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A new scaling relation for HII regions in spiral galaxies: unveiling the true nature of the mass-metallicity relation

AbstractWe demonstrate the existence of a -local- relation between galaxy surface mass density, gas metallicity, and star-formation rate density using spatially-resolved optical spectroscopy of HII regions in the local Universe. One of the projections of this distribution, -the local mass-metallicity relation- extends over three orders of magnitude in galaxy mass density and a factor of eight in gas metallicity. We explain the new relation as the combined effect of the differential radial distributions of mass and metallicity in the discs of galaxies, and a selective star-formation efficiency. We use this local relation to reproduce -with remarkable agreement- the total mass-metallicity relation seen in galaxies, and conclude that the latter is a scale-up integrated effect of a local relation, supporting the inside-out growth and downsizing scenarios of galaxy evolution.

Topics: Galaxy formation and evolution (59%), Spiral galaxy (58%), Galaxy (58%), Metallicity (55%)

Summary (3 min read)

1. INTRODUCTION

  • The existence of a strong correlation between stellar mass and gas-phase metallicity in galaxies is a well-known fact (Lequeux et al. 1979).
  • Considerable work has been devoted to understanding the physical mechanisms underlying the M–Z relation.
  • The proposed scenarios to explain its origin can be broadly categorized as: (1) the loss of enriched gas by outflows (T04; Kobayashi et al. 2007); (2) the accretion of pristine gas by inflows (Finlator & Davé 2008); (3) variations of the initial mass function with mass (Köppen et al. 2007); (4) selective star formation efficiency or downsizing (Brooks et al.
  • Nowadays, the imaging spectroscopy technique can potentially prove to be the key to understanding many of the systematic effects that hamper the role of the distribution of mass and metals in galaxies.

2. DATA SAMPLE AND ANALYSIS

  • The study was performed using IFS data of a sample of nearby disk galaxies, part belonging to the PINGS survey (RosalesOrtega et al. 2010), and a sample of face-on spiral galaxies from Mármol-Queraltó et al. (2011) as part of the feasibility studies for the CALIFA survey (Sánchez et al. 2012a).
  • The H ii regions in these galaxies were detected, spatially segregated, and spectrally extracted using HIIexplorer (Sánchez et al. 2012b).
  • The emission lines were decoupled from the underlying stellar population using fit3d (Sánchez et al. 2007), following a robust and well-tested methodology (Rosales-Ortega et al. 2010; Sánchez et al. 2011).
  • The estimated error in the derived ΣLum is ∼0.25 dex, taking into account the error in the flux calibration of their IFS data set (Rosales-Ortega et al. 2010; Mármol-Queraltó et al. 2011), and the expected uncertainty of the Bell & de Jong (2001) formulation.
  • The relation between the mass surface density and radius was checked by normalizing the mass profile by the effective radius, finding a similar slope for all galaxies closer to unity, i.e., the mass profile follows an exponential law, which is what is expected for disk galaxies (e.g., Bakos et al. 2008).

3. THE LOCAL M–Z RELATION

  • The left panel of Figure 1 shows the striking correlation between the local surface mass density and gas metallicity for their sample of nearby H ii regions, i.e., the local M–Z relation, extending over ∼3 orders of magnitude in ΣLum and a factor ∼8 in metallicity.
  • Also remarkable is the tightness of the correlation; the 1σ scatter of the data about the median is ±0.14 dex.
  • The authors obtain the same shape of the relation (and similar fit) if they adopt the R23 metallicity calibration of T04, but with a higher scatter (∼20%) due to the lowest number of H ii regions in their sample with the [O ii]λ3727 line.
  • Note that the local M–Z relation holds for individual galaxies with a large-enough dynamical range in ΣLum and metallicity to cover the whole parameter space of the relation, i.e., it is indeed a local relationship.
  • This functional relation is evident in a three-dimensional (3D) space with orthogonal coordinate axes defined by these parameters, consistent with |EW(Hα)| being inversely proportional to both ΣLum and metallicity, as shown in Figure 2.

