Investigating [X/Fe], Imf and Compositeness in Integrated Models

INVESTIGATING [X/FE], IMF AND COMPOSITENESS IN INTEGRATED MODELS

By BAITIAN TANG

A dissertation submitted in partial fulﬁllment of the requirements for the degree of

DOCTOR OF PHILOSOPHY

WASHINGTON STATE UNIVERSITY Department of Physics and Astronomy

MAY 2015

The members of the Committee appointed to examine the dissertation of BAITIAN TANG ﬁnd it satisfactory and recommend that it be accepted.

Guy Worthey Ph.D., Chair

Sukanta Bose, Ph.D.

Matthew Duez, Ph.D.

ii ACKNOWLEDGEMENT

First and foremost I oﬀer my sincerest gratitude to my advisor, Dr. Guy Worthey, who supported my study and research with motivation, enthusiasm, and immense knowledge. There were times when research funding was scarce, but his optimism, diligence and patience

taught me the true meanings of research. Dr. Worthey gave me lots of free space in pursuing the research that interested me, and backed me up with his astrophysical proﬁciency. I would also like to thank the rest of my committee members: Dr. Sukanta Bose, and Dr. Matthew Duez for their encouragements and comments. Their courses, general relativity and astrophysical ﬂuids, have expanded my eyesight to a much broader horizon. My sincere thanks also go to Dr. Qiusheng Gu and Dr. Zhaohui Shang, who supported my job applications and gave many insightful suggestions. During my Ph.D. study, I have been blessed with a friendly and cheerful group of fellow

students. We enjoyed the great life and culture of the northwest. My friends and colleagues in China also responded to my daily or research questions with great welcome. The Department of Physics and Astronomy has provided the support I have needed to ﬁnish the courses and complete my dissertation. NASA and the College of Arts and Sciences have funded my studies.

Last, but not the least, I would like to thank my parents for giving birth to me and supporting me spiritually throughout my life.

iii INVESTIGATING [X/FE], IMF AND COMPOSITENESS IN INTEGRATED MODELS

Abstract

by Baitian Tang, Ph.D. Washington State University May 2015

Chair: Guy Worthey

This dissertation explores several existing challenges of evolutionary stellar population synthesis models in integrated light: age-metallicity degeneracy, initial mass function (IMF), elemental abundances, and compositeness. First, we search for age-sensitive and metal- sensitive colors in three photometric systems. We also add to the discussion of optical to near-infrared Johnson-Cousins broad band colors, finding a great decrease in age sensitivity when updated isochrones are used. Then we investigate the element abundances and compositeness of our models, in which we assume a single-peak abundance distribution and the same elemental abundance trends as the Milky Way bulge stars. Varying the width of the abundance distribution function reveals novel “red lean” and “red spread” effects. Next, we study three effects that co-determine the dwarf/giant ratio: the IMF slope, the IMF low mass cut-off (LMCO), and AGB star contributions. This degeneracy can be lifted for old, metal-rich stellar populations, although at an observationally challenging level ( 0.02 mag). ≈ Finally, we select and reduce more than 200 z 0.4 red galaxy spectra from the DEEP2 ∼ sky survey, and measure the Lick-style spectral indices from the composite spectra. Multiple

iv optical IMF-sensitive indices suggest a shallower IMF that qualitatively agrees with current literature.

v TABLE OF CONTENTS

ACKNOWLEDGEMENT ...... iii

ABSTRACT ...... iv

TABLE OF CONTENTS ...... vi

LIST OF TABLES ...... ix

LIST OF FIGURES ...... x

CHAPTER

1 INTRODUCTION TO STELLAR POPULATION SYNTHESIS ..... 1

2 ON DISTINGUISHING AGE FROM METALLICITY WITH PHOTO- METRIC DATA ...... 12 2.1 Introduction...... 12 2.2 Analysis ...... 14

2.2.1 DDO,BATC&Str¨omgren ...... 14 2.2.2 Element Sensitivity ...... 21 2.2.3 (B V ) vs. (V K)Plots ...... 22 − − 2.3 Discussion...... 26

2.3.1 Str¨omgren System: Empirical Leverage? ...... 26 2.3.2 ModelGridDiﬀerences...... 27

vi 2.4 Summary ...... 30

3 COMPOSITE STELLAR POPULATIONS AND ELEMENT BY ELE-

MENT ABUNDANCES IN THE MILKY WAY BULGE AND ELLIP- TICAL GALAXIES ...... 32 3.1 Introduction...... 32 3.2 Composite Stellar Populations with Metallicity-dependent Chemical Compo-

sition...... 35 3.2.1 Abundance Distribution Functions (ADFs) ...... 38 3.2.2 Milky Way Bulge Chemical Composition ...... 42 3.2.3 300 km s−1 Elliptical Galaxy Chemical Composition ...... 46 3.3 Results...... 47

3.4 Discussion...... 52 3.4.1 Varying the Widths of the ADFs: Red Lean and Red Spread . . . . . 52 3.4.2 Comparing Chemical Compositions of the Milky Way Bulge and El- liptical Galaxies ...... 56

3.4.3 Recovering Abundances with Simple Stellar Population Models . . . . 59 3.4.4 Detectability of ADF Width ...... 61 3.5 Summary ...... 63

4 ON DISENTANGLING INITIAL MASS FUNCTION DEGENERACIES IN INTEGRATED LIGHT ...... 65 4.1 Introduction...... 65

4.2 IMFslope,LMCO,andAGB ...... 68 4.2.1 Modeldescription...... 68 4.2.2 An Old, Metal-rich Population ...... 70 4.2.3 A Young, Metal-rich Population ...... 71

vii 4.2.4 Colors and Indices Broken into Evolutionary Phases ...... 72 4.3 ADF-IMFcoupling ...... 79 4.4 Discussion...... 83 4.4.1 SwappingModels ...... 83

4.4.2 Feasibility of Breaking the Degeneracy ...... 85 4.4.3 A Combination of Multiple Eﬀects ...... 88 4.4.4 Recovering [X/Fe], IMF slope, LMCO, and AGB Percentage . . . . . 90 4.5 Summary ...... 93

5 INITIAL MASS FUNCTION OF RED GALAXIES AROUND z = 0.4: A SPECTROSCOPIC APPROACH ...... 94 5.1 Introduction...... 94

5.2 SpectralReduction ...... 98 5.2.1 SampleSelection ...... 98 5.2.2 Composite Spectra and Index Measurements ...... 101 5.3 Non-universalIMF ...... 103

5.3.1 ModelsandLocalObservables ...... 103 5.3.2 Comparison ...... 105 5.4 Discussion...... 107 5.4.1 PossibleIMFDegeneracies ...... 107

5.4.2 IMF in High-redshift Galaxies ...... 108 5.4.3 TheWaystoImprove...... 109 5.5 Summary ...... 109

BIBLIOGRAPHY ...... 111

viii List of Tables

2.1 Metallicity Sensitivities at 8 Gyr, Z⊙ ...... 15

2.2 Index Changes at 8 Gyr, Z⊙ ...... 21

3.1 Mean [M/H] for Composite Populations Peaking at [M/H] = 0 ...... 53 3.2 Recovery of Population Parameters Under an SSP Hypothesis ...... 60

4.1 Colors and Indices of Each Phase for the Old Population ...... 75

5.1 Optical IMF-sensitive Indices ...... 98

ix List of Figures

2.1 DDOC(35-48)vs.C(41-42)plot ...... 16 2.2 BATC5795-6075vs. 6075-6660plot...... 17

2.3 Str¨omgren [c1] vs. [m1]plotofW94models...... 19

2.4 Str¨omgren [c1] vs. [m1]plotofB09models ...... 20 2.5 (B V ) vs. (V K)plotofB94models...... 24 − − 2.6 (B V ) vs. (V K)plotofB09models...... 25 − − 2.7 Str¨omgren plot with star forming galaxies ...... 28

2.8 (B R) vs. (R K)plotofB94andB09models ...... 31 − −

3.1 FouranalyticalADFs...... 39 3.2 ObservedADFsvs. normal-widthADF...... 40 3.3 MilkyWayBulgeADFs ...... 41 3.4 Abundance trends in the Milky Way bulge ...... 44

3.5 Integrated light index diagrams ...... 49 3.6 Narrow,normalandwidewidthADFs ...... 55 3.7 DetectabilityofADFwidth ...... 62

4.1 Color-color and index-index plots for old, metal-rich population ...... 69

4.2 Color-color and index-index plots for young, metal-rich population...... 71 4.3 Number of stars, luminosities, and colors vs. evolutionary points ...... 73 4.4 Vectors presenting star number increment in diﬀerent phases...... 74 4.5 Spectraandspectralratiosofeachphase...... 78

x 4.6 IMFslopedriftsofeachphaseatoldage ...... 80 4.7 IMFslopedriftsofeachphaseatyoungage ...... 81 4.8 CSPs with IMF [M/H]dependence...... 84 − 4.9 Color-color and index-index plots at old age using FSPS models ...... 86

4.10 Color-color and index-index plots at young age using FSPS models ..... 87 4.11 Symposium of multiple eﬀects ...... 89 4.12 Recoveringparameters ...... 92

5.1 Galaxy color magnitude diagram ...... 100

5.2 Spectrabeforeandafterstacking...... 102 5.3 Comparingobservablesandmodels ...... 106

xi CHAPTER 1

INTRODUCTION TO STELLAR POPULATION

SYNTHESIS

Galaxies, the building blocks of our mysterious Universe, have attracted increasing attention since the great debate by Harlow Shapley and Heber Curtis in 1920. Early workers, such as Edwin Hubble1, revealed that hundreds of thousands of galaxies wander outside the Milky

Way galaxy. By studying the resolved stars in the central region of the Andromeda galaxy and its two companion galaxies, Baade (1944) proposed two distinct stellar populations: Population I stars are young and luminous, while Population II stars are old and highly evolved. Historically, two different types of routines were postulated to decode the stellar constitution from the integrated light of galaxies. The first type of routine is basically a star-by-star addition problem. The idea is to construct galaxy models with different relative proportion of stars, and then the one which best matches the observables is chosen to represent the stellar constitution of the given galaxy. This is often termed as “empirical population synthesis”. Spinrad and Taylor (1971) picked the mock galaxy that best matched the spectrophotometric observables with a trial-and-error approach. To improve the computational efficiency, Faber (1972) applied quadratic programming to replace the trial-and-error portion of assigning weights with numerical optimization. A spectrum fitting of 17 elliptical and lenticular galaxies using stellar spectral libraries was later performed by

1In 1924, Edwin Hubble concluded that some spiral nebulae were too distant to be part of the Milky Way and were, in fact, galaxies like our own.

1 Pickles (1985). However, two drawbacks from empirical population synthesis should be also noticed. First, the solution is not unique. For example, the spectra of a G type giant and a G type dwarf closely resemble each other, since the general spectral shape is determined by its temperature. Models with diﬀerent proportions of giants and dwarfs of the same type are

degenerate. Second, empirical population synthesis was never able to include a metallicity axis since most of the stars used in the models were of solar abundance. The concept of the stellar population was later generalized to a group of stars that resemble each other in spatial distribution, chemical composition, or age. The so-called “Single Stellar Population” (SSP) assumes all the stars have the same metallicity and form

at the same time. Thus, the relative ratios of stars in each phase can be constrained by stellar evolution models, which reduces the uncertainties of weight-assigning, and leads to a diﬀerent type of routine, often called evolutionary stellar population synthesis (SPS) — deriving the integrated-light models based on theoretical evolutionary tracks of diﬀerent mass stars and a

given initial mass function (IMF). One may solve the problem with analytic stellar expression or numerical computation, depending on research interest. The former approach extracts the analytical stellar relations from idealized models to derive the unknown galactic quantities. The major advantage is the ability to show clearly the impact of model parameters and

assumptions on the results. In this regard, under the basic assumptions of mass, luminosity, life time relationships, and IMF, Tinsley (1972, 1973); Tinsley and Gunn (1976) predicted that the luminosity of an old stellar system evolves with time as a function of t−1.6+0.3α, where α is the power-law slope of the IMF. This is crucial for the study of cosmic IMF evolution.

But given the complex nature of our universe, analytic expressions that can replicate all the details are, by and large, rare. As more observational measurements and much more eﬃcient computers are available, numerical calculations become more and more popular. Tinsley (1968), which was recognized as a pioneer work in this ﬁeld, calculated the evolu-

2 tion of population I stars using discrete time steps of 109 years and 13 stellar masses. By upgrading the major components of SPS models, namely, the stellar isochrones, the stellar libraries, and the IMF, new models with more realistic conditions were developed, e.g., Bruzual (1981); Bruzual A. and Charlot (1993); Worthey (1994); Bruzual and Charlot (2003);

Maraston (2005); Dotter et al. (2008); Conroy and Gunn (2010). In standard evolutionary SPS models, stellar isochrones specify the locus of a given mass, given metallicity star at one

2 instant in the luminosity (L) vs. eﬀective temperature (Teff ) space. Then the observables

of this star are searched in the stellar libraries, often by the Teff , surface gravity (log(g)), and metallicity ([Fe/H]) of that locus. IMF is used to estimate the number of stars at the

locus after stellar evolution. Finally, SSP models are obtained by the weighted sum (regu- lated by the IMF) of the observables along one isochrone. Each of the three components is an independent subject which deserves in-depth investigation. Stellar isochrones are derived from theoretical evolutionary tracks of various stars. A

stellar track describes the evolutionary path of a given mass star during its whole lifetime.

An isochrone is constructed by connecting the log(g)-Teff (or luminosity-Teff ) loci of diﬀer- ent mass stars at a given time. It represents the theoretical curve that should be found in the color-magnitude diagram (CMD) of a SSP. However, the stellar models, which determine the

stellar tracks, are known to depend on several volatile factors, like convection, opacity, rotation, heavy-element mixing, helium content, mass loss, and magnetic ﬁeld. Unfortunately, as the interior of a star is blocked by optically thick photosphere, one can only infer these processes by various exterior properties under diﬀerent environments. After years of studies, we have gained basic knowledge from star cluster CMDs and other observational facts.

Various theoretical stellar models with diﬀerent assumptions are published. For example, the STERN models (Brott et al., 2011), the Geneva models (Ekstr¨om et al., 2012; Georgy et al., 2013), the Padova models (Bertelli et al., 1994; Marigo et al., 2008; Bertelli et al.,

2 2 4 Teff is deﬁned by L = 4πR σTeff in stellar models.

3 2008, 2009), and the publicly available MESA codes (Paxton et al., 2011, 2013). Detailed treatments on convection, mass loss, and rotation in these models were nicely summarized in Martins and Palacios (2013). Incorporating all the factors into stellar models might be a promising task, but most of the time it is computationally expensive and unnecessary. For

instance, rotation is the highlight of Geneva models, while Padova group focuses on getting accurate AGB models. Given the fast rotation of massive stars and the lifetime of AGB stars, it is reasonable to pick Geneva models for starburst, young stellar populations, and Padova isochrones for intermediate to old stellar populations. The IMF regulates the mass distribution of stellar populations, and thus the number of stars at a given locus along the stellar isochrone. The IMF is usually deﬁned as the number of stars N in a volume of space V observed at an instant of time per (logarithmic) mass interval: d(N/V ) dn ξ(log m)= = (1.1) d log m d log m

By simple math: dn 1 ξ(m)= = ξ(log m) (1.2) dm m(ln 10)

Depending on its application, two types of IMF were deﬁned:

ξ(log m) m−x (1.3) ∝

ξ(m) m−α (1.4) ∝

where x = α 1. Salpeter (1955) adopted an IMF slope (α) of 2.35 for solar neighborhood − stars. To derive the IMF directly from star counts, several steps are generally required: From the photometric images, we determine the luminosity function (Φ(M)) for a given sample. Here M means the absolute magnitude. Then we correct the luminosity function for the eﬀect of stellar evolution and binary star fraction. What we get is the initial luminosity

4 function (Φ0(M)). Given that dM ξ(m)= Φ [M(m)] (1.5) dm 0

mass-magnitude relation is required to estimate the IMF. However, this relation is highly

complex at the low mass end. Therefore, direct IMF derivation depends on the accuracy of stellar evolution, binary star fraction, and mass-magnitude relation. With so many uncertain factors at play, it took nearly half a century for astronomers to settle down on the Galactic IMF. Studies of the Milky Way stars revealed a peaked IMF, peaking at a few tenths of

the solar mass (Miller and Scalo, 1979; Scalo, 1986; Kroupa, 2001; Chabrier, 2003). But the IMF in distant galaxies may vary due to diﬀerent star formation environments (Larson, 1998, 2005; Marks et al., 2012). For external galaxies, direct IMF derivation is limited by the low angular resolution power of telescopes. Alternatively, indirect methods based on IMF-sensitive feature lines or luminosity evolution were proposed (Spinrad and Taylor, 1971;

Tinsley and Gunn, 1976). Toward this end, van Dokkum and Conroy (2010); Conroy and van Dokkum (2012b) inspected the giant sensitive [Ca ii]triplet, and the dwarf sensitive [Na i], FeH Wing-Ford band. They suggested low mass stars are enhanced in massive elliptical galaxies, comparing with a standard Salpeter IMF.

On the other hand, the IMFs for redshifted galaxies are more uncertain. van Dokkum (2008) compared the luminosity evolution (∆ log (M/L )) to color evolution (∆(U V )) for B − massive galaxies in clusters at 0.02

IMF. Thus, the IMFs in these galaxies are supposed to be top-heavy (more massive stars) or bottom-light (less low mass stars). To summarize, the IMFs in the Milky Way, elliptical galaxies, and redshifted galaxies are consistent with a variable scheme, in which massive galaxies have comparatively more low mass stars. As one of the main ingredients of evolutionary SPS, diﬀerent IMF forms should be set to mimic the actual situation in these environments.

5 Stellar libraries are necessary for converting the Teff and log(g) of a stellar model to observable quantities. Theoretical libraries, like ATLAS (Kurucz, 1970; Castelli and Kurucz, 2004) and MARCS (Gustafsson et al., 1975, 2008) are constructed by theoretical calculations of the stellar atmosphere. No spectroscopic observation is required if one uses theoretical libraries, which makes them necessary for stellar population study in the absence of suﬃcient observed data. What is more, theoretical libraries accept variable abundance patterns and have nearly unlimited spectral resolution. But the accuracy of these calculations of atomic and molecular lines various physical environments are subject to defects, for example, incomplete or incorrect line lists, the uncertainty of convection, and the lack of chromospheres

(Tripicco and Bell, 1995; Chavez et al., 1997; Franchini et al., 2004; Serven et al., 2005). Meanwhile, empirical libraries, like ELODIE (Prugniel and Soubiran, 2001; Prugniel et al., 2007), INDO-US (Valdes et al., 2004), and MILES (Sánchez-Blázquez et al., 2006c) are free from model uncertainties, but a great deal of effort is required in observation. There are several factors to judge the quality of an empirical library: the wavelength coverage, the spectral resolution, the Teff -log(g)-[Fe/H] space coverage, etc. For example, the MILES library consists of 985 stars with spectroscopic observations covering the wavelength 3525– 7500 A˚ at 2.3 A˚ (full width at half-maximum, FWHM) spectral resolution. In order to further extend the wavelength coverage, MIUSCAT merged the MILES, CaT (Cenarro et al., 2001), and INDO-US libraries to acquire 3465–9469 A˚ coverage (Vazdekis et al., 2012); Conroy and van Dokkum (2012a) merged the MILES and IRTF (Cushing et al., 2005; Rayner et al., 2009) libraries to study the low mass stars which show IMF-sensitive feature lines in the red wavelengths. At the same time, UV libraries are required to model hot stars, like massive main sequence stars, blue-horizontal branch stars, and blue stragglers, but a mature, well- appreciated UV empirical library has not emerged yet. The most auspicious one is the new generation stellar library (NGSL, Gregg et al. 2006), covering 1675–10196 A˚ with a resolution of R 1000. This library has been partially reduced (e.g., Koleva and Vazdekis 2012), and ∼

6 the expansion of the library is now on its way. Besides full spectra, stellar libraries may include indices, which are more directly related to the astrophysical environment of the galaxies, e.g., age, metallicity, and element abundance. The most well known index system must be the Lick index system. Deﬁned in the 90s by Burstein et al. (1984); Faber et al. (1985); Gorgas et al. (1993); Worthey et al. (1994); Worthey and Ottaviani (1997), the Lick index system has totally 25 indices, including Balmer lines, iron lines, magnesium lines, and other element sensitive feature lines. Each index is deﬁned by a central feature bandpass, a blue psedocontinuum bandpass and a red psedocontinuum bandpass. The equivalent width is used as the index value:

λ2 F EW = (1 Iλ )dλ (1.6) Zλ1 − FCλ

The index value for a molecular line is deﬁned as:

1 λ2 F Mag = 2.5 log[( ) Iλ dλ] (1.7) − λ2 λ1 Z F − λ1 Cλ

Where FIλ and FCλ are the ﬂuxes per unit wavelength in the index passband and the straight- line continuum ﬂux in the index passband, respectively. Limited by the current telescope observation capabilities, most of the observable stars are solar neighbors, and therefore the empirical libraries are swamped with scaled-solar stars. However, the line strengths of metal-poor halo stars, galactic bulge, and elliptical galaxies indicate their elemental abundances have a non-solar pattern (Worthey et al., 1992; Davies et al., 1993; Kuntschner, 2000). Even-number (alpha) elements, O, Ne, Mg, Si, S, Ar, Ca, and Ti, are mainly the products of Type II core-collapsed supernovae, though Ca may have an additional origin (Thomas et al., 2011). The earliest studies concentrated on the [Mg/Fe] ratio and used it as a proxy for all alpha elements, since the diagnostic features, Mg b, Fe5270, and Fe5335 were adjacent to each other in the spectrum and thus plausibly insulated

7 from wavelength dependent changes. Meanwhile, the iron peak elements, clustering around Z = 26 (atomic number), are mostly generated by the deﬂagration obliterations of white dwarfs, which is also known as the Type Ia supernovae. These two groups of elements show disparate signatures, and what makes the situation more complicated is that the elements

of each group do not necessary follow the others under diﬀerent circumstances, like the case of Ca. In order to model the non-lockstep heavy element enrichment in stellar libraries, Tripicco and Bell (1995) presented the ﬁrst comprehensive table about Lick index response to abundance changes. After that, Serven et al. (2005) extended this table by including 54 Lick style equivalent width indices focused on heavy element feature lines. As a consequence

of element variation, stellar evolution models are also inﬂuenced by changes in opacities. Dotter et al. (2007a,b) and Lee et al. (2009) explored the eﬀects of chemical variation on stellar isochrones, and the corresponding changes in integrated colors, Lick indices, and synthetic spectra.

