Topics on HI in the Context of Galaxy Evolution:

Baryonic Tully Fisher Relation and its Extension

Tsutomu T. TAKEUCHIwith

Hiroshi Jacky ISHIKAWA

Division of Particle and Astrophysical Science, Nagoya University, Japan

SKA High-z Group Workshop 2013, 20-21 Feb., 2013, Kyoto, Japan

Dark halo

1. Introduction

Dark halos form and merge with time. Then, first stars and galaxies form and evolve in their potential.

First stars

1. Introduction

Dark halos form and merge with time. Then, first stars and galaxies form and evolve in their potential.

Galaxy

1. Introduction

Dark halos form and merge with time. Then, first stars and galaxies form and evolve in their potential.

1. Introduction

Dark halos form and merge with time. Then, first stars and galaxies form and evolve in their potential.

1. Introduction

Dark halos form and merge with time. Then, first stars and galaxies form and evolve in their potential.

1. Introduction

Dark halos form and merge with time. Then, first stars and galaxies form and evolve in their potential.

1. Introduction

Dark halos form and merge with time. Then, first stars and galaxies form and evolve in their potential.

The relation between dark halos and galaxies (baryons) is the key to understand the galaxy evolution.

The relation between the rotational velocity or velocity dispersion and luminosity of galaxies are tightly correlated. The former is the Tully-Fisher relation, and the latter is the Faber-Jackson relation.

In general, we can summarize these relation as the velocity-luminosity relation.

Rotational velocity

Abs

olut

e m

agni

tude

Willick (1999)

Velocity-luminosity relation

Velocity-luminosity relationFrom the virial theorem, we have an approximate relation as follows.

The baryonic Tully-Fisher relationAfter the first proposal by Tully & Fisher (1977), it was found that at the small circular velocity regime, galaxies tend to deviate downward from the TF relation defined by large galaxies.

More fundamentally, the classical Tully-Fisher relation depends on the observed wavelength because it uses optical/NIR luminosity, which is strongly dependent on the star-formation history.

The baryonic Tully-Fisher relationAfter the first proposal by Tully & Fisher (1977), it was found that at the small circular velocity regime, galaxies tend to deviate downward from the TF relation defined by large galaxies.

McGaugh et al. (2000) discovered that if we add the gas mass of galaxies to the stellar mass, we can recover the single power law.

More fundamentally, the classical Tully-Fisher relation depends on the observed wavelength because it uses optical/NIR luminosity, which is strongly dependent on the star-formation history.

The baryonic Tully-Fisher relation

McGaugh et al. (2000)

Now, the TF relation appear as a fundamental relation between the baryon mass (galaxy mass) and dynamical mass of a halo.

Circular velocity [kms-1]

Stel

lar

mas

s [M

☉]

Tota

l bar

yon

mas

s [M

☉]

Somerville & Primack (1999)

Example: The functional forms of the halo mass function and galaxy stellar mass function are significantly different.

Related to the physics of galaxy formation

Relation between dark and baryonic mass functions

Somerville & Primack (1999)

Example: The functional forms of the halo mass function and galaxy stellar mass function are significantly different.

There are roughly two different ways to connect the halo mass function and stellar (baryon) mass function.1. Velocity-baryonic mass

relation2. Halo occupation distribution

(HOD)

Relation between dark and baryonic mass functions

Somerville & Primack (1999)

Example: The functional forms of the halo mass function and galaxy stellar mass function are significantly different.

There are roughly two different ways to connect the halo mass function and stellar (baryon) mass function.1. Velocity-baryonic mass

relation2. Halo occupation distribution

(HOD)

Relation between dark and baryonic mass functions

Among empirical relations of galaxies, relations with star formation are also interesting subject.

Star-formation main sequence

On the stellar mass-specific SFR plane, there appears a prominent sequence of star-forming galaxies: star-formation main sequence.

cf. the blue cloud on the color-magnitude diagram.

Define the specific star formation rate (SSFR)

Schiminovich et al. (2007)

Empirical relations including star formation

If we consider the size of galaxies, we may also be interested in the column (surface) density of gas and star formation, leading to the Schmidt-Kennicutt law.

