Emmy Noether Application

Proposal for an
Emmy Noether Research Grant in
Theory of Massive Star
Formation
Robi Banerjee
4. 6. 2007

1. General Information
1.1 Principal Investigator
Robi Stefan Banerjee
Dr. rer. nat.
born: 21. October 1967
in Nürnberg, Bayern
german citizen
Current work address
Institut für Theoretische Astrophysik
Universität Heidelberg
Albert-Ueberle-Str. 2
69120 Heidelberg
Private address
Hauptstr. 114
69117 Heidelberg
Phone: (06221) 6505888
1.2 Topic
1.3 Code Words
Emmy Noether Application
Phone: (06221) 54-8967
Fax: (06221) 544221
E-Mail: banerjee@ita.uni-heidelberg.de
URL: http://www.ita.uni-heidelberg.de/˜banerjee
(Curriculum vitae and publication list are attached)
Theory of Massive Star Formation
Theoretical Astrophysics, Star Formation, Massive Stars
1.4 Scientific Discipline and Field of Work
The scientific discipline for this proposal is theoretical astrophysics in particular the field of
star formation.
1.5 Supporting Institute
The host institute for the proposed research work is the Institut für Theoretische Astrophysik
(ITA) at the University of Heidelberg. The ITA is part of the Zentrum für Astronomie
der Universität Heidelberg (ZAH) which also includes the Astronomisches Rechen-Institut
(ARI) and the Landessternwarte Königsstuhl (LSW). The proposed research group will work
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closely with the star formation group of Prof. Ralf Klessen at the ITA. The working environment
at the ITA offers the best possible conditions for the proposed project. The great
expertise of Ralf Klessen and his collaborators on modelling star formation and validating
models with observational data will be most fruitful for the presented project. Additionally,
being located in the vicinity of the Max-Planck-Institut für Astronomie (MPIA) is also very
advantageous for the proposed research team. One of the most active Astronomers in observing
massive star formation regions, Henrik Beuther, currently heads a Emmy-Noether
Research Group at the MPIA. Close collaborations with him and his research group will give
the proposed group valuable input from observational data. Generally, the research environment
in Heidelberg for astronomy and astrophysics is internationally rewarded and known for
its active success.
1.6 Scheduled Total Duration
The expected duration for this project is five years.
1.7 Proposal Period
We would like to set up our research group at 1 December 2007.
1.8 Summary
Massive stars are the brightest stars in our Universe. They can be observed copiously in
our own Milky Way and beyond it in other galaxies. Despite the substantial amount of observational
data, our theoretical knowledge of how such massive stars form is far from being
complete. Difficulties in understanding the formation of massive stars arise from the complexity
of this problem. For instance, massive stars form preferentially in clusters where the
neighbouring stars influence each other by outflows and strong radiation feedback. The aim
of this proposal is to develop a comprehensive model of massive star formation which will
integrate all the different processes of this issue.
So far, our understanding of massive star formations comes from separate, only loosely
connected, research directions. For the proposed projects we are going to combine these
different areas. In particular we will include feedback from radiation, winds and jets produced
by the newly formed massive star. As we will self-consistently trace star formation within
a large fraction of the parent molecular cloud our results will also include the effect from
interactions between the newly formed stars in the cluster. We will also keep track of the
chemical evolution within the star-forming region which we will use to validate our models
with observational data.
2. State of the Art and own contributions
2.1 State of the Art in the Theory of Massive Star Formation
Massive stars play a crucial role in the evolution of the universe. The first stars in the universe
were most likely massive stars with masses of a few hundred times the mass of the sun (Abel
et al., 2002). These stars have a short lifetime on the order of a few million years where their
subsequent supernova (SN) stage enriches the primordial gas with heavy elements and
dust. The evolution of the chemical composition of the interstellar medium (ISM) changes
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drastically the star formation history. Present day star formation takes place in molecular
and giant molecular clouds (GMC) which consist mainly of molecular hydrogen enriched with
heavy element molecules and dust.
Our general picture of present day star formation is based on the collapse of overdense,
gravitationally unstable cores within GMCs. In the current paradigm of modern astrophysics
these protostellar cores are built up in shock regions of compressive, supersonic turbulence
which pervades the clouds (Klessen et al., 2000; Elmegreen & Scalo, 2004; Mac Low &
Klessen, 2004; Ballesteros-Paredes et al., 2007). Initially the contracting gas cools efficiently
via molecular excitations and gas-dust interactions and the collapse proceed essentially
isothermally. At densities of about n(H2) ∼ 10 10 cm −3 the gas becomes optically thick
and the core starts to heat up while the contraction slows down. If the temperature in this
first core approaches about 2000K (at about n(H2) ∼ 10 16 cm −3 ) molecular hydrogen starts
to dissociate. The dissociation of H2 efficiently cools the contracting gas and collapse follows
again an isothermal track. At the time when all of the hydrogen molecules are dissociated
the collapse comes to a halt. This hydrostatic object is called the second core (e.g., Larson,
1969, 2003). The core then gains mass by accreting gas from the surrounding envelope. At
this class 0 phase the envelope is still much more massive than the central object. During
this accretion phase, gas with large specific angular momentum settles closer to the central
core and builds up a protostellar disc. Subsequently the core gains mass and eventually
becomes more massive than the surrounding disc. This stage is usually accompanied by
powerful outflows which make up the class I phase of the protostellar evolution and are observed
as Herbig-Haro (HH) objects (see e.g., Reipurth & Bally, 2001). In the next stage,
i.e. the class II phase, the envelope is drained onto the central core and planets might form
in the disc while the hydrostatic core approaches the main-sequence, i.e. it starts to fuse
hydrogen. Subsequently, the remnant gas in the disc will be depleted and the remaining
configuration (e.g. star-planets) is a long-living stellar system.
The above description of star formation is fairly general and does not include a number of
complexities. In particular, massive stars (stars whose mass exceed M > 8M⊙ and go off
as type II, i.e. core collapse, supernovae at the end of their lifetime) accrete most of their
mass while the released radiation exerts a substantial pressure on the surrounding gas and
dust (e.g., Kahn, 1974; Wolfire & Cassinelli, 1987; Yorke, 2002; Yorke & Sonnhalter, 2002). In
principle, the radiation could be strong enough to stall accretion onto the central star. To keep
the standard paradigm of star formation where stars assemble through accretion, several
suggestions have been made to overcome this problem. For instance, Wolfire & Cassinelli
(1987) concluded that dust opacities must be modified to assemble massive stars. Norberg &
Maeder (2000) and McKee & Tan (2003) suggested that the accretion rates should be higher
than the standard values known from low-mass star formation which could then squeeze the
radiation pressure. Jijina & Adams (1996) and Yorke & Sonnhalter (2002) showed that nonspherical
accretion through the disk can help to assemble high-mass stars. Krumholz et al.
(2005b) showed that radiation will escape through cavities carved by outflows or through
radiation driven instabilities (Krumholz et al., 2005a), again relaxing the upper mass limits
set by radiation.
Changes to the standard paradigm where also suggested to solve the problem of radiation
limited accretion. Such scenarios assume that massive protostars assemble by coalescence
of small and intermediate size cores (Bonnell et al., 1998; Bally & Zinnecker, 2005). Massive
stars are mainly found in dense star clusters with star densities of about 10 8 pc −3 where
encounters are feasible (e.g., Beuther et al., 2007).
This latter property, that massive stars are predominately observed in clusters, adds another
level of complexity to the understanding of massive star formation (e.g., Tan, 2005). In such
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a dense and clustered environment, different protostellar cores would compete for the gas
during their accretion phase. Such model predicts a certain mass spectrum of the stars within
the cluster depending on their location and multiplicity (Bonnell et al., 1997, 2004). It could
be that a dense environment is essential to build up massive stars whereas the few observed
massive field stars are ejecta from the cluster (de Wit et al., 2005). Additionally, massive
stars emit strong UV radiation which ionise the surrounding gas and might photoevaporate
the gaseous reservoir. This process will set limits of how many stars and how massive stars
could get in such an environment (Kroupa & Weidner, 2005).
Despite the progress within the last decade, so far we do not have a complete theoretical
model of how massive stars assemble. Our knowledge of star-forming regions where highmass
stars form comes mainly from observations. But even there, the precursors of massive
stars, the high-mass starless cores (HMCSs, following the classification of Beuther et al.,
2007), are rarely discovered because they are cold and faint, short lived, and most probably
deeply embedded in clusters. More examples are known from high-mass protostellar
objects (HMPOs) which already harbour massive protostars which will heat the surrounding
media. These objects emit in the mid-infrared wavelength from the heated dust (e.g., Campbell
et al., 2006). Protostellar discs, typically associated with low-mass star formation, were
also observed around massive protostars (e.g., Chini et al., 2004; Cesaroni et al., 2005; Patel
et al., 2005). Furthermore, recent observations of an ammonia line revealed direct infall
of gas onto a massive star suggesting high accretion rates (Beltrán et al., 2006). These
observations suggest that our hitherto existing picture of star formation might also be applicable
to the birth of massive stars. But the theory of massive star formation is just in its
commencement where significant uncertainties and competing models impede an integrated
description of this process. Further detailed investigations are vital to develop a consistent
theory of massive star formation.
2.2 Own contributions to the field
Our contributions to the field of massive star formation include studies on the early stage of
collapsing molecular cloud cores, outflows and jets from protostellar discs, and turbulence
in molecular clouds. This investigations are based on numerical simulations and resulted in
a number of publications (Banerjee et al., 2004; Banerjee & Pudritz, 2006; Banerjee et al.,
2006; Banerjee & Pudritz, 2007; Banerjee et al., 2007).
The numerical simulations were performed with an adapted version of FLASH code (Fryxell
et al., 2000) which is an adaptive mesh refinement (AMR) Eulerian grid code based on the
standard PARAMESH AMR library (Olson et al., 1999). With this technique we are able to
resolve up to 7 orders of magnitude in lengthscale in one simulation. This corresponds to
resolve an collapsing object from 1pc (e.g. a typical size of a star forming region) down to
a few solar radii. This is also important from a numerical point of view: To avoid artificial
fragmentation the local Jeans length, which scales ∝ ρ −1/2 , must be resolved by at least 4
grid points (Truelove criterion, Truelove et al., 1997). We implemented a refinement criterion
to resolve the local Jeans length with an arbitrary amount of grid cells. For our production
runs we used typically 8 or more grid cells to resolve the Jeans length.
The FLASH code is a versatile tool which includes a number of modules to solve different
physical processes independently or in combination. Apart from solving the hydrodynamic
(HD) and magneto-hydrodynamic (MHD) differential equations it can handle, for instance,
self-gravity, cooling and heating processes, ionisation from luminous sources, gravitating
particles, nuclear-reaction networks. The FLASH code runs on many computing clusters
independent on the hardware architecture (it is written in Fortran 90). Furthermore it is
4

