Transcript The Formation of High Mass Stars

The Feedback Effects of Radiation and Protostellar
Outflows on High Mass and Low Mass Star Formation
Frontiers in Computational Astrophysics
Lyon, France October 11, 2010
Richard I. Klein
UC Berkeley, Department of Astronomy
and
Lawrence Livermore National Laboratory
Collaborators
Andrew Cunningham (LLNL), Charles Hansen (UC Berkeley),
Mark Krumholz (UCSC), Chris McKee (UC Berkeley), Stellar
Offner (CFA)
LLNL-PRES-414260
Regimes of Importance in Radiation Hydrodynamics
•
We consider 3 regimes of importance:
 << 1,
(streaming limit, weak coupling)
 >> 1,
 <<1 (static diffusion limit, strong coupling)
 >> 1,
 >>1 (dynamic diffusion limit, strong coupling)
Dynamic Diffusion:
In stellar interior optical depth from core to surface of sun
 ~ 1011, vconv >> 10-11c = 0.3 cm s-1 so  >>1
Static Diffusion:
Outer accretion disk around a forming massive protostar
Regimes continued
Specific opacity / ~ 1 cm2 g-1,  ≤ 10-12 g cm -3 for distances more than a few AU
from star
For a disk of scale height h ~ 10 AU, optical depth to escape is:
The velocity is approximately the Keplerian speed:
The
system is in static diffusion  <<1 by ~2 orders of magnitude
Outstanding Challenges of Massive Star
Formation
•
What is the formation Mechanism: Gravitational collapse of an
unstable cloud; Competitive Bondi-Hoyle accretion; Collisional
Coalescence?
•
How can gravitationally collapsing clouds overcome the Eddington
limit due to radiation pressure?
•
What determines the upper limit for High Mass Stars?
(120Msun  150Msun)
•
How do feedback mechanisms such as protostellar outflows and
radiation affect protostellar evolution? These mechanisms can also
have a dramatic effect on cluster formation
Theoretical Challenges of High Mass Star Formation
1.
Effects of Strong Radiation Pressure and Radiative Heating
— Massive stars M  20 M have tK < tform (Shu et al. 1987) and begin
nuclear burning during accretion phase
Radiates enormous energy
For M  100 M
4Gmp cM
L* ~ Ledd 
~ 3 106 LΟ
T
however dust >> T
f rad  f grav for M  10 M Ο
But, observations show M ~ 100 M (Massey 1998, 2003)
Fundamental Problem: How is it possible to sustain a sufficiently
high-mass accretion rate onto protostellar core despite
“Eddington” barrier?
Do radiation pressure and radiation heating provide a natural limit to
the formation of high mass stars?
Theoretical Challenges of High Mass Star
Formation (cont.)
2.
Effects of Protostellar outflows
— Contemporary Massive stars produce strong radiation driven
Ýv  L /c
stellar winds with momentum fluxes M
— Massive YSO have observed (CO) protostellar outflows where
Ýv ~ 100 L /c (Richer et al. 2000; Cesaroni 2004)
M

If outflows where spherically symmetric this would create a
greater obstacle to massive star formation than radiation

pressure
but, flows are found to be collimated with collimation factors 2-10
(Beuther 2002, 2003, 2004)
Fundamental Problem: How do outflows effect the formation of
Massive stars? How do outflows interact with radiation from the
protostar? Do outflows limit the mass of a star?
Equations of Radiation Hydrodynamics ORION-RMHD-AMR
Laboratory Frame Equations of Radiation Hydrodynamics (Mihalas &
Klein 1982)
Equations of Radiation Hydrodynamics Cont.
where , v, e and P are the gas density, velocity, specific energy
and thermal pressure, and E, F and  are the radiation energy
density, flux and pressure tensor
(G0,G) is the radiation four-force density in the Laboratory frame
T, = —G
Equations of Radiation Hydrodynamics Cont.
cG0 is the rate of energy absorption from the radiation field
minus the rate of energy emission for the fluid time-like
component
G is the rate of momentum absorption from the radiation field
minus the rate of momentum emission  space-like components
The radiation four-force to all orders of v/c:
Scaling Arguments Simplify Lorentz Transformations
•
Using the pressure tensor with  = 0 and F we can simplify the
radiation 4-force density and obtain the transformed 4-force:
Mixed Frame Equations of Gravito-Radiation
Hydrodynamics to order v/c (Krumholz, Klein & McKee 2007a)

