The Formation of Very Massive Stars Mark Krumholz (UC Santa Cruz) IAU Joint Discussion on Very Massive Stars Beijing, China August 20, 2012 Overview •  Introduction and observations •  Massive star formation models –  Fragmentation –  Companions –  The radiation pressure problem –  Stellar collisions? •  Summary AA48CH10-Meyer
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The Observed IMF 23 July 2010
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Associations
Dense clusters
Field
Open clusters
Globular clusters
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Binarity Higher mass •  Most low mass stars are single •  Most massive stars are members of binary (or higher multiple) systems •  The companions to massive stars are also Multiple system fraction versus stellar mass in three different regions (Brown 2001) usually massive (Sana+ 2008) Star-­‐Forming Clouds and Cores Pipe nebula with cores circled (Alves+ 2007) The Core Mass Function •  CMF slope matches the IMF slope •  Seen in many regions •  Suggests IMF set by gas fragmentation and universal physics Core mass function in the SPerpens, ipe Nebula Perseus, & Ophiuchus clouds (Enoch+ (red), compared to stellar IMF (gray), 2008) (Alves+ 2007) Massive Cores We see centrally concentrated gas cores the right mass and size to be the progenitors of massive stars: M ~ 100 M, R < 0.1 pc, Σ ~ 1 g cm-­‐2 Core in IRDC 18223-­‐3 in mid-­‐IR (Spitzer, color) and mm (Plateau de Bure Interferometer, contours), (Beuther+ 2005) Caveat: fragmentation at unresolved scales Assembling the tail of the IMF Problem 1: Fragmentation •  Fragmentation scale is MJ ~ cs3 / G3/2 ρ1/2 ~ 1 M •  Why do some objects run away to > 100 MJ? Hydrodynamic simulation of the fragmentation of a massive core (Dobbs et al. 2005) Accretion Luminosity •  Accretion can produce > 100 L even for 0.1 M stars •  Accretion luminosity dominates energetics in star-­‐forming regions Temperature vs. radius before (red) and after (blue) star formation begins in a 50 M, 1 g cm-­‐2 core (Krumholz 2006) Simulation of a Massive Core Isothermal 200 M centrally-­‐condensed core (Myers+ 2012) Both simulations use MHD, sink particle, AMR Radiative Massive Stars in a Cluster (Krumholz+ 2011, 2012)
Column density Temperature 1000 M cloud with properties comparable to Orion; simulation includes protostellar outflows, no B fields Matching the IMF Massive Cores Problem 2: Massive Binaries •  Radiative heating seems to suppress fragmentation into many stars •  Can we still explain the high fraction of massive stars that are binaries, and why those companions are also massive? Binaries from Cluster Simulation Massive Disk Properties •  Accretion rate onto star + disk is ~ σ3 / G ~ 10–3 M / yr in a massive core •  Max mass transfer rate through a stable disk (α < 1, Q > 1) is ~ cs3 / G ~ 5 x 10–5 M / yr at T = 100 K •  Core accretes faster than stable disk can process ⇒ massive, unstable disks (Kratter+ 2006, 2008) Surface density (upper) and Toomre Q (lower); Krumholz+ 2007 Gravitational Instability in Disks (Kratter+ 2010; Krumholz & Burkert 2010)
Simulation shows growth of instability in rapidly-­‐fed disk, leading to fragmentation, and inward migration of fragments The Radiation Pressure Problem •  Dust absorbs UV & visible, re-­‐
radiates IR frad
fgrav
L
=
4⇥r2 c
GM
= 2
r
•  frad > fgrav for (L/M) > 2500 •  Stars exceed this at ~20 M (Larson & Starrfield 1971; Wolfire & Cassinelli 1987)"
⇒  Massive stars exceed the dust Eddington limit while forming Beating RP: Disks Kuiper+ 2011 (also see Nakano
+ 1995, Jijina & Adams 1996) Mfin >~ 140 M Beating RP: Disks + RT Instability Krumholz+ 2009 Mfin > 43 + 29 M Beating RP: Outflows The Astrophysical Journal,
(18pp), 2011 October 20
Cunningham+ 2011740:107
Cunningham et al.
