SDSS-IV MaNGA: Environmental dependence of the Mgb/<Fe>-sigma_* relation for nearby galaxies

TL;DR

This study analyzes how alpha element abundance, indicated by Mgb/<Fe>, correlates with galaxy properties and environment using MaNGA data, revealing stellar velocity dispersion as a key factor with modest environmental effects.

Contribution

It provides new insights into the environmental dependence of alpha abundance ratios within galaxies, emphasizing the role of stellar velocity dispersion and galaxy formation history.

Findings

Mgb/<Fe> correlates tightly with sigma_* across all galaxies.

Old low-sigma_* galaxies in dense environments show enhanced Mgb/<Fe>.

Gradients of Mgb/<Fe> are mostly flat and depend on sigma_.

Abstract

We use a sample of ~3000 galaxies from the MaNGA MPL-7 internal data release to study the alpha abundance distribution within low-redshift galaxies. We use the Lick index ratio Mgb/<Fe> as an alpha abundance indicator to study relationships between the alpha abundance distribution and galaxy properties such as effective stellar velocity dispersion within 0.3 effective radii (sigma_*), galaxy environment, and dark matter halo formation time (z_f). We find that (1) all galaxies show a tight correlation between Mgb/<Fe> and sigma_*; (2) `old' (H_beta < 3) low-sigma_* galaxies in high local density environment and inner regions within galaxy groups are enhanced in Mgb/<Fe>, while `young' (H_beta>3) galaxies and high-mass galaxies show no or less environmental dependence; (3) `old' galaxies with high-z_f show enhanced Mgb/<Fe> over low- and medium-z_f; (4) Mgb/<Fe> gradients are close to zero and show dependence on sigma_* but no obvious dependence on the environment or z_f. Our study indicates that stellar velocity dispersion or galaxy mass is the main parameter driving the Mgb/<Fe> enhancement, although environments appear to have modest effects, particularly for low- and medium-mass galaxies.

Figures

Tables

Table 1. Table 1: Spectral index definitions used in this paper are from Trager et al. ( 1998 ) . The bandpass is the wavelength range covering the absorption lines and the blue and red continuum are wavelength ranges around the bandpass for fitting the continuum slope within the bandpass. The wavelengths are measured in air and all numbers are in unit of Å.

Name	Index Bandpass	Blue continuum	Red continuum
H$\beta$	4847.875 - 4876.625	4827.875 - 4847.875	4876.625 - 4891.625
Mgb	5160.125 - 5192.625	5142.625 - 5161.375	5191.375 - 5206.375
Fe5270	5245.650 - 5285.650	5233.150 - 5248.150	5285.650 - 5318.150
Fe5335	5312.125 - 5352.125	5304.625 - 5315.875	5353.375 - 5363.375

Table 2. Table 2: Fitting parameters for Eq. 1 . Note that the values of p 5 subscript 𝑝 5 p_{5} are very small, so we show 10 5 × p 5 superscript 10 5 subscript 𝑝 5 10^{5}\times p_{5} in this table. Also, p 0 subscript 𝑝 0 p_{0} , p 2 subscript 𝑝 2 \,\,p_{2} , p 3 subscript 𝑝 3 \,\,p_{3} , p 4 subscript 𝑝 4 \,\,p_{4} , p 6 subscript 𝑝 6 \,\,p_{6} and p 7 subscript 𝑝 7 p_{7} have been fixed at the specific values in the table in fitting for Mgb.

Name	$p_0$	$p_1$	$p_2$	$p_3$	$p_4$	${10}^5{p}_5$	$p_6$	$p_7$
H$\beta$	0.15$\pm 0.07$	0.92$\pm 0.04$	1.03$\pm 0.02$	0$\pm 0.02$	0.57$\pm 0.89$	$0.11\pm 0.17$	1.22$\pm 0.21$	1.93$\pm 0.21$
Mgb	0	$0.83\pm 0.15$	1	0	0	$110\pm 50$	1	1
Fe5270	0.54$\pm 1.4$	0.97$\pm 0.01$	1.01$\pm 0.01$	-0.46$\pm 1.39$	0.037$\pm 0.10$	$76\pm 1.6$	0.87$\pm 0.02$	1.48$\pm 0.03$
Fe5335	-0.02$\pm 0.02$	1.04$\pm 0.01$	0.97$\pm 0.01$	0$\pm 0.008$	0.46$\pm 0.4$	$0.52\pm 0.08$	1.01$\pm 0.02$	2.03$\pm 0.02$

Table 3. Table 3: Numbers of galaxies with different environment measurements.

