Variations of the IMF through environment
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Poster P14
Variations of the IMF through environment
• Investigate the emergence of the IMF using high-resolution models of
a piece of a molecular cloud
• Test predictions from turbulent fragmentation
• Only cores with high
density unstable • All cores unstable
# Stars
• Turnover connected • IMF follows CMF
to distribution of • Powerlaw from
dense gas turbulence
Peak set by mass of
Bonnor-Ebert core
with confinement by
turbulent pressure
Troels Haugbølle – EPOS 2018 Mass Haugbølle, Padoan, Nordlund (2018)
Numerical model
• RAMSES with essential ingredients
Turbulence Gravity Magnetic Fields
• Resolution: 4 parsec à 50 AU. Extensive convergence study.
• Four models to probe different environments: Mbox=1500-12000 Msun
Numerical model
• Use RAMSES. Simplest possible model
Turbulence Gravity Magnetic Fields
• Resolution: 4 parsec to 50 AU. Extensive convergence study
• Four different models to probe different densities
The virial number is the ratio of the kineti
Virial parameter
binding regulates
energy. For evolution
a uniform sphere it is given
These results were confirmed and exten 2
2E
parameter study by Federrath 5
kin and Klessen 1D
↵vir grid
on 34 uniform
= simulations= with the Fla
a resolution of up to 512
E grav
3 GM
computational p
AMR run with maximum resolution equiva
where computational points). Six of their runs
SFRff ≈ ½ exp(-1.38 ⍺vir ½) incl
field, covering the range 1.3 MA 13, b
proximately the same sonic Mach number,
the 3 2of =dependence
⍺vir
lack 0.21, 0.42, 0.83,
of SFR ↵ on 1.67
Ms fo
Ekin = et al. 1D M
(2012) could not be verified. On the
E
2
28 runs without magnetic fields span a wide
of sonic Mach number, 2.9 Ms 52,
Given a density profile ⇢(r),
Federrath a projection
and Klessen
Padoan+2011, (2012) to factor
Padoan+2012, confirm thei
numerical
the change in the gravitational result ofbinding
Federrath+2012. Padoan andenergy
See also Poster Nordlund
P7
the non-magnetized case SFR↵ increases w1/2 grid, light, high, 1/2
for the run high. Furthermore, 3/23Proot
G256 0
(1 + Ms ) heavy andMmassive
s
The IMFs are all sampled at SFE= 0.024, co
shed that the value of mpeak in
which is a Variation
goodof 2.07, of IMF
0.83,
approximation with
0.46, andtoenvironment
0.23
theMyr, respectivel
turnover mas
fully converged (see Fig. 5), it is
the turbulent of the first star. Except for the top one, the h
fragmentation models mentioned ab
alue of mpeak in the run massive providing
vertically by a factor of 1/4 (heavy), 1/16 (h
anPredicted
intuitive explanation of the origin of
The dotted
Figure 10.Assumption: IMF lines
peak areaccording
lognormal tofits between
equation (6
as the total mass in this run is IMF peak.
sus cloud mass,To test
where
for
cores
the
the
Outer IMF
Galaxy
are
validityconfined
appears
Survey
by
oftoclouds
this prediction
be complete and
from Heyer
aller than in the run high. The express
(1998) and turbulent
the IMF
the m pressure
. The
peak
Galactic
peak as IMF
Ring peak clouds
Survey clearly from
shiftsRoman-
toward
of numerical convergence with mean
et al. (2010), more densitythan
massive increases.