4. THE GLOBAL M–Z RELATION

  • In order to test whether the global M–Z relation observed by T04 using SDSS data is a reflection (aperture effect) of the local H ii region mass density versus metallicity relation, the authors perform the following exercise.
  • The effective radius of the mock galaxy is estimated using the well-known luminosity-scale relation (e.g., Brooks et al. 2011) assuming a normal standard deviation of 0.3 dex (Shen et al. 2003).
  • Then, the metallicity is calculated at different radii up to an aperture equal to the SDSS fiber (3 arcsec) in 100 bins using Equation (1), i.e., the metallicity that corresponds to the mass density surface at each bin.
  • The authors used the O3N2 metallicity conversion by Kewley & Ellison (2008, hereafter K08) to convert to the T04 base.
  • The correspondence can be clearly seen by comparing the distribution of points with the overlaid lines corresponding to the T04 fit and the K08 ±0.2 dex relation (blue), for which the agreement is extremely good over a wide range of masses.

5. ON THE ORIGIN OF THE LOCAL AND GLOBAL M–Z RELATIONS

  • The authors interpret the local M–Z–EW(Hα) relation as the consequence of a more subtle relation between the mass, metallicity, and star formation history with galaxy radius.
  • The observed trend agrees qualitatively with this scenario: the inverse gradient of |EW(Hα)| versus ΣLum or metallicity would reflect an evolutionary sequence across the disk of the galaxies, i.e., lower values of |EW(Hα)| corresponding to lower SSFR, and vice versa.
  • As the galaxy evolves and grows with time, the star formation progresses radially, creating a radial metallicity gradients in the disk of spirals.
  • In such a case, the local M–Z relation would reflect a more fundamental relation between mass, metallicity, and star formation efficiency as a function of radius, equivalent to a local downsizing effect.

6. CONCLUSIONS

  • By using the IFS of a sample of nearby galaxies, the authors demonstrate the existence of a local relation between the surface mass density, gas-phase oxygen abundance, and |EW(Hα)| in ∼2000 spatially resolved H ii regions of the local universe.
  • In both projections, the value of |EW(Hα)| is inversely proportional to mass and metallicity.
  • Notably, the local M–Z relation has the same shape as the global M–Z relation for galaxies observed by T04.
  • F.F.R.-O. acknowledges the Mexican National Council for Science and Technology for financial support under the program Estancias Posdoctorales y Sabáticas al Extranjero para la Consolidación de Grupos de Investigación, 2010–2011.

