SDSS IV MaNGA: Dependence of Global and Spatially Resolved SFR–M_∗ Relations on Galaxy Properties

The advent of the MaNGA survey (Bundy et al. 2015; Law et al. 2015; Yan et al. 2016a), which spatially resolves stellar and gas properties, offers an excellent opportunity to examine the Hα–M_* relation. MaNGA is part of the fourth generation of the Sloan Digital Sky Survey (SDSS-IV; Gunn et al. 2006; Blanton et al. 2017) and aims to obtain the spatially resolved spectroscopy of 10,000 galaxies with median redshift ∼0.03 by 2020. Further details on the MaNGA sample selection can be found in Wake et al. (2017). MaNGA has a wavelength coverage of 3600–10300 Å, with a spectral resolution varying from R ∼ 1400 at 4000 Å to R ∼ 2600 around 9000 Å (Smee et al. 2013; Yan et al. 2016b). MaNGA uses five different types of IFU, ranging in diameter from 19 (125) to 127 fibers (325). The IFUs are installed in six SDSS cartridges. Each MaNGA cartridge has 17 science IFUs¹⁵ and 12 seven-fiber IFUs for calibration. The IFU sizes and the number density of galaxies on the sky were designed jointly to allow more efficient use of IFUs (e.g., to minimize the number of IFUs that are unused due to a tile with too few galaxies), and to allow us to observe galaxies in the redshift range to at least 1.5 effective radii (Drory et al. 2015; Wake et al. 2017).

This study draws data from the fourth MaNGA Product Launches (MPL-4), corresponding to SDSS DR13 (Albareti et al. 2017). The observational data was reduced using the MaNGA data-reduction-pipeline (DRP; Law et al. 2016).

The reduced spaxel-wise data cubes were analyzed using the Pipe3D pipeline to extract the physical parameters from each of the spaxels in each galaxy. Pipe3D fits the continuum with stellar population models and measures the nebular emission lines. Details of the procedures and uncertainties of the process are described in Sánchez et al. (2016a, 2016b) and Sanchez et al. (2017).

We briefly summarize the fitting of stellar continuum and the derivation of emission line flux here. The stellar continuum was first modeled using a simple-stellar-population (SSP) library with 156 SSPs, comprising 39 ages and 4 metallicities (Cid Fernandes et al. 2013; Sánchez et al. 2016b). Before the fitting, spatial binning is performed to reach a signal-to-noise ratio (S/N) of 50 across the field of view. Then the stellar population fitting was applied to the coadded spectra within each spatial bin. Finally, the stellar population model for spaxels with continuum S/N > 3 is derived by rescaling the best-fitted model within each spatial bin to the continuum flux intensity in the corresponding spaxel. The stellar mass is obtained using the stellar populations derived for each spaxel, then normalized to the physical area of one spaxel to get the surface density (Σ_*) in units of M_☉ kpc⁻². The stellar mass per spaxel is also coadded to derive the integrated stellar mass of the galaxies (M_*(global)).

The stellar population models are subtracted from the data cube to create an ionized gas emission line cube (with noise). The emission line fluxes were measured spaxel by spaxel. The SFR was derived using the Hα emission line. It is again possible to compute the total Hα luminosity (Hα(global)) and SFR (SFR(global)) by integrating the spatially resolved quantities over spaxels. The integrated Hα luminosity was derived using the Hα fluxes for all the spaxels with S/N > 3.

To study the effect of non-star-formation-powered Hα on the Hα–M_* relation, we use a set of emission line ratios to spatially distinguish the ionization mechanisms of Hα in galaxies (see Section 3.2). To ensure reliable emission line ratios, we also limit the spatially resolved analysis to spaxels¹⁶ with S/N(Hα), S/N(Hβ), S/N([O iii]), and S/N([N ii]) > 3. The fluxes are converted to luminosities and corrected for extinction. The method described in the Appendix of Vogt et al. (2013) is used to compute the reddening using the Balmer decrement at each spaxel of the IFU cube. The extinction-corrected Hα luminosity is converted into SFR surface density (Σ_SFR in M_☉ yr⁻¹ kpc⁻²) using the empirical calibration from Kennicutt (1998) that adopts the Salpeter IMF.