Figure 1: Summarises the effects of different cooling processes which we included in our
collapse calculations. Initially the gas is efficiently cooled by molecular line emissions and
gas-dust interactions. This isothermal regime (constant Temperature and an adiabatic index
γ = 1) lasts until the gas becomes optically thick at densities about n > ∼ 1011 cm −3 . From
here on the core contracts almost adiabatically with a γ ≈ 4/3. This is the critical value
for self-gravitating, collapsing gas cores. During this stage the central core heats up (with
T ∝ n 1/3 ) until dissociation of molecular hydrogen sets in at temperatures around 1200K.
The dissociation process is an efficient coolant as it extracts 4.48eV of energy for each destroyed
hydrogen molecule from the gas. At the onset of hydrogen dissociation the central
density already reached n ∼ 10 16 cm −3 . Due to the strong temperature dependence the
dissociation process is self-regulating. The subsequent contraction proceeds almost isothermally
again. If all of the H2 is dissociated the so called second core contracts on a Kelvin-
Helmholtz timescale (not reached in our calculations, see e.g., Larson, 2003). Graphs taken
from Banerjee et al. (2006)
developed for parallel computing, based on the standard Message Passing Interface (MPI)
library and. So far, we have performed simulations with the FLASH code at: The Canadian
Sharcnet facilities which consist of Alpha and PC clusters with up to 3000 CPUs, the PC and
IBM clusters of the Max-Planck-Gesellschaft in Garching, the small (20 CPUs) PC cluster at
ARI, the IBM p690 Cluster at the Jülich Computing Center, the supercomputing cluster of the
of the National University of Mexico (UNAM), and others. Typical large production runs take
about two weeks on a 128 CPUs, i.e. about 43 thousand CPU hours.
Given the complexity of astrophysical processes we will continue to use numerical simulations
to study the formation of massive stars. These will be mainly performed with the FLASH
code which we will amend and extend for our research purposes.
Cooling processes
To study the collapse of molecular cloud cores in detail it is important to base this calculations
on a realistic model of cooling processes. The cooling efficiency depends mainly on
the density, temperature, and composition of the gas. The resulting spacial and temporal
variation of the cooling efficiency has a strong influence on the evolution and structure of
the collapsing core. For instance, it will affect the fragmentation of cores or discs and will
determine the appearance and structure of shocks.
For our first study of collapsing cloud cores we we included radiative cooling from molecular
excitations based on the treatment by Neufeld & Kaufman (1993) and Neufeld et al. (1995)
in our calculations (Banerjee et al., 2004). Neufeld et al. calculate the cooling rates for many
molecular species, most important of them are water, CO, and O2, and self-consistently ac-
5

Figure 2: Shows the evolution of the density and radial velocity profiles in the early isothermal
collapse phase of an initial Bonnor-Ebert sphere. The quantities are given in dimensionless
units: density ρ in units of the initial core density ρ0 , radius ξ in units of rBE = c/ √ 4π ρ0,
and infall velocity in units of the sound speed c. This non-homologous, outside-in collapse
maintains a flat core density which size is of the order of the local Jeans length. The infall
velocities become supersonic and peak always around the edge of the core region and therefore
moving towards the centre with time. Inside the core the velocity decreases sharply and
are zero at the centre. Graphs taken from Banerjee et al. (2004).
counted for the abundance of the different species as well as for the freeze-out of affected
lines if they become optically thick. Although these calculations assume that the gas mix
is in chemical equilibrium, it is a very realistic treatment as chemical timescales are usually
much shorter than the dynamical timescale of the collapsing system. In the next step, which
we adopted firstly in Banerjee et al. (2006), we included cooling by dust-gas interactions. It
turns out that dust-gas collisions are the dominant cooling process at number densities above
n > ∼ 105 cm −3 . Our treatment is based on the the calculations by Goldsmith (2001) which assumes
that dust grains radiate their excess energy in a blackbody spectrum and have a flat
size distribution. We also used temperature dependent opacities based on the compilation
of Semenov et al. (2003) which account for the fact of partially frequency independent opacities
and dust melting above T > ∼ 1500K. At densities above n > ∼ 10 11 cm −3 the gas becomes
opaque to the emitted infrared radiation. In this optically thick regime radiation escapes the
dense region in a process which can be described as diffusion. We developed a simplified
model of radiation diffusion which is valid for collapse calculations. Herein we approximated
the typical length-scale over which the radiation field varies significantly with the local Jeans
length. This is a valid approximation as long as the system is collapsing and the Jeans length
is the dominating length-scale. For future studies we will particularly improve the treatment
of radiation in the optically thick regime and use a flux-limited diffusion approach (see also
Section 3.2). Additionally, we included effects from molecular hydrogen formation and dissociation
in our recent calculations. In particular the dissociation of molecular hydrogen has
a large impact on the evolution of a collapsing protostar. The dissociation of a single H2
molecule requires an energy of 4.48eV. This energy is removed from thermal energy of the
gas and the gas is efficiently cooled. Our treatment of H2 dissociation is based on the calculations
by Shapiro & Kang (1987) formulation. Generally, the H2 dissociation depends very
strongly on the gas temperature. Therefore it is a self-regulating process during the core
contraction where slight temperature declines by dissociative cooling stops this process and
the gas will be compressively heated until dissociation starts again. This happens in a very
small temperature window around 1200K. In Figure 1 we summarise the cooling effects from
6

Figure 3: Shows the mass accretion and infall velocities for different setups during the early
phase of collapsing massive (M ∼ 170M⊙) cloud cores. Due to the supersonic infall of
gas the mass accretion could be high enough to squeeze the emitted radiation from the
young central star. Then accretion could continue resulting in a (or more) massive star(s).
The different models refer to our magnetised (mag), pure hydrodynamic (hydro, including
radiative cooling), and isothermal (iso) calculations. The highest mass accretion rates are
achieved in the case where the core temperature are highest (here hydro) because the infall
velocity is always a few times the local sound speed. Graphs taken from Banerjee & Pudritz
(2007).
one of our spherical collapse simulations.
Collapse of Molecular Cloud Cores, Accretion
As mentioned earlier, one of the outstanding questions in the theory of massive star formation
is how accretion overcomes the radiation pressure. If massive stars assemble through accretion
of the surrounding gas they will have reached the main-sequence in the Hertzsprung-
Russell diagram while assembling most of their mass there. As pointed out by Wolfire &
Cassinelli (1987) to overcome the strong radiation pressure produced by the young star,
mass accretion rates must exceed ˙ M > ∼ 10 −3 M⊙ yr −1 . Estimates for mass accretion rates
adopted from specific, analytic collapse calculations (Shu, 1977) give numbers of the order
of ˙ M ≈ c 3 /G ∼ 2 × 10 −6 M⊙ yr −1 , where c ≈ 0.2km sec −1 is the speed of sound in the cold
T ∼ 10K core, and G is Newton’s gravitational constant. This solution applies to a singular
isothermal sphere (SIS) which density diverges at the centre.
We started our investigation of collapsing cloud cores with initial core models which are
close to a hydrostatic equilibrium. Dense self-gravitating molecular cores might pass through
such a phase of nearly hydrostatic equilibrium before they start contracting in a runaway collapse.
Spherical gas cores in hydrostatic equilibrium are described by a Lane-Emden-type
differential equation and are called Bonnor-Ebert spheres if they maintain a critical configuration
(Ebert, 1955; Bonnor, 1956). Bonnor-Ebert spheres have a flat density distribution
in the inner region and a power-law type envelope (close ρ ∝ r −2 ). Many molecular cores
which follow a Bonnor-Ebert profile have been observed so far, the most prominent one is
the Bok globule Barnard 68 observed by Alves et al. (2001) with extinction measurements.
We used such Bonnor-Ebert density profiles as initial configurations for many studies of collapsing
cloud cores. Figure 2 shows a typical example of a supercritical (i.e. gravitational
unstable) collapsing Bonnor-Ebert sphere in the isothermal regime from our earlier calculations
(Banerjee et al., 2004). As already noted by Larson (1969) the collapse solution is
non-homologous, proceeds from outside-in, and the infall velocity becomes supersonic, un-
7