Table 3
Outflow Ejection
t = 0.30tff
Σ = 1.0 f(0 ° ) / f(90 ° ) = 3.2 f(90 ° ) = 0.79
Σ = 2.0 f(0 ° ) / f(90 ° ) = 7 f(90 ° ) = 0.28
Σ = 10.0
Σ = 2.0
f(0 ° )
/
f(90 ° ) = 31
f(90 ° ) = 0.15
Top: simulation of HM star formation with turbulence + outflows Left: radiation flux vs. polar angle (also see Krumholz+ 2005) Σ (g cm−2 )
tend (tff )
vesc (km s−1 )
v̄w |t=tend (km s−1 )
#core
#wind,simulation
#wind
1.0
0.6
4.27
87.7
0.70
1.06
0.42
2.0
0.8
5.08
72.2
0.73
0.342
0.370
10.0
0.8
7.60
71.0
...
0.0563
...
Notes. Simulation results (rows 1–4 and 6) and analytic model predictions
(rows 5 and 7). The columns indicate the cases of Σ = 1.0 g cm−2 , Σ =
2.0 g cm−2 , and Σ = 10.0 g cm−2 from left to right. As discussed in the text, the
Σ = 10.0 g cm−2 simulation was not evolved sufficiently far in time to compare
with the analytic model.
t = 0.40tff
Mfin = 65 M Due to constraints on computational time, we have not run
numerical simulations sufficiently long to determine the final
star formation efficiency. To facilitate comparison between the
numerical and analytic model, we focus our attention to the ratio
to be at rest, so that
n as they gain mass,
er. In contrast to the
Bonnell 2008; Davis
system does not fall
the range 0.3–30.0 M# , at which point the gas is expelled by fiat.
All of the simulations presented here are performed with a global
star formation efficiency of 30 per cent. The stars and gas are both
initially Plummer potentials with matching scale radii. Initial experiments with alternative density structures do not qualitatively alter
Collisions? Results are at 2 Myr for the 32k runs and 3 Myr for the 2k runs unless noted otherwise.
ρ c (M# pc−3 )
rhm (pc)
ρ m (M# pc−3 )
rm (pc)
N col
M > 30 M#
5.1 × 107
0.08
2.5 × 106
0.14
57
602, 46, 39
0.19
0.20
0.20
0.20
0.20
0.20
33
29
41
26
26
80
276, 37
344
356, 31
368
321
283, 46, 35
0.24
0.25
0.24
0.24
0.24
7
10
11
6
4
100
143
145
65, 45
57, 39
0.29
1
–
0
2
0
0
2
–
50
–
–
55
1.2 × 107
1.6 × 107
1.3 × 107
1.4 × 107
1.3 × 107
1.3 × 107
6.5 × 106
5.9 × 106
6.0 × 106
6.6 × 106
7.1 × 106
2.5 × 106
4.5 × 103
2.5 × 104
1.7 × 104
2.9 × 104
2.4 × 104
0.14
0.13
0.14
0.13
0.14
0.14
0.19
0.19
0.19
0.19
0.19
0.29
8.0 × 105
8.1 × 105
8.1 × 105
8.0 × 105
7.9 × 105
8.3 × 105
4.2 × 105
4.0 × 105
4.2 × 105
4.3 × 105
4.1 × 105
2.1 × 105
0.68
0.65
0.83
0.58
0.58
Moeckel & Clarke 2011; also see Baumgardt & Klessen 2011 d by the total mass and mean radius of stars within 1 pc.
1 pc.
Even for perfectly efficient collisional growth, strong gas drag with no stellar feedback, collisional growth important only at ρ* > 107 pc−3 and C. J. Clarke
Collision Problems Moeckel & Clarke 2011 1816
H. Baumgardt and R. S. Klessen
Baumgardt & Klessen 2011 Arches cluster (observed) Arches cluster (observed) Figure 7. Final mass function of stars at T = 10 Myr in the four masssegregated models with the highest number of collisions. Dashed line shows
the expected number of stars for a Kroupa (2001) IMF extending up to
100 M! . Stellar collisions do not lead to the build-up of such a mass function, instead they mainly lead to the formation of single, very massive stars.
The behaviour is similar to the runaway merging scenario found for mainsequence stars in dense star clusters.
Figure 8
rate in ru
collision
since e.g
sequence
main-seq
larger rate are more extended, which will lead to a higher number
of collisions. However, larger accretion rates also lead to shorter
Fig. 9
stars. Th
rh = 0.
10 Myr
smaller
•  Even Arches cluster not dense enough for collisions •  IMF produced by collisions never bserved unsegregated.o
According
to equation (2), stars accreting with a
ensity profiles at 2 Myr for the same runs shown in Fig. 2. The dashed horizontal line is the cluster density o
Summary •  Radiation solves fragmentation problem •  Binarity of massive stars is explained by n-­‐
body dynamics, disk gravitational instability •  Radiation pressure does not limit stellar masses •  Collisions likely unimportant