Inclination correction is applied to the Hα luminosity and stellar mass of all spaxels of a galaxy equally. The galaxy inclination measured by the disk ellipticity in Simard et al. (2011) is adopted (see the next section). Such a correction is based on the assumption of thin disks, whereas for round bulges or more spheroidal galaxies it may systematically overestimate the effect of projection and thus underestimate the Hα luminosity and stellar mass. However, we also note that the correction does not affect the sSFR related quantities since it is applied to both Hα luminosity and stellar mass.

MaNGA galaxies are selected to have spectroscopic coverage to 1.5–2.5 effective radii (R_e). The exact range varies from galaxy to galaxy. The mean offset between the Pipe3D M_*(global) and the aperture-corrected NSA¹⁷ stellar mass is 0.07 dex, corresponding to the difference between the adopted cosmologies and the differences in IMFs. We then assume that the aperture effect has a minimal impact on the stellar mass. To estimate how much of the SFR in a galaxy may be unaccounted for due to the finite fiber aperture, we assume that Hα follows a simple exponential profile out to infinite radius. The disk exponential profile in the r-band of each galaxy derived by Simard et al. (2011) is adopted. We estimate the total SFR out to infinite radii and SFR inside the MaNGA IFUs for all galaxies, and find that most of the star formation (on average, 84 ± 15%) occurs within the MaNGA IFUs. In light of this, we assume that the aperture effect does not significantly affect the SFR measurement as well.

MaNGA targets galaxies in the redshift range 0.01 <z < 0.15 (Wake et al. 2017). Since the spatial resolution is different across the sample, we repeat the analysis in this work by using the subsamples selected by distance. The main results are not severely affected by the varying physical size of spaxels.

Galaxy structural parameters are taken from the bulge–disk decomposition catalog from Simard et al. (2011). Simard et al. (2011) perform the two-dimensional bulge and disk decompositions using the GIM2D software package (Simard et al. 2002) on the g-band and r-band images of SDSS DR7 galaxies. In the model, the bulge Sérsic index (n) is treated as a free parameter and the disk component has n = 1. Structural parameters measured in the r-band are used in this work. We use the bulge-to-total light ratio (B/T) as a proxy for bulge dominance. The bulge and disk regions are separated by the radius at which 50% of the light is contributed by the bulge and disk component respectively. Specifically, for each galaxy, we look for the intersection of the one-dimensional fractional r-band Sérsic profile of the bulge and the exponential profile of the disk. It must be noted that the radius does not indicate the physical size of the bulge, but the boundary of the bulge-dominated and the disk-dominated regions.

The sample has been selected to only include galaxies that have measurements from both Pipe3D and Simard et al. (2011). With this requirement, 1037 out of ∼1400 galaxies in MPL-4 are left.

Figure 1 shows the Hα(global)–M_*(global) relation using total Hα luminosity and M_* of galaxies. The small circles present the individual galaxies color-coded by B/T from white to black. The dashed lines denote log(sSFR/yr⁻¹) of −9.5, −10.5, and −11.5 (from top to bottom). As reported in the literature, galaxies populate two distinct sequences, with a clear separation between star-forming and quiescent galaxies.

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To characterize the dependence of the Hα(global)–M_*(global) relation on B/T and M_*(global), we binned the galaxies by these two quantities. Big circles are the median values of Hα(global) of the whole sample in different M_*(global) bins, colored according to B/T (following the scheme of Figure 2 in Whitaker et al. 2015). The discontinuity in the median values of Hα(global) at log(M_*(global)/M_⊙) ∼ 10 is caused by a decreasing number of quiescent targets on the low-mass end.

