# Is velocity dispersion the major driver of stellar population properties over sub-galaxy scales? An SDSS MaNGA IFU study

I. Ferreras, M. Trevisan, O. Lahav, R. R. de Carvalho, J. Silk

► To cite this version:

I. Ferreras, M. Trevisan, O. Lahav, R. R. de Carvalho, J. Silk. Is velocity dispersion the major driver of stellar population properties over sub-galaxy scales? An SDSS MaNGA IFU study. Monthly Notices of the Royal Astronomical Society, 2025, 540, pp.1069-1083. 10.1093/mnras/staf712. insu-05101643

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# Is velocity dispersion the major driver of stellar population properties over sub-galaxy scales? An SDSS MaNGA IFU study

I. Ferreras<sup>1,2,3★</sup> M. Trevisan,<sup>4</sup> O. Lahav,<sup>1</sup> R. R. de Carvalho<sup>5,6</sup> and J. Silk<sup>7,8,9</sup>

Accepted 2025 April 29. Received 2025 March 28; in original form 2024 December 4

## ABSTRACT

Thanks to Integral Field Unit survey data, it is possible to explore in detail the link between the formation of the stellar content in galaxies and the drivers of evolution. Traditionally, scaling relations have connected galaxy-wide parameters such as stellar mass ($M_s$), morphology or average velocity dispersion ($\sigma$) to the star formation histories (SFHs). We study a high quality sample of SDSS–MaNGA spectra to test the possibility that sub-galaxy (≤2 kpc) scales are dominant, instead of galaxy-wide parameters. We find a strong correlation between local velocity dispersion and key line strengths that depend on the SFHs, allowing us to make the ansatz that this indicator – that maps the local gravitational potential – is the major driver of star formation in galaxies, whereas larger scales play a role of a secondary nature. Galactocentric distance has a weaker correlation, suggesting that the observed radial gradients effectively reflect local variations of velocity dispersion. In our quest for a cause, instead of a correlation, we contrast $\sigma$ with local stellar mass (or surface mass density), that appears less correlated with population properties. We conclude that the inherently higher uncertainty in $M_s$ (or $\Sigma_M$) may explain its lower correlation with respect to $\sigma$, but the extra uncertainty needed for $\sigma$ to have similar correlations as stellar mass is rather high. Therefore, we posit local velocity dispersion as the major driver of evolution, a result that should be reproduced by hydrodynamical models at the proper resolution.

**Key words:** methods: data analysis – techniques: spectroscopic – galaxies: evolution – galaxies: fundamental parameters – galaxies: statistics – galaxies: stellar content.

## 1 INTRODUCTION

Over the past two decades, large scale spectroscopic surveys have revolutionized our understanding of extragalactic astrophysics. Before these large data sets became available, most studies were based on relatively small numbers of well-chosen targets. Survey data enable us to tackle this problem in a statistical sense, looking for the general trends that reveal the fundamental processes driving the formation of galaxies, confronting the observations with models that encapsulate the main mechanisms transforming gas into stars and framing this in a cosmological context. Scaling trends such as the colour-magnitude relation, the fundamental plane, or the Tully–Fisher relation provide evidence of a strong trend between a local physical quantity, say gravitational potential in its many guises, and the formation of galaxies. For instance, we now know that there is a strong correlation between the age and the mass of a galaxy, with

more massive systems being preferentially older, and predominantly supported as hot dynamical systems (see e.g. Silk & Mamon 2012, for a general review). The well-established bimodality (e.g. Strateva et al. 2001a; Baldry et al. 2004; Angthopo, Ferreras & Silk 2019) reveals a blue cloud/red sequence transition where the processes that quench star formation appear to hold the key to understanding how galaxies evolve. In this context, an important issue concerns the ‘drivers’ of galaxy formation, i.e. the fundamental properties that control this evolution. A large number of papers look for these drivers, mainly proposing options at the galactic level, i.e. scales of several kpc versus environment, group/cluster scales of hundreds of kpc, and beyond (to name a few, Weinmann et al. 2006; Peng et al. 2010; Rogers et al. 2010; Etherington & Thomas 2015). At the galaxy level, relevant parameters are the mass, velocity dispersion, gravitational potential, dynamical support, or morphology. The more recent IFU-based surveys (e.g. Bacon et al. 2001; Cappellari et al. 2011a; Sánchez et al. 2012; Bryant et al. 2015; Bundy et al. 2015a) brought this analysis into a new level, as galaxies could be probed spectroscopically in much more detail, regarding both the dynamical

<footnote n="1"><sup>1</sup>Department of Physics and Astronomy, University College London, London WC1E 6BT, UK</footnote>

<footnote n="2"><sup>2</sup>Instituto de Astrofísica de Canarias, Calle Vía Láctea s/n, E-38205, La Laguna, Tenerife, Spain</footnote>

<footnote n="3"><sup>3</sup>Departamento de Astrofísica, Universidad de La Laguna, E-38206 La Laguna, Tenerife, Spain</footnote>

<footnote n="4"><sup>4</sup>Departamento de Astronomia, Universidade Federal do Rio Grande do Sul, 91501-970 Porto Alegre-RS, Brazil</footnote>

<footnote n="5"><sup>5</sup>NAT - Universidade Cidade de São Paulo, 01506-000, SP, Brazil</footnote>

<footnote n="6"><sup>6</sup>Universidade de São Paulo, IAG, Rua do Matão 1226, Cidade Universitária, São Paulo 05508-900, Brazil</footnote>

<footnote n="7"><sup>7</sup>Institut d'Astrophysique de Paris, 98 bis Boulevard Arago, F-75014 Paris, France</footnote>

<footnote n="8"><sup>8</sup>BIPAC, Department of Physics, University of Oxford, Keble Road, Oxford OX1 3RH, UK</footnote>

<footnote n="9"><sup>9</sup>Department of Physics and Astronomy, The Johns Hopkins University, Baltimore, MD 21218, USA</footnote>

<footnote>* E-mail: i.ferreras@ucl.ac.uk</footnote>
state and the stellar population content, with fundamental results into the way these two aspects relate to each other (e.g. Cappellari et al. 2011b; Wang, Peng & Cappellari 2024).

While many of the IFU-based studies statistically approach the spatially resolved properties with radial gradients of targeted observables, such a result only produces a first view of resolved galaxy formation, and depends on how the local properties match with galactocentric distance. Gradient studies of stellar populations reveal interesting trends where the central regions tend to be dominated by old, metal rich stars, whereas the outer regions tend to be metal poorer, reflecting a different formation mode (see e.g. Kuntschner et al. 2010; La Barbera et al. 2012; González Delgado et al. 2015; Greene et al. 2015; Parikh et al. 2018; Ferreras et al. 2019; Zibetti et al. 2020; Parikh et al. 2021). These observational trends can be explained within a simple framework based on simulations (Oser et al. 2010), where most of the formation of a galaxy is separated into two major phases, an *in situ* phase that generates the stellar component of the most massive, parent, halo, and the *ex situ* phase that consists of later additions to the galaxy from mergers (Naab, Johansson & Ostriker 2009). While this working hypothesis is a powerful way to understand the spatially resolved results, it hardwires the interpretation to monolithic versus hierarchical growth.