      0
t
(Continuity)

        P     R F (Gas momentum)
t
c
(Gas energy)
 P
 R

e    e        4  c   2  1   F
t
 R
 c


2  4G    M i x  xi  (Poisson)
i


(Radiation energy)
  c

 

E
 3  R2

   
E    Li x  xi    4  cE    2 P  1  E    
E 
t
 2

 R
 i
 R

F
 cE 
E
R
(Flux-limited diffusion approximation)
Equations exact to (v/c) in static diffusion regime.
Formation of a Massive Binary (Krumholz, Klein,
McKee, Offner and Cunningham Science, 2009)
Qu ickT im e™ an d a
T IFF (Un com pre ssed ) d e com pre ssor
a re ne ed ed to see thi s pi ctu re .
•
Gravitational instability in disk  massive binary system 32 M and 18M
and low mass star 0.1 M at t= 44 Kyr
•
Radiative feedback from massive binary results in highly asymmetric
bubble formation and radiative heating supressing small scale frag.
Formation of a Massive Binary System (Krumholz,
Klein and McKee, Science, 2009)
QuickTime™ and a
YUV420 codec decompressor
are needed to see this picture.
•
Observations indicate most
massive O-stars have one or
more companions; binaries are
common (> 59%) Gies 2008
•
Massive protostellar disks are
unstable to fragmentation at R≥
150AU for M* ≥ 4 M (Kratter &
Matzner 2006)
•
Cores above ~ 20 M will form a
multiple through disk
fragmentation. Higher mass
systems form binaries earlier in
their evolution (Kratter, Matzner
and Krumholz 2008)
•
Radiation driven RayleighTaylor instability breaks
Eddington Barrier(KKM ‘05, ‘09)
•
Gravitational instability in disk
 massive binary system
32 M and 18 M and low mass star
0.1 M
Formation of Radiation Driven Bubble and Evolution
of Radiative Heating of Protostellar Core
QuickTime™ and a
YUV420 codec decompressor
are needed to see this picture.
Evolution of 100 Solar Mass Turbulent Protostellar Core
with Effects of Radiation Feedback on Fragmentation
Evolution of 100 Solar Mass Turbulent Isothermal
Protostellar Core
Feedback Effects of Protostellar Outflows
•
High mass protostars have outflows that look like larger
versions of low mass protostellar outflows (Beuther et al. 2004)
•
•
Outflows are launched inside star’s dust destruction radius
•
•
Because grains are small, outflow cavities are optically thin.
•
Krumholz, McKee & Klein, (2005) using toy Monte-Carlo
radiative transfer calculations find outflows cause a factor of
5 – 10 radiation pressure force reduction
•
Outflows may be responsible for driving turbulence in clumps
Due to high outflow velocities, there is no time for dust grains
to regrow inside outflow cavities. Grains reach only ~10–3m by
the time they escape the core.
Thin cavities can be very effective at collimating protostellar
radiation, reducing the radiation pressure force in the
equatorial plane
HMSF with Protostellar Outflows: Late Time Evolution
t= 60 kyr (Cunningham, Klein, McKee and Krumholz 2010, ApJ to be
submitted)
QuickTime™ and a
YUV420 codec decompressor
are needed to see this picture.
•
52 M accreted through disk to protostellar system; 30% ejected into outflow wind
 reduction in radiation forces in disk results in protostar still building mass
•
Final evolution results in a massive primary with 35 M and a massive secondary
with > 17 M Each has a protostellar disk of 4.5 M and 2.9 M respectively
HMSF with Protostellar Outflows in Turbulent Core:
(Cunningham, Klein, McKee and Krumholz 2010, ApJ)
QuickTime™ and a
YUV420 codec decompressor
are needed to see this picture.
• Early evolution t= 12.8 Kyr results in a massive primary with 13.5 M and a secondary
with 2.3 M forming in a highly asymmetric turbulent disk
• Outflow has large dynamical affect in sweeping out wide region of turbulent core as wind
becomes entrained in turbulent filaments
 Outflow cools core relieving radiation pressure resulting in formation of high mass
star
Radiation Feedback, Fragmentation and Environmental
Dependence of the IMF (Krumholz,Cunningham, Klein & McKee ApJ, 2010)