Type	Number of galaxies
All	2997
Local density	2447
LSS type	2447
Isolated/Central/Satellite	2663
Projected halo-centric radius (satellite only)	811
Formation redshift (all types)	2423
Formation redshift (central & isolated only)	1632

Equations

$$x_0=p_0+p_1{x}^{p_2}+p_3{\sigma }^{p_4}+p_5{x}^{p_6}{\sigma }^{p_7},$$

$${\sigma }_{\ast }=\sqrt{\frac{{\Sigma }_k{F}_k(v_k^2+{\sigma }_k^2)}{{\Sigma }_k{F}_k}},$$

Full text

1 Introduction

The $\alpha$-to-iron ratio ([$\alpha$/Fe]) is an important indicator for star formation histories because $\alpha$-elements ($\rm O,Ne,Mg,Si,Ca,Ti$) are mostly produced in core-collapse supernovae, whose progenitors are high-mass stars, while irons (Fe) are mostly produced by type Ia supernovae, whose progenitors are low-mass compact stars. Therefore, a galaxy formed in a single burst with a top-heavy initial mass function (IMF) will be enhanced in [$\alpha$/Fe] in comparison with a galaxy formed with an extended star formation history and a bottom-heavy IMF (Thomas et al., 1998; Thomas, 1999; Matteucci, 1994, and references therein).

There have been many studies on the [$\alpha$/Fe] ratios of nearby galaxies and a major finding is that the [$\alpha$/Fe] ratios of early type galaxies are best correlated with stellar velocity dispersion $\sigma$ 111Here we use $\sigma$ to denote velocity dispersion measured from the literature, which are mostly measured using single fiber or long slit spectra and has various aperture sizes and definitions. We use $\sigma_{*}$ (in later text) to denote effective velocity dispersion measured within 0.3 effective radius using IFU data (see detailed definition of $\sigma_{*}$ is in Section 2.3). (e.g. Worthey, 1992; Trager et al., 2000; Thomas et al., 2005; Sánchez-Blázquez et al., 2006a; Sansom et al., 2008; Thomas et al., 2010; Kuntschner et al., 2010; Johansson et al., 2012; Liu et al., 2016b). Studies which do not have morphological cut (e.g. Proctor & Sansom, 2002; Smith et al., 2007; Scott et al., 2017) find similar trends for late type galaxies, albeit using smaller sample sizes.

The [$\alpha$/Fe]-$\sigma$ correlation implies that high-$\sigma$ (mostly massive) galaxies have a shorter star formation time scale and quench more sharply than low-$\sigma$ (mostly low-mass) galaxies. If the star formation is quenched in less than $\sim$ 1Gyr, later type Ia supernovae explosions will not be able to cause iron enrichment for stellar populations. Quenching could be due to internal processes such as supernovae (Dekel &Silk, 1986) or AGN feedback (King, 2003; Segers et al., 2016). Detailed explanation for [$\alpha$/Fe]-$\sigma$ relation includes IMF variation, stellar yields, inflow/outflow rates and other galaxy evolution parameters (e.g. Pipino et al., 2009; Arrigoni et al., 2010; Yates et al., 2013). However, the effects of many parameters are degenerate. Also, high-mass galaxies are more likely to have a bottom-heavy IMF (Zhou et al. submitted; Cappellari et al., 2012; Li et al., 2017; Parikh et al., 2018), which results in an opposite [$\alpha$/Fe]-$\sigma$ relation comparing to the observations because a bottom-heavy IMF leads to relatively fewer massive stars and thus produces less $\alpha$-elements as a result of fewer core collapse supernovae.

Environmental effects, such as harassment (e.g. Moore et al., 1998), strangulation (e.g. Balogh et al., 2000; Peng et al., 2015), or gas stripping (e.g. Gunn & Gott, 1972), could also quench star formation and thus enrich [$\alpha$/Fe], especially for low-mass galaxies. Gas accretion from galaxy surroundings (Larson et al., 1980) can, in the other hand, cause continuous star formation and decrease the $\alpha$-to-iron ratio. Many observational studies using galaxies in clusters (e.g. Smith et al., 2007; Michielsen et al., 2008; Chilingarian et al., 2008; Matković et al., 2009; Spolaor et al., 2010; Liu et al., 2016a) and poor groups (e.g. Annibali et al., 2011) show that galaxies in dense regions are indeed enhanced in [$\alpha$/Fe]. While some other studies (e.g. Sánchez-Blázquez et al., 2003; Annibali et al., 2007; Paudel et al., 2011; McDermid et al., 2015; Thomas et al., 2010) claim little environmental effects on [$\alpha$/Fe] enhancement for early type galaxies.

Recently, Liu et al. (2016b) compiled measurements from the literature of [$\alpha$/Fe] and the Lick index ratios Mgb/$\langle$Fe$\rangle$ of thousands of early type galaxies in different environments and found that the low-$\sigma$ end of the [$\alpha$/Fe]-$\sigma$ relation has larger intrinsic scatters and is dependent on environment: low-$\sigma$ early type galaxies in high density clusters are enhanced in Mgb/$\langle$Fe$\rangle$ and [$\alpha$/Fe]. However, these measurements are from different telescopes and instruments and have different systematic offsets and different apertures. Also, most previous works (except for Kuntschner et al., 2010; Greene et al., 2015; Scott et al., 2017) focus on the central part of early type galaxies. Galaxy outskirts are more likely to be affected by interactions with nearby galaxies and thus experience different star formation histories (e.g. Bakos et al., 2008; Ruiz-Lara et al., 2016). Furthermore, since galaxies are formed in dark matter halos and could experience many mergers during their formation, the distribution of [$\alpha$/Fe] could also be affected by halo merger histories. Therefore, it is important to study the dependence of [$\alpha$/Fe]-$\sigma$ relation on environments and formation histories using a uniform survey with spectroscopic coverage to galaxy outskirts.

