How Galaxies Form Stars
Vadim Semenov(University of Chicago)
with Andrey Kravtsov and Nick Gnedin
Formation of individual stars in galaxies
is an inherently multiscale complex process
10 pc
And yet, on kiloparsec and larger scales star formation
rates correlate tightly with the amount of gas
log Total gas surface density(M
sun/pc2)
log
Sta
r fo
rmatio
n r
ate
su
rface
de
nsit
y(M
su
n/y
r/kp
c2)
Schmidt ‘59,‘63; Kennicutt ’89,’98; Sanduleak ’69; Madore+’74; Bigiel+’08,’10; Genzel+’10
Kennicutt & Evans 2012, ARAA 50, 531
This correlation is known as the Kennicutt-Schmidt relation:
Low surface
brightness
Starbursts
Normal
star-forming
The inverse of normalization
is gas depletion time:
~ Gyrs
For example, in the Milky Way:
=>
An important factor is the inefficiency
of actively star-forming regions:
much longer than any relevant dynamical timescale:
only few %
The value of gas depletion time is a long-standing puzzle
~ 0.1 - 0.5 Gyrs
i.e. star formation in galaxies is surprisingly inefficient.
but their depletion times are shorter
than global τdep and thus cannot explain τdep
Depletion time plays a key role in galaxy evolution:
it controls gas masses and star formation rates
Feedback
mass-loading
factor
Bouché+’10; Davé+’12; Krumholz & Dekel ‘12; Lilly+’13; Peng & Maiolino ‘14; Dekel & Mandelker ‘14; Feldmann ‘13,‘15
Depletion time plays a key role in galaxy evolution:
it controls gas masses and star formation rates
is the timescale of galaxy evolution
Feedback
mass-loading
factor
Bouché+’10; Davé+’12; Krumholz & Dekel ‘12; Lilly+’13; Peng & Maiolino ‘14; Dekel & Mandelker ‘14; Feldmann ‘13,‘15
10 pc
The origin of depletion times can be studied in simulations
The origin of depletion times can be studied in simulations
10 pc
A popular choice:
with efficiency per freefall time εff assumed to be constant
in gas satisfying some criteria (ρ > ρsf, T < Tsf, etc.)
Different works use different εff values between ~1% and 100%
Gas structure on small scales cannot be self-consistently resolved,
therefore star formation is modeled using “subgrid” prescriptions
FIRE simulations (Hopkins+’18)
Simulations can reproduce long global depletion time
but also show rather counter-intuitive behavior
Local εff varied by 4 orders of magnitude
but global depletion time remains the same
In this regime, global depletion time
scales linearly with feedback strength
Results of other simulations show that
when feedback is weak, depletion time
becomes dependent on local εff
Dobbs+’11; Agertz+’13,’15; Hopkins+’13,’18; Orr+’18
such behavior is usually described as
“self-regulation”
Lookback time (Myr)
Sta
r fo
rmation r
ate
(Msun/y
r)
Sta
r fo
rmation r
ate
(Msun/y
r)
Lookback time (Myr)
Agertz & Kravtsov ‘15
Depletion time of molecular gas
on ~kpc scale is also long:
Wong & Blitz ‘02; Bigiel+’08,’11; Leroy+’08,’13;Genzel+’10,’15; Bolatto+’17; Utomo+’17; Colombo+’18
Linear slope implies that
τH2 is independent of
molecular gas surface density
Surprising because models
of star formation predict a dependence
e.g., τ~Σ-0.5 is expected
if self-gravity alone regulates SF
log
Molecular gas
surface density(M
sun/pc2)
log
Sta
r fo
rmation r
ate
su
rface
de
nsit
y(M
su
n/y
r/kp
c2)
Leroy+’13
Another part of the puzzle is the observed near-linear
correlation between star formation rates and molecular gas
Molecular Kennicutt-Schmidt relation:
In the remainder of this talk
• Why gas depletion times are long?
• How to explain the behavior
of depletion times in simulations?
