Atomic Gas, Molecular Gas, andDust in Galaxy Evolution
Tsutomu T. TAKEUCHIDivision of Particle and Astrophysical Science,
Nagoya University, Japan
Opening Up Terahertz Astronomy in Antarctica, Mitaka, 18-19
Nov., 2015, Japan

The cosmic star formation rate density

1 Interesting epochs of galaxy evolution(Today)(Early epoch)(Hopkins & Beacom 2006)

The cosmic star formation rate density

1 Interesting epochs of galaxy evolution(Today)(Early epoch)(Hopkins & Beacom 2006)

The cosmic star formation history
Focused property in previous studies on galaxy evolution:
star formation rate (SFR)
Observational indicator of SFR• Ionizing UV photons from OB stars• Recombination lines from HII regions• Forbidden lines from HII regions• Non-ionizing UV photons• IR re-emission from dust
• PAH band emission from photodissociation regions• Synchrotron radiation, etc.
Though they give information on the SFR, but does not provide
more fundamental information on the transformation from gas
to stars.

2 Transition from atomic to molecular gas on dust
What are dust grains?
Dust grains are formed by condensation of heavy elements.

Dust grain
Heavy elements

Heavy elements are supplied only by stars, hence tightly
connected to galaxy evolution.
However, the formation and evolution of dust has been fully
theoretically formulated only recently (Asano et al. 2013a, b,2014; Nozawa et al. 2015), and more observational
examinations are still needed.

Role of dust for the star formation
Molecular formation is the key process for star formation,and molecules are predominantly formed on surface ofdust grains (e.g., Gould & Salpeter 1963).
Molecularformation

Atoms

Molecular and dust
coolingDust
Star formation

These processes depend strongly on the amount and size
distribution of dust grains.

Role of dust for the star formation

w/ dust grains

w/o dust grains
Hirashita & Ferrara (2002)
Dust grains drive the star formation, and actually this is thetrigger of the initial starburst, i.e., galaxy formation.

3 Gas mass function of galaxies
Gas mass function of galaxies
Gas mass function of galaxies describes how much HI and H2
gas exists in galaxies, i.e., the raw materials to form stars.
⇒ It provides complementary information to stellar mass andSFR functions.

Local HI mass function (Lemonias et al. 2013)

Current status of the observational gas mass function
It is not a trivial task to estimate the gas mass function
from observation, and currently both HI and H2 massfunctions are obtained only at z ~ 0 (Keres et al. 2003;
Lemonias et al. 2013).

Local H2 mass function (Kereset al. 2003)

Current status of the observational gas mass function
It is not a trivial task to estimate the gas mass function
from observation, and currently both HI and H2 massfunctions are obtained only at z ~ 0 (Keres et al. 2003;Lemonias et al. 2013).
Problem:• No dedicated wide-area survey for H2 (in practice, CO),and no ideal survey for HI (as for HI, wide-area survey
exists but redshifts are taken from optical surveys).
• Statistical methods are inadequate: the method often
adopted to obtain the gas mass function gives a biased
result.

Current status of the observational gas mass function
It is not a trivial task to estimate the gas mass function
from observation, and currently both HI and H2 massfunctions are obtained only at z ~ 0 (Keres et al. 2003;
Lemonias et al. 2013).
Problem:• No dedicated wide-area survey for H2 (in practice, CO),and no ideal survey for HI (as for HI, wide-area survey
exists but redshifts are taken from optical surveys).
• Statistical methods are inadequate: the method often
adopted to obtain the gas mass function gives a biasedresult.
⇒ Many further investigations are necessary.

Gas mass estimate from dust emission
For high-z galaxies, it is fashionable to convert the dust
continuum emission to the total gas (HI+H2) mass (e.g.,Groves et al. 2015).
If it can be used for all types of galaxies, it is extremely
useful for statistical studies of gas mass at various
redshifts.

Gas mass estimate from dust emission
For high-z galaxies, it is fashionable to convert the dust
continuum emission to the total gas (HI+H2) mass (e.g.,
Groves et al. 2015).
If it can be used for all types of galaxies, it is extremely
useful for statistical studies of gas mass at various
redshifts.
An empirical relation between metallicity and gas-to-dust
mass ratio for local giant galaxies is used. However, aHershel observation revealed that it is not valid: a strong
nonlinearity was discovered at low metallicity range.

Gas mass estimate from dust emission
For high-z galaxies, it is fashionable to convert the dust
continuum emission to the total gas (HI+H2) mass (e.g.,
Groves et al. 2015).
If it can be used for all types of galaxies, it is extremely
useful for statistical studies of gas mass at various
redshifts.
An empirical relation between metallicity and gas-to-dust
mass ratio for local giant galaxies is used. However, aHershel observation revealed that it is not valid: a strong
nonlinearity was discovered at low metallicity range.
⇒ A better understanding is needed!

Dust and matter circulation in a galaxyatoms,molecules

destruction(SN shocks)

grain
growthdust
shattering
AGB stars, SNe II
coagulation
astration
We have developed a theoretical framework to explain thisrelation (Asano et al. 2013a, b, 2014; Nozawa et al. 2015).

