Unique Tracks Drive the Scatter of the Spatially Resolved Star Formation Main Sequence

There exists a multitude of transformations to infer SFRs in galaxies. These are typically based on UV spectrum slopes, Hα and far-infrared (IR) fluxes, and more (see Kennicutt 1998b; Calzetti 2013; Davies et al. 2016 for a review). These derivations can generally be traced back to motivation by the star formation (or K-S) law, which describes the SFR dependency on the total gas density and photo-reionization models (Schmidt 1959; Kennicutt 1998a, 1998b), though varying ranges of SFRs can be obtained. This variation stems from the use of different wavebands, stellar population models, initial mass functions (IMFs), dust absorption models, and so on applied to each calibration (e.g., Kennicutt 1983). In principle, one single SFR ought to characterize a particular region over a given timescale; the source of SFR differences is also examined below.

The most common transformation is that of Kennicutt (1998b, hereafter K98), where the Hα emission line flux becomes a tracer of instantaneous star formation. This emission arises from ionized hydrogen surrounding a newly formed star, re-emitting the light produced by the young star. This proxy for SF applies to short timescales of ≲20 Myr, as only massive (O and B) stars with those ages can heat the gas to suitable temperatures (K98; Davies et al. 2016). Assuming a Salpeter IMF, the SFR conversion is

$\begin{eqnarray}&&{\mathrm{SFR}}_{{\rm{K}}98,{\rm{H}}\alpha }({M}_{\odot }\,{\mathrm{yr}}^{-1})=7.9\times {10}^{-42}\,{L}_{{\rm{H}}\alpha }(\mathrm{erg}\,{{\rm{s}}}^{-1}).\end{eqnarray} \tag{ 1 }$

The largest limitation of this method is accounting for extinction in the Hα emission, which is specific to the environment of study K98.

Young stars also emit copious amounts of ultraviolet photons, which can be absorbed by dust and re-emitted at mid-infrared (MIR) wavelengths, making that light another reliable tracer of SF (Cluver et al. 2014, hereafter C14). The process of light absorption and re-radiation is slow and MIR fluxes typically trace SF over longer timescales of ∼100 Myr. Cluver et al. (2017, hereafter C17) have developed two SFR conversions motivated by a Kroupa IMF for the WISE W3 (12 μm) and W4 (23 μm) bands:

$\begin{eqnarray}&&\mathrm{log}({\mathrm{SFR}}_{{\rm{C}}17,W3}/{M}_{\odot }\,{\mathrm{yr}}^{-1})=0.889\,\mathrm{log}({L}_{W3}/{L}_{\odot })-7.76,\end{eqnarray} \tag{ 2 }$

$\begin{eqnarray}&&\mathrm{log}({\mathrm{SFR}}_{{\rm{C}}17,W4}/{M}_{\odot }\,{\mathrm{yr}}^{-1})=0.915\,\mathrm{log}({L}_{W4}/{L}_{\odot })-8.01.\end{eqnarray} \tag{ 3 }$

If the light is not fully re-radiated, these formulae may actually underestimate the true SFR. The W4 conversion (23 μm; Equation (3)) may be preferable over the W3 (12 μm; Equation (2)) conversion, as the latter lies within the regime of emission from excited polycyclic aromatic hydrocarbon (PAH) molecules (Jarrett et al. 2013), and therefore has a more complex mapping to SFR. The W4 transformation, which lies beyond the bulk of PAH emission, is therefore favored here. Rosario et al. (2016) compared the corresponding W4 SFRs to those derived from optical tracers (i.e., Hα) in star-forming galaxies and found comparable agreement. Caution is offered for survey galaxy selections motivated by the W4 band emission, which may bias the analysis toward warm dust regions, and valuable information from cold dust regions would be lost. Fortunately, our target selection was motivated by SINGG, and therefore HIPASS, which is sensitive to H i emission and unbiased by warm dust.

