STELLAR POPULATION MODELS AND INDIVIDUAL ELEMENT ABUNDANCES. II. STELLAR SPECTRA AND INTEGRATED LIGHT MODELS

Little is known about the influence of individual element abundances on the integrated flux of a stellar population. As present, it is impossible to derive an accurate age within 10% from the integrated light of a clusterlike single-age and single-abundance stellar population, and the primary reason is the complication due to abundance ratio effects (Worthey 1998). The secondary reason is that the input ingredients and choices made in even the most sophisticated stellar evolution calculations induce scatter in the results (Charlot et al. 1996). The tertiary reason is the set of difficulties associated with stellar flux knowledge, such as colors, line strengths, or spectra, that are needed at each stellar evolutionary phase to represent the component stars. Additional uncertainties exist, such as dust extinction, stellar rotation and activity, the blue straggler frequency, and the effects of close binaries.

Dotter et al. (2007b, hereafter Paper I), explored the effects of 12 chemical mixtures on the L, T_eff, and lifetimes of stars along stellar evolutionary isochrones and upon the opacities needed to calculate the stellar models. The mixtures explored were solar, α-element enhanced, and 10 cases where only one element at a time was enhanced, for elements C, N, O, Ne, Mg, Si, S, Ca, Ti, and Fe. The mixtures were re-scaled so that the mass fraction of heavy elements, Z, was constant.⁹

The conclusions from that paper could be summarized by splitting the elements that were investigated into three categories. "Displacers" include O, C, N, and Ne. These are elements that are abundant but supply less opacity per unit mass than heavier elements. At fixed Z, boosting a displacer element will therefore decrease the opacity. This leads to shorter stellar lifetimes and hotter stars. "Boosters" include Mg and Si. These elements are good opacity sources, so that boosting a booster will increase opacity and make cooler stars that live somewhat longer. "Oddball" elements defy these trends, and include Ca and Ti, both of which make cooler stars, that, nevertheless, have shorter lifetimes. Another oddball is S, which decreases low-temperature opacity but increases high-temperature opacity so that its ultimate effect on temperatures and lifetimes is small. An element worth special mention is Fe, because its high-temperature opacity has considerable structure. One of its opacity peaks corresponds to the temperature characteristics of the outer edge of the convective core that develops in stars slightly more massive than the Sun. Increasing the Fe abundance therefore strongly couples to the onset of convective core overshooting effects, and leads to a strong luminosity effect in the region of the main sequence turnoff. The temperature, luminosity, and lifetime effects are illustrated in Paper I, but further consequences will be illuminated in this paper.

Besides isochrones, the other major ingredient in any population synthesis effort is some representation of stellar flux for each star in the isochrone. The effects of individual element abundances on the spectra of stars have been studied for years, and enormous progress has been made in finding the structure of stellar atmospheres and calculating the emergent flux. The two most cited programs for constructing model atmospheres of stars are ATLAS (Kurucz 1970) and MARCS (Gustafsson et  al. 1975), and we use results from these codes in this work. For spectral synthesis of the emergent flux, we use SYNTHE (Kurucz 1970), FANTOM (Coelho et al. 2005; Cayrel et al. 1991), and SSG (Bell et al. 1994). For ordinary population synthesis, empirical spectra or colors can be used (Vazdekis 1999), but for investigating element-by-element effects, using synthetic spectra is clearly the way forward. Investigations into the effects of individual elements on stellar spectra, but with the intent of applying the results to galaxy spectra, include Tripicco & Bell (1995) and Korn et al. (2005), who gauged the effects of 10 individual elements on the Lick system of 25 pseudo-equivalent width indices (Worthey et al. 1994; Worthey & Ottaviani 1997). Serven et al. (2005) investigated 24 elements in spectra that ran from 3500 Å to 9000 Å with velocity smoothing appropriate for dynamically hot systems such as elliptical galaxies.

The present paper combines the new isochrones described in Paper I with greatly extended and updated synthetic spectra in order to obtain ab initio population synthesis models as a function of individual element abundances.¹⁰ All parts of the models, including high-temperature and low-temperature opacities, stellar evolutionary models, and synthetic spectra, include the altered abundances in the same way. At present the grid includes only solar Z, but calculations are underway to extend to many different abundances. This paper describes the new spectra and their color index results in Section 2, Lick index results in Section 3, concluding with a discussion and summary section.

The new isochrones were described in Paper I, and we refer the reader to that paper for details. Twelve chemical mixtures were explored self-consistently with both high-temperature and low-temperature opacities adjusted properly, and evolution is complete only to the end of the red giant branch. It should be emphasized that the models are thus incomplete and should not be used blindly when comparing to real stellar populations until the helium-burning phases are properly incorporated.¹¹ This is planned for the ongoing improvement of these models. In careful, differential ways, the present models give us important pointers to the behavior of stellar populations with variable element mixtures, but the absolute values of colors and indices are not to be trusted. The mixtures explored were solar, α-element enhanced, and 10 cases where only one element at a time was enhanced (C, N, O, Ne, Mg, Si, S, Ca, Ti, and Fe). The mixtures were re-scaled so that the mass fraction of heavy elements, Z, was held constant.