Besides all the uncertainties in the evolutionary SPS, there are other problems that make it diﬃcult to compare models with observables. Dust acts as a screen between the observer and the source, and it changes the colors and the spectral slopes by reddening. Nebular emission commonly found in star-forming galaxies might change the stellar absorption strength of hydrogen Balmer lines. This makes the Balmer absorption features, which are important age indicators, very hard to measure. Another challenge comes from the age-metallicity degeneracy. According to Worthey (1994), most of the optical colors and absorption feature strengths appear identical if the changes of age and metallicity satisfy δ log (age) 3/2 δ log (Z). This blocks the way to ≈ − estimate galaxy accurate ages from optical broad band colors. At spectroscopically narrow bands, however, several age-sensitive or metallicity-sensitive Lick indices, taken in pairs, are eﬀective at breaking this degeneracy. Balmer indices vs. Fe-peak indices are widely used, for example, because they are relatively easy to observe (all features are in the optical so

8 one spectrograph can cover them all) and the model grids in the observed index-index space open up to nearly orthogonal grids rather than collapsed into linear, degenerate overlapping segments. Recently, colors pertaining to near infrared magnitudes, like (V K), (B J) − − have also been proposed as age indicator (de Jong, 1996; James et al., 2006; Pessev et al.,

2008), since AGB stars, the main contributors of near infrared bands, are observed to be very strong in clusters between 0.5 to 2 Gyr. But detailed AGB models with dust (Ventura et al., 2012, 2014) and statistical ﬂuctuation (Frogel et al., 1990; Santos and Frogel, 1997; Bruzual and Charlot, 2003; Salaris et al., 2014) involved are diﬃcult to work out (Marigo et al., 2008; Girardi et al., 2010, 2013).

Yet another problem that attracts research attention is the difficulty of composite stellar populations (CSPs). For simplicity, stellar populations with the same age and the same metallicity are often assumed. But the nature of our universe is often complex, the stars in a galaxy may form at different time, with different abundances. To model CSPs that may be present in galaxies, several research groups linearly combine SSPs in the way that minimizes the difference (χ2) between the observed and model spectra, e.g., Bica (1988), MOPED (Heavens et al., 2000), STARLIGHT (Cid Fernandes et al., 2005), ULySS (Kol- eva et al., 2009), and etc. Their capability of recovering star formation history is highly desired in galaxy evolution research, but some complications that may increase the uncertainty should also be noted. In a galaxy with mixed young and old populations, the strong masking effect of the young populations hinders the interpretation of integrated light, since the young populations are much brighter. Similar effect also exists for metal-poor and metal- rich populations, in the sense that metal-poor populations outshine their counterparts. As a consequence, when the “SSP-equivalent” properties are derived, the young, metal-poor populations get more weight than the old metal-rich populations. After introducing the SPS models, one remaining question is: which type of galaxies are more appropriate for model application and calibration? Based on the surrounding environ-

9 ment, there are field and cluster galaxies. Based on central black hole activity, there are active (Quasars and AGNs) and inactive galaxies. Based on the integrated magnitude and color, there are red sequence, green valley and blue cloud galaxies. Based on morphology, there are elliptical, spiral, barred, and irregular galaxies. As always, we begin the systematic study from the relatively simple case. Provided the obviously complex star formation history in spiral and irregular galaxies, elliptical galaxies are reasonable candidates for beginning research. These plain, red galaxies are filled with stars that have large velocity dispersions. In such intensive environment, cool gas is not expected to survive for long and hence recent star formation should be rare. However, recent observations suggest a few percent of elliptical galaxies are more complicated than a simple system of old stellar populations. Cool interstellar medium, like dust and molecular gas, have been reported in elliptical galaxies (Knapp et al., 1989; Temi et al., 2004; Kaneda et al., 2008; Kaviraj et al., 2012). These cool dust and gas might be accreted from nearby galaxies or intergalactic medium (Kereˇset al., 2005), and cause recent star formation. Observationally, SSP models revealed a spread of 10 Gyr or greater in ages for local ellipticals (Trager et al., 2000b,a; Sánchez-Blázquez et al., 2006a,b; Tang et al., 2009) — low velocity dispersion galaxies appear younger. Possible explanations are, for example, the existence of a small portion of young stars (Trager et al., 2000a), or a more extended star-formation history (Sánchez-Blázquez et al., 2006b). Though a small number of elliptical galaxies are more complex than previously thought, the majority are still the brightest and relatively simple stellar systems that exist in the local Universe. For- tunately, the star-forming elliptical galaxies can be separated by [O ii] and Hα feature lines. Furthermore, the implementation of a flexible star formation history or an initial metallicity distribution function may alleviate the discrepancies between models and observations (e.g.: Cid Fernandes et al. 2005; Trager and Somerville 2009; Tang et al. 2014).

This dissertation explores some of the existing challenges of evolutionary SPS, such as age-metallicity degeneracy, IMF, elemental abundances, and compositeness.

10 Chapter 2 presents our eﬀort to search for age-sensitive and metal-sensitive colors in three photometric systems. We also add to the discussion of optical to near-infrared Johnson- Cousins broad band colors, which are proposed to break the age-metallicity degeneracy. Chapter 3 investigates the element abundances and compositeness of our CSP models, in

which we assume a single-peak abundance distribution and the same elemental abundance trends as the Milky Way bulge stars. Varying the width of the abundance distribution function reveals novel “red lean” and “red spread” effects. Chapter 4 studies three effects that co-determine the dwarf/giant ratio: IMF slope, IMF low mass cut-off (LMCO), and AGB star contribution. This degeneracy can be lifted for

old, metal-rich stellar populations, although at an observationally challenging level ( 0.02 ≈ mag). Chapter 5 illustrates the selection and reduction of z 0.4 red galaxy spectra from ∼ DEEP2 sky survey. Multiple optical IMF-sensitive indices suggest a shallower IMF that

qualitatively agrees with the current literature.

11 CHAPTER 2

ON DISTINGUISHING AGE FROM METALLICITY

WITH PHOTOMETRIC DATA

2.1 Introduction

Since the concept of stellar populations was invented (Baade, 1944), stellar population synthesis (SPS) has proven to be a useful tool for revealing clues about galaxy formation (Tins- ley, 1968, 1978; Bruzual A. and Charlot, 1993). Research on several crucial factors of stellar modelling, like convection, opacity, heavy-element mixing, helium content, and mass loss (Charlot et al., 1996), resulted in increasingly accurate SPS models (Bruzual A. and Char- lot, 1993; Worthey, 1994; Bertelli et al., 1994; Bruzual and Charlot, 2003; Dotter et al., 2008; Bertelli et al., 2008, 2009). In this scheme, estimation of single burst equivalent age and metallicity, was accomplished by comparing integrated light of observed galaxy with that of SPS models. However, most of the colors and absorption feature strength appear identical if the changes of age and metallicity satisfy δ log (age) 3/2 δ log (Z). This ≈ − so-called age-metallicity degeneracy (Worthey, 1994) blocks the way to estimating galaxy accurate ages from optical broad band colors. At spectroscopically narrow bands, however,

several age sensitive or metallicity sensitive Lick indices (Burstein et al., 1984; Faber et al., 1985; Gorgas et al., 1993; Worthey et al., 1994; Worthey and Ottaviani, 1997; Thomas et al., 2003), taken in pairs, are eﬀective at breaking this degeneracy. Balmer indices vs. Fe-peak

12 indices are widely used, for example, because they are relatively easy to observe (all features are in the optical so one spectrograph can cover them all) and the model grids in the observed index-index space open up to nearly orthogonal grids rather than collapsed into linear, degenerate overlapping segments.

Spectroscopy is effective, but photometry also has its strong points. It is much more efficient for faint objects and low surface brightness galaxies. In the epoch of large sky surveys, like Sloan Digital Sky Survey (SDSS), Two Micron All Sky Survey (2MASS), Spitzer Space Telescope (SST), Large Synoptic Survey Telescope (LSST), and James Webb Space Telescope (JWST), photometry is undoubtedly more feasible than spectrometry. In fact, optical near-infrared (near-IR) colors have been exploited to possibly constrain age and metallicity by several studies (Peletier et al., 1990; de Jong, 1996; Bell and de Jong, 2000; Carter et al., 2009; Conroy et al., 2009). Cardiel et al. (2003) suggested (V K) color shows − good balance between parameter degeneracy and sensitivity. Pessev et al. (2008) found that four age intervals (>10 Gyr, 2 9 Gyr, 1 2 Gyr, and 0.2 1 Gyr) are clearly separated in the − − − optical near-IR color-color plot. These results hinge upon the models, and specifically upon the number of thermally pulsing asymptotic giant branch (TP-AGB) stars, which dominate near-IR light between 0.3 and 2 Gyr of age (Maraston, 2005; Lee et al., 2007).

This chapter looks for age-sensitive or metallicity-sensitive indices in three photometric systems: David Dunlap Observatory (DDO, McClure and van den Bergh 1968; McClure 1976), Beijing-Arizona-Taiwan-Connecticut (BATC, Fan et al. 1996; Shang et al. 1998), and Strömgren (Strömgren, 1966; Rakos et al., 1991, 1996) systems. These filters are narrower in wavelength than Johnson-Cousins broad band filters, but resemble the NIRCam narrow

ﬁlters1 on board JWST . Can we ﬁnd indices which are practical to break the age-metallicity degeneracy? The tables and graphs in 2.2.1 explore this issue. In addition, equipped with § the latest stellar evolutionary isochrones of the Padova group2 (Bertelli et al. 2008, 2009,

1http://ircamera.as.arizona.edu/nircam/ 2http://stev.oapd.inaf.it/YZVAR/

13 hereafter B09), we plot the model grids in (B V ) vs. (V K) space, and compare with − − previous models in 2.2.3. Observables from three samples are chosen to verify the credibility § of parameters given by the model grids. Discrepancies between two model grids are brieﬂy discussed in 2.3, and a brief summary of the results and outlook for the future is given in § 2.4. §

2.2 Analysis

2.2.1 DDO, BATC & Str¨omgren

In order to ﬁnd the age-sensitive or metallicity-sensitive index, we calculate the the metallicity- to-age sensitivity parameter (Zsp) using the evolving Worthey (1994, hereafter W94) models, following Worthey (1994) and Serven et al. (2011). The spectral library is synthetic and is sensitive to individual elemental abundances in the 300 to 1000 nm wavelength range. The metallicity sensitivity parameter is:

δIm/δ log (Z) Zsp = (2.1) δIa/δ log (age)

Where δIm/δ log (Z) is the metallicity partial derivative of the index at 8 Gyr, and δIa/δ log (age) is the age partial derivative of the index at solar metallicity. Thus, Zsp is the metallicity sensitivity at 8 Gyr, solar metallicity.

3 Zsp is surveyed for indices in three photometric systems . We refer the readers to related papers for detailed description of ﬁlters and indices (See 2.1). As shown in Worthey (1994), § indices with Zsp close to 1.5 are less likely to break the age-metallicity degeneracy. Hence,

4 indices with extreme Zsp values are selected as candidates and listed in Table 2.1 . What

3http://astro.wsu.edu/models/isochrones.html 4Since the K band is suggested to be sensitive to young stellar populations, nonstandard colors relative to the K band, like DDO41 K, BATC6075 K, were also examined. However, no promising index is found. − −

14 Table 2.1: Metallicity sensitivities at 8 Gyr, solar metallicity, for our best candidate pairs of colors Index Zsp DDO C(41-42) -0.60 DDO C(35-48) 1.42 BATC 6075-6660 1.15 BATC 5795-6075 1.97 Strömgren [m1] 1.23 Strömgren [c1] 2.41 is not quantified in Table 2.1 is the dynamic range (compared to observational error) of a given index, and the dynamic range is low in DDO C(41-42), alas.

DDO system • 5 The extremely low Zsp value of C(41-42) color makes it a promising age indicator to break the degeneracy. Figure 2.1 shows C(35-38) vs. C(41-42) plot of our models

using W94 stellar evolution. The isochrones are well separated, except SSPs with very low metallicities. However, the major problem is small dynamic range ( 0.05 mag) ≈

of C(41-42). A little observational error or dust content (AV = 1.0 mag is sketched in Figure 2.1 to estimate the extinction eﬀect) will destroy the well spaced isochrones.

The short distance between the central wavelengths of DDO 41 and 42 ﬁlters ( 100 ≈ A)˚ is the reason for this defect.

BATC system • BATC 6075-6660 6 and 5795-6075 colors show potential of breaking the degeneracy

for their Zsp values. However, Figure 2.2 does not work out as expected. Though the

super-solar metallicity SSP isochrones are separated as indicated by Zsp, the sub-solar metallicity SSP isochrones are still highly degenerate. We note that the 6660 ﬁlter contains Hα, which explains age sensitivity of the 6075-6660 color. However, we also

note that the dynamic range of both colors is small compared to the AV = 1.0 mag 5Magnitude of DDO41 filter subtracts magnitude of DDO42 filter 6Magnitude of 6075 filter subtracts magnitude of 6660 filter

15 Figure 2.1: DDO C(35-48) vs. C(41-42) plot. SSPs of the same age are connected as isochrones. Our models (W94) are given at age= 1.5, 2, 3, 5 with log (Z) = 0.225, 0, 0.25, 0.50, and age= 8, 12, 17 Gyr with log (Z) = 2.0, 1.5, 1.0, 0.50−, 0.25, 0, 0.25, 0.50. Solar metallicity SSPs are marked as ﬁlled − − − − − squares to guide the eye. A vector for AV =1.0 mag is sketched to estimate the extinction eﬀect.

16 Figure 2.2: BATC 5795-6075 vs. 6075-6660 plot. Isochrones are described in Figure 2.1. A vector for AV =1.0 mag is also sketched to estimate the extinction eﬀect.

17 extinction vector, and that the 6075-6660 color only spans 0.06 mag total, which seems small compared to reasonable observational errors. Furthermore, since it is Hα that is driving the age sensitivity of this color, it will be sensitive also to nebular emission, which can easily overwhelm the stellar absorption in many galaxies.

Str¨omgren system • 7 Since [c1] and [m1] are reddening independent (Str¨omgren, 1966), and they also have

promising Zsp values, we take a close look at these two indices. Rakos et al. (1991)

suggested m1 is a metal-line idex, while c1 is a Balmer discontinuity index. Figure

2.3 conﬁrms [m1] as a metallicity sensitive index, because the SSP isochrones lie al-

most parallel to the [m1] axis. With its reasonable dynamic range ( 0.6 mag) and ≈

its reddening free advantage, [c1] vs. [m1] plot is a promising candidate index that might break the age-metallicity degeneracy. Three samples are selected to test the

competency of the [c1] vs. [m1] plot: (1) Ellipticals (Es) and S0s from Schombert et al. (1993), shown as ﬁlled Triangles in Figure 2.3; (2) Nearby Es and globular clusters

(GCs) from Rakos et al. (1990). They are labelled separately for clarity (crosses); (3) Es from Odell et al. (2002), shown as filled circles. Note that the last two samples are recorded in a modified Strömgren filter system called uz, vz, bz, yz. The relations of Rakos et al. (1996) are employed to convert the observables to the uvby system. Figure

2.3 shows that our model grids based on W94 evolution do not ﬁt the observations well. B09 model grids are also plotted along the observables in Figure 2.4. Comparing with Figure 2.3, the coverage improves greatly in the later model grids, but isochrones of

age between 5 and 17 Gyr are still partially degenerate. Obviously, the [m1] indices of old metal-rich SSPs in B09 models are systematically larger than that in W94 models.

We also note that two sets of tracks are not the same, e.g., young age, low metallicity SSPs are not included in W94 models. To investigate the topic furthermore , we draw 7 c1 (u v) (v b), m1 (v b) (b y); ≡ − − − ≡ − − − [c1] c1 0.2(b y), [m1] m1 +0.18(b y). ≡ − − ≡ −

18 Figure 2.3: Str¨omgren [c1] vs. [m1] plot. Isochrones are described in Figure 2.1. Ages are not labelled for narrow space, but they can be easily inferred from Figure 2.4. Observables from three samples are labelled with diﬀerent symbols: Filled Triangles: Es and S0s from Schombert et al. (1993). Crosses: Nearby Es and GCs from Rakos et al. (1990). Filled Circles: Es from Odell et al. (2002).

19 Figure 2.4: Str¨omgren [c1] vs. [m1] plot of B09 models. The models are given at age= 0.1, 1, 2, 5, 10, 17 Gyr with log (Z)= 2.23, 1.23, 0.53, 0, 0.37. Solar metallicity SSPs are − − − marked as ﬁlled squares to guide the eye. Observable symbols are the same as in Figure 2.3.

20 Table 2.2: Index changes at 8 Gyr, solar metallicity Index C N O Na Mg Fe DDO C(41-42) 0.028 0.039 -0.018 -0.001 -0.002 -0.001 DDO C(35-48) 0.068 0.026 -0.033 -0.005 -0.002 0.045 BATC 6075-6660 -0.009 -0.006 0.002 0.000 0.001 0.002 BATC 5795-6075 0.005 0.001 -0.004 0.004 -0.001 0.001 Str¨omgren [m1] 0.024 0.021 -0.025 -0.003 -0.032 0.029 Str¨omgren [c1] -0.078 -0.015 0.054 0.003 0.080 -0.009

the [c1] vs. [m1] plot of B94 models ( 2.2.3), which looks strikingly similar to Figure 2.4 § (not shown here). Thus, the stellar phases causing the dramatic discrepancies between

Figure 2.3 and 2.4 must be diﬀerent in W94 and B09 models, but similar in B94 and B09 models. We defer discussion of the speciﬁc stellar phases because it is beyond the scope of this dissertation.

2.2.2 Element Sensitivity

In a non-solar scaled environment, indices may reflect those abundance changes. To trace the effects of different elements, we increase the stellar atmosphere model abundances of six major elements (C, N, O, Na, Mg, Fe) by 0.3 dex8, one single element at a time. The sensitivity is modeled only in the stellar library; the isochrones are kept as published. Table 2.2 outlines the index changes at 8 Gyr, solar metallicity.

The prominent carbon and nitrogen eﬀect on DDO C(41-42) color is not surprising, • since the DDO 41 band overlaps CN1 and CN2 Lick indices in wavelength. Fe and CN absorption lines are the main features under 4000 A,˚ which explains the DDO C(35-48) color changes at super-solar C, N, and Fe abundances. The behavior of increased O

is opposite due to molecular balancing: The CO molecule has the strongest binding

energy and so adding O decreases the C supply, weakening C2 and CN features. Thus,

80.15 dex for C, to avoid the danger of turning to a carbon star (Serven et al., 2005). Dex is the unit of log scale.

21 adding more O causes bluer DDO C(41-42) and C(35-38) colors.

The BATC 6075-6660 and 5795-6075 colors are relatively unaﬀected by six major • elements, which makes them good colors to study systems with unknown element en- hancements. What we ﬁnd matches the basic philosophy of creating this photometric

system: avoiding known bright feature lines and sky lines, in order to study the continuum of the spectrum (Fan et al., 1996).

Strömgren [m1] and [c1] are different from the four colors above, because they are the • subtractions of two colors. [m1] is found to be metallicity sensitive in 2.2.1, which § is consistent with its behavior in Table 2.2: Five elements have substantial influences

on [m1]. The trend of the [c1] index change due to C and O abundance variations is reverse compared to other indices. Since u and v bands are both blanketed by CN absorption lines, our models predict that the impact of CN on the v band is greater than that on the u band. Therefore, higher CN abundance means a larger magnitude

increase in the v band than that in the u band, leading to a smaller [c1] value. The

strong Mg eﬀect on [c1] is echoed by the Mg3835 (u band) and Mg4780 (b band) indices deﬁned in Serven et al. (2005).

2.2.3 (B V ) vs. (V K) Plots − − The possibility of breaking age-metallicity degeneracy with optical plus near-IR colors (de

Jong, 1996; James et al., 2006; Pessev et al., 2008), and the upcoming era of near-IR telescopes (eg: JWST ) inspire us to delve into the optical near-IR color color plot. Prior to − this work, Lee et al. (2007) inspected the (B V ) vs. (V K) plot using Bruzual and − − Charlot (2003, hereafter BC03), Maraston (2005), and BaSTI (Cordier et al., 2007) models.

They suggested different treatments of convective core overshooting and differences in the TP-AGB phase cause the inconsistency among different model grids (also see Maraston et al.

22 2006). To further discuss the robustness of the models, we investigate the isochrones that looked so promising (B94) and a later, even more complete version (B09) from the same group.

B94 models • Perhaps partly because of the inclusion of all stellar evolutionary phases, B94 models were widely adopted as basic stellar evolution isochrones for evolutionary synthesis models, such as: BC03; PEGASE (Fioc and Rocca-Volmerange, 1997, 1999); and

STARBURST99 (Vázquez and Leitherer, 2005) models. Figure 2.5 shows the (B − V ) vs. (V K) plot of B94 models. Three observational samples are selected for − comparison: (1) old, metal-poor GCs from Burstein et al. (1984) (filled circles); (2) old, metal-rich Es from Peletier (1989) (filled triangles); (3) SWB9 type IV VI Large − Magellanic Cloud (LMC) star clusters (crosses). The reddening-corrected (B V ) − and (V K) colors come from van den Bergh (1981) and Persson et al. (1983). The − last sample is selected as “intermediate age” SSPs, roughly 1 to 8 Gyr according to Persson et al. (1983). Generally speaking, observables of these three samples appear

at expected locations on the model grids.

B09 models • With improved understanding of TP-AGB phase, Padova group updated the stellar evolution models. Compared with previous models of this group (B94; Girardi et al. 2000), B09 models adopted a sophisticated TP-AGB model which includes third dredge-up, hot bottom burning, and variable molecular opacities (Marigo et al., 2008).

Also, basic observables of AGB stars in the Magellanic Clouds (MCs) were reproduced by the new models (Girardi and Marigo, 2007). The (B V ) vs. (V K) plot of the − − B09 models are shown in Figure 2.6. Observables are also plotted as in Figure 2.5. Isochrones of age larger than 5 Gyr are consistent with that of the B94 models. Es and

9Searle et al. (1980)

23 Figure 2.5: (B V ) vs. (V K) plot of B94 models. The models are given at age= 0.1, 1, 2, 5, 10−, 17 Gyr with− log (Z) = 1.7, 0.7, 0.4, 0, 0.4. Solar metallicity SSPs − − − are marked as filled squares to guide the eye. SSPs of the same age are connected by solid lines, while SSPs of the same metallicity are connected by dotted lines. A vector for AV =1.0 mag is sketched to estimate the extinction effect. Observables from three samples are labelled by different symbols: Filled Triangles: Es from Peletier (1989). Filled Circles: GCs from Burstein et al. (1984). Crosses: SWB type IV VI Large Magellanic Cloud star clusters − from van den Bergh (1981) and Persson et al. (1983).

24 Figure 2.6: (B V ) vs. (V K) plot of B09 models. The models are given at age= 0.1, 1, 2, 5, 10, 17− Gyr with log− (Z) = 2.23, 1.23, 0.53, 0, 0.37. Other symbols are the − − − same as in Figure 2.5.

25 GCs locate on the metal-rich and metal-poor sides, respectively. However, isochrones of 1 and 2 Gyr change substantially: the (V K) color of log (Z)= 0.53 becomes red- − − der than that of solar metallicity. An unreported “S” shape is found if log (Z)= 0.53 − SSPs are connected. Another unexpected change is about the isochrone of the youngest

age, 100 Myr: the (V K) color of the lowest metallicity (log (Z) = 2.23) is even − − redder that of the highest metallicity (log (Z)=0.37).

