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«Galaxy Masses: A Review St´phane Courteaua, Michele Cappellarib, Roelof S. de Jongc, Aaron A. Duttond, Eric Emselleme, e Henk Hoekstraf, ...»

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Galaxy Masses: A Review

St´phane Courteaua, Michele Cappellarib, Roelof S. de Jongc, Aaron A. Duttond, Eric Emselleme,


Henk Hoekstraf, L.V.E. Koopmansg, Gary A. Mamonh, Claudia Marastoni, Tommaso Treuj,

Lawrence M. Widrowa

a Queen’s University, Department of Physics, Engineering Physics and Astronomy, Kingston, Ontario, Canada

b Sub-department of Astrophysics, Department of Physics, University of Oxford, Denys Wilkinson Building, Keble

Road, Oxford OX1 3RH, UK

arXiv:1309.3276v1 [astro-ph.CO] 12 Sep 2013 c Leibniz-Institut f¨r Astrophysik Potsdam (AIP), An der Sternwarte 16, 14482 Potsdam, Germany u d Max-Planck-Institut f¨r Astronomie, K¨nigstuhl 17, 69117 Heidelberg, Germany u o e European Southern Observatory, Karl-Schwarzschild-Strasse 2, 85748, Germany and Universit´ Lyon 1, e Observatoire de Lyon, Centre de Recherche Astrophysique de Lyon and Ecole Normale Sup´rieure de Lyon, 9 e avenue Charles Andr´, F-69230 Saint-Genis Laval, France e f Leiden Observatory, Leiden University, P.O. Box 9513, NL-2300 RA Leiden, The Netherlands g University of Groningen, Kapteyn Astronomical Institute, P.O.Box 800, 9700 AV, Groningen, The Netherlands h Institut d’Astrophysique de Paris (UMR 7095: CNRS & UPMC), 98 bis Bd Arago, F-75014 Paris, France i University of Portsmouth, Institute of Cosmology and Gravitation, Dennis Sciama Building, Burnaby Road,

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1. Introduction The distribution of matter in cosmological structures is a fundamental property of nature as the mass of a system is likely the major driver of its evolution. This is especially true for stars whose evolution depend almost fully on their initial mass (and chemical composition) on the main sequence, as embodied by the (idealistic) Vogt-Russell theorem. Mass also plays a fundamental role in galaxy evolution. Galaxies have largely been shaped through mergers and galaxy interactions in hierarchical fashion whereby small systems merged into bigger ones. At early times, star formation was most effective in massive galaxies but as the Universe aged, star formation was likely quenched in those massive systems but continued in smaller galaxies, a phenomenon now called “downsizing”.

Oldest stars are thus found in the most massive systems. The complex interplay between star formation efficiency and quenching is likely modulated by a galaxy’s total mass.

Measurements of the distribution of matter in the Universe enable a variety of tests of structure formation models on different scales. For instance, the distribution of galaxy masses on all scales enables the closest possible, though not direct, comparison of predicted mass functions for baryonic and non-baryonic matter in the Universe. The relative fraction of baryonic to non-baryonic matter is also indicative of fundamental, yet poorly understood, processes in galaxy formation which typically give rise to tight scaling relations based on the stellar and dynamical masses of galaxies.

Because galaxy masses play such a critical role in our understanding of the formation and evolution of cosmic structures, we wish to review the variety and reliability of mass estimators for gas-poor and gas-rich galaxies and discuss our ability to derive from those estimators meaningful constraints of theoretical galaxy formation models. While certain techniques enable only the measurement of galaxy masses on large scales, others allow the decomposition of individual mass components such as gas, stars and dark matter at different galactocentric radii. The latter methods probe the gravitational potential through the dynamics of visible tracers where baryons are (sub-)dominant. Although many galaxies may be safely assumed to be virialized, uncertainties in their mass estimates remain, for instance due to anisotropies in the velocity distributions. Furthermore, baryon-dominated regions remain poorly understood, which complicates a direct comparison of galaxy formation models to observational data.