2.1. Synthetic Spectra

2.2. Synthetic Spectra Accuracy

An interpolation routine was constructed so that spectra of arbitrary temperature, gravity, and abundance mixture could be produced on demand. Linear interpolation in the log of the flux seemed to give the most predictive results. Interpolation was done for all input variables: temperature, log g, and the whole set of abundance parameters. Tests in which one star in the grid was compared with its interpolated version calculated from the flanking temperature grid points indicate that, within the dense 4000–6000 K part of the grid, interpolations yield better than 1% accuracy at any given flux point, since the spectra change more with temperature than with the other parameters. Given the nonlinear temperature response of many lines, e.g., Gray & Brown (2001), this is encouragingly good. Doubtless, in the future, we will demand a denser temperature grid, but 1% accuracy is better than we need for the present study.

Toward the more fundamental question of how well the synthetic spectra match real spectra, there is little we can add to discussions in Martins & Coelho (2007), Coelho et al. (2005), Korn et al. (2005), and Tripicco & Bell (1995). Serven et al. (2005) did discover some too-strong lines due to chromium (that is, mistakes in the line list) via stellar comparisons, but these lines do not affect the present conclusions at all. More worrisome is silicon because the features that show Si effects are mostly SiH lines in the blue, but these line lists may be immature (R. Peterson 2007, private communication). All conclusions regarding Si should be regarded with great suspicion until this question is satisfactorily resolved.

In Figures 1 and 2, we compare the high-resolution spectra of the Sun and Arcturus with the grid-interpolated synthetic spectra near the regions of the Hβ and the Mg b lines, respectively. For the solar parameter we employ T_eff = 5777 K, log g = 4.44, and [Fe/H] = 0, and for Arcturus T_eff = 4290 K, log g = 1.9, and [Fe/H] = −0.7 with [α/Fe] = +0.4 dex (e.g., Peterson et al. 1993; Griffin & Lynas-Gray 1999; Carretta et al. 2004; Fulbright et al. 2007; Koch & McWilliam 2008). The top panels are the solar spectra and the bottom panels are Arcturus. The thicker (black) lines are the observations and the thinner (red) ones are the synthetic. The degraded low-resolution spectra, Gaussian-smoothed to 8 Å FWHM or about 200 km s⁻¹—somewhat better than the best Lick-system resolution, are overlaid on top of the high-resolution spectra. We investigate the individual element effects over a rather broad wavelength region for the Lick indices and broadband colors in this paper. In this context, it is useful to find that the notable mismatches between the synthetic and the observed spectra in the high-resolution comparisons are smeared out and become subtle at low resolution.¹³

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Table 1 presents some comparisons between synthetic colors and empirical color behavior for the stars in the temperature range 4000–6000 K. Columns 2–5 refer to synthetic spectra, and Columns 6–8 refer to the empirical calibration of Worthey & Lee (2008). The synthetic spectra were converted to UBVR_CI_C colors as in Worthey (1994) using Bessell's (1990) filter responses zeroed to Vega's colors. There is at least a 10 mmag uncertainty just from that procedure, and probably at least 20 mmag for U − B. The "dwarf" is log g = 4.5, and the "giant" is log g = 2.5. Columns 2 and 6 present the colors for the star listed, synthetic and empirical, respectively. The most serious mismatches are the U − B color for the 6000 K dwarf and for the 4000 K and 5000 K giants. These facts suggest some room for improvement in model atmospheres and line lists (especially at shorter wavelengths).

Table 1. Gross Color Behavior with Metallicity Increase

Color	Synthetic Color (mag)	Δ Color, 24 Elements Enhanced (mmag)	Δ Color, All Elements Enhanced (mmag)	Δ Color Teff (mmag)	Empirical Color (mag)	Δ Color, All Elements Enhanced (mmag)	Δ Color, Teff (mmag)
Dwarf,Teff = 4000 K
U −B	1.26	21	81	−106	1.36 ± 0.07	58	−85
B −V	1.43	43	35	−137	1.36 ± 0.02	22	−81
V −R	0.89	16	24	−94	0.82 ± 0.01	3	−74
V −I	1.60	13	24	−176	1.58 ± 0.02	−5	−176
Dwarf,Teff = 5000 K
U −B	0.61	123	111	−179	0.71 ± 0.07	160	−169
B −V	0.91	55	45	−90	0.96 ± 0.02	62	−101
V −R	0.52	21	19	−62	0.52 ± 0.01	11	−55
V −I	0.98	15	14	−103	0.96 ± 0.02	13	−97
Dwarf,Teff = 6000 K
U −B	0.02	113	95	−33	0.16 ± 0.07	114	−75
B −V	0.58	39	37	−50	0.61 ± 0.02	42	−70
V −R	0.33	15	11	−28	0.34 ± 0.01	4	−33
V −I	0.66	16	5	−55	0.65 ± 0.01	1	−60
Giant,Teff = 4000 K
U −B	1.34	115	137	−182	1.69 ± 0.07	52	−194
B −V	1.45	39	57	−166	1.44 ± 0.02	22	−103
V −R	0.83	5	21	−120	0.79 ± 0.01	5	−82
V −I	1.51	−4	20	−198	1.51 ± 0.02	4	−182
Giant,Teff = 5000 K
U −B	0.57	159	147	−159	0.77 ± 0.07	161	−194
B −V	0.93	52	60	−107	0.97 ± 0.02	63	−116
V −R	0.48	18	12	−46	0.49 ± 0.01	10	−52
V −I	0.92	9	−1	−80	0.94 ± 0.01	11	−87
Giant,Teff = 6000 K
U −B	0.16	79	83	19	0.11 ± 0.07	109	−81
B −V	0.55	48	54	−64	0.55 ± 0.02	41	−85
V −R	0.31	12	9	−35	0.31 ± 0.01	4	−36
V −I	0.61	12	4	−69	0.64 ± 0.01	1	−70

Notes. 1. The "Dwarf" islog g = 4.5, and the "Giant" islog g = 2.5. 2. Column 2 presents the calculations at[R/H] = 0, where R is the generic heavy element (see Section 2.2). 3. Column 3 presents the case where 24 elements (C, N, O, Na, Mg, Al, Si, S, Cl, K, Ca, Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, Sr, Ba, Eu) are enhanced by 0.3 dex. 4. Columns 4 and 7 present the calculations at[R/H] = 0.3 dex. 5. Columns 5 and 8 present the color changes when the temperature is increased by 250 K, synthetic and empirical, respectively.