2400 AU
150 AU
Figure 4: Shows the structure (iso-densities) of the filamentary core which harbours a protostellar
disc. The initial conditions for this simulation were taken from calculations of Tilley &
Pudritz (2005) in which cores formed from supersonic turbulence. Here, an initially elongated
core collapses to a filament at which a thin sheet is attached. This off-centre sheet supports
the central disc with high angular momentum gas (see also Figure 5 for density slices through
the filament). Figure taken from Banerjee et al. (2006)
like in the case of a singular isothermal sphere Shu (1977). These results are also confirmed
by many other calculations (e.g., Foster & Chevalier, 1993; Hennebelle et al., 2003).
Already in our earliest investigation where we studied high-mass (M ∼ 170M⊙) and lowmass
(M ∼ 2.1M⊙, resembling the parameters of Barnard 68) collapsing cloud cores we
showed again that mass accretion rates are much higher than expected from the collapse
of a singular isothermal sphere (Banerjee et al., 2004). We re-visited this particular point
in Banerjee & Pudritz (2007) where focused on the early stage of massive star formation.
Here, we find mass accretion rates as high as 10 −3 M⊙ yr −1 . These might exceed the limits
calculated by Wolfire & Cassinelli (1987) necessary to overcome the radiation pressure. The
high accretion rates results have a simple explanation: The infall velocities are supersonic
which means that the estimate for the mass accretion ˙ M ∼ c 3 /G cannot be valid in this
regime and has to be replaced by ˙ M ∼ v 3 r /G, where vr is the proper gas infall speed.
Therefore, even moderate infall speeds of Mach 3 will result in a almost 30 times higher
accretion rate than given by c 3 /G. This does not yet account for the fact that the gas heats
during contraction which implies even higher infall speeds in the warm core. We find that the
infall speed is always of the order of 2 − 3 times the local sound speed. Together with this
effect the mass accretion rates can easily exceed 100 × c 3 /G as shown in Figure 3. Recent
observations of collapsing cloud cores clearly indicate supersonic infall speeds (Beltrán et al.,
2006; Furuya et al., 2006).
Similar theoretical results were obtained by McKee & Tan (2002) in a different approach.
These authors show that high accretion rates can be obtained if the surrounding pressure
stays high. This will be naturally achieved in the turbulent environment in which stars form.
If our results will persist even in a more realistic setup (i.e. including radiation feedback) this
would support an unified picture of star formation where low-mass and high-mass stars form
though accretion of the gas from their respective parental cloud core.
Turbulent Cloud Cores
To move towards a more realistic description of massive star formation we studied the collapse
of massive cloud cores which were assembled in a turbulent environment (Banerjee
8
37 AU

Figure 5: Shows different density slices through the filamentary core (see also Figure 4; the
shown scale is ∼ 200AU). Left panel: Shows the disc edge-on; parallel through the filament.
Right panel: Shows a cut in the disc plane. Most of the high velocity gas is accreted along the
filament. The central disc is supported by the gas which flows along the thin sheet. Images
taken from Banerjee et al. (2006)
et al., 2006). For this investigation we used final data from the numerical study by Tilley &
Pudritz (2005) as initial conditions for our simulations. Tilley & Pudritz studied the formation
of molecular cloud cores by decaying supersonic turbulence which is the current paradigm
of core formation (e.g. Elmegreen & Scalo, 2004; Scalo & Elmegreen, 2004; Mac Low &
Klessen, 2004). These simulations were performed with the ZEUS 3D code which use a
static grid to solve the hydrodynamical equations, including self-gravity. With a static grid approach
one can not follow the collapse much beyond its onset. The violation of the Truelove
criterion in this case will lead to unreliable results. Therefore, we used the FLASH AMR code
to follow the collapse of the cores formed in the Tilley & Pudritz simulations. The densest
region of a full spectrum of cores has the shortest free fall time, tff = (3π/32Gρ) 1/2 , and will
collapse first. The core we followed in our simulation had a free fall time of tff ∼ 1800yrs, a
corresponding density of ρ ≈ 1.35 × 10 −15 g cm −3 (n ≈ 4.0 × 10 8 cm −3 ), and a mass of about
23M⊙. We were able to continue the calculation for another ∼ 2400yrs corresponding to 1.3
times the initial free fall time.
The core is initially elongated and has a non-vanishing angular momentum distribution due
to oblique shocks which formed the core in the first place. In the subsequent evolution the
core collapses to a filament which size is several thousand AU (see Figure 4). Attached to
the filament is a thin sheet which connects slightly off-centre to the filament. Deep inside the
filament one can observe the formation of a protostellar disc. The disc plane lies perpendicular
to the major axis of the core. The spin orientation of the disc comes from the high
angular momentum gas which is flowing along the off-centre sheet towards the protostar in
the centre (see also Figure 5). So far the disc is not yet in Keplerian rotation and the central
protostar gathered only about 10% of a solar mass. Still most of the gas is accreted along
the filament and is ’raining’ onto the disc. This might change as soon an outflow along the
rotation axis is launched (this is a non-magnetised core for which we do not expect outflows
at this stage). This funnelled accretion with highly supersonic infall velocities is even more
efficient than for the idealised spherical clouds. We find mass accretion rates of more than
10 −2 M⊙ yr −1 onto the hot (T ∼ 1000K) protostellar core.
9

Figure 6: Shows the structure of the same protostellar region at two different scales. The initially
homogeneous magnetic field lines (indicated as yellow streamlines) are wound around
the rotation axis and pinched towards the centre. At large scales (left panel) the outflow (red
velocity isosurfaces) is driven by magnetic pressure and a magnetic tower configuration is
build up (Lynden-Bell, 2003). At small scales the onset of a magneto-centrifugally driven jet
can be observed. The protostellar disc is shown as a gray density isosurface. Applied to massive
star formation, this configuration will help radiation to escape through cavities punched
by such outflows and jets which in turn could relax the radiation pressure limiting accretion
onto the central star Krumholz et al. (2005b). Images taken from Banerjee & Pudritz (2006).
Outflows and Jets, Magnetic fields
Another outstanding problem of massive star formation is the influence and backreactions
from outflows. Outflows and jets are frequently observed around young stars and connected
to their formation through disc accretion (e.g., Bally et al., 2007; Arce et al., 2007). The
launching of these jets and outflows are often linked to magnetic fields where the plasma is
magneto-centrifugally expelled (Blandford & Payne, 1982; Pudritz & Norman, 1983; Fendt
& Camenzind, 1996; Pudritz et al., 2007) or lifted off the disc plane by magnetic pressure
(Lynden-Bell, 2003). In Banerjee & Pudritz (2006) we studied the self-consistent launching
of jets and outflows from collapsing, magnetised cloud cores. We used again the FLASH
code which also solves the magneto-hydrodynamic (MHD) equations describing the evolution
of a magnetised compressible fluid (i.e. plasma). For this investigation we used again
initial cloud cores modelled on the low-mass Barnard 68 Bok globule whose density distribution
follows closely a Bonnor-Ebert-type profile (Alves et al., 2001). Initially the slightly
rotating cloud core is threaded with a uniform, weak magnetic field (few micro Gauss) which
is aligned with the rotation axis of the sphere. After an initial phase during which a substantial
amount of angular momentum is removed by magnetic braking (Mouschovias & Paleologou,
1980) the supercritical cloud core collapses under its own weight. In this initial phase the
magnetic field is wound around the rotation axis and a toroidal magnetic field component is
build up. Because the magnetic field lines are frozen in in the ideal MHD case they follow
the condensing plasma and get pinched. This compression of the magnetic field and further
winding due the ever faster spinning disc eventually results in a configuration where magnetic
forces overcome the gravitational forces and material is lifted off the disc plane.
In the inner core region cooling becomes inefficient and the core starts to heat up. High
velocity material falling onto the warm, slowly contracting core shocks and heats up even
more. Typically we observe two or more shock fronts above an below the disc plane (see
10

Figure 7: Shows cuts through the density structure of a collapsing massive (M ∼ 170M⊙),
magnetised cloud core at two different scales. Similar to the low-mass case (see Figure 6)
a large scale outflow and a jet is launched if magnetic fields are present (the 2D magnetic
flow lines are shown in green). This indicates that that outflows and jets are also expected
around massive stars, at least in the very early phase. Again, the outflows punch cavities
in the infalling envelope through which radiation from the young massive star could escape.
Images taken from Banerjee & Pudritz (2007).
also Banerjee et al., 2004).
One distinguishes two different magnetically driven launching mechanisms. In a magnetic
tower type configuration (e.g., Lynden-Bell, 2003) it is the magnetic pressure from the dynamically
build up toroidal field component which lifts the gas off the disc plane. In such a
situation a magnetic ’bubble’ is inflating the inner region of such a configuration. Here the
magnetic field with its strong toroidal component act like a spring which tries to expand. Such
a configuration can be seen in the left panel of Figure 6. For every rotational turn of the disc
in which the magnetic field is anchored the tower grows by a certain amount. The subsequent
outflow has a relative low speed of about 0.4km sec −1 . The onset of this outflow and
the magnetic tower configuration is associated with the first shock fronts which appear above
the disc. In the shock fronts, beneath which infalling gas is essentially stalled the external
ram pressure and internal thermal pressure are equal. The additional magnetic pressure in
the inner region lifts the gas and the shock fronts upwards.
Further into the gravitational potential where the magnetic field is more pinched and wound
the outflow is driven by magneto-centrifugal forces: The gas plasma is attached to the magnetic
field lines like beads on a wire. It is known that centrifugal forces can launch disc winds
if the magnetic field lines have an angle of more than 30 ◦ with the rotation axis (Blandford &
Payne, 1982; Pudritz & Norman, 1983). Such a configuration can be seen the right panel of
Figure 6 where the magnetic structure appears to have a pinched hourglass shape. Clearly
the angle between the vertical axis and the magnetic field lines is larger than 30 ◦ . Here the
wind speeds are higher than in the pressure driven case of the magnetic tower. A stronger,
i.e. more compressed, magnetic field and a larger disc rotation expels the gas with velocities
up to 2km sec −1 . We like to note here that we are looking at the very onset of the jet
launching where the protostellar disc is not yet Keplerian and no central star has formed,
i.e. the disc is still much more massive than the central object. We expect that this mechanism
will accelerate the gas to much higher velocities indicative for jets from young stellar
objects (YSO jets) when the disc has settled to a Keplerian state and the central protostar
11