The original Schmidt-Kennicutt law is a power-law relation between the surface gas mass density and surface density of the SFR.

The slope of this power law is still under debate.

Kennicutt & Evans (2012)

Neutral and molecular gas surface density and SFR

Kennicutt & Evans (2012)

The SFR is supposed to correlate with dense molecular gas density.

However, in the case of the Milky Way, this is not necessarily true.

Neutral and molecular gas surface density and SFR

Kennicutt & Evans (2012)

The SFR is supposed to correlate with dense molecular gas density.

However, in the case of the Milky Way, this is not necessarily true.

Neutral and molecular gas surface density and SFR

Kennicutt & Evans (2012)

The SFR is supposed to correlate with dense molecular gas density.

However, in the case of the Milky Way, this is not necessarily true.

A comprehensive analysis of the SFR, stellar mass, dynamical mass, and size of galaxies will be ideal.

Aim of the study

We try to extend the scaling relation of galaxies to incorporate the star formation properties of galaxies.

By this analysis, we can connect the halo mass, baryon mass, and their star formation properties. The resulting fundamental relation should include1. Baryon TF (BTF) relation2. SFR-baryon mass relation3. Kennicutt-Schmidt lawas well as other relations.

In this talk, we present the result related to 1 and 2.

2. Data

(1) McGaugh & Wolf (2010)Dwarf spheroidals

(2) Torres-Flores et al. (2011) Spirals and irregulars from GHASP (Gassendi HAlpha survey of SPirals )

(3) Gurovich et al. (2010)Isolated undisturbed spirals

The sample was compiled from previous studies for the baryonic Tully-Fisher relation. To have a large mass (circular velocity) range, we used the following three samples. Then, the sample is heterogeneous.

Parent data

Measurement of SFR

The SFR is measured from UV and IR.

1. UVWe measured the UV flux from GALEX FUV images (l = 1530Å). The SFR from directly observable UV is obtained by

This formula was obtained by Starburst99 model assuming a constant SFR for 108 yr and the Salpeter initial mass function (Salpeter 1955) with a mass range from 0.1M☉ to 100M☉.

2. IRWe cross-matched the AKARI point source catalog and quoted fluxes from the data. The SFR hidden by dust is calculated by

where h is the fraction of IR luminosity heated by old stars which are not related to the current SFR.

Here LTIR stands for the total IR luminosity obtained by the formula of Takeuchi et al. (2010) using the AKARI FIS WIDE-S and WIDE-L:

Measurement of SFR

The total SFR is then given by

Measurement of SFR

Not all the galaxies in the parent sample have GALEX images or AKARI point source counterpart. The final sample contains 35 galaxies.

Redshifts of the sample were obtained from NED, and we assumed h = 0.73, WM0 = 0.24, WL0 = 0.76.

3. ResultsBaryonic Tully-Fisher relation

Circular velocity Vc [kms-1]

Tota

l bar

yon

mas

s Mba

r [M

☉]

We obtained a BTF relation from the sample for quite a large circular velocity range.

3. ResultsBaryonic Tully-Fisher relation

We obtained a BTF relation from the sample for quite a large circular velocity range.

We note that even we take into account the stellar and gas mass, we find a downward deviation from a single power law.

⇒ We revisit this issue later.

Circular velocity Vc [kms-1]

Tota

l bar

yon

mas

s Mba

r [M

☉]

Stellar mass-SFR relation (SF main sequence)

Stellar mass M* [M☉]

SFR

[M☉

yr-1]

(r = 0.766)

cf. Elbaz et al. (2007)

Total baryon mass-SFR relation

Total Baryon mass Mbar [M☉]SF

R [M

☉yr

-1]The slope is steeper than the M*-

SFR relation.

The added gas mass fraction is larger for smaller galaxies, i.e., small galaxies have formed stars slowly, and they have a large gas reservoir.

Velocity-total baryon mass-SFR relation

Velocity-total baryon mass-SFR relation

We have a non-trivial dependence on both circular velocity and baryon mass.