2.3 Discussion

2.3.1 Str¨omgren System: Empirical Leverage?

Prior to this work, c1 or m1 were paired with (u v), (b y), or other colors to estimate − − galaxy age (Russell and Bessell, 1989; Rakos et al., 1996). In this chapter, the extinction

independent Q-indices [c1] and [m1] are assembled, but do a mediocre job breaking the age- metallicity degeneracy. As seen in Figure 2.4, several observables lie outside the B09 model grids. Three reasons are hypothesized for these outliers: First, the conversion relations

between uz, vz, bz, yz and uvby system presented in Rakos et al. (1996) are empirical, which

inevitably increases the uncertainty; Second, the dynamic range of [c1] index is not large compared to the observational error; Third, isochrones of age between 5 and 17 Gyr are partially degenerate, which reduces the span of model grids.

The model isochrone of 100 Myr lies low in the [c1] vs. [m1] plot. This is similar to the statement in Rakos et al. (1996) that most of the starburst galaxies have mz values10 less than 0.2, and they are well separated from other types of galaxies. To test the potential of − [m1] index as an star formation rate indicator, S (“star formation rates equivalent to normal disk galaxy”) and S+(“starburst objects”) from Odell et al. (2002) are selected and shown in Figure 2.7. Most of the mz values of this sample are less than 0.1, supporting the idea that − 10mz (vz bz) (bz yz) ≡ − − −

26 starburst galaxies are bluer in [m1]. However, we detect no clear [m1] value that separates Es and star forming galaxies. Str¨omgren system photometry is far less developed than broad band photometry for galaxies, however. That, plus the large apparent observational scatter in Figures 2.3, 2.4 and 2.7 lead us to conjecture that Str¨omgren photometry may still have great potential for breaking the age-metallicity degeneracy, but higher quality data are needed to be certain.

2.3.2 Model Grid Diﬀerences

Three SPS models are assembled in this chapter: W94, B94, and B09 (i.e., primitive, com- petent, and sophisticated, respectively.). Figure 2.3, 2.4, 2.5, and 2.6 clearly illustrate the model diﬀerences in [c1] vs. [m1] and (B V ) vs. (V K) plots. During the whole work, − − we calculate the magnitudes of each bands in three SPS models with the same codes, thus W94, B94, B09 models share the same spectral library, IMF (Salpeter, 1955) with lower mass limit Mmin = 0.1M⊙, upper mass limit Mmax = 100M⊙, and etc. Most of the model grid discrepancies rely on diﬀerent stellar evolution descriptions:

W94 models are a merging of isochrones and tracks from many sources. Compared to • B94, W94 models have a factor of two more stars in the upper RGB. The core-helium burning phase was approximated by a single red clump. The luminosities and lifetimes of AGB stars were drawn from theoretical tracks.

B94 models included all phases of stellar evolution until the remnant stage in all mass • ranges. Convective core overshooting was also considered in the models. Nevertheless, the analytic prescription of TP-AGB phase was approximate. (Marigo et al., 2008)

B09 models adopted the latest TP-AGB model of Marigo et al. (2008). Compared with • previous ones, this TP-AGB model has included the crucial eﬀects of third dredge-up, hot bottom burning, and variable molecular opacities, and it was calibrated by the

27 Figure 2.7: Str¨omgren [c1] vs. [m1] plot of B09 models. The models are discribed in Figure 2.4. Solar metallicity SSPs are marked as ﬁlled squares to guide the eye. Filled Circles: S and S+ of Odell et al. (2002).

28 basic observables of AGB stars in the MCs.

In Figure 2.6, SSPs with log (Z)= 0.53 have the reddest (V K) colors along isochrones − − of 1 and 2 Gyr. This feature is not seen in B94 model grids. Since B94 and B09 models mainly diﬀer in TP-AGB model treatments, which aﬀect the near-IR color seriously between

0.3 and 2 Gyr (Maraston, 2005), it is suggested diﬀerent treatments of TP-AGB stars are responsible for the changes of model grids. Considering the metallicities of star clusters in the LMC (mean log(Z) = 0.42 for clusters with 1 t < 2 Gyr and 0.57 for clusters − ≤ − with 2 t< 10 Gyr, Pessev et al. 2008), SWB IV VI star clusters are better ﬁtted in B09 ≤ − models — B94 models give much higher metallicities. Nevertheless, noting that B09 models are calibrated by AGB stars from the MCs, and that the metallicities of star clusters in the LMC are around log(Z)= 0.53, this consistence is somewhat expected. However, the − scarcity of AGB stars in MCs might cause counting statistics problem (Frogel et al., 1990; Santos and Frogel, 1997; Bruzual and Charlot, 2003; Salaris et al., 2014). In fact, Girardi et al. (2010, 2013) cautioned that the numbers of AGB stars might be over-predicted in this model version. Another unexpected feature in Figure 2.6 is the twist of the 100 Myr isochrone. This youngest isochrone is unique: the (V K) color at the lowest metallicity is redder than that − of the highest metallicity. This is inconsistent with the usual sense that metal-rich SSPs are redder than metal-poor SSPs (See the 100 Myr isochrone of Figure 2.5). The change of the 100 Myr isochrones between B94 and B09 models challenge the method of estimating ages and metallicities of young SSPs (0.1

29 colors along the 1 and 2 Gyr isochrones in B09 models; The (R K) color at the lowest − metallicity is redder than that at the highest metallicity along the 100 Myr isochrone of B09. Thus, these features are dependent upon near-IR band (K), instead of visible bands (V or R). Considering the TP-AGB treament diﬀerences of B94 and B09 models and the TP-AGB eﬀects on K band, it is again suggested TP-AGB stars are responsible for the changes of young SSP isochrones (0.1

2.4 Summary

Motivated by the need of estimating ages and metallicities from photometric systems, this chapter explored the DDO, BATC, Strömgren systems in the hope of finding age sensitive or metallicity sensitive indices. Three index index plots were examined but only Strömgren − [c1] vs. [m1] plot showed moderate age-metallicity separation. Four indices of the DDO and Strömgren systems changed substantially while increasing C and N abundances. O traces an opposite trend compared to C and N, since O tends to form CO with C. Then, we turned to the literature-posited age-metallicity disentangling space — the optical plus near- IR color color plot. Updated stellar evolution gives no support for clear disentanglement − of age. Even mean age, therefore, is a subtle effect in colors, and would require, seemingly, both finer-tuned models and observations of greater accuracy.

30 Figure 2.8: (B R) vs. (R K) plot of B94 and B09 models. The B94 models are given at age= 0.1, 1, 2−, 5, 10, 17 Gyr− with log (Z) = 1.7, 0.7, 0.4, 0, 0.4, while the B09 models are given at age= 0.1, 1, 2, 5, 10, 17 Gyr with− log (Z−) = −2.23, 1.23, 0.53, 0, 0.37. Note − − − that the two sets of tracks are not identical. Isochrones of B09 models are labelled by solid lines, and isochrones of B94 models are labelled by dashed lines. Solar metallicity SSPs are marked as ﬁlled squares to guide the eye. A vector for AV =1.0 mag is sketched to estimate the extinction eﬀect.

31 CHAPTER 3

COMPOSITE STELLAR POPULATIONS AND

ELEMENT BY ELEMENT ABUNDANCES IN THE

MILKY WAY BULGE AND ELLIPTICAL

GALAXIES

3.1 Introduction

For the better part of a century, the pursuit of chemical abundances in astronomical objects

has driven scientiﬁc innovation in the hope of better understanding the origin and evolution of the universe and the objects in it. Recently, this quest has extended to the integrated light of early type galaxies, which seem to have heavy element abundance ratio patterns that both do and do not ﬁt those seen in the Milky Way galaxy (MW), e.g., Johansson et al.

(2012). Stellar abundances for stars in the MW that span a large range of [Fe/H] show a pattern of heavy element enrichment that is largely consistent with two sources for chemical enrichment, Type II and Type Ia supernovae, where the ratio of Type Ia products increases with increasing metallicity1 (Wheeler et al., 1989). Type II supernovae, the core collapses

1 Contrary to stellar spectroscopy tradition, we deﬁne “metallicity” as [M/H] log Z/Z⊙, where Z is the mass fraction of heavy elements. We assume here that a stellar evolutionary isochrone≈ at ﬁxed Z will not vary with detailed chemical mixture, because isochrone sets that do have yet to be computed.

32 and bounces of massive stars, are thought to be rich in elements seeded by 12C plus the addition of 4He nuclei, termed alpha-capture elements, or α elements for short. They thus include even-numbered elements O, Ne, Mg, Si, S, Ar, Ca, Ti, and possibly Cr, although Cr is more often included in the group of elements termed the iron peak. Type Ia supernova,

runaway deflagration obliterations of white dwarfs, have a signature more tilted toward the iron peak group, though some models produce substantial quantities of Si, S, Ar, Ca, and Ti as well (Nomoto et al., 1997). Since the two sources are so disparate in origin, it is not difficult to imagine many ways in which the relative proportions could be made to shift and mix in different ways in different environments. Possible causal variables include the time

interval since star formation, the mass function at formation, the binary fraction, and the heavy element composition. There is now a plethora of evidence that this two-source picture is too simple (e.g. Edvardsson et al. 1993) especially when stars from dwarf spheroidal satellite galaxies are considered (e.g. Geisler et al. 2005; Shetrone et al. 2001, 2003) and also when MW bulge stars are considered (e.g. Fulbright et al. 2007; Bensby et al. 2013; Mel´endez et al. 2008). To explain the discrepancies, it is further hypothesized that the Type II enrichment pattern may change with progenitor mass and progenitor chemical abundance (Fulbright et al., 2007).

More evidence of multiple sources of enrichment is found in the integrated light of early type galaxies. The initial result that more massive elliptical galaxies had higher [Mg/Fe] (Worthey et al., 1992) was satisfactorily explained as a Type II/Type Ia ratio eﬀect. But Worthey (1998) considered more elements (Na, Ca, and N) and could not reconcile the trends in MW disk, MW bulge, and elliptical galaxies under a two-source model.

The MW bulge has the potential to be a good analog for elliptical galaxies, being a spheroidal component of the Galaxy and having a stellar age that predates most of the disk (Ortolani et al., 1995; Zoccali et al., 2003), and yet being near enough so that individual stars can be studied in some detail. In that spirit, Terndrup et al. (1990) made integrated

33 light models by integrating the observed bulge luminosity function of the giants, predicting TiO strengths and VJHK colors. Both bulge stars and local stars were used as spectral templates. The fascinating conclusion of comparisons of those models with elliptical galaxies is that the bulge template matched better than the solar neighborhood template.

Using this conclusion as a springboard, we explore in this chapter ﬁrstly the idea that using bulge templates is a superior match to early type galaxies using additional observables than Terndrup et al. (1990) and secondly the hypothesis that elemental ratio changes are the cause. To achieve our goals adequately, the issue of compositeness in the stellar populations must

be addressed. Compositeness is a term that in general would encompass mixtures of stellar population ages and abundances. However, in cases of systems that formed most of their stars in the ﬁrst half of the universe’s existence, the issue of age is strongly suppressed due to (1) the strong decline of stellar population luminosity with increasing age (Bruzual A. and

Charlot, 1993) combined with (2) the approximate three-halves rule (Worthey, 1994) that states that, for example, a factor of three youthening of a population can be counterbalanced by a factor of two increase in metallicity and the integrated spectrum will change very little. By virtue of the fact that a factor of three in age looms large against the age of the universe

for an old population, but a factor of two is small in comparison to the range of two to three orders of magnitude for overall heavy element abundance, it follows that compositeness in age is a very minor eﬀect compared to compositeness in heavy element abundance. This chapter is organized as follows: Composite stellar populations (CSPs) with metallicity- dependent chemical composition are illustrated in 3.2. After that, we confront the models § with observables from three elliptical samples in 3.3. The implications are discussed in 3.4, § § and then a brief summary of the results is given in 3.5. §

34 3.2 Composite Stellar Populations with Metallicity-dependent

Chemical Composition

An aspect of compositeness that might conceivably have been present in Terndrup et al. (1990) is that stars of inappropriate heavy element abundance may have been inserted into the luminosity function model. Models: A version of integrated-light models (Worthey, 1994; Trager et al., 1998) that use a new grid of synthetic spectra in the optical (Lee et al., 2009) in order to investigate the eﬀects of changing the detailed elemental composition on an integrated spectrum was used to create synthetic spectra at a variety of ages and metallicities for single-burst stellar populations.

For this work, we adopt the isochrones of Bertelli et al. (2008, 2009) using the thermally- pulsing asymptotic giant branch (TP-AGB) treatment described in Marigo et al. (2008). This treatment is calibrated by comparing with AGB stars in the Magellanic Clouds. Perhaps due to counting statistics (Frogel et al., 1990; Santos and Frogel, 1997; Bruzual and Charlot, 2003;

Salaris et al., 2014), the numbers of AGB stars might be over-predicted (Girardi et al., 2010, 2013) in this model version. Indeed, Tang and Worthey (2013) found abruptly reddened V K for metal poor SSPs at the age of 0.1, 1 and 2 Gyr from this isochrone set. For now, − however, our main concern is the optical wavelength region, so we are insulated from this effect. Furthermore, the models are modular as regards isochrone libraries, and swapping from one set to another does not affect our conclusions. Following Poole et al. (2010), stellar index fitting functions were generated from indices measured from the stellar spectral libraries of Valdes et al. (2004) and Worthey et al. (2014a), both transformed to a common 200 km s−1 spectral resolution. Multivariate polynomial

fitting was done in five overlapping temperature swaths as a function of θeff = 5040/Teff , log g, and [Fe/H]. The fits were combined into a lookup table for final use. As in Worthey

35 (1994), an index was looked up for each bin in the isochrone and decomposed into “index” and “continuum” ﬂuxes, which added, then re-formed into an index representing the ﬁnal, integrated value after the summation. This gives us empirical index values. After that, additive index deltas were applied as computed from the grid of Lee et al. (2009) synthetic

spectra when variations in chemical composition are needed. The grid of synthetic spectra is complete enough to predict nearly arbitrary composition changes. Abundance errors: Regarding error propagation from individual stars to integrated light, the calibration of the indices depends directly upon high resolution analysis in that the hundreds of local stars that are ﬁt have stellar atmospheric parameters and abundances

taken from the body of previous high resolution work. We therefore expect systematic drift (from that source) approximately equal to the error in the mean. For argument’s sake, if the scatter is 0.2 dex, and the sample is 100 stars, the systematic drift should be of order σ 0.2/√100 = 0.02. True errors from this source will be smaller for well populated sys ≈ parts of the HR diagram such as G dwarfs and K giants. Mildly more serious is a systematic eﬀect from the Milky Way itself in that the local stellar [X/Fe]2 trends are frozen into the index ﬁts. If these are not scaled-solar then they introduce systematic drifts. Examining results from local stars, however, and concentrating

on thin disk stars only, e.g. (Chen et al., 2000; Bensby et al., 2003, 2014; Reddy et al., 2006), the [X/Fe] trends versus [Fe/H] appear flat within a 0.1 dex range for stars near solar metallicity ([O/Fe] might have a stronger tilt than that, but it is difficult to tell within the increased uncertainty of this element), and scatterlings appear in substantial numbers if thick disk stars are included. A unified high resolution study of the exact sample of stars that enter

the low-resolution index ﬁts has not been done. We therefore must presume that the stars ﬁtted obey the average trend. In integrated light, fortunately, these stars are weak-lined and few in number, leading to a few-hundredths change in overall [X/Fe] for unfavorable

2“X” represents any one of the heavy elements discussed in this work.

36 cases. Overall, we expect that systematic abundance errors are a few hundreths of a dex for most [X/Fe], but higher for elements that are diﬃcult to measure with high resolution spectroscopy (C, N, and O, for example) (Grevesse et al., 2007; Asplund et al., 2009; Ryde et al., 2010).

The most serious systematic error is a purely integrated-light problem arising from modeling uncertainties in stellar temperatures along the isochrone. Temperature changes mas- querade as either age or [M/H] drifts, rendering an absolute [M/H] quite uncertain. This does not, however, affect [X/Fe] measurements except via subtle amplification/attenuation effects if the [M/H] is chosen incorrectly.

Other caveats: Observed indices that the model grids simply do not cover occur from time to time. Reasons are as follows. The observational errors (in this work) are not dominated by photon statistics or wavelength solution errors. Errors in matching line of sight velocity dispersion are present, and might contribute more strongly. But the dominant

error in the observations is probably relative fluxing, in the sense of incomplete removal of instrumental signatures in the spectrophotometric shape over tens or hundreds of angstroms of wavelength span. Evidence that this effect is serious can be found in that indices with larger wavelength spans in their definitions from blue side to red side often drift more from

the models than narrower ones. Also, this defect shows up more in weaker features than in stronger ones. On the model side, the index fitting functions rest upon stellar spectra for which the fluxing is imperfect as well, and so the same kinds of fluxing effects can be expected at a modest level from the stellar index fitting process as well. The fitting process also runs the

risk of oversimplifying the behavior of the indices with stellar parameters.

37 3.2.1 Abundance Distribution Functions (ADFs)

In the process of making composite stellar populations with single-burst ages but composite abundance distribution functions (ADFs) there is clear empirical guidance for the shape of the function. It has been clear for many years that the simplest one-zone, constant-yield, no inﬂow, no outﬂow, instantaneous-recycling model of chemical evolution produces too many metal-poor stars compared to observations in the solar neighborhood (e.g. Pagel 1997). It has also become clear in recent years that other chemically-evolved places in the universe also have ADFs that are more narrow than the Simple model (Worthey et al., 1996, 2005). Figure 3.1 shows the Simple Model for the case of heavy element yield equal to the solar value, along with the analytical function variants that we adopt in this study. A convenient analytical function is the rational decreasing yield formula from Worthey et al. (2005). It narrows the Simple model by having the yield start high and decrease with increasing metallicity. We use parameters p = 0.00019 and ǫ = 0.004 in the formula for a smooth curve that has a FWHM of 0.62 dex, and we call it our normal width ADF. From there, we scale the width a factor of 1.5 narrower (narrow-width ADF), or a factor of 1.5 wider (wide-width ADF), and also transform it along the [M/H] axis, as desired. The Simple Model is the widest of all, at a FWHM of 1.06 dex. While the rational decreasing yield model is not a complete physical model in itself, it does a good job of reproducing the observations, some of which are summarized in Figures 3.2 and 3.3. Note that some authors, e.g., Hill et al. (2011); Babusiaux et al. (2010); Ness et al. (2013), argue that the MW bulge ADF is a multiple-peaked function that plausibly represents distinct stellar populations. Without contradicting that in the slightest, we pragmatically note that the match between the observed and model ADFs is nevertheless fairly good, especially in an integrated sense, and so we use the single-peaked function throughout this chapter.

38 Narrow 0.20 Normal Wide Simple Model

0.15

0.10

0.05 Normalized Abundance Distribution Abundance Normalized

0.00

−1.0 −0.5 0.0 0.5 [Fe/H]

Figure 3.1: The four analytical ADFs we consider are shown, normalized to integral unity given bin widths of 0.1 dex, and set to peak at solar abundance. The ADFs come in narrow (thin line), normal (thick line), and wide (dotted line) variants of the rational decreasing yield model, and the still-wider one zone Simple Model with yield = 0 (dash-dot line). The most metal rich population we can consider is [M/H] = 0.65 due to model limitations.

39 Normalwidth model ADF M31 Integrated 0.20 Haywood (2001) 0.1 Jorgensen (2000) M32 outskirts + 0.1 0.15

0.10

0.05 Normalized Abundance Distribution Abundance Normalized

0.00 −1.5 −1.0 −0.5 0.0 0.5 [Fe/H]

Figure 3.2: Observed ADFs are compared, normalized to integral one with a bin width of 0.1 dex along the [Fe/H] axis. Also shown is our normal width ﬁtting function (heavy line), set to peak at [Fe/H] = 0.1. Other observed cases are M31, considered as a whole (dashed histogram) from photometry− of red giants (Worthey et al., 2005)), a ﬁeld with mostly M32 stars (dash-dot histogram) also from photometry (Worthey et al., 2004) and shifted to the right by 0.1 dex for comparison, and two solar cylinder analyses, one from Jørgensen (2000) (thin solid histogram) and one from Haywood (2001), with corrections to the whole cylinder taken from Wyse and Gilmore (1995) and shifted 0.1 dex to the left for comparison. Roughly, the observed ADFs are comparable in width to, or a bit narrower than, the analytical function.

40 0.16 Normalwidth model ADF

0.14 Fulbright (2006) Zoccali (2008)0.15 Ness (2013)+0.2 0.12

0.10

0.08

0.06

0.04 Normalized Abundance Distribution Abundance Normalized

0.02

0.00 −3.0 −2.5 −2.0 −1.5 −1.0 −0.5 0.0 0.5 1.0 1.5 [Fe/H]

Figure 3.3: Milky Way Bulge ADFs from Fulbright et al. (2006); Zoccali et al. (2008); Ness et al. (2013) (dashed, dash-dotted, and star-marked dotted lines, respectively) are shown in comparison with the normal-width analytical function (bold line).

41 3.2.2 Milky Way Bulge Chemical Composition

Our composite models are sensitive to element ratios, and the trends of element ratios are included as a function of [M/H]. For incorporation into the models, [Fe/H] and [X/Fe] are treated with exactitude at the spectral library level, but at the isochrone level [Fe/H] is equated with [M/H] due to the lack of elemental mixture sensitivity in the isochrones.

The MW bulge literature abundance measurements come from the following sources.

1. Mel´endez et al. (2008) acquired high resolution near infrared spectra of 19 MW bulge giants. C, N, O and Fe abundances were obtained by spectrum synthesis of a number of lines from the MARCS (Gustafsson et al., 2008) 1D hydrostatic model atmospheres.

2. Using similar methods as Mel´endez et al. (2008), Ryde et al. (2010) showed the C, N, and Fe abundances of 11 MW bulge giants. We exclude one outlier: Arp 4203, due to its unusual C and N abundances.

3. Alves-Brito et al. (2010) observed optical spectra of 25 Galactic bulge giants in Baade’s window. O, Na, Mg, Al, Si, Ca, Ti and Fe abundances were derived from 1D local

thermodynamics equilibrium analysis using Kurucz (Castelli et al., 1997) and MARCS models. We choose the abundance ratios determined by MARCS models for consistence among diﬀerent sets of measurements. These author’s oxygen abundances are excluded, because oxygen’s trend is much diﬀerent than the other samples at super-

solar metallicity. In addition, Alves-Brito et al. argue that the oxygen abundances obtained from several IR OH lines (e.g., Mel´endez sample) are preferable to these determined from only one or two optical forbidden lines.

4. Bensby et al. (2013) presented element abundance analysis of 58 dwarf and sub-giant

stars in the MW bulge using microlensed spectra. MARCS model stellar atmospheres with Fe I NLTE (non-local thermodynamic equilibrium) corrections were employed to

42 extract the stellar parameters.

5. Hill et al. (2011) performed observations upon a sample of stars in the Baade’s window with GIRAFFE spectrograph at the VLT. Mg and Fe abundances were derived in 163 bulge clump giants using the MARCS models.

6. Johnson et al. (2012) presented Na, Al, and Fe abundances of 39 red giant branch (RGB) stars and 23 potential inner disk red clump stars located in Plaut’s window, while Johnson et al. (2013) showed the abundances of [Fe/H], [O/Fe], [Si/Fe], and [Ca/Fe] for 264 RGB stars in three Galactic bulge oﬀ-axis ﬁelds. Note that these

abundances are calculated relative to Arcturus. In order to consist with other sources which use solar abundances as reference, we adjust the reported abundances by adding the Arcturus abundances reported by Johnson et al.

7. Rich and Origlia (2005); Rich et al. (2007, 2012) collected a total of 61 bulge giants using NIRSPEC at the Keck telescope. They derived abundances for Fe, C, O and

four α elements (Mg, Si, Ca, and Ti) with reference solar abundances from Grevesse and Sauval (1998).

To incorporate the empirical abundance trends into our integrated-light models, we fit the observed [X/Fe]–[Fe/H] relations. We use a one-error least square fitting, in which the variances of [X/Fe] are considered as weights during the procedure of finding the minimum χ2. We adopt an uncertainty of 0.10 dex for the Meléndez sample and 0.11 dex, 0.09 dex for C and N abundances in the Ryde sample. Most of the abundances in the other data sets have individual errors, and the few without error estimates are excluded before the fitting. For simplicity, we consider only two possible fitting functions, a linear function or a quadratic function. The better one is chosen after individual inspection for both.

C and N •

43 0.8 2.0 0.2 A 0.7 B C 1.5 0.6 0.0 0.5 1.0 0.4 0.5 −0.2 0.3 [C/Fe] [N/Fe] [O/Fe] 0.2 0.0 −0.4 0.1 −0.5 0.0 −0.6 −0.1 −1.0 −2.0 −1.5 −1.0 −0.5 0.0 0.5 −2.0 −1.5 −1.0 −0.5 0.0 0.5 −2.0 −1.5 −1.0 −0.5 0.0 0.5

1.0 0.8 1.2 0.8 D E 1.0 F 0.6 0.6 0.8 0.4 0.4 0.6 0.2 0.2 0.4 0.0 [Al/Fe] [Na/Fe] [Mg/Fe] 0.2 −0.2 0.0 −0.4 0.0 −0.2 −0.6 −0.2 −0.8 −0.4 −0.4 −2.0 −1.5 −1.0 −0.5 0.0 0.5 −2.0 −1.5 −1.0 −0.5 0.0 0.5 −2.0 −1.5 −1.0 −0.5 0.0 0.5

1.4 1.0 0.8 1.2 G H I 0.6 1.0 0.5 0.8 0.4 0.6 0.0 0.2 0.4 [Ti/Fe] [Si/Fe] [Ca/Fe] 0.2 0.0 0.0 −0.5 −0.2 −0.2 −0.4 −1.0 −0.4 −2.0 −1.5 −1.0 −0.5 0.0 0.5 −2.0 −1.5 −1.0 −0.5 0.0 0.5 −2.0 −1.5 −1.0 −0.5 0.0 0.5 [Fe/H] [Fe/H] [Fe/H]

Figure 3.4: Abundance trends in the Milky Way bulge. Measurements from Rich and Origlia (2005); Rich et al. (2007, 2012) (open downward triangles), Johnson et al. (2012, 2013) (open squares), Hill et al. (2011) (open pentagons), Bensby et al. (2013) (open circles), Alves-Brito et al. (2010) (open upward triangles), Ryde et al. (2010) (crosses) and Mel´endez et al. (2008) (open diamonds) are shown. Our ﬁts are shown as thick solid lines. Errorbars are the published uncertainties.

44 Most of the carbon abundances from Mel´endez et al. (2008); Ryde et al. (2010) are close to solar, while Rich and Origlia derived sub-solar abundances [C/Fe] 0.2. This ∼ − disparity might originate from the complexity of infrared spectral feature lines: C, O, and other stellar parameters are obtained by simultaneous spectral ﬁtting of several

CO and OH molecular bands, which are sensitive to temperature, gravity and micro- turbulence (Origlia et al., 2002). In the cases of C and N, one might be concerned with alterations in surface abundance due to dredge up of nucleosynthetic processes. In the case of carbon, the mere fact that carbon abundances are near-solar or even sub-solar imply that the third dredge-up has not brought up signiﬁcant amount of

CNO-cycled rest-products to the surface (Mel´endez et al., 2008). However, super-solar nitrogen abundances are observed and seem to require extra sources besides the CNO cycle such as the neutrino process in massive stars suggested by Timmes et al. (1995) or primary nitrogen3. In this work, we model [C/Fe] and [N/Fe] as linear functions of

[Fe/H] (Figure 3.4A and 3.4B).

O and Mg • According to the abundance yields of type II supernovae (e.g.: Woosley and Weaver 1995), O and Mg are two of the primary alpha elements produced, and they are produced in almost the same ratio for stars of disparate mass and progenitor heavy element abundance. In Figure 3.4C and 3.4E, O diﬀers from Mg below [Fe/H] 1, due to the ∼ − scarcity of available data points for [Mg/Fe] at these metallicities. We ﬁt them with quadratic functions.

Na and Al • Na and Al are closely aﬀected by the excess neutrons associated with 22Ne generation (the beta decay of 18F to 18O) during the helium burning (Arnett, 1971; Clayton,

3The primary nitrogen has a production rate that does not rely on the prior presence of carbon in the interstellar gas from which the stars formed (Clayton, 2007).

45 2007). In Figure 3.4D and 3.4F, [Na/Fe] is an increasing function of [Fe/H], while [Al/Fe] decreases as metallicity increases. We ﬁt them with quadratic functions.

Si, Ca, and Ti • Based on the similar trend of Si, Ca, and Ti as a function of [Fe/H], we ﬁt these three elements with quadratic functions (Figure 3.4G, 3.4H, and 3.4I). These three elements are grouped together as explosive alpha elements sharing a similar nucleosynthetic

origin. However, they do not show the same trend in elliptical galaxies (Worthey et al., 2011, 2014b; Conroy et al., 2014). We search for the physical reason underlying this disorder of facts in 3.4. §

Generally speaking, the overall trend is clear in all the panels of Figure 3.4, but the scarcity of data for [Fe/H] < 1.0 renders the detailed form of the function vague for some − elements. When integrated, the fraction of metal poor stars is small in elliptical galaxies, so the uncertainty of ﬁtting function at [Fe/H] < 1.0 does not aﬀect our conclusions. −

1 3.2.3 300 km s− Elliptical Galaxy Chemical Composition

Since elliptical galaxies also seem to have a unique chemical composition but we do not have the luxury of star-by-star chemical analysis, we assume abundance ratios that are constant at all [M/H]. We incorporate the most up-to-date elliptical galaxy abundance ratios into our CSP models, and call that variant the EG CSP. Johansson et al. (2012); Worthey et al. (2014b) and Conroy et al. (2014) have obtained the abundances of several major elements from the integrated light spectra. Given the disparities of their methods, it gives conﬁdence that the ﬁnal results are generally consistent with each other (See Conroy et al. 2014). In this work, we adopt the set of element abundance ratios extracted from stacked 300 km s−14 SDSS early-type galaxy spectra, namely, [C/Fe]=0.21, [N/Fe]=0.27, [O/Fe]=0.28, [Na/Fe]=0.43,

4Velocity dispersion of the galaxy

46 [Mg/Fe]=0.22, [Al/Fe]=0.0, [Si/Fe]=0.16, [Ca/Fe]=0.02, [Ti/Fe]=0.12, set to be constant at all [M/H].

3.3 Results

In this section, we show several indices for the three CSPs that we assemble: 1. CSPs with scaled solar element abundances (SS CSPs, solid lines); 2. CSPs with Galactic bulge element abundances (GB CSPs, dashed lines); 3. CSPs with 300 km s−1 elliptical galaxy element abundances (EG CSPs, dotted lines). We compute the CSPs at the age of 2, 4, 6, 8, 10, 12,

and 14 Gyr with ﬁve shifted [M/H] distributions: peak [M/H]= 0.4, 0.2, 0.0, 0.2, 0.4. We − − present model indices at σ =300 km s−1 resolution, where the transformation from 200 km s−1 to 300 km s−1 is accomplished via smoothing of synthetic model spectra. Observational material: Three sources are used for galaxy indices in Figure 3.5, which displays how well a bulge template matches elliptical galaxy observations.

1. Graves et al. (2007) presented an analysis of red sequence galaxy spectra (0.06

0.08) from the SDSS, which uses a dual-ﬁber spectrograph, with resolution R 1800, ≈ wavelength coverage λ = 3800 9200A,˚ and ﬁber diameter d =3′′ which translates to − physical scales between 3.4 and 4.6 kpc. They labeled the red sequence galaxies with neither Hα or [O ii] detected (at the 2σ level) as “quiescent” galaxies, and divided these quiescent galaxies (N=2000) into 6 bins in velocity dispersion (σ = 70 120, 120 − − 145, 145 165, 165 190, 190 220, and 220 300 km s−1). All the spectra were − − − − broadened to σ = 300 km s−1 before stacking. The indices extracted from the stacked spectra are represented by open diamonds in Figure 3.5.

2. Trager et al. (2008) obtained the spectra of 12 early-type galaxies in the Coma cluster with 41 <σ< 270 km s−1, including the cD galaxy NGC 4874. The slitlet spectra were corrected along the slit to mimic a circular aperture of 2′′.7, which corresponds

47 to a physical diameter of 637 pc. These spectra were smoothed to σ = 300 km s−1. Indices are shown as ﬁlled squares in Figure 3.5.

3. Serven and Worthey (2010) presented spectra of mostly Virgo elliptical galaxies with 80 <σ< 360 km s−1. The observations were taken by the Cassegrain Spectrograph

mounted on the 4m Mayall telescope at Kitt Peak National Observatory. Serven extracted the spectra at an aperture of 13′′.8, which corresponds to a physical diameter of 1.1 kpc for most of the galaxies (the ones in the Virgo cluster), and then smoothed the spectra to σ = 300 km s−1 .This sample is denoted by blue triangles in Figure 3.5.

Age and Metallicity: Balmer line index – iron index plots are known to partially break the age-metallicity degeneracy that otherwise prevails in most diagrams (Worthey, 1994). 5 (Gonz´alez, 1993) is sensitive mainly to elemental Fe and thus is a good analog of [Fe/H]. Hβ is widely used as an age indicator due to its nonlinear response to main sequence turnoﬀ temperature. Compared to bluer HδF , Hβ is more susceptible to nebular emission contamination. We apply nebular emission corrections for Hβ and HδF to the Graves sample and Serven sample following the recipe of Serven and Worthey (2010). Five emission-corrected galaxies in the Serven sample are labelled as open triangles, since larger uncertainties might be expected for these galaxies in plots involving Balmer features. Figure

3.5A and 3.5B show that the inferred ages are consistent with the expectation that elliptical galaxies are generally old and metal rich. One obvious exception is found at the top of Figs. 3.5A and 3.5B: NGC 3156, a small elliptical galaxy with clear signs of a recent burst of star formation (Kuntschner et al., 2006). All age-sensitive diagrams agree that elliptical galaxies are slightly more metal rich than the GB, since we model the GB with a peak metallicity of solar, while the elliptical galaxies in Fig. 3.5 cluster around the +0.2 peak line.

5=(Fe5270 + Fe5335)/2.

48 4.0 0.4 A 4 B SS C 2 0.2 6 GB 3.5 0.0 EG 3 5 0.2 Serven 0.4 3.0 Peak [M/H] 4 Graves 2 Trager

4 F β 2.5 δ H

H 3 6 Fe4383 2.0 8 1 10 2 12 14 1.5 Age (Gyr) 0 1

1.0 0 1.0 1.5 2.0 2.5 1.0 1.5 2.0 2.5 1.0 1.5 2.0 2.5

0.25 5.5 D E F 8 0.20 5.0 7 0.15 4.5 6 0.10 4.0 5 1 3.5

4668 0.05 CN 2 Mg b Mg

C 4 3.0 0.00 3 2.5 −0.05 2 2.0 −0.10 1.5 1.0 1.5 2.0 2.5 1.0 1.5 2.0 2.5 1.0 1.5 2.0 2.5

26 6 G H 5 I 24 5 22 4 20 4 3 18 Na D Na Ca HK Ca 3 16 Ti4296 2 14 2 1 12 1 10 0 1.0 1.5 2.0 2.5 1.0 1.5 2.0 2.5 1.0 1.5 2.0 2.5

Figure 3.5: Integrated light index diagrams, all versus . CSP models with ADF peaks at [M/H] = -0.4, -0.2, 0, 0.2, 0.4 dex (blue, green, black, magenta and red lines, respectively) are shown for three chemical mixtures, SS CSPs (solid lines), GB CSPs (dotted lines), and EG CSPs (dashed lines). Ages (2 through 14 Gyr in steps of 2 Gyr) are shown as ticks along the lines. Serven (blue triangles), Graves (open diamonds), and Trager (green squares) observations are shown. Five Balmer emission galaxies in the Serven sample (open blue triangles) have had additional corrections applied.

49 Iron: Figure 3.5C, the Fe4383 – plot, is highly degenerate, showing similar eﬀects of target elements on Fe4383 and ; that is, both indices are sensitive to Fe, age, and overall abundance at approximately the same rate. Compared with SS CSPs, GB CSPs and EG CSPs shift toward weaker values of by about 0.1 A.˚ This is an artifact of

the fact that [M/H] is held constant, so that enhancement of the target elements comes at the expense of Fe (c.f., the analytical derivation in Johansson et al. (2012)). Restricted to Fe-sensitive indices, SS, GB, or EG mixtures are all able to reproduce the observations.

Carbon and Nitrogen: In the C24668 – plot (Fig. 3.5D), EG CSPs shift upward,

but GB CSPs shift downward with respect to SS CSPs. This is because C24668 is mainly

controlled by C2 with additional contributions from Fe, Mg, Cr, and Ti (Worthey et al., 1994) plus the evident fact that [C/Fe] 0.2 for the GB but [C/Fe]= 0.21 for EG. The ∼ − observations lie close to the EG CSPs, but the GB is apparently not a good template for this spectral region.

Regarding Fig. 3.5E, CN1 is known to closely depend on C, N, and O (Serven et al., 2005). The fact that GB CSPs and EG CSPs overlap means that the amalgamated eﬀects wrought by C, N, and O are almost the same in these two CSPs, despite the individual abundance ratios being diﬀerent ([C/Fe] 0.2, [N/Fe] 0.3, [O/Fe] 0.3 for GB6, [C/Fe]= ∼ − ∼ ∼ 0.21 [N/Fe]= 0.27, [O/Fe]= 0.28 for EG). In Fig. 3.5E, the GB and EG CSPs shift upward, showing somewhat better agreement with the data points than SS CSPs. Some of the data points, especially the Serven sample, are stronger-lined than the model grid. Partly, that is an artifact of taking an average value for the models, but it might also be because the apertures of the Serven spectra concentrate on the nuclei of the galaxies, zeroing in on the

most extremely metal rich stellar populations and also magnifying near-nuclear eﬀects such as lingering star formation or low level Active Galactic Nuclei (AGN) activity. Magnesium: Mg, one of the primary alpha elements, is observed to be enhanced in

6From 3.4.3 §

50 massive elliptical galaxies (Worthey et al., 1992; Conroy et al., 2014) and its strong absorption feature at 5170A˚ is found to be closely related to galactic velocity dispersion (Burstein et al., 1984; Davies et al., 1993; Bender et al., 1993; Trager et al., 2000a; Sánchez-Blázquez et al., 2006a). In Figure 3.5F, GB CSPs and EG CSPs show a much better match to the data points than SS CSPs. The stellar observations in the bulge and elliptical galaxies imply [Mg/Fe] 0.21, and this appears an adequate match to the data. ∼ Sodium: Na D, a strong absorption feature in the optical, has complex contributing factors. Na D is very sensitive to the Na abundance and is somewhat sensitive to the initial mass function (IMF), but it also suffers from possible interstellar absorption (Worthey et al.,

1994). In Figure 3.5G, we ﬁnd that the locus of GB CSPs is not suﬃcient to match all the data points. On the other hand, the EG CSP value of [Na/Fe]= 0.43 seems to miss the average and match only the most Na-strong elliptical galaxy data points. In our models, the IMF is set to a Salpeter one, and although IMF variation is not the subject of this chapter,

model experiments show that IMF variation causes only minor changes in the Na D index, leading Jeong et al. (2013), for example, to conclude that the Na abundance in Na excess objects might be truly enhanced. Calcium: Ca HK, ﬁrst deﬁned in Serven et al. (2005), was employed to study the

Ca abundance in Worthey et al. (2011) in part due to its insensitivity to the IMF. Given that Ca is one of the alpha elements and Ca yields closely track Mg (Nomoto et al., 2006; Kobayashi et al., 2006), the decreasing trend of Ca HK as a function of elliptical galaxy velocity dispersion is puzzling. Worthey et al. (2011) nevertheless concluded that chemical abundance variation is the explanation for the unusual Ca HK behavior. In Figure 3.5H we

see that enhanced [Ca/Fe], as in the GB CSPs, drives the model grids even further away from the data points. When we look at the EG CSPs, [Ca/Fe]= 0.02, and we would expect almost no change in Ca HK, but because other element ratios are changing, especially Mg, the model Ca HK index drops lower. However, even the amalgamated eﬀects of all the target

51 elements are insuﬃcient to cover the data points. The problem is eased when one notes that the Serven sample might lie low due to a spectral response systematic (Worthey et al., 2011). Titanium: Ti, the heaviest alpha element, is found to display little evidence of varying as a function of velocity dispersion in elliptical galaxies (Conroy et al., 2014; Worthey et al., 2014b). Here, we estimate Ti abundance by adopting a rarely used Ti index, Ti4296. The Ti4296 – plot looks similar to a inverted Balmer lines – plot due to its red pseudocontinuum passband encroaching on Hγ, and therefore has decent capability of breaking the age–metallicity degeneracy. In addition, it has relatively low response to most of the heavy elements (Serven et al., 2005). Figure 3.5I shows that a scaled solar or mildly enhanced Ti abundance is suﬃcient for elliptical galaxies.

3.4 Discussion

The clear basic result is that the [M/H]-dependent elemental mixture in the GB is not a good template for massive elliptical galaxies, although the conclusion of Terndrup et al. (1990) that the GB is a better template than local stars also seems perfectly valid. We now go on to discuss some extensions and implications of this work.

3.4.1 Varying the Widths of the ADFs: Red Lean and Red Spread

The width of the ADF is a parameter with signiﬁcant importance in our CSP models. To measure this width via observed spectra or models is an attractive goal. Some basic properties of the CSP models are summarized in Table 3.1, where we sample only ages 2 and 12 Gyr, and use ADFs that peak at the solar value. The widths (FWHM) of narrow, normal, wide ADFs are 0.41, 0.62, and 0.93 dex, respectively. Note that our wide-width ADF is almost the same width as the classical Simple model (FWHM 1.06 dex), but has a sharper cutoﬀ at high metal abundance. The weighted means are calculated in the usual way. For

52 Table 3.1: Mean [M/H] for Composite Populations Peaking at [M/H] = 0

Model Mass-Weighted B-Weighted K-Weighted [M/H] [M/H] [M/H] Narrow, Age 2 0.13 0.18 0.15 − − − Narrow, Age 12 0.13 0.20 0.13 Normal, Age 2 −0.19 −0.29 −0.21 Normal, Age 12 −0.19 −0.31 −0.18 − − − Wide, Age 2 0.26 0.42 0.28 Wide, Age 12 −0.26 −0.46 −0.25 Simple, Age 2 −0.25 −0.42 −0.28 − − − Simple, Age 12 0.25 0.46 0.23 − − − example, to compute the B flux weighted mean metallicity we convert to a pseudoflux and weight as: [M/H] w [M/H]= i i P wi P −0.4Bi where i is the index over bins in the ADF, wi = Si10 , Si is the ADF itself, i.e., the mass fraction of each stellar population, and Bi is the absolute magnitude of the stellar population at fixed initial mass.

Examination of Table 3.1 tells us that the mean metallicity is less than the peak metallicity due to the asymmetry of the ADF. Also, the B band light samples the ADF at about 0.2 dex lower metallicity than the mass-weighted or K-band-weighted would. This is due to the fact that metal-poor populations are brighter, coupled with the fact that they are also bluer. On the other hand, K band light balances the effect of brighter (even at K band) metal poor populations with the color change that boosts the K output of metal-rich populations so that the net effect at K is almost the same as the true, mass-weighted mean. Note that the CSPs investigated in 3.3 are modelled with the normal-width ADF. § Figure 3.6 quantifies the influence of ADF width. Using the EG chemical mixture, we plot narrow width (solid), normal (dashed), and wide (dotted) lines in the Hβ and − Mgb plots. The three elliptical galaxy samples from 3.3 are plotted along with the − §

53 CSP model grids. We see two main effects. The first effect is that the narrower the ADF, the more metal- rich it appears (“red lean”). The second effect is an amplification of the disparity between narrow and wide ADFs as the peak metallicity shifts to higher [M/H] (“red spread”).

Both red lean and red spread originate from the fact that metal poor populations are more luminous than their metal rich counterparts (for the same initial mass). As the width decreases, the more-potent metal-poor fraction decreases, and the overall average moves toward the metal-rich in a light-weighted sense as seen in Table 3.1, or, in looser words, it leans toward the red. The red spread eﬀect relies upon, in addition, the increased volatility of red giant branch temperatures for cooler, more metal rich stellar populations (cf. Fig 4 of Worthey (1994)) coupled with the backwarming of cooler stars due to increased line- blanketing (Mihalas, 1970). The increased ∆T and color change from backwarming combine to create a greater spectral change in the metal rich regime than the metal poor regime for

the same ∆[M/H], and thus an ampliﬁed spectral change for the more metal-rich ADFs. Not all the ADF widths are physically reasonable. With logic similar to that surrounding Figure 2 of Worthey et al. (1996) concerning the Simple Model, the wide-width ADFs seem ruled out by inspection of Figure 3.6. That is, in order to make a wide-width model match

the observed spectral indices of elliptical galaxies, the maximum [M/H] required becomes unreasonably large: Since the peak = +0.4 model still falls short of observation, a wide-width model that matches would have most of its stars at [M/H] greater than several times the solar abundance. Although the normal-width ADF (and not the narrow width) ﬁt nicely, we cannot (yet) show evidence from integrated light that would exclude the narrow width

ADF, even though star-by-star analyses always show ADFs wider than our narrow model.

54 4.0 A

3.5

3.0

β 2.5 H

2.0

1.5

1.0 1.0 1.5 2.0 2.5

5.5 EG normal B 5.0 EG narrow EG wide 4.5 Serven Graves Trager 4.0

3.5 Mgb 3.0

2.5

2.0

1.5 1.0 1.5 2.0 2.5

Figure 3.6: Hβ and Mgb plot for narrow (solid lines), normal (dashed lines), − − and wide (dotted lines) ADFs. Peak [M/H] = -0.4, -0.2, 0, 0.2, 0.4 dex are indicated by blue, green, black, magenta and red lines, respectively. We choose EG CSPs for illustration purpose, but other CSPs would not change our conclusions. Elliptical galaxies are labelled the same as Figure 3.5.