has formed.
Recent direct detections of the magnetic field configuration in the protostellar accretion disc
FU Orionis confirm the idea that magnetic fields are wound up and pinched in such a
disc (Donati et al., 2005). The lack of a strong collimated outflow from this object could
be due to a strong magnetic braking effect which slows down the disc plasma. We proposed
a follow-up observation of this protostar (Jean-Francois Donati being the principal investigator)
with the ESPaDOnS instrument on the Canada-France-Hawaii Telescope (CFHT). Within
the proposed 15 day observational period we hope to get clear Zeeman signatures which will
reveal in unprecedented detail the magnetic field structure in this object.
We also studied the influence of magnetic fields during the collapse of massive molecular
cores (Banerjee & Pudritz, 2007). For a similar setup than described above but a higher
core mass (M ∼ 170M⊙) we could show that outflows and jets can be launched by the
same mechanism than in low-mass case (see Figure 7). Even if these outflows are not long
lived, i.e. do not propagate far into the cloud, this has particular interesting implications for
massive star formation: These outflows and jets will punch cavities into the infalling envelope.
It is known that radiation, then emitted from the young massive star, will choose the way of
least resistance and escape through the outflow carved cavities (Krumholz et al., 2005b).
Krumholz et al. showed that these radiation funnels lower the radiation pressure exerted
on the gas next to the funnels and the disc. Therefore, upper mass limits for massive stars
derived from radiation pressure (e.g., Wolfire & Cassinelli, 1987) will be weakened or even
removed by this mechanism.
Another implication due to outflows and magnetic fields comes from the extraction of angular
momentum. Disc winds extract angular momentum while physically removing gas with nonvanishing
specific angular momentum from the disc. Magnetic fields exert torques on the
disc if their field lines connect fast and slowly circulating gas at the same time (e.g., Pudritz,
2003). Typically, the disc fields connect to slower rotating gas further out (like in the case
where the magnetic field is dragged inwards by the infalling gas) and the resulting torques
spin down the disc. This in turn will increase accretion as gas with high specific angular
momentum at the edge of the disc can settle deeper into the gravitational potential. By
removing angular momentum from the disc magnetic fields and outflows can actually help to
assemble massive stars quickly. In Banerjee & Pudritz (2006) we showed that the magnetic
torque and the angular momentum loss by the disc wind are comparable to the angular
momentum gain by the infalling gas.
In Section 3.1 we discuss how we will extend and improve the work we did so far on studying
outflows and jets. In particular, with the prospective sink particle approach we will be able to
study these outflows for much longer dynamical time and more rational periods.
Driving of Supersonic Turbulence
Massive stars are formed in an environment of supersonic turbulence (e.g., Elmegreen &
Scalo, 2004; Mac Low & Klessen, 2004; Ballesteros-Paredes et al., 2007). It is known that
supersonic turbulence decays quickly and has to be continuously driven to maintain (e.g.,
Stone et al., 1998; Mac Low et al., 1998; Padoan et al., 1999). So far we do not have a
conclusive mechanism which could serve as a driving source for the observed supersonic
turbulence in molecular clouds. Many proposals have been made among are such which
inject energy into the gas from inside the cloud. Norman & Silk (1980) firstly proposed
that jets from YSOs could sufficiently stir up their environment. This is an interesting idea
in the context of turbulence regulated star formation. Supersonic turbulence can, on small
scales, prevent star formation because here it supports the gas against gravity. On large
scales, it can compress enough gas in clumps and cores which can become supercritical
12

Figure 8: Summarises the main results form our study on jet-driven turbulence. The left panel
shows probability density functions (PDFs) of the velocity distribution in the gas at different
times (dimensionless units). The PDFs are normalised to the volume which is affected by
the jet and can be interpreted as volume fractions which are occupied by a certain velocity
interval. The jet itself, here Mach 10, is clearly visible in the peak at v/c = 10. Apart from it,
almost non supersonic fluctuations are excited by the jet although it is driven continuously.
Most of the fluctuations are highly sub-sonic and peak below v/c < 0.1. The reason is that
supersonic fluctuations do not propagate far from its source and decay quickly in time as
can be seen in the right panel. Here, we show the evolution of the kinetic energy for the
supersonic (v > c) and subsonic (v < c) regime separately. After the driving force is shut
off at t = 1.3 the supersonic part of the energy decays much faster than the subsonic part.
From the evolution of the total energy it is also obvious that the energy is transfered from the
supersonic to the subsonic regime. Graphs taken from Banerjee, Klessen, & Fendt (2007).
and collapse under their own weight, therefore initiate star formation. If YSO jets could
maintain supersonic turbulence on all scales star formation within a molecular cloud would
be a self-regulating process.
In a recent study we re-addressed the question of of jet-driven turbulence (Banerjee, Klessen,
& Fendt, 2007). For this investigation we used again numerical two and three-dimensional
simulations performed with the FLASH code. Here we model the supersonic jet as a momentum
injection from one side of the simulation box. The jet diameter is only a small fraction
of the side length of the simulation box which allows us to simulate the jet for many sound
crossing times until the gas will leave the box (we use outflow boundary conditions). We can
vary various parameters of the jet and the background properties. Among these are the jet
speed, the density and pressure of jet, the duration of the jet, the strength and orientation of
a background magnetic field, and we can set up clumps with which the jet interacts.
If jets are the driving source of supersonic turbulence in molecular clouds they should entrain
a large fraction of the surrounding gas and excite supersonic fluctuations in it. Supersonic
jets running into a gaseous medium develop a bow shock at their tip which opening angle
depends on the speed of the jet. The opening angle is smaller for faster jets and becomes
very narrow for highly supersonic jets (vjet > 10c). It is mainly this bow shock which entrains
the surrounding gas as long as the jet does not become unstable. But, the velocity in the
bow shock region decreases with increasing distance from the jet axis and becomes subsonic
shortly beyond the edge of the jet. Usually, instabilities develop at the edge of the jet. Due
to shear flows Kelvin-Helmholtz instabilities can build up at the boundary layers between the
moving jet and the non-moving surrounding gas. These instabilities are most prominent if the
jet moves with transonic speeds, i.e. close to the sound velocity. For highly supersonic jets, as
13

they are observed around YSOs, the instabilities are compressive and damped quickly until
the fluctuations become subsonic. This is a general feature of supersonic random motions,
i.e. turbulence (e.g., Mac Low et al., 1998) and shows the dilemma of jet-driven supersonic
turbulence: A fast jet, which has the potential capability to excite large velocity fluctuations,
is stable, has a small bow shock region, and stays very well collimated without entraining
much of the surrounding volume. Otherwise, a transonic jet becomes easily unstable and will
entrain a large fraction of the gas but has little energy to excite supersonic motions.
By varying different jet parameters we find a general trend which is summarised in Figure 8.
Here we show the probability density function (PDF) of velocity fluctuations and the time
evolution of the kinetic energy for the sub- and supersonic regime separately. Essentially, the
PDF shows the fraction of the total gas which moves with a certain velocity (we normalise
the PDF to the volume which has non-zero velocity for each time t). In this example the
jet has a continuous speed of v = 10c and is visible as a sharp peak in the PDF. The
interesting feature is that the supersonic fluctuations are dramatically damped. The jet is
not able, although continuously driven, to excite a large fraction of supersonic motions in the
gas. As mentioned earlier, supersonic fluctuations are highly compressive and their energy
is mainly consumed in compressing the gas instead of pushing the gas to high velocities.
The expansion of the compressed gas in turn excites only subsonic and highly subsonic
fluctuations. This is the reason for the ’abyssal plain’ between the jet peak (v/c = 10) and
the transonic (v/c = 1) regime. The subsonic fluctuations are largely incompressible and
can propagate far into the medium. Given some time these subsonic fluctuations will occupy
most of the excited gas and the PDF peaks around v/c ∼ 0.1.
The right panel of Figure 8 shows the results from a transient jet calculation where the jet
is switched off at t = 1.3 (dimensionless time units). From the subsequent decay of the
kinetic energy one can see that supersonic motions also decay much faster in time than the
subsonic ones. The typical decay laws for the kinetic energy of the supersonic and subsonic
fluctuations are Ekin(v > c) ∝ t −2 and Ekin(v < c) ∝ t −1 , respectively. The total kinetic
energy decays as Ekin ∝ t −1.2 in accordance with other studies of decaying supersonic
turbulence (e.g., Mac Low et al., 1998; Mac Low, 1999). The time shift between the peaks
of the supersonic and subsonic energies (the subsonic kinetic energies start to decay later)
comes again from the fact that supersonic fluctuations excite mainly subsonic motions.
From our investigation of jet-driven turbulence we concluded that jets from YSOs are unlikely
candidates to power the supersonic turbulence in molecular clouds. Together with Ralf
Klessen and coworkers we will pursue our study of putative driving sources. Among such
could large scale flows in the warm neutral medium (WNM) of the interstellar gas, or SN
explosions in the vicinity of the molecular cloud.
3 Scientific Objectives and Working Schedule
3.1 Scientific Objectives
The aim of this project is to develop a comprehensive description of massive star formation.
Different, so far unconnected, pieces in the models of high-mass star formation should be
improved and combined to one global picture. For this goal, it will be important to develop
realistic models for the early accretion phase, radiation feedback, and outflows within one
framework which can then be combined to calculate, self-consistently, the formation of stars
from collapsing massive cloud cores.
The proposed research group, consisting of two PhD candidates and the applicant, should
14

e considered as an unit, working together on a complex problem. The complete project
will naturally be divided into working parts, which can be handled by the individuals of the
group, while always bearing in mind that the pieces are closely interconnected. As outlined
in Chapter 2, the main ingredients of massive star formation are the collapse and accretion
phase, and the radiation feedback from the newly formed pre-main-sequence star. Both
treatments should be improved substantially within two separate PhD projects. The applicant
will, apart from supervising and coordinating the PhD projects, work on outflows and jets and
study MHD effects.
The main scientific objectives of the proposed project can be summarised in addressing the
following issues:
• What are the initial conditions which result in massive star clusters and how do
massive protostars assemble?
As mentioned earlier, there is a strong evidence that massive stars form predominantly
in high-density star clusters. It is one of the outstanding problems in star formation to
understand the conditions under which such clusters form, to quantify the mass distribution
of protostars within such clusters, and to describe their fate until they reach the
main-sequence of the evolutionary track. For instance, the early protostars might form
in relative isolation and move towards the gravitational centre of the forming cluster with
time. Intermediate sized protostars could as well formed quite clustered and coalesce
to form massive stars (e.g., Bonnell et al., 1998). Based on the adapted numerical
tool, where we will include sink particles, we will be able to perform extensive parameter
studies which can be used to distinguish between different formation and evolution
scenarios. The incorporated different cooling mechanisms of the gas (Banerjee et al.,
2006, which we will extend for this purpose) will build these star formation scenarios on
a realistic ground.
• Does radiative feedback imply an upper mass limit?
The other key issue in understanding the formation of massive stars is to know what determines
the final mass of the star and whether there is an upper limit to it from radiation
feedback. So far, one- dimensional (Wolfire & Cassinelli, 1987) and two-dimensional
(Yorke & Sonnhalter, 2002) models show that the final mass of the star is limited by
the radiation pressure released by the already active star. However, anisotropies of
the radiation field (e.g. by outflows and disc accretion) and radiation instabilities could
relax these limits in more realistic scenarios (Krumholz et al., 2005b,a). We will study
the feedback from radiation pressure for isolated and multiple massive stars. These
investigations will be based on self-consistent three-dimensional collapse calculations
which will include backreaction from the released stellar radiation.
• How quickly must massive stars form within clusters before feedback evaporates
the cloud?
Radiation feedback may not only inhibit accretion onto the newly formed stars but it
could dissolve the circumstellar discs and the entire parental molecular cloud depending
on the luminosity of the stars in the cluster. Hence, the assembly of stars in a
massive star cluster competes with the dissolution of the cloud itself. It is therefore
important to know how quickly such a cluster has to form until the gas reservoir is
gone. We will investigate this process with three-dimensional cluster simulations which
will include feedback by photo-ionising UV radiation and photo-evaporation of the surrounding
gas and dust.
15