Many techniques exist for the determination of galaxy masses. The most popular involves the measurement of Doppler shifts of nebular and/or stellar atomic lines due to internal dynamics.

Stellar motions can also be resolved in the closest galaxies, such as our The Milky Way, Andromeda, and other Local Group stellar systems; galaxy masses of more distant systems otherwise rely on integrated spectra. Another mass estimator consists of converting the galaxy light profile into a mass profile using a suitable stellar mass-to-light ratio (usually derived from stellar population models). A more global approach has also involved the mapping of gravitational lensing effects, both strong and weak. This list is not meant to be complete, as we review below. However, in all cases, galaxy mass estimates account for matter encompassed within a specified radius and are thus always a lower limit to the total galaxy mass.

This review has evolved from discussions which took place during the celebrations of Vera Rubin’s career at Queen’s University in June 20091. All the authors of this review were indeed present at that conference. While each section of this review was initially written by separate teammates, the final product reflects the full team’s imprimatur. This review was inspired by, and 1 See http://www.astro.queensu.ca/GalaxyMasses09 for workshop presentations and photographs.

is meant as a modern revision of, early treatises on the masses and mass-to-light ratios of galaxies by Burbidge & Burbidge (1975) and Faber & Gallagher (1979), respectively.

The review is organized as follows: we first present in §2 the central topic of stellar M/L determinations from stellar population models. This is followed by a discussion of the mass estimates for gas-rich galaxies in §3, including the special (resolved) case of the Milky Way in §4. Gas-poor galaxies are addressed in §5 and weak and strong lensing techniques are presented in §6 and §7, respectively. Conclusions, with a view towards future developments, are presented at the end of each section.

This review is naturally incomplete; conspicuously missing topics include the measurement of stellar and dynamical masses of high redshift galaxies (e.g. F¨rster Schreiber et al. 2006; Bezanson o et al. 2011; Alaghband-Zadeh et al. 2012), the direct comparison of stellar and dynamical mass estimates (e.g. de Jong & Bell 2007; Taylor et al. 2010), mass function determinations (e.g. stellar mass functions: Bundy et al. 2006; Pozzetti et al. 2010; Maraston et al. 2012) (e.g. dynamical mass functions: Trujillo-Gomez et al. 2011; Papastergis et al. 2011, 2012), constraints on halo masses by statistical techniques such as those involving satellite kinematics (More et al. 2011a; Wojtak & Mamon 2013), group catalogs (Yang et al. 2009), and abundance matching (Behroozi et al. 2013), to name a few.

Furthermore, this review is restricted to mass analyses based on Newtonian dynamics. Alternatives exist, the most popular being MOND (e.g. Milgrom 1983), but a proper treatment of them is beyond the scope of this review. Readers interested in alternative models, MOND or others, are referred to the review by Famaey & McGaugh (2012).

2. From light to mass: modelling the stellar M ∗ /L ratio

2.1. Modelling galaxies and their Stellar Populations, a Historical Introduction.

The stellar mass M ∗ of a galaxy is a key physical parameter of galaxy formation and evolution studies as it traces the galaxy formation process. The stellar mass of a galaxy grows through processes such as the internal conversion of gas and dust into stars via star formation, or external events like major interactions with other galaxies and subsequent merging which may induce further star formation, as well as minor events such as accretion of satellites. Moreover, knowledge of the galaxy stellar mass is crucial in order to decompose the contributions from stars and dark matter to the dynamics of galaxies. Modern galaxy formation models embedded in a Λ-Cold Dark Matter universe can also predict the evolution of the galaxy mass assembly over cosmic time (e.g. De Lucia et al. 2007).

Galaxies shine because their stars radiate the energy they produced via nuclear reactions in their cores. The theory of stellar evolution describes the amount of energy released by a star given its initial mass. Hence, by modelling the light emitted by all the stars in a galaxy over all wavelengths

- the so-called “integrated spectral energy distribution (SED)” - one can in principle derive the stellar mass that is responsible for such radiation. However, a certain fraction of evolved stars no longer shine yet still contribute to the galaxy mass budget in the form of stellar remnants such as white dwarfs, neutron stars and black holes. The sum of living stars plus remnants makes up the “stellar mass”, M ∗, of a galaxy.