Yet another SFR transformation by Calzetti et al. (2007, hereafter C07) capitalizes on both Hα and MIPS 24 μm to account for dust obscured and unobscured SF environments, in order to produce robust SFR estimates over short and long timescales. Therefore, this calibration should hold over all scales across a galaxy. The hybrid conversion adopts a Kroupa IMF from Starburst99:

$\begin{eqnarray}&&\begin{array}{l}{\mathrm{SFR}}_{{\rm{C}}07,{\rm{H}}\alpha +24\mu {\rm{m}}}({M}_{\odot }\,{\mathrm{yr}}^{-1})=5.3\times {10}^{-42}\,[{L}_{{\rm{H}}\alpha }(\mathrm{erg}\,{{\rm{s}}}^{-1})\\ \qquad \quad +\,0.031* {L}_{\nu ,24\mu {\rm{m}}}(\mathrm{erg}\,{{\rm{s}}}^{-1}\,{\mathrm{Hz}}^{-1})].\end{array}\end{eqnarray} \tag{ 4 }$

This conversion is calibrated to the MIPS 24 μm band, which differs slightly from the W4 band; see Figure 2 of Brown et al. (2014). Since these band responses are reasonably consistent, this conversion should be applicable to W4 luminosities, although the differences should be in the sense that SFRs will be slightly underestimated using the W4 band. Fortunately, the overall W4 contribution in this conversion is small, so the impact is arguably negligible.

Calzetti (2013) presents a thorough review and comparison of the many SFR indicators available, examining their motivating physics, unique advantages, and applicable scales. At large scales, single emission line tracers are most reliable under low attenuation conditions. However, as dust contributions increase, as is common in SF galaxies, then a hybrid combination of Hα and 24 μm compensates for any attenuated line emission, by accounting for re-radiated dust emission at 24 μm (see also, Lee et al. 2013). On increasingly small scales and therefore regions of lower SFR, such indirect tracers become increasingly vulnerable to regions without SF that still emit such light. Across all SFR tracers, the generalization of underlying stellar populations and IMFs that occurs on large scales is likely no longer appropriate. This highlights the complexity and increased vulnerability of tracers at the local, resolved scale. Overall, while each tracer has its own strengths or weaknesses, especially at low SFR regimes, emission line tracers may be the least vulnerable to underlying stellar population assumptions due to the short SF timescales (Calzetti 2013).

Figure 1 compares SFR transformations for both local (orange) and integrated (blue and green) measurements. While global values display some scatter, it is considerably smaller than for local measurements. Innate scatter is expected by the nature of each transformation and the specific SF conditions and timescales of their corresponding tracer represents. However, the increased scatter from global to local values is significant and must be understood. The conversions by C07 (Equation (4)) and C17 (W4, Equation (3)) produce the most consistent SFRs, while the former transformation has the highest overall agreement among all SFR transformations. This could be due to the fact that Hα and W4 are also in the K98 and C17, though despite the dominant contribution of Hα in C07, there is greater consistency with the W4 C17 conversion. The above calibrations, and their impact on the SFMS, are compared in Section 5 in order to isolate the variations in SFR estimates from different tracers. The C07 transformation (Equation (4)) is favored in this analysis since it utilizes both Hα, which remains stable across varying stellar populations, and W4 emission, which accounts for dust attenuation effects.

Zoom In Zoom Out Reset image size

Catalán-Torrecilla et al. (2015) and Davies et al. (2016) also compare different SFR tracers and calibrated transformations. Their calibrations are constructed from CALIFA (Calar Alto Legacy Integral Field sepctroscopy Array) survey and GAMA (Galaxy and Mass Assembly) measurements, respectively. Catalán-Torrecilla et al. (2015) calibrated Hα, UV and TIR based transformations, including hybrid combinations of these bands. Using Hα SFRs as the standard to calibrate to, the resulting SFRs from UV and TIR luminosities (or hybrid combinations) are matched to the standard with minimized scatter. The Davies et al. (2016) analysis accounted for Hα, W3, and W4 bands as SFR tracers, along with [O ii] emission, near and far-ultraviolet, u-band, 100 μm, infrared, and spectral energy distribution fitting. Unique to this study, they examined the consistency of the resulting SFR estimates from each method and their effect on the SFMS. Assuming that SFRs should be the same regardless of the transformation (though this should be cautioned against, as SFRs are dependent on the representative timescale of that tracer), they use SFR calculation discrepancies and SFMS fits to propose revised SFR calibrations for each tracer that ultimately produces SFRs and a SFMS with highest fidelity. The reported hybrid calibration with Hα and W4 by Catalán-Torrecilla et al. (2015) is consistent with the C07 calibration (Equation (4)); the revised calibrations by Davies et al. (2016) are unique. In Section 5, the Davies et al. (2016) calibrations are applied to our data and interpreted in the context of measurements external to the GAMA survey.

