1. Sternentstehung - Star Formation
Sommersemester 2006
Henrik Beuther & Thomas Henning
24.4 Today: Introduction & Overview
Public Holiday: Tag der Arbeit
15.5 Physical processes, heating & cooling, cloud thermal structure
22.5 Physical processes, heating & cooling, cloud thermal structure (H. Linz)
29.5 Basic gravitational collapse models I
Public Holiday: Pfingstmontag
12.6 Basic gravitational collapse models II
19.6 Accretion disks
26.6 Molecular outflow and jets
Protostellar evolution, the stellar birthline
10.7 Cluster formation and the Initial Mass Function
Massive star formation, summary and outlook
Extragalactic star formation
More Information and the current lecture files:

2. Summary protostellar evolution
The “first core” contracts until temperatures are able to dissociate H2 to H.
H-region spreads outward, T and P not high enough to maintain equilibrium,
further collapse until H gets collisionally ionized. The dynamically stable
protostar has formed.
- Accretion luminosity. Definition of low-mass protostar can be “mass-gaining
object where the luminosity is dominated by accretion”.
- Structure of the protostellar envelope and effects of rotation.
- Stellar structure equations: follow numerically the protostellar and then
later the pre-main sequence evolution.
Convection and deuterium burning.
End of protostellar/beginning or pre-main sequence evolution --> birthline.
Pre-main sequence evolution in the Hertzsprung-Russel (HR) diagram.
Connection of HR diagram with protostellar and pre-main sequence
class scheme.

3. Clusters and the Initial Mass Function (IMF)
Msun
Muench et al. 2002
Shu et al. 2004

4. General properties of the IMF
Almost all stars form in clusters, isolated star formation is exception.
Seminal paper 1955 by E. Salpeter: linear: dN/dM ~ M-2.35
log: d(logN)/d(logM) ~ (logM)-1.35
derived for stars approximately larger than 1Msun.
- More detailed current description of the total IMF (e.g., Kroupa 2001):
dN/dM ~ M-a with
a = > 0.01 ≤ M/Msun ≤ (brown dwarf regime)
a = > 0.08 ≤ M/Msun ≤ 0.5
a = > 0.5 ≤ M/Msun
- Characteristic mass plateau
around 0.5 Msun
- Upper mass limit of ~ 150Msun
- Largely universally valid, in
clusters and the field in our
Galaxy as well as in the
Magellanic Clouds .
Shu et al. 2004

5. Star cluster NGC3603 6 x 6 pc 1 pc diameter
stars between 0.5 & 120 Msun
Stolte et al. 2006

6. Mass segregation
NGC3603
Stolte et al. 2006

7. Westerlund 1
Brandner et al. 2006

8. Deviations from the IMF I: Taurus
Hartmann 2002
- Taurus: filamentary, more
distributed mode of star
formation.
- The core-mass function already
resembles a similar structure.
Grey: 12CO
Goodwin et al. 2002

9. Deviations from the IMF II: The Arches cluster
Stolte et al. 2005

10. Cloud mass distributions
Orion B South
13CO(2-1)
Kramer et al. 1996

11. Pre-stellar core mass functions I
Motte et al. 1998

12. Pre-stellar core mass functions II
Constant T
T from
Bonnor-Ebert
fits
M-0.5
M-1.5
Orion B South
Johnstone et al. 2006

13. Gravitational fragmentation
Initial Gaussian density
fluctuations
With the Jeans mass:
MJ = 1.0Msun (T/(10K))3/2 (nH2/(104cm-3)-1/2
one can in principal obtain all masses.
- Unlikely to be the sole driver for IMF:
- Initial conditions have to be very spatial and
nearly always the same.
- With the usual temperatures and densities,
the most massive fragments are hard to
produce.
Klessen et al. 1998

14. (Gravo)-turbulent fragmentation I
Freely
decaying
tubulence
field
Driven
turbulence
with wave-
number k
(perturbations
l= L/k)
Klessen
2001
Low k: large-
scale driving
High K: small-
- Turbulence produces complex network
of filaments and interacting shocks.
- Converging shock fronts generate
clumps of high density.
Collapse when the local Jeans-length
[lJ = (pat2/Gr0)] gets smaller than the
size of fluctuation.
- Have to collapse on short time-scale
before next shock hits the region.
--> Efficiency of star formation depends
strongly on the wave-number and
strength of the turbulence driving.
--> Large-scale less strongly driven
turbulence results in clustered
mode of star formation.
--> Small-scale srong driving results
in more low-mass protostars
and more isolated star formation.

15. (Gravo)-turbulent fragmentation II
Histogram:
Gas clumps
Grey:
Jeans un-
stable clumps
Dark:
Collapsed
core
- 2 steps: 1.) Turbulent fragmentation --> 2.) Collapse of individual core
Large-scale driving reproduces shape of IMF.
However, under discussion whether largest fragments really remain stable
or whether they fragment further …

16. Competetive Accretion
- Gas clump first fragments into a large number
of clumps with approximately a Jeans mass.
Hence fragmentation on smaller scales.
Then each clump subsequently accretes gas
from the surrounding gas potential. Even gas
that was originally far away may finally fall
onto the protostar.
Bonnell et al. 2004
Distance of
gas that is
ultimately
accreted.

