~

20pc

銀河進化研究会＠愛媛

Disentangling the physical parameters
for gaseous nebulae and galaxies
Daichi Kashino (ETH Zurich)
In collaboration with Akio K. Inoue
Image Credit Brian DavisDaichi Kashino (ETH Zurich) 銀河進化研究会＠愛媛

How do the gas properties connect withthe galaxy’s mass and SF activity?
No. 2, 2004

ORIGIN OF MASS-METALLICITY RELATION

9

Mass—metallicity relation (MZR)•

Metallicity reflects the history ofstar formation, inflow and outflow
of gas content.

•

Established in the local Universe(z~0.07) using 53,000 galaxies
from SDSS•

A tight correlation~0.1 dex in Z at fixed M✱•

MZR evolves with redshift:
now studied up to z~5

Fig. 6.—Relation between stellar mass, in units of solar masses, and gas-phase oxygen abundance for '53,400 star-forming galaxies in the SDSS. The la
black filled diamonds represent the median in bins of 0.1 dex in mass that include at least 100 data points. The solid lines are the contours that enclose 68% and 9of the data. The red line shows a polynomial fit to the data. The inset plot shows the residuals of the fit. Data for the contours are given in Table 3.

Tremonti+04

mass, we invoke another well-known empirical correlation,
the Schmidt star formation law (Schmidt 1959; Kennicutt
1998), which relates the star formation surface density to thegas surface density.
For each of our galaxies we calculate the star formation rate

(Note that the numerical coefficient has been adjusted toclude helium in !gas.) Combining our spectroscopically
rived M/L ratio with a measurement of the z-band surfa
brightness in the fiber aperture, we compute !star , the stelsurface mass density. The gas mass fraction is then "gas

Daichi Kashino (ETH Zurich) 銀河進化研究会＠愛媛

Mass—metallicity—SFR relation:
The Astrophysical Journal, 765:140 (23pp), 2013 March 10
The fundamental metallicity relation

Downloaded from http://mnras.oxfordjournals.org/ at ETH-Bibliothek on November 14, 2016

Mannucci+102119

Figure 11. The direct method M⋆ –Z–SFR relation for the M⋆ –SFR stacks(circles color-coded by SFR) in the mass–metallicity plane. The thick solid lines
color-coded by SFR show the asymptotic logarithmic fits (see Equation (5)) for
the M⋆ –SFR stacks. The thick black line shows the direct method MZR from✱ gray lines show the median, 68%
Figure 10. The solid, dashed, and dotted
contour, and 95% contour, respectively, of the Tremonti et al. (2004) MZR. The
error bars correspond to the mean error for the M⋆ –SFR stacks of a given SFR.
The metallicities and fit parameters for the stacks are given in Tables 3 and 4,
respectively.
(A color version of this figure is available in the online journal.)

Andrews&Martini 13•

Metallicity is inversely correlated with SFR at fixed M at z~0.1.

•

Z(M✱, SFR) has been proposed to be redshift-independent up to z~2(Fundamental Metallicity Relation: FMR), while it remains under
debate.
We note that the direct method and D02 MZRs have similar•slopes and normalizations over a wide range in masses fromlog(M⋆ ) = 8.5–10.0.

Gas mass may play a central role: elevated inflow rate could enhance
SFR while diluting metallicity.

Figure 2. Three projections of the FMR among M⋆ , SFR and gas-phase metallicity. Circles without error bars are the median values of metallicity of local
SDSS galaxies in bin of M⋆ and SFR, colour-coded with SFR as shown in the colour bar on the right-hand side. These galaxies define a tight surface in the 3D
space, with dispersion of single galaxies around this surface of ∼0.05 dex. The black dots show a second-order fit to these SDSS data, extrapolated towards
higher SFR. Square dots with error bars are the median values of high-redshift galaxies, as explained in the text. Labels show the corresponding redshifts. The
projection in the lower left-hand panel emphasizes that most of the high-redshift data, except the point at z = 3.3, are found on the same surface defined by
low-redshift data. The projection in the lower right-hand panel corresponds to the mass–metallicity relation, as in Fig. 1, showing that the origin of the observed

5.2. Mass–Metallicity–SFR Relation

o
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Daichi Kashino (ETH Zurich) 銀河進化研究会＠愛媛
The Astrophysical Journal, 816:23 (24pp), 2016 January 1

Sanders et al.