103 M (see main text fo
could then explain the observed of Mm
tails about the cloud peak ⌘ ✏BE
selection). TheM error , give the mea
BE,tbars
BE , we get a modified turbulent B
iction of equation 6. mpeak standard deviation of mpeak in six logarithmic bins of Mcl .
where ✏BE is a local efficiency 1.182parameter
4 analogou
ms velocity assuming a tempera- ✏star-forming
in the sink particle accretion th model, M BE,0
and use
tem size (or total mass) based on acc M
regions.BE,t ⇡
We can3/2 express =
1/2 mpeak as a 2fun 1/
simulations to verify whether
of the nondimensional parameters G P
it provides (1 +a M
good
0 of the simulation s ) fi
ity-size relation (see § 3). If we the total This
the numerical
mass:gives
IMFs.
observed Larson velocity–size re- For this purpose, is
which wea use
goodthe approximation
four simulations to thel
ocity and the size (or total mass) high, heavy, and mthe turbulent
⇡
massive
peak 1.124 M
with fragmentation
a
tot Mroot
s
4 3/2 models
↵
grid
vir ,of 256 3
escaled, as long as the nondimen- and six AMR levels, with four di↵erent values of theofv
providing an intuitive explanation
e simulation, Ms and ↵vir , were which shows
parameter that
(seeIMF for
Table constant
peak.
1).2 The ↵vir and
To test
virial the for standard
validity
parameter of va
is t
1/2
may suspect that the predicted relations, express
M tot / the
L IMF
and peak
v /
by leaving the rms velocity constant and, increasin
son as
L mpeak is
with the numerical IMFs only for stant. However,
decreasing observed
the mean density MCs havemass)
(total a rangein of valu
the com
mpeak ⌘ ✏BE MBE,t ,
mperature or system size, but it ↵
tational
vir and yield Larson relations with a
volume by a factor of two or four relative to significant
at this agreement is immune to ter and with
reference exponents
where
run high (see✏BE§ 3in ageneral
isand local di↵erent
Tableefficiency from
paramt
1). The overden
lation. The virial parameter can standard at
threshold values.
✏acc Thus,
which in the
the rootour
sink
gridIMF model
particle
is refined isshould
accretion
changed pr
mf1/2 grid, light, high, 1/2
for the run high. Furthermore, 3/23Proot
G256 0
(1 + Ms ) heavy andMmassive
s
The IMFs are all sampled at SFE= 0.024, co
shed that the value of mpeak in
which is a Variation
goodof 2.07, of IMF
0.83,
approximation with
0.46, andtoenvironment
0.23
theMyr, respectivel
turnover mas
fully converged (see Fig. 5), it is
the turbulent of the first star. Except for the top one, the h
fragmentation models mentioned ab
alue of mpeak in the run massive providing
vertically by a factor of 1/4 (heavy), 1/16 (h
anPredicted
intuitive explanation of the origin of
The dotted
Figure 10.Assumption: IMF lines
peak areaccording
lognormal tofits between
equation (6
as the total mass in this run is IMF peak.
sus cloud mass,To test
where
for
cores
the
the
Outer IMF
Galaxy
are
validityconfined
appears
Survey
by
oftoclouds
this prediction
be complete and
from Heyer
aller than in the run high. The express
(1998) and turbulent
the IMF
the m pressure
. The
peak
Galactic
peak as IMF
Ring peak clouds
Survey clearly from
shiftsRoman-
toward
of numerical convergence with mean
et al. (2010), more densitythan
massive increases.
103 M (see main text fo
could then explain the observed of Mm
tails about the cloud peak ⌘ ✏BE
selection). TheM error , give the mea
BE,tbars
BE , we get a modified turbulent B
iction of equation 6. standard deviation of mpeak in six logarithmic bins of Mcl .
where ✏BE is a local efficiency 1.182parameter
4 analogou
ms velocity assuming a tempera- ✏star-forming
in the sink particle accretion th model, M BE,0
and use
tem size (or total mass) based on acc M
regions.BE,t ⇡
We can3/2 express =
1/2 mpeak as a 2fun 1/
simulations to verify whether
of the nondimensional parameters G P
it provides (1 +a M
good
0 of the simulation s ) fi
ity-size relation (see § 3). If we
Figure 9. Values of the IMF peak, m , from the lognormal the total This
the numerical
mass:gives
IMFs.