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The remaining columns present color changes induced by either an abundance increase of 0.3 dex or a temperature increase of 250 K (color changes in millimagnitudes). Column 4 is a complete scaled-solar enhancement of 0.3 dex in every element and with new atmospheres calculated, while Column 3 is a 0.3 dex enhancement of only the 24 elements that are explicitly traced in the spectral library, a superset of those followed in the isochrone library.¹⁴ Comparison of Columns 3 and 4 indicates that, for the "heart" of the spectral library between 4000 and 6000 K, the sum of the available one-by-one element tweaks approximately equals the scaled-solar analog operation. The list of 24 elements in linear combination thus appears to approximate the full-blown calculation of a spectrum in most cases. This allows the approximate calculation of a new spectrum at arbitrary composition in an eye blink rather than many minutes for a whole new synthetic spectrum calculation.

In general, the synthetic colors are within a few hundredths of a magnitude of the empirical colors and track the empirical color responses to abundance and temperature in an approximate way. The worst outlier is the U − B color for the 6000 K giant, in which the color gets redder rather than bluer with increasing temperature (see also Martins & Coelho 2007). Strong conclusions are not possible with this comparison, but the agreement is fairly encouraging.

Tables 2 and 3 show the spectral effects of element-by-element enhancements of 0.3 dex (except carbon which is increased by 0.15 dex, see footnote 12) on some selected color indices for the stars in the temperature range 4000–6000 K. In Table 2, the elements were re-scaled to constant heavy-element fraction Z, while in Table 3, Z was allowed to increase. One technical subtlety is that, since neon is not tracked in the spectral library, the only effects that appear in Table 2 for Ne are due to the re-scaling, and there are no effects at all in Table 3. Table 3 can be visually explained by taking a look at the spectra.¹⁵ Figure 3 displays one example. Here, the flux ratio between 0.3 dex Mg-enhanced spectra and that of the solar-scaled are shown for a 4000 K giant star. The B − V becomes bluer (e.g., more B-band flux over V-band flux) and V − R, V − I become redder (e.g., comparably more R- and I-band fluxes over V-band flux). The U − B also becomes similarly bluer just like B − V because the B-band filter response curve goes all the way to ∼5400 Å. Now the effects of Mg that we read from Table 3 are clearly understood from this illustration. It is confirmed that Mg is the most important α-element that influences the U − B and B − V colors as already described in Cassisi et al. (2004).

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Table 2. Color Behavior with Enhancements at Constant Z

Color	C	N	O	Ne	Mg	Si	S	Ca	Ti	Fe	α
Dwarf, Teff = 4000 K
U − B	−13	8	19	−2	−66	−36	0	−40	15	136	−103
B − V	17	−2	−50	−4	−19	35	0	−7	15	22	−33
V − R	−2	−1	−7	−1	31	−1	0	−14	4	12	8
V − I	−5	−1	−5	−1	31	−1	0	−14	4	14	10
Dwarf, Teff = 5000 K
U − B	13	18	−61	−13	−26	−39	−2	−4	11	61	−120
B − V	17	1	−40	−6	−32	5	−1	6	7	18	−58
V − R	−3	−5	−8	−2	8	−2	0	0	3	10	−3
V − I	−12	−11	0	−1	10	−1	0	−1	3	15	7
Dwarf, Teff = 6000 K
U − B	−4	10	−48	−13	5	−19	−2	1	8	30	−59
B − V	8	1	−20	−4	−14	−7	0	6	5	11	−34
V − R	0	−1	−7	−1	0	−1	0	0	2	7	−9
V − I	0	−3	−8	−1	0	0	0	0	2	10	−10
Giant, Teff = 4000 K
U − B	7	11	−50	−13	−26	−50	−2	−20	22	112	−129
B − V	17	−1	−47	−4	−30	37	0	−3	12	19	−37
V − R	−10	−5	2	0	21	0	0	−8	3	13	15
V − I	−21	−9	14	1	23	0	0	−9	2	17	29
Giant, Teff = 5000 K
U − B	10	23	−74	−17	24	−39	−3	6	11	19	−82
B − V	18	5	−34	−6	−22	−6	−1	8	6	8	−52
V − R	1	−10	−8	−1	1	0	0	0	2	9	−6
V − I	−7	−23	1	0	6	2	0	0	3	16	10
Giant, Teff = 6000 K
U − B	−5	6	−34	−9	12	−9	−2	6	8	9	−25
B − V	1	0	−23	−5	−5	−3	−1	9	5	9	−23
V − R	0	0	−5	−1	−1	0	0	0	2	5	−7
V − I	0	−1	−6	−1	0	0	0	−1	2	7	−9

Note. 1. All elements scaled individually by +0.3 dex, except C, which is increased by +0.15 dex.

