What determines the fraction of elliptical galaxies in clusters?

Mon. Not. R. Astron. Soc. 419, 1324–1330 (2012) doi:10.1111/j.1365-2966.2011.19789.x What determines the fraction of elliptical galaxies in clusters? Gabriella De Lucia,1 Fabio Fontanot1 and David Wilman2 1 INAF – Astronomical Observatory of Trieste, via G. B. Tiepolo 11, I-34143 Trieste, Italy 2 Max-Planck-Institut für Extraterrestrische Physik, Giessenbachstraße, D-85748 Garching, Germany Accepted 2011 September 8. Received 2011 September 7; in original form 2011 August 10 ABSTRACT Key words: galaxies: bulges – galaxies: clusters: general – galaxies: evolution – galaxies: formation – galaxies: interactions. 1 I N T RO D U C T I O N It has long been known that early-type galaxies (ellipticals and lenticulars) reside preferentially in dense regions of the Universe such as rich clusters, while late-type galaxies represent a larger fraction of the galaxy population inhabiting regions of ‘average’ density. Such a morphology–density relation was noticed in early observational studies (indications of a correlation between the type of nebulae and the environment can be found in ‘The Realm of Nebulae’ by Hubble 1936), and was firmly established by Dressler (1980). In the past decades, much observational information has been collected on the morphological distributions of cosmic galaxy populations, and on its dependence on the environment. Butcher & Oemler (1978a, 1984) showed, for the first time, that the fraction of blue (star-forming) galaxies in clusters increases with increasing redshift. Detailed morