2013 年度 第 43 回 天文・天体物理若手夏の学校

Baryonic Tully-Fisher relation and star formation rate
小林 将人 (名古屋大学大学院理学研究科・素粒子宇宙物理学専攻・銀河進化学研究室 M1)

Abstract
We investigated the relation between rotational velocity, baryonic mass, and star formation rate (SFR)
for several sample galaxies, and found a fundamental plane in three dimension on which those galaxies
are located. In order to understand the galaxy evolution, we first need to investigate physical propertiesof galaxies. Many discussions have already been made and shown as a form of scaling laws that connect
two physical properties of galaxies, such as the Tully-Fisher relation, the baryonic Tully-Fisher relation,
star-formation main sequence, the Schmidt-Kennicutt law, and so on. In reality, however, they exist
seperately. Therefore, when it comes to understanding and determining the galaxy evolution, it isessential to combine those scaling laws to construct a unified theory that explains the galaxy evolution
universally in terms of their physical properties. In this study, we compiled observational data for 130
galaxies to confirm the baryonic Tully-Fisher relation (BTFR), star-formation main sequence, and lastly
found a fundamental plane in three dimension. This would be the first step to see what properties weneed to concern primarily to establish the unified theory.

1Introduction
To understand the galaxy evolution, it is one ofness in the TFR implies there would be a strong relation between dark matter and baryon. Although
the TFR is a well-established linear relation, it had

the most important viewpoints to know the relation
been known that low mass galaxies are deviatedbetween dark halos and galaxies because galaxies
from this tight power-law relation.
form and evolve in these dark halos potential. InMcGaugh (2000) discoverd that this power-law
the history of the Universe, dark halos first formed
realtion is restored if we use baryonic mass insteadand merged with each other as time passed, andof luminosity. (Baryonic mass is the sum of stellar
first stars were born inside these dark halos. Then,mass and gas mass of a galaxy.) This revised powergalaxies have formed there and evolved.
law relation is called the baryonic Tully-Fisher reThe Tully-Fisher relation (Tully & Fisher. 1977:lation (BTFR.) This power-law indicates baryonicTFR) is an empirical relation between the galaxy
mass is more fundamental properties than luminosrotational velocity and luminosity. This relation
ity because low mass galaxies basically contatin aworks effectively to determine the distance of rellot of gas that is still not turned into stars and do
atively nearby galaxies. However, the TFR actunot creat stars as effectively as bright galaxies do.
ally does not just provide the way to determine theSince the rotational velocity is generated in the podistances, but also work as an important relation
tential of dynamical mass, the BTFR is a strong
to connect the baryon and dark matter of a galaxy.
standpoint to invest the galaxy evolution as an inThe dynamical mass, which is the sum of baryonicteraction of dark matter and baryon in general. It
mass and dark matter mass of a galaxy, generates
is now often discussed to how extent we can extend
the rotational velocity, and the stars contained in athe BTFR towards much lower mass galaxies.
galaxy contribute to its luminosity. Thus, the tight-

2013 年度 第 43 回 天文・天体物理若手夏の学校
Another intersting empirical relation of galax- some points from the outcomes. We conclude inies is star-formation main sequence (SFMS.) Star- Section 5, and list future prospects in Section 6.
forming galaxies gather and get aligned to make thisprominent sequence on the two dimensional plane
spanned by stellar mass and specific star formation
rate (SSFR.) SSFR is defined by2

DataIshikawa.H.J.

(2013)

quotedthreepapers:

SFR
SSFR =M∗(1) Torres-Flores et al. (2011), Gurovich et al. (2010),and McGaugh & Wolf. (2010). He calculated SFR
Here, SFR is a rate at which a galaxy creats stars by using AKARI and GALEX data, but the dwarf
in the unit of M year−1 , and M∗ is stellar massthat a galaxy hold now.

spheroidal satellite galaxies in McGaugh’s paper
are difficult to determine their SFR in this way.