55 3.4.2 Comparing Chemical Compositions of the Milky Way Bulge

and Elliptical Galaxies

Throughout this chapter, we investigate the possibility of using Milky Way bulge abundance trends to interpret elliptical galaxy observables. What we found in 3.3 can be summarized § as this: Fe, Mg, and Ti match the elliptical galaxy abundances, but more C, Na and less

Ca are required to explain the absorption indices of elliptical galaxies. In other words, MW bulge mimic the elliptical galaxies better than scaled solar stars do, but concrete disparities still exist between the bulge and elliptical galaxies. The MW bulge and elliptical galaxies both consist of old stellar populations, but they are otherwise dissimilar. The obvious diﬀerence is that the MW bulge is a subcomponent of a spiral galaxy. Also, Tremaine et al. (2002) found MW bulge velocity dispersion is close to 95 km s−1, while the mean velocity dispersion of our elliptical galaxies is about 200 km s−1. The various nucleosynthetic processes associated with diﬀerent mass stars are likely the key to understand the element abundance trends in both environments, but we still lack a clear connection between galaxy mass or formation history and nucleosynthetic outcome.

We ﬁnd more C in elliptical galaxies than in the MW bulge using C24668. The N and

O abundance can be estimated by including other element-sensitive indices, like CN1 and

TiO2 (Graves et al., 2007; Johansson et al., 2012; Conroy et al., 2014), but since such precise abundance calculation is beyond the scope of this work, we defer the discussion of N and O abundances to other papers such as Worthey et al. (2014b). In terms of C enhancement, many studies show that intermediate mass stars contribute signiﬁcant amounts of C due to dredge up in the asymptotic giant branch phase (van den Hoek and Groenewegen, 1997;

Woosley et al., 2002). But Pipino and Matteucci (2004) found the C abundance generated by these models is lower than the observed values. Recently, Geneva group (Ekstr¨om et al., 2012; Georgy et al., 2013) showed rotation in massive stars signiﬁcantly changes the C yield. In that

56 spirit, Pipino et al. (2009) included stellar rotation in their chemical evolution models and found an increased C abundance which produce a trend consistent with Graves et al. (2007). It is possible that the discrepancy of C abundance between the MW bulge and elliptical galaxies might be also caused by stellar rotation. Following this logic, then for more C we

would require more massive stars to form during the evolution of elliptical galaxies, since rotation is more significant for massive stars (Ekström et al., 2012; Georgy et al., 2013). This could mean a top-heavy IMF, but not necessarily because increased effectiveness of massive star yields can be achieved by a Salpeter IMF with a galaxy mass-dependent star formation rate (Pipino et al., 2009).

The case of calcium is even more puzzling. Given the similarity of old stellar populations in the MW bulge and elliptical galaxies, the dichotomous behavior of Ca challenge most of the nucleosynthesis theories. To summarize the empirical evidence: 1. Ca has sub-solar abundance in elliptical galaxies. That Ca feature strengths generally decline with elliptical galaxy velocity dispersion (Saglia et al., 2002) is not a low mass stellar IMF eﬀect (Worthey et al., 2011) but instead a real decline in [Ca/Mg], a modest decline in [Ca/Fe], and possibly a small decline in [Ca/H] as well. Near solar or sub-solar Ca abundances are also found by Graves et al. (2007); Johansson et al. (2012); Worthey et al. (2014b). 2. Ca loosely resembles

Mg and O in the MW bulge ( 3.2 & Fulbright et al. 2007), which seems agree with its alpha § element origin, nevertheless Ca in elliptical galaxies approximately follows [Fe/H] (Graves et al., 2007; Johansson et al., 2012; Worthey et al., 2014b; Conroy et al., 2014). According to the Type II supernova yields of Nomoto et al. (2006), Ca and Mg seem in lockstep with each other, trending the same with progenitor mass and metallicity, and leaving a clear impression that Ca should follow Mg always. So what is the reason for this Ca-Mg dissimilarity of the elliptical galaxies? Two scenarios have been proposed to explain Ca’s atypical alpha element behavior under the classic one zone, two sources (Type Ia and II supernova) hypothesis.

1. Pipino and Matteucci (2004); Pipino et al. (2009) suggested the Ca underabundance

57 relative to Mg found in their chemical evolution models is caused by a non-negligible Ca contribution via Type Ia supernova (Nomoto et al., 1997). According to the delayed detonation model described in Nomoto et al. (1997), Ca yield does come out higher than Mg yield for Type Ia supernova. Following this logic, the enhanced Mg abundance

in massive elliptical galaxies would still come from increased Type II contributions, but Ca would be diluted as more Type II products are added. Note that is necessary for Type II supernovae to produce less Ca than current yields predict for this scheme to be successful.

More speculatively, there might be a connection with the recent studies of silicon group elements: Based on the classical W7 models (Nomoto et al., 1984; Thielemann et al., 1986), De et al. (2014) propose the “W7-like” models that are now capable of varying

the 22Ne mass fraction freely. They notice the electron fraction of the progenitor white dwarfs, which anti-correlates with the 22Ne mass fraction, systematically inﬂuences the nucleosynthesis of the silicon group elements (Si, S, and Ca) in the sense that Ca shows a nearly quadratic increasing trend with electron fraction, while Si is almost insensitive

to the electron fraction. Observationally speaking, Si is a fair alpha element compared to Ca, since it roughly follows Mg and O in both the MW bulge and elliptical galaxies7. Therefore, the observations imply more Ca, but the same amount of Si are generated in low mass ellipticals via Type Ia supernova. The Ca and Si yields would reconcile

with the theory of De et al. (2014) if the electron fraction is a decreasing function of stellar velocity dispersion. However, we also notice the dynamical range of electron fraction is small in De et al. (2014), which means an observational demonstration is unlikely.

If the MW bulge is an analog of a low-σ elliptical galaxy (MacArthur et al., 2009), its Ca contribution from Type Ia supernova should be higher than massive elliptical galaxies

7S is left out due to a lack of spectral lines (Serven et al., 2005).

58 (c.f. Thomas et al. 2011 for a similar statement). Given that the decreasing trend of [α/Fe] versus [Fe/H] is usually explained by a Type Ia supernova contribution of Fe (Wheeler et al., 1989), an increase of Type Ia supernova Ca would ﬂatten its negative slope against [Fe/H], and make Ca dissimilar to other alpha elements. Unfortunately

for the Type Ia Ca origin hypothesis, the [Ca/Fe] and [Mg/Fe] trends in Figure 3.4 look very similar.

2. Alternatively, the Ca behavior could be conceived to be the result of Ca yield suppression in massive ellipticals. This conjecture might be caused by a mass-dependent

Ca yield in supernova, where the highest-mass stars contribute less Ca but continue to contribute Si, O, and Mg, and massive ellipticals would favor these highest-mass stars. This was suggested long ago (Worthey et al., 1992) but the speciﬁc question of Ca yield is ambiguous (Woosley and Weaver, 1995; Nomoto et al., 2006). On the other hand, Ca yield suppression might connect with a metallicity-dependent yield. Fulbright

et al. (2007) suggested inclusion of metallicity-dependent wind may change the alpha element yields from massive Type II progenitors in Woosley and Weaver (1995). As metallicity increases, the yield of hydrostatic elements (e.g., O, Mg) increases and the yield of explosive elements (e.g., Si, Ca, Ti) declines. This seems qualitatively correct.

A metallicity-dependent yield has not been systematically studied by any theoretical group to the best of our knowledge.

3.4.3 Recovering Abundances with Simple Stellar Population Mod-

els

Eﬀorts to discover the detailed chemical composition of galaxies and most eﬀorts to discover the ages of old stellar populations use single-burst, single-composition simple stellar population (SSP) models. Going from inherently CSP populations but interpreting them via SSP

59 Table 3.2: Recovery of Population Parameters Under an SSP Hypothesis

Quantity Mass-Weighted Recovered Standard Value Value Deviation Age 8 5.7 0.9 Age 12 10.6 2.2 [M/H] 0.19 0.19 0.15 [C/Fe] −0.23 −0.27 0.05 − − [N/Fe] 0.38 0.14 0.09 [O/Fe] 0.32 0.24 0.19 [Na/Fe] 0.06 0.17 0.17 [Mg/Fe] 0.25 0.25 0.14 [Si/Fe] 0.17 0.25 0.03 [Ca/Fe] 0.19 0.20 0.07 [Ti/Fe] 0.18 0.37 0.18

models might introduce systematics. To explore this, we perform the following theoretical exercise. In Worthey et al. (2014b), a chemical mix-sensitive inversion program that uses SSP based on Bertelli et al. (1994) evolution was applied to several samples of galaxies. Here, we use the same inversion program on the CSP models, built with evolution based upon Marigo et al. (2008) as well as being composite in metallicity. Uncertainties in each index were calculated by a photon noise model normalized to S/N = 25 per A˚ at 5000A˚ in Fλ units. The comparison is presented in Table 3.2 for the average of two ages (8 and 12 Gyr) computed from a CSP model with normal-width ADF peaked at solar abundance and with a run of bulge chemical mixtures and more recent stellar evolution, interpreted with older models under a single-burst hypothesis. As in Worthey et al. (2014b), sensitivities to diﬀerent elements were turned on and oﬀ in order to generate a crude “permutational”

estimate of uncertainty. Table 3.2 shows approximate agreement between CSP input and SSP-recovered parameters, with interesting systematic drifts. The mean ages drift slightly younger, especially with

60 [Si/Fe] set to zero. Letting [Si/Fe] vary allows the ages to relax about 1.5 Gyr older. This is due to the molecular SiH features in the blue covarying with some of the Balmer indices, from which the bulk of the age information comes. With some permutations of which elements were allowed to vary, there arises a correlation between age and a few of the [X/Fe],

often [Na/Fe] for example. This is slippage in the inversion scheme and a caution for future work with this inversion program. The mean [M/H] is recovered well. The abundance parameters are adequately recovered, with [N/Fe] too low, and [Ti, Si/Fe] too high at marginal statistical signiﬁcance. Table 3.2 is encouraging in terms of basic coherence between models and in the fact that the element ratios can be recovered in a way that resembles the actual,

metallicity-and-mass-weighted mean. One can also safely say that more work is needed to truly understand all possible systematics.

3.4.4 Detectability of ADF Width

We are able to fuzzily reject a too-wide abundance distribution, but we are so far unable to distinguish narrow from normal ADFs in integrated light. We now attempt to point

a way forward by considering the spectral shape of the composite population as a whole. Compositeness of stellar populations, be it age-composite or abundance-composite, can be expected to increase the variety of stellar temperatures present in the population, and thus increase the width of the overall integrated sum of near-blackbody stellar ﬂuxes. Thus,

sampling the spectrum over a broad span of wavelength may yield diagnostic information. We attempt to illustrate how this might work in Figure 3.7. We note several encouraging things. In that color plane, age and abundance effects are nicely orthogonal. The effects of ADF width increase as the population ages. If we measure UV bump strength from farther in the UV and if we measure the metallicity from optical spectral indices, then it does indeed seem as if the narrow and normal widths can be distinguished, with the only effect unaccounted for being dust extinction. We therefore

61 7.0

Na 6.5

No 6.0 E(B-V)=0.2 Na Peak=+0.4

5.5 No W Peak=solar 5.0 W 14 Z 12 10 4.5 GALEX_NUV - I - GALEX_NUV Age (Gyr) 8 6 4.0 4 3.5 UV bump 3.0 2 1.9 2.0 2.1 2.2 2.3 I-L

Figure 3.7: Integrated light color-color diagram that shows sensitivity to the width of the ADF involving the GALEX NUV filter (0.2 m) and Johnson-Cousins I (0.7 m) and L (3.4 m). Colors are set to zero magnitude for the spectral shape of Vega. As in previous figures, stellar population ages between 2 and 14 Gyr are shown, for three ADF widths (marked “W” for wide, “No” for normal, and “Na” for narrow) and two peak metallicities, peak [M/H] = solar (bold lines) and peak [M/H] = +0.4 (thinner lines). The effect of dust screen extinction, the increase of metallicity, and including a hot UV-bump component are illustrated with labelled vectors.

62 tentatively judge that the prospects are bright for measuring the ADF width galaxies whose ages are fairly unimodal and whose dust content is characterized well. Using near-UV spectral indices as a proxy for photometric color would presumably lessen the eﬀects of dust extinction and make the method more robust.

3.5 Summary

Using the evolving Worthey models (Worthey, 1994; Trager et al., 2008; Lee et al., 2009; Tang and Worthey, 2013; Worthey et al., 2014a), we investigate composite stellar population models with diﬀerent metallicity spreads. In integrated light, the narrower ADF appears more metal rich (“red lean”) and the disparity between narrow and wide ADFs widens as

peak [M/H] move to a higher metallicity (“red spread”). Wide-width ADFs and the Simple Model ADF are ruled out because of the need for unreasonably large [M/H]8. Star by star, we conﬁrm that the normal-width ADF replicates the observed solar neighborhood and MW bulge ADFs, and our modeling indicates that the normal-width or narrow-width ADF also ﬁts elliptical galaxies in integrated light.

The good match of elliptical galaxy colors and TiO strengths with MW bulge templates (Terndrup et al., 1990) inspires us to find out if the MW bulge element abundance trend can be applied to elliptical galaxies. We model CSPs with MW bulge chemical compositions, tracking the detailed behavior of each element as a function of [M/H], CSPs with scaled solar abundances, and CSPs with an elemental mixture chosen to match massive elliptical galaxies (Conroy et al., 2014), then compare model absorption feature indices with observed indices. Iron, Ti, and Mg vector about the same for the MW bulge and elliptical galaxies, while the trends of C, Na, and Ca are different. If the MW bulge is analogous to a low velocity dispersion elliptical galaxy, attempting to discern implications about elliptical galaxy evolution based on various nucleosynthetic processes associated with different environments

8For additional discussion of the Simple Model ADF, see Worthey et al. (1996)

63 (star formation timescales, galactic winds, stellar population IMF, supernova mass- and metallicity dependent yields, and white dwarf electron density) leads to no clear astrophysical frontrunner as to the cause of the abundance trends. We perform an exercise to feed our MW bulge CSP models based on one set of stellar evolutionary isochrones into a chemical mixture inversion program based on a diﬀerent set of stellar evolutionary isochrones and ﬁnd that the parameters were recovered fairly well in the sense of matching the ADF-weighted mass average abundances. Our particular exercise uncovered a systematic trend toward younger ages. Elemental mixtures are recovered well, though in our case [N/Fe] came out on the low side, while [Ti/Fe] and [Si/Fe] were too high.

The age and abundance systematics uncovered serve to urge further study of the inversion process. We investigate whether the width of an ADF could be measured from integrated light alone, and ﬁnd a successful technique: photometric colors of very long wavelength span.

The main caveats for old stellar populations are dust content and the correct subtraction of whatever ultraviolet-bright subpopulation might be present.

64 CHAPTER 4

ON DISENTANGLING INITIAL MASS FUNCTION

DEGENERACIES IN INTEGRATED LIGHT

4.1 Introduction

Deriving astrophysical parameters from integrated-light observables is a widely accepted practice in the ﬁeld of Galactic and extragalactic research. However, increasing evidence shows that single-burst, single-composition stellar populations oversimplify the underlying stellar systems (Gratton et al., 2012; Kaviraj et al., 2007). Additional parameters in the modelling process, such as: multiple burst-age stellar populations (Trager et al., 2000a, 2005; Goudfrooij et al., 2011), metallicity and helium abundance variation (Norris, 2004; Lee et al., 2005), initial mass function (IMF) variation (Weidner et al., 2013a; Bekki, 2013; Chabrier et al., 2014), and chemical abundance variation (Dotter et al., 2007a; Lee et al.,

2009) were investigated in hopes of reconciling various contradictions between observation and theory. In this spirit, we explored the Abundance Distribution Function (ADF; the mass fraction of the stellar population located at each [M/H]) eﬀect in Chapter 3. The ADF shape is a gentle rise at low abundance, a peak, and a steeper fall-oﬀ at high abundance.

In Chapter 3, we constructed various ADF-width composite stellar populations (CSPs), and discovered the novel “red lean” and “red spread” phenomena. “Red lean” means that a narrower ADF appears more metal rich than a wide one, and “red spread” describes that

65 the spectral difference between wide and narrow ADFs increases as the ADF peak is moved to more metal-rich values. We continue to explore in this chapter two underexplored effects that might entangle with the IMF slope effect in integrated stellar population (SP) models. A Low-mass cut-off for the IMF (LMCO)1 exists in every set of SP models. It is the mass limit of stars included at the low mass end — any star with mass smaller than this limit is assumed to have no contribution in the SP models. Often, the LMCO is a pragmatic choice dictated by the choice of stellar evolutionary isochrones that go into the SP models. It is readily appreciated that the LMCO is closely related to the fraction of low mass stars, and thus the dwarf/giant ratio. Note that the gravity sensitive spectral indices (e.g., CaT, [Na i], and Wing-Ford band), widely used for IMF slop determination, are designed to measure the dwarf/giant ratios. Therefore, we may encounter degeneracy when determining IMF slope and LMCO simultaneously. The LMCO is variable among different SP models found in the literature.

For example, the Padova isochrones (Bertelli et al., 2008, 2009) set 0.15 M⊙ as the LMCO, while the composite isochrones of Conroy and van Dokkum (2012a) sets 0.08 M⊙ as the LMCO. As a result, the derived IMF slope values may change when swapping between SP models.

The second eﬀect we explore may also mimic an IMF slope variation. It is the logical possibility that the dwarf/giant ratio may come as easily from modulating the number of giants as modulating the number of dwarfs. The bolometrically brightest giants, AGB stars, have long been known to be diﬃcult to constrain in most SP models (Conroy and Gunn, 2010; Girardi et al., 2010, 2013), due to uncertain stellar evolution (in turn due to uncertain rules

about mass loss in giants) and also diﬃcult to empirically constrain due to counting statistics (Frogel et al., 1990; Santos and Frogel, 1997; Bruzual and Charlot, 2003; Salaris et al., 2014). We suggest that ADF-AGB-IMF masquerading is a hypothetical but well motivated trend

1Throughout this dissertation, IMF LMCO is called LMCO for short.

66 where increased metallicity causes cooler giants, which causes increased mass-loss, which causes fewer AGB stars, which resembles an increase in IMF slope (Worthey, in preparation). To attempt to provide a solid ground for future IMF research, here we study multiple spectral and photometric variations in response to simultaneous changes of IMF slope,

LMCO, and AGB strength ( 4.2). We show that the degeneracies can be marginally lifted for § old, metal rich populations, but the degeneracies are still firm in young populations ( 4.2.2 & § 4.2.3). Next, we explore the mechanism behind all these variations by studying the number § of stars, luminosity, color, and index of each phase ( 4.2.4). § Bottom-heavy IMFs are indicated in local massive and metal-rich elliptical galaxies in most studies (Cenarro et al., 2003; van Dokkum and Conroy, 2010; Conroy and van Dokkum, 2012b; Cappellari et al., 2012). On the other hand, star-formation theories such as Larson (1998, 2005) and Marks et al. (2012) imply that the metal-free early Universe favors a top-heavy IMF. Weidner et al. (2013a) points out a time-independent bottom-heavy IMF generates too little metal and fewer stellar remnants than observed. The hypothesis that IMF steepens as the Universe evolves from metal-poor to more metal-rich, we call here ADF-IMF coupling. In 4.3, we build rough models with ADF-IMF coupling to explore the § ramifications, at least qualitatively. The coupled models appear more metal-rich than the noncoupled models, due to the suppression of metal-poor stars. Finally, we test parameter recovery using a Monte Carlo approach. We uncover covari- ances among the IMF slope, LMCO, and AGB effects when combined with the more usual age and metallicity effects. Though the magnitudes of the IMF-related effects are smaller than the latter effects, these two groups of effects vector almost orthogonally ( 4.4.3), and § we prognosticate bright hopes for disentangling all of these stellar population parameters. A summary of our results are given in 4.5. §

67 4.2 IMF slope, LMCO, and AGB

4.2.1 Model description

A new version of old integrated-light models (Worthey, 1994; Trager et al., 1998) is adopted. The new models use a new grid of synthetic spectra in the optical (Lee et al., 2009) in order to address the eﬀects of changing the detailed elemental composition on an integrated spectrum.

The models retain single burst age and metallicity as parameters, but were expanded to also include metallicity-composite populations, and the three IMF-related parameters we discuss (IMF slope, LMCO, and AGB modulation). For this work, we adopt the isochrones of Bertelli et al. (2008, 2009) using the thermally- pulsing asymptotic giant branch (TP-AGB) treatment described in Marigo et al. (2008). Following Poole et al. (2010), stellar index ﬁtting functions were generated from indices measured from the stellar spectral libraries of Valdes et al. (2004) and Worthey et al. (2014a), both transformed to a common 200 km s−1 spectral resolution. Multivariate polynomial

fitting was done in five overlapping temperature swaths as a function of θeff = 5040/Teff , log g, and [Fe/H]. The fits were combined into a lookup table for final use. As in Worthey (1994), an index was looked up for each bin in the isochrone and decomposed into “index” and “continuum” fluxes, which added, then re-formed into an index representing the final, integrated value after the summation.

To constrain the responses of diﬀerent characteristics to the IMF slope, LMCO, and AGB eﬀects, we parametrize the IMF slope2 with 2.35 and 1.70, the LMCO with 0.15 and 0.30

M⊙, and the AGB contribution with full and 80% strength. We deﬁne the AGB phase as isochrone that begins at 0.5 mag smaller than the red clump, and ends before the dwarf

phase. The number of AGB stars of each mass bin is reduced to 80% to simulate a weaker AGB strength model. This 80% AGB strength model is designed as a toy model to study the

2A power-law function, where 2.35 is the Salpeter (1955) slope and 1.70 is a bottom-light hypothesis.

68 age=10 Gyr, log[Fe/H]=0.37 0.026 3.44 1 IMF slope 1.44 1 2 LMCO 0.024 1.42 3 AGB 3 3.42 3 1.40 0.022 3.40 2 1.38 NaI VK 2 bTiO 0.020 1 1.36 3.38 3 A =0.02 1.34 V 0.018 1.32 3.36 1 2 0.016 1.30 1.100 1.105 1.110 1.115 1.120 1.125 1.130 1.135 1.140 3.72 3.74 3.76 3.78 3.80 3.82 3.72 3.74 3.76 3.78 3.80 3.82 BV [MgFe] [MgFe] 1.00 0.094 0.70 0.68 0.98 1 0.092 0.66 2 0.96 0.090 0.64 3 3 3 0.62 JK 1 0.94 TiO2 0.088 1

WingFord 0.60 0.92 0.086 0.58 2 2 0.56 0.90 0.084 1.100 1.105 1.110 1.115 1.120 1.125 1.130 1.135 1.140 3.72 3.74 3.76 3.78 3.80 3.82 3.72 3.74 3.76 3.78 3.80 3.82 BV [MgFe] [MgFe] 2.80 0.000 1

2.78 −0.002

2.76 −0.004 3 2 RK 2.74 3 CaH1 −0.006 1 2 2.72 −0.008

2.70 −0.010 1.740 1.745 1.750 1.755 1.760 1.765 1.770 1.775 1.780 3.72 3.74 3.76 3.78 3.80 3.82 BR [MgFe]

Figure 4.1: Color-color and index-index plots for an old, metal-rich population. The IMF slope, LMCO, AGB eﬀects are labelled as vectors 1, 2, 3, respectively. At the bottom right of each plot involving photometric colors, an extinction vector of AV =0.02 mag is sketched.