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The Astrophysical Journal Letters, 756:L31 (5pp), 2012 September 10 doi:10.1088/2041-8205/756/2/L31
C
2012. The American Astronomical Society. All rights reserved. Printed in the U.S.A.
A NEW SCALING RELATION FOR H ii REGIONS IN SPIRAL GALAXIES: UNVEILING
THE TRUE NATURE OF THE MASS–METALLICITY RELATION
F. F. Rosales-Ortega
1,3
,S.F.S
´
anchez
2,3
, J. Iglesias-P
´
aramo
2,3
,A.I.D
´
ıaz
1
,J.M.V
´
ılchez
2
,
J. Bland-Hawthorn
4
,B.Husemann
5
,andD.Mast
2,3
1
Departamento de F
´
ısica Te
´
orica, Universidad Aut
´
onoma de Madrid, E-28049 Madrid, Spain; frosales@cantab.net
2
Instituto de Astrof
´
ısica de Andaluc
´
ıa (CSIC), Camino Bajo de Hu
´
etor s/n, Aptdo. 3004, E-18080 Granada, Spain
3
Centro Astron
´
omico Hispano Alem
´
an, Calar Alto, CSIC-MPG, C/Jes
´
us Durb
´
an Rem
´
on 2-2, E-04004 Almeria, Spain
4
Sydney Institute for Astronomy, School of Physics A28, University of Sydney, NSW 2006, Australia
5
Leibniz-Institut f
¨
ur Astrophysik Potsdam (AIP), An der Sternwarte 16, D-14482 Potsdam, Germany
Received 2012 May 21; accepted 2012 July 25; published 2012 August 22
ABSTRACT
We demonstrate the existence of a local mass, metallicity, star formation relation using spatially resolved
optical spectroscopy of H ii regions in the local universe. One of the projections of this distribution—the local
mass–metallicity relation—extends over a wide range in this parameter space: three orders of magnitude in mass
and a factor of eight in metallicity. We explain the new relation as the combined effect of the differential distributions
of mass and metallicity in the disks of galaxies, and a selective star formation efficiency. We use this local relation
to reproduce—with a noticeable agreement—the mass–metallicity relation seen in galaxies, and conclude that the
latter is a scale-up integrated effect of a local relation, supporting the inside-out growth and downsizing scenarios
of galaxy evolution.
Key words: galaxies: abundances galaxies: fundamental parameters galaxies: ISM galaxies: stellar content
techniques: imaging spectroscopy
Online-only material: color figures
1. INTRODUCTION
The existence of a strong correlation between stellar mass and
gas-phase metallicity in galaxies is a well-known fact (Lequeux
et al. 1979). These parameters are two of the most fundamental
physical properties of galaxies, both directly related to the
process of galaxy evolution. The mass–metallicity (
MZ)
relation is consistent with more massive galaxies being more
metal-enriched. It was established observationally by Tremonti
et al. (2004, hereafter T04), who found a tight correlation
spanning over 3 orders of magnitude in mass and a factor of 10
in metallicity, using a large sample of star-forming galaxies up
to z 0.1 from the Sloan Digital Sky Survey (SDSS). The
MZ
relation appears to be independent of large-scale environment
(Mouhcine et al. 2007) and has been established at all accessible
redshifts (e.g., Savaglio et al. 2005; Erb et al. 2006; Maiolino
et al. 2008).
Considerable work has been devoted to understanding the
physical mechanisms underlying the
MZ relation. The pro-
posed scenarios to explain its origin can be broadly categorized
as: (1) the loss of enriched gas by outflows (T04; Kobayashi
et al. 2007); (2) the accretion of pristine gas by inflows
(Finlator & Dav
´
e 2008); (3) variations of the initial mass func-
tion with mass (K
¨
oppen et al. 2007); (4) selective star formation
efficiency or downsizing (Brooks et al. 2007; Ellison et al. 2008;
Calura et al. 2009; Asari et al. 2009); or a combination of these.
Recent studies also show evidence of a relation with star for-
mation rate (SFR) inferring a fundamental
MZ–SFR relation
(hereafter FMR; Lara-L
´
opez et al. 2010; Mannucci et al. 2010;
Yates et al. 2012).
As yet, there has been no major effort to test the
MZ
relation using spatially resolved information. The most likely
Based on observations collected at the Centro Astron
´
omico
Hispano-Alem
´
an (CAHA) at Calar Alto, operated jointly by the Max-Planck
Institut f
¨
ur Astronomie and the Instituto de Astrof
´
ısica de Andaluc
´
ıa (CSIC).
example might be ascribed to Edmunds & Pagel (1984) and
Vila-Costas & Edmunds (1992) who noticed a correlation
between surface mass density and gas metallicity in a number
of galaxies. Nowadays, the imaging spectroscopy technique can
potentially prove to be the key to understanding many of the
systematic effects that hamper the role of the distribution of
mass and metals in galaxies. In this work, we use integral field
spectroscopy (IFS) observations of a sample of nearby galaxies
to demonstrate (1) the existence of a local
MZ–star-formation
relation and (2) how the global
MZ relation seen in galaxies
can be reproduced by the presence of the local one. We present
convincing evidence that the observed
MZ relations represent
a simple sequence in astration.
2. DATA SAMPLE AND ANALYSIS
The study was performed using IFS data of a sample of nearby
disk galaxies, part belonging to the PINGS survey (Rosales-
Ortega et al. 2010), and a sample of face-on spiral galaxies from
M
´
armol-Queralt
´
oetal.(2011) as part of the feasibility studies
for the CALIFA survey (S
´
anchez et al. 2012a). The observations
were designed to obtain continuous coverage spectra of the
whole surface of the galaxies. The final sample is comprised
of 38 objects, with a redshift range between 0.001–0.025.
Although this sample is by no means a statistical subset of
the galaxies in the local universe, it is a representative sample
of face-on, mostly quiescent, spiral galaxies at the considered
redshift range. Theywere observed with the PMAS spectrograph
(Roth et al. 2005) in the PPAK mode (Verheijen et al. 2004;
Kelz et al. 2006) on the 3.5 m telescope in Calar Alto with
similar setup, resolutions, and integration times, covering their
optical extension up to 2.4 effective radii within a wavelength
range 3700–7000 Å. Data reduction was performed using r3d
(S
´
anchez 2006), obtaining as an output a data cube for each
galaxy, with a final spatial sampling between 1–2 arcsec pixel
1
,
1