observed Larson velocity–size re-pa- For this purpose, is
which wea use
goodthe approximation to thel
peak
fits of the previous figure, plotted as a function of the virial
rameter of each simulation (a proxy for the inverse of the mean gas four simulations
ocitydensityand thermssize
at constant velocity (or total
and size). mass)
The filled circle shows
the value predicted by equation 6 for the simulation high, assuming high, heavy, and mthe turbulent
⇡
massive
peak 1.124 M
with fragmentation
a
tot Mroot
s
4 3/2 models
↵
grid
vir ,of 256 3
escaled, and six AMR levels, with four di↵erent values of theofv
providing an intuitive explanation
an efficiencyas long
factor ✏ BE as inthe
= 0.64, order nondimen-
to match exactly m peak
measured from the simulation. Assuming this fixed value of ✏ , BE
e simulation, Ms and
three simulations. The measured value for ↵
thevir , wererun
the open circles show the prediction of equation 6 for the other
highest-density
which shows
parameter that
(seeIMF for
Table constant
peak.
1).2 The ↵vir and
To test
virial the for standard
validity
parameter of va
is t
1/2
is larger than the prediction, possibly because of a decreasing nu-
may
merical suspect that
convergence of the value of the
m peak aspredicted
this becomes smaller express
tot / the IMF peak
v /
by leaving the rms velocity constant and, increasin
son relations, M L and as
L mpeak is
with increasing mean density.
with the numerical IMFs only for stant. However,
decreasing observed
the mean density MCs havemass)
(total a rangein of valu
the com
mpeak ⌘ ✏BE MBE,t ,
mperature or
these four simulations system
are shown insize, Figure but
8, whereitthe
histograms are shifted vertically by a factor of four be-
↵
tational
vir and yield Larson relations with a
volume by a factor of two or four relative to significant
at tween
this agreement
consecutive runs, exceptis for immune
the top histogram, to to ter and with
reference exponents
where
run high (see✏BE§ 3in ageneral
isand local di↵erent
Tableefficiency from
paramt
1). The overden
minimize the confusion of overlapping plots. The IMFs
lation. Theatvirial
are all sampled SFE= 0.024, parameter
corresponding tocan a time standard at
threshold values.
✏acc Thus,
which in the
the rootour
sink
gridIMF model
particle
is refined isshould
accretion
changed pr
mf1/2 grid, light, high, 1/2
for the run high. Furthermore, 3/23Proot
G256 0
(1 + Ms ) heavy andM massive
s
The IMFs are all sampled at SFE= 0.024, co
shed that the value of mpeak in
which is a Variationgood of 2.07, of IMF
0.83,
approximation with
0.46, andtoenvironment
0.23
theMyr, respectivel
turnover mas
fully converged (see Fig. 5), it is
the turbulent of the first star. Except for the top one, the h
fragmentation models mentioned ab
alue of mpeak in the run massive providing
vertically by a factor of 1/4 (heavy), 1/16 (h
anPredicted
intuitive explanation of the origin of
Figure 10. The dotted
IMF lines
peak are lognormal
according to fits between
equation (6
as the total mass in this run is IMF
sus cloud peak. Assumption:
mass,To test
where
for Outer
cores
the
the IMF
Galaxy
are
validity confined
appears
Survey
by
oftoclouds
this prediction
be complete
from Heyer and
aller than in the run high. The express
(1998) and turbulent
the IMF
the m pressure
peak
Galactic
peak . Theas IMF
Ring peak clouds
Survey clearly from
shiftsRoman-
toward
of numerical convergence with et al. (2010), more mean densitythan
massive increases.
103 M (see main text fo
could then explain the observed tails about the cloud of Mm peak ⌘ ✏BE
selection). TheM error , give the mea
BE,tbars
BE , we get a modified turbulent B
iction of equation 6. standard deviation of mpeak in six logarithmic bins of Mcl .
where ✏BE is a local efficiency 1.182parameter
4 analogou
ms velocity assuming a tempera- 11
✏star-forming
in the sink particle accretion th model, M BE,0
and use
tem size (or total mass) based on acc M
regions. We
BE,t ⇡ can express
1/2
=m peak as a fun
2 1/
and size). simulations to verify
of the nondimensional parameters whether G 3/2it
P provides (1 +a
0 of the simulation
M
good s ) fi
ity-size
open cir- relation (see § 3). If we the numerical This gives
IMFs.