• What is the influence of outflows and jets on the formation process and their
feedback to the parental cloud?
Star formation is usually accompanied by outflows and jets (e.g. Bally et al., 2007; Arce
et al., 2007). It is not yet clear what particular influence they have on the star-forming
cluster. Stellar outflows from young objects or disc-driven jets could, on the one hand,
reduce the mass accretion onto individual stars or, on the other hand, elevate accretion
while extracting angular momentum (e.g. Banerjee & Pudritz, 2006; Banerjee & Pudritz,
2007). On larger scales the outflows could disperse the parental molecular cloud or
otherwise trigger more star formation through compressing the gas in the bow shock
region. We will include outflows and jets based on stellar outflow and disc-jet models
and study their backreaction to the accretion process and feedback in the surrounding
gas.
3.2 Work Program
The above outlined scientific goals should be pursued within two PhD projects which will
cover different parts of the complete project. The results and outcomes of these part-projects
will be consolidated by the applicant who also will conduct research covering additional issues
of the proposed project. A description of the individual projects and schedules is given
in what follows.
PhD Thesis: Modelling the protostar and protostellar accretion phase
One of the missing links in our understanding of massive star formation is a self-consistent
model of the accretion phase of young protostars. The currently existing models do not
cover the full complexity of this process. For example the two-dimensional calculations of of
collapsing molecular cores by Yorke & Sonnhalter (2002) include a young star which emits
radiation, accretes and ejects gas but cannot move within the parent cloud. This treatment
handles only a single central object and does not capture the possibility of disc fragmentation
and multiple interacting massive stars. Recent three-dimensional models of collapsing
cloud cores with radiative feedback form young stars are still approximative (Dale et al.,
2005; Krumholz et al., 2007). The SPH approach by Dale et al. (2005) can handle several
interacting stars at the same time, but so far only the first one which forms emits radiation.
Additionally, this (single frequency) radiation only ionises the surrounding gas but does not
contribute to the radiation pressure. One the other hand, the Krumholz et al. (2007) model,
which also captures the protostellar phase with a sink cell technique (Krumholz et al., 2004),
treats the radiation from young stellar objects in a diffusion approximation (i.e. no ray-tracing).
Therefore, this approach does not account for ionising effects by the luminous, newly formed
massive star.
The aim of this thesis is to model the accretion phase of protostellar objects. Because of the
complexity of this problem this should be done with the help of numerical simulations based
on the FLASH code. The PhD candidate should develop a ’sink particle’ description within
this numerical framework to model the properties of dense, accreting objects which can
be interpreted as protostars (i.e. adiabatic cores which do not emit radiation at this stage).
These sink particles should be able to move freely, i.e. independent of the underlying grid
structure, within the simulated region to capture the full dynamics of interacting stars within
a gaseous environment. This Lagrangian treatment of the sink particles will combine the
advantages of grid codes (shock capturing, proper handling of instabilities) with the ones
from SPH (accurate treatment of N-body interactions). So far no publicly available grid code
includes a treatment for accreting sink particles. This model has to account for the dynamical
16

mass growth of the individual newly formed stars based on the underlying accretion history.
In particular the sink particles should be able to gain mass during the collapse phase (by
infalling gas) as well as through disc accretion and Bondi-Hoyle accretion while the central
object is moving through the ambient gas. The model should also guarantee a self-consistent
treatment of the emerging circumstellar disc and be able to follow the long-term evolution of
the protostar-disc system. Together with the ability of the modelled protostars (implemented
as Lagrange particles) to move freely in the star-forming region, the performed calculations
could then capture the entire dynamics of a stellar-cluster forming region. This will include
interactions of multiple stars and star-disc encounters.
Upon implementation and testing of the protostellar accretion model the PhD candidate will
study the collapse of dense molecular clouds and calculate the long-term evolution of the
(multiple) massive protostars. The study should lead to a quantification of initial conditions
which result in the formation of star clusters; it should address the question of how massive
protostars acquire their mass, i.e. via the collapse of single, dense cores or from the coalescence
of intermediate size clumps. The long-term evolution of the formed protostars will be
studied in the context of the accretion history (i.e. which protostar accretes how much of the
surrounding gas?) and merger history (i.e. how many stars form through merger events?).
As the treatment of the gas already includes radiative processes from molecular excitations
and gas-dust collisions (Banerjee et al., 2004, 2006) the results from these studies will result
in a realistic description of the formation and evolution of massive protostars in star-forming
clusters.
In an independent, second step this model for protostellar objects should then be combined
with the radiation feedback treatment which will be developed within a second PhD project
(see below). Therefore, code design for the sink particles must be well documented and
extendable to include additional stellar properties like mass outflow and radiation. The PhD
candidate should also keep in mind that the implementation of sink particles should become
part of the public FLASH version which can then be used within the astrophysical community.
First year
At the beginning the PhD candidate should get familiar with astrophysical processes which
determine the formation of stars. The proximity of the star formation group at the ITA and
the research school IMPRS, run by the MPIA and the University of Heidelberg is a great
advantage for new students to quickly acquire the necessary knowledge to start their research
projects. He or she should get quickly involved with the numerical technique and
perform well arranged test problems which cover different aspects of astrophysics. Being
confident with the structure of the code and the computing facilities the candidate can then
start to implement their own modifications. The FLASH code contains a basic module to
handle gravitating, Lagrangian particles. Based on this module the PhD candidate should
incorporate fully active sink particles, which feature the gross properties of the newly formed
protostars. This modifications to the code will be fairly complex and time consuming, but can
be done in intermediate steps. (We recently tested the FLASH particle module and started
to adapt it for the purpose described here. From these investigations we found that this approach
is the right way to model protostars for our future calculations.) The implementation
will include the ability of the sink particles to accrete infalling gas, i.e. grow in mass, and
change linear and angular momentum accordingly to the absorbed gas. The dynamical increase
of the particle mass will change the gravitational potential which must be properly
accounted for. Therefore, the PhD candidate has to modify the existing self-gravity part of
the code. He or she will also face technical details involving the adaptive refinement handling
so that the physical relevant scales will be properly resolved and numerical artefacts avoided.
17

Second year
At the end of the first project year the candidate should have finished implementing accreting
sink particles into the numerical scheme. At the beginning of the second year into the project
he or she can then start with the rigorous testing of the model. The test calculations should
be compared to analytic and semi-analytic solutions of accretion problems (e.g. Bondi-Hoyle
accretion) and orbiting problems (two or more orbiting objects with different masses). These
comparison calculations should lead to a first publication showing the capability and limits of
the developed model for protostellar cores. This will also give the PhD candidate the chance
to acquire and/or improve his or her presentation and writing skills. At the same time this
documentation will serve as an individual chapter for his or her PhD thesis.
Third year
At the end of the second year the candidate should have finalised the code development and
testing stage and should then proceed with large scale collapse calculations to study the first
stage of massive protostars. This investigation will be based on a comprehensive parameter
study whose results will constitute the main content of the PhD thesis. As mentioned earlier,
this study should result in the quantification of initial conditions which produce putative massive
stars. Based on characteristic calculations the study should quantify the accretion and
merger history of the newly formed protostars. The performed long-term simulations should
then be used to study possible disc fragmentation, the influence by interacting protostars,
and star-disc encounters on the accretion evolution. The results will then be used to address
the open questions in relation with massive star formation listed above. This project should
result in one or more scientific articles which should be published in established scientific
journals.
The PhD candidates should collaborate closely and exchange design concepts before implementation
to allow for a smooth incorporation of the two projects.
At the end of the third year the PhD candidate should write up the developed techniques
and research results in a thesis work. We will make sure that the prospect candidate can
complete the PhD within the specified three years.
Follow-up projects: Fourth and Fifth year
In the fourth and fifth year into the project the developed sink particle approach to capture accretion
properties of protostellar objects should be extended to calculate feedback by mass
ejection from young stellar objects. Ideally this work should be done by the (former) PhD candidate
who then will be most familiar with the numerical techniques. Almost all young stellar
objects are associated with mass outflows, whether stellar winds or disc-driven jets, whose
influence on the formation of massive stars should be taken into account in a comprehensive
calculation. Unfortunately, our knowledge of the launch mechanism of such gas outflows is
not yet conclusive. Therefore we will conduct a comprehensive parameter study where we
will vary mass outflow rates and jet angles which can then be compared to observations to
limit the physical parameter space.
Furthermore we will study the coupling of magnetic fields to the cloud gas. Magnetic fields
permeate the interstellar medium and are associated with all astrophysical objects. Including
these fields in the calculations will also contribute to our understanding of star formation.
So far the FLASH code can solve the ideal MHD equations which are sufficient to study
18