As has been noticed by many authors (e.g., Wuyts et al. 2011), the sequence with a lower Hα(global)-to-M_*(global) ratio, i.e., lower sSFR(global), is occupied prevalently by bulge-dominated galaxies (B/T ≥ 0.2), whereas the star-forming sequence is composed of all populations (but note that disk-dominated galaxies with B/T < 0.2 appear to be almost exclusively star-forming galaxies). A flattening of the lower-B/T galaxies (∼0.2) at log(M_*(global)/M_⊙) > 11 is observed. This has been explained as the increasing fraction of the mass being given by bulges that have begun to quench, indicating a transition from disk- to bulge-dominated properties.

The spatially resolved Σ_Hα and Σ_* maps of MaNGA allow us to probe the driver of the Hα(global)–M_*(global) relation in more detail. Figure 2(a) presents the inclination-corrected spatially resolved Σ_Hα(all)–Σ_*(all) relation using all spaxels of galaxies. The galaxies are binned by their M_*(global) and B/T: from the upper left to the bottom right subpanel, galaxies go from disk-dominated to bulge-dominated. The number of galaxies in each bin is indicated in the upper left corner. Bulge and disk regions are shown by red and blue contours, respectively. The number of spaxels in each subpanel ranges from ∼900 to 39,000 for the bulge and ∼6500 to 70,000 for the disk.

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For galaxies with log(M_*(global)/M_⊙) < 10, bulge and disk lie along a similar Σ_Hα(all)–Σ_*(all) relation. As the stellar mass increases to 10 < log(M_*(global)/M_⊙) < 11, the high-mass ends of the bulge sequence start to move downward (i.e., decrease in the Σ_Hα(all)-to-Σ_*(all) ratio). The decrease is more pronounced in the high-B/T galaxies than in the low-B/T galaxies. In the most massive galaxies (log(M_*(global)/M_⊙) > 11), the entire bulge sequence drops below the relations of the lower-mass objects. Meanwhile, the disk sequence also shows a slight drop in the Σ_Hα(all)-to-Σ_*(all) ratio at the log(M_*(global)/M_⊙) and B/T values above 10 and 0.4, respectively (lower-right subpanel). The combination of these leads to the high-M_*(global) and/or high-B/T systems being pulled off the main sequence on the integrated Hα(global)–M_*(global) plane. Such turnover also indicates the inside-out quenching of galaxies. The quenching process is beyond the scope of the present paper, but is of major importance in the context of galaxy evolution (e.g., Li et al. 2015; González Delgado et al. 2016; Belfiore et al. 2017; Lin et al. 2017; Spindler et al. 2017; Ellison et al. 2018).

We now turn our attention to the powering source of Hα. It is known that massive stars are not the only sources capable of providing ionizing photons. To disentangle different powering sources, we use the emission line ratio diagnostics, the BPT diagram (Baldwin et al. 1981) and Hα equivalent width (EW) to spatially identify the regions ionized by different physical processes in each galaxy. The emission line regions are classified into star-forming H ii regions, LI(N)ER, Seyfert, and composite regions (mix of multiple sources) based on their locations on the [O iii] 5007/Hβ versus [N ii] 6584/Hα plane (Kewley et al. 2001; Kauffmann et al. 2003; Cid Fernandes et al. 2010). In addition, the criterion of EW > 6 Å is also applied when selecting star-forming regions (Sánchez et al. 2014; Sanchez et al. 2017).

Armed with the spatially resolved ionization sources of each galaxy, we use the identified H ii spaxels to construct the Σ_Hα(H ii)–Σ_*(H ii) relation driven by star formation alone. The result is presented in Figure 2(b). For the star-forming regions, Σ_Hα(H ii) and Σ_*(H ii) are much more tightly correlated than that including all ionized regions of the galaxies. Moreover, the bulge sequence shifts upward to be close to that of the disk. In other words, at least for the star-forming regions, the Σ_Hα(H ii)-to-Σ_*(H ii) ratio of bulge and disk, which is proportional to the local sSFR, do not differ significantly from each other. In light of this, the turnover seen in the Σ_Hα(all)–Σ_*(all) relation can be attributed to non-H ii regions; moreover, the non-H ii ionizing sources tend to generate lower Hα luminosity than that of star-forming regions and the difference can vary by up to an order of magnitude. Therefore, the total Hα luminosity of a galaxy strongly depends on the relative proportion between H ii and non-H ii regions.