17. Simulation example SPH simulation. Initial conditions: Uniform density
1000Msun
1pc diameter
Temperature 10K

18. Pre-stellar core mass functions III
Motte et al. 2001

19. General properties (maybe) governing the IMFor
fragmentation
Rather general agreement that
characteristic mass plateau must be due
to the original fragmentation processes.
At the low-mass end, fragmentation
may not be efficient enough and
dynamical ejection could help.
- Are large, massive fragments stable enough to be responsible for the
Salpeter tail of the IMF, or do large clumps further fragments that later
competitive accretion sets the masses of the high-mass end?
-- Initially, one would expect fragmentation down to the original
Jeans-mass at the beginning of collapse.
-- However, early accretion luminosity may heat the surrounding gas
relatively far out --> This would increase the Jeans-mass and inhibit
further fragmentation.
--> Not finally solved yet!

20. Characteristic mass defined by thermal physics
Larson 1985
Tempereature variation
with increasing density
- Jeans mass depends on T:
MJ = m1at3/(r01/2G3/2)
= 1.0Msun (T/(10K))3/2 (nH2/(104cm-3)-1/2
The number of bound fragments is
generally similar to the number of
Jeans-masses within the cloud.
At low densities, temperature decreases with increasing density, regions
can cool efficiently via atomic and molecular line emission.
--> decreasing MJ suggests that fragmentation may be favored there.
With further increasing density gas thermally couples to dust and clouds
become partially optically thick. Cannot cool well enough anymore
--> temperature increases again.
--> MJ decreases slower, potentially inhibiting much further fragmentation.
- Regime with lowest T should then correspond to the preferred scale for
fragmentation. The Bonnor-Ebert mass at this point is about 0.5 Msun.

21. The IMF in extreme environments
Stolte et al. 2005
- Low-mass deficiency in Arches cluster near Galactic center.
The average densities and temperatures in such an extreme
environment close to the Galactic Center are much higher
--> Gas and dust couples at higher temperatures.
--> Clouds become earlier opaque for own cooling.
--> Larger characteristic mass for the fragmentation process!

22. Clustering around intermediate-mass stars
- The clustering increases with the mass of the dominating sources.

23. Going to high-mass star formation
Shirley et al. 2003
Williams et al. 2004
Reid et al. 2005
Beltran
et al. 2006
Log[M/Msun]
Cumulative mass functions
from single-dish surveys
of massive star-forming
regions resemble
Salpeter-IMF.
But regions sample
evolving clusters?!

24. Fragmentation of a massive protocluster
12 clumps within
each core
Integrated masses
98Msun (south)
42Msun (north)
--> 80 to 90% of
the gas in halo
Clump masses
1.7Msun to 25Msun
Column densities
1024cm-2 -->Av~1000
Spatial filtering affects only large scale halo
on scales >20’’
Assumptions: - All emission peaks of protostellar nature
- Same temperature for all clumps (46K, IRAS)
Caveats: - Temperature structure
- Peaks due to different emission processes, e.g., outflows?
Beuther & Schilke 2004

25. Order of star formation
Kumar et al. 2006
- Detection of a large fraction of embedded clusters around young High-
Mass Protostellar Objects. Since the detected sources are largely class I
and II, and the massive HMPO are still forming, it indicates that low-
mass sources may form first and high-mass sources later.

26. Summary The most widespread mode of star formation is clustered.
The IMF is almost universally valid, Salpeter-like for >1Msun, characteristic
mass plateau around 0.5Msun.
- Mass segregation in clusters.
- Hertzsprung-Russel diagrams allow to estimate cluster ages.
- Anomalous IMFs (e.g., Taurus or Arches).
- Cloud mass distributions versus pre-stellar core mass distributions.
- Gravitational fragmentation.
- Gravo-turbulent fragmentation.
- Competitive accretion.
- General features of the IMF. The plateau at 0.5Msun maybe explicable by
thermal physics.
- High-Mass star formation differences?
- Order of star formation.

27. Sternentstehung - Star Formation
Sommersemester 2006
Henrik Beuther & Thomas Henning
24.4 Today: Introduction & Overview
Public Holiday: Tag der Arbeit
15.5 Physical processes, heating & cooling, cloud thermal structure
22.5 Physical processes, heating & cooling, cloud thermal structure (H. Linz)
29.5 Basic gravitational collapse models I
Public Holiday: Pfingstmontag
12.6 Basic gravitational collapse models II
19.6 Accretion disks
26.6 Molecular outflow and jets
Protostellar evolution, the stellar birthline
10.7 Cluster formation and the Initial Mass Function
Massive star formation, summary and outlook
Extragalactic star formation
More Information and the current lecture files: