SDSS-IV MaNGA: Environmental Dependence of the Mgb/${\boldsymbol{\langle }}{\bf{Fe}}{\boldsymbol{\rangle }}$–${{\boldsymbol{\sigma }}}_{{\boldsymbol{* }}}$ Relation for Nearby Galaxies

MaNGA (Bundy et al. 2015) is an IFU survey targeting about 10,000 nearby galaxies selected from the SDSS-IV (Gunn et al. 2006; Blanton et al. 2017). The wavelength coverage is between 3600 and 10300 Å with a spectral resolution R ∼ 2000 (Smee et al. 2013; Drory et al. 2015). The MaNGA sample is selected so that the number density of galaxies is roughly independent of the i-band absolute magnitude M_i. Each galaxy is covered by the IFU out to either 1.5 effective radii (R_e) or 2.5R_e (Yan et al. 2016b; Wake et al. 2017) and the sizes of the IFUs vary for different galaxies from 12'' for a 19-fiber IFU to 32'' for a 127-fiber IFU (Drory et al. 2015; Law et al. 2015). The observed data are reduced by the MaNGA data reduction pipeline (DRP; Law et al. 2016; Yan et al. 2016a) and the final products of the DRP are datacubes, which are composed of "spaxels" with an angular size of 05 × 05, as well as row stacked spectra.

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

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

We follow the definitions of spectral indices from Trager et al. (1998). Detailed bandpass and pseudo-continua wavelength ranges for the four spectral indices are reproduced in Table 1. Uncertainties in the spectral index values are estimated following Cardiel et al. (1998).

We measure these four spectral indices for all spaxels with S/Ns larger than 10. For studying stellar population related science using spectral indices, the threshold requirement for spectral S/N is very high (S/N ≳ 50–100). Therefore, we divide each galaxy into three radial bins to enhance S/N: central ($r\lt 0.3{R}_{e}$), intermediate ($0.3{R}_{e}\lt r\lt 0.7{R}_{e}$), and outer ($0.7{R}_{e}\lt r\lt 1.3{R}_{e}$) regions, where r is the semimajor axis of an elliptical aperture. We then calculate average values of the spectral indices within each radial bin. The averaged spectral index values are similar to values derived using each radial bin's stacked spectra, which usually have S/N ≳ 50–100.

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

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Velocity dispersion broadening has a nonnegligible effect on spectral index values, especially for spectra with stellar velocity dispersion values larger than 100 km s⁻¹. We therefore have to correct for velocity dispersion broadening in our spectral index measurements. Many previous studies perform velocity dispersion corrections in a very time consuming way: one fits the observed spectra with template spectra and then measures spectral indices using the fitted template spectra with and without velocity dispersion to derive the correction factor. Here we use a new method to correct for the velocity dispersion effect: we assume a simple polynomial relation between spectral indices with and without velocity dispersion broadening,

$$\begin{eqnarray}&&{x}_{0}={p}_{0}+{p}_{1}\,{x}^{{p}_{2}}+{p}_{3}\,{\sigma }^{{p}_{4}}+{p}_{5}\,{x}^{{p}_{6}}\,{\sigma }^{{p}_{7}},\end{eqnarray} \tag{ 1 }$$

where σ is velocity dispersion in units of km s⁻¹, x and x₀ are the spectral index values before and after velocity dispersion correction, and ${p}_{0}-{p}_{7}$ are fitting parameters. We use MILES template spectra (which have similar spectral resolution to SDSS; Sánchez-Blázquez et al. 2006b; Vazdekis et al. 2010) with different velocity dispersion values to fit the parameters in Equation (1). The fitted parameters for each of the four spectral indices are listed in Table 2. We then verify the fitted parameters using the Maraston & Strömbäck (2011) single stellar population templates with Chabrier (2003) IMF and MILES stellar library: we perform velocity dispersion correction by applying Equation (1) with parameters in Table 2 to spectral index values derived using template spectra with different velocity dispersions, and then compare the corrected values with spectral index values of the original Maraston & Strömbäck (2011) templates. The results are shown in Figure 3. The corrected values show little difference from the real values (mostly within 2%) except for small values (<1) of Mgb, Fe5270, and Fe5335, which are rarely seen in our galaxy sample. These parameters can also be applied to other observations that have similar instrumental spectral resolutions to SDSS. Using these fitted parameters and measured velocity dispersion values, we are able to calculate spectral indices without velocity dispersion for little computational cost. For our sample galaxies, we use velocity dispersion measurements (for each spaxel) from the MaNGA Data Analysis Pipline (DAP; Westfall et al. 2019), which uses the pPXF (Cappellari 2017) full spectral fitting technique in deriving kinematical properties.