In a insightful review, Sánchez et al. (2021) suggested that local properties within galaxies are also subject to the same scaling relations as those found over galaxy scales, so that the latter can be interpreted as an integrated version of the former (see also Sánchez 2020). Such an interpretation goes back to scaling relations such as the Schmidt-Kennicutt law that defines the star formation rate by the local gas density, either as a projected surface density (Kennicutt 1989) or the 3D volume density (Schmidt 1959). Integral field spectroscopy has enabled the analysis of intra-galaxy scales and the role of local physics in driving the relations that originally manifested themselves over whole galaxies. For instance, Ellison et al. (2018) and Cano-Díaz et al. (2019) show that the star forming main sequence traced by the Schmidt-Kennicutt law holds within galaxies, when defining local surface measures of the star formation rate and the stellar mass. The origin of quenching at the global and local level is also explored in IFU data by Jing & Li (2024), finding surface mass density as the dominant driver of quenching. The gradients of spatially resolved stellar population properties are explored, e.g. in González Delgado et al. (2015), Zibetti et al. (2017), and Ferreras et al. (2019), with velocity dispersion or stellar mass showing a key role in the trends. Beyond gradients, local studies of stellar ages and metallicities reveal a substantial correlation with surface stellar mass density (Barone et al. 2018; Zibetti & Gallazzi 2022).

Local relations provide a more detailed framework than the standard two-phase scenario and give small scale mechanisms a more important role. In our paper we adopt the ansatz that a local observable – roughly defined over a physical scale of ≲2 kiloparsec (limited by the size of the optical fibre and the effective resolution) – controls the overall properties of the stellar populations therefore also determining its past star formation and chemical enrichment histories. The excellent quality of the publicly available data from the SDSS-IV IFU survey MaNGA (Bundy et al. 2015b) allows us to tackle such a proposal. In addition, we also explore which of the typical local properties are more strongly correlated, and thus can potentially serve as the major driver of galaxy evolution. Our conclusions strongly favour *local* stellar velocity dispersion as the dominant driver. Such a hypothesis requires a revision of some of the established ideas regarding galaxy formation, and offers a strong constrain to test the validity of hydrodynamical cosmological simulations.

This paper is structured as follows. After this introductory section, we describe the MaNGA IFU data set in Section 2, followed by the description of the scaling properties in Section 3 that motivate us to propose the ansatz that the star formation histories are mainly controlled by physical quantities over sub-galaxy scales, with the velocity dispersion ($\sigma$) posited as the main driver. Thus far these trends are shown as observational correlations. In Section 4, we further consider whether $\sigma$ and not stellar mass represents the cause of these trends. Section 5 takes a look at the connection between the observed local trends and the evolutionary stage of the galaxies. Finally, we summarize our conclusions in Section 6.

## 2 THE SAMPLE

The parent catalogue for this work is the Angthopo et al. (2019, 2020) sample that is based on a detailed analysis of high quality data from the Legacy SDSS spectra, classified into the three standard evolutionary states (blue cloud, green valley, and red sequence) using one of the most robust indicators of the stellar population content, the 4000 Å break strength. That sample is restricted in redshift ($0.05 \le z \le 0.1$) and in the signal to noise ratio of the single fibre spectra (median S/N>10 over pixels in the SDSS-$r$ band), and consists of over 200 thousand galaxies. We cross-match this catalogue with the DR17 version (Abdurro’uf et al. 2022) of the SDSS-IV/MaNGA (Bundy et al. 2015b) IFU survey, that comprises ~10 000 galaxies. We also make use of the Marvin (Cherinka et al. 2019) data products. The cross-match results in a set of 2034 galaxies, but one galaxy does not have the science-ready data from Marvin (mangaID 1–80510), and a few other galaxies have repeated observations (see table 1 from Westfall et al. 2019), for which we retrieve the ones with the best seeing according to the SEEMED keyword. The final set comprises 2024 galaxies, and constitutes our working sample. Fig. 1 shows the distribution of the sample with respect to a number of important parameters defined in each galaxy observation (clock-wise from top-left: signal-to-noise ratio measured within one effective radius, the physical effective radius in kpc – assuming a vanilla flavoured $\Lambda$CDM cosmology with $h = 0.7$ and $\Omega_m = 0.3$ – the galactocentric distance of the outermost useable spaxel ($R_M$) in units of $R_e$, the same $R_M$ in units of the HWHM of the PSF (defined as $R_{PSF}$), stellar mass, and velocity dispersion in units of $100 \text{ km s}^{-1}$). By ‘useable’ spaxels, we enforce a minimum S/N (also in the SDSS-$r$ band) of 5 for *individual spectra*. In addition, we discard spaxels where the individual velocity dispersion estimate is uncertain, or outside of the [50 300] km s$^{-1}$ interval. Both constraints ensure that the resulting individual measurements are reliable. The final sample of 2024 galaxies produces a set of 1025 841 spaxels.

The novel approach of this paper lies in our relinquishing the connection of the data with the ‘host’ galaxy, turning instead to the analysis of *individual spaxels*, representing local regions of galaxy formation and evolution. In other words, we consider this sample as a set of over one million good quality independent spectra of local star forming regions. At the median redshift of the sample ($z_M = 0.064$), the size of a spaxel (0.5 arcsec) maps a physical scale of 0.6 kpc. We note that the MaNGA spaxel is much smaller than the actual optical fibres of the spectrograph (2 arcsec). Moreover, the typical point spread function is 1–2 arcsec, so that the effective spatial resolution in projected physical units is ≲2 kpc. We explore several types of ‘local indicators’: stellar velocity dispersion ($\sigma$, measured locally in each spaxel), projected galactocentric distance ($R$), stellar mass ($M_s$), stellar mass surface density ($\Sigma_M$, defined as the ratio between the stellar mass in the spaxel and the physical area spanned by the fibre at the location of the galaxy) and the bulk velocity ($v$). The observables
<figure><img src="image_2.png" /><figcaption>**Figure 1.** Distribution of general observables of the galaxy sample from SDSS-MaNGA. The corresponding parameter (horizontal axis) is labelled in each panel. Clockwise from top-left we show the signal to noise ratio of the spectra within one effective radius in the SDSS-r band, the effective radius in physical units, the ratio between the galactocentric distance of the outermost useable spaxel in each galaxy ($R_M$) and the effective radius, the ratio between $R_M$ and $R_{PSF}$ (i.e. the HWHM of the point spread function), the (logarithm) of the stellar mass in solar units, and the averaged stellar velocity dispersion in units of 100 km s$^{-1}$.</figcaption></figure>