The Astrophysical Journal Letters, 756:L31 (5pp), 2012 September 10 Rosales-Ortega et al.
which translates to a linear physical size between a few hundreds
of parsecs to 1 kpc (depending on the size of the object).
Details on the sample, observing strategy, setups, and data
reduction can be found in Rosales-Ortega et al. (2010) and
M
´
armol-Queralt
´
oetal.(2011).
The H ii regions in these galaxies were detected, spatially seg-
regated, and spectrally extracted using HIIexplorer (S
´
anchez
et al. 2012b). We detected a total of 2573 H ii regions with good
spectroscopic quality. This is by far the largest spatially resolved,
nearby spectroscopic H ii region survey ever accomplished.
Note that for the more distant galaxies the segregated H ii regions
may be comprised of a few classical ones, i.e., H ii aggregations,
which may not be useful in analyzing additive/integrated prop-
erties as in individual H ii regions (e.g., Hα luminosity function),
but are perfectly suited for the study of line ratios and chemical
abundances. The emission lines were decoupled from the under-
lying stellar population using fit3d (S
´
anchez et al. 2007), fol-
lowing a robust and well-tested methodology (Rosales-Ortega
et al. 2010;S
´
anchez et al. 2011). Extinction-corrected flux in-
tensities of the stronger emission lines were obtained and used
to select only star-forming regions based on typical BPT diag-
nostic diagrams (Baldwin et al. 1981) using a combination of
the Kewley et al. (2001) and Kauffmann et al. (2003) demarca-
tion curves. Our final sample is comprised of 1896 high-quality,
spatially resolved H ii regions/aggregations of disk galaxies in
the local universe. Details on the procedure can be found in
S
´
anchez et al. (2012b).
Gas-phase oxygen abundances were estimated using the
O3N2 calibrator (Pettini & Pagel 2004), based on the [O iii],
Hβ,[Nii], and Hα emission lines. We use this indicator because
it is less dependent on dust attenuation and we could use the
whole H ii region sample (given the lack of [O ii]
λ3727 in
some galaxies due to redshift). We used the prescriptions given
by Bell & de Jong (2001) to convert B V colors into a B-band
mass-to-light ratio (M/L) to derive the (luminosity) surface
mass density (Σ
Lum
, M
pc
2
) within the area encompassed by
our IFS-segmented H ii regions. The B- and V-band surface
brightness within the considered areas were derived directly
from the (emission-line-free) IFS data. The estimated error in
the derived Σ
Lum
is 0.25 dex, taking into account the error in the
flux calibration of our IFS data set (Rosales-Ortega et al. 2010;
M
´
armol-Queralt
´
oetal.2011), and the expected uncertainty of
the Bell & de Jong (2001) formulation. The relation between the
mass surface density and radius was checked by normalizing
the mass profile by the effective radius, finding a similar slope
for all galaxies closer to unity, i.e., the mass profile follows an
exponentiallaw,which is what is expected for disk galaxies (e.g.,
Bakos et al. 2008). Furthermore, we compared our radial mass
profiles with the more sophisticated K-band derived profiles of
those common galaxies in our sample with the DiskMass Survey
(Bershady et al. 2010; Martinsson 2011) finding an agreement
within 20%, strengthening the validity of our derived masses.
3. THE LOCAL
MZ RELATION
The left panel of Figure 1 shows the striking correlation
between the local surface mass density and gas metallicity for
our sample of nearby H ii regions, i.e., the local
MZ relation,
extending over 3 orders of magnitude in Σ
Lum
and a factor 8
in metallicity. As in the case of the global
MZ relation (e.g.,
T04), the correlation is nearly linear for lower Σ
Lum
, flattening
gradually at higher values. Also remarkable is the tightness of
the correlation; the 1σ scatter of the data about the median
is ±0.14 dex. The notable similarity with the global
MZ
Figure 1. Left panel: the relation between surface mass density and gas-phase
oxygen metallicity for 2000 H ii regions in nearby galaxies, the local
MZ
relation. The first contour stands for the mean density value, with a regular
spacing of four times this value for each consecutive contour. The blue circles
represent the mean (plus 1σ error bars) in bins of 0.15 dex. The red dashed-
dotted line is a polynomial fit to the data. The blue lines correspond to the
T04 relation (±0.2 dex) scaled to the relevant units. Typical errors for Σ
Lum
and metallicity are represented. Right panel: distribution of H ii regions along
the local
MZ relation for three galaxies of the sample at different redshifts.
The size of the symbols are linked to the value of |EW(Hα)|, being inversely
proportional to Σ
Lum
and metallicity as shown.
(A color version of this figure is available in the online journal.)
relation can be visually recognized with the aid of the blue
lines which stand for the T04 fit (±0.2 dex) to the global
MZ
relation, shifted arbitrarily both in mass (5 mag; to account
for the difference in size between galaxies and H ii regions)
and metallicity (0.15 dex; due to the well-known effect of
metallicity scale) to coincide with the peak of the H ii region
MZ distribution, which clearly follows the T04 relationship.
With this offset, the local
MZ values stand within 90% of the
95% range of the T04 relation. A polynomial fit of the Σ
Lum
versus metallicity relation yields
12 + log(O/H)
O3N2
= 8.079
±0.141
+0.525
±0.143
Σ
Lum
0.098
±0.035
[Σ
Lum
]
2
, (1)
valid over the range 1 < log Σ
Lum
< 3. We obtain the same
shape of the relation (and similar fit) if we adopt the R
23
metallicity calibration of T04, but with a higher scatter (20%)
due to the lowest number of H ii regions in our sample with the
[O ii]λ3727 line. Other typical calibrations were tested finding
2