self-consistently magnetically launched outflows (Banerjee & Pudritz, 2006) but has to be
extended to capture effects from non-ideal MHD (i.e. ambipolar diffusion and Ohmic resistivity)
and to handle stellar magnetic fields.
PhD Thesis: Radiation feedback from massive stars
One of the key issues to understand the formation of massive stars is the proper treatment
of feedback from the progenitor stars. As mentioned earlier, massive stars accrete a substantial
fraction of their final mass by the time they already start their nuclear burning phase,
i.e. approached the main-sequence track. The resulting radiation feedback cloud in principal
set a mass limit for such stars via radiation pressure (Kahn, 1974; Wolfire & Cassinelli, 1987;
Yorke & Sonnhalter, 2002). Despite such theoretical upper limits on the mass of massive
stars, observations reveal more and more massive stars whose mass exceed the predicted
limitations. Typically, the theoretically predicted limits are two to four times below the masses
from the observed most massive stars (e.g. Pistol star, Eta Carinae, dozens of stars in 30
Doradus). Therefore, we have to considerably improve our models of radiation feedback to
close the gap between theory and observations. So far very few attempts have been made
to tackle this problem in a self-consistent way, i.e. including the collapse phase as well as
the radiation feedback in the same calculation. One of the most sophisticated calculations
was done by Yorke & Sonnhalter (2002) who implemented a wavelength dependent radiation
transfer treatment in their collapse simulations. Although they could show that the wavelength
dependent radiation transfer relaxes the upper mass limits, the final masses are still substantially
below the observed ones. These simulations were restricted to two-dimensional,
axi-symmetric cases. Fully three-dimensional calculations will lead to more realistic results.
In particular outflows and instabilities of radiation bubbles might help to elevate or rid mass
limitations as proposed by Krumholz et al. (2005b,a). This has yet to be shown in a selfconsistent
calculation and will be a main aspect of the proposed research project.
Furthermore the emitted radiation from young stars heat, ionise, and can even photoevaporate
the surrounding gas. These processes, if once operative, will alter the cluster evolution.
Whether the feedback from the first formed massive star will initiate or inhibit nearby star
formation should also be investigated in this thesis project. The implementation of the photoheating
and ionisation should be based on the ray-tracing module developed by Rijkhorst
et al. (2006) for the FLASH code. This module calculates the column density for different
sources with a parallel ray-tracing algorithm which in turn is used to compute the ionisation
and heating rates. We already performed several successful test calculations with this
module which convinced us of the usability of it. This treatment has to be adapted for the
purpose studied in this project. In particular it should be able to handle different chemical
compositions which will alter the ionisation cross sections and the cooling and heating rates.
Furthermore, the calculations should also take into account the possibility of moving sources
which will be important in studying star forming cluster. It should be mentioned here again
that the two PhD candidates should exchange their design and technical concepts before
implementation so that both parts can be smoothly merged for future calculations.
Despite the vast developments of computer technology in the last couple of years we are still
far from being able to calculate the complete radiative transfer equations in three-dimensions.
The complete treatment of these equations would involve the knowledge of the intensity as
a function of eight independent variables (i.e. three spacial variables of the intensity location,
three directional angles, frequency, and time). The storage and computation of such an
eight dimensional variable with sufficient resolution can not be handled with the presently
accessible computing clusters. Therefore the radiative transfer part of this projects has to
be based on reasonable approximations which will reduce the degrees of freedom for the
19

intensity field. Such approximations can be a flux limited diffusion approach (e.g. Yorke &
Sonnhalter, 2002; Krumholz et al., 2007) which essentially averages the intensity field over
all directions. This approach can also be extended with higher-order spherical harmonics to
account for the main contributions of anisotropies.
The radiation itself is emitted by the newly formed massive star or multiple stars. The PhD
candidate should model these stars as luminous sources which vary with time. The model
should be based on the evolution of pre-main-sequence and zero-age-main-sequence tracks
from stellar evolution theory. A viable calculation of the stellar luminosity function is described
in Yorke & Sonnhalter. (Helpful details can also be found in the book of Bodenheimer et al.,
2006). Herein, the mass and radius of the central star is calculated based on a nuclear equation
of state, mass accretion and mixing efficiency. The actual luminosity is then determined
from previously published pre-main-sequence tracks; in this case the D’Antona & Mazzitelli
(1994) calculations were used. It is expected that the radiation from luminous massive stars
emit sufficient photons to photoevaporate the protostellar envelope and the circumstellar disc.
The study of this process with a realistic description of the central massive star and radiation
field should be the main effort of this part of the PhD project.
Within this thesis project the PhD candidate should develop a realistic model for radiation
feedback from young massive stars and study its influence on the formation of massive stars
in isolation and clusters.
First year
As for the other PhD project, the PhD candidate should begin by getting familiar with the
astrophysical processes which are operative in star formation. In particular, he or she should
get a profound knowledge of radiative processes and approximate descriptions of them. The
candidate should also early on get involved in performing numerical simulations of relevant
problems. Again, when the PhD candidate has acquired the basic concepts of the physics
and has gotten familiar with the structure of the code, he or she should start implementing
a proper treatment of radiative processes. These processes should include photon-heating,
photoionisation, dissociation of molecules, formation and destruction of dust grains, and cooling
by collisional excitations of molecules and dust. This subproject should be based on the
ray-tracing module by Rijkhorst et al. (2006) to calculate the photon induced processes and
on the treatment of collisional cooling by Banerjee et al. (2006). Subsequently the candidate
should adapt the ray tracing part so that multiple moving stars can be included in the calculations.
This part of the numerical calculations should be verified with known solutions of test
problems (e.g. Spitzer solution of a propagating ionisation front).
Second year
At the end of the first year into the project the PhD candidate should have completed the
first part of the project drafted above and should now start to implement a realistic treatment
of the radiation intensity and its interaction with the molecular gas and dust. This approach
could be based on a flux limited diffusion approximation as outlined above and used in the
two-dimensional calculations of Yorke & Sonnhalter (2002). Having the ray-tracing module,
one can then use the consistently calculated optical depth to determine interaction efficiency
between the photons and the gas. At the same time the candidate should implement a
model for the time dependent luminosity of the massive star which is the source of the radiation
field. The model again can be based on a similar approach described in Yorke &
Sonnhalter (2002). After elaborate test calculations of the radiation field and stellar model
the PhD candidate should publish this results in a scientific journal. As in the case of the
other candidate, this will give him or her the chance to structure the collected works and
20

improve the presentation skills.
Third year
After finalising the implementation and testing of the models the candidate should study the
effects of radiation feedback on massive star formation. In the first step this should be done
with isolated massive stars where realistic initial conditions can be obtained from the collapse
simulations performed for the other PhD project or from earlier calculations by Banerjee et al.
(2006). The candidate will then have everything needed to address crucial questions of massive
star formation: Is there an upper mass limit for stars set by radiation pressure? How
large is the final mass of the massive star within is model? What are the timescales for photoevaporating
the surrounding gas and disc? Do radiation instabilities develop and how do
they influence the accretion evolution? In a second step the radiation description should be
applied to large scale cluster simulations. Ideally this should be done together with the sink
particle approach developed in the other thesis project. In case the two projects are not quite
synchronised the cluster calculations can also be performed independently using initial data
from previously generated collapse simulations. These calculations should be used to study
the influence of multiple massive stars on the evolution of individual (proto-)stars and the
entire cluster. Apart from compiling the results in the thesis these extensive studies should
also result in one or more scientific publications. As for the other PhD candidate we will make
sure that he or she can complete the PhD within the specified three years.
Follow-up projects: Forth and Fifth year
In the forth and fifth year into the project the former PhD candidate or an other postdoc should
extend the above described model with a network of non-equilibrium chemistry. This project
has two important implications. First, the chemical composition of the gas determines to a
great extend the evolution of star formation through cooling and heating processes. Second,
the spacial distribution of molecules at each time can be compared with observations which
use particular tracer molecules. Again, the expertise of astronomers and astrophysicists
at the Heidelberg institutes will be very beneficial for this project. In particular, to study
the chemical evolution within massive star forming regions we will collaborate with Dimitry
Semenov and his co-workers (MPIA, chemical evolution calculations) and Henrik Beuther
(MPIA, observations).
Further projects that we will work on are be based on the fact that massive stars are very
short lived and will end up as supernovae within a few million years after their formation. This
supernova explosion will most probably stir up the entire parental molecular cloud, enrich the
gas with metals and dust, and initiate further star formation. With a realistic model of this
process one could study in detail the evolution of molecular clouds during and after the supernova
phase.
Principal Investigator
It is expected that the applicant will spent about 1/3 of the time supervising the PhD projects
and coordinating the group’s developments. In the remaining 2/3 of the available time we will
work on the following projects within the proposed group and with other collaborators:
• Extending the existing cooling model for the density and temperature range important
to study massive star formation
• Improving the FLASH code. Particularly, the self-gravity solver for the FLASH code has
to be made more efficient to perform long-term simulations in reasonable computing
time
21