redFigure
value 9. Values of the IMF peak, m , from the lognormal
observed
responds Larson velocity–size
peak
re-pa- the total mass: which is a use
goodthe approximation to thel
fits of the previous
rameter
elated
figure, plotted as a function of the virial
lo- of each simulation (a proxy for the inverse of the mean gas For this purpose, we four simulations
ocitydensityand
accretion the
at constant rmssize
velocity (or total
and size). mass)
The filled circle shows
high, heavy, m
andthe turbulent
⇡
massive1.124 M
with fragmentation
a M root
4 3/2 models
↵
grid , of 256 3
the value predicted by equation 6 for the simulation high, assuming peak tot s vir
escaled,
an efficiencyas
measured from
BElong
factor
the
✏ as
= 0.64,
simulation.
the
in order nondimen-
Assuming
to match exactly m
this
peak
fixed value of ✏ , and six AMR providing
levels, with an
four intuitive
di↵erent explanation
values of the ofv
with BE
epeak
simulation, Ms and value for ↵ , wererun
the open circles show the prediction of equation 6 for the other which shows that
IMF for constant
peak. To ↵vir and
test the for standard
validity of va t
with
three
crepancy
thesimulations. The measured thevir
highest-density
is larger than the prediction, possibly because of a decreasing nu-
may
merical suspect that
value of the aspredicted
parameter
son relations,
(see
Notice Table
that /
express
M tot
1).
Mthe
tot
L MIMF
2 The
and
virial
s ≈ constant
-4
peak
v /
parameter
as
L if on
1/2
, increasin
mpeak is
is
cant, it is convergence of the
with increasing mean density.
peak m this becomes smaller by leaving the rms velocity
Larson relations. constant and
with
certaintythe numerical IMFs only for stant.
decreasing However,
the observed
mean density MCs havemass)
(total a range in of valu
the com
hermore, mpeak ⌘ ✏BE MBE,t ,
mperature
these
mpeak in
four
histograms
or system size, but it
simulations are shown in Figure 8, where
are shifted vertically by a factor of four be-
the ↵
tational
vir and yield Larson relations with
volume by a factor of two or four relative to a significant
at
g. 5),this
it
tween
n massive
is agreement
consecutive runs, exceptis for immune
the top histogram, to to ter and with
reference run exponents
where
high (see✏BE§ 3 in
isandageneral
local
Table di↵erent
efficiency
1). The from
paramt
overden
minimize the confusion of overlapping plots. The IMFs
lation.
his run all
are The
is sampled atvirial
Figure SFE= parameter
10. Predicted
0.024, tocan
IMF peak according
corresponding a time standard
to equation
sus cloud mass, for Outer Galaxy Survey clouds from Heyer
(6) ver-
threshold
et al.
values.
at ✏acc Thus,
which in the
the root our
sink
grid IMF model
particle
is refined isshould
accretion
changed pr
mfTime Evolution of IMF and Growth of Stellar Mass 13 A
1 pc
F1
F2
F6 F3
F5
a F4 b
12 Haugbølle, Padoan, Nordlund
Perrotto+ 2013
surveys, the mean and standard deviations are mpeak = Fig. 1. a) Mid-infrared Spitzer composite image (red: 8 µm
It takes time for a star to form: 0.6 ±Figure
Figure 12. Time evolution of the mass distribution of sink par- 0.25 M 13. andTime
mpeak = 0.26 ±
evolution of 0.09 M parameters
the IMF for the outer derived from indicated with yellow dashed lines, emphasizing their conver
ticles in the reference simulation high. The time of each IMFand inner
the fitsGalaxy
shown respectively,
in the previous with over The
figure. 90%IMF of these
peak is already
centre is usually interpreted as a signature of powerful outflow
• Massive stars do not form through massive cores
since the formation of the first sink particle is given next to each
histogram. The histograms are shifted vertically by an arbitrary
established
star-forming
particles,
mpeak < 1.0 M .