Stellar masses can be derived through multiple methods; these include color to mass-to-light ratio relations (CMLRs), multiband SED fitting, or straight band flux to stellar mass transformations. Each method takes advantage of specific wavelengths, and this study capitalizes on the availability of the WISE 3.4 μm and 4.6 μm bands. Jarrett et al. (2013) advocate the advantage of near-infrared light since low mass; evolved stellar populations dominate the emission in that wavelength range and comprise most of a galaxy's stellar mass. With the appropriate IMFs and M_*/L range, the total stellar mass in a region can be determined from this IR light.

CMLRs have been widely studied, especially for optical bands (Taylor et al. 2011; Roediger & Courteau 2015; Zhang et al. 2017). Optical M_*/L rise with color and dust emission effects are feeble in this wavelength regime. Both Taylor et al. (2011) and Roediger and Courteau (2015) have shown that optical colors result in strongly linear relations since degeneracy from dust, age, or metallicity scatter along the relation, rather than away it. They use SED fitting (though with different algorithms) to derive stellar masses and extract CMLRs. Roediger and Courteau (2015) emphasize, however, that the reliability of M_* estimates improves with the number of bands utilized, thus favoring SED fitting.

An increase in dust emission in SF galaxies translates to a reddening of MIR colors, with W1 − W2 > 0. This reddening is unlike that for optical colors from low-mass stars (which would correspond to increasing M_*/L_W1), whereas red MIR colors lower M_*/L_W1 as the light emission is largely dominated by dust (Querejeta et al. 2015). One must distinguish whether the detected emission has been corrected for dust effects in order to apply the appropriate calibration to stellar mass. MIR CMLRs are highly sensitive to dust and the presence of dust changes mechanisms driving the relation between the MIR color and M_*/L_W1. Such trends are demonstrated in Figure 2. If W1 − W2 > 0, dust is typically present. Although Wright et al. (2010) and C14 show in their Figures 12 and 5, respectively, that the range of W1 − W2 colors corresponding to spiral galaxies is roughly between −0.2 and 0.6, values exceeding W1 − W2 = 0.3 represent AGNs or starbursts and should be avoided (Stern et al. 2012, C14).

Zoom In Zoom Out Reset image size

These considerations are critical in seeking accurate stellar masses from the WISE (MIR) data. Before selecting a stellar mass transformation for this analysis, the methods utilizing the 3.4 and 4.6 μm bands, we first compare the methods that apply for the 3.4 and 4.6 μm bands. We enforce that each transformation caters to different galactic environments (E12, C14, M14) and note that these CMLR conversions can be applied only for a specific W1 − W2 color range.

The stellar mass conversion by C14 improves upon the preliminary WISE conversion by Jarrett et al. (2013). The original transformation was derived using a Charbrier-type IMF that takes into account general models of star formation histories, stellar population age and composition, dust content, and AGN activity. Improvements by C14 use in-depth calibrations of GAMA stellar mass estimates by Taylor et al. (2011) for more than 110,000 low redshift (z) galaxies. It represents a robust sampling of galactic environments, similar to our study. The conversion is meant to apply to "normal" galaxies and avoids warmer regions that may contain AGN or starbursting environments where the relation breaks down (beyond W1 − W2 = 0.3). Therefore strict color limits of −0.02 ≤ W1 − W2 ≤ 0.17 have been enforced. The proposed relation is

$\begin{eqnarray}&&\mathrm{log}{({M}_{* }/{L}_{W1})}_{{\rm{C}}14}=-0.17-2.54\times (W1-W2),\end{eqnarray} \tag{ 5 }$

where M_* is recovered from the resulting M_*/L_W1 by multiplying by the corresponding luminosity, ${L}_{W1}({L}_{\odot })={10}^{-0.4({M}_{W1}-{M}_{\odot })}$, where M is an absolute magnitude.

Eskew et al. (2012, hereafter E12) proposed an alternate form of a M_* conversion, directly calculated from W1 and W2 band fluxes. This transformation was derived by calibrating 3.6 and 4.5 μm fluxes to previously existing stellar maps of the Large Magellanic Cloud (LMC). The stellar mass maps by E12 were derived from the detailed star formation history (SFH) maps produced by Harris and Zaritsky (2009), who adopted a Salpeter IMF. With known SFHs, the uncertainty on resulting M_* is greatly reduced and strengthens the calibration.