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Table 2.  Fitting Parameters for Equation (1)

Name	p0	p1	p2	p3	p4	${10}^{5}{p}_{5}$	p6	p7
Hβ	0.15 ± 0.07	0.92 ± 0.04	1.03 ± 0.02	0 ± 0.02	0.57 ± 0.89	0.11 ± 0.17	1.22 ± 0.21	1.93 ± 0.21
Mgb	0	0.83 ± 0.15	1	0	0	110 ± 50	1	1
Fe5270	0.54 ± 1.4	0.97 ± 0.01	1.01 ± 0.01	−0.46 ± 1.39	0.037 ± 0.10	76 ± 1.6	0.87 ± 0.02	1.48 ± 0.03
Fe5335	−0.02 ± 0.02	1.04 ± 0.01	0.97 ± 0.01	0 ± 0.008	0.46 ± 0.4	0.52 ± 0.08	1.01 ± 0.02	2.03 ± 0.02

Note. Note that the values of p₅ are very small, so we show 10⁵ × p₅ in this table. Also, p₀, p₂, p₃, p₄, p₆, and p₇ have been fixed at the specific values in the table in fitting for Mgb.

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Star-forming galaxies may have Hβ emission, so we also have to correct for emission line flux when calculating the Hβ index. We correct for Hβ emission by subtracting a Gaussian emission line profile with a total flux equal to the Hβ emission flux value provided by the MaNGA DAP (Westfall et al. 2019).

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

$$\begin{eqnarray}&&{\sigma }_{* }=\sqrt{\displaystyle \frac{{{\rm{\Sigma }}}_{k}{F}_{k}({v}_{k}^{2}+{\sigma }_{k}^{2})}{{{\rm{\Sigma }}}_{k}{F}_{k}}},\end{eqnarray} \tag{ 2 }$$

where v_k and σ_k are the velocity and stellar velocity dispersion of the kth IFU spaxel, respectively, and F_k is the flux in the kth IFU spaxel. This σ_* definition has been proven to be close (mostly within ∼10%) to the velocity dispersion measured from a stacked spectrum using spectra within the same aperture (Cappellari et al. 2013; Li et al. 2018).

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

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

Note that not all galaxies in our sample have environment information. The numbers of galaxies with different environment measurements are shown in Table 3.

The spectral index ratio Mgb/$\langle \mathrm{Fe}\rangle$, where $\langle \mathrm{Fe}\rangle \,=(\mathrm{Fe}5270+\mathrm{Fe}5335)/2$, is a widely used indicator in previous studies for the α-to-iron ratio (see Figure 4 of Thomas et al. 2003). We note that $\mathrm{Mgb}/\langle \mathrm{Fe}\rangle$ is indicative for general element ratio trends but detailed element ratio calculations would require more sophisticated techniques such as model fitting (see the discussion in Section 4.2). We also derived a α-to-iron ratio ([α/Fe]) by fitting the spectral indices with Thomas et al. (2011) models; however, the relations and environmental dependence of [α/Fe] are less obvious because of large scatters. We therefore focus on Mgb/$\langle \mathrm{Fe}\rangle$ in the main text and append the [α/Fe] related results in the Appendix.

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

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It is obvious that Mgb/$\langle \mathrm{Fe}\rangle$ is well correlated with σ_* and most galaxies lie in close vicinity around the linearly fitted straight line (solid line in the upper panel of Figure 5). The Spearman's rank correlation coefficient is r_S = 0.76. This means that not only early-type but all types of galaxies in our sample follow the Mgb/$\langle \mathrm{Fe}\rangle$–σ_* relation. We can also see from the color coding that high-σ_* galaxies mostly have small Hβ values (relatively old) and low-σ_* galaxies mostly have large Hβ values (relatively young). Low-σ_* ($\lt 80\,\mathrm{km}\,{{\rm{s}}}^{-1}$) galaxies have larger scatters but are still centered around the solid line, which is consistent with Liu et al. (2016a).