The Astrophysical Journal Letters, 756:L31 (5pp), 2012 September 10 Rosales-Ortega et al.
Figure 2. 3D representation of the local MZ–EW(Hα) relation. The size and
color scaling of the data points are linked to the value of logΣ
Lum
(i.e., low-blue
to high-red values). The projection of the data over any pair of axes reduces to
the local
MZ, M–EW(Hα), and metallicity–EW(Hα) relations. An online 3D
animated version is available at http://tinyurl.com/local-MZ-relation.
(A color version of this figure is available in the online journal.)
similar results (e.g., N2; Denicol
´
oetal.2002), i.e., the scale
of the relation changes when using different indicators, but the
overall, qualitative shape does not change.
Note that the local
MZ relation holds for individual galaxies
with a large-enough dynamical range in Σ
Lum
and metallicity to
cover the whole parameter space of the relation, i.e., it is indeed
a local relationship. This is shown in the right panel of Figure 1,
displaying the local
MZ relation for the H ii regions of three
galaxies in our sample at different redshifts. For the closest
galaxy (NGC 1058; z 0.0017), the relationship holds for
3maginΣ
Lum
, and even with the loss of spatial resolution at
higher redshifts the relation persists over a large dynamic range.
In addition, we find the existence of a more general relation
between mass surface density, metallicity, and the equivalent
width of Hα, defined as the emission-line luminosity normalized
to the adjacent continuum flux, i.e., a measure of the SFR per unit
luminosity (Kennicutt 1998). This functional relation is evident
in a three-dimensional (3D) space with orthogonal coordinate
axes defined by these parameters, consistent with |EW(Hα)|
being inversely proportional to both Σ
Lum
and metallicity, as
shown in Figure 2. The projection of the local
MZ–EW(Hα)
relation on the planes defined in this 3D space correspond to the
local
MZ, M–EW(Hα), and metallicity–EW(Hα) relations.
Figure 3 shows the projection of log |EW(Hα)| as a strong and
tight function of Σ
Lum
extending over more than three orders of
magnitude. The projection on the |EW(Hα)| versus metallicity
plane shows an existent but weaker correlation.
4. THE GLOBAL
MZ RELATION
In order to test whether the global
MZ relation observed by
T04 using SDSS data is a reflection (aperture effect) of the local
H ii region mass density versus metallicity relation, we perform
the following exercise. We simulate a galaxy with typical M
B
and B V values drawn from flat distributions in magnitude
(15 to 23) and color (0.4–1). A redshift is assumed for the
mock galaxy, drawn from a Gaussian distribution with mean
Figure 3. Relationbetween|EW(Hα)| and surface mass density, i.e., a projection
of the local
MZ–EW(Hα) relation. Contours and symbols as in Figure 1.The
red line is a polynomial fit to the data.
(A color version of this figure is available in the online journal.)
0.1 and σ = 0.05, with a redshift cut 0.02 <z<0.3
in order to resemble the SDSS T04 distribution. The mass of
the galaxy is derived using the integrated B-band magnitudes,
B V colors and the average M/L ratio following Bell &
de Jong (2001). The effective radius of the mock galaxy is
estimated using the well-known luminosity-scale relation (e.g.,
Brooks et al. 2011) assuming a normal standard deviation of
0.3 dex (Shen et al. 2003). Once the mass and effective radius are
known, the surface brightness at the center of the mock galaxy
is derived assuming an exponential light distribution. Then, the
metallicity is calculated at different radii up to an aperture equal
to the SDSS fiber (3 arcsec) in 100 bins using Equation (1),
i.e., the metallicity that corresponds to the mass density surface
at each bin. The metallicity assigned to the mock galaxy is the
mean value determined within the aperture, assuming an error
equal to the standard deviation of the derived distribution plus
a systematic error of 0.1 dex, intrinsic to the derivation of
the metallicity. We used the O3N2 metallicity conversion by
Kewley & Ellison (2008, hereafter K08) to convert to the T04
base. The process is repeated over 10,000 times in order to
obtain a reliable distribution in the mass and metallicity of the
mock galaxies.
Figure 4 shows the result of the simulation, i.e., the distri-
bution of the mock galaxies in the
MZ parameter space. We
reproduce the overall shape of the global
MZ relation assum-
ing a local
MZ relation and considering the aperture effect
of the SDSS fiber, over 5 orders of magnitude in mass and
1.5 in metallicity. The correspondence can be clearly seen
by comparing the distribution of points with the overlaid lines
corresponding to the T04 fit (black) and the K08 ±0.2 dex re-
lation (blue), for which the agreement is extremely good over a
wide range of masses. The deviations of the T04 relation at the
high-mass end are somewhat expected given that the choice
of this metallicity calibrator has a significant effect on the
y-intercept of the
MZ relation (K08). The result is remark-
able considering that we are able to reproduce the global
MZ
relation over a huge dynamical range, using a local
MZ re-
lation derived from a galaxy sample with a restricted range in
mass (9.2 < log M
Lum
< 11.2) and metallicity (8.3 < 12 +
log(O/H) < 8.9), indicated by the rectangle shown in Figure 4.
3