Additionally, with the conversion being calibrated to spatially resolved stellar maps, it can be appropriately applied to the resolved regions of our spiral targets. Like the C14 relation, it has been calibrated over a wide range of environments, albeit increasing uncertainty in strongly SF (warmer) environments. The transformation is given as

$\begin{eqnarray}&&{M}_{{\rm{E}}12}^{* }({M}_{\odot })={10}^{5.65}\,{F}_{W1}^{2.85}(\mathrm{Jy})\,{F}_{W2}^{-1.85}(\mathrm{Jy})\,{\left[\displaystyle \frac{D(\mathrm{Mpc})}{0.05}\right]}^{2}.\end{eqnarray} \tag{ 6 }$

In order to compare this transformation with that of C14 (Equation (5)), we have recast Equation (6) using a similar notation as Equation (5) (see Appendix B):

$\begin{eqnarray}&&\mathrm{log}{({M}_{* }/{L}_{W1})}_{{\rm{E}}12}=-0.08-0.74\times (W1-W2).\end{eqnarray} \tag{ 7 }$

The appropriate color range for their transformation is not explicitly specified, though the limits can easily be calculated from their Figures 3 and 4. We estimate their limits to be −0.12 ≤ W1 − W2 ≤ 0.34. This is much broader than those reported by C14, as seen in Figure 2; however, the resulting M_*/L_W1 range remains physical. These limits just breach into the range of colors that may result from AGN and strongly SF environments (W1 − W2 > 0.3) that Stern et al. (2012) and C14 caution against. Although E12 did not derive this conversion specifically for the WISE bands, we argue that the 3.6 and 4.5 μm Spitzer bands are reasonably consistent with the 3.4 and 4.6 μm WISE bands. This calibration may thus be applied to WISE, as the respective bands trace the same behavior. A disadvantage of this calibration is the low-metallicity of to the LMC; thus the conversion mostly applies to similarly low-metallicity regions.

Meidt et al. (2014, hereafter M14) produced an alternate conversion using spatial maps of 2300 galaxies from the Spitzer Survey of Stellar Structure in Nearby Galaxies (S⁴G). These maps preserve the structural information that is necessary in our study of the spatially resolved SFMS. Their derivation involves fitting [3.6]–[4.5] μm colors to previously calculated M_*/L_3.6's that assume a Chabrier IMF, with a focus on resolving the age–metallicity degeneracy, which is not accounted for in the E12 study, yielding the relation

$\begin{eqnarray}&&\mathrm{log}{({M}_{* }/{L}_{W1})}_{{\rm{M}}14}=0.13+3.98\times (W1-W2).\end{eqnarray} \tag{ 8 }$

This calibration, however, requires first removing the contribution of "contaminants" from the detected emission, in order to isolate the old stellar populations. Such contaminants in the [3.6]–[4.5] μm range from hot dust emission, asymptotic giant branch stars to red supergiants. M14 outlines the procedure to eliminate such non-stellar emission by their "Independent Component Analysis" (ICA). To separate purely old stellar populations further, they restrict their study to regions with blue MIR colors, specifically −0.15 < [3.6]–[4.5] < −0.02. This is consistent with the W1 − W2 < 0 regime discussed previously for dust-corrected, old stellar populations. This method therefore applies to data sets where dust contributions to MIR emission have been eliminated.

M14 also demonstrate the vulnerability of stellar masses to the adopted IMF. For their preferred Chabrier IMF, they report an average constant M_*/L_W1 = 0.6; for a Salpeter IMF, M_*/L_W1 nearly doubles (1.07). Fortunately, the range of M_*/L_W1 for each transformation examined here is small and averages about 0.5. Figure 2 shows CMLRs based on both Chabrier (C14 and M14) and Salpeter (E12) IMFs; the resulting ranges in M_*/L_W1 show overall consistency.

Numerous studies have advocated for the characterization of a given galaxy stellar population composite by a constant M_*/L whose uncertainty encompasses any variations possibly accounted for by CMLRs. The commonly proposed range, M_*/L_W1 = 0.45−0.6 (E12, M14, Norris et al. 2014; McGaugh & Schombert 2015; Kettlety et al. 2018; Ponomareva et al. 2018). For instance, Kettlety et al. (2018) compared stellar masses from SED fits and CMLRs with those derived from a constant M_*/L_W1, and found matching results. The constant value of M_*/L_W1 = 0.5 shown in Figure 2 is clearly a good match to the applicable color range and consistent within the uncertainty associated with stellar mass approximations.

The upper panel of Figure 3 demonstrates the consistency of various M_*/L methods, despite the varying MIR color ranges and M_*/L_W1 trends (Figure 2) among common transformations. Here, stellar masses are compared for regions where the MIR color is appropriate for both M_* transformations. Although the scatter about the one-to-one line (in black) is non-negligible, it is quite minimal compared to the uncertainty associated with such transformations. This comparison of stellar mass estimates is similar to that of Drory et al. (2004), and we observe a similar degree of scatter.

Zoom In Zoom Out Reset image size

Interestingly, the increased discrepancies that arise in SFR estimates when calculating resolved local values versus total galactic values (Figure 1) do not hold for stellar mass estimates. Figure 3, which compares M_* values from each method, demonstrates that total integrated M_* values (in blue), M_* values integrated out to R_eff (in green), and resolved local M_* values (in orange) show a tight correlation with the one-to-one line, with no increased scatter in local values. The constant scatter for local and global values is emphasized in the lower panel of Figure 3, suggesting that the increased scatter in the local SFMS (Section 5.2) would be dominated by scatter in SFRs or local processes rather than from stellar masses. The consistency among stellar masses integrated out to R_eff and total integrated values demonstrates that, despite a slight shift between those two, there is no significant growth in M_* beyond R_eff. Therefore global M_* measurements are likely dominated by the inner regions of a galaxy.

In this latter figure, sharp colors limits are imposed in accordance with the M_* transformation. Within those regions, the stellar mass estimation methods are clearly consistent. However, beyond these color limits, the physical environments, involving starbursts and AGN activity, are less well constrained, and so are the M_* estimates. Such regions are excluded from our study, and hence sharp residual limits are seen in Figure 3.

Since we do not correct for dust emission, dust free and dust polluted regions could potentially be blended. The W1 − W2 colors in each region may serve as an indicator for such emission; if W1 − W2 < 0, the dust contribution is likely minimal and the M14 transformation should be applied. Conversely, if W1 − W2 > 0, then dust is likely contributing some of the emission, and either E12 or C14 can be applied.

Such uncertainty justifies the use of a constant M_*/L_W1 ratio (M14; Norris et al. 2014; Lelli et al. 2016; Kettlety et al. 2018; Ponomareva et al. 2018). Figure 3 highlights that a constant M_*/L_W1 produces fairly consistent stellar masses with all three transformations and appropriate MIR color range. Though stellar masses may be slightly underestimated compared to the E12 and M14 transformations, the resulting values are nonetheless consistent with those estimated in other studies, such as González Delgado et al. (2016) or Ellison et al. (2018; see Figure 6). This study traces considerably more low-mass systems than CALIFA or MaNGA, which are limited to log(M_*,tot/M_⊙) > 9; the upper limits in stellar mass are consistent (Walcher et al. 2014; Ellison et al. 2018). Additionally, the constant M_*/L_W1 is not limited by color range. For this reason, we adopt a constant M_*/L_W1 = 0.5 for our M_* estimates across the full range of colors.

We have tested for other conversions and obtained statistically consistent SFMS results for the various stellar masses and SFRs (compare Tables 1 and 2).

The global SFMS is calculated using total integrated values for each galaxy, which are determined from total enclosed SINGG and WISE measurements integrated out to the same, matched radius. Multiple transformations were examined, as outlined in Section 3. Figure 6 displays the SFMS constructed with stellar masses using a constant M_*/L_W1 = 0.5 and SFRs from the C07 transformations (Equation (4)). Refer back to Sections 3.1 and 3.2 for the motivation for these transformations. The E12 and C14 M_* transformations yield essentially the same results (see additional SFMS results in Appendix C).

Zoom In Zoom Out Reset image size

The top panel of Figure 6 shows the SFMS integrated values are overlayed in blue and green. Local values, plotted in orange in the bottom panel, will be discussed in Section 5.2. The blue points represent the total integrated measurement out to the maximum radius of detection, while green dots are measurements integrated out to R_eff. The blue and green sequences are roughly the same (a_blue = 0.84 vs. a_green = 0.84, b_blue = −8.92 vs. b_green = −8.81, and σ_blue = 0.30 vs. σ_green = 0.29), demonstrating that regions beyond R_eff do not considerably affect the global SFMS, and the choice of maximum radius has minimal impact on the global SFMS. In Sections 5.2 and 6 we will compare the SFMS in inner and outer regions. The strong positive linear correlation in the global SFMS already reported by others (e.g., Noeske et al. 2007; Speagle et al. 2014; Salmon et al. 2015) is reproduced here with SINGG and WISE data. Linear fits to the SFMS with the equation $\mathrm{log}(\mathrm{SFR})=a\mathrm{log}({M}_{* })+b$ using different SFR and M_* transformations are listed in Table 1, and the global fit is overlayed in solid black in Figure 6.

Our measured slopes (a), ranging from about 0.8 to 1.1, are consistent with those reported by Noeske et al. (2007), Wuyts et al. (2011), Speagle et al. (2014), and Tomczak et al. (2016), accounting for evolutionary factors, excluding fits with the re-calibrated Hα and W4 SFR transformations by Davies et al. (2016). The wider range of slopes in Speagle et al. (2014) is largely due to the broad range of environments encompassed, including starbursting to quenched environments. Similarly, the trend of decreasing SFRs with lower redshift (Noeske et al. 2007; Tomczak et al. 2016) results in our magnitude of SFRs, consistent with Wuyts et al. (2011) at z ≈ 0.02–0.2. However, Table 1 makes clear that our fits, even for the same data set, are not constant. This suggests that the SFMS error budget may be largely spoiled by systematic errors in the adopted transformations, rather than intrinsic environmental factors. The regimes of global SFMS measurements by González Delgado et al. (2016) and Ellison et al. (2018) are outlined in the top panel of Figure 6 in gray, and lie approximately within the same regime as our data, although the CALIFA and MaNGA samples are restricted to $\mathrm{log}({M}_{* })\,\gt 9.0$ systems (Walcher et al. 2014; Ellison et al. 2018). The CALIFA sample also has a larger contribution of early-type, quiescent galaxies, which accounts for the lower SFR measurements at high M_* by González Delgado et al. (2016). While our SFRs are somewhat smaller than those of Ellison et al. (2018), they are broadly consistent with González Delgado et al. (2016), and all agree within the level of uncertainty attached to these transformations (about a factor of two). The higher range of stellar masses show broad consistency with all other considered samples.

The left panel of Figure 7 shows the varying global SFMS fits (slope and intercept) produced using different SFR transformations, as discussed in Section 3.1. Four of them were taken from Davies et al. (2016). With the exception of the solid green and solid blue lines from Davies et al. (2016) for Hα and W4 transformations, the various SFMS fits appear to be highly consistent with each other. However, the calibrations by Davies et al. (2016), originally calibrated for stellar masses above 10⁹ M_⊙, produce unreasonably high SFRs at lower stellar masses. This figure otherwise suggests that the common suite of transformations compares favorably on global, integrated scales. Interestingly, the C17 W3 and W4 transformations have higher SFRs compared to other transformations at high M_* values. This could arise from the higher dust content at high SFR and stellar mass, and the W3 and W4 may perform better in this regime. The W3 and W4 transformations could therefore be more robust on global scales, while a hybrid calibration would be more suitable for local measurements.

Zoom In Zoom Out Reset image size

The local SFMS, seen in the bottom panel of Figure 6 in orange, was derived from radially resolved profiles of ${{\rm{\Sigma }}}_{{M}_{* }}$ and Σ_SFR for each galaxy, using transformations by C07 and C14; the motivation for these is presented in Sections 3 and 5.1. Each measurement represents an annular ring centered around the galactic center, and each ring has a width of ≈500 pc by design. The strong positive, linear correlation between SFR and M_* typically seen in the the global SFMS is also evident on local ${{\rm{\Sigma }}}_{{M}_{* }}$ and Σ_SFR scales. The local fit in the bottom panel of Figure 6 is shown by black solid line. This further confirms that these two tracers of star formation are strongly coupled not only among galaxies but within themselves; their variations closely track each other. The SFMS regime studied by González Delgado et al. (2016) and Ellison et al. (2018) is again outlined in the bottom panel of Figure 6 in gray, and overlaps with our data. However, unlike the CALIFA and MaNGA samples, significantly lower values of ${{\rm{\Sigma }}}_{{M}_{* }}$ and Σ_SFR measurements are probed in our study thanks to our inclusion of lower stellar mass systems.