$\sigma$, $R$, $v$ are all taken from the MaNGA Data Analysis Pipeline (DAP v3.1.0, Westfall et al. 2019). We refer the reader to that publication for details of the methodology. In a nutshell, the kinematics is derived with the code pPXF (Cappellari 2017), using a special version of the MILES stellar library (Sánchez-Blázquez et al. 2006) where the number of templates is reduced with a hierarchical clustering method (MILES-HC; Westfall et al. 2019). The values are quoted for each spaxel. The stellar mass and surface stellar mass density are obtained from the Portsmouth Firefly Value Added Catalogue (Wilkinson et al. 2017; Neumann et al. 2022). Stellar masses require a population synthesis analysis to derive the stellar M/L that, combined with the photometry, provides the estimates of stellar mass. We use the estimates derived from the stellar population models of Maraston & Strömbäck (2011), based on the MILES library for a Kroupa (2001) IMF. We adopt version 3.1.1 of the Firefly VAC, and use HDU11 (first channel: stellar mass per spaxel) and HDU14 (surface mass density quoted as $\log M_{\odot} \text{ kpc}^{-2}$). Both stellar mass quantities are obtained within Voronoi cells, but are quoted per spaxel. Regarding stellar mass (within a spaxel), we note that this quantity is indeed redshift dependent. Over the $z = 0.05$ to 0.1 range, the 0.5 arcsec spaxel maps a physical length from 0.5 to 0.9 kpc, and so, identical galaxies will have more massive spaxels at higher redshift, as these will cover a larger physical extent. However, our working hypothesis that local properties drive the evolution of stellar populations, makes this argument irrelevant. Each spaxel, on its own, represent a local region where some amount of stellar mass is present and with the associated stellar population indicators. Therefore, it is still a valid assumption to use stellar mass per spaxel as a potential indicator of evolution. Nevertheless, we will see below that both stellar mass and surface stellar mass density (redshift independent) follow very similar trends.

These indicators can be defined in an absolute sense (i.e. each spaxel is labelled by a $\sigma$ in km s$^{-1}$, an $R$ in kpc, a $M_s$ in $M_{\odot}$, a $\Sigma_M$ in $M_{\odot} \text{ kpc}^{-2}$), or as a relative dimensionless quantity: $\sigma$, $M_s$ and $\Sigma_M$ being given as a fraction of the maximum value of the relevant quantity in the corresponding galaxy, and $R$ measured in units of the effective radius, $R_e$ (also taken from the MaNGA DAP). For the bulk velocity, we use two definitions: the absolute measurement combines it with velocity dispersion, $\sqrt{\sigma^2 + v^2}$ and serves as a proxy of kinetic energy. The relative definition is the standard ratio $|v|/\sigma$ that traces the level of rotational support versus random motion, a direct indicator of morphology (see e.g. Cappellari et al. 2011b). In Appendix A, we show the distribution of spaxel measurements for a few individual galaxies, comparing them with respect to the distribution of the complete spaxel sample as we will show in the next section. We emphasize that our analysis rests on the assumption that the statistical distribution of individual spaxels reflects an inherent causality at sub-galaxy ($\sim 2$ kpc) scales, regardless of the stellar mass, morphology, etc, corresponding to the parent galaxy.

## 3 THE ANSATZ: LOCAL PROPERTIES DRIVE THE AVERAGE STAR FORMATION HISTORY

Fig. 2 shows, as a density plot, the distribution of spaxel data of the whole sample for three targeted line strengths, from top to bottom, the 4000Å break strength, adopting the definition of Balogh et al. (1999), the wide (A) definition of the Hδ Balmer line of Worthey & Ottaviani (1997), and the [MgFe] index that combines the traditional Lick indices Mgb, Fe5270 and Fe5335 in a way that minimizes the dependence on the [Mg/Fe] abundance ratio
<figure><img src="image_3.png" /><figcaption>**Figure 2.** Bivariate plots of three fundamental line strengths shown with respect to five indicators of galaxy 'position', as defined for each individual spaxel, (from left to right) velocity dispersion, galactocentric distance, stellar mass, surface stellar mass density, and a proxy of kinetic energy, $\sqrt{\sigma^2 + v^2}$. The data consist of over 1 million measurements comprising individual spaxels, regardless of the galaxies they correspond to. The contours engulf (from the inside out) 25, 50, 75, and 90 per cent of all data points, starting in the regions of higher data point density. The red line in each panel follows the running median of the distribution with respect to the abscissa.</figcaption></figure>

(Thomas, Maraston & Bender 2003). These three indices lock a large amount of 'information' (in the entropy sense) or variance, so they are ideal indicators to explore the population properties, especially in data covering a wide range of S/N values (see Ferreras et al. 2023). Very roughly, we can assume that $D_n(4000)$ traces overall stellar age, $H\delta_A$ is prominent in regions with recent star formation activity, and [MgFe] features a strong dependence with metallicity. However, the reader should be cautious in the interpretation as these indices (or any other) have a substantial age-metallicity degeneracy (e.g. Ferreras, Charlot & Silk 1999; La Barbera et al. 2013), and are strongly correlated with respect to the fundamental population properties (Ferreras et al. 2023). For reference, we also include below the analysis for the stellar age and metallicity derived by adopting a standard methodology (Wilkinson et al. 2017).

Fig. 2 presents the data with respect to the indicators defined in an absolute sense: stellar velocity dispersion ($\sigma$, in km s$^{-1}$), galactocentric distance ($R$, in kpc), stellar mass ($M_s$, in $M_\odot$), stellar mass surface density ($\Sigma_M$ in $M_\odot$ kpc$^{-2}$), and a proxy for the kinetic energy, i.e. combining velocity dispersion and bulk motion in quadrature ($\sqrt{\sigma^2 + v^2}$ in km s$^{-1}$). We emphasize that these are local indicators, defined for specific spaxels, and all the spaxels in all galaxies from the sample are included here to produce these distributions. In addition to the greyscale density plot, to guide the

eye, we overlay contours at levels that engulf (from the inside out) 25, 50, 75, and 90 per cent of the total set. Each of the indices is corrected for velocity dispersion effects using the term provided in the Marvin data set (for instance: specindex_corr_hdeltaa for the correction of the $H\delta_A$ line strength, defined as a multiplicative correction). Our hypothesis – that the stellar population content is 'driven' by local quantities – is supported by the trends shown in the figure, where the line strengths are strongly correlated with local velocity dispersion, regardless of galaxy type, mass, etc. In addition, Fig. 3 shows the same observables defined in the previous figure, but in a relative sense: for $\sigma$, $M_s$, and $\Sigma_M$ we take the ratio between the measured value in each spaxel and the maximum of the distribution for each individual galaxy, and for $R$ it is given as the ratio with respect to the effective radius, taken from the official SDSS/MaNGA data. Finally, we include the ratio between the bulk velocity in absolute value and the velocity dispersion (both concerning the stellar component).