Downloaded from http://mnras.oxfordjournals.org/
Downloaded from http://mnras.oxfordjournals.org/
at Nagoya University on Octoberat Nagoya
5, 2015
University on October 5, 2015

Electron density ne of HII regions◀Shimakawa+15

z~2.5▼Sanders+15 z~2.3

Figure 6. [S II]λλ6716,6731 (bottom row) and [O II]λλ3726,3729 (top row) as a function of stellar mass (left), SFR (middle), and sSFR (right). Blue and green points
show the z ∼ 2.3 [O II] and [S II] density samples, respectively. The gray two-dimensional histogram in the bottom row shows the distribution of the local comparison
Figure 3. From top, log (a) [O II] λλ3726, 3729 line ratio, (b) stellar mass, sample. Spectra from SDSS do not have a high enough spectral resolution to resolve the components of the [O II] doublet. The blue, green, and gray dashed lines show(c) sSFR, (d) # SFR , and (e) O32 as a function of log electron density. Dia- the median line ratios for the corresponding sample. Dotted lines show the line ratios corresponding to denities of 10, 100, 1000, and 10,000 cm−3.

•

Typical ne ranges from a few to <100 cm-3 in the local SDSS galaxies•

At higher z (z≳1.5), ne is often estimated to be >100–1000 cm-3.

monds indicate our sample, HAEs at z = 2.5. Error bars of ne are determinedfrom flux errors of [O II] λλ3726, 3729. Blue star symbols represent ne of relative populations in the higher and lower ionized states.
the stacked data separated by ne = 160 cm−3 and those y-values show meni
T¯ Q0
.
x i
(10)
dian values and 1σ scatters. Dotted lines show the best-fitting lines for ourni
Bi 4Qr 2n etargets.
Here, Q0 is the rate of production of hydrogen-ionizing photons(hν 13.6 eV). The ﬁrst term (T̄i Bi ) on the right-hand side ofthis expression is a constant that will change for each ionicspecies. The second term (Q0/4π r2ne) contains only properties
Figure 3. From top, log (a) [O II] λλ3726, 3729 line ratio, (b) stellar mass, of the ionizing source and the gas, and is not dependent on the
Table 1. Fitted slopes (N) and those standard errors to the(c) sSFR, (d) # SFR , and (e) O32 as a function of log electron density. Dia- speciﬁc ionic species. The dimensionless ionization parameter
HAEs on log stellar mass, sSFR, # , or O32 (y) plottedmonds indicate our sample, HAEs at z = 2.5. SFR
Error bars of ne are determined - is deﬁned as the second term on the right-hand side ofagainst log electron density (x≡log(ne /cm3 )). Third and Fourthfrom flux errors of [O II] λλ3726, 3729. Blue star symbols represent n of Equation (10) divided by the speed of light, c.

•of the number density of hydrogen-ionizing photons to thenumber density of the hydrogen gas. When working with H II
regions it is convenient to deﬁne the dimensionless ionization
parameter using the radius of a canonical Strömgren sphere, RS,
as the distance between the gas and the ionizing source
- 

Q0
.
4QRS2 cn e

(12)

may correlate with the global SF activity (sSFR and/or Σ_SFR).
ecolumns indicate Spearman’s rank correlation coefficients andQ0
the stacked data separated by ne = 160 cm−3 and those y-values show me.
- (11)their significance in the respective diagram suggested for the4Qr 2 cn edian values and 1σ scatters. Dotted lines show the best-fitting lines for our
HAEs at z = 2.5.
targets.
Accordingly, the ratio of the relative population in an upper

Often, the dimensional ionization parameter, q  c q -, isused instead, which is the ratio of the ﬂux of ionizing photons
at the Strömgren radius to the hydrogen number density. The
deﬁnition of the Strömgren radius, based on a balance between
ioniziation and recombination rates assuming case B recombination, is
⎛

3Q

⎞1 3

⎛

3Q

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Daichi Kashino (ETH Zurich) 銀河進化研究会＠愛媛

Ionization parameter U = Sion/cnH (c = speed of light)
the ratio of ionizing photon flux to hydrogen density (nH≈ne).

(1) Rest EW(Lyα). For the z  3.1 objects, the EW is estimated from the BV–NB497 color. The EW of LAE 93564 is derived from spectroscopy. A 3T lowers given if the object is not detected signiﬁcantly in the BV image. (2) Conﬁrmed or not from previous rest FUV spectroscopy. (3) Nebular redshift. (4) [O III]7, 4959/[O II]λ 3727 ratio. (5) R23-index. (6) Yion under the assumption of a zero fesc . (7) SFR under the assumption of a zero fesc , estimated from the Hβosity. An upper limit of 3T is adopted in Columns (4)–(7) if the line is not detected. (8) Stellar mass derived from SED ﬁtting, which adopts an SMC dust law.
bsolute UV magnitude measured from an SED around 1500–1600 Å.
Yion,0 , stellar mass, and MUV estimates are less certain due to less precise optical photometry.