The Astrophysical Journal Letters, 756:L31 (5pp), 2012 September 10 Rosales-Ortega et al.
Figure 4. Distribution of simulated galaxies in the MZ plane assuming a local
MZ relation and considering the aperture effect of the SDSS fiber, as explained
in the text. The contours correspond to the density of points, while the circles
represent the mean value (plus 1σ error bars) in bins of 0.15 dex. The black line
stands for the T04 fitting, while the blue lines correspond to the K08 ±0.2 dex
relation. The rectangle encompasses the range in mass and metallicity of the
galaxy sample of this work.
(A color version of this figure is available in the online journal.)
5. ON THE ORIGIN OF THE LOCAL AND
GLOBAL
MZ RELATIONS
We interpret the local
MZ–EW(Hα) relation as the con-
sequence of a more subtle relation between the mass, metal-
licity, and star formation history with galaxy radius. Galaxies
are known to have radial gradients in their physical properties
(e.g., Searle 1971; McCall et al. 1985; Vila-Costas & Edmunds
1992; Zaritsky et al. 1994; Bell & de Jong 2000). The fact that
gas metallicity increases with mass surface density is just re-
flecting the existence of radial metallicity gradients and radial
surface mass density gradients in spirals. On the other hand,
the |EW(Hα)| is a parameter that scales with the SFR per unit
mass, i.e., the specific SFR (SSFR) and is a proxy of the stellar
birthrate parameter b-Scalo, which is the ratio of the present to
past-average SFR (Kennicutt et al. 1994; Kennicutt 1998). Mul-
tiphase chemical evolution models for spiral disks show that
both the distributions of neutral and molecular gas show max-
ima that move from the center outward through the disk as the
galaxy evolves. Accordingly, the maximum of the star forma-
tion activity, very high in the central regions at early times, also
moves throughout the disk as the gas in the central region is very
efficiently consumed. This leads to high present-day abundances
and low current SSFRs in the center and radial abundance gradi-
ents that flatten with time. The location on the disk of the maxima
in the gas distributions at the present time, which reflects the
degree of evolution, is related to the galaxy morphological type
with early-type galaxies showing the peak of the star formation
at outer regions compared to late-type galaxies, which implies
a higher degree of evolution and a flatter galaxy for early-type
galaxies (Molla et al. 1997;Moll
´
a&D
´
ıaz 2005).
The observed trend agrees qualitatively with this scenario:
the inverse gradient of |EW(Hα)| versus Σ
Lum
or metallicity
would reflect an evolutionary sequence across the disk of the
galaxies, i.e., lower (inner) values of |EW(Hα)| corresponding
to lower SSFR, and vice versa. In this scenario, the inner regions
of the galaxy form first and faster, increasing the gas metallicity
of the surrounding interstellar medium. As the galaxy evolves
and grows with time, the star formation progresses radially,
creating a radial metallicity gradients in the disk of spirals.
Mass is progressively accumulated at the inner regions of the
galaxy, raising the surface mass density and creating a bulge,
with corresponding high metallicity values but low SSFR (low
|EW(Hα)|), i.e., an “inside-out” galaxy disk growth. In such a
case, the local
MZ relation would reflect a more fundamental
relation between mass, metallicity, and star formation efficiency
as a function of radius, equivalent to a local downsizing effect.
Following this reasoning, the origin of the global
MZ
relation can be explained as the combined effect of the existence
of the local
MZ relation, and (as a second-order effect) an