A first test to determine which of these local indicators is dominant, we calculate the Pearson correlation coefficient ($r_{XY}$) for all the bivariate plots presented in Fig. 2 for absolute observables and Fig. 3 for relative observables. The results are shown in the top portions of Tables 1 and 2, respectively. The quoted uncertainties correspond to $1\sigma$ of the distribution of correlation coefficients derived from
<figure><img src="image_4.png" /><figcaption>**Figure 3.** Equivalent of Fig. 2 for relative observables, as described in the text. In addition to (from left to right) stellar velocity dispersion, galactocentric distance, stellar mass, and stellar mass surface density, we also include the ratio between the absolute value of bulk velocity and velocity dispersion of the stellar component, as an estimator of rotational support. All measures are referred to over 1 million individual spaxels. The contours engulf (from the inside out) 25, 50, 75, and 90 per cent of all data points, starting in the regions of higher data point density. The red line in each panel tracks the running median of the distribution with respect to the abscissa.</figcaption></figure>

<table><caption>**Table 1.** Correlation coefficients between stellar population line strengths and observables measured in an absolute way in spaxels with S/N≥5 (see Fig. 2).</caption><thead><tr><th>Index</th><th>σ</th><th>R</th><th>log M<sub>s</sub></th><th>log Σ<sub>M</sub></th><th>√σ<sup>2</sup> + v<sup>2</sup></th></tr></thead><tbody><tr><td colspan="6" style="text-align: center;">Correlation coefficient</td></tr><tr><td>D<sub>n</sub>(4000)</td><td>+0.756±0.001</td><td>-0.236±0.001</td><td>+0.578±0.001</td><td>+0.548±0.001</td><td>+0.610±0.001</td></tr><tr><td>Hδ<sub>A</sub></td><td>-0.669±0.001</td><td>+0.297±0.001</td><td>-0.562±0.001</td><td>-0.563±0.001</td><td>-0.522±0.001</td></tr><tr><td>[MgFe]<sup>'</sup></td><td>+0.548±0.001</td><td>-0.310±0.001</td><td>+0.518±0.001</td><td>+0.511±0.001</td><td>+0.401±0.001</td></tr><tr><td>log t<sub>LW</sub></td><td>+0.361±0.001</td><td>-0.162±0.001</td><td>+0.614±0.001</td><td>+0.645±0.001</td><td>+0.275±0.001</td></tr><tr><td>log t<sub>MW</sub></td><td>+0.183±0.001</td><td>-0.045±0.001</td><td>+0.434±0.001</td><td>+0.466±0.001</td><td>+0.134±0.001</td></tr><tr><td>log Z<sub>LW</sub></td><td>+0.490±0.001</td><td>-0.198±0.001</td><td>+0.476±0.001</td><td>+0.454±0.001</td><td>+0.452±0.001</td></tr><tr><td>log Z<sub>MW</sub></td><td>+0.403±0.001</td><td>-0.144±0.001</td><td>+0.454±0.001</td><td>+0.433±0.001</td><td>+0.350±0.001</td></tr><tr><td colspan="6" style="text-align: center;">Standard deviation (and 1σ error)</td></tr><tr><td>D<sub>n</sub>(4000)</td><td>0.17±0.04</td><td>0.27±0.02</td><td>0.22±0.05</td><td>0.23±0.05</td><td>0.21±0.03</td></tr><tr><td>Hδ<sub>A</sub></td><td>2.14±0.33</td><td>2.89±0.29</td><td>2.43±0.58</td><td>2.41±0.60</td><td>2.52±0.24</td></tr><tr><td>[MgFe]<sup>'</sup></td><td>0.82±0.04</td><td>0.93±0.12</td><td>0.83±0.12</td><td>0.83±0.14</td><td>0.88±0.05</td></tr><tr><td>log t<sub>LW</sub></td><td>0.23±0.03</td><td>0.25±0.04</td><td>0.19±0.04</td><td>0.18±0.03</td><td>0.24±0.02</td></tr><tr><td>log t<sub>MW</sub></td><td>0.22±0.03</td><td>0.22±0.03</td><td>0.19±0.04</td><td>0.18±0.04</td><td>0.22±0.02</td></tr><tr><td>log Z<sub>LW</sub></td><td>0.14±0.03</td><td>0.17±0.02</td><td>0.14±0.03</td><td>0.15±0.03</td><td>0.15±0.02</td></tr><tr><td>log Z<sub>MW</sub></td><td>0.24±0.07</td><td>0.27±0.04</td><td>0.22±0.07</td><td>0.23±0.07</td><td>0.24±0.06</td></tr></tbody></table>

1000 randomly selected samples each one comprising 75 per cent of the whole set. This coefficient is defined to look for linear trends in data sets. Figs 2 and 3 show that these correlations are not necessarily linear, but r<sub>XY</sub> provides a useful quantification of correlatedness – much in the same way as covariance in non-Gaussian distributions. We also explored non-linear statistics, such as the