906

Nakajima+16

K. Nakajima and M. Ouchi
Nakajima+14

Lower Z

qion = cU

Higher U

e 3. [O III]λλ5007, 4959 /[O II]λ 3727 line ratio vs. R23-index for the MOSFIRE and other samples. Red and blue ﬁlled circles represent the newly observedand LBGs, respectively; AGN 86861 is shown with a gray diamond. Orange symbols show LyC leaking objects, and other red and blue symbols are high-z
and LBGs, respectively, compiled from the literature as shown in the legend. Gray shading illustrates the equivalent distribution for SDSS galaxies. The black
indicates the shift expected for a harder ionizing radiation (see the text).

•

Figure 3. Average ionization parameter and metallicity for our galaxy samples (Table 1).

Commonly estimated from [OIII]/[OII], but the Z-dependence has
to be accounted for.

harder ionizing radiation ﬁeld than LBGs (also refer toMatthee et al. 2016). The difference is apparent at athe
ﬁxed local
UVgalaxy samples. For the SDSS sample, only the values
magnitude suggesting a higher production rate of ionizingin the high-Z branch are given, since the average metallicity forphotons.

otwithstanding the three with upper limits, the Hβted LAEs have an average Yion,0 larger than that inferred
=3.8–5.0 LBGs by ∼0.2–0.5 dex. They support theention deduced from Figure 3 that LAEs typically have a•

Higher [OIII]/[OII] ratios are often themeasuredfor high-z LBGs andlow-Z branch, 12 + log (O/H) =7.7–8.1, is significantly lower
than between
that estimated with
R23-index
and N2-index (Fig. 1). We have
LAEs — possible strong correlation
U
and
sSFR
checked that the SDSS high-Z branch metallicity of 12 + log (O/H)
4•= 8.92–9.12 (Table 1) is consistent with our estimate in Section 3,
as well as those estimated in previous studies (e.g. Tremonti et al.
2004; Mannucci et al. 2010). For GPs, LBAs, and LyC leakers,

Anticorrelation appears to exist between U and Z

Daichi Kashino (ETH Zurich) 銀河進化研究会＠愛媛

Origins of the inverse U−Z correlations
Theoretically, some explanations have been proposed.
(e.g., Dopita et al. 2006)
At higher Z, ionizing photons that contribute to ionization of the gas
reduces because
higher opacity of stellar winds absorb more ionizing photons.

•

radiationenergy is more eﬃciently
converted
into kinetic energy Vol.
of 555618
INOUE, HIRASHITA,& KAMAYAthe winds.
cannot Ðnd the correlation for the extragalactic H II•

regions.4 Thus, we consider that the correlation in Figure 3a
may be caused by our sample selection. Hence, we assumeconservatively in this paper that N@ does not depend on
Ly
the metallicity. In Figure 3b the correlation
between themetallicity and the electron number density, n , is not
e on thefound. Thus, we does not consider that n depends
metallicity. In Figure 3c interestingly, we ecan Ðnd a correlation between n and N@ for only samples in Table 2.
e
Ly
Next, in the Figures
3dÈ3f,
we present the dependence of fon the parameters of H II regions. The estimated f is regarded as a function of the metallicity in Figure 3d, i.e., as themetallicity in an H II region increases, f becomes smaller.
This is because, in our formulation, the dust-to-gas ratio(i.e., metallicity) has a positive dependence on the opticaldepth of dust as shown in equation (7), and then, a larger
dust content leads to a larger optical depth of dust andsmaller f. Although the correlation in Figure 3d is not theresult directly derived via the analysis of the observational

higher dust content in the HII region
absorb more ionizing photons.

▶︎ Fraction of the “contributing”

photons vs. dust-to-gas mass ratio
Inoue+01, Inoue01

Contributing fraction•

Indv. HII regs.

log Mdust/Mgas
FIG. 4.ÈEstimated f vs. dust-to-gas mass ratio, D. Open symbols are
the representative giant H II regions in Table 1, and Ðlled symbols are H II