• Why τdep of molecular gas is independent
of molecular gas surface density?
much longer than any relevant timescale
log
Molecular gas surface density
(Msun
/pc2)
log
Sta
r fo
rmatio
n r
ate
su
rface
de
nsit
y
(Msu
n/y
r/kpc
2)
Suite of isolated ~L* galaxy simulations
20 kpc
Adaptive mesh refinement code ART
40 pc resolution
ICs from AGORA code comparison project (Kim+’14,’16)
Feedback calibrated against supernova remnant simulations (Martizzi+’15)
Subgrid turbulence model (Schmidt+’14)
Gas surface density (Msun/pc2) Temperature (K) Unresolved turbulent
velocity (km/s)
Similar predictions
of analytic models:
Krumholz & McKee ‘05
Padoan & Nordlund ‘11
Federrath & Klessen ‘12
Actively
star-forming
state
Non-star-forming
state
Gravity TurbulenceSimulations of star formation
on small scales (Padoan+’12)
SF
eff
icie
ncy p
er
fre
e-f
all
tim
e
Theoretical models predict strong dependence of star
formation efficiency on turbulence in SF regions
Th
erm
al +
tu
rbu
len
t
ve
locit
y d
ispers
ion
(km
/s)
Gas density (cm-3)
Gas temperature (K)
102 103 104 105 106
Star formation criterion:
Local star formation rate:
Star formation on resolution scale in our simulations
Stronger gravity
Str
onger
support
Non-star-forming state
Semenov, Kravtsov & Gnedin 2017, ApJ 845, 133 (arXiv:1704.04239)
Surface density of HI+H2
(Msun
/pc2)
Surface density of H2
only
(Msun
/pc2)
Su
rface d
ensit
y o
f sta
r fo
rmati
on r
ate
(Msu
n/y
r/kp
c2)
Gala
cto
ce
ntr
ic r
ad
ius (kp
c)
Milky Way
Bigiel et al 2008
Bigiel et al 2010
Leroy et al 2013
Total gas Molecular gas
Our fiducial simulation reproduces Kennicutt-Schmidt relation
• Correct normalization (i.e. long global depletion time)
• For molecular gas the slope is close to linear (despite steeper local relation)
=> Can use simulations to understand the origin of KS normalization and slope
and in gas withFiducial SF prescription:
Gas density (cm-3)
Th
erm
al +
tu
rbu
len
t
ve
locit
y d
ispers
ion
(km
/s)
Non-star-forming state
• Gas cycles between SF and non-SF states on <100 Myr timescale
• Feedback disperses SF regions making SF stages short
• Most of the time gas spends in the non-SF state
ISM gas evolution is rapid and cyclic
Semenov, Kravtsov & Gnedin 2017, ApJ 845, 133 (arXiv:1704.04239)
Th
erm
al +
tu
rbu
len
t
ve
locit
y d
ispers
ion
(km
/s)
Gas density (cm-3)
3
10
30 Non-star-forming state
Mass fraction of star-forming gas:
Depletion time of star-forming gas
explicitly depends on the SF recipe
Gas depletion time:
(depletion time) = (depletion time in SF state) + (total time in non-SF state over Ndep cycles)
Although each cycle is short, depletion is long because the number of cycles is large
Semenov, Kravtsov, Gnedin 2017 ApJ 845, 133Semenov, Kravtsov, Gnedin 2018 ApJ 861, 4
Physical origin of long gas depletion times
Molecular state
2018 FIFA World Cup Final. Image from https://www.whoscored.com
Direct analogy: “inefficiency” of a soccer match
It takes ~20 seconds to cross the field
and yet each team scores only few times over 90 minutes
Typical PDF of
the ball position
Dependence of depletion time on local SF efficiency
points – simulation resultslines – model predictions
Glo
bal d
ep
leti
on
tim
e (G
yr)
Local SF efficiency
By definition:
Feedback limits SF stages:
Model explains self-regulation!
(i.e., insensitivity of global
depletion time to local εff)
Dobbs+’11; Agertz+’13,’15; Hopkins+’13
Semenov, Kravtsov, Gnedin 2018 ApJ 861, 4
Hopkins+’18Orr+’18
Lookback time (Myr)
SFR
(M
sun/y
r)
points – simulation resultslines – model predictions
Dependence of depletion time on feedback strengthG
lob
al d
ep
leti
on
tim
e (G
yr)
Local SF efficiency
By definition:
Feedback limits SF stages:
Semenov, Kravtsov, Gnedin 2018 ApJ 861, 4
and
feedback strength per
unit mass of young stars
feedback x 5
feedback x 1/5
Model explains why τdep
scales with feedback strength
in the self-regulation regime
Hopkins+’18, Orr+’18
Lookback time (Myr)
SFR
(M
sun/y
r)
points – simulation resultslines – model predictions
Dependence of depletion time on feedback strengthG
lob
al d
ep
leti
on
tim
e (G
yr)
Local SF efficiency
By definition:
Feedback limits SF stages:
Mass f
ractio
n o
f g
as
in S
F r
eg
ions, f s
f
Local SF efficiency Semenov, Kravtsov, Gnedin 2018 ApJ 861, 4
and
feedback strength per
unit mass of young stars
feedback x 5
feedback x 1/5
Star-forming gas mass fraction
has the opposite behavior:
fsf can be used to constrain εff
Hopkins+’13
τdep constrains feedback
but cannot constrain εff
Semenov, Kravtsov, Gnedin 2018 ApJ 861, 4
The model helps to constrain the parameters
of star formation and feedback prescriptions
Both depletion time and star-forming mass fraction should be used.