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Table 3. Color Behavior with Enhancements at Constant [R/H]

Color	C	N	O	Ne	Mg	Si	S	Ca	Ti	Fe	α
Dwarf, Teff = 4000 K
U − B	−11	10	30	⋅⋅⋅	−65	−35	0	−40	15	139	−97
B − V	22	0	−31	⋅⋅⋅	−17	38	0	−7	15	26	−5
V − R	0	0	0	⋅⋅⋅	31	0	0	−13	4	14	19
V − I	−3	0	1	⋅⋅⋅	32	−1	0	−14	4	16	19
Dwarf, Teff = 5000 K
U − B	28	26	−10	⋅⋅⋅	−20	−33	0	−3	11	74	−57
B − V	24	4	−14	⋅⋅⋅	−30	8	0	6	7	24	−23
V − R	−1	−3	2	⋅⋅⋅	9	−1	0	0	3	12	11
V − I	−10	−10	7	⋅⋅⋅	11	0	0	−1	3	16	18
Dwarf, Teff = 6000 K
U − B	8	17	1	⋅⋅⋅	11	−13	0	2	8	41	8
B − V	13	3	0	⋅⋅⋅	−12	−5	0	7	5	15	−8
V − R	2	0	0	⋅⋅⋅	0	0	0	0	2	8	0
V − I	1	−2	0	⋅⋅⋅	0	0	0	0	2	11	0
Giant, Teff = 4000 K
U − B	21	18	1	⋅⋅⋅	−20	−44	0	−20	22	125	−63
B − V	22	0	−27	⋅⋅⋅	−28	39	0	−3	12	23	−10
V − R	−9	−4	5	⋅⋅⋅	21	0	0	−8	3	13	19
V − I	−22	−9	11	⋅⋅⋅	23	0	0	−9	2	17	26
Giant, Teff = 5000 K
U − B	29	33	−9	⋅⋅⋅	31	−32	0	7	11	34	5
B − V	24	8	−9	⋅⋅⋅	−19	−3	0	8	6	13	−20
V − R	4	−9	0	⋅⋅⋅	2	0	0	0	2	11	5
V − I	−6	−22	6	⋅⋅⋅	7	2	0	0	3	17	17
Giant, Teff = 6000 K
U − B	3	11	1	⋅⋅⋅	16	−5	0	7	8	17	25
B − V	7	2	0	⋅⋅⋅	−3	0	0	10	5	14	9
V − R	1	0	0	⋅⋅⋅	0	0	0	0	2	6	0
V − I	1	0	0	⋅⋅⋅	0	0	0	0	2	8	0

Note. 1. All elements scaled individually by +0.3 dex, except C, which is increased by +0.15 dex.

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Comparing corresponding entries in the two tables, especially at the 6000 K giant, one sees that oxygen have little effect on the spectrum by themselves; it is the effect of the decrease of the rest of the elemental abundances that causes the bulk of the spectral change in the constant-Z case. Unsurprisingly, it is also clear from the table that cooler stars are more susceptible to element-by-element effects than warmer stars, at least at optical wavelengths.

2.3. Integrated-Light Color Results

Table 4 presents color results for the isochrone-summed models assuming a Salpeter (1955) initial mass function and using the Worthey (1994) machinery for some disparate ages of populations. The bolometric correction (BC) row includes both isochrone effects and direct stellar spectral effects with the caveat that our synthetic spectra are limited in wavelength coverage, so the fluxes at given wavelengths were normalized to the older low-resolution Worthey (1994) flux library at the same Z. Thus, only effects that affect wavelengths between 3000 and 10000 Å are considered, and there may be additional, small effects present that are not accounted for. However, in absolute value, all of the BC shifts are quite small, the largest being 6% for the case of all α-elements enhanced. It is unlikely that element ratio effects will be of major concern for the mass estimation of clusters and galaxies from their luminosities (see also Cassisi et al. 2004).

Table 4. Model Population Color Behavior with Enhancements at Constant Z

Color	Synthetic Color (mag)	ΔI (C) (mmag)	ΔI (N) (mmag)	ΔI (O) (mmag)	ΔI (Ne) (mmag)	ΔI (Mg) (mmag)	ΔI (Si) (mmag)	ΔI (S) (mmag)	ΔI (Ca) (mmag)	ΔI (Ti) (mmag)	ΔI (Fe) (mmag)	ΔI (α) (mmag)
Population age 1 Gyr
BCV	⋅⋅⋅	−0.3	0.0	5.5	1.9	2.9	2.6	1.6	−1.2	0.8	−3.8	8.0
U − B	0.050	−3.7	2.3	−14.9	−4.0	1.6	−5.5	−1.9	2.6	2.2	14.8	−20.7
B − V	0.361	−1.0	−0.2	−34.6	1.3	5.7	9.1	6.2	6.0	2.4	−1.1	−11.6
V − R	0.223	−1.1	−0.2	−17.1	2.4	7.6	7.4	4.8	1.0	1.9	−1.7	−2.3
V − I	0.458	−4.0	0.4	−26.3	5.8	15.2	15.2	10.7	2.0	7.2	−7.6	4.5
Population age 2 Gyr
BCV	⋅⋅⋅	−9.9	−4.5	11.1	0.7	12.2	4.5	0.6	−17.5	15.5	3.9	46.6
U − B	0.171	0.5	12.1	−30.2	4.9	7.7	−6.6	4.8	−2.8	16.7	12.5	−18.4
B − V	0.664	16.1	6.3	−20.6	12.9	−10.0	10.4	8.2	−2.4	15.2	−2.5	−10.4
V − R	0.428	0.5	−1.6	−1.9	6.6	8.8	7.1	4.2	−14.2	14.2	4.6	22.0
V − I	0.877	−15.5	−4.9	10.0	8.5	23.3	13.9	6.2	−43.3	47.2	9.8	97.5
Population age 5 Gyr
BCV	⋅⋅⋅	−21.1	−11.1	10.5	−2.8	12.0	0.0	−3.0	−2.7	20.2	−1.6	48.8
U − B	0.369	−10.7	5.7	−75.5	−13.1	14.9	−19.8	−8.1	−2.7	5.1	41.1	−71.3
B − V	0.861	9.7	−4.8	−52.3	−4.3	−15.6	5.8	−5.7	1.5	−3.0	15.1	−54.8
V − R	0.537	−9.1	−10.8	−15.6	−3.3	11.2	1.4	−3.7	−3.9	6.2	8.7	4.2
V − I	1.087	−40.9	−22.5	−3.5	−8.1	18.4	−0.4	−8.4	−5.7	40.6	5.0	71.9
Population age 12 Gyr
BCV	⋅⋅⋅	−22.5	−10.4	11.8	−3.5	21.4	2.8	−1.5	−1.2	30.4	7.2	55.3
U − B	0.599	2.5	14.7	−101.8	−15.7	31.1	−14.7	−7.1	−0.8	9.2	68.8	−99.0
B − V	0.988	21.1	0.8	−58.1	−4.9	−8.3	15.7	−3.4	4.2	−0.4	26.3	−65.8
V − R	0.604	−6.1	−8.4	−15.0	−3.6	22.4	5.3	−1.8	−2.3	11.7	17.1	5.8
V − I	1.200	−37.2	−17.3	1.5	−8.4	36.3	7.9	−3.9	−1.6	57.2	22.2	78.6