Our local SFMS slopes average a ∼ 1 and are slightly steeper than integrated SFMS slopes (Table 1). They are also consistent, though at the high end, with reported slopes (a ∼ 0.7–1.0) from other studies of the spatially resolved SFMS (Pérez et al. 2013; Wuyts et al. 2013; Hemmati et al. 2014; Cano-Díaz et al. 2016; González Delgado et al. 2016; Magdis et al. 2016; Abdurro'uf & Akiyama 2017; Maragkoudakis et al. 2017). The right panel of Figure 7 shows that SFMS fits from a variety of SFR transformations are highly consistent for local measurements, the exception being the green, cyan, and blue solid lines corresponding to the Davies et al. (2016) relations. This can likely be attributed to the fact that these new calibrations were applied to higher mass systems and were not spatially resolved, whereas the K98 and C07 transformations have been calibrated to such resolved environments. GAMA Hα measurements in Davies et al. (2016) also have a limited aperture size of 2 arcsec that may cause systematic offsets, and the W4 detections were quite poor due to the redshift limits (z ≲ 0.13). Although environment becomes more stochastic at lower M_* regimes, it is interesting that these local SFMS fits and their scatter remain consistent. There is a slight increase in scatter about spatially resolved measurements, and Section 6 investigates the influences by regions within a galaxy versus at a global scale more closely.

We first examine any correlation of the SFMS with the total H i mass. Our galaxy sample is drawn from the SINGG, which itself targets were H i-rich galaxies selected in HIPASS. Therefore, we wish to assess if this selection biases our sample in any relevant way. Of particular interest is the claim by Saintonge et al. (2016) of a correlation between the ratio of total H i mass to total stellar mass of a galaxy and its position (scatter) within the global SFMS. However, our own examination of the SFMS residuals with H i mass (Figure 8) reveals no such dependence for our sample. This suggests, at least for our sample of star-forming galaxies (with few, if any, quiescent early-type galaxies), that the role of the H i mass in regulating star formation is minimal.

Zoom In Zoom Out Reset image size

It is also necessary to examine any correlation with morphology, as CALIFA SFMS results continue to find strong dependence of the local SFMS scatter on morphology (González Delgado et al. 2016, 2017; López Fernández et al. 2018). According to them, morphology tracks perpendicularly to the SFMS on both global and local scales, suggesting that the host galaxy determines the general SFMS trends (slope and zero point) throughout all regions within the galaxy. While our morphological type coverage is not as extensive, by virtue of the HIPASS sample selection, we do have a broad selection of early-type to late-type to irregular galaxies. Our scatter analysis in fact yields a different trend. Figure 9(a) shows that late-type galaxies (T-Types from 0 to 7) lie throughout the local SFMS, whereas very early-type (T-Type −6 to −3) and irregular (T-Type 8 to 10) galaxies appear to dominate in the low ${{\rm{\Sigma }}}_{{M}_{* }}$ regime. There is no clear orthogonal trend to this relation. This contradictory trend that we find could result from early-type and irregular galaxies still showing a significant amount of observable SF (at least as traced by the presence of HI by HIPASS), but not having enough mass build-up to contribute to the higher mass regions of the SFMS and likely having much smaller systems than typical early-type galaxies. Sample selection is clearly key in establishing the trends observed in our respective analyses of morphological dependence.

Zoom In Zoom Out Reset image size

The radial dependence of the SFMS requires additional scrutiny. Gradient and residual trends are shown in Figures 10(a) and (b) against the radial parameter, R/R_eff. Little correlation is detected in these plots, as is true for most other SFMS residual analyses (again, see Appendix D).

Zoom In Zoom Out Reset image size

However, patterns emerge when the individual paths of a random selection of galaxies, each distinguished by a unique color, are plotted in Figure 11. These reveal the unique behavior of each galaxy within the SFMS, where a galaxy's central data point is denoted by a star. Galaxies with local mass densities higher than log(${{\rm{\Sigma }}}_{{M}_{* }}$) ∼ 7.5 seem to define two trajectories as their tracks progress from the galactic center to their outskirts. One class (A) initially plateaus in Σ_SFR with decreasing ${{\rm{\Sigma }}}_{{M}_{* }}$. Its radial track then decreases in both Σ_SFR and ${{\rm{\Sigma }}}_{{M}_{* }}$ in lock-step with the SFMS. The alternate class (B) bypasses the initial plateau in Σ_SFR, plunging from high values of Σ_SFR and ${{\rm{\Sigma }}}_{{M}_{* }}$ in lock-step with the SFMS from the center out. Below log(${{\rm{\Sigma }}}_{{M}_{* }}$) ∼ 7.5, individual galaxy tracks lack structure and show random paths (C). The scale of log(${{\rm{\Sigma }}}_{{M}_{* }}$) ∼ 7.5 appears to mark an important transition; whether a galaxy follows the tracks identified above or not, all trends vanish for local SFMS tracks below log(${{\rm{\Sigma }}}_{{M}_{* }}$) ∼ 7.5. This suggests distinctly different mechanisms for high and low-mass density environments. These three galactic behaviors are projected for clarity in the bottom right panel of Figure 11; we label them as the type A, B, and C galaxy groups. The schematics given in the bottom right panel of Figure 11 are representative of the broad ${{\rm{\Sigma }}}_{{M}_{* }}$ and Σ_SFR regimes found in our sample; exceptions also exist.

