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