Spearman correlation coefficient (r<sub>S</sub>), which is better suited to track monotonicity. We find very similar results that confirms these results. For instance, the correlation between (absolute) velocity dispersion and D<sub>n</sub>(4000) is r<sub>XY</sub> = +0.756, r<sub>S</sub> = 0.774, and the equivalent result for the trend with (absolute) galactocentric radial distance and D<sub>n</sub>(4000) is r<sub>XY</sub> = -0.236, r<sub>S</sub> = -0.224.
<table><caption>**Table 2.** Correlation coefficients between stellar population line strengths and observables measured in a relative way in spaxels with S/N ≥ 5 (see Fig. 3).</caption><thead><tr><th>Index</th><th>σ/σ<sub>0</sub></th><th>R/R<sub>e</sub></th><th>log M<sub>s</sub>/M<sub>0</sub></th><th>log Σ<sub>M</sub>/Σ<sub>0</sub></th><th>|v|/σ</th></tr></thead><tbody><tr><td colspan="6">Correlation coefficient</td></tr><tr><td>D<sub>n</sub>(4000)</td><td>+0.651±0.001</td><td>-0.207±0.001</td><td>+0.062±0.001</td><td>+0.060±0.001</td><td>+0.036±0.001</td></tr><tr><td>Hδ<sub>A</sub></td><td>-0.605±0.001</td><td>+0.240±0.001</td><td>-0.117±0.001</td><td>-0.117±0.001</td><td>-0.007±0.001</td></tr><tr><td>[MgFe]<sup>′</sup></td><td>+0.520±0.001</td><td>-0.292±0.001</td><td>+0.175±0.001</td><td>+0.177±0.001</td><td>-0.027±0.002</td></tr><tr><td>log t<sub>LW</sub></td><td>+0.317±0.001</td><td>-0.111±0.001</td><td>+0.398±0.001</td><td>+0.396±0.001</td><td>-0.004±0.002</td></tr><tr><td>log t<sub>MW</sub></td><td>+0.136±0.001</td><td>+0.004±0.001</td><td>+0.318±0.001</td><td>+0.315±0.001</td><td>+0.007±0.002</td></tr><tr><td>log Z<sub>LW</sub></td><td>+0.458±0.001</td><td>-0.207±0.001</td><td>+0.118±0.001</td><td>+0.120±0.001</td><td>+0.013±0.001</td></tr><tr><td>log Z<sub>MW</sub></td><td>+0.385±0.001</td><td>-0.139±0.001</td><td>+0.125±0.001</td><td>+0.124±0.001</td><td>+0.013±0.002</td></tr><tr><td colspan="6">Standard deviation (and 1σ error)</td></tr><tr><td>D<sub>n</sub>(4000)</td><td>0.21±0.03</td><td>0.27±0.02</td><td>0.28±0.02</td><td>0.28±0.02</td><td>0.23±0.03</td></tr><tr><td>Hδ<sub>A</sub></td><td>2.37±0.29</td><td>2.91±0.35</td><td>3.00±0.27</td><td>3.00±0.27</td><td>2.61±0.26</td></tr><tr><td>[MgFe]<sup>′</sup></td><td>0.84±0.04</td><td>0.93±0.12</td><td>0.96±0.11</td><td>0.96±0.11</td><td>0.89±0.05</td></tr><tr><td>log t<sub>LW</sub></td><td>0.24±0.03</td><td>0.25±0.04</td><td>0.22±0.04</td><td>0.22±0.04</td><td>0.24±0.02</td></tr><tr><td>log t<sub>MW</sub></td><td>0.22±0.03</td><td>0.22±0.03</td><td>0.20±0.03</td><td>0.20±0.03</td><td>0.22±0.03</td></tr><tr><td>log Z<sub>LW</sub></td><td>0.15±0.02</td><td>0.16±0.02</td><td>0.17±0.02</td><td>0.17±0.02</td><td>0.16±0.02</td></tr><tr><td>log Z<sub>MW</sub></td><td>0.24±0.07</td><td>0.27±0.05</td><td>0.27±0.03</td><td>0.27±0.03</td><td>0.26±0.05</td></tr></tbody></table>

A second measure of the correlation, better suited to non-linear trends, say between $X = \sigma$ and $Y = D_n(4000)$, involves producing a running median $Y_R = f(X)$ by taking sliding intervals (of size 1000) in increasing X. For each interval we define the general trend by the running median: $f(X_i) = \text{median}(X_i)$, shown as red lines in each panel of Figs 2 and 3). We now define the residuals with respect to this trend: $\delta_i = (Y_i - f(X_i))$ for each data point (i.e. spaxel), from which we quote the standard deviation: $\sqrt{\langle(\delta^2) - \langle\delta\rangle^2\rangle}$, in the bottom portion of Tables 1 and 2, along with its own standard deviation, serving as an indicator of the quality of this number as a tracer of correlation.

The strongest correlation is found for stellar (local) velocity dispersion in all three line strengths, especially $D_n(4000)$. Note that of the three choices, the 4000 Å break strength is the one least sensitive to systematic effects of velocity dispersion<fnref n="1" />, confirming the strong relation between stellar population content and $\sigma$, i.e. excluding a potential systematic. Both the absolute case ($\sigma$ presented in km s⁻<fnref n="1" />) or the relative one (adopting the dimensionless ratio $\sigma/\sigma_0$) produce similar coefficients, although the latter appears less correlated with population properties. The kinetic energy proxy ($\sqrt{\sigma^2 + v^2}$) is also strongly correlated, but less so than velocity dispersion. Moreover, note the weaker linear correlation of $|v|/\sigma$, which leads us to conclude that the strong correlation found in $\sqrt{\sigma^2 + v^2}$ is dominated by $\sigma$. Note that if we want to use a proxy to determine, e.g. $D_n(4000)$, velocity dispersion happens to be the best indicator, as it traces the full range in a relatively smooth way. In contrast, $|v|/\sigma$ features two distinctive regimes, at low $|v|/\sigma$, there is a bimodal distribution, dominated by older populations, whereas at large $|v|/\sigma$, the younger populations dominate. However, if we use $\sigma$ as the reference parameter, the variation of the stellar population indicators shows a stronger general correlation. It is important to note that at low $D_n(4000)$, there is a wide range of $|v|/\sigma$, i.e. rotational support implies younger populations, but not the other way round.

It is also worth noting that the measured bulk velocity depends on inclination, weakening the expected trends. Regarding stellar mass and stellar mass surface density, it is quite remarkable to note the strong correlation for the absolute estimators (Table 1) but the substantially lower level of correlation for the relative observables

(Table 2). We emphasize that the relative values are simply referenced with respect to the maximum value of the observable in each galaxy. Such a behaviour is not found for velocity dispersion where both absolute and relative estimates appear strongly correlated with the line strengths.

In stark contrast, galactocentric distance is very weakly correlated with any of the population parameters, either in absolute or relative estimates. Our measurements of galactocentric distance adopt the official MaNGA parameter based on the elliptical Petrosian half-light radius as $R_e$, a more robust indicator than parameters based on Sérsic fitting (Wake et al. 2017). Note also the jagged behaviour of the running median lines, especially concerning radial distance, produced because of two factors: weaker correlation and in some cases, the presence of a bimodality of line strength measurements within the same range of galactocentric distance. In contrast, the plots with velocity dispersion separate better the two distributions (e.g. strong vs weak 4000 Å break strength). We note that while spatial resolution may introduce a systematic, mainly as the size of the PSF is not small with respect to the extent of the observations (see Fig. 1), the effect would induce lower correlations in both galactocentric distance and velocity dispersion, whereas we find a notable difference between these two local indicators.