Depletion time (or global SFR) does not constrain εff because of self-regulation
points – simulation results
lines – predictions of the model:
Mass fraction of gas in SF regions
Glo
bal d
ep
leti
on
tim
e (
Gyr)
Milky Way
100% 10%1%
0.01%
0.1%
log
Molecular gas
surface density(M
sun/pc2)
log
Sta
r fo
rmation r
ate
su
rface
de
nsit
y(M
su
n/y
r/kp
c2)
Leroy+’13 Normalization:
The model explains global depletion time
and its connection to star formation,
feedback, and dynamical processes
on small scales
The origin of the molecular Kennicutt-Schmidt relation
Linear slope:
Can our model also explain why depletion
time of molecular gas is independent
of molecular gas surface density?
Scatter:
• Intrinsic variation of relevant timescales
• Non-equilibrium states of ISM patches
• Decoupled evolution of gas and SFR tracers
• Imperfect sampling of evolution stages
Feldmann+’11, Kruijssen & Longmore+’14, Semenov+’17
Wong & Blitz ‘02; Bigiel+’08,’11; Leroy+’08,’13;Genzel+’10,’15; Bolatto+’17; Utomo+’17; Colombo+’18
De
ple
tio
n t
ime
of
mo
lecula
r g
as
avera
ged o
n 1
kpc (
Gyr)
Molecular gas surface density
averaged on 1 kpc (Msun
/pc2)
Slope adopted at the resolution scale
Observations
Slope of molecular Kennicutt-Schmidt relation
Star formation rate
surface density (Msun
/yr/kpc2)
Molecular gas
1 kpc
Simulation results
Simulations can reproduce the linear slope, i.e. τdep,H2is constant on kpc scale
independent of the assumptions on resolution scale (40 pc)
De
ple
tio
n t
ime
of
mo
lecula
r g
as
avera
ge
d o
n 1
kpc (G
yr) FiducialNo feedback Local
Molecular gas surface density averaged on 1 kpc (Msun
/pc2)
Feedback becomes more important
Effect of feedback on the slope of molecular KS relation
Slope adopted at the resolution scale Semenov, Kravtsov, Gnedin 2018b arXiv:1809.07328
De
ple
tio
n t
ime
of
mo
lecula
r g
as
avera
ge
d o
n 1
kpc (G
yr) FiducialNo feedback Local
Local slope different from 1.5 εff dependent on ρ
Molecular gas surface density averaged on 1 kpc (Msun
/pc2)
Therefore, when depletion time is insensitive to εff
it is also insensitive to the local slope!
Effect of feedback on the slope of molecular KS relation
Slope adopted at the resolution scale Semenov, Kravtsov, Gnedin 2018b arXiv:1809.07328
Origin of constant τH2
independent of the local slope
Semenov, Kravtsov, Gnedin 2018b arXiv:1809.07328
time in molecular state
during each cycle
=> dependence on SF recipe cancels out in
Feedback limits star-forming stages:
Origin of the linear slope:
Trends of and with
cancel out leading to constant
Summary
• τdep is long because gas has to go through a large number of
cycles spending only a small fraction of time in the SF state
• Global τdep is longer than τdep,sf in SF regions because
large fraction of time gas spends in the non-SF state
• τdep shows two limiting regimes with qualitatively different
dependence on star formation and feedback parameters
Resolved the puzzle of inefficient star formation in galaxies,
i.e. explained the normalization of the Kennicutt-Schmidt relation (KSR)
Linear slope of molecular KSR
(dependence of τdep,H2 on ΣH2)
• Also shows two limiting regimes with
different dependence on the local slope
• Efficient feedback leads to a linear molecular
KSR independent of the local SF recipe
(another manifestation of self-regulation) Semenov, Kravtsov, Gnedin 2017 ApJ 845, 133Semenov, Kravtsov, Gnedin 2018 ApJ 861, 4Semenov, Kravtsov, Gnedin 2018b arXiv:1809.07328