Note. 1. All elements scaled individually by +0.3 dex, except C, which is increased by +0.2 dex (see footnote 18).

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The other immediate conclusion from Table 4 is that older populations show larger spectral effects due to element-by-element abundance changes. This is a straightforward consequence of the earlier conclusion that cooler stars are more sensitive; the light of older populations is dominated by stars that are cooler than those present in younger ones.¹⁶ Oxygen and neon tend to make the colors bluer, while species that contribute more to the lines in the spectrum generally make them redder. Exceptions can easily be explained if one knows where the lines contribute the most. For instance, magnesium has most of its absorption near 5100 Å, i.e., in the V band, so adding Mg makes B − V bluer while it makes V − R and V − I redder. The former, the bluer B − V, is also partly due to the increase in the flux in the region around 4000 Å from the Mg-enhanced spectra as shown in Figure 3 and described in Cassisi et al. (2004). The latter, the redder V − R and V − I, also reflect the cooler red giant branch as illustrated in Figure 8 of Paper I. Figure 4 displays this Mg-enhanced integrated case at 5 Gyr (thick line) over the single-star case of a 4000 K giant (thin line). The populations respond rather like the stars do, as can be seen from Figure 4. Based on this, one would suspect that isochrone-caused effects are relatively minor though non-negligible, and this conclusion will be confirmed and amplified in the following section.

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The effects of element-by-element enhancement on the Lick indices (Worthey et al. 1994) are described in this section.¹⁷ The synthetic indices are not very accurate in absolute predictions (see Korn et al. 2005; Serven et al. 2005), so we employ a differential approach in which the fitting functions of Worthey et al. (1994) and Worthey & Ottaviani (1997) are used as the zero point, and delta-index information as a function of element ratio is incorporated via measuring the synthetic spectral library. This procedure is similar to that of previous investigations (e.g., Trager et al. 2000a, 2000b; Proctor & Sansom 2002; Thomas et al. 2003; Lee & Worthey 2005; Schiavon 2007) but more sophisticated since an entire grid of delta-index information was used. That is, 350 spectra at solar Z, plus similar grids for four other Z values for this work, as opposed to two or three synthetic stars at solar abundance only for previous works.

To maintain an exact correspondence with Paper I, all the elements are 0.3 dex enhanced, except carbon, which is enhanced by 0.2 dex.¹⁸ In the cases of carbon, nitrogen, and oxygen enhancements, we investigate both at fixed total metallicity and at fixed [Fe/H] (and [R/H]). The cases at fixed [Fe/H] are denoted with plus sign in the figures (e.g., C+, N+, O+). Also in the figures, solar-scaled solar metallicity predictions are connected by a solid line from 1 Gyr to 12 Gyr and the element-enhanced cases are marked at 1, 2, 5, and 12 Gyr.

We have selected Fe5406 as a reference index in most plots. Among eight Lick iron indices (Fe4383, Fe4531, Fe5015, Fe5270, Fe5335, Fe5406, Fe5709, and Fe5782), we predict that Fe5406 is insensitive to every element except iron (see Figures 10 and 11 and Table 5 and online spectra described in footnote 17), making it a convenient independent variable.

As has already been mentioned in the literature (Lee et al. 2007b), for most of the cases the isochrone effects are relatively minor compared to the stellar spectral effects (see also Schiavon 2007). For some cases, however, isochrone effects are non-negligible and quite important (see Hβ in Figure 11; see also Figure 17 in Coelho et al. 2007).

It may be worthwhile to mention for clarity that "isochrone effects" indicate the temperature, luminosity, and stellar lifetime effects from element ratio changes, and, in the case of the iron-enhanced mixture, the altered [Fe/H] value that goes into the empirical fitting functions in our experiment. When calculating observables, we would still use a scaled-solar-ratio spectral library. These isochrones were presented in Paper I. In the present Paper II, we add the detailed spectral effects due to element-by-element enhancement at the stellar atmosphere/stellar flux level. The "direct stellar spectral effects" are those that come purely from the emergent spectra with isochrones held fixed.