• Column densities L= 0.1, M=1.0, H=10.0 g cm-2
(Diffuse clouds such as Taurus, Perseus and
Ophiuchus; typical galactic massive star forming
regions; extra-galactic super star clusters)
• Surface density determines effectiveness of
trapping radiation and accretion luminosities of
forming stars (Krumholz, McKee 2008)
• As surface density increases, the suppression of
fragmentation increases  (L) small cluster, no
massive stars, depleted disks; (M) massive binary
with 2 circumstellar disks and large circumbinary
disk; (H) single large disk with single massive star
Higher surface density environments produce
higher accretion rates and thus higher accretion
luminosities from embedded protostars.
Higher  environments lead to higher optical depths
which trap resulting radiation more effectively
Cumulative Distribution Function of Stellar Mass t= 0.6 tff
(Krumholz, Cunningham, Klein & McKee ApJ 2010)
•
(L) system consists of several low mass stars of roughly
comparable mass; (M) most of mass in 2 stars forming binary; (H)
comparable fraction of mass in single massive star
HMSF with Protostellar Outflows in Turbulent Core: Environmental
Effects (Cunningham, Klein, McKee and Krumholz 2010)
•
We consider the evolution of high mass cores with protostellar outflows with  = 0.25, 1.0,
2.0, 10.0 contrasted with no wind for  = 2.0
•
Lower density cases are less heated; inefficient trapping of radiation results in higher
fragmentation, greater structure in disk and higher rate of multiplicity scale: (0.1rcloud)2
•
Comparison of wind (col 3) vs no wind (col 5) for  = 2.0 g cm-2 shows that winds reduce
thermal support in disk resulting in unstable spiral disk structure; No wind case has more
stable, coherent disk formation
Environmental Effects on Radiation Beaming in HMSF in
a Turbulent Core (Cunningham, Klein, McKee and Krumholz 2010)
•
Radiation beaming is most collimated for  = 10 g cm-2 where cavity is well
confined
•
•
 pole to equator contrast ≈ 7
(consistent with KKM 2005)
For less dense cores, beaming effect is diminished.
Flashlight effect is destroyed as core becomes more depleted by strong
dynamical effects of winds in low density environments
Cumulative Distribution Function of Stellar Mass with
Protostellar Outflows t= 0.5 tff
•
Lower surface density cases have a less concentrated gravitational
potential and therefore show slower accretion per unit of free fall time than
higher surface density which have a higher SFR
•
High surface density  = 10 lacks a secondary companion. Lower surface
density cores fragment to produce a secondary with greater than 1 M
•
Transition to high mass star formation appears to be shifted toward  = .25
Radiative Feedback in Low Mass Star Formation
(Offner, Klein, McKee, Krumholz ApJ 2009)
•
To assess effects of radiation on the formation of low mass stars we perform
comparative simulations with RT including radiative transfer and feedback
from stellar sources and simulations with an EOS to describe thermal
evolution of the gas
•
Initial conditions: 3D turbulent cloud with mach = 6.6 and  ≈ 1
Ti = 10K; L= 0.65 pc; <> = 4.46 x 10—20 g cm—3; Mtotal = 185 M
•
Turbulence continues to be driven with constant energy injection rate for
one global free fall time ~ 0.315 Myr
Calculations performed with 2 resolutions and multiple levels of grid
refinement (AMR):
effective resolution 40963 where x = 32 AU and 65,5363 with x = 2 AU
Cluster Formation in Driven Turbulent Cloud with Radiation Feedback
show Local Environs Affected within 0.05 pc
QuickTime™ and a
YUV420 codec decompressor
are needed to see this picture.
Column density
Density weighted temperature
• Radiation pressure effects not significant anywhere in cloud since advection of radiation
enthalpy is small compared to rate of radiation diffusion