Another notable feature in Figure 2(b) is the lack of H ii spaxles toward higher masses and higher B/T. The number fraction of galaxies with H ii spaxels relative to the total number of galaxies in each bin is given in the upper left corner of each subpanel. The fraction is generally inversely correlated with M_*(global) and B/T, suggesting a decreasing role of star formation as an ionizing source toward high-mass and high-B/T galaxies.

The box plots in Figure 3 describe the distribution of the fraction of non-H ii contribution in the total Hα luminosity of a galaxy (f_{non-H ii}) in different M_*(global) bins. Three columns from the left, respectively, present the fraction of Hα contributed by composite, LI(N)ER, and Seyfert, respectively, e.g., in the left-most column, f_{non-H ii} = Hα(composite)/Hα(global). The green line drawn across the box is the sample median. The ends of the box are the upper and lower quartiles (the interquartile range, IQR), i.e., 50% of the sample is located in the box. The two whiskers (vertical lines) outside the box extend to 1.5 × IQR, i.e., 99% of the sample is inside the caps of the whiskers. In the following paragraphs, we will discuss f_{non-H ii} as a function of M_*(global), B/T, and galactic substructures.

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Figure 3(a) presents the dependence of f_{non-H ii} on the bulge dominance, B/T. The upper and lower rows show the results for B/T < 0.2 and >0.2, respectively. Several features are readily apparent. Most notably, the (nonzero) median f_{non-H ii} increases in general with increasing M_*(global) in both populations, suggesting that the non-H ii sources become more important with increasing M_*(global) (see also Catalán-Torrecilla et al. 2017). For some M_*(global) bins, the median and the whiskers are subsumed in a single location due the large number of galaxies with small f_{non-H ii}.

Moreover, in the bulge-dominated galaxies, the non-H ii contribution is exclusively dominated by LI(N)ER, whereas the three mechanisms all make a certain contribution, but typically lower than LI(N)ER in the high-B/T galaxies, in the disk-dominated galaxies. This originates from the fact that the old stellar population, such as post-AGB stars, have become the main source of ionizing photons after star formation has ceased (Yan & Blanton 2012; Singh et al. 2013; Belfiore et al. 2016; Hsieh et al. 2017). As a whole, the rightmost column shows that f_{non-H ii} increases from less than a percent for log(M_*/M_⊙) < 10 to a few to several tens of percent at log(M_*/M_⊙) > 10. Besides, high-B/T galaxies generally display a higher, or just comparable, median f_{non-H ii} to the low-B/T galaxies over the entire range of masses.

Figure 3(b) explores the dependence of f_{non-H ii} on sub-galactic regions. The upper and lower rows show the disk and bulge regions, respectively. Bulges generally exhibit a higher fraction of non-H ii contribution than the disks, and the nonzero median f_{non-H ii} increases with increasing M_*(global). When accounting for all non-H ii mechanisms (the rightmost column), median f_{non-H ii} is no higher than 20% (mostly below 10%) for disks across all stellar mass bins, and increases to several tens of percent in bulges when log(M_*/M_⊙) exceeding 10. The result is consistent with the study based on a 2D spectral decomposition of the bulge and disk component (Catalán-Torrecilla et al. 2017). The high f_{non-H ii} of the bulge is presumably due to the fact that the non-H ii sources (e.g., AGNs, evolved stars, and shocks) are naturally found most often in this old central component. The above-mentioned characteristics echo the turnover feature of the bulge Σ_Hα(all)–Σ_*(all) relation toward higher masses and higher B/T in Figure 2(a).