after yielding
clouds
although
less then 1values
it is a
Myr from
bit larger
the range
in the
around
creation
1.5
0.1of <
Myr
the first sink
(top panel). column density image of SDC335. The locations of the filam
value, except for the case of 0.03 Myr that shows the actual num-
ThisThe power-law tail at large masses takes approximately 2 Myr to
scatter in the10peak of this image is 2500 (yellow circle), that of Herschel at 350
M of andthe stellara IMF
stablepredicted
• Massive stars are not due to competitive accretion
ber of stars in each mass bin. The dotted lines are log-normal
fits between the smallest mass bin where the IMF appears to be
develop
for di↵erent
beyond
MCs is the consequence
achieve
with Salpeter’s value (bottom panel). The of the
slope, , consistent
scatter in thebuild up of
progressive
2 ⇥ 1022 cm 2 , and from 2.15 ⇥ 1023 to 4.15 ⇥ 1023 cm 2 in
calculated the SDC335 and Centre region masses quoted in T
velocity-size
complete (based on a sharp cuto↵ at lower masses, more apparent and mass-size relations,
the tail and the decreasing value of or, equivalently,
are reflectedthe by a gradual
where two cores are identified, MM1 and MM2. The rms no
Rather we find that matter is fall in through inertial flows and there is
scatter
in histograms with narrower bins and corresponding to late times)
and 2 M . The solid lines are power-law fits above 2 M .
in the in
increase relation
the width
(middle panel).
(see Figures
between
of thevirial
IMF,parameter
m , during
31, 33, 34 and 35 in Padoan et al. (2016b)
and
themass
initial 1.7 Myr
from 22 to 62 in steps of 10 mJy/beam. The yellow ellipse rep
a maximum accretion rate that can be sustained – see poster P30 and
and Figures 5, 6 and 7 in Padoan et al. (2016a)). We have
rest of the mass has to be accreted through a circum- recently cles,shown
such that
as insupernova
the work(SN) by Padoan et al. (2014b). In
driven turbulence
talk by Padoan
stellar disk fed by the same converging flows that had generates Padoan MCsetwithal. (2014b),
propertiesusing a simulation
consistent with the ob- with almost witnessing the early stages of the formation of, at least, t
sive stars.
assembled the prestellar core. In other words, the stel- servationsidentical physical
(Padoan et al.and numerical
2016b; Pan et al. parameters
2016; Padoan as the model
Consequence: the IMF only emerges after ≈1.5 – 2 Myr
lar mass predicted by the PN02 model should be seen et al.high
as the total mass available to form a star, while the ac- tween
2016a).
MCs
Because
in this
selected
work,ofwe
from
this
our
successful
obtained
simulation
comparison
nearly
and
1300 sink
the
over a time of 3.2 Myr, with a mass function closely fol-
be- particles
observa-
The goal of this paper is to map the dense gas kinem
SDC335 and analyse it in the context of massive star f
tual mass of a prestellar core (prior to its collapse into a tions,lowing
we can ause the simulation
Chabrier IMF at to small
infer that most and
masses of thea SalpeterDiscussion points • We find numerical evidence that the IMF is not universal, but depends on environment. • The environmental dependence of the peak can be understood in the framework of turbulent fragmentation à there is a “simple” connection between cores and low-mass stars? • Can we observe the time-dependence of the IMF; what does it tell us about accretion time-scales? • Extreme star formation regions may be an interesting window to test our theories for the IMF. But important locally driven feedback (radiation, outflow) may limit applicability.
Numerical Convergence
• Non-trivial to reach convergence – high resolution needed
• In addition, multiple systems will show up with increasing resolution
• Convergence debated! Guszejnov+ 2018, Lee & Hennebelle 2018a,b, suggest
continous fragmentation, BUT only include HD
• B-field regulating small fragments by ”non-thermal” pressure floor?
0.14
0.12
0.10
0.08 16
SFE
32
0.06
low
0.04 med
high
0.02
fit
0.00
0.0 0.5 1.0 1.5 2.0
time [ tff ]
0.14
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