In addition to the line strengths directly measured in the spaxels, we include in Fig. 4 the distribution of population parameters derived from the spectra. From bottom to top, we show the stellar age (luminosity weighted and mass weighted) and the metallicity (also luminosity weighted and mass weighted). The results are retrieved from the Portsmouth port of the MaNGA data base using the Firefly code (Wilkinson et al. 2017). Our trends are consistent with the analysis of CALIFA data presented in Zibetti & Gallazzi (2022), where the comparison is made with respect to total stellar mass (global) and surface stellar mass density (local). The correlations found with light-weighted age and metallicity lead the authors to propose stellar mass as the ‘glocal’ driver of populations, as the trends operate on both scales. A similar trend was found in the SAMI survey (Barone et al. 2018). Our claim goes beyond and proposes that local properties are the dominant drivers of evolution of the stellar component, and we put more emphasis on line strengths (stronger correlation) and velocity dispersion. Note the stellar ages and metallicities are subject to the systematics produced by fitting the spectra to a set of population synthesis models. The same

<footnote n="1">¹because it is defined in a wider spectral range.</footnote>
<figure><img src="image_5.png" /><figcaption>**Figure 4.** Equivalent of Fig. 2 for the Luminosity- (LW) and Mass-Weighted (MW) stellar age and metallicity, as derived from the FireFly fitting procedure (Wilkinson et al. 2017).</figcaption></figure>

measurements of the correlation coefficient and scatter with respect to the running median is shown for these parameters in Tables 1 for absolute indicators and 2 for relative indicators. We should emphasize that the stellar mass used in this work is also dependent on the same type of analysis – in order to translate the observed flux into a stellar mass. Therefore, it comes as no surprise that these parameters show substantial correlation. However stellar velocity dispersion – a more independent observable to the derivation of population parameters – is also found to correlate at a similar level.

Finally, in order to illustrate that redshift does not introduce any strong trend in the results, we give some more information in Appendix B, that confirms the lack of any redshift-dependent bias.

## 4 WHICH ONE IS THE MAJOR DRIVER OF POPULATION PROPERTIES?

Finding the fundamental driver of star formation in galaxies is a complicated task. Most of the work in statistics is geared towards the search, quantification and analysis of correlations, but the mantra of causal inference states that ‘correlation does not imply causation<fnref n="2" />’. Indeed, interesting cases abound where highly correlated variables clearly do not cause the trend under study – such as the textbook example of the correlation between ice cream sales and drowning,

where the fundamental ‘driver’ of the relation is climate (typically called confounder variable; see e.g. Pearl & Mackenzie 2018). An illustrative point regarding the relationship of the local indicators explored in this paper is shown in Fig. 5, where the four choices are compared against one another as a density plot. The most conspicuous relation is unsurprisingly found between stellar mass and surface stellar mass density, as $\Sigma_M$ simply adds to $M_s$ a second variable, the mapping of the 0.5 arcsec spaxel into a physical area. A very relevant plot is the weak correlation between $\sigma$ and $R$, that, linked to the previously found correlation with line strengths, leads us to discard galactocentric distance as a key variable in the analysis. Moreover, if we plot $R/R_e$ instead of $R$, the trend also shows low correlation. Stellar mass and $\sigma$ do have a substantial correlation, and it is worth noting that these two variables are derived in independent ways, so this trend shows a physical connection. We therefore consider $\sigma$ and $M_s$ as candidates of the ‘main’ variable. But which of these two is more important?

A first test is shown in Fig. 6, where the sample is split primarily with respect to velocity dispersion (left column), or stellar mass (right column). In each case, we bin the main variable in ten intervals within which we assume the main variable is roughly ‘fixed’, i.e. defined by the chosen bin. In each interval, the other variable (log $M_s$ when binning in $\sigma$ and vice-versa) is used to select a subset at the 25th and 75th percentile levels from the distribution. The top panels in each case trivially show the sample selection, with the high (low) subsets shown in red (blue), and the total sample in grey. The points represent

<footnote n="2">²but sometimes it does!</footnote>
<figure><img src="image_6.png" /><figcaption>**Figure 5.** Relationship between local indicators, shown as a density plot of the distribution of all spaxel data. The contours engulf (from the inside out) 25, 50, 75, and 90 per cent of all data points, starting from the regions of higher data point density.</figcaption></figure>

the median in each case, along with the standard deviation, shown as an error bar. The middle and bottom panels show the equivalent median and standard deviation of the 4000 Å break and the $H\delta_A$ line strength. The variation in the line strengths at fixed $\sigma$ is smaller than the corresponding one at fixed stellar mass, suggesting that stellar mass plays some role, but in a subdominant way with respect to velocity dispersion.

Previous studies aiming at the cause of the observed population trends within galaxies only conclude that stellar velocity dispersion is the most correlated variable with stellar populations (see e.g. Ferreras et al. 2019). However, one could argue that $\sigma$ is the measurement with the lowest intrinsic uncertainty – its derivation mainly depends on a comparison of many absorption lines in the spectrum of the galaxy with a smoothing kernel, and thus minimizes the potential systematics regarding the method. In contrast, stellar mass suffers from a more elaborate set of systematic effects that depend on the modelling of the stellar populations to infer a mass-to-light ratio. We reject radial distance as a major driver, as it suffers from relatively low measurement systematics, and the correlation coefficients are substantially lower than the other local measures (while correlation is not causation, we need a strong correlation to justify the cause). Fig. 7 compares the Pearson correlation coefficient and associated scatter of the running median (as presented in Table 1) of the trends between $D_n(4000)$ (top) or $H\delta_A$ (bottom) and stellar velocity dispersion. The horizontal axis corresponds to a parameter, $\Delta$ that represents the standard deviation of an extra component of random Gaussian noise added to each measure of velocity dispersion. As $\Delta$ increases, we expect the correlation to decrease. Such an experiment seeks to answer the following question: what type of additional random noise is needed to make the correlation of the population indices

with velocity dispersion comparable to that of the trends with stellar mass? For reference, the latter are marked with a horizontal dashed line. In all cases we find that Gaussian noise at the level $\Delta \sim 0.2$ dex can mimic the trends found. It is not uncommon to expect such an uncertainty in stellar mass estimates, although comparisons of independent methods suggest lower values, around $\lesssim 0.1$ dex (see, e.g. Santini et al. 2015; Dogruel et al. 2023; Pacifici et al. 2023). These uncertainties are mainly produced by the methodology, regarding template fitting, mismatch of targeted populations, photometric error, fitting of the total luminosity, etc. The additional error we need in velocity dispersion is on the high side to bring the observed correlations with $\sigma$ and $M_s$ in line. Therefore, we conclude that it may be possible to confirm $\sigma$ as the major driver of population properties, but unknown uncertainties in the stellar mass may also make this parameter a major driver. In any case, note that while $M_s$ and $\sigma$ are found in very different ways, the trends are fully consistent with the ansatz that local variables determine, statistically, the stellar population properties in galaxies.