How does the integrated Hα–M_* relation look after excluding the non-H ii contribution? Figure 4 shows the integrated Hα(H ii)–M_*(H ii) relation in panel (a), the Hα(H ii)–M_*(global) relation in panel (b), and the traditional Hα(global)–M_*(global) relation in panel (c) (same as in Figure 1), where Hα(H ii) and M_*(H ii) represent Hα and M_* integrated over only H ii spaxels in galaxies. Symbol styles and colors are the same as in the Figure 1. We note here that the Hα(H ii) distribution could become highly skewed if there are extreme values, such as a value of zero. In this case, the standard deviation, which is shown as error bars here, would become meaningless. This only affects Figure 2(b), so the error bars are thus omitted in this plot.

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Figure 4(a) represents the integrated relation for star-forming regions. When only looking at star-forming regions, the Hα(H ii)–M_*(H ii) relation shows a relatively tight sequence. The figure is simply an integrated version of Figure 2(b). As noted before, the spatially resolved relations become similar for the bulge and disk when accounting for only star-forming regions. This leads naturally to the tight and close to linear correlation in the integrated Hα(H ii)–M_*(H ii) relation.

We now shift our focus to the Hα(H ii)–M_*(global) relation in Figure 4(b). For reference, the traditional Hα(global)–M_*(global) relation is displayed in Figure 4(c). The most noticeable feature in Figure 4(b) is the emergence of galaxies with low Hα(H ii)-to-M_*(global) ratios (lower than the Hα(global)-to-M_*(global) ratios of quiescent galaxies in the traditional relation). This population is largely comprised of the quiescent galaxies, which are dominated by non-H ii regions. Note that since a significant fraction of the highest-B/T and highest-mass galaxies have little to no Hα from star formation, the median Hα(H ii) of these populations drops to close to zero.

It is also worth noting that the strong sequence of quiescent galaxies observed in the traditional relation becomes scattered in the Hα(H ii)–M_*(global) relation; no clear scaling relation is found between Hα(H ii) and M_*(global) for this population. Such a lack of bimodality in the SFR distribution at a given stellar mass is very similar to that using the SSP-based SFR by González Delgado et al. (2016) and using MAGPHYS¹⁸ rather than based on Hα by Eales et al. (2018).

Thus what processes fundamentally drive the two strong sequences in the traditional Hα(global)–M_*(global) relation in Figure 1? From left to right, the four panels in Figure 5, respectively, present the Hα luminosity integrated over star formation spaxels (same as Figure 4(b)), composite spaxels, LI(N)ER spaxels, and Seyfert spaxels against M_*(global). The high Hα-to-M_* ratio regime is heavily populated by star formation, while other mechanisms occupy the low ratio regime. The Hα(composite)–M_*(global) and Hα(Seyfert)–M_*(global) relations show relatively large scatter for a given M_*(global), on the other hand, Hα(LI(N)ER) and M_*(global) appear to be more tightly correlated to each other. The relation is very similar to the quiescent population in the traditional Hα(global)–M_*(global) relation. In other words, Hα powered by LI(N)ER is directly correlated with the underlying stellar mass. This has been explained as the hot, evolved stars as the dominant mechanism powering the Hα emission in quiescent galaxies (e.g., Belfiore et al. 2016; Hsieh et al. 2017). Our Figure 3 is also in line with this scenario.

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Finally, we remind the reader that the non-H ii spaxels are not necessarily devoid of star formation, but are simply dominated by mechanisms other than star formation. That is to say, the Hα(global)–M_*(global) relation and the Hα(H ii)–M_*(global) relation represent bracketing scenarios, as the true SFR of the galaxies would be found between Hα(H ii) and Hα(global). Moreover, the flatting (or turnover) of the integrated SFR–M_* relation would become more pronounced as we move from the traditional integrated SFR(global)–M_*(global) relation to the true SFR versus M_*(global) relation.