Thanks to the Sloan Digital Sky Survey (SDSS) Mapping Nearby Galaxies at APO (MaNGA, Bundy et al., 2015) project, we are able to obtain integrated field unit (IFU) spectra and thus maps of $\alpha$- and iron-abundance sensitive spectral indices for a large sample of galaxies. We therefore can study $\alpha$-to-iron ratio distributions within different types of galaxies and explore their environmental dependence. In this paper, we use environment information derived through a method based on reconstructed density field (Wang et al., 2009, 2012, 2016) instead of neighboring galaxies. Wang et al. (2016) also provides us with the halo formation redshift for individual galaxies, which enables us to investigate the effect of formation histories. We also explore the effects of central/satellite galaxies and projected halo-centric radius (projected distance between the satellite galaxy to the group center) using information from Yang et al. (2007).

The outline of the paper is as follows: we describe the data and briefly introduce the measurements of spectral indices and different environment indicators in Section 2; we then present our results in Section 3 and discuss them in Section 4; we summarize our conclusions in Section 5. A discussion on the environmental dependence of [$\alpha$/Fe] is in Appendix A.

2 Data and Methodology

2.1 MaNGA sample

MaNGA (Bundy et al., 2015) is an IFU survey targeting about 10 000 nearby galaxies selected from the SDSS-IV (Blanton et al., 2017; Gunn et al., 2006). The wavelength coverage is between 3600 and 10300 Å with a spectral resolution $R\sim 2000$ (Drory et al., 2015; Smee et al., 2013). The MaNGA sample is selected so that the number density of galaxies is roughly independent of the $i$-band absolute magnitude $M_{i}$. Each galaxy is covered by the IFU out to either 1.5 effective radii ($R_{e}$) or 2.5$R_{e}$ (Yan et al., 2016b; Wake et al., 2017) and the sizes of the IFUs vary for different galaxies from $12\arcsec$ for a 19-fiber IFU to $32^{\prime\prime}$ for a 127-fiber IFU (Drory et al., 2015; Law et al., 2015). The observed data are reduced by the MaNGA data reduction pipeline (DRP; Law et al., 2016; Yan et al., 2016a) and the final products of the DRP are datacubes, which are composed of ‘spaxels’ with an angular size of $0.5^{\prime\prime}$x$0.5^{\prime\prime}$, as well as row stacked spectra.

In this work, we use datacubes from the MaNGA internal data release MPL-7, which is equivalent to the SDSS DR15 public release (Aguado et al., 2019). The MPL-7 sample contains 4621 galaxies and has a redshift range $0.01<z<0.15$ with a peak around $z=0.03$. We exclude galaxies with obvious interaction features (125 galaxies), galaxies with unreliable velocity dispersion measurements due to very low signal-to-noise ratios (468 galaxies) and galaxies with bad background subtractions (e.g. obvious spikes) around 5000Åor very broad emission lines (identified by eye, 1031 galaxies). The total number of galaxies used in this work is 2997. We do not have morphological cut and we include not only red sequence galaxies but also blue sequence and green valley galaxies (see stellar mass versus NUV-r color diagram in Fig. 1).

2.2 Spectral index measurements

Absorption line indices have been widely used for studies of stellar population parameters, especially for $\alpha$ abundance (e.g. Worthey, 1994; Thomas et al., 2005, 2011). There are many $\alpha$-element sensitive and iron-sensitive indices within the MaNGA wavelength coverage. Within these indices, H$\beta$, Mgb, Fe5270 and Fe5335 (see below for definitions) have been proven to be the strongest and best set of spectral indices for studying $\alpha$ abundances (e.g. Thomas et al., 2011; Liu et al., 2016b). H$\beta$ is sensitive to stellar age and has a negative correlation with age; Mgb is most sensitive to magnesium, which is an important $\alpha$-element; Fe5270 and Fe5335 are most sensitive to iron abundance (Thomas et al., 2003, 2011). We therefore focus on these four spectral indices in this paper.

We follow the definitions of spectral indices from Trager et al. (1998). Detailed bandpass and pseudo-continua wavelength ranges for the four spectral indices are reproduced in Table LABEL:sindx_def. Uncertainties in the spectral index values are estimated following Cardiel et al. (1998).

We measure these four spectral indices for all spaxels with signal-to-noise ratios (SNR) larger than 10. For studying stellar population related science using spectral indices, the threshold requirement for spectral SNR is very high ($\rm SNR\gtrsim 50-100$). Therefore, we divide each galaxy into three radial bins to enhance SNR: central ($r<0.3R_{e}$), intermediate ($0.3R_{e}<r<0.7R_{e}$), and outer ($0.7R_{e}<r<1.3R_{e}$) regions, where $r$ is semi-major axis of an elliptical aperture. We then calculate average values of the spectral indices within each radial bin. The averaged spectral index values are similar to values derived using each radial bin’s stacked spectra, which usually have $\rm SNR\gtrsim 50-100$.