Despite our detailed knowledge of stellar evolution, the modelling of a galaxy spectrum - which is the superposition of all spectra from individual stars - is a challenging exercise since the exact stellar composition of a galaxy and its overall stellar generations are unknown a priori. These depend on the history of star formation, chemical enrichment, accretion and interaction. Unlike stellar clusters whose vast majority of stars are coeval and share the same chemical composition, galaxies are a complicated ensemble of stellar generations. Recent extensive reviews of SED modelling of galaxies have appeared in Walcher et al. (2011) and Conroy (2013).

As recognised early on by Oort (1926) and Baade (1944), our own Milky Way is composed of various populations of stars, each featuring different dynamics, chemical properties, and formation epochs. Thus, from a stellar content viewpoint, galaxies can be broken into stellar populations with shared definable properties. The “simple stellar population” (SSP) is defined as a group of coeval stars with homogeneous chemistry (at birth) and similar orbits/kinematics. A recent, comprehensive text book on stellar populations in galaxies is due to Greggio & Renzini (2011).

Star clusters, either open or globular, are the closest realisation of SSPs in nature. The main unknown of an SSP is the stellar Initial Mass Function (IMF), which gives the mass spectrum of the stellar generation at birth. The latter is not known from first principles. Empirical determinations of the IMF based on solar neighborhood data were first modeled by Salpeter (1955) as a power-law with exponent of ∼ −2.35. An IMF must be assumed when calculating the properties of population models. While galaxies are not SSPs, they can be viewed as a sum of all present SSPs: that is, Galaxies = j SSPj. The distribution of stellar generations in time and chemical enrichment is called the “Star Formation History” (SFH). Several analytical laws describe plausible SFHs which depend on the timescale of the Star Formation Rate (SFR), such as exponentially-declining models, or τ -models, models with constant star formation, models with time-increasing star formation, etc.

Examples of such SFHs are shown in Figure 1.

Figure 1: Time evolution of the exponential (upper panel) and Sandage (1986a) (lower panel) star formation histories (solid curves). The dotted curve is a Sandage-style burst of star formation in which 10% of the total mass of stars are formed. From MacArthur et al. (2004).

Ultimately, the stellar content of a galaxy over time, t, may be thought of as:

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with Y the Helium abundance and Z the abundance of heavier elements (metallicity). Note that Y, Z, and the IMF may vary between different stellar generations, i.e. amongst different SSPs, but they do not vary within an SSP by definition.

It is useful to note that little is known about the physical processes that drive the rate of star formation and the emerging mass spectrum (the IMF). We know that stars form from dense, cold gas in gas that is shock compressed (e.g. in disks, during galaxy interactions or dynamical instabilities), but a theory which predicts the SFR and the IMF in different galaxies and as a function of time has yet to be written. For these reasons, these two physical quantities are parametrized in population models and observations to guide ongoing developments. Indeed, our limited knowledge about the SFR and IMF is a major problem in the precise determination of a galaxy’s stellar mass.

Historically, the problem of modelling a galaxy spectrum has been approached in two ways.

In the so-called “optimised population synthesis” (Spinrad & Taylor 1971; Faber 1972; O’Connell 1976; Pickles 1985; Bica & Alloin 1986), empirical stellar spectra are combined in proportions such that the resulting composite spectrum can best reproduce the galaxy spectrum. These proportions can be ad hoc, hence neither necessarily obeying stellar evolution timescales nor a realistic stellar IMF. The obtained best-fit model can provide an excellent representation of the galaxy spectrum, but it cannot be evolved with time. Hence the optimised spectral fitting does not allow to study galaxy evolution in a cosmological context. Still, it can provide important insights on the types of stars which are effectively present in a stellar system (e.g. MacArthur et al. 2009). Optimised synthesis can also be used to obtain an instantaneous description of a galaxy spectrum in order to achieve accurate estimates of broadening of absorption lines for velocity dispersion measurements (see §5).

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