ADF-AGB-IMF masquerading, as the isochrone level investigation has started with MESA recently (Worthey et al., in preparation). The SP model with IMF slope of 2.35, LMCO of 0.15 M⊙, and full AGB strength is chosen as the standard model. Parameter variations from these nominal values are linearized, meaning that if the parameters drift too far from nominal they can no longer be considered as well-modeled. To illustrate the diﬀerent eﬀects we vary one single parameter at a time. That is, the results we display graphically are partial derivatives (∂index/∂effect).

69 4.2.2 An Old, Metal-rich Population

Since most of the elliptical galaxies in the local Universe are old and metal-rich, we pick age = 10 Gy, and log(Z)=0.37 to mimic a typical elliptical galaxy. In the left column of Figure 4.1, we show the optical-near infrared (NIR) color-color plots. Note that we set the same y axis dynamic range (0.1 mag) for all the color-color plots3. An extinction vector of AV = 0.02 mag is sketched on the bottom right of each plots. We note that 1) the IMF slope, LMCO, and AGB effects are not parallel vectors, which means it is practical to lift the degeneracy of a single index with a mix of different colors. However, we note that these effects are detectable at the level of 0.02 mag. Such accuracies are comparable to ∼ contemporary detection limits and therefore technically challenging by today’s standards. In addition, 2) the (J K) vs. (B V ) plot shows the weakest drifts among the three plots, due − − to the wavelength-proximity of these two pairs of filters. This wavelength-proximity is also the reason for small extinction vector. Insensitivity to dust promotes the diagnostic value of this plot. We also find that 3) decreasing the IMF slope and AGB strength tend to change

the (X K) colors in the opposite direction. Interestingly, increasing the LMCO leads to a − decrease in (V K) and (R K), but an increase in (J K), implying blue (J K) colors − − − − for stars between 0.15 and 0.30 M⊙ ( 4.2.4). § In the middle and right columns of Figure 4.1, we plot [MgFe]4 versus ﬁve IMF-sensitive

indices. We introduce to the Worthey models the optical IMF-sensitive indices bTiO and CaH1 from Spiniello et al. (2014a), and plan to use them for future high redshift galaxy IMF research (Chapter 5). We notice that (1) the drifts caused by weakening the AGB strength are the smallest, due to low ﬂux contribution of the AGB stars at the age of 10 Gyr ( 4.2.4). § We also see that (2) decreasing the IMF slope tends to decrease the [MgFe] index (about 0.02 A),˚ while increasing the LMCO leads to small variation of [MgFe]. In addition, (3) the

30.01 mag and 0.15 A˚ for magnitude and angstrom unit indices, respectively. 4[MgFe]= Mgb (Fe5370 + Fe5335)/2) p ∗

70 age=2 Gyr, log[Fe/H]=0.37 3.15 0.018 1.20 1 IMF slope 2 LMCO 1.18 3.10 3 AGB 0.016 1 1.16 3.05 0.014 1.14 3 1 2

NaI 1.12 VK 3.00 bTiO 0.012 2 2 1 1.10 AV =0.02 3 2.95 3 0.010 1.08 1.06 2.90 0.008 0.860 0.865 0.870 0.875 0.880 0.885 0.890 0.895 0.900 2.76 2.78 2.80 2.82 2.84 2.86 2.76 2.78 2.80 2.82 2.84 2.86 BV [MgFe] [MgFe] 1.05 0.082 1 0.54 1.00 0.080 0.52

0.50 1 0.95 0.078 0.48 2 1 JK TiO2 2 0.90 3 0.076 2 0.46 3 WingFord 0.44 0.85 0.074 3 0.42 0.80 0.072 0.40 0.860 0.865 0.870 0.875 0.880 0.885 0.890 0.895 0.900 2.76 2.78 2.80 2.82 2.84 2.86 2.76 2.78 2.80 2.82 2.84 2.86 BV [MgFe] [MgFe] 2.60 0.005

2.55 1 0.000

2.50 2 −0.005 RK 2.45 CaH1 3 −0.010 3 1 2.40 2

2.35 −0.015 1.385 1.390 1.395 1.400 1.405 1.410 1.415 1.420 1.425 2.76 2.78 2.80 2.82 2.84 2.86 BR [MgFe]

Figure 4.2: Color-color and index-index plots for a young, metal-rich population. The IMF slope, LMCO, AGB effects are labelled as vectors 1, 2, 3, respectively. At the bottom right of each color-color plot, an extinction vector of AV =0.02 mag is sketched. smaller dwarf/giant ratios induced by the IMF slope and LMCO effects lead to smaller values for IMF-sensitive indices. But the magnitude ratios of these two effects vary for different indices. The results that the LMCO drifts are larger than the IMF slope drifts in TiO2 and Wing-Ford band suggest caution should be taken when interpreting these two indices as a clean IMF slope indicator.

4.2.3 A Young, Metal-rich Population

Schiavon et al. (2006) suggested young elliptical galaxies with ages of the order of 1 Gyr

71 prevail in the early Universe (z 0.9). Studying these galaxies places important constraints ∼ on the elliptical evolution models. Here we pick age = 2 Gyr, and log(Z)=0.37 to mimic a young elliptical galaxy. In the all the plots of Figure 4.2, weakening the AGB strength induces a stronger drift than the old population, due to the high ﬂux contribution of AGB stars at the age of 0.2 2 Gyr (Maraston et al., 2006). To accommodate the large AGB − drifts, the y axis dynamic ranges are set to 0.25 mag for color-color plots. Note that this may causes visual diﬀerences between the color-colors plots of Figures 4.1 and 4.2. In the optical-NIR color-color plots of Figure 4.2, (1) increasing the LMCO leads to negligible signal, while weakening the AGB strength shows a drift that is a factor of two

larger as the old population. Another noticeable change is (2) the optical colors on x axis. Instead of getting bluer as the old population does, decreasing the IMF slope of a young population drives the (B V ) and (B R) colors redder, probably due to stronger post − − main sequence phases ( 4.2.4). Comparing with the extinction vectors, (3) the AGB drift § and the IMF slope drift should be clearly detectable at 0.02 mag level. In the middle and right columns, (1) the index increases for bTiO, TiO2, and the Wing- Ford band caused by decreasing the IMF slope of a young population conﬁrm that IMF determination is sensitive to the age parameter. We also see that (2) the shallower IMF

slope model has greater [MgFe] than the standard model. In addition, (3) the AGB and IMF slope effects vector almost oppositely in most of the Figure 4.2 plots. The partial derivative nature of our results reveals the degeneracy of IMF slope and AGB strength is still firm for the young population. We further discuss the reasons for different drift directions by inspecting the luminosity weights, colors, and indices of each evolutionary phase in 4.2.4. §

4.2.4 Colors and Indices Broken into Evolutionary Phases

To illustrate the reasons behind the color drifts of three eﬀects, we show the number of stars, luminosities, and colors in Figure 4.3. First, we take a look at the old population. In Figure

72 age=10 Gyr, log[Fe/H]=0.37 age=2 Gyr, log[Fe/H]=0.37 7.5 7.5 A Standard F 7.0 IMF slope=1.7 7.0 LMCO=0.3 80% AGB 6.5 6.5 6.0 6.0

log(dN/dm) log(dN/dm) 5.5

5.5 5.0

5.0 4.5 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 m m 7.5 ini 7.5 ini B G 7.0 7.0 6.5 6.5 6.0 6.0

log(dN/dm) log(dN/dm) 5.5

5.5 5.0

5.0 4.5 0 50 100 150 200 250 300 350 0 100 200 300 400 500 Evolutionary points Evolutionary points 7 8 C H 6 7 6 5 *dN) *dN)

V V 5 4

log(L log(L 4

3 0.3M ⊙ MSTO EAGB 3 0.3M ⊙ MSTO EAGB

2 2 0 50 100 150 200 250 300 350 0 100 200 300 400 500 Evolutionary points Evolutionary points 1.8 1.8 D I 1.6 1.6 1.4 1.4 1.2 1.2

B-V B-V 1.0 1.0 0.8 0.8 0.6 0.6 0.4 0 50 100 150 200 250 300 350 0 100 200 300 400 500 Evolutionary points Evolutionary points 12 10 E J 10

8 8

6 6 V-K V-K

4 4 2 2 0 0 50 100 150 200 250 300 350 0 100 200 300 400 500 Evolutionary points Evolutionary points

Figure 4.3: The number of stars, luminosities, and colors of the old, and young populations are plotted against evolutionary points along the isochrone or mini. The evolutionary points better illustrate post main sequence phases. Four phases are deﬁned as: phase a, 0.15 < mini < 0.30 M⊙; phase b, mini =0.30 M⊙ to the main sequence turn-oﬀ (MSTO); phase c, from MSTO to the beginning of the AGB phase, or early AGB (EAGB); phase d, the AGB phase.

73 age=10 Gyr, log[Fe/H]=0.37 age=2 Gyr, log[Fe/H]=0.37 3.55 3.25 A d E 1 - IMF slope 3.20 d 3.50 2 - LMCO 3.15 3 - AGB a a 3.10 1 3.45 1 c 3.05 V-K V-K 3.40 3.00 2 c 2 3 2.95 3.35 3 2.90 b 3.30 b 2.85 1.09 1.10 1.11 1.12 1.13 1.14 1.15 1.16 1.17 0.84 0.86 0.88 0.90 0.92 0.94 B-V B-V B a 0.030 F d a 0.035 0.025 d 0.030 0.020 bTiO bTiO

0.025 0.015 1 b c b 2c 1 3 0.010 3 0.020 2 3.75 3.76 3.77 3.78 3.79 3.80 3.813.82 3.83 3.84 2.75 2.80 2.85 2.90 2.95 3.00 3.05 0.13 [MgFe] [MgFe] C a G a 0.11 0.12 d d 0.11 0.10

TiO2 0.10 TiO2 0.09 c 1 0.09 1 0.08 b3 c 2 2 b 0.08 0.07 3 3.74 3.76 3.78 3.80 3.82 3.84 2.75 2.80 2.85 2.90 2.95 3.00 3.05 0.80 [MgFe] [MgFe] D a 0.65 H a 0.75 0.60

0.70 d 0.55 d 0.65 c

Wing-Ford 1 Wing-Ford 3 0.50 1 0.60 b c 2 2 0.45 3 0.55 b 3.76 3.77 3.78 3.79 3.80 3.81 3.82 3.83 3.84 2.75 2.80 2.85 2.90 2.95 3.00 3.05 [MgFe] [MgFe]

Figure 4.4: To illustrate the connections of eﬀects and evolutionary phases, we connect the standard models with the contributions of each phase. The phase vectors (a,b,c,d) are shrunk to one tenth of the original magnitude to accommodate the three eﬀect vectors. The vector of each phase is labelled by the corresponding phase name.

74 Table 4.1: Colors and Indices of Each Phase for the Old Population

OLD POPULATION PHASE a PHASE b PHASE c PHASE d (B-V) 1.46939 0.69314 0.93189 1.48725 (V-K) 4.04228 1.75775 2.87041 4.84277 [MgFe] 3.77325 2.34650 2.83331 4.98660 bTiO 0.17246 -0.00274 0.00573 0.18546 TiO2 0.44303 0.01672 0.07097 0.33609 Wing-Ford 2.07944 0.06787 0.35408 1.16696

4.3A, we plot the logarithmic number of stars per initial mass (log(dN/dm)) versus initial mass (mini). All stars with mini & 1.0 M⊙ have evolved to the stellar remnant phase, thus they do not contribute to the optical-NIR integrated light any more. The shallower IMF model has smaller dN/dm than the standard model in the range of 0.15 to 1.0 M⊙, while ∼ the model with 0.3 M⊙ LMCO has more stars in the range of 0.3 to 1.0 M⊙, due to ∼ a normalization correction (all stellar population are normalized to the same initial mass, so, for example, raising the LMCO means that more mass and more light is distributed to the stars that remain). The 80% AGB model is not discernible here, because the AGB stars have very small initial mass range ( 1.0 M⊙). To inspect the strong variance of the ∼

post main sequence phase, we use the evolutionary points as x variables instead of mini. The evolutionary points are deﬁned as points with the same interval arc length along the

isochrones in the HR diagram. Figure 4.3B clearly shows different number of stars for the standard model and the 80% AGB strength model. In Figure 4.3C, we find that the post main sequence stars, though small in number, have major contribution in the V band integrated light. Then we plot the (B V ), and (V K) colors in Figure 4.3D and 4.3E. Obviously, − − the very low mass stars and the giants have comparable (B V ) colors, but the giants, on − average, show redder (V K) colors. − To better quantify the contribution of different phases, we first define four phases: phase

75 a, 0.15 < mini < 0.30 M⊙; phase b, mini =0.30 M⊙ to the main sequence turn-oﬀ (MSTO); phase c, from MSTO to the beginning of the AGB phase, or early AGB (EAGB); phase d, the AGB phase. Next, we run the models with only one phase on by nullifying the contribution of all other phases. For example, to study the integrated light from phase a stars, we set

the number of stars in phase b, c, and d to zero. The colors and indices of each phase are tabulated in Table 4.1. A vector that connects the standard model and one of these points indicates the drift direction if more stars in the corresponding phase are added. In Figure 4.4, these vectors are shrunk to one tenth of the original magnitude to accommodate the three drift vectors. In the (V K) vs. (B V ) plot, the phase a vector is in the opposite − − direction of the LMCO drift, and similarly the phase d vector has an angle of almost 180 degrees with the AGB drift. These indicate the LMCO drift in this color-color plot is mainly caused by decreasing the contribution of phase a stars, and the AGB drift is mainly caused by decreasing the contribution of phase d stars. These two conclusions might be obvious,

but no vector seems directly related to the IMF slope drift. The IMF slope eﬀect changes the number of stars of all masses, which means the high-to-low-mass ratio of each phase is not a constant. Therefore, we need to take the ﬂux contribution of each phase into consideration. In Figure 4.5E, we plot the integrated optical spectra of four phases. The spectra of phase

b and c are both luminous, although phase c stars become brighter than phase b stars as wavelength exceeds log(λ) 3.65 ( 4467 A).˚ In Figure 4.5A, 4.5B, 4.5C, and 4.5D, we ≈ ≈ search for the spectral variation signals. The spectra of each phase are first normalized at log(λ)=3.815. Then the spectrum of the shallower IMF model is divided by the standard model. The spectral ratios show shallower IMF model tends to blue the spectrum of phase b stars, but redden the spectrum of phase c stars. Therefore, the bluing and reddening effects compete again each other to determine the integrated color drifts, depending on the flux ratios of phase b stars to phase c stars at different wavelengths. Let us take the (B V ) vs. − (V K) plot as an example. The b/c flux ratio is close to unity at the B and V bands, but −

76 much smaller than 1 at the K band. Thus the (B V ) color is governed almost equally by − both the phase b stars and phase c stars, while the (V K) color is mainly controlled by the − phase c stars that redden the spectrum. The (B V ) color drifts blue due to the stronger − spectral variation of phase b stars (Figure 4.5B) compared to phase c stars (Figure 4.5C).

In the index-index plots of Figure 4.4B, 4.4C, and 4.4D, similar conclusions as Figure 4.4A can be drawn for the LMCO and AGB drifts, based on the a and d vector directions. However, the index variations for the IMF slope effect cannot be easily determined from Figure 4.5. To better quantify the response of different phases, we show the index-index plots of all four phases in Figure 4.6. We notice the drift magnitudes of the phase b stars are much greater than the phase c stars. Since the smallest b/c flux ratio is about 0.5 (Wing- Ford band, Figure 4.5E), phase b stars dominate the index variation, pushing all the indices to lower values. Next, we switch to the young population. A major difference compared to the old population is that stars with mass between 1.0 to 1.66 M⊙ still exist (Figure 4.3F). Two ∼ curves of different slopes intersect at 1.64 M⊙, thus the shallower IMF model has more ∼ AGB stars than the standard model! Furthermore, Figure 4.3H shows a longer post main sequence phase than the old population. In Figure 4.3I and 4.3J, we clearly see the MSTO hook features near the curve minimum. The hook feature happens when the star transitions from core burning to shell burning, with a brief gravitational-energy-dominated moment. The (V-K) color of the RGB tip is smaller than the old population, due to higher stellar mass and thus higher surface temperature of the RGB tip stars at young age. In Figure 4.4E, 4.4F, 4.4G, and 4.4H, the directions of vector a and d again testify to the previous statement that the LMCO drift is mainly caused by phase a stars, while the AGB drift is mainly caused by phase d stars. To constrain the major contributor of the IMF slope effect, we plot the spectra and spectral ratios of all four phases in the right column of Figure 4.5. The spectrum of phase a is dwarfed by the flux increase of other three phases. Phase c is

77 age=10 Gyr, log[Fe/H]=0.37 age=2 Gyr, log[Fe/H]=0.37

1.04 IMF slope=1.7 A 1.04 F 1.02 1.02

ratio(a) 1.00 1.00 λ 0.98 0.98

NormH 0.96 0.96 3.5 3.6 3.7 3.8 3.9 4.0 3.5 3.6 3.7 3.8 3.9 4.0 1.10 1.10 B G 1.08 1.08 1.06 1.06 1.04 1.04 ratio(b)

λ 1.02 1.02 1.00 1.00 0.98 0.98 NormH 0.96 0.96 3.5 3.6 3.7 3.8 3.9 4.0 3.5 3.6 3.7 3.8 3.9 4.0 1.010 1.02 C H 1.005 1.01 1.000 1.00 0.99 0.995

ratio(c) 0.98 λ 0.990 0.97 0.985 0.96

NormH 0.980 0.95 0.975 0.94 3.5 3.6 3.7 3.8 3.9 4.0 3.5 3.6 3.7 3.8 3.9 4.0 +9.98e−1 1.0006 0.0035 D I 1.0004 1.0002 0.0030 1.0000 0.0025

ratio(d) 0.9998 λ 0.9996 0.0020 0.9994 0.0015

NormH 0.9992 0.9990 0.0010 3.5 3.6 3.7 3.8 3.9 4.0 3.5 3.6 3.7 3.8 3.9 4.0 120 500 phase a E J 100 phase b 400 80 phase c phase d 300

λ 60 H 200 40 20 100 0 0 3.5 3.6 3.7 3.8 3.9 4.0 3.5 3.6 3.7 3.8 3.9 4.0 log λ(A) log λ(A)

Figure 4.5: The upper four panels show the ﬂux ratio between the shallower IMF models and the standard models, for four diﬀerent phases. The very bottom panels plot the spectra of the standard models, subdivided into four phases.

78 the most signiﬁcant of all, starting to overcome phase b at log(λ) 3.53. As a result, phase ≈ c stars contribute most of the light in our optical, NIR colors and indices. Obviously, the spectral bluing and reddening competition of phase b and phase c stars (Figure 4.5 G and H) is won by the latter one, leading to redder (B V ) and (V K) colors for shallower IMF − − slope. Comparison of the (B V ) color drifts of the old and young populations inspires us − to search for the critical age where (B V ) color changes from drifting blue to drifting red. − We ﬁnd that the (B V ) colors of age less than 6 Gyr drift blue, but the (B V ) colors of − − age greater than 8 Gyr drift red. Therefore, at 6 Gyr

increase.

4.3 ADF-IMF coupling

To explore the ADF-IMF coupling, we built a toy model in which a hypothetical linear IMF [M/H] relation is assumed. This linear relation is set by two points: α = 2.35 at − log [M/H] = 0,and α =1.35 at log [M/H]= 1. Similar to Chapter 3, we employ CSPs with − single-burst ages but normal-width composite abundance distribution functions (ADFs). Our normal-width ADF matches well the average solar neighborhood ADFs and Milky Way bulge ADFs. To complete the models, the ADF-weighted Single Stellar Populations (SSPs) are combined to construct CSPs, in which the IMF slope of each mass bin matches the assumed

IMF [M/H] relation. To isolate the consequences of assuming a IMF [M/H] relation, we − − also construct another CSP models with the normal-width ADF, but instead of assuming

79 age=10 Gyr, log[Fe/H]=0.37

phase a phase b phase c phase d

0.176 0.022 0.110 0.022 0.174 0.020 0.108 0.020 1 0.172 0.018 0.106 1 bTiO 1 0.018 0.170 0.016 0.104 0.016 0.168 0.014 0.102 1 0.014 3.70 3.75 3.80 3.85 3.65 3.70 3.75 3.80 3.70 3.75 3.80 3.85 3.90 4.25 4.30 4.35 4.40 [MgFe] [MgFe] [MgFe] [MgFe] 0.350 0.450 0.110 0.050 0.345 0.445 0.105 0.045 0.340 0.440 0.100 0.040 1 0.335 1 0.435 0.095 TiO2 0.035 0.330 0.430 0.090 0.030 1 0.325 0.425 0.085 0.025 1 3.70 3.75 3.80 3.85 3.65 3.70 3.75 3.80 3.70 3.75 3.80 3.85 3.90 4.25 4.30 4.35 4.40 [MgFe] [MgFe] [MgFe] [MgFe] 0.80 2.15 1.25 0.30 0.75 2.10 1.20 0.25 0.70 2.05 1.15 0.20 0.65 1 1

WFB 2.00 1.10 0.15 1 0.60 1.95 1.05 0.10 1 0.55 1.90 1.00 0.05 3.70 3.75 3.80 3.85 3.65 3.70 3.75 3.80 3.70 3.75 3.80 3.85 3.90 4.25 4.30 4.35 4.40 [MgFe] [MgFe] [MgFe] [MgFe]

Figure 4.6: IMF slope drifts of each phase at old age.

80 age=2 Gyr, log[Fe/H]=0.37

phase a phase b phase c phase d 0.002 0.010 0.190 0.176 0.000 0.008 0.188 0.174 −0.002 0.186 0.006 1 1 0.172 bTiO 1 −0.004 0.004 0.184 0.170 1 −0.006 0.002 0.182 0.168 3.603.653.703.753.803.853.903.95 2.152.202.252.302.352.402.452.50 2.652.702.752.802.852.902.953.00 4.804.854.904.955.005.055.105.15 [MgFe] [MgFe] [MgFe] [MgFe] 0.030 0.085 0.350 0.455 0.025 0.080 0.345 0.450 0.020 0.075 0.340 0.445 1 1 0.070 0.335

TiO2 0.015 0.440 1 0.010 0.065 0.330 0.435 0.005 0.060 0.325 0.430 1 3.603.653.703.753.803.853.903.95 2.152.202.252.302.352.402.452.50 2.652.702.752.802.852.902.953.00 4.804.854.904.955.005.055.105.15 [MgFe] [MgFe] [MgFe] [MgFe] 0.50 0.20 1.30 2.20 0.45 0.15 1.25 2.15 0.40 0.10 1.20 2.10 0.35 1 1 1.15

WFB 0.05 2.05 1 0.30 0.00 1.10 2.00 0.25 1 −0.05 1.05 1.95 3.603.653.703.753.803.853.903.95 2.152.202.252.302.352.402.452.50 2.652.702.752.802.852.902.953.00 4.804.854.904.955.005.055.105.15 [MgFe] [MgFe] [MgFe] [MgFe]

Figure 4.7: IMF slope drifts of each phase at young age.