## 5 A NOTE ON THE LINK WITH THE EVOLUTIONARY STAGE

Once we determine the potential main driver of population properties over small scales, a question remains regarding the connection with the general evolutionary stage, as posed by the well-established bimodality in colour (Strateva et al. 2001b), line strengths (Angthopo et al. 2019), and star formation rate (Speagle et al. 2014). A clear separation is found with regards to star formation activity, or lack thereof, along with a intriguing transitioning phase, the Green Valley,
<figure><img src="image_7.png" /><figcaption>**Figure 6.** Evolution of the median of 4000 Å break strength (middle) and $H\delta_A$ (bottom) as a function of velocity dispersion (left) or stellar mass (right). The whole sample is shown in grey, along with the subsets at low (25 percentile, blue) and high (75 percentile, red) of the distribution within each bin in $\sigma$ or log $M_s$. The points are the median values, whereas the error bars represent the standard deviation in each bin. The top panels illustrate the sample selection strategy.</figcaption></figure>

that encode the details of the feedback mechanisms that quench galaxy growth (see e.g. Salim 2014; Schawinski et al. 2014).

In this exercise, we focus on this evolutionary trend by adopting two classification schemes: one is the segregation into blue cloud (BC), green valley (GV) and red sequence (RS), as presented in Angthopo et al. (2019). In that paper, the selection is based on a bivariate plot formed by $D_n(4000)$ and velocity dispersion, measured in the SDSS Legacy spectra, measured in single 3 arcsec diameter fibres. A second scheme is based on the traditional BPT (Baldwin, Phillips & Terlevich 1981) diagram. Using once more the analysis from the SDSS Legacy (single fibre) spectra, as presented in the data products of Brinchmann et al. (2004), we separate galaxies into quiescent (Q), star forming (SF) and AGN.

Fig. 8 shows the distribution of spaxel data with respect to $\sigma$ for the three line strengths targeted in this paper. However, given that the classification method is based on the central spectra of galaxies, we restrict the sample to the outermost spaxels ($R>1.5R_e$). This allows us to explore the local properties of individual spaxels without introducing the obvious selection bias. The figure complements our previous results as the correlation remains in all cases. Unsurprisingly, the RS and Q data favours higher 4000Å break strengths and weaker Balmer absorption, along with higher [MgFe]'. The BC and SF sets mostly populate the regions expected by younger populations, whereas the GV and AGN live somewhere in between the two major cases of the bimodality. While this is an expected result, we should emphasize that these data correspond to spaxels outside of the regions where the selection was produced. Therefore, while we claim that sub-galaxy (around 2 kpc) scales drive the trends in the line strengths, the evolutionary stage (which is defined over galaxy scales) does

indeed affect the distributions. In other words, the outside spaxels 'know' they belong to a galaxy of a given evolutionary type.

Note also the interesting differences between both classification schemes (left versus right in Fig. 8). The RS sample does feature a substantial fraction of weak $D_n(4000)$ data at low $\sigma$, in contrast with the Q sample. Similarly, the AGN versus GV comparison also suggests a fraction of AGN that would not be classified as GV. Note that the BPT selection relates to substantially shorter time-scales (regarding the nebular emission of the diffuse gas), whereas the Angthopo et al. (2019) classification is based on the 4000 Å break, therefore associated to the longer time-scales of stellar evolution. The consistency confirms that the recent behaviour is statistically connected with those larger time-scales.

# 6 CONCLUSIONS

In this paper, we make use of the SDSS-IV MaNGA IFU data set (Bundy et al. 2015b) in a novel way: instead of exploring the data with galaxies as fundamental units, we adopt the ansatz that local properties – defined within each spaxel – determine the stellar population properties in a statistical way. Given that these properties relate to the star formation history, this claim goes beyond the standard framework, and provides an observational trend that any model of galaxy formation should be able to reproduce. Our sample involves 2024 high quality IFU datacubes of galaxies at redshift $0.05 < z < 0.1$ (median $z_M = 0.065$) from which we extract over one million spaxels, treated independently in this work, only to be related to quantities defined by the spaxels themselves. The analysis makes use of the Marvin data products (Cherinka et al. 2019).
<figure><img src="image_8.png" /><figcaption>**Figure 7.** The correlation coefficient (left) and standard deviation of the residual (right) is shown as Gaussian noise is randomly added to the measurement of stellar velocity dispersion. Two line strengths are considered: 4000 Å break (top) and HδA (bottom). As the noise level (Δ) increases, the correlation (standard deviation) decreases (increases). For reference, the values obtained for the relations with respect to stellar mass are shown as blue horizontal dotted lines.</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>**Figure 8.** Line strength plot for galaxies segregated with respect to the classification of Angthopo et al. (2019) (Left) or regarding nebular activity via the standard BPT diagram (Right). The data points correspond to individual spaxels in the outermost regions of the chosen galaxies (>1.5Re, S/N > 5).</figcaption></figure>

From the set of local properties considered, we find that local stellar velocity dispersion is the one with the strongest correlation, although the intrinsically low systematics may be the reason that it fares better than stellar mass of stellar mass surface density. Galactocentric radial distance is readily ruled out as a fundamental driver, as it consistently shows lower correlation coefficients and higher scatter. In light of this, one should consider that radial

gradients of galaxy properties are a consequence of radial variations in the local stellar velocity dispersion at different radii, a tracer of the gravitational potential. We also note that the dominant role of stellar velocity dispersion found in these data may parallel the strong trend between the central supermassive black hole mass and the velocity dispersion of the bulge (Ferrarese & Merritt 2000; Kormendy & Ho 2013). However, we should emphasize that
the strong correlation found in our data extends to the spaxels in the outermost regions (see Fig. 8), where the potential contamination from the bulge should be minimal, as illustrated in Appendix C.

Our results support and complement the suggestion of Sánchez et al. (2021) giving emphasis on sub-galaxy (~2 kpc) scales as dominant in the formation history of galaxies, with larger scales showing the equivalent of an integrated relation. Our analysis goes beyond short-time-scale relations, such as those probed by emission lines. The trends with respect to stellar populations depend on substantially longer time-scales and concern the star formation and chemical enrichment histories of galaxies. We also support the idea that galaxy-wide scales play some role, as suggested by Fig. 8, but the trends regarding smaller scales should be taken into account in any successful theory of galaxy formation.

Finally, it did not escape our attention that the correlations with line strength indicators are stronger than those with physical parameters such as age or metallicity, derived from population synthesis modelling. Given that the line strength measurements are observationally produced in an independent way to velocity dispersion, we propose that the model fitting process introduces a scatter that does not truly reflect the strong connection between star formation histories and local velocity dispersion.