• Star formation commences at t~ .50 tff T = 10 - 50K variation in cloud
Heating Rate due to Protostellar Sources,
Viscous Dissipation and Compresion
•
•
•
At t = 0 only source of heating is due to turbulent motions
Viscous dissipation dominates heating prior to star formation
After star formation commences protostellar output and
accretion luminosity rather than compression and viscous
dissipation is responsible for majority of radiative feedback
At t ~ 1 tff Hproto > 10 Hvisc; Hproto ~ 103 Hcomp
Stellar Mass Distribution of Star-disk System at 1tff
•
Large temperature range in the RT simulation has profound effect on stellar
mass distribution
•
Increased thermal support in protostellar disk acts to suppress
gravitational disk instability and secondary fragmentation In the core
•
Protostellar disks in the NRT simulation suffer high rates of fragmentation
 SFRff (NRT) = 13%
(Krumholz and Tan 2007)
SFRff (RT) = 7% good agreement observations
Low Mass Cluster Formation with Radiation and
Protostellar Outflow Feedback (Hansen, Klein, McKee 2010)
QuickTime™ and a
YUV420 codec decompressor
are needed to see this picture.
•
Winds interacting with filaments lead to
enhanced star formation
•
Lower mass stars form due to enhanced
fragmentation and outflow loss results in lower
luminosities and lower heating
 less thermal support so higher
fragmentation
 < L > = 6.5 L; Lmed = 1.7 L
Obser. < L > ~ 5.3 L; Lmed ~ 1.5 L
C2D sample Dunham, Evans 2010
•
If a weak wind shock interacts with an already fragmenting filament, it will lead to more
fragmentation
•
•
If it interacts with a marginally gravitationally bound filament, it can initiate collapse
•
If a strong shock hits a filament, it can move a mass of gas away and then that can collapse.
If it interacts with a low density filament, the extra compression can eventually lead to more
fragmentation when that filament finally does collapse
Velocity Dispersion of Gas in Low Mass Cluster Formation with
Protostellar Outflows: Where Does the Wind Deposit energy?
No Winds
•
•
Winds
With winds, low density gas is accelerated to higher velocities than high density
Winds deposit enough energy to prevent the turbulent decay of high density gas
 maintains a fairly constant Mach number
• Without winds, infalling dense gas surrounding most massive stars speeds up due to
steepening of gravitational potential well
Stellar Mass Distribution: Effect of Protostellar Outflows
IMF Wind outflow
•
IMF No outflow
Protostellar outflows in low mass clusters result in shift toward
larger production of low mass stars
Conclusions
High Mass Star Formation
3-D high resolution Rad-Hydro AMR simulations with ORION demonstrate:
•
Two new mechanisms to overcome radiation pressure barrier to achieve high mass star formation
 high mass binary system
— 3-D Rayleigh-Taylor instabilities in radiation driven bubbles appear to be important in
allowing accretion onto protostellar core
— Protostellar outflows resulting in optically thin cavities promote focusing of radiation and
reduction of radiation pressure  enhances accretion
— Radiation feedback from accreting protostars inhibits fragmentation (KKM 2007)
— Outflows dynamically effect larger volume of core and may result in lower ∑threshold
Low Mass Star Formation
— Inclusion of RT has a profound effect on temperature distribution, accretion and final stellar
masses
— Heating by RT stabilizes protostellar disks and suppresses small scale frag
— Vast majority of heating from protostellar Rad. Not comp or visc. dissipation
— For low mass SF, heating is local so, no inhibition of Turb. Frag. Elsewhere
— Outflows interact with filaments enhancing small scale multiplicity
•
High surface density environments produce higher accretion rates and higher accretion
luminosities as well as more effective trapping of radiation  higher efficiency in Massive Star
Formation