As shown in the previous subsection, $\mathrm{Mgb}/\langle \mathrm{Fe}\rangle$ is well correlated with σ_*. Therefore, in order to examine the environmental dependence, we need to take out the effect by σ_*. We first follow the method of Liu et al. (2016a) and divide galaxies into three different velocity dispersion ranges: low-σ_* (${\sigma }_{* }\lt 80\,\mathrm{km}\,{{\rm{s}}}^{-1}$), medium-σ_* ($80\,\mathrm{km}\,{{\rm{s}}}^{-1}\lt {\sigma }_{* }\,\lt 158\,\mathrm{km}\,{{\rm{s}}}^{-1}$), and high-σ_* (${\sigma }_{* }\gt 158\,\mathrm{km}\,{{\rm{s}}}^{-1}$). We further divide galaxies in these σ_* ranges into three different environments based on local densities: low-density ($\lt 2{\rho }_{0}$), medium-density ($2{\rho }_{0}\lt \rho \lt 12.6{\rho }_{0}$), and high-density (>12.6ρ₀), where ρ₀ is the average cosmic mean density, $7.16\times {10}^{10}{M}_{\odot }/h/{(\mathrm{Mpc}{\text{}}{h}^{-1})}^{3}$. The velocity and local density ranges are chosen so that each velocity or local density range has roughly the same number of galaxies. Figure 6 shows the $\mathrm{Mgb}/\langle \mathrm{Fe}\rangle$–σ_* relation for the central regions (within ${{\rm{R}}}_{e}/3$) in the three different local density ranges. In the lower panels of Figure 6, we plot the residuals ($\delta \mathrm{log}(\mathrm{Mgb}/\langle \mathrm{Fe}\rangle$)). We also plot average values of galaxies in these three different environments and three different σ_* ranges. Low- and medium-σ_* galaxies in the high-density environment (upward-triangle) show enhancement in Mgb/$\langle \mathrm{Fe}\rangle$.

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

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

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

For satellite galaxies, we divide them into three groups according to their projected halo-centric radii (in units of virial radius of the group R_V)—inner ($R\lt 0.18{R}_{V}$), intermediate ($0.18{R}_{V}\lt R\lt 0.7{R}_{V}$), and outer ($R\gt 0.7{R}_{V}$)—and make plots accordingly in the bottom row of Figure 8. The residuals for "old" low-σ_* galaxies in the inner regions ($R\lt 0.18{R}_{V}$) of galaxy groups are obviously large compared to those of galaxies in the outer and intermediate regions. "Old" medium-σ_* and high-σ_* galaxies also show a similar trend but less obviously. There is no clear systematic trend for "young" galaxies. Note that the number of satellite galaxies is relatively small (see Table 3).

We investigate dependence on galaxy halo formation redshift (z_f) and the results are shown in Figure 9. We do not see any clear systematic trend along formation redshifts; however, for "old" galaxies, those with high formation redshift (formed earlier) have relatively larger residuals. This is true for almost all σ_* bins and all galaxy regions. For "young" galaxies, this signature is not obvious.

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

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

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

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

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

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A comparison between our measurements of Mgb/$\langle \mathrm{Fe}\rangle$ and various archival data from Liu et al. (2016a) is shown in Figure 16. Our Mgb/$\langle \mathrm{Fe}\rangle$–σ_* relation is steeper than that of Liu et al. (2016a) and has a ∼0.05 dex systematic difference at the high-mass end. Note that data from different sources have different calibration procedures; our spectral index values are corrected to the SDSS resolution ($\sim 70\,\mathrm{km}\,{{\rm{s}}}^{-1}$) while data collected in Liu et al. (2016a) may have different spectral resolutions; also Liu et al. (2016a) has different aperture definitions from us when measuring spectral indices and velocity dispersions.

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

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

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