• Modelling of jets and outflows from young massive stars and study their backreaction
into the parental molecular cloud
• Study of MHD effects at the formation of massive stars
• Study of molecular cloud formation in colliding flows
• Post-processing and interpreting the simulation data; comparison with observational
data
• Implementation of non-equilibrium chemistry
The work program would proceeded as follows:
Cooling and heating processes
As described in Chapter 2, cooling of self-gravitating molecular gas is vital for star formation
because it is the mechanism which rids the excessive thermal pressure during the gravitational
collapse and allows the cloud cores to condense to stellar densities. At the beginning
of the first year we will extend the existing cooling model (see Section 2.2) to cover the full
density and temperature range which is reached by the collapse of molecular cloud cores.
So far the existing cooling and heating model includes four main processes: 1) cooling by
collisional molecular excitations based on the calculations by Neufeld & Kaufman (1993);
Neufeld et al. (1995); 2) energy exchange by gas-dust collisions based on the formulation
by Goldsmith (2001); 3) formation of molecular hydrogen on dust grains following the Hollenbach
& McKee (1979) description; 4) dissociation of H2 using the Shapiro & Kang (1987)
dissociation rates. In particular, the available Neufeld and co-worker data cover only a density
range of 10 3 cm −3 ≤ n ≤ 10 10 cm −3 . We will extend this range on both sides to densities
of 100cm −3 and 10 12 cm −3 , respectively. The necessary calculations should be based on a
similar approach explained in Neufeld & Kaufman (1993); Neufeld et al. (1995). Furthermore,
we will include in our equilibrium chemistry three body processes in which molecular hydrogen
forms at high densities. This will be necessary as this formation process can compete
with H2 dissociation in the same density and temperature range. The implementation will be
done in collaboration with Simon Glover (currently at the AIP) who is an expert in the field
of chemical evolution in star-forming regions (see e.g. Glover & Mac Low, 2006a,b). We will
also adapt the implementation of heating by ionising photons for the purpose of our investigations.
As mentioned in the description for the radiation feedback PhD project, the treatment
of photoheating should be based on the Rijkhorst et al. (2006) description. As these are
simplifications of the original DORIC routines developed by Mellema & Lundqvist (2002) and
Frank & Mellema (1994) it will be appropriate to closely collaborate with Garrelt Mellema on
this subject and eventually visit him in Stockholm.
Improvements of numerical techniques
In order to study the formation of massive stars it will be important to perform long-term numerical
simulations to cover all the different impacts on this process. Therefore we have to
invest some time in improving certain modules of the numerical tool before we are performing
large scale production runs. In particular we found that the self-gravity solver for the FLASH
code can be optimised substantially. The solver is based on the standard multigrid technique
used by many other grid codes but performs somehow inefficient. One reason is the communication
overhead during the V-cycles (the multigrid solver iterates towards a solution of the
Poisson equation for each resolution level separately and goes back and forth between these
levels, hence V-cycle). We will investigate into this communication bottleneck during parallel
computing and bundle it to a minimum. It is also known that the Gauss-Seidel iteration
22

scheme which is used in the FLASH code for the smoothing operations does not perform as
fast as other algorithms in parallel computing (see e.g. Adams et al., 2003). We are planing
to implement alternative algorithms like the polynomial method described in Adams et al.
(2003). As a third improvement of the self-gravity module we will develop an adaptive time
stepping in this routine. So far, the solution for the Poisson equation is achieved on every
refinement level at each time step assuming that coarse-grain data advance at the same
(fast) speed as the fine-grain data. One can take advantage of the fact that the change in
density on coarser resolution proceeds slower than on higher resolution (this is the case at
least for most of our collapse calculations). This adaptive time stepping will also improve
the performance of the prospective simulations. In the past we had good experience in discussing
problems and suggestions for the FLASH code directly with the developing group at
the ASC Center in Chicago (e.g. we visited the Center for an AMR meeting in 2003 and held
a FLASH workshop at the McMaster University in 2005). We will continue our collaboration
with the Chicago group and take advantage of their expertise. It might be helpful if one or
more members of the proposed group visit the ASC Center to exchange informations or if
fundamental changes to the FLASH code need support
Outflows and jets
Outflows and jets are commonly observed around young stars (Andre et al., 2000; Bally
et al., 2007; Arce et al., 2007, e.g.). For low-mass star formation it is believed that the observed
outflows are accretion-ejection phenomena powered by disc-accretion and collimated
by magnetic fields (see e.g. Camenzind, 1990; Ferreira & Pelletier, 1993). These outflows
could be disc-winds (Pudritz & Norman, 1983) or X-winds (Shu et al., 1994, 1995). Whether
a similar mechanism would also work for high-mass star formation is still under debate. Outflows,
although less collimated ones, are observed around massive young stars (Shepherd
& Churchwell, 1996b,a; Beuther & Shepherd, 2005) which suggest that a scaled-up version
of the accretion-ejection mechanism from low-mass star formation might be in place. Otherwise,
as pointed out by Arce et al. (2007), up to now there are no observational examples
of collimated outflows from young stars above 30M⊙ which could suggest that this ejection
mechanism is not operative for massive stars.
In a recent study we showed that winds from magnetised massive discs can be launched,
at least for very idealised configurations (Banerjee & Pudritz, 2007, see also Section 2.2).
Whether these winds can be collimated and will persist long enough to leave observational
imprints has to be determined in further investigations. We will pursue our initial study based
on more realistic configurations and advance the calculations for a longer time, i.e. for many
disc rotations. In the first step we will employ the sink particle module, developed within the
outlined PhD project, to perform long-term calculations during which putative outflows can
be followed until they could leave the dense molecular cloud core. These calculations will
consistently cover the collapse phase, the accreting protostellar phase in which the circumstellar
disc develops, and the outflow launching and propagation (and possible collimation).
Furthermore, we will study feedback effects from these outflows or jets and describe their
influence on the accretion history of the central star as well as the impact onto the parental
cloud.
In the next step we will allow the central star to ’switch on’, i.e. it will emit radiation according
to the description of the main-sequence track developed within the other PhD project. The
strong stellar radiation might either strengthen or weaken the outflows. Outflows and jets
usually leave cavities in the surrounding gas. It could be possible, and has to be studied
in detail, that the radiation is funnelled through these cavities thereby accelerating the outflowing
gas even further. Such a scenario, if operative, would be an interplay between stellar
23

winds and disc-driven outflows. However, the emitted stellar radiation could drive instabilities
(through radiation bubbles or thermal instabilities) which could strongly de-collimate the
magnetically driven outflows. This could be a reason why outflows from massive young stars
(stars which mass exceed 30M⊙) so far eluded observations.
Another implication from the strong radiation field comes with its ability to ionise the protostellar
disc. As long as the disc is not yet evaporated the ionising UV radiation keeps the disc
well conducting and ensures that ions and neutrals are well coupled. In such an environment
the threading magnetic field will then be also well coupled to the gas. Therefore, non-ideal
MHD effects like Ohmic resistivity and ambipolar diffusion, i.e. the relative slipping of ions
and neutrals, are strongly suppressed. This allows the magnetic fields to follow closely the
accreting and orbiting gas in the disc. Thus the magnetic field can be strongly compressed
reaching large field strengths (> 10 4 Gauss) in the inner region of the disc and could launch
high velocity jets from there.
At the end phase of the disc lifetime (the disc is most probably dissolved by the stellar radiation
field), possible disc-driven jets will die off. The lifetime of discs around massive stars is
most likely much shorter compared to the ones around low-mass stars. Hence, disc-driven
jets from around massive stars are only powered for a short time and might propagate a
shorter distance compared to the low-mass counterpart. This could also be another reason
that outflows around massive stars are not observed. We will study this disc-dissolution
phase in connection with disc-driven jets with magneto-hydrodynamical calculations.
For these projects we are planing to collaborate closely with Debra Shephered (NRAO, USA),
one of the leading experts in observing outflows around massive stars. We will also take
advantage of the expertise of Hendrik Beuther (MPIA) when comparing our results with observational
data, and will work together with Christian Fendt (MPIA) as an expert in the field
of magnetically driven jets as well as continue to collaborate with Ralph Pudritz (McMaster,
Canada) in this field. Furthermore, we will collaborate with Jean-Francois Donati (Obs. Midi-
Pyrenees, Toulouse) who proposed to measure Zeeman signature of the low-mass protostar
FU Ori with the CFHT.
Magneto-hydrodynamic effects
Magnetic fields are observed on all astrophysical scales and permeate molecular clouds
and cloud cores (e.g. Crutcher et al., 1999; Bourke et al., 2001). The influence of magnetic
fields is most prominently seen in magneto-centrifugally driven jets as discussed above. But
other effects can be also important. In the context of fragmentation, whether cloud cores
or discs, magnetic fields could have stabilising or disruptive effects. They could, on the one
hand, prevent easy fragmentation of collapsing cloud cores as found by Hosking & Whitworth
(2004), or, on the other hand, enhance fragmentation as shown in earlier simulations by Boss
(2002). We will re-visit this problem in the context of massive star formation. In particular we
will use initial conditions from large scale magneto-hydrodynamic simulations done by Tilley
& Pudritz (2005) which reproduce realistic features of star-forming regions. The overdense
regions and the self-gravitating cores are built up in shock layers which are the result of
supersonic turbulence as observed in molecular clouds. With the adaptive mesh technique
and the newly developed sink particles we will be able to follow the collapse of these cores
down to pre-stellar densities and keep track of several disc rotations (we already performed
similar follow-up calculations for non-magnetised clouds in Banerjee & Pudritz, 2006). With
this setup we can study in detail the influence of the magnetic field on the fragmentation of
cores and discs. Furthermore, we will investigate the impact of these fields on the accretion
evolution of the massive protostar.
Currently we are also implementing a description for ambipolar diffusion into the existing
24