[Carbon and nitrogen: CN₂]: Lick indices CN₁ and CN₂ have identical central bandpasses, but CN₂ has a narrower blue continuum which makes the CN₂ somewhat less prone to abundance variations other than those due to elements C and N. We compare CN₂ with G4300 as carbon, nitrogen, oxygen, silicon, and iron are enhanced in Figure 5. The upper panels show that CN₂ is both carbon and nitrogen sensitive. Nitrogen's effect is more prominent (partly because carbon is enhanced only by 0.2 dex compared to the 0.3 dex nitrogen enhancement). The bottom right panel also suggests that silicon and iron affect CN₂ in a non-negligible way when stellar populations become older than 5 Gyr. We can tell from Table 5 that the silicon effect is mostly from the stellar spectra, while the iron effect is largely from the isochrones. The oxygen-enhanced case is displayed in the bottom left panel. It shows that simply adding O alters CN₂ and G4300 by a small amount (increases at young ages and decreases at old ages; the latter via consumption of more C into the CO molecule via molecular equilibrium balance¹⁹), but if Z is held constant both indices decrease much more due to the displacement of C and N to lower abundance because of the O-enhancement and fixed sum. G4300 is N-insensitive. Also, we note that CN₂ has little sensitivity to Mg-, S-, Ca-, or Ti-enhancement.

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[Carbon: G4300 versus C₂4668]: in Figure 6, G4300 and C₂4668 are plotted as a function of Fe5406. The left panels show C- and Fe-enhanced models, while the right panels show the effects of Si- and Ti-enhancement. G4300 and C₂4668 are known to be good carbon indicators among Lick indices along with CN₁ and CN₂. The left panels show that this is indeed the case. In the bottom left panel, however, it can be seen that C₂4668 is also highly iron sensitive, as indicated by its former name, Fe4668 (Worthey 1994).²⁰ Contrary to C₂4668, G4300 shows a negligible iron sensitivity. Furthermore, the right panels show that C₂4668 is influenced by Si and Ti, whereas G4300 shows only slight Ti sensitivity. Both G4300 and C₂4668 show little sensitivity by N-, Mg-, S-, or Ca-enhancement.

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The prospects for disentangling C, N, and O are now fairly good, because it appears that there is a lot of sensitivity among various indices. However, at the moment it appears that, with the indices available, there will be considerable degeneracy among the three quantities. In the future, adding NH, CH, and CO features may help considerably (e.g., Yong et al. 2008; Martell et al. 2008; Marmol-Queralto et al. 2008).

[Calcium: Ca4227 versus Ca4455]: Figure 7 compares Ca4227 and Ca4455 with Fe5406. Carbon-, nitrogen-, and oxygen-enhanced cases at fixed [Fe/H] are displayed at the left panels, while the right panels depict calcium- and iron-enhanced cases at fixed Z. It is clear from the upper-right panel of Figure 7 that Ca4227 is significantly boosted with calcium enhancement, the effect increasing with age. To a lesser degree, Ca4227 is also affected by C, N, O, and Fe. Carbon and nitrogen enhancements make Ca4227 weaker by 0.3 Å, whereas the oxygen enhancement does the opposite mostly due to their effects at the blue continuum (see also Prochaska et al. 2005).

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Contrary to Ca4227, Ca4455 is hardly influenced by any of those elements. According to this study, Ca4455 is found to be the most element-enhancement-free Lick index. This is consistent with the previous findings by Tripicco & Bell (1995) and Korn et al. (2005) although our presentation is based on a large spectral grid weighted by isochrones rather than three stars. One concern, however, is that two recent data sets of Milky Way globular clusters, by Cohen et al. (1998) and Puzia et al. (2002), both significantly disagree with theoretical model predictions and also each other (Figure 3 of Lee & Worthey 2005). According to Tables 1–3 of Tripicco & Bell (1995), Ca4455 has the strongest dependence on the bandpass placement (wavelength shift error) among Lick indices. This is because that the blue continuum and the index bandpass of Ca4455 share the strong Ca absorption line feature near 4455 Å and consequently cancel out its effect, but only if the wavelength match is perfect. This phenomenon at the stellar level with 10 km s⁻¹ velocity dispersion is displayed in Figure 8. Both Ca4227 and Ca4455 are rather insensitive to Mg-, Si-, S-, or Ti-enhancement.

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[Titanium: Fe4531 and Fe5015]: Fe4531 and Fe5015 are displayed in Figure 9 with Fe5406. TB95, Trager (1997), KMT05, LW05, and Serven et al. (2005) indicate that these two indices are titanium sensitive, and we confirm that their titanium sensitivity is indeed strong and almost comparable to the iron sensitivity. Fe5406, on the other hand, demonstrates little titanium sensitivity.

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[Balmer lines: Hβ, Hγ_A, Hγ_F, Hδ_A, Hδ_F]: Balmer lines are widely used as an age indicator because of their nonlinear temperature sensitivity in stars, tracing better than many indices the temperature of the main-sequence turnoff. However, Lee & Worthey (2005) and earlier work (Worthey et al. 1994; Thomas et al. 2004; Coelho et al. 2007) found that they are also abundance sensitive to some degree. In Figures 10–18, we look into their element-by-element sensitivity in detail.