If only dark matter were involved in the galaxy Therefore, Ishikawa finally excluded this data fromevolution, the related Physics would be relatively his analysis. We also started from only Torressimple because dark matter basically interacts with Flores et al. (2011) and Gurovich et al. (2010). To
each other only gravitationally. But, the active evo- make this fundamental property analysis reliable,lution includes baryons and baryons involve many we sought for more data of disk galaxies and lastly
physical processes to make this evolution compli- chose three other papers: Puech et al. (2010),
cated. Thus, the analysis of galaxy evolution cannot Brosch et al. (2011), McGaugh. (2012).
stand without research of the baryonic properties.
Three samples from our data are shown at theThe SFMS is an star-forming aspect of these bary- top on the next page as an example. In total, we
onic properties and represents the combination of compiled 130 galaxies data.
star formation histroy of a galaxy and its current
stellar mass. Then, we expected a similar relation
Investigation and Result
would exist between SFR and baryonic mass as well. 3
Although these two relations seem to be obvious,
the physical justification for the reason why they

We extracted the data of rotational velocity, stel-lar mass, gas mass, baryonic mass, and star formaare so tight is actually still under debate.
tion rate from each paper. We abbreviate stellar
In this work, we considered these two empiricalmass as M∗ , gas mass as Mgas , baryonic mass as
relations to find fundamental properties underlying
Mbar , and rotational velocity as Vrot hereafter. If
all galaxies on an analytic basis of observational
the gass mass and baryonic mass are not available,
data. In Section 2, we show the data we quoted
we convert Hi mass to gas mass byfrom several papers. In Section 3, we plot thesample galaxies on several two dimensional planes
Mgas = 1.4MHI(2)
and confirm the BTFR and SFMS. Moreover, weM= M +M
(3)
bar∗

gas

make three dimensional real space spanned by roWe plotted these data on several different planes
tational velocity, total baryonic mass, and SFR toplot galaxies. This corresponds to an incorporation and in a space. First, on Mbar -Vrot plane, we conof two scaling laws: the BTFR and SFMS. We cal- firmed the BTFR in our data. We found the BTFR
culate a fit two dimensional plane on which theselog Mbar = 2.76 log Vrot + 4.08
(4)galaxies are located and finally find a fundamental plane that hold a relation between these three having the slope of 2.76, which is realtively smallgalactic properties. In Section 4, we briefly discuss compared with the ones from previous research (e.g.

2013 年度 第 43 回 天文・天体物理若手夏の学校

表 1: An example of sample galaxies (cited from Puech et al. 2010)∆Vflatlog(Mstellar M −1 )SFR∆SFRlog(Mgas M −1 )∆ log(Mgas M −1 )

15026

10.29

5.7

4.1

9.82

0.33

550123

11.44

8.5

0.2

9.89

0.04

18022

10.61

17.2

0.3

10.21

0.11

IAU ID

Vflat

J033210.25-274819.5
J033210.76-274234.6
J033212.39-274353.6

McGaugh & Wolf. 2010, Gurovich et al. 2010,
Torres-Flores et al. 2011, and so on.)Second, on SFR-Mbar plane, we foundlog SFR = 1.30 log Mbar − 13.1.
Third, on SSFR-M∗ plane, we foundlog SSFR = −0.50 log M∗ − 4.35.

4Discussion
We actually have small deviations from theBTFR by Eq.(4) in the low mass region. This de(5) viation can be a contribution not only from thelow mass galaxies properties themselves, but also
(6)

from the large mass galaxies properties in our samples. Those large mass galaxies are from Puech