Model of galaxy evolution
Evolution of the total stellar mass, M* , ISM mass, MISM, metal
mass, MZ, dust mass, Md in a galaxy

Model of galaxy evolution
Evolution of the total stellar mass, M* , ISM mass, MISM, metalmass, MZ, dust mass, Md in a galaxy・Injection/ejection from stars
・Destruction by SN shocks
・Grain growth in the ISM

Result: evolution of gas-to-dust mass ratio

Small grain production by shattering activates the graingrowth.

Application to the observed data
The model well reproduced the Herschel observation of thedust-to-gas mass ratio for local galaxies.

Rémy-Ruyer et al. (2014)

Need for the establishment of the gas-to-dust mass ratio
The empirical relation between metallicity and gas-to-dust
mass ratio for local giant galaxies is not valid. For theestimation of gas mass for galaxies, we should replace it withthe prediction of Asano model.
We should establish the gas-to-dust mass ratio and its
evolution for the studies of gas in high-z galaxies.
⇒ A large dust continuum survey at various redshifts isdesired.
The Antarctic terahertz telescope has a high survey
efficiency for dust continuum, and we expect a goodperformance.

4 HI-H2 bivariate mass function
HI-to-H2 transition in star formation
Total gas mass-stellar mass relation carries significant
information for the star formation process.
We, however, are interested in more detailed process in thestar formation in galaxies at various redshifts. From a
global point of view, star formation proceeds like:neutral (HI) gas ⇒ molecular (H2) gas ⇒ star formation

4 HI-H2 bivariate mass function
HI-to-H2 transition in star formation
Total gas mass-stellar mass relation carries significant
information for the star formation process.
We, however, are interested in more detailed process in thestar formation in galaxies at various redshifts. From a
global point of view, star formation proceeds like:neutral (HI) gas ⇒ molecular (H2) gas ⇒ star formation
Hence, HI-to-H2 transition is fundamental to understandthe physics of star formation.

The HI-H2 bivariate mass function and its extension
If we have a bivariate distribution function of HI and H2 ingalaxies as a function of redshifts, it can work as a direct
measure of the HI-H2 transition and its evolution.
If we further incorporate it with the stellar mass and SFR
distribution, it will give a complete picture of the (global)
star formation in galaxies.

The HI-H2 bivariate mass function and its extension
If we have a bivariate distribution function of HI and H2 ingalaxies as a function of redshifts, it can work as a direct
measure of the HI-H2 transition and its evolution.
If we further incorporate it with the stellar mass and SFR
distribution, it will give a complete picture of the (global)
star formation in galaxies.

The HI-H2 bivariate mass function and its extension
If we have a bivariate distribution function of HI and H2 ingalaxies as a function of redshifts, it can work as a direct
measure of the HI-H2 transition and its evolution.
As a relation between (the density of) gas and SFR, theKennicutt-Schmidt (KS) law is well known.
The HI-H2 bivariate mass function
corresponds to a further analysis of theKS law.

Kennicutt & Evans (2012)

Construction of the HI-H2 bivariate mass function
In general, construction of a bivariate distribution is not atrivial task because of complicated combination of selection
effects.
This problem is particularly serious in astronomy!

Construction of the HI-H2 bivariate mass function
In general, construction of a bivariate distribution is not atrivial task because of complicated combination of selectioneffects.
This problem is particularly serious in astronomy!
We developed a general method to construct a bivariate(and multivariate) distribution function with treating thesample selection effects appropriately (Takeuchi 2010;Takeuchi et al. 2013).
∂ 2C [F1 ( x1 ), F2 ( x2 )]g ( x1 , x2 ) =f1 ( x1 ) f 2 ( x2 )∂x1∂x2≡ c[F1 ( x1 ), F2 ( x2 )] f1 ( x1 ) f 2 ( x2 )Construction of the HI-H2 bivariate mass function

Example with various correlation (Takeuchi 2010)

What can we learn from the bivariate function?
(1)

H2 mass

H2 mass(2)(3)
HI mass(1) Proportional(2) More HI, less H2(3) More HI, more H2(4) HI is consumed to form H2

HI mass(1) Stochastic(2) Deterministic(3) Transitive

Construction of the HI-H2 bivariate mass function
Data
HI: 21 cm line observation by Square Kilometre Array(SKA) Phase 1 (2023 ~)H2: Dust continuum/line observation by the Antarctic
telescope (10 m) (2023 ~)Benefit: both are highly efficient in surveys, and coherently
obtain the data with simple selection.
⇒ Gas mass of galaxies up to z ~ 1.
We will be able to constrain the theoretical model with theHI-H2 bivariate mass function.