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Effects of the individual 10 chemical elements' enhancement on the Hβ and Fe5406 are shown in Figure 10. The effects of carbon, nitrogen, and oxygen enhancements are of great importance but they are relatively difficult to understand here because our experimental setup preserves the total metallicity. In other words, it is not straightforward to determine whether we are seeing the effects of C-, N-, and O-enhancement or whether we are seeing other elements (such as Mg and Fe) countereffects due to their depression. Hence, in Figure 11, we display C-, N-, and O-enhancement cases both at the fixed total metallicity and at the fixed [Fe/H] (the plus signs). It is seen from the left panels of Figure 11 that unlike nitrogen, oxygen at young ages and carbon at old ages influence Hβ. The top and bottom right panels of Figure 11 illustrate that it is mostly the isochrone-level effects of carbon and oxygen enhancements that affect Hβ. Figure 10 further shows that Hβ is similarly altered by the Mg-enhancement and in this case it is mostly due to the synthetic spectra (see also Table 5 and Figure 12).

In the lower-right panel of Figure 10 (also in the bottom panels of Figure 11), a grid with a range of metallicity ([Fe/H] = −2.0, −1.0, −0.5, 0.0, and 0.5) is displayed at 1, 2, 5, and 12 Gyr. These additional calculations are of solar-scaled chemical mixtures (Dotter et al. 2007a). We have also depicted α-element enhanced cases both at the fixed Z and at the fixed [Fe/H] (Alpha+).²¹ It is intriguing to note that the effect due to the Fe-enhancement by 0.3 dex is seen over the [Fe/H] = 0.5 grid line. This is because these grids only reflect the mere isochrone effects of iron variation with solar-scaled chemical mixtures, while the 0.3 dex Fe-enhancement case shows both isochrone and spectral effects combined.

We find that the Hβ becomes weaker in the α-element enhanced case at fixed [Fe/H] mostly because of the effects of Mg (both isochrone and spectral as one could see from Table 5), while it stays nearly unchanged in the α-element enhanced case at the fixed Z mostly because of the reflection of depression of Fe. At 12 Gyr, a comparison of integrated spectra uncovers that adding Mg brings down the blue continuum, making Hβ weaker,²² but adding Fe brings down the central bandpass as well as the red continuum, the net effects of which tend to cancel out effects from Fe. Alpha-enhancement at fixed Z mostly reflects the decrease of Fe due to dilution rather than overt, direct spectral effects from α-elements. They are displayed in Figures 12–14. The solid lines are the index bandpass and the dashed lines are the blue- and the red-continuum edges.

Figures 15 and 16, in contrast, display that both Hγ and Hδ become mildly (∼0.7 Å) stronger with Mg-enhancement. Furthermore, the top panels of Figures 15 and 16 illustrate that the broader A indices (Hγ_A, Hδ_A) show sensitivity to Fe-enhancement and become significantly weaker with increasing age, by up to 3 Å at 12 Gyr for the case of the Hδ_A. This is mostly due to spectral effects, as can be seen from Table 5. They are illustrated in Figures 17 (Hγ) and 18 (Hδ). From this experiment, it seems that for the high-order Balmer lines, the F indices (Hγ_F, Hδ_F) are less prone to abundance changes because of their narrower index definition and therefore may possibly serve as more robust age indicators. Furthermore, it is found that Hδ_F among Balmer lines has the least sensitivity to C, N, and O (see also Schiavon et al. 2002; Prochaska et al. 2007).

In Figure 19, we show some selected diagrams for illustrating element enhancement. In the upper-left panel, CN₂ and G4300 are compared and the effects of carbon and nitrogen enhancements are depicted. The plot shows that CN₂ is sensitive to both carbon and nitrogen. CN₂ index values go up by 0.04 mag at 12  Gyr with 0.3 dex nitrogen enhancement here. G4300, in contrast, is primarily a carbon-sensitive index. Ca4227 and G4300 are contrasted in the lower-left panel of Figure 19 and the effects of sulfur, calcium, and titanium are illustrated. It is seen that Ca4227 is significantly affected by calcium enhancement whereas G4300 is not much altered by anything but carbon. In the upper-right panel, Mg b and Fe5406 are compared and the effects of magnesium and silicon are shown. It is clear that Mg b is notably affected by the magnesium enhancement. Hβ and Fe5406 are contrasted in the lower-right panel and, as we have seen in Figures 10 and 13, Hβ is not Fe-enhancement sensitive, while Fe5406 is significantly affected by Fe.

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Figure 20 is basically same as Figure 19, but here the isochrone effects are decoupled from those of synthetic spectra. The lines show the combination of isochrones and stellar spectral effects, while the points depict the isochrone effects alone at 1, 2, 5, and 12 Gyr. It is seen again from Figure 20 that the synthetic spectra make the spectral lines stronger and/or weaker, while isochrones play a comparatively minor role. The displacement of points in the bottom right panel is mostly due to the different [Fe/H] values that go into the index value calculations rather than the isochrone changes (see Figure 1 of Paper I).

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We have commenced this project to make stellar population models which incorporate flexible chemistry, so that almost any interesting chemical mixture can be interpolated. Paper I dealt with the effects on the stellar evolution models, examining the temperature and luminosity changes due to the altered opacities when 10 chemical elements are individually tweaked to the end of the red giant branch. In this paper, we combine those isochrone effects with the stellar spectral effects in order to investigate their mixed effects on the integrated spectrophotometric indices as well as in their integrated spectra themselves. We again emphasize here that the models in this study are incomplete in terms of inclusion of all stellar evolutionary phases and should not be used blindly when comparing to real stellar populations until the helium-burning phases are properly incorporated. A version with a full range of metallicity and with horizontal branch and AGB stars included is planned. Comparison of our models with observations of Virgo cluster galaxies will be presented as well (J. L. Serven et al. 2009, in preparation).