This shows the galaxies in our data also form SFMS. et al. (2010) and Brosch et al. (2011). Especially,Fourth, on SSFR-Mbar plane, we found
Brosch et al. (2011) reported candidate high-mass
disk galaxies that they provided in their paper delog SSFR = −0.60 log M∗ − 3.31.
(7)viate significantly from the TFR defined by lower
This shows a similar power-law relation correspond- mass galaxies, which leads to make a less inclined
ing to the SFMS on the previous plane.
power-law relation.
Finally, in SFR-Mbar -Vrot three dimensional
We found a slgiht relation between baryonic massspace, we found the realtion between these three and SFR by Eq.(5), but low mass galaxies and highproperties as follows:mass galaxies seem to have different slopes.
log SFR = −3.78 log Vrot + 1.99 log Mbar − 11.2 (8)This relation constructs a two dimensional funda-

We confirmed that the galaxies in our data also
reproduce SFMS by Eq.(6) but several galaxies deviate far from the fitting line. These galaxies may
have already passed their most active star-forming
era and now finishing their star formations.
We presented that SSFR-Mbar relation by Eq.(7)also demonstrates SFMS.
We finally showed that the galaxies are on a fundamental plane defined by Eq.(8). This result has
two big differences from the previous research doneby Ishikawa.H.J. (2013). Ishikawa concluded thatthese three properties are connected as follows;
log SFR = 1.49 log Vrot + 0.552 log Mbar − 8.17. (9)図 1: SFR-Mbar -Vrot relation

First, SFR depends more on Vrot than on Mbar inEq.(9), but depends more on Mbar than on Vrot inmental plane which subsumes all galaxies on its sur- Eq.(8). Second, SFR is proportional to a power offace. Here, we weighted each sample with the in- Vrot in Eq.(9), but inversly proportional in Eq.(8).
verse of their error bars along the SFR axis.

2013 年度 第 43 回 天文・天体物理若手夏の学校
We need to discuss these differences further and fol- we should work on how far we can extend the funlow up what Eq.(8) physically mean.
damental plane in the three dimension as well. Observational progress for low mass but star-forming
galaxies will be in demand. This is one of the ex-5Conclusion

pectations on SKA.
(6) There is another attracting scaling law related
We quoted data from Gurovich et al. (2010),
to star formation: Schmidt-Kennicutt law (KSTorres-Flores et al. (2011), Puech et al. (2010),law). Since this is a realtion between two surface
Brosch et al. (2011), and McGaugh. (2012) todensity quantities, radius will be the next appropriplot them on two dimensional graphs with differate property that we can take into account when weent properties: Vrot , M∗ , Mbar , SFR, and SSFR.
incoporate KS-law into the three dimensional relaThrough these relations, we found the BTFR withtion Eq.(8). This immediately commands you toa relatively small slope of 2.76. We confirmed SFMS
handle higher dimensional manifolds and involves
and also a similar sequence on SSFR-Mbar plane.
high-dimensional analysis, such as PCA.
Then, we demonstrated three dimensional rela(7) To exmaine how the relation between dark mattions between Vrot , Mbar , and SFR as
ter and bayon evolved, we need to analyze the three
dimensional relation at different redshift and establog SFR = −3.78 log Vrot + 1.99 log Mbar − 11.2.
lish the extended BTFR.
This relation could underly all galaxies so thatit represents the relation between dark matter,baryon, and the star formation history of galaxies.

Reference
6Future Prospects

Tully,R.B., & Fihser,J.R. 1977, A&A, 54, 661
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dence on Vrot and Mbar represented by Eq.(8) and McGaugh,S.S., & Wolf,J. 2010, APJ, 722, 248
find physical meaning in this relation.
(2) From 図 1 , mass range should be broad forthe general analysis. This, however, also warn that

Gurovich,S., & Freeman,K. & Jerjen,H., & StaveleySmith,L., & Puerari,I. 2010, APJ, 140, 663
Torres-Flores,S. & Epinat,B., & Amram,P., & Plana,H.,

more fundamental discussions require to treat dif& Mendes de Oliveira,C. 2011, MNRAS, 416, 1936
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Serrano,R., & Rodrigues,M., & Yang,Y. 2010, A&A,(3) In this work, the way to calculate SFR differes
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Ishikawa,H.J. 2013, Master Thesis, Nagoya University