A comparison of spectral indices derived using stacked spectra versus average spectral index values of individual spaxels is shown in Fig. 2. As can be seen these two methods are consistent with each other. The outliers in the upper-right (Mgb) and lower-right (Fe5335) panels are caused by bad stacked spectra, i.e. our method is even more robust in calculating mean spectral indices for regions with a few problematic spaxels.

Velocity dispersion broadening has a non-negligible effect on spectral index values, especially for spectra with stellar velocity dispersion values larger than 100 km/s. We therefore have to correct for velocity dispersion broadening in our spectral index measurements. Many previous studies perform velocity dispersion corrections in a very time consuming way: one fits the observed spectra with template spectra and then measures spectral indices using the fitted template spectra with and without velocity dispersion to derive the correction factor. Here we use a new method to correct for the velocity dispersion effect: we assume a simple polynomial relation between spectral indices with and without velocity dispersion broadening,

[TABLE]

where $\sigma$ is velocity dispersion in unit of km/s, $x$ and $x_{0}$ are the spectral index values before and after velocity dispersion correction, and $p_{0}-p_{7}$ are fitting parameters. We use MILES template spectra (which have similar spectral resolution to SDSS, Sánchez-Blázquez et al., 2006b; Vazdekis et al., 2010) with different velocity dispersion values to fit the parameters in Eq. 1. The fitted parameters for each of the four spectral indices are listed in Table LABEL:fitting_parameter. We then verify the fitted parameters using the Maraston & Strömbäck (2011) single stellar population templates with Chabrier (2003) IMF and MILES stellar library: we do velocity dispersion correction by applying Eq. 1 with parameters in Table LABEL:fitting_parameter to spectral index values derived using template spectra with different velocity dispersions, and then compare the corrected values with spectral index values of the original Maraston & Strömbäck (2011) templates. The results are shown in Fig. 3. The corrected values show little difference from the real values (mostly within 2%) except for small values ($<1$) of Mgb, Fe5270 and Fe5335, which are rarely seen in our galaxy sample. These parameters can also be applied to other observations which have a similar instrumental spectral resolution to SDSS. Using these fitted parameters and measured velocity dispersion values, we are able to calculate spectral indices without velocity dispersion for little computational cost. For our sample galaxies, we use velocity dispersion measurements (for each spaxel) from the MaNGA Data Analysis Pipline (DAP, Westfall et al. submitted), which uses the pPXF (Cappellari, 2017) full spectral fitting technique in deriving kinematical properties.

Star forming galaxies may have H$\beta$ emission, so we also have to correct for emission line flux when calculating the H$\beta$ index. We correct for H$\beta$ emission by subtracting a Gaussian emission line profile with a total flux equal to the H$\beta$ emission flux value provided by the MaNGA DAP (Westfall et al. submitted).

2.3 Effective stellar velocity dispersion

As shown in the introduction, stellar velocity dispersion is well correlated with the $\alpha$-to-iron ratio. Stellar velocity dispersion values from the literature (e.g. Liu et al., 2016b) are mostly measured using single fibers with fixed angular sizes or long slits with arbitrary apertures and thus may introduce biases for very small or large galaxies. Here we use an effective stellar velocity dispersion $\sigma_{*}$ (Li et al., 2018; Cappellari et al., 2013) estimated in a $0.3R_{e}$ aperture calculated for each galaxy. The $\sigma_{*}$ is defined as the square-root of the luminosity-weighted average second moments of the velocity within the $0.3R_{e}$ aperture:

[TABLE]

where $v_{k}$ and $\sigma_{k}$ are the velocity and stellar velocity dispersion of the $k$-th IFU spaxel respectively, and $F_{k}$ is the flux in the $k$-th IFU spaxel. This $\sigma_{*}$ definition has been proven to be close (mostly within $\sim 10\%$) to the velocity dispersion measured from a stacked spectrum using spectra within the same aperture (Li et al., 2018; Cappellari et al., 2013).

2.4 Environment and formation history

In this paper, we consider four environment indicators: local mass density, types of large scale structure (LSS), isolated/central/satellite types, and projected halo-centric radius (for satellite galaxies only). The first two environment indicators are taken from the ELUCID project (Exploring the Local Universe with the reConstructed Initial Density field; Wang et al., 2014), which uses the halo-domain method developed by Wang et al. (2009) to reconstruct the cosmic density field in the local universe from the SDSS DR7 galaxy group catalogue (Yang et al., 2007). As shown in Wang et al. (2016), the reconstructed density field matches well the distributions of both the galaxies and groups. The local mass density environment indicator of a galaxy is the density at the position of the galaxy smoothed by a Gaussian kernel with a smoothing scale of 1 Mpc$/h$ (see Fig. 4, effective stellar velocity dispersion v.s. local density distribution for our sample galaxies). The morphology of the LSS is very complex and we adopt a dynamical classification method developed by Hahn et al. (2007), which uses the eigenvalues of the tidal tensor to determine the type of the local structure in a cosmic web. The LSS environment is classified into four categories following the definition by Hahn et al. (2007): a $cluster$ has three positive eigenvalues (fixed points); a $filament$ has two positive and one negative eigenvalues (two-dimensional stable manifold); a $sheet$ has one positive and two negative eigenvalues (one-dimensional stable manifold); and a $void$ has three negative eigenvalues (unstable orbits). We refer the reader to Wang et al. (2016) for details of the reconstruction methods and Zheng et al. (2017) for more examples of utilizing these two environment indicators. Each galaxy is also classified into three types according to Yang et al. (2007): isolated (the only galaxy member in a group), central (the most massive galaxy in a group) and satellite. For satellite galaxies, we also examine dependences on their projected halo-centric radii (Yang et al., 2007).