Velocity-total baryon mass-SFR relation

The principal component analysis may be a better tool for this analysis.

The HI Parkes All Sky Survey (HIPASS) team showed

This is steeper than the luminosity TF. However, it is still too shallow.

4VM B

4. DiscussionHIPASS result

Meyer et al. (2008)

URL: http://www.atnf.csiro.au/research/multibeam/release/

Some recent works showed a possible downward deviation from a single power law.

McGaugh et al. (2010)Toward lower HI masses!

The slope becomes steeper from the largest to the smallest structures (clusters: violet symbols, giant galaxies: blue symbols, and dwarf spheroidals: red symbols).

⇒ Possible effect of feedback?

However, gaseous dwarfs are missing on this plot.

The “extended” BTF

HI emission: down to HI mass = 103 M☉(~ baryonic mass of dSph)

at 3 Mpc.

N.B. These galaxies are extended.

Required sensitivity (for Local galaxies)

Jy][kms 1010

501

1-sun

3

vMMS

Theoretical attempt

Trujillo-Gomez et al. (2011) discussed this issue based on LCDM (Bolshoi) + halo abundance matching and HIPASS data.

Trujillo-Gomez et al. (2011)

They claim that the velocity-luminosity relation is naturally reproduced simultaneously with correlation functions etc.

Theoretical attempt

Trujillo-Gomez et al. (2011) discussed this issue based on LCDM (Bolshoi) + halo abundance matching and HIPASS data.

Trujillo-Gomez et al. (2011)

They claim that the velocity-luminosity relation is naturally reproduced simultaneously with correlation functions etc.

How about SF properties?

Star formation properties revisited

Kennicutt & Evans (2012)

Surface densities of total gas (HI + H2) and SFR are correlated.

We should extend our result to include a galaxy size (radius) to address the issues related to Schmidt-Kennicutt law.

To extend the analysis to higher dimensions, the data must be very large (aka the curse of dimension).

⇒ SKA survey!

The basic BTF are related mainly to disk galaxies, which have SF activity in general.

The general scaling relation includes elliptical galaxies as the Faber-Jackson relation. We note that TF and FJ relations are not the same.

The SF galaxies only appears in the SF-related subspace in the multidimensional data-vector space.

How to deal?

Star formation properties revisited

Connecting the properties of dark halos and resident galaxies is one of the most fundamental issues in the physics of galaxy formation and evolution. 1. Dynamical properties are explored via TF or FJ relation

(velocity-luminosity relation). 2. Some important empirical relations including star-

formation properties are known (SF main sequence, Schmidt-Kennicutt law).

3. We constructed a sample of Local galaxies with a large mass range, and found a three-dimensional relation:

4. Some theoretical works seem to succeed in explaining these relations, but still various problems remain unsolved.

4. Summary and Prospects

With SKA, we expect various extension and development for this work.1. Enlarge the sample with a homogeneous selection. 2. For Local sample, the study on the BTF is not very

demanding for the performance of the instruments (50 Jy for Local dwarfs).

3. In order to extend it to include the size effect to discuss Schmidt-Kennicutt-type laws, we need a very large sample, but this request will be automatically satisfied.

4. For such a high-dimensional analysis, PCA will be useful.5. Current theoretical works are based on the HIPASS results.

SKA will enables us to much more precise discussions. We can refine the theoretical works.

etc., etc…

4. Summary and Prospects

1. Introduction

Halo occupation distribution (HOD)

Halo model assumes that the two-point correlation (or power spectrum) of galaxies consists of two components, one-halo and two-halo terms.

Peacock (2002)

1. Introduction

Halo occupation distribution (HOD)

In this framework, the distribution function of the number of galaxies in one halo as a function of the halo mass is referred to as the halo occupation number (HOD).

By connecting the HOD (or more precisely, conditional luminosity function) with the halo mass function, we can obtain the galaxy luminosity function. Kravtsov (2003)

Empirical relations including star formation

Kennicutt & Evans (2012)