magneto-hydrodynamic module in FLASH. This work is mainly done by Dennis Duffin, one
of Ralph Pudritz’ master students at McMaster University, Canada. Ambipolar diffusion,
i.e. the separation of ions and neutrals, can become effective in media of low ionisation. If
operative, magnetic fields which are only coupled directly to ions within the gas, will not be
as compressed as in the ideally coupled case. This will have implications for the fate of
the magnetic field itself, as one can trap less magnetic flux in the central object, and for its
subsequent ramifications. These will concern the spin history of the central star (magnetic
braking is less efficient for weaker magnetic fields) and could alter the accretion rates onto
the central object. Upon completion of the ambipolar diffusion treatment we will study its
possible implication.
Cloud formation from large scale colliding flows
Massive stars are the result of collapsing cloud cores within cold molecular clouds. But how
did these molecular clouds assemble in the first place? Several suggestions answering this
question have been made. One of which is the idea that large colliding flows compress the
diffuse warm neutral medium (WNM) in shock layers of the flow (Vázquez-Semadeni et al.,
2006, 2007). The compressed media can cool sufficiently due to molecular excitation in these
overdense regions. These clouds show a strong sign of turbulence, become self-gravitating
and and are not in equilibrium. All this is reminiscent of observed molecular clouds. We
will amend this model with the inclusion of magnetic fields. As mentioned above magnetic
fields pervade the entire galaxy and interstellar medium and might have a dynamical importance
in forming molecular clouds (e.g., Crutcher et al., 1999). Together with together
with Enrique Vázquez-Semadeni, Ralf Klessen, Mordecai Mac Low, and co-workers we will
study the influence of magnetic fields in this cloud formation process. This investigation will
again be based on numerical simulations performed with the FLASH code as it provides
all the necessary functionality (MHD, self-gravity) to study this process. First test runs with
a two-dimensional configuration at UNAM cluster demonstrated the functionality of the setup.
Postprocessing and data interpretation
It will be particular important for the success of the proposed project to develop a coherent
picture from the different results of the sub-projects. Ideally this will be done by explaining
and predicting phenomena which can be observed in future surveys or are already observed.
Therefore we will use our calculations to (re-)produce particular observational data. This
can be done by using our simulation data as input for post-processing tools. We already
developed interfaces which connect the spectral code URANIA, developed by Pavlyuchenkov
& Shustov (2004), with our simulation data. With this tool we are able produce synthetic
molecular line spectra out of a given set of numerical calculations and compare with available
observational data. URANIA is a radiative transfer code base on a Monte Carlo method
which self-consistently calculates the molecular excitations within the local radiation field.
Yaroslav Pavlyuchenkov is working at the MPIA in Heidelberg which gives us the chance
to continue the collaboration with him and his group if the proposed project will be funded.
Again, we will then take advantage of the expertise of Hendrik Beuther (MPIA) to connect the
results from the synthesised spectra to real observational data. The large amount of different
spectral lines (mainly in the sub-millimetre and millimetre range) and additional continuum
observations from his data sets can then be used to compare the data from our theoretical
predictions with the observed ones.
25

4. Requested Funding
4.1 Personnel Costs
To successfully reach the goals of proposed project it will be necessary to build up a small
research group. This group should consist of two PhD candidates and the applicant supervising
the research team. Based on the proposed research group the personnel costs will
be:
• One position according to BAT Ia: Dr. Robi Banerjee
The applicant will head and coordinate the proposed research group and supervise the
two prospective PhD candidates. It is expected that the coordination and supervision
of the ongoing research within the group will consume about 1/3 of the applicant’s time.
The remaining 2/3 of the time will be used to pursue the research program outlined in
Section 3.2. This will include the interpretation and post-processing of the simulation
data, modelling of jets and outflows, studying large scale flows and MHD effects, and
the improvement of the numerical techniques.
• Two positions according to BAT IIa/2: Two prospective PhD candidates
The proposed research group should also consist of two prospective PhD candidates
who are necessary to successfully reach the goals of the overall project. As described
in Section 3.2 the candidates should model the protostellar- and accretion phase and
radiation feedback from massive stars, respectively.
Ideally, the prospective PhD candidates already have basic knowledge of astrophysical
processes, in particular the ones which are relevant for present-day star formation, and
have some experience and interest in computational work.
Both PhD candidates should complete their PhD within the usual three years time starting
at the beginning of the proposed project. Depending on the progress of the research
projects we will pursue the follow-up projects with postdocs (ideally the former PhD candidates)
or further PhD candidates. In the case of working with postdocs for the fourth
and fifth year into the full project we will ask for conversion of the BAT IIa/2 positions
into full BAT IIa positions.
4.2 Scientific Instrumentation
26
• Desktop PCs for each group member
A typical choice would be Dell Precision T 690 for 3,803.24 C– each (inclusive sales tax
and shipping, price from April 2007)
The total expected costs for the three desktop computers are: 12,000.00 C–
This should include slight modifications to the standard configurations like additional
hard-drives, different keyboards and monitors.
• PC cluster with 16 nodes for code developing and test purposes
We would like to add 16 computing nodes to Ralf Klessen’s PC cluster which will be
installed at the Astronomisches Rechen-Institut (ARI) in Heidelberg. The proposed
add-on nodes will limit the costs for a computing cluster to a minimum. We requested

offers from three different computer companies who could install such a cluster at ARI.
The offers range from 44,151.40 C– to 78,561.06 C– including sales tax. Assuming that
lowest priced offer will fit our purpose, we
expect the total costs for the add-on cluster to be: 44,151.40 C–
This should include additional hard drives, cabling, and other accessories to install the
cluster.
• Laptop for travel purposes and presentations
Mac Book Pro 15” 2.33 GHz 2,499.00 C–
4.3 Consumables
Recurrent costs and consumables are supported from the host institute budget.
4.4 Travel Expenses
Relevant conferences are not yet announced for the year 2008 and later. We expect that the
group members will attend several conference meetings, visits and invite their collaborators
during the proposed five year project. We give an estimate of the costs below.
• PhD candidates
We expect that each PhD candidate will attend one conference meeting per year and
an additional one in the last year into their PhD. We estimate the average costs for an
one week stay in Europe and overseas to 800.00 C– which includes the hotel costs and
a per diem of 24.00 C– . Travels within Europe should average to 300.00 C– , whereas we
estimate an average overseas-flight to cost 1200.00 C– . We assume two European and
two overseas trips for each PhD candidate. This adds to a total amount of:
2 × 2 × (800.00 C– + 300.00 C– ) + 2 × 2 × (800.00 C– + 1200.00 C– ) : 12,400.00 C–
• Principal Investigator
We expect that the applicant will attend three to four conference meetings each year.
We assume an averaged conference fee of 300.00 C– for each conference which adds
to the above cost per meeting. In the five year period we estimate 10 European and 7
overseas conferences which totals to:
10 × (1100.00 C– + 300.00 C– ) + 7 × (1100.00 C– + 1200.00 C– ) : 30,100.00 C–
• Visits to and from collaborators
We expect to have at least one work-session with one of our external collaborators
each year. Each work-session will last for about 2 – 3 weeks. The cost are often
shared by the two institutes involved. For one work-session we expect daily cost of
100.00 C– which includes the per diem. For an average work-session of 2 1/2 weeks
27

the cost without travel would be about 1750.00 C– . For the five year period we expect 2
sessions within Europe and 3 sessions to or from overseas. The total estimated cost
for our collaborations would be:
2 × (1750.00 C– + 300.00 C– )/2 + 3 × (1750.00 C– + 1200.00 C– )/2 : 6,475.00 C–
4.5 Publication Costs
We expect expenses for publishing our results in astronomical and astrophysical journals.
For this purpose we request 750.00 C– per year, in total 3750.00 C– for the project duration of
five years.
5. Preconditions for Carrying out the Project
5.1 Group Composition
• Applicant: Dr. Robi Banerjee
• two prospective PhD candidates
5.2 Collaborations in the Proposed Projects
28
• Prof. Dr. Ralf Klessen and group (ITA, Heidelberg): All aspects of massive star formation.
In particular, turbulence, cloud and cluster formation, cluster dynamics. Head of
the Star Formation Group at the ITA
• Dr. Henrik Beuther and group (MPIA, Heidelberg): Comparison with his observational
data, post-processing. Head of the Emmy-Noether Research Group “Earliest Stages
of Massive Star Formation”
• Priv. Doz. Dr. Christian Fendt (MPIA, Heidelberg): Jets and outflows, magnetic fields,
disc-jets, jet instabilities. Coordinator of the Heidelberg IMPRS Graduate Program
• Dr. Paul Clark (ITA, Heidelberg): Cluster formation and cluster dynamics, cloud formation,
comparison with Smooth Particle Hydrodynamics (SPH) simulations
• Dr. Simon Glover (AIP, Potsdam): Chemical evolution, cooling, non-equilibrium cooling
• Dr. Dimitry Semenov (MPIA, Heidelberg): Data post-processing, chemical evolution
• Dr. Yaroslav Pavlyuchenkov (MPIA, Heidelberg): Data post-processing using his URA-
NIA tool, radiation transfer, chemical evolution
• Dr. Jim Dale (Lund, Sweden): Ionisation, radiation feedback, cooling heating processes,
outflows, comparison with SPH simulations
• Prof. Dr. Garrelt Mellema (Stockholm): Ionisation, ray-tracing. Developed the DORIC
routines for ionisation which are used in the FLASH code
• Prof. Dr. Ralph Pudritz and group (McMaster University, Canada): Collapse of cloud
cores, outflows and jets, magnetic fields, ambipolar diffusion, general issues of massive
star formation (Ralph Pudritz will stay at the ITA for his sabbatical in 2008)

• Prof. Dr. Enrique Vazquez-Semadeni and co-workers (UNAM, Mexico): cloud formation,
collapse of cloud cores, magnetic fields
• Dr. Mordecai-Mark Mac Low (New York, AMNH): Cloud formation, turbulence, cluster
dynamics, magnetic fields (is at the ITA since April 2007 for his sabbatical)
• Dr. Debra Shepherd (NRAO, USA): Observations of outflows around massive stars,
comparison with observational data
• Dr. Jean-Francois Donati (Toulouse): Comparison with observations of magnetic field
structures, FU Ori measurements of Zeeman signatures. Director of research of CNRS
• Dr. Tomek Plewa, (ASC Center Chicago, FLASH): Code development, numerical techniques.
5.3 Scientific Equipment
• Three desktop computers
• Proposed PC Cluster
• Access to the Jülich Computing Center (JUMP and Blue Gene cluster)
• Access the High Performance Computing Center Stuttgart
• Access to the MPG Computing Centre in Garching
6. Declarations
This request for an Emmy Noether Research Grant has not been submitted elsewhere. If we
submit the full proposal or parts of it to other funding agencies I will notify the DFG immediately.
7. Signature
Heidelberg, 4.6.2007 Robi Banerjee
29

8. Attachments
a) Curricula vitae
b) Publication list
c) Copies of for relevant publications in the context of this application
d) Diplomzeugnis und Promotionsurkunde (Kopien)
e) DFG Applicant Questionnaire
f) Einladungsschreiben, Prof. Dr. Joachim Wambsganß, ZAH
g) Arbeitgebererklärung, ZAH/ITA
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