1
1 .5
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)
Orion Ia
Orion Ib
Orion Ic
ONC
Center
vsini (km/sec)
h and c Per: A Laboratory for Probing
the Effects of Initial Conditions?
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 c, which are still bound clusters
The h and c Rotation Sample
-6
-5
-4
15 Mo
Mv
-3
12 Mo
-2
9 Mo
7 Mo
-1
5 Mo
0
4 Mo
3 Mo
1
4.5
4.45
4.4
4.35
4.3
4.25
Log Teff
4.2
4.15
4.1
4.05
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
h and c 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 b, co
– Field & cluster samples span the same ranges in b, co
• Sample divided into 3 bins:
– 3 < M/M
< 4.5
– 4.5 < M/M < 8
– 8 < M/M < 11
h and c Persei Compared with Field Stars:
3 < M/M < 4.5
0.4
hField
and Stars
c Persei
Fraction of Total
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
1 to 50
51-100
101-150
151-200
201-250
vsini (km/s)
251-300
301-350
351-400
h and c Persei Compared with Field Stars:
3 < M/M < 4.5
1
0.9
Fraction of Total
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
50
100
150
200
vsini (km/sec)
250
300
350
400
h and c Persei Compared with Field Stars:
4.5 < M/M < 8
0.4
Field
h andStars
c Persei
Fraction of Total
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
1 to 50
51-100
101-150
151-200
201-250
vsini (km/s)
251-300
301-350
351-400
h and c Persei Compared with Field Stars:
4.5 < M/M < 8
1
0.9
0.8
Fraction of Total
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
-50
0
50
100
150
200
vsini (km/sec)
250
300
350
400
h and c Persei Compared with Field Stars:
8 < M/M < 11
0.5
hField
and Stars
c Persei
0.45
Fraction of Total
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
1 to 50
51-100
101-150
151-200
201-250
vsini (km/s)
251-300
301-350
351-400
h and c Persei Compared with Field Stars:
8 < M/M < 11
1
0.9
0.8
Fraction of Total
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
-50
0
50
100
150
vsini (km/sec)
200
250
300
350
Conclusions
• Primary differences between h and c 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 c Per rotate on average
nearly twice as fast as their field counterparts
• Maximum rotations similar for field and h and c 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?