The ELUCID project also derives initial conditions for our universe using the reconstructed density field in the SDSS DR7 region and use the initial conditions to simulate the formation history of dark matter halos in this region. This ELUCID simulation can reliably reproduce most of the massive groups (Wang et al., 2016, 2018). We use the formation redshift derived from the ELUCID simulation to indicate galaxy formation histories and investigate dependance of Mgb/$\langle$Fe$\rangle$ on formation redshift in the following sections. The formation redshift, $z_{f}$, is defined as the highest redshift at which half of the final halo mass has assembled into progenitors more massive than $10^{11.5}h^{-1}M_{\odot}$ (Wang et al., 2018).

Note that not all galaxies in our sample have environment information. The numbers of galaxies with different environment measurements are shown in Table LABEL:envtable.

3 Results

3.1 Mgb/$\langle$Fe$\rangle$ - $\sigma_{*}$ relation

The spectral index ratio Mgb/$\langle$Fe$\rangle$, where $\rm\langle Fe\rangle=(Fe5270+Fe5335)/2$, is a widely used indicator in previous studies for the $\alpha$-to-iron ratio (see Fig. 4 of Thomas et al., 2003). We note that $\rm Mgb/\langle Fe\rangle$ is indicative for general element ratio trends but detailed element ratio calculations would require more sophisticated techniques such as model fitting (see discussion in Section 4.2). We also derived $\alpha$-to-iron ratio ([$\alpha$/Fe]) by fitting the spectral indices with Thomas et al. (2011) models, however, the relations and environmental dependence of [$\alpha$/Fe] are less obvious because of large scatters. We therefore focus on Mgb/$\langle$Fe$\rangle$ in the main text and append the [$\alpha$/Fe] related results in the Appendix A.

It has been claimed that Mgb/$\langle$Fe$\rangle$ (or [$\alpha$ /Fe]) is best correlated with stellar velocity dispersion (e.g. Kuntschner et al., 2010; Thomas et al., 2010; Liu et al., 2016b). We hence plot Mgb/$\langle$Fe$\rangle$ versus the effective stellar velocity dispersion $\sigma_{*}$ for the central regions (within 0.3$R_{e}$) of all our sample galaxies in Fig. 5.

It is obvious that Mgb/$\langle$Fe$\rangle$ is well correlated with $\sigma_{*}$ and most galaxies lie in close vicinity around the linearly fitted straight line (solid line in the upper-panel of Fig. 5). The Spearman’s rank correlation coefficient is $r_{S}=0.76$. This means that not only early type but all types of galaxies in our sample follow the Mgb/$\langle$Fe$\rangle$-$\sigma_{*}$ relation. We can also see from the color coding that high-$\sigma_{*}$ galaxies mostly have small H$\beta$ values (relatively old) and low-$\sigma_{*}$ galaxies mostly have large H$\beta$ values (relatively young). Low-$\sigma_{*}$ ($<80\rm\,km/s$) galaxies have larger scatters but are still centered around the solid line, which is consistent with Liu et al. (2016b).

3.2 Environmental dependence

As shown in the previous subsection, $\rm Mgb/\langle Fe\rangle$ is well correlated with $\sigma_{*}$. Therefore, in order to examine the environmental dependence, we need to take out the effect by $\sigma_{*}$. We firstly follow the method of Liu et al. (2016b) and divide galaxies into three different velocity dispersion ranges: low-$\sigma_{*}$ ($\sigma_{*}<80\,\rm km/s$), medium-$\sigma_{*}$ ($80\,\rm km/s<\sigma_{*}<158\,\rm km/s$) and high-$\sigma_{*}$ ($\sigma_{*}>158\,\rm km/s$). We further divide galaxies in these $\sigma_{*}$ ranges into three different environments based on local densities: low-density ($<2\rho_{0}$), medium-density ($2\rho_{0}<\rho<12.6\rho_{0}$) and high-density ($>12.6\rho_{0}$), where $\rho_{0}$ is the average cosmic mean density, $\rm 7.16\times 10^{10}M_{\odot}/{\it h}/(Mpc\,{\it h}^{-1})^{3}$. The velocity and local density ranges are chosen so that each velocity or local density range has roughly the same number of galaxies. Fig. 6 shows the $\rm Mgb/\langle Fe\rangle$ -$\sigma_{*}$ relation for the central regions (within $\rm R_{e}/3$) in the three different local density ranges. In the lower panels of Fig. 6, we plot the residuals ($\rm\delta\log(Mgb/\langle Fe\rangle$)). We also plot average values of galaxies in these three different environments and three different $\sigma_{*}$ ranges. Low- and medium-$\sigma_{*}$ galaxies in the high-density environment (upward-triangle) show enhancement in Mgb/$\langle$Fe$\rangle$.