Daichi Kashino (ETH Zurich) 銀河進化研究会＠愛媛

Origins of the inverse U−Z correlations

Theoretically, some explanations have been proposed.
(e.g.,No
Dopitaet al. 2006)
observational
confirmation of the “partial” anti-correlation
906
K. Nakajima and M. Ouchi
At higher Z, ionizing photons that contributeto ionization of the gas
The sequence of SDSS galaxies presents an upturn from highR23-index values. This trend is probably caused by the prese
reduces because
–1.5
This
“apparent”
U∝ Z
a hidden
AGN activity in a galaxy. In this regime, the SDSS ga
departing from the model curve would be also dominated by oanticorrelation
includes• higher opacity of stellar winds absorb morewith a ionizing
low SFR and a photons.
high M (Section 4.5; see also Dopita
2006a). of changes in othereﬀects• radiationenergy is more eﬃciently
converted
into kinetic energy Vol.
of 555618
INOUE, HIRASHITA,& KAMAYAparameters.
4.4 Dependence of [O III]/[O II] on M and SFR
the winds.
cannot Ðnd the correlation for the extragalactic H II•

regions.4 Thus, we consider that the correlation in Figure 3a
may be caused by our sample selection. Hence, we assumeconservatively in this paper that N@ does not depend on
Ly
the metallicity. In Figure 3b the correlation
between themetallicity and the electron number density, n , is not
e on thefound. Thus, we does not consider that n depends
metallicity. In Figure 3c interestingly, we ecan Ðnd a correlation between n and N@ for only samples in Table 2.
e
Ly
in ionization
the Figures
3dÈ3f,
wethe fordependencefFigure 3. Next,
Averageparameter
andpresent
metallicity
our galaxyof
samon theples (Table1). parameters of H II regions. The estimated f is regarded as a function of the metallicity in Figure 3d, i.e., as themetallicity in an H II region increases, f becomes smaller.
This
is because,in ourthe dust-to-gas
ratio
the local
galaxysamples.
For formulation,
the SDSS sample,
only the values(i.e., metallicity) has a positive dependence on the opticalin the high-Z
given,in since
the average
metallicity
fordepth ofbranch
dust asareshown
equation(7), and then,a largerthe low-Z
12leads+ logto(O/H)=7.7–8.1,
significantly
dustbranch,content
a larger
optical isdepthof dust lower
andthan that
estimatedwith R23-index
and N2-index(Fig.
We thehave
smallerf. Although
the correlationin Figure3d 1).
is notdirectly
the analysisof theobservational
checkedresultthat theSDSSderived
high-Zvia
branchmetallicity
of 12+ log (O/H)!

Contributing fraction∗∗

In Section 4.3, we have estimated the typical ionization paramfor our galaxy samples from the comparisons of the photoioni
models with the measurements of [O III]/[O II] and R23-inde
compared them (Fig. 3). However, these comparisons do not
on possible dependencies on galaxy global properties suchand SFR. Fig. 2 presents a relatively large scatter in [O III]ratios at a given
R23-index
in one galaxy sample. This scatter
Indv.
HII regs.
be originated from the galaxy global properties. To addre
issue, we examine the dependencies of the [O III]/[O II] ratio
galaxy global properties.
Fig. 4 shows [O III]/[O II] ratios as a function of M∗ , SFR
cific SFR (sSFR; SFR divided by M∗ ), and µ0.32 (equation
α = 0.32). Fig. 4 indicatesthat the [O III]/[O II] ratio correlate
log Mdust/Mgas
the galaxy global properties of M∗ , SFR, sSFR, and µ0.32 . A
FIG. 4.ÈEstimated f vs. dust-to-gas mass ratio, D. Open symbols are
, and
high
[O III]/[O II] ratio is found in low M , low µ0.32arethe representative giant H II regions in Table 1, and∗Ðlled symbols
H II

higher dust content in the HII region How strong is the “partial”
absorb more ionizing photons.
(=“intrinsic”) dependence?
▶︎ Fraction of the “contributing”

photons vs. dust-to-gas mass ratio
Inoue+01, Inoue01

Daichi Kashino (ETH Zurich) 銀河進化研究会＠愛媛

The conditions of the gas and the global properties of hostgalaxies are connected through various physical processes.
Our goal:
Quantifying the scaling relationships between them:here M✱, sSFR, Z, ne, and U
Especially, we aim to reveal their “partial” correlations.
It requires “direct” metallicity estimates to avoid
systematic dependencies on other parameters inherent in
the commonly-used strong-line indicators.