5 Conclusions
1. To have a complete picture of star formation in galaxies, thetransition from HI to H2 is fundamental.
2. Gas mass function of galaxies is a useful statistical tool toexplore the physics of galaxy evolution.
3. Currently dust emission is used to estimate the total gas
mass in galaxies. But recently both from observational andtheoretical sides, the empirical relation is not valid at low
metallicity.
4. We developed a new theoretical model for the dust evolution,and it should be examined observationally with the Antarctic
telescope.
5. HI-H2 bivariate gas mass function gives more information
than simple total mass function.
6. HI data will be provided by SKA, and H2 at the same
redshift range can be well covered by the Antarctic telescope.

Appendix

Formulation of the grain-size dependent evolution of dust mass
Model settings
・Closed-box model(total baryon mass is a constant)・Two-phase ISM (WNM and CNM)
・Schmidt law : SFR(t) = MISM(t)/τSF・Dust formation by SNe II and AGB stars
・Dust reduction through the astration
・Dust destruction by SN shocks in the ISM
・Grain growth in the CNM
・Grain-grain collisions (shattering and coagulation)in the ISM (mass-preserving processes)

Formulation of the grain-size dependent evolution of dust mass
Md (a, t) = m(a)f(a, t)da : dust mass with a grain radius [a, a+da]
at a galactic age t
SFR(t ) + Yd (a, t )Formulation of the grain-size dependent evolution of dust mass
Md (a, t) = m(a)f(a, t)da : dust mass with a grain radius [a, a+da]
at a galactic age t
SFR(t ) + Yd (a, t )Stellar effects

Formulation of the grain-size dependent evolution of dust mass
Md (a, t) = m(a)f(a, t)da : dust mass with a grain radius [a, a+da]
at a galactic age t
SFR(t ) + Yd (a, t )Destruction
by SN shocks

Formulation of the grain-size dependent evolution of dust mass
Md (a, t) = m(a)f(a, t)da : dust mass with a grain radius [a, a+da]
at a galactic age t
SFR(t ) + Yd (a, t )Grain growth

Formulation of the grain-size dependent evolution of dust mass
Md (a, t) = m(a)f(a, t)da : dust mass with a grain radius [a, a+da]
at a galactic age t
SFR(t ) + Yd (a, t )ShatteringFormulation of the grain-size dependent evolution of dust mass
Md (a, t) = m(a)f(a, t)da : dust mass with a grain radius [a, a+da]
at a galactic age tSFR(t ) + Yd (a, t )Coagulation

Evolution of the grain size distribution[µm]

Dust supply

Log-normal distribution
Large size grains are produced
Winters et al. (1997)
Yasuda & Kozasa (2012)
Dust mass data
Zhukovska et al. (2008)

Grain size
distribution

AGB stars

grain size [cm]Broken power-law
Biased to large grains
Nozawa et al. (2007)
Dust mass data
Nozawa et al. (2007)

Grain size
distribution

Type II Supernovae (SNe II)

grain size [cm]

Dust destruction and grain growth

Nozawa et al. (2006)
Grain growth(metal accretion onto grains)
Smaller grains grow to larger
grains.

0.01µmTime after the explosion [yr]Grain size distribution

Smaller grains are mainly
destroyed by SN shocks.

Grain size [cm]Dust destruction by SN shocks

1.0µm

Hirashita & Kuo (2011)

Grain size [µm]

Shattering and coagulation (driven by ISM turbulence)
Coagulation
Larger grains are producedby smaller grains
Grain size distribution

Grain size distribution

Shattering
Smaller grains are producedby larger grainsHirashita (2010)

Hirashita (2012)

Star Formation Rate (SFR) and Initial Mass Function (IMF)Star Formation Rate (SFR)
Schmidt law (Schmidt 1959)
SFR(t) ∝MISMn(1 < n < 2)

We assume n = 1 for simplicity.
Initial Mass Function (IMF)
Larson IMF (Larson 1998)

Normalization：
We adopt α = 1.35 and mch = 0.35 M๏ in our study.

Timescales of dust destruction and grain growth
Dust destruction by SN shocks in the ISM
ε : dust destruction efficiency
mswept : ISM mass swept by a SNshock
γSN : SN rate (e.g., McKee 1989)
Grain growth by metal accretiona : mean grain sizenH : number density of the ISM
T : ISM temperatureEvolution of the grain size distribution

Parameter setting :Total baryon mass : 1010 M๏
Star formation timescale :5 Gyr
CNM mass fraction : 0.5
WNM mass fraction : 0.5

Evolution of the grain size distribution

Parameter setting :Total baryon mass : 1010 M๏
Star formation timescale :5 Gyr
CNM mass fraction : 0.5
WNM mass fraction : 0.5
Early stage : stars

Evolution of the grain size distribution

Parameter setting :Total baryon mass : 1010 M๏
Star formation timescale :5 Gyr
CNM mass fraction : 0.5
WNM mass fraction : 0.5
Small scale goes up byaccretion & shatteringEvolution of the grain size distribution

Parameter setting :Total baryon mass : 1010 M๏
Star formation timescale :5 Gyr
CNM mass fraction : 0.5
WNM mass fraction : 0.5
The peak shifts to larger scaleby coagulation