Thomas et al. (2010) showed that old and young galaxies may have different dependance on environments. We therefore also divide our sample into ‘old’ (central H$\beta<3$) and ‘young’ (central H$\beta>3$) populations using the H$\beta$ index and plot cumulative probability distributions in Fig. 7 of the residuals for the central regions of galaxies in different H$\beta$, $\sigma_{*}$ and local density environment bins. For ‘old’ galaxies (upper panels), we see a clear large residual in the low-$\sigma_{*}$ high-local density bin (red line in upper-left panel). The red line (high-local density) in the medium-$\sigma_{*}$ bin (upper-middle panel) is also large comparing to other lines (lower local densities) although less obvious. The difference disappears in the high-$\sigma_{*}$ bin (upper-right panel). For ‘young’ galaxies (lower panels), the environmental dependance is not clear.

Since we have IFU data for all our sample galaxies, we can investigate the environmental dependence of the residuals for the intermediate and outer regions in addition to the central regions of galaxies. We calculate weighted mean values of the residuals in bins constructed with different galaxy regions, H$\beta$, $\sigma_{*}$ and local density environments and plot them in the first row of Fig. 8. The weights used in this calculation are from Wake et al. (2017). For all three regions, ‘old’ low-$\sigma_{*}$ galaxies in a high local density environment show an obvious large residual, however, this kind of signature is not obvious for ‘young’ galaxies and/or high-$\sigma_{*}$ galaxies.

We also explore dependence on LSS types, isolated/central/satellite types and make similar plots using these environment indicators in the second and third rows of Fig. 8. There is no clear systematic trend along LSS types (second row), and similarly there is no obvious systematic trend along isolated/central/satellite types either (third row). ‘Old’ satellite galaxies (in the third row), however, have the highest residual in all $\sigma_{*}$ bins and all galaxy regions.

For satellite galaxies, we divide them into three groups according to their projected halo-centric radii (in units of virial radius of the group $R_{V}$): inner ($R<0.18R_{V}$), intermediate ($0.18R_{V}<R<0.7R_{V}$) and outer ($R>0.7R_{V}$); and make plots accordingly in the bottom row of Fig. 8. The residuals for ‘old’ low-$\sigma_{*}$ galaxies in the inner regions ($R<0.18R_{V}$) of galaxy groups are obviously large comparing to those of galaxies in the outer and intermediate regions. ‘Old’ medium-$\sigma_{*}$ and high-$\sigma_{*}$ galaxies also show a similar trend but less obviously. There is no clear systematic trend for ‘young’ galaxies. Note that the number of satellite galaxies is relatively small (cf. Table LABEL:envtable).

3.3 Formation redshift dependence

We investigate dependence on galaxy halo formation redshift ($z_{f}$) and the results are shown in Fig. 9. We do not see any clear systematic trend along formation redshifts, however, for ‘old’ galaxies, those with high formation redshift (formed earlier) have relatively larger residuals. This is true for almost all $\sigma_{*}$ bins and all galaxy regions. For ‘young’ galaxies, this signature is not obvious.

According to Wang et al. (2018), the $z_{f}$ provided is the formation redshift of the main halo and mostly reflects the formation time of the central/isolated galaxy. Satellite galaxies residing in separate sub-halos may have formation times different from the main halo. Consequently, we remove satellite galaxies and remake the plot showing dependance on $z_{f}$ as Fig. 10. Generally, error bars are larger by comparison with Fig. 9. For ‘old’ galaxies, those with high formation redshift (formed earlier) still have relatively larger residuals but not in all panels. For ‘young’ galaxies, there is still no clear signatures.

3.4 Gradients of Mgb/$\langle$Fe$\rangle$ within galaxies

The other interesting study enabled by IFU observations is Mgb/$\langle$Fe$\rangle$ gradients within galaxies. However, we only have three radial bins for each galaxy because of our requirement for high SNR. We therefore study this question in a simple way: plot histograms of the inner-to-outer ratio of Mgb/$\langle$Fe$\rangle$ (see Fig. 11). The inner and outer regions are defined as $r<0.3R_{e}$ and $0.7R_{e}<r<1.3R_{e}$ respectively. The average gradient for all galaxies is flat (inner-to-outer ratio of Mgb/$\langle$Fe$\rangle$ close to 1). We tried to divide galaxies into different environments, but still no gradients are observed for galaxies in different environments.

We then separate galaxies into different $\sigma_{*}$ bins in Fig. 12. This shows a more obvious difference: galaxies with high-$\sigma_{*}$ have a peak value around 1 (flat, zero-gradient) but with an extended tail towards larger values (negative gradient), while galaxies with low-$\sigma_{*}$ tend to have a positive Mgb/$\langle$Fe$\rangle$ gradient.

We further divide galaxies into different $\sigma_{*}$-environment bins, but do not see a clear dependence on local density either. One example using $\sigma_{*}$-local density bins is shown in Fig. 13. We also plot the inner-to-outer ratio of Mgb/$\langle$Fe$\rangle$ versus $\sigma_{*}$ color-coded by local density in Fig. 14. We can see a clear dependence of Mgb/$\langle$Fe$\rangle$ gradients on $\sigma_{*}$ and we see no clear dependence on local density.