81 an IMF [M/H] relation, we set the IMF to be always Salpeter (α =2.35). We name these − latter models Constant-IMF CSPs (CCSPs), and call the former models Variable-IMF CSPs (VCSPs). To verify the robustness of our models, we assemble elliptical galaxy spectra from three diﬀerent sources: Graves et al. (2007), Trager et al. (2008), and Serven (2010).

Readers are referred to Chapter 3 for sample descriptions. Note that all the model and observed indices are corrected to 300 km s−1 resolution. First, we take a look at the optical-NIR color-color plots (Figure 4.8A). The CCSPs and VCSPs are similar, but show diﬀerences, especially for the metal-poor populations. Since the photometric observations are not included in the above samples, we retrieve the (B V ) − and (V K) colors from Peletier (1989) and Persson et al. (1979). −

1. Peletier (1989): In order to avoid focusing on only the cores of elliptical galaxies, we choose the colors at maximum isophotal radius. These colors are corrected for Galactic extinction before plotting.

2. Persson et al. (1979): We choose the well-tabulated (B V ) and (V K) colors of − − ﬁeld galaxies. These colors have been corrected for Galactic extinction in that paper.

The (B V ) and (V K) observables are only partially covered by the model grids. We − − suggest that the peak metallicity might be too small, which means CSPs with peak [M/H]>

0.4 may be required. Note that CSP peak [M/H] may be diﬀerent than the SSP-equivalent metallicity (Chapter 3). Figure 4.8B is the Hβ [MgFe] plot, which is an age-metallicity diagnostic diagram. Gen- − erally speaking, the observational data points from the three samples locate at the old, metal-rich region, which is consistent with what we expect. Next, we pick several IMF-sensitive indices to study the model variations. It is encouraging to ﬁnd the observed data from Graves et al. (2007) are well-covered by our models, and the variation trend looks reasonable.

82 In all the panels of Figure 4.8, we ﬁnd that the VCSPs appear more metal-rich than the CCSPs. According to our IMF [M/H] relation, the IMFs of the metal-poor populations in − the VCSPs are shallower. We show that the shallower IMF model appear dimmer than the standard IMF model in Figure 4.3. Therefore, the metal-poor populations appear dimmer in the VCSPs. Note that metal-poor populations outshine their metal-rich counterparts5, and thus the smaller integrated-light contribution from the metal-poor populations leads to more metal-rich appearing VCSPs.

4.4 Discussion

4.4.1 Swapping Models

To test the robustness of the model drifts, we also perform similar experiments with the Flexible Stellar Population Synthesis (FSPS, Conroy and Gunn 2010). We arranged to utilize the FSPS with the same age, IMF slope, and LMCO as our models. But the maximum metallicity of the Padova+MILES option is log[Fe/H]= 0.20, which is different than the metallicity we chose above (0.37). All the IMF-related effects might be age and metallicity sensitive. Since the wavelength coverage of MILES is 3600 7400 A,˚ the [Na i]and Wing- − Ford band are not available for analysis. To evaluate the AGB effect in FSPS, we choose the original Padova TP-AGB treatment as the standard model, and compare it with the

TP-AGB treatment of Conroy and Gunn (2010). Note that the latter TP-AGB treatment effectively reduces the NIR related colors at age around 1 Gyr, which well fit the colors of star clusters in the Magellanic Cloud (See their Figure 3). But both TP-AGB treatments have similar descriptions at old ages, and thus we expect small AGB drift for the old population in FSPS. This is different than the way we change the AGB strength in 4.2.2: the AGB § strength is always reduced to 80% of the full strength, regardless of the age.

5If both populations have similar number of stars

83 3.8 4.0

3.6 3.5 3.0 3.4 2.5 3.2 2.0 β H VK 3.0 1.5 1.0 2.8 0.5 2.6 0.0 2.4 −0.5 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.0 1.5 2.0 2.5 3.0 3.5 4.0 BV [MgFe] 0.13 0.04 0.12 0.03 0.11 0.10 0.02 0.09 0.01 bTiO TiO2 0.08 0.07 0.00 0.06 −0.01 0.05 0.04 −0.02 1.0 1.5 2.0 2.5 3.0 3.5 4.0 1.0 1.5 2.0 2.5 3.0 3.5 4.0 [MgFe] [MgFe] 1.4 0.6 1.3 1.2 0.5 1.1 1.0 0.4

NaI 0.9

0.8 WingFord 0.3 0.7 0.6 0.2 0.5 1.0 1.5 2.0 2.5 3.0 3.5 1.0 1.5 2.0 2.5 3.0 3.5 [MgFe] [MgFe]

Figure 4.8: The VCSPs (red solid lines) and CCSPs (blue solid lines) are described in 4.3. In the top left panel, measurements from Persson et al. (1979) (orange triangles), and Peletier (1989) (green triangles) are shown. The medians of diﬀerent velocity dispersions (<150, 150 200, 200 250, >250 km s−1) are indicated as magenta stars. In the optical index plots, Serven− (blue− triangles), Graves (open diamonds), and Trager (green squares) observations are shown.

84 We show the color-color plots and optical index plots in Figure 4.9 and 4.10. To compare with the results from our models, all the dynamic ranges are set to be the same as Figure 4.1 and 4.2. It is encouraging to find a lot of similarities in the directions and magnitudes of the drifts between two sets of models, but discrepancies still exist. For the old population, all the AGB drifts are very small, as expected. The IMF slope drifts seem smaller in the (V K) colors, but show much bigger magnitudes in the negative [MgFe] direction. Note − that the LMCO drift is no longer greater than the IMF slope drift for the TiO2 index: the IMF slope effect is the leading effect, now. Turning to the young population model, the color drifts of LMCO and IMF slope seem robust between two sets of models, but the AGB drifts

are greater in the FSPS models, due to the strong reduction of TP-AGB stars around 1 Gyr. Surprisingly, the index drifts are much smaller than our models. This is possibly because of the diﬀerent index derivation routines of these two model sets: The index derivation is taken as an individual process in our models, with polynomial ﬁtting, decomposition, and

reformation (see model description for details).

4.4.2 Feasibility of Breaking the Degeneracy

Exploring whether the apparent steep IMF in massive elliptical galaxies might be partially due instead to the decreasing number of AGB stars requires one to be able to ﬁnd an observational signature distinguish the two eﬀects. We add to that list the LMCO, of course,

but also note that various age and metallicity effects need to also be addressed, historically derived from the Hβ 6 or Hγ plot (Trager et al., 2000b,a; Tang et al., 2009). − F − For a young elliptical galaxy, the color-color plots of Figure 4.2 show substantial drifts ( 0.03 mag) for the IMF slope and AGB effects. Note that the AGB and IMF slope effects ∼ vector oppositely in most of the Figure 4.2 plots . Since our results should be interpreted in a partial derivative sense, the opposite vectors in fact do nothing to disentangle the IMF

6=(Fe5270 + Fe5335)/2 (Gonz´alez, 1993).

85 age=10 Gyr, log[Fe/H]=0.20

3.24 1 - IMF slope 2 - LMCO 0.072 1 3.22 3 - AGB 0.070 3 3 3.20 V-K bTiO 0.068 2 3.18 0.066 2 3.16 0.064 1 0.960 0.965 0.970 0.975 0.980 0.985 0.990 0.995 1.000 5.12 5.14 5.16 5.18 5.20 B-V [MgFe] 0.98 0.082

0.96 0.080 1 0.94 2 0.078 2 3 J-K

3 TiO2 0.92 0.076

0.90 0.074 1

0.88 0.960 0.965 0.970 0.975 0.980 0.985 0.990 0.995 1.000 5.12 5.14 5.16 5.18 5.20 B-V [MgFe] 2.64 0.046 2.62 0.044 2.60 1 3 0.042 R-K 2.58 CaH1 1 2 3 0.040 2.56 2 0.038 2.54 1.590 1.595 1.600 1.605 1.610 1.615 1.620 1.625 1.630 5.12 5.14 5.16 5.18 5.20 B-R [MgFe]

Figure 4.9: Color-color and index-index plots at old age using FSPS models.

86 age=2 Gyr, log[Fe/H]=0.20

1 3.20 0.052

3.15 0.050 2 3 3.10 0.048 V-K bTiO 2 1 3.05 0.046

3.00 0.044 3 0.750 0.755 0.760 0.765 0.770 0.775 0.780 0.785 0.790 3.76 3.78 3.80 3.82 3.84 B-V [MgFe] 1.04 1 1.02 0.060 2 1.00 1 0.058 0.98

J-K 2 3 TiO2 0.056 0.96 3 0.94 0.054 0.92 0.90 0.052 0.750 0.755 0.760 0.765 0.770 0.775 0.780 0.785 0.790 3.76 3.78 3.80 3.82 3.84 B-V [MgFe] 2.70 1 0.040 2.65 2 0.038 2.60 3

R-K 0.036 1 CaH1 2 2.55 0.034 2.50 3 0.032 1.270 1.275 1.280 1.285 1.290 1.295 1.300 1.305 1.310 3.76 3.78 3.80 3.82 3.84 B-R [MgFe]

Figure 4.10: Color-color and index-index plots at young age using FSPS models.

87 slope and AGB effects. That is to say, the degeneracy is still firm and hard to break in this case. But for an old, metal-rich galaxy, the color-color plots of Figure 4.1 show the LMCO, IMF slope, and AGB effects are distinguishable if the photometric accuracy is better than 0.02 mag. The index-index plots reveal robust IMF slope drift in the [MgFe] direction, reaching an amplitude of 0.02 A.˚ This separates the IMF slope effect from the LMCO effect, for the latter one causes much smaller drifts in the [MgFe] direction. Note that the [MgFe] index is insensitive to [α/Fe], giving the [MgFe]-related plots advantage to different alpha-enhanced environment.

We ﬁnd therefore that it is practical to lift the degeneracies using optical-red spectra and optical-NIR photometry if the measurements are accurate enough. We estimate these accuracies should be achieved: 1. dust attenuation σAV <0.01 mag; 2. photometric accuracy σ <0.01 mag; 3. index accuracy σ <0.02 A.˚ As stellar photometric accuracy reaches milli-

mag these days (Clem et al., 2007), an accuracy of 0.01 mag is feasible for nearby galaxies if one is precise about the observational complications. To list a few of them: dust attenuation, both Galactic and in-situ; sky subtraction for extended sources; aperture matching for spectroscopic and photometric extractions.

We also notice that the [Na i]index seems to be insensitive to the AGB eﬀect for both the old and the young populations in spite of [Na i]’s red central wavelength. A look at the index ﬁtting functions at the stellar level reveals this insensitivity may relate to the similar [Na i]indices of giants and dwarfs. The [Na i]index might be a way out of the “ADF-AGB- IMF masquerading”.

4.4.3 A Combination of Multiple Eﬀects

Age and metallicity eﬀects are generally strong, but also degenerate in most of the colors and indices (Worthey, 1994). To obtain a bigger picture besides the three eﬀects that we

88 age=10 Gyr, log[Fe/H]=0.37 age=2 Gyr, log[Fe/H]=0.37 3.50 A 7 3.5 1 - IMF slope E 6 2 - LMCO 3.45 1 4 3.4 3 - AGB 4 - Age 3.40 3.3 5 - [Fe/H] 4 2 6 - Na ADF 3 7 - VCSP 3.35 3.2 7 V-K V-K 3.1 1 3.30 6 5 3.0 5 2 3.25 2.9 3 3.20 2.8 1.06 1.08 1.10 1.12 1.14 1.16 1.18 1.20 0.80 0.85 0.90 0.95 1.00 1.05 0.027 B-V 0.018 B-V B F 0.026 4 0.016 5 0.025 7 4 6 0.014 7 1 0.024 6

bTiO 0.023 bTiO 0.012 2 0.022 3 5 3 0.010 0.021 2 1 0.020 0.008 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4.0 4.1 2.4 2.6 2.8 3.0 3.2 3.4 0.105 [MgFe] 0.090 [MgFe] C G 0.100 6 0.085 4 7 0.095 4 1 6 0.080 5 7 TiO2 0.090 TiO2 13 0.075 2 0.085 2 3 5 0.080 0.070 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4.0 4.1 2.4 2.6 2.8 3.0 3.2 3.4 0.75 [MgFe] 0.60 [MgFe] D 0.58 H 4 0.70 6 0.56 7 4 0.54 0.65 0.52 6 3 1 0.50 1 0.60 7

Wing-Ford Wing-Ford 0.48 2 0.46 2 0.55 5 3 0.44 5 0.50 0.42 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4.0 4.1 2.4 2.6 2.8 3.0 3.2 3.4 [MgFe] [MgFe]

Figure 4.11: To visualize eﬀects that may impact the SSP parameter determination, IMF slope, LMCO, AGB, age, metallicity, ADF, and VCSP eﬀects are labelled as vector 1 to 7, respectively.

89 discuss in this chapter, we summarize the effects concerning IMF slope, LMCO, AGB, age, metallicity, ADF, and VCSP in Figure 4.11. They are labelled as arrow 1 to 7, respectively. The parametrization of the first three effects is described in 4.2.1. The age effect is estimated § by calculating SP models of age=12 Gyr, log[Fe/H]=0.37, and age=4 Gyr, log[Fe/H]=0.37

(∆ age=+2 Gyr), while the metallicity effect is estimated by calculating SP models of age=10 Gyr, log[Fe/H]=0.185, and age=2 Gyr, log[Fe/H]=0.185 (∆ log[Fe/H]=0.185). To investigate the effects concerning CSPs, we move the models of normal-width ADF, peak [M/H]= 0.4, and constant IMF slope to the center. The ADF effect is shown as a displacement from the normal-width ADF CSPs to the narrow-width ADF CSPs, and the ADF-IMF coupling is represented by a vector from the CCSPs to the VCSPs. Age and metallicity effects are parallel and degenerate as expected. They are joined by two new effects concerning the CSPs: the ADF and VCSP effects. In fact, the ADF effect is the same as the “red lean” effect (Chapter 3) where a narrower ADF appears more metal-rich

than a wider one. The reasons for the VCSP effect are explained in 4.3. Careful readers § may find that the ADF and VCSP effects both originate from the suppression of metal-poor populations, which leads to a metal-richer appearing integrated-light model. The similar origins and vector directions drive us to put the age, metallicity, ADF and VCSP effects

in one group, and label them as group I effects. On the flip side, we find that the IMF slope, LMCO, and AGB effects (group II effects) are almost orthogonally to the group I effects. Though group I effects are more prominent in magnitude, the orthogonality suggests observations of group II effects are still feasible.

4.4.4 Recovering [X/Fe], IMF slope, LMCO, and AGB Percentage

Worthey et al. (2014b) showed our eﬀorts to recover elemental abundances from observed spectra. In this work, we upgrade our inversion program by replacing the SSP models with normal-width ADF CSP models and adding the IMF slope, LMCO, and AGB percentage

90 (AGB%) parameter determination. To examine the uncertainties of our inversion program, 500 mock galaxy spectra are constructed by Monte Carlo simulation. First, a model is produced with known age, abundance, IMF slope, LMCO, and AGB fraction. In this model the indices and colors are altered by random numbers which have a normal distribution. The standard deviation of the normal distribution function is set to 0.7σstd, where σstd is a vector composed for reasonable guesses for the observational uncertainty in each color or index. We supply the inversion program with each of these mock galaxy spectra in turn, and compare the recovered values with input values. Figure 4.12 showed the recovered and input values at age = 12 Gyr, peak [M/H] =

0.1. − In Figure 4.12A, the age and peak [M/H] are quantized in the current inversion algorithm. These two basic parameters are determined by closest-match rather than a smooth interpola- tion within the model grid. Age-metallicity degeneracy is the reason for the anti-correlation found in the ﬁrst panel. In Figure 4.12B, we see tight correlation between [C/R] and [N/R], since these two elements are determined by common indices, the CN bands around 4100 A.˚ In Figure 4.12F, 4.12G, and 4.12H, the correlations among IMF slope, LMCO, and AGB% are generally loose. This implies the degeneracies among these three parameters are, for the most part, broken by our selection of indices. Though modest scatter exists in the recovered values, all of the mean recovered values agree with the input values inside the error range without alarming systematics. Some of the mean recovered values are especially close to the input values, e.g., IMF slope, [O/R] and [Na/R]. This success encourages us to apply our inversion program to observed galaxy spectra and colors in the future.

91 18 0.15 A B 16 0.10 14 0.05 12 age [C/R] 0.00 10

8 −0.05

6 −0.10 −0.3 −0.2 −0.1 0.0 0.1 −0.10−0.050.00 0.05 0.10 0.15 0.20 0.25 0.30 peak [M/H] [N/R] 0.25 0.20 0.20 C D 0.15 0.15 0.10 0.10 0.05 0.05 0.00 [O/R] −0.05 [Mg/R] 0.00 −0.10 −0.05 −0.15 −0.20 −0.10 −0.15−0.10−0.05 0.00 0.05 0.10 0.15 0.20 −0.10 −0.05 0.00 0.05 0.10 0.15 [Na/R] [Fe/R] 0.15 4.0 E F 0.10 3.5 3.0 0.05 2.5

[Fe/R] 0.00 2.0 IMF slope IMF

−0.05 1.5

−0.10 1.0 1.0 1.5 2.0 2.5 3.0 3.5 4.0 −0.050.000.050.100.150.200.250.300.350.40 IMF slope LMCO 4.0 0.40 G 0.35 H 3.5 0.30 3.0 0.25 0.20 2.5 0.15 2.0 LMCO 0.10 IMF slope IMF 0.05 1.5 0.00 1.0 −0.05 60 70 80 90 100 110 120 130 140 150 60 70 80 90 100 110 120 130 140 150 AGB% AGB%

Figure 4.12: The recovered values (scattered dots) are compared with the input values (solid lines). The mean recovered values and their corresponding standard deviations are labelled with error bars.

92 4.5 Summary

We begin a modeling study of various new parametric eﬀects on integrated light by exploring

the Abundance Distribution Function (ADF) effect (Chapter 3) and then continuing on (in this chapter) to explore two underexplored effects that might mimic the IMF slope variation: the LMCO and the AGB effects. If we posit that the steep IMF in massive elliptical galaxies might be partially due to the decreasing number of AGB stars, the question arises, can we

ever know it among the forest of other stellar population degeneracies. We conclude that we do find degeneracy of steepening IMF and decreasing AGB strength for young, metal- rich populations. However, the IMF slope, LMCO, and AGB degeneracies can be lifted for old (age 10 Gyr), metal-rich populations using optical-near infrared photometry and ≈ spectroscopy, though at an observationally challenging level ( 0.02 mag). ≈ We broke our models into different evolutionary phases to better dissect the leading factors for the IMF-related effects. We also investigated an ADF-IMF coupling in which metal rich populations favor low mass star formation. Models with ADF-IMF coupling appear more metal-rich than the noncoupled models. Though the magnitudes of the IMF slope, LMCO, and AGB effects are smaller than the age and metallicity effects, these two groups of effects vector almost orthogonally. Fine study of the IMF-related effects in integrated-light observations is feasible if all the observational pitfalls are addressed adequately.

93 CHAPTER 5

INITIAL MASS FUNCTION OF RED GALAXIES

AROUND z =0.4: A SPECTROSCOPIC APPROACH

5.1 Introduction

Booming developments of astrophysics have shown the immense importance and ubiquity of the initial mass function (IMF) in many active research ﬁelds, such as early Universe studies, galaxy evolution, star cluster formation, and star formation. The IMF regulates the mass distribution of stellar populations, leading to impacts on the luminosity function, mass to light (M/L) ratio, and chemical abundance, and therefore the formation of all the planets upon which the only known intelligent species lives! However, direct IMF derivations are limited by: observational capabilities, uncertainties concerning the mass-luminosity relation, stellar evolution, dynamical evolution, binary fraction, and many other factors. To make the IMF even harder to study, additional complications may come from IMF variations in diﬀerent galactic environments (Larson, 1998, 2005; Marks et al., 2012). More than half a century ago, Salpeter (1955) described the IMF with a power-law distribution, ξ(m) m−α, and adopted an IMF slope (α) of 2.35 for solar neighborhood ∝ stars. However, the observations of faint stars uncovered substantial deviation from the standard IMF at sub-solar mass. Studies of the Milky Way stars revealed a peaked IMF, peaking at a few tenths of the solar mass (Miller and Scalo, 1979; Scalo, 1986; Kroupa, 2001;

94 Chabrier, 2003). There are mainly two ways to describe the mathematical form of an IMF: a power law or log-normal function. For example, Kroupa (2001) developed a series of power laws to ﬁt the mass distribution, while Chabrier (2003) adopted a log-normal distribution for

1 m< 1M⊙ as representative of the log-normal probability density function of the turbulent gas. But since their parameters are calibrated by observational data, they show similar distribution between 0.2 and 0.8M⊙ (Bastian et al., 2010; Greggio and Renzini, 2012; Oﬀner et al., 2014). Contrary to the Milky Way IMF studies that are based on counting individual stars, recent studies continue to debate the universality of extragalactic IMF using integrated light and dynamical models. Gravity-sensitive integrated spectral features, like the giant-sensitive [Ca ii]triplet, and dwarf-sensitive [Na i]and FeH Wing-Ford band features may indicate that systematic IMF variation exists as a function of stellar velocity dispersion (Cenarro et al., 2003; van Dokkum and Conroy, 2010; Conroy and van Dokkum, 2012b). This trend was ﬁt by Ferreras et al. (2013) and Spiniello et al. (2014a), but the slope of the former study is a factor of two greater than the latter one. The discrepancy implies that minimizing the uncertainties arising from the ingredients of stellar population (SP) models is still crucial to the future IMF study (Spiniello et al., 2014b). Another popular approach for studying unresolved stellar systems is using dynamical models with a dark matter halo involved. The IMF is estimated by comparing the M/L of the dynamical models and the stellar population models(Auger et al., 2010; Cappellari et al., 2012; Dutton et al., 2012; Posacki et al., 2015). For example, Cappellari et al. (2012) concluded an universal IMF is inconsistent with early- type galaxies (ETGs), although this kinematic result is unable to distinguish between more stellar remnants and relatively more low mass stars (“bottom-heavy” IMF). The nucleosynthesis of a time-independent, bottom-heavy IMF suggests a small number of stellar remnants and low metallicity. However, super-solar metallicities are found in

1 A power law function for m & 1M⊙

95 elliptical galaxies (Trager et al., 2000a,b; Tang et al., 2009). What is more, the number of stellar remnants is not small in massive elliptical galaxies. For example, Kim et al. (2009) suggested the number of low-mass X-ray binaries in three nearby elliptical galaxies with

11 mass about 10 M⊙ is similar to that of the Milky Way. Peacock et al. (2014) found

a constant number2 of black holes and neutron stars among eight diﬀerent mass ETGs. To reconcile these facts with a bottom-heavy IMF, Weidner et al. (2013a,b) simulated a galaxy evolution model with time-dependent IMF, in which the IMF slope steepens as the star formation rate decreases gradually (Also see Gargiulo et al. 2015 for a similar semi- analytical model). From the perspective of the interstellar medium (ISM) physics, the high

cosmic background temperature, low metallicity, and intensive radiation from young stars and core-collapse supernova during the star formation at early times inevitably increase the proto-stellar cloud temperature, which favors a higher Jeans mass ( T 3/2 at fixed density, ∝ Larson 1998). As a result, the high star formation rate of the early universe implies the existence of a top-heavy IMF (Larson, 1998, 2005). However, if the galactic distance increases at the rate of D, then the flux of an object decreases at the rate of D2. This fact significantly lowers the quality of images and spectra of distant galaxies, and becomes the major obstacle in studying the cosmic evolution of

IMF. A direct way of improving the signal to noise (S/N) ratio is to build telescopes with large aperture. While the next generation of telescopes (e.g., JWST, LSST, TMT, MMT ) are under construction, logical thinking has discovered a few indirect paths to constrain the IMF at cosmic distance. Luminosity evolution betrays the IMF slope in the sense that a top-heavy galaxy fade more rapidly than a galaxy with the standard IMF, since the present luminosity of ETGs mainly comes from the old stellar populations ( 1 M⊙). According ∼ to Tinsley and Gunn (1976), the luminosity of an old stellar population is proportional to t−1.6+0.3α. Therefore, shallower IMF, or top-heavy IMF, means more dramatic luminosity

2Scaled by the amount of K-band stellar light covered

96 change over a ﬁxed amount of time. In that spirit, van Dokkum (2008) compared the luminosity evolution (∆ log (M/L )) to color evolution (∆(U V )) for massive galaxies in B − clusters at 0.02

these galaxies are supposed to be top-heavy. However, as illustrated in Greggio and Renzini

(2012), luminosity evolution at 0

1.4 M⊙. The default assumption that constant IMF slope over all masses is not guaranteed. In other words, luminosity evolution is able to reveal the evolution of the ratio of high-mass stars to low-mass stars, but cannot distinguish top-heavy IMF from bottom-light IMF3.