Daichi Kashino (ETH Zurich) 銀河進化研究会＠愛媛

Data
2×105 galaxy spectra from SDSS DR7 (0.027≤z≤0.25)
Stellar mass and SFR from the MPA-JHU catalog
Composite spectra in M✱-sSFR bins
The direct method requires [OIII]4364 and/or [OII]7320,7330
Example ofstellar template
subtraction

Daichi Kashino (ETH Zurich) 銀河進化研究会＠愛媛

Gas-phase metallicity
via direct Te method using [OIII]4363 and/or [OII]7320,30

log sSFR [yr–1]

succeeded for N=133 stacks with Δlog M✱ =0.2, Δlog sSFR=0.25
Ngal~1–104 per bin

Preliminarylog Stellar Mass M✱ /M⦿Daichi Kashino (ETH Zurich) 銀河進化研究会＠愛媛

Electron density

log sSFR [yr–1]

via [SII] 6716,6731 doublet ratio, incl. the Te dependence.

Preliminarylog Stellar Mass M✱ /M⦿Daichi Kashino (ETH Zurich) 銀河進化研究会＠愛媛

Ionization parameterlog sSFR [yr–1]

from [OIII]5007/[OII]3727, incl. the Z and ne dependences.

Preliminarylog Stellar Mass M✱ /M⦿Daichi Kashino (ETH Zurich) 銀河進化研究会＠愛媛

Z

Preliminary
These key ISM parameters
are all strong functions ofM✱ and sSFR.

U

PreliminarynePreliminary

Daichi Kashino (ETH Zurich) 銀河進化研究会＠愛媛

Z

Preliminary
These key ISM parameters
are all strong functions ofM✱ and sSFR.

U

Preliminary

Increase
DecreasenePreliminary

Daichi Kashino (ETH Zurich) 銀河進化研究会＠愛媛

Colored by sSFR

Z

U

ne

M✱

sSFR

Z

ne

Daichi Kashino (ETH Zurich) 銀河進化研究会＠愛媛

Interpretation with simple ansatze

μgas

Fueling(Mgas/M*)

M*

Compression

Gravity

ne

sSFR
SFE
Radiation

Enrichment

DilutionZ

Expected correlation
Positive
Negative

By deﬁnition

U≡Sion/cnH

Absorption /Conversion to kinetic energy

Daichi Kashino (ETH Zurich) 銀河進化研究会＠愛媛

Interpretation with simple ansatze

μgas

We have no
information on
the gas content.

Fueling(Mgas/M*)

M*

Compression

Gravity

ne

sSFR
SFE
Radiation

Enrichment

DilutionZ

Expected correlation
Positive
Negative

By deﬁnition

U≡Sion/cnH

Absorption /Conversion to kinetic energy

Daichi Kashino (ETH Zurich) 銀河進化研究会＠愛媛

Interpretation with simple ansatze

μgas

We have no
information on
the gas content.

Fueling(Mgas/M )*M*

Compression

Gravity

ne

sSFR
SFE
Radiation

Enrichment

DilutionZ

Expected correlation
Positive
Negative

By deﬁnition

U ≡Sion/cnH

Absorption /Conversion to kinetic energy

Focused on now

Assuming a power law (linear in log):
log U= α log sSFR + β log (O/H) + γ log ne + Const.

Daichi Kashino (ETH Zurich) 銀河進化研究会＠愛媛

Results: dependencies of Ionization parameterU ∝ sSFRα Zβ neγ
α = 0.55±0.01
β = –0.45±0.02
γ = –0.46±0.04

Primarily controlled by sSFR, but alsosignificantly “negatively” dependent on Z and ne

Residual dependence after regressing onto sSFR:
y-axis = Log U – α (log sSFR/Gyr–1)

Color: neColor: Z
Log ne12+LogO/H

Daichi Kashino (ETH Zurich) 銀河進化研究会＠愛媛

How does sSFR govern U ?
Lower-sSFR galaxy
Possible pictures of higher-sSFR galaxy (fixed M✱)

Increase in N of HII regions,but each of them is similar to
those in lower-sSFR objects➡ No increase in the “local”

ionization parameter

Probably,…
• Enhanced SF in a single HII region➡ increase in ionizing radiation• Overlap of HII regions• Escape of ionizing photons— “density-bounded” case➡ eﬀectively increase [OIII]/[OII] ratios

Daichi Kashino (ETH Zurich) 銀河進化研究会＠愛媛

Summary and Caveats
Goal of this work was:Quantifying the relationships between the key ISM and global parameters.
!

Observationally, we demonstrate that U is primarily controlled by sSFR, as
well as that “partial” anti-correlations to Z and ne exist.
!

Functional forms are obviously over-simplified.
!

Still, our results provide us with useful bench marks to be reproduced (onaverage) in galaxy models.
!

Many parameters are not considered:
Gas content, galaxy size (ΣM and ΣSFR), morphology, clumpiness, dust,
escape fraction, diﬀuse HII gas, etc… may also aﬀect the ISM conditions.
!

Beyond the local Universe with e.g., PFS and MOONS