4 Discussion

4.1 Comparison with other studies

We compare in Fig. 15 our spectral index measurements with the Portsmouth VAC (MaNGA Value Added Catalog produced by Portsmouth University). Our measurements are consistent with the Portsmouth VAC, which uses the same sample but with a different algorithm. The spectral index measurement algorithm used by the Portsmouth VAC is similar to the MaNGA DAP code (Westfall et al. submitted) and the algorithm of Parikh et al. (2018). We note that there are some discrepancies for high H$\beta$ ($>3$), however, we only use H$\beta$ values to classify ‘old’ and ‘young’ galaxies and it does not cause much discrepancies in this classification.

A comparison between our measurements of Mgb/$\langle$Fe$\rangle$ and various archival data from Liu et al. (2016b) is shown in Fig. 16. Our Mgb/$\langle$Fe$\rangle$-$\sigma_{*}$ relation is steeper than that of Liu et al. (2016b) and has a $\sim 0.05$ dex systematic difference at the high-mass end. Note that data from different sources have different calibration procedures; our spectral index values are corrected to the SDSS resolution ($\rm\sim 70km/s$) while data collected in Liu et al. (2016b) may have different spectral resolutions; also Liu et al. (2016b) has different aperture definitions from us when measuring spectral indices and velocity dispersions.

4.2 Implications for galaxy formation histories

Our results show that both ‘old’ and ‘young’ galaxies have good correlations between Mgb/$\langle$Fe$\rangle$ and $\sigma_{*}$, which is consistent with previous studies. The dependence of the residuals on local density environment (as well as projected halo-centric radius) is slight but significant enough to be identified visually. Also, the environmental dependence seems to be more obvious in low- and medium-$\sigma_{*}$ galaxies than in high-$\sigma_{*}$ galaxies. This implies that $\sigma_{*}$ or galaxy mass is the main parameter driving $\alpha$ enhancement and that environments only have significant effects for low- and medium-mass galaxies. Low-mass galaxies in dense regions may have experienced fast quenching due to environmental effects and thus have a shorter star formation time scale resulting in a higher $\alpha$-to-iron ratio or Mgb/$\langle$Fe$\rangle$. ‘Young’ galaxies generally have lower residuals in comparison to ‘old’ ones, and they do not show clear environmental dependence. This might be explained by the fact that the ‘young’ galaxies have recent star formation. The young stars in these galaxies are expected to have formed from the ISM that is polluted by Type Ia supernovae that have a lower $\alpha$-to-iron ratio. This recent star formation could also reduce the fast quenching signature produced by the environment.

The gradients of Mgb/$\langle$Fe$\rangle$ are close to 0 (flat), which is consistent with recent spatially resolved spectroscopic studies (e.g. Mehlert et al., 2003; Kuntschner et al., 2010; Spolaor et al., 2010; Greene et al., 2015; McDermid et al., 2015; Parikh et al., 2019). The gradients are less effected by environment but more determined by $\sigma_{*}$ or galaxy mass (see Fig. 12). Kuntschner et al. (2010, Fig. 14) using 48 early type galaxies showed that their [$\alpha$/Fe] gradients are slightly negatively correlated with stellar velocity dispersion but does not depend on environment. This is also consistent with previous studies on environmental dependence of stellar population gradients such as Zheng et al. (2017) and Goddard et al. (2017). This implies that the internal stellar population structures of galaxies are more affected by secular evolution processes driven by parameters such as galaxy mass.

We note that the spectral indices Mgb, Fe5270 and Fe5335 do not only depend on chemical abundances, but also on age, metallicity and star formation histories (Maraston et al., 2003; Thomas et al., 2003). The index ratio Mgb/$\langle$Fe$\rangle$ does show a clear positive relation with [$\alpha$/Fe] but with larger scatters with larger age range (Thomas et al., 2003). Our separation using H$\beta$ has partly removed some of the degeneracy introduced by age.

5 Summary and conclusion

We derived H$\beta$, Mgb, Fe5270 and Fe5335 index maps for all MaNGA MPL-7 (equivalent to SDSS DR15) galaxies. We studied $\sim 3000$ MaNGA galaxies and use Mgb/$\langle$Fe$\rangle$ as an $\alpha$-to-iron ratio indicator to study $\alpha$-abundance distribution within these galaxies. We studied environmental dependence of Mgb/$\langle$Fe$\rangle$-$\sigma_{*}$ relation using different different environment indicators: local density, large scale structure type, isolated/central/satellite type, and projected halo-centric radius. We also investigated the effects of galaxy halo formation redshift as well as gradients of Mgb/$\langle$Fe$\rangle$ versus $\sigma_{*}$ and environment. The main findings are:

• •

All galaxies show a good correlation between Mgb/$\langle$Fe$\rangle$ and $\sigma_{*}$ ($r_{S}=0.76$), but have larger scatters in low $\sigma_{*}$ ($<80$km/s) bins.

• •

For ‘old’ (H$\beta<3$) low-$\sigma_{*}$ galaxies, their Mgb/$\langle$Fe$\rangle$ shows an obvious enhancement in high-local density regions and inner regions within galaxy groups. This trend is not clear for ‘young’ (H$\beta>3$) and/or high-$\sigma_{*}$ ($>158$km/s) galaxies.