Amongst diﬀerent studies of IMF cosmic evolution (Dav´e, 2008; van Dokkum, 2008), the gravity-sensitive integrated spectral features are seldom mentioned, due to several obstacles. Most of the spectroscopic work takes advantage of the fact that M type giants and dwarfs emit most of their light and show important feature lines ([Ca ii], [Na i], FeH Wing-Ford band) at red wavelengths (van Dokkum and Conroy, 2010; Conroy and van Dokkum, 2012b; Smith et al., 2012). However, the inevitable redshift of spectral lines over cosmic distance and the relatively low quality of spectra obtainable beyond 1 m has made this method infeasible for distant objects. It motivates us to look for IMF-sensitive indices in a more accessible band like the optical. NaD, TiO1, and TiO2 indices from the Lick/IDS system (Worthey et al., 1994; Trager et al., 1998) are known to be IMF-sensitive, though possible interstellar absorption contamination may complicate the interpretation of the NaD index. Recently, several optical IMF-sensitive indices published by Spiniello et al. (2014a) and La Barbera et al. (2013) have given us more options in index selection (Table 5.1). Unfortunately, these indices are also sensitive to other elements, such as Na, Ti, and Ca. What is worse, the accurate element abundance calculation is impeded by the uncertainties in SP models and spectral observations (Johansson et al., 2012; Conroy et al., 2014; Worthey et al., 2014b).

3With additional constraints, like absolute M/L ratio, this degeneracy may be broken (van Dokkum, 2008).

97 Table 5.1: Optical IMF-sensitive Indices Index Units Blue Pseudo-continuum Central feature Red Pseudo-continuum Source bTiO mag 4742.750-4756.500 4758.500-4800.000 4827.875-4847.875 Spiniello13 aTiO mag 5420.000-5442.000 5445.000-5600.000 5630.000-5655.000 Spiniello13 NaD A˚ 5860.625-5875.625 5876.875-5909.375 5922.125-5948.125 Worthey94 TiO1 mag 5816.625-5849.125 5936.625-5994.125 6038.625-6103.625 Worthey94 TiO2 mag 6066.625-6141.625 6189.625-6272.125 6372.625-6415.125 Worthey94 TiO2SDSS mag 6066.625-6141.625 6189.625-6272.125 6442.000-6455.000 La Barbera13 CaH1 mag 6342.125-6356.500 6357.500-6401.750 6408.500-6429.750 Spiniello13

The element sensitivity problem is eased if multiple IMF-sensitive indices with diﬀerent element sensitivity are used.

Observationally, the ﬁne DEEP2 spectra (6500 9100 A),˚ which targeted diﬀerent redshift − objects, are suitable for cosmic evolution study. The combination of spectral observations plus new spectral indicators may yield new ideas about the IMF cosmic evolution at low to intermediate redshift.

This chapter is organized as follows: The procedure of stacking DEEP2 spectra is illustrated in 5.2. After that, we compare the measured indices from these composite spectra § with the local measurements and two sets of models in 5.3. The implications on IMF § evolution are discussed in 5.4, and then a brief summary of the results are given in 5.5. § §

5.2 Spectral Reduction

5.2.1 Sample Selection

By inspecting the wavelengths of the optical IMF-sensitive indices, we ﬁnd they are deﬁned around 4500 6500 A.˚ To retrieve the redshifted spectra, we mine the DEEP2 Galaxy Red- − shift Survey. This survey utilizes the DEIMOS multi-object spectrograph (Faber et al., 2003)

on the Keck II telescope. Most of the spectra cover 6500 9100 A,˚ with spectral resolution − R 6000 (Newman et al., 2013). In order to match two spectral wavelength ranges and take ∼ advantage of more indices, we choose galaxies around z = 0.4. Table 5.1 lists the optical IMF-sensitive indices used in this work.

98 First, we pick galaxies4 with redshift between 0.3 and 0.5 from the Data Release 4 (DR4) redshift catalog, and make sure these galaxies have photometric measurements by matching them with the DR4 photometric catalogs. The photometric data were taken with the CFH12K camera on board 3.6-meter Canada-France-Hawaii Telescope (Coil et al., 2004).

The redshift range 0.3

histories of the late type galaxies (LTGs), we pick ETGs using the galaxy color-magnitude diagram (CMD). We plot the (B-R) vs. R CMD in Figure 5.1. 302 galaxies have (B-R) color redder than 1.8 mag and R band magnitude brighter than 22 mag, and they make up the pool of our red galaxy sample. Redshifts of these galaxies are reasonably well determined:

260 galaxies have quality code 4 (99.5% reliability rate), and 42 galaxies have quality code 3 (95% reliability rate, Newman et al. 2013). According to Weiner et al. (2005), at z 1 LTGs comprise about 25% of the red popula- ≤ tion. Since we lack morphology information, we lose the chance of unambiguously excluding

the LTGs with images. However, we may use [O iii] and Hα emission lines to eliminate LTGs with strong emission lines (Weiner et al., 2005; Schiavon et al., 2006). Based on the wavelength coverage of the deredshifted spectra, [O iii] EWs5 can be measured in 282 galaxies. Among those, 7 galaxies have [O iii] EW< 5 A˚6. As a result, 275 galaxies are left in − the [O iii] selected sample (Sample I). At the same time, 5 out of 77 galaxies with Hα EW measurements have Hα EW< 5 A,˚ and thus an Hα selected sample (Sample II) consists − of 72 galaxies.

4Confirmed by examining the “CLASS” parameter in the catalog. 5Defined in González (1993) 6Weiner et al. (2005) showed the median error in rest-frame EW is 6.2 A.˚ Schiavon et al. (2006) suggested 5 A˚ for the EW limit, though they use [O ii] due to different rest-frame wavelength range. −

99 Color Magnitude Diagram

2.5

2.0 R

m 1.5 − B m

1.0

0.5

20 21 22 23 24 mR

Figure 5.1: Galaxy color magnitude diagram. The number densities are indicated by colors and contours. Spots with bluer color have larger number density. From the top left to the bottom right, there are the red sequence, green valley, and blue cloud. Therefore, the red galaxies are selected by mR < 22 mag (vertical red line), and mB mR > 1.8 mag (horizontal red line). −

With a large galaxy sample at z 0.9 and a selection criteria of [O ii] EW> 5 A,˚ Schiavon ∼ − et al. (2006) estimated the LTG proportion of their sample is at most 5%. Though there is similarity between our selection method and theirs, our sample size is smaller and less complete, thus we estimate the LTG portion of our sample is 5 25%, between the predictions − of Schiavon et al. (2006) and Weiner et al. (2005).

100 5.2.2 Composite Spectra and Index Measurements

We retrieved the one dimensional spectra from the DEEP2 Data Release 4 website7. Ac- cording to the description of the spec2d reduction pipeline, all the two dimensional spectra obtained from DEIMOS are flat-corrected and wavelength-calibrated. The pipeline also takes care of the sky subtraction and cosmic ray rejection. One dimensional spectra are extracted from each of the slitlets using two methods: the boxcar extraction and the optimal extraction (Horne, 1986). We pick the latter one for its higher S/N ratio. The Horne optimal extraction assumes a constant Gaussian profile at all wavelengths, which implies the spectral extraction region is the whole visible galaxy. Note that flux calibration is not attempted along the process, and the flux unit is DEIMOS counts per hour (e−/hour). To stack the spectra, we used the pipeline programs developed by the DEEP2 team. We modified the “coadd” program to meet our need of flux correction. For spectral index measurement, linear corrections, like extinction correction and flux calibration, do not affect the estimation of central pseudo-continuum. But the response curve correction is not linear, thus we implemented this correction. We divided each spectrum by the throughtput of DEIMOS in spectroscopic mode for the gold 1200-line/mm grating8. Next, each individual spectrum is shifted to the rest-frame and normalized by dividing the median spectrum. The composite spectra of Samples I & II are achieved by coadding the normalized spectra, where the inverse variance of each pixel is used as weight (see Figure 5.2). We determine the velocity dispersions (σ) of the composite spectra by both the Faber- Jackson relation and the cross-correlation method. (1) We K-correct the R band magnitude to B band magnitude using the code published by Blanton and Roweis (2007). Then the velocity dispersion is calculated by adopting the Faber-Jackson relation presented in Whit- more and Kirshner (1981). The average σ of our 302 red galaxy pool is about 235 km s−1,

7http://deep.ps.uci.edu/DR4/spectra.html 8http://www.ucolick.org/ ripisc/results.html ∼

101 DEEP2 Spectra, z~0.4

1.2 Single Spectrum

1.0

0.8 Sample I

0.6 , Vertically Offset Vertically , λ

0.4 Sample II Relative, F Relative, 0.2

0.0 4800 4900 5000 5100 5200 5300 5400 Rest Wavelength (A◦ )

Figure 5.2: Spectra before and after stacking. The S/N of a single spectrum (top) is too insuﬃcient for stellar population analysis. After stacking 275 (72) spectra, we then have Sample I (Sample II) spectra with higher S/N.

102 with 40 km s−1 standard deviation. (2) We cross-correlate the composite spectra with model stellar spectrum templates. Composite spectra of Sample I and Sample II show σ 225 ∼ km s−1, and 215 km s−1, respectively. The velocity dispersions determined by these two ∼ methods agree with each other reasonably well. Unless indicated otherwise, we adopt the cross-correlation velocity dispersion for later analysis. We broadened the spectra to 300 km s−1 (σ2 = σ2 σ2 ) , and measured broaden 300 − sample spectral indices and associated errors. Our index table consists of the Lick indices (Worthey et al., 1994; Trager et al., 1998), Serven’s indices (Serven et al., 2005), and the IMF-sensitive indices (Table 5.1). The measured indices and errors are shown as red (Sample I) and light grey (Sample II) ﬁlled circles with error bars in Figure 5.3.

5.3 Non-universal IMF

In this section, we evaluate the underlying astrophysical properties of z 0.4 red galaxies ∼ by comparing observables and models.

5.3.1 Models and Local Observables

Worthey models: Integrated-light models (Worthey, 1994; Trager et al., 1998) that use a new grid of synthetic spectra in the optical (Lee et al., 2009) in order to investigate the eﬀects of changing the detailed elemental composition on an integrated spectrum was used to create synthetic spectra at a variety of ages and metallicities for single-burst stellar populations. For this work, we adopt the isochrones of Bertelli et al. (2008, 2009) using the thermally- pulsing asymptotic giant branch (TP-AGB) treatment described in Marigo et al. (2008). Following Poole et al. (2010), stellar index ﬁtting functions were generated from indices measured from the stellar spectral libraries of Valdes et al. (2004) and Worthey et al. (2014a), both transformed to a common 200 km s−1 spectral resolution. Multivariate polynomial

103 fitting was done in five overlapping temperature swaths as a function of θeff = 5040/Teff , log g, and [Fe/H]. The fits were combined into a lookup table for final use. As in Worthey (1994), an index was looked up for each bin in the isochrone and decomposed into “index” and “continuum” fluxes, which was added, then re-formed into an index representing the

ﬁnal, integrated value after the summation. Our models are recently updated with variable IMF options, therefore in this work, we are able to calculate SSP models with three IMF slopes: α =1.7, 2.35, 3.0. For each IMF slope, our SSP models are given at the ages of 2, 5, 10, 14 Gyr with log (Z)= 0.33, 0, 0.37, − 0.62.

FSPS: We also employ the Flexible Stellar Population Synthesis models (FSPS, Conroy and Gunn 2010), which include IMF-variant models. FSPS is restricted to mainly solar metallicity old stellar populations (>3 Gyr), except at 13.5 Gyr, where individual abundance variation and alpha element enhancement are investigated. A “ﬂexible” IMF shape can be

defined by the users. For our illustration purpose, we adopt the spectra presented in Conroy and van Dokkum (2012a)9. These spectra are the stellar population model output at four different ages: 3, 5, 7, and 9 Gyr; with four different types of IMFs: α = 3.5, α = 3.0, Salpeter, and Chabrier IMFs. We measured indices after we broadened the spectra to 300

km s−1. Local galaxies: As stellar population models still suﬀer from uncertainties (Charlot et al., 1996; Conroy et al., 2009; Tang et al., 2014), local galaxies are needed to testify the models and give a more straightforward comparison. Since our sample galaxies consist of a majority of ETGs and a smaller amount of LTGs, templates of both galaxy types are retrieved. (1) We were kindly provided with the updated mean elliptical spectra by G. Graves, which were processed as follows. First, the galaxies from SDSS DR7 were selected with the following criterion: (1) 0.025

9http://people.ucsc.edu/ conroy/CvD12.html ∼

104 (Peek and Graves, 2010); (3) Median S/N>5 per A.˚ Then, the galaxies were divided into six bins in log σ: 1.86 2.00, 2.00 2.09, 2.09 2.18, 2.18 2.27, 2.27 2.36, 2.36 2.50. Finally, − − − − − − the spectra were broadened to 300 km s−1. (2) We also retrieved the Sb galaxy template from Kinney et al. (1996). This optical template is a combination of two Sb galaxies, NGC

210 and NGC 7083, whose spectra were obtained at the CTIO 1 m telescope with the two- dimensional Frutti detector. The CTIO spectra covers 3200 10000 A˚ with a resolution of − 8 A.˚ This template is also broadened to 300 km s−1. We measured the indices on the ETG and LTG template spectra, and show the results in Figure 5.3.

5.3.2 Comparison

The first row of panels show that our sample galaxies consist of old, and solar metallicity populations, whereas the α abundances are slightly enhanced. The fact that Samples I & II show close proximity to local ETG observables, instead of LTG observables, further proves that our sample galaxies are dominated by ETGs. The middle and bottom rows of panels focus on the optical IMF-sensitive indices. Our models show a clear trend that steeper IMF models have larger IMF-sensitive index values, except for young, metal-poor populations. Readers are referred to Chapter 4 for the astrophysical reasons of this exception. The FSPS model isochrones (green lines and dots) also suggest shallower IMF for smaller indices between the age of 3 9 Gyr. Using the FSPS and our models as reference, it is clear that − the local elliptical sample of Graves indicates massive ETGs with larger velocity dispersion tend to have a steeper IMF. Note that this conclusion agrees with the scientific results from the red IMF-sensitive indices (Cenarro et al., 2003; van Dokkum and Conroy, 2010; Conroy and van Dokkum, 2012b), and verifies the feasibility of optical IMF-sensitive indices. Our two samples of galaxies10 and the LTGs (Kinney & Calzetti) seem to have lower index values than the local ETGs, implying shallower IMFs in these systems. One exception is found in

10Sample II observables are missed for blue indices, such as bTiO, due to lower redshifts.

105 3.5 12 5.0

4.5 3.0 10 4.0 8 2.5 3.5 6

Mgb 3.0 Hbeta

2.0 Fe4668 4 2.5 1.5 2 2.0

1.0 0 1.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 [MgFe] [MgFe] [MgFe] 7 0.06 0.14

6 0.05 0.12 5 0.04 0.10 4 TiO1 TiO2 NaD 0.03 0.08 3

2 0.02 0.06

1 0.01 0.04 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 [MgFe] [MgFe] [MgFe] 0.030 0.13 1.8 0.12 1.6 0.025 0.11 1.4 0.10 0.020 1.2 0.09

SDSS 1.0

bTiO 0.08 0.015 Mg4780 0.8 TiO2 0.07 0.6 0.010 0.06 0.05 0.4 0.005 0.04 0.2 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 [MgFe] [MgFe] [MgFe]

Figure 5.3: Our SSP models are given at age=2, 5, 10, 14 Gyr with log (Z) = 0.33, 0, − 0.37, 0.62. IMF slopes of 1.7 (magenta lines), 2.35 (black lines), and 3.0 (blue lines) are shown. SSP models with the same age are connected with lines. The FSPS models are given at ages=3, 5, 7, 9 Gyr and solar metallicity, with four different types of IMFs: α = 3.5, α = 3.0, Salpeter, and Chabrier IMFs (green dots); The green lines connect models with the same age. The observables include: Graves (open diamonds), Kinney & Calzetti (cyan filled triangles), Sample I (red filled circles), and Sample II (light grey filled circles). The measurement uncertainties of Sample I and Sample II spectra are indicated by error bars.

106 the NaD index, where our sample galaxies appear to have a comparable NaD index value with the local ETGs. We caution that the NaD index is sensitive to Na and may have interstellar absorption contamination.

5.4 Discussion

The shallower IMF of our sample galaxies indicated by most of the optical IMF-sensitive indices is consistent with the star-formation theories at high redshift (Larson, 1998, 2005; Marks et al., 2012), in which massive stars are favored.

5.4.1 Possible IMF Degeneracies

Estimating IMF slope from spectral indices might be complicated by additional eﬀects. In this section, we discuss the robustness of our conclusion by listing eﬀects that may impact the IMF-sensitive indices. .

Effects in Chapter 4: In Chapter 4, we studied several effects that might entangle • with the IMF slope determination, namely the IMF Low Mass Cut-Off (LMCO), and AGB contribution effects. The degeneracies are due to their common relationships with

the stellar dwarf/giant ratio. However, we showed in Chapter 4 that this degeneracy may be lifted by combined plots of colors and indices, though at an observationally challenging level ( 0.02 mag). We also investigated the age, metallicity, Abundance ≈ Distribution Function (ADF), and Variable IMF Composite Stellar Population (VCSP)

effects besides the three IMF-related effects. We showed that these effects can be divided into two groups based on their vector directions, where group I includes the age, metallicity, ADF, and VCSP effect, and group II includes the IMF slope, LMCO, and AGB effects. The two groups of effects are clearly distinguishable in the bTiO (TiO2) vs. [MgFe] plots.

107 Non-solar element abundance eﬀect: The Ti4553 and Ti5000 indices indeed show • sub-solar Ti abundances for our sample galaxies. Thus the small values of Ti-related indices may be partially due to the low Ti abundances. However, we do not consider the sub-solar Ti abundances as the sole reason for small IMF-sensitive indices, since

Mg4780 index is not Ti-sensitive, yet indicates a shallower IMF.

α element enhancement eﬀect: Mgb index suggests only mildly α enhanced popu- • lations for our sample galaxies. What is more, Thomas et al. (2011) showed that the α element enhancement eﬀect is weak in TiO1 and TiO2, though they caution that the

TiO1 and TiO2 are diﬃcult to calibrate.

5.4.2 IMF in High-redshift Galaxies van Dokkum (2008) compared the luminosity evolution (∆ log (M/LB)) to color evolution (∆(U V )) for massive galaxies in clusters at 0.02

the trend predicted by the standard IMF models. By modelling the characteristic mass Mˆ

2 as a function of redshift: M=ˆ 0.5(1 + z) M⊙ (z < 2), Davé(2008) successfully brought the observed and predicted M∗–SFR relation into broad agreement. In other words, Davé suggested shallower IMFs for high-redshift galaxies. However, invariant IMFs are recently proposed by dynamical models and spectroscopic studies. Shetty and Cappellari (2014) derived the mass/light (M/L) ratios of 68 field galaxies in the redshift range of 0.7 0.9 with −

both dynamical modelling and stellar population modelling. The comparison of (M/L)dyn

and (M/L)pop implies a Salpeter IMF, which is also possessed by nearby galaxies with similar masses. Meanwhile, Mart´ın-Navarro et al. (2014) estimated the IMF slope of a sample of 49

massive quiescent galaxies at 0.9

11.0 10.5 10 M⊙) show a bottom-heavy IMF (α = 3.2 0.2), and lighter galaxies (10

108 has remained unchanged for the late 8 Gyr. Therefore, we caution controversy still exists ∼ regarding the high-redshift IMF. The stark diﬀerences among literature results (and ours) suggest more work should be done in this ﬁeld.

5.4.3 The Ways to Improve

We may improve the spectroscopic study of IMF cosmic evolution in several ways:

1. Given that DEEP2 Galaxy Redshift Survey is designed for galaxies at z 1, the rest ∼ wavelength range corresponds to the DEEP2 observed wavelength range at this redshift is the near-ultraviolet. To study the IMF at z 1, we may search for IMF-sensitive indices ∼ in the ultraviolet. However, this is known to be a formidable task since, the ultraviolet

spectral features are very sensitive to hot stellar components (young stars and horizontal branch stars) but less sensitive to low mass stars. 2. Alternatively, we may ﬁnd other surveys which focus on galaxies at 0.3

3. As near-infrared detector engineering advances, improvements in the quantity and quality of near-infrared spectroscopic surveys beyond 1 m will make the classical feature lines (e.g. [Na i], [Ca ii], and Wing-Ford band) available for cosmic evolution study.

5.5 Summary

Whether the IMF is universal has been debated for more than half a century. Recent research on nearby galaxies suggests variable IMFs and questions the universality of the IMF seen around the solar neighbourhood. For those high-redshift galaxies, the red IMF-sensitive indices shift out of the optimal optical wavelength range. In this chapter, we apply optical IMF-sensitive indices to the studies of intermediate-redshift galaxies. Our sample red galaxies

109 are selected from the DEEP2 Galaxy Redshift Survey, but with marginal spectral S/N ratio. To overcome this, we stack more than 200 spectra together whose redshifts range from 0.3 to 0.5, and then measure spectral indices from the composite spectrum. Comparing the measured indices with two sets of models and local observables suggests the intermediate- redshift red galaxies might possess a shallower IMF. However, synthesis of the previous studies and ours do not give a conclusive trend on cosmic IMF evolution.

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