Within our spectral coverage (3000–10000 Å), we have investigated the broadband color behaviors in the UBVR_CI_C filter set. As one would expect, older populations show larger spectral effects due to element-by-element abundance changes. This mostly reflects temperature effects. We have also confirmed that Mg is the most important α-element that shapes the U − B and B − V colors as already depicted in Cassisi et al. (2004).

From our investigation of Lick indices using the integrated spectra, we find that (1) CN₂ is a useful nitrogen indicator once we have good carbon abundances from G4300 and C₂4668, but good silicon (and also titanium for the C₂4668) abundances are also needed, (2) Ca4227 is a robust calcium indicator with some good constraints of C, N, and O, (3) Fe4531 and Fe5015 are very useful titanium indicators where an independent iron abundance is provided, (4) Mg b and Fe5406 are good magnesium and iron indicator, respectively, and (5) the variation of individual elements affects the Balmer lines. We defer the investigation of NaD and TiO₁ and TiO₂ indices until we have the Na-enhanced isochrones and can model TiO molecular effects with confidence. Below, we illuminate some points that we have described here with the help of full spectra.

Fe4531 and Fe5015: from Figure 9 we see that both Fe4531 and Fe5015 prove to be good titanium indicators. They are almost equally sensitive to titanium and iron. Figures 21–23 show the SAURON (Bacon et al. 2001) spectral range, 4810–5350 Å, that includes Hβ, Fe5015, Mg₁, Mg b, Fe5270, and a part of Fe5335. Here the integrated spectra of solar-scaled, Mg-, Fe-, and Ti-enhanced cases are shown at 2 Gyr with 300 km s⁻¹ velocity dispersion normalized at 4750 Å. Hβ is not influenced much by the enhancement of these elements at this age, as Figure 10 also shows. Mg b is mostly sensitive to Mg, as Figure 21 shows, while Fe5015, Fe5270, and Fe5335 are notably sensitive to Fe-enhancement, although Fe5015 is equally sensitive to titanium, as Figures 22 and 23 display.

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Moreover, we have found that the Fe-enhanced and Ti-enhanced spectra show their centroids at different wavelengths in the case of Fe4531, opposite sides from the scaled-solar spectra, because of different locations of iron and titanium lines in their index bandpass. Figure 24 displays this case.²³ We have preliminary hints from high-S/N, high-resolution spectra of Virgo cluster galaxies taken at the Kitt Peak 4 m telescope (J. L. Serven et al. 2009, in preparation) that galaxies with the higher velocity dispersion tend to have their centroids at the longer wavelengths, indicating higher Ti-enhancements. If confirmed, this would indicate a Ti–σ relation, similar to the well-known Mg–σ relation (see also Milone et al. 2000).

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Hβ: the bottom right panel of Figure 10 shows that, in an α-enhanced mixture at the fixed [Fe/H] (Alpha+), Hβ becomes weaker. This sounds a bit different from the conclusion of LW05 where Hβ is α-element insensitive. As we can see from Table 5, the effects that we see from the bottom right panel of Figure 10 are mostly isochrone effects, especially at young ages. The Hβ index becomes weaker because of the decrease of temperature of stellar isochrones from the α-enhanced case at fixed [Fe/H] (see also Coelho et al. 2007; Schiavon 2007). LW05 used only solar-scaled isochrones at solar and super-solar metallicities, although these authors employed modified stellar spectra because of the α-enhancement.

Moreover, it is worth emphasizing that α-enhanced isochrones at fixed Z are now no longer significantly hotter than the solar-scaled ones. This has been revealed by Paper I, in its Figure 11, after incorporating the latest development of low-temperature opacities by Ferguson et al. (2005). If this behavior is indeed true, it will certainly affect the conclusions of earlier works (e.g., Thomas & Maraston 2003) that are based upon the Salasnich et al. (2000) isochrones, which were later shown by Weiss et al. (2006) to present problems.

Hγ and Hδ: Fe-enhancement makes these indices significantly weaker, especially for the broader indices, Hγ_A and Hδ_A (see also Graves & Schiavon 2008). Figures 17 and 18 show that this is because of Fe lines that inhabit the continuum region. It is suggested therefore that the narrower indices (Hγ_F and Hδ_F) may serve as better age indicators in case the stellar systems are of wildly different chemical mixtures.

Our goals are to narrow down the uncertainties of mean age estimations to 10% when derived from a single integrated light spectrum. We believe that we can reach these goals as we are able to take into account the effects from individual chemical elements. The ultimate goal then obviously would be the understanding of the chemical enrichment and star formation histories of galaxies, stepping away from the study of mean ages and mean metallicities to begin to tackle the more realistic problem of multi-age, multi-metallicity stellar populations as they exist in galaxies. We believe that several efforts such as STARLIGHT (Cid Fernandes et al. 2005), SPECKMAP (Ocvirk et al. 2006), and MOPED (Panter et al. 2007), will be even more useful once they use sophisticated stellar population models with flexible chemistry as inputs.

We are grateful to the referee, Ricardo Schiavon, for a thorough reading which greatly helped us to improve the paper. We also thank Jim Rose, Jon Fulbright, and Andreas Koch for useful discussions on the Mg-enhancement of the metal-rich cool giants. Support for this work was provided by the NSF through grant AST-0307487, the New Standard Stellar Population Models (NSSPM) project. H.-c.L. also acknowledges J P Blakeslee's support via NASA grant. P.C. acknowledges the support by the European Community under a Marie Curie International Incoming Fellowship.