• •

We do not find a systematic trend for the LSS environment or the central/satellite environment. ‘Old’ satellite galaxies, however, have the highest residual ($\delta\log$(Mgb/$\langle$Fe$\rangle$)) values in most $\sigma_{*}$ bins and galaxy regions.

• •

‘Old’ galaxies with high formation redshift ($z_{f}>1.5$) have the highest residuals in all $\sigma_{*}$ bins and all galaxy regions, however, there is no clear systematic trend with formation redshift.

• •

The Mgb/$\langle$Fe$\rangle$ gradient is close to 0 (flat) and depends on $\sigma_{*}$ but not obviously on environments.

In conclusion, both the Mgb/$\langle$Fe$\rangle$ overall values and gradients mainly depend on galaxy properties such as stellar velocity dispersion. Environment plays a slight but obvious role in shaping the overall values of Mgb/$\langle$Fe$\rangle$; it has, however, no clear effect on Mgb/$\langle$Fe$\rangle$ gradients.

Acknowledgements

This work is supported by the National Natural Science Foundation of China No. 11703036 (ZZ). This work is also partly supported by the National Key Basic Research and Development Program of China (No. 2018YFA0404501 to SM), by the National Science Foundation of China (Grant No. 11333003, 11390372 and 11761131004 to SM, and 11874057 to CLiu). HW is supported by NSFC 11733004, 11522324 and 11421303. The Science, Technology and Facilities Council is acknowledged for support through the Consolidated Grant Cosmology and Astrophysics at Portsmouth, ST/N000668/1.

This work makes use of data from SDSS-IV. Funding for SDSS-IV has been provided by the Alfred P. Sloan Foundation and Participating Institutions. Additional funding towards SDSS-IV has been provided by the U.S. Department of Energy Office of Science. SDSS-IV acknowledges support and resources from the Centre for High-Performance Computing at the University of Utah. The SDSS web site is www.sdss.org.

SDSS-IV is managed by the Astrophysical Research Consortium for the Participating Institutions of the SDSS Collaboration including the Brazilian Participation Group, the Carnegie Institution for Science, Carnegie Mellon University, the Chilean Participation Group, the French Participation Group, Harvard-Smithsonian Center for Astrophysics, Instituto de Astrofísica de Canarias, The Johns Hopkins University, Kavli Institute for the Physics and Mathematics of the Universe (IPMU) / University of Tokyo, Lawrence Berkeley National Laboratory, Leibniz Institut f$\ddot{\rm u}$r Astrophysik Potsdam (AIP), Max-Planck-Institut f$\ddot{\rm u}$r Astronomie (MPIA Heidelberg), Max-Planck-Institut f$\ddot{\rm u}$r Astrophysik (MPA Garching), Max-Planck-Institut f$\ddot{\rm u}$r Extraterrestrische Physik (MPE), National Astronomical Observatory of China, New Mexico State University, New York University, University of Notre Dame, Observat$\acute{\rm a}$rio Nacional / MCTI, The Ohio State University, Pennsylvania State University, Shanghai Astronomical Observatory, United Kingdom Participation Group, Universidad Nacional Aut$\acute{\rm o}$noma de M$\acute{\rm e}$xico, University of Arizona, University of Colorado Boulder, University of Oxford, University of Portsmouth, University of Utah, University of Virginia, University of Washington, University of Wisconsin, Vanderbilt University, and Yale University.

Appendix A [$\alpha$/Fe]-$\sigma_{*}$ relation

We fit the four measured spectral indices (H$\beta$, Mgb, Fe5270 and Fe5335) with the Thomas et al. (2011) model. The Thomas et al. (2011) model provides spectral indices in MILES resolution ($\sim 2.7$ Å  FWHM), which is similar to the SDSS MaNGA resolution. The model has a fine age grid: t = 0.1,0.2,0.4,0.6,0.8,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15 Gyr; a relatively coarse metallicity grid: [Z/H] = -2.25, -1.35, -0.33, 0.0, 0.35, 0.67; and a very coarse $\alpha$ abundance grid: [$\alpha$/Fe] = -0.3, 0.0, 0.3, 0.5. Following Liu et al. (2016b), we interpolate the model using a finer grid, i.e. using a step of 0.01 dex in the [Z/H] and [$\alpha$/Fe] grid.

The fitted [$\alpha$/Fe] values for the central regions of our sample galaxies are presented in Fig. 17. The [$\alpha$/Fe] also has a good correlation with $\sigma_{*}$, which is consistent with previous studies (cf. black contour in Fig. 17), however, the [$\alpha$/Fe] - $\sigma_{*}$ relation has a smaller slope and a much larger scatter comparing to the Mgb/$\langle$Fe$\rangle$ - $\sigma_{*}$ relation.

We also show the environmental dependence of [$\alpha$/Fe] - $\sigma_{*}$ in Fig. 18. It has much less environmental dependence comparing to the Mgb/$\langle$Fe$\rangle$ - $\sigma_{*}$ relation (Fig. 8). This could be due to the large scatter in [$\alpha$/Fe] derivation.