aperture bias due to the different covering factors of the SDSS
fiber, as suggested by the exercise performed in Section 4.
On the other hand, although we cannot reproduce the FMR
in our simulation given that there is no empirical way of
determining an SFR of the mock galaxies, the existence of the
FMR could also be interpreted as a scaled-up version of the
local
MZ–SSFR relation. Furthermore, under the proposed
scenario, the flattening of the
MZ relation at the high-mass
end could be explained as the combined observational effect
of: (1) an intrinsic saturation of the enriched gas due to the
low SSFR in the inner regions of the galaxies; (2) a deviation
from linearity of the abundance gradients in the center of spiral
galaxies, i.e., a flattening (or drop) in the metallicity gradient at
the innermost radii as suggested by recent works (e.g., Rosales-
Ortega et al. 2011; Bresolin et al. 2012;S
´
anchez et al. 2012b)
and predicted from chemical evolution models (Molla et al.
1997); and (3) the depletion of the oxygen emission lines in the
optical due to high efficiency of cooling in high-metallicity
(12+log(O/H) > 8.7), low-temperature (T
e
< 10
4
K) H ii
regions.
6. CONCLUSIONS
By using the IFS of a sample of nearby galaxies, we
demonstrate the existence of a local relation between the surface
mass density, gas-phase oxygen abundance, and |EW(Hα)| in
2000 spatially resolved H ii regions of the local universe.
The projection of this distribution in the metallicity versus
Σ
Lum
plane—the local MZ relation—shows a tight correlation
expanding over a wide range in this parameter space. A similar
behavior is seen for the |EW(Hα)| versus Σ
Lum
relation. In both
projections, the value of |EW(Hα)| is inversely proportional to
mass and metallicity. Notably, the local
MZ relation has the
same shape as the global
MZ relation for galaxies observed by
T04. We explain the new relation as the combination of: (1) the
well-known relationships between both the mass and metallicity
with respect to the differential distributions of these parameters
found in typical disk galaxies, i.e., the inside-out growth; and
(2) the fact that more massive regions form stars faster (i.e., at
higher SFRs), thus earlier in cosmological times, which can be
considered a local downsizing effect, similar to the one observed
in individual galaxies (e.g., P
´
erez-Gonz
´
alez et al. 2008).
We use the local
MZ relation to reproduce the global
MZ relation by means of a simple simulation which considers
the aperture effects of the SDSS fiber at different redshifts.
We conclude that the
MZ relation in galaxies is a scale-up
integrated effect of a local
MZ relation in the distribution
of star-forming regions across the disks of galaxies, i.e., the
relationship is not primary, but obtained from the sum of a
number of local linear relations (and their deviations) with
respect to the galaxy radius. Under these premises, the existence
of the FMR in galaxies might be explained by the presence
of an intrinsic local
MZ–SSFR relation, which relates the
4

The Astrophysical Journal Letters, 756:L31 (5pp), 2012 September 10 Rosales-Ortega et al.
distribution of mass, metallicity, and SFR across the galaxy
disks, driven mainly by the history of star formation, within an
inside-out growth scenario.
F.F.R.-O. acknowledges the Mexican National Council for
Science and Technology (CONACYT) for financial support un-
der the program Estancias Posdoctorales y Sab
´
aticas al Ex-
tranjero para la Consolidaci
´
on de Grupos de Investigaci
´
on,
2010–2011. A.I.D. thanks the Spanish Plan Nacional de As-
tronom
´
ıa program AYA2010-21887 C04-03.
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