## ACKNOWLEDGEMENTS

IF acknowledges support from the Spanish Research Agency of the Ministry of Science and Innovation (AEI-MICINN) under grant PID2019-104788GB-100. MT acknowledges the support of CNPq (process #307675/2018-1). OL acknowledges STFC Consolidated Grant ST/R000476/1 and a Visiting Fellowship at All Souls College and at the Physics Department, Oxford. RRdC acknowledges the support from FAPESP through grant 2020/16243-3. Funding for SDSS-III has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Science Foundation, and the U.S. Department of Energy Office of Science. The SDSS-III web site is http://www.sdss3.org/.

## DATA AVAILABILITY

This work has been fully based on publicly available data: galaxy spectra were retrieved from the SDSS DR17 archive and stellar population synthesis models can be obtained from the respective authors. The excellent MaNGA/Marvin database can be accessed at this link.

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to representative galaxies in the blue cloud, green valley, and red sequence, respectively. Each diagram includes as coloured dots the 4000 Å break strength with respect to stellar velocity dispersion, galactocentric distance (measured in fractions of the effective radius), and stellar mass surface density. Each panel also shows, as contours, the distribution of the total spaxel sample (i.e. the results of Fig. 2). For reference, a coloured stamp is included to the right of each set of panels, including in pink the footprint of the MaNGA IFU.

## APPENDIX A: DISTRIBUTION OF LINE STRENGTHS FOR INDIVIDUAL GALAXIES

We show in Fig. A1 the distribution of line strengths measured in a few galaxies from the sample. From left to right, they correspond

<figure><img src="image_10.png" /></figure>

**Figure A1.** Distribution of spaxel measurements of D<sub>H</sub> (4000) in a small selection of galaxies. A stamp of each galaxy is included for reference. The subset is colour coded regarding their identification – from Angthopo et al. (2019) – as blue cloud (left), green valley (middle) or red sequence (right).
## APPENDIX B: REDSHIFT DEPENDENCE

The redshift range of our working sample is $z \in [0.05, 0.1]$. The difference in lookback time between the extreme values of z is 0.6 Gyr, and represents 5 per cent of the age of the Universe at the median redshift. If we take the redshift distribution of the 1 million spaxels of the SN $> 5$ sample (assigning the redshift of the parent galaxy to each spaxel), we get a median redshift $z_M = 0.064$, with the lower (25 per cent) and higher (75 per cent) quartiles at $z_{Q1} = 0.057$ and $z_{Q4} = 0.077$. In order to assess the potential effect of a different

lookback time, we explore the 4000 Å break strength in two sets of spaxels selected in a narrow range of velocity dispersion. For each one, we study the running median of $D_n(4000)$ with respect to redshift. No trend is apparent (Fig. B1) in either set, although the lower $\sigma$ subset runs out of spaxels at higher redshift. Moreover, we show in Fig. B2 the equivalent of Fig. 2 for the 4000 Å break strength in the lowest redshift (lower panels, blue) and highest redshift (upper panels, red) quartiles. There is no substantial difference between the two subsets, confirming the lack of a redshift-dependent bias.

<figure><img src="image_11.png" /><figcaption>**Figure B1.** Running median of the 4000 Å break strength as a function of redshift for two subsets of spaxels, selected within a narrow range of velocity dispersion, as labelled.</figcaption></figure>
<figure><img src="image_12.png" /><figcaption>**Figure B2.** Equivalent of Fig. 2 for the 4000 Å break strength with respect to the chosen five local indicators. The sample is selected with respect to redshift, with the spaxels in the lower quartile shown in the lower panels (blue, 0.05<z<0.057) and the upper quartile shown in red in the upper panels (0.077<z<0.1).</figcaption></figure>

## APPENDIX C: CORRELATION IN THE OUTERMOST SPAXELS

One might argue that most of the results in this sample could be mainly caused by the stellar populations in the central regions, i.e. dominated in most cases by the bulge component. In fact, the dominant role of velocity dispersion may be reminiscent of the well-known correlation between supermassive black hole mass and the velocity dispersion of the bulge (Ferrarese & Merritt 2000). In this appendix, we show that the inherent trend cannot be simply ascribed to the bulge. Fig. C1 shows the equivalent of Fig. 2 for

the subset of spaxels at galactocentric distance $R \ge 5$ kpc (keeping the S/N threshold above 5). This subset comprises 460 203 spaxels, and the trends are consistent with the full sample – of course noting that, by construction, the range in galactocentric radii is restricted. In addition, we show in Table C1 the equivalent of Table 1 for these outermost spaxels. We conclude that neither the limited spatial resolution (PSF) nor the role of the bulge is significant in the trends found in this paper. Incidentally, note that the bimodality in the population indicators appears quite strongly at all of the outer radii, whereas the line strengths depend sensitively on the velocity dispersion.
<table><caption>**Table C1.** Correlation coefficients between stellar population line strengths and observables measured in an absolute way in spaxels with S/N ≥ 5 in the outermost spaxels (R ≥ 5 kpc, see fig C1).</caption><thead><tr><th>Index</th><th>σ</th><th>R</th><th>log M<sub>s</sub></th><th>log Σ<sub>M</sub></th><th>√σ<sup>2</sup> + v<sup>2</sup></th></tr></thead><tbody><tr><td colspan="6">Correlation coefficient</td></tr><tr><td>D<sub>n</sub>(4000)</td><td>+0.766±0.001</td><td>-0.193±0.001</td><td>+0.554±0.001</td><td>+0.534±0.001</td><td>+0.569±0.001</td></tr><tr><td>Hδ<sub>A</sub></td><td>-0.672±0.001</td><td>+0.193±0.001</td><td>-0.501±0.001</td><td>-0.510±0.001</td><td>-0.496±0.001</td></tr><tr><td>[MgFe]<sup>'</sup></td><td>+0.513±0.001</td><td>-0.205±0.001</td><td>+0.425±0.001</td><td>+0.421±0.001</td><td>+0.334±0.002</td></tr><tr><td colspan="6">Standard deviation (and 1σ error)</td></tr><tr><td>D<sub>n</sub>(4000)</td><td>0.18±0.03</td><td>0.29±0.01</td><td>0.24±0.03</td><td>0.24±0.03</td><td>0.22±0.04</td></tr><tr><td>Hδ<sub>A</sub></td><td>2.28±0.24</td><td>3.14±0.10</td><td>2.73±0.32</td><td>2.69±0.33</td><td>2.65±0.35</td></tr><tr><td>[MgFe]<sup>'</sup></td><td>0.91±0.06</td><td>1.05±0.05</td><td>0.96±0.06</td><td>0.96±0.07</td><td>0.97±0.07</td></tr></tbody></table>

<figure><img src="image_13.png" /><figcaption>**Figure C1.** Equivalent of Fig. 2 for the subset of the outermost spaxels, located at galactocentric radial distance R ≥ 5 kpc.</figcaption></figure>

This paper has been typeset from a TeX/LATEX file prepared by the author.