Zoom In Zoom Out Reset image size

While density measurements eliminate the variation in area among all measurements, so as to better compare different galaxy sizes and internal/radial locations, absolute measurements lack the additional uncertainty introduced from distance errors with density values. We therefore present in Figure 12 a complementary representation of Figure 11 to further emphasize the distinction between these three types. In this space, the type A population displays an initial sharp rise in the SFR (rather than plateau), whereas type Bs follow the SFMS at all radial points. The stochasticity in type C measurements is also clear in Figure 12, the log(${{\rm{\Sigma }}}_{{M}_{* }}$) ∼ 7.5 in density space transitions to log(M_*) ∼ 8.5 for absolute measurements.

Zoom In Zoom Out Reset image size

The type A curved tracks provide compelling motivation for inside-out quenching in higher mass systems, as the Σ_SFR at the center appears to be significantly reduced compared to the corresponding high stellar mass density. However, we now seek distinguishing features between this and the type B straight, seemingly unquenched, galaxy group that lies in the same local stellar mass density regime. The type B galaxy group generally has higher Σ_SFR at a given ${{\rm{\Sigma }}}_{{M}_{* }}$, as evident in Figure 11.

Another striking feature that emerges from Figure 11 is that the scatter for structures above log(${{\rm{\Sigma }}}_{{M}_{* }}$) ∼ 7.5 appears to be caused by a systematic offset between galaxies. Disregarding the initial rise in Σ_SFR among the type A galaxies, each galaxy appears to lie roughly parallel the SFMS fit, suggesting that the scatter is driven on global scales across galaxies. In fact, applying a linear fit to each individual galaxy track yields consistent slopes (a) with varying intercepts, and the scatter about the SFMS fit associated with an individual galaxy is less than the total scatter of the SFMS, supporting the notion that scatter is dominated by vertical offsets between galaxies, for type A and B galaxies.

By contrast, below log(${{\rm{\Sigma }}}_{{M}_{* }}$) ∼ 7.5, SFMS measurements appear to be stochastic in all parts of the galaxies. Interestingly, the overall scatter (∼0.3 dex) remains constant at all ${{\rm{\Sigma }}}_{{M}_{* }}$. It is likely that the random scatter in lower mass density systems is due to stochastic sampling of SF behaviors and environments at such small ${{\rm{\Sigma }}}_{{M}_{* }}$ scales, and the vertical offsets in type A and B galaxies would be due to varying global accretion rates. The age and accretion histories are difficult to quantify observationally, but stellar mass and SFR-density distributions across a galaxy may potentially inform us of their impact. In this context, a future investigation of star formation and accretion histories with semi-analytic models is certainly warranted.

The global parameters available in this study are still insufficient for the identification of distinguishing features among the three galaxy groups. Out of structural parameters like the concentration index, morphology, bulge-to-total ratio (B/T), and effective surface brightness, only the total stellar and H i masses (M_tot and M_{H i}) offer any differentiation among the three galaxy groups. Figure 13 shows the A and B type galaxies are generally higher stellar and H i mass systems, as expected, whereas the stochastic signature of C types is found in less massive environments. The slight shift upward in total stellar mass (M_tot) of A type galaxies suggests a more active history of accumulation of stellar mass via higher SFRs in the past. The matching offset in total H i mass is, however, not substantial enough to cleanly delineate the A and B populations. It can be said that As simply have a slightly larger star formation fuel reservoir. No distinction in bulge strength (B/T ratio) was observed between type A and B galaxies, though perhaps the activity within the bulge differentiates the two populations, rather than the bulge size itself. Mechanisms such as central mass accretion or SF quenching may also explain the behaviors seen in type A and B galaxies. In order to better understand the different mechanisms distinguishing these galaxy track types, the mean radial profiles of these three groups is examined in Section 7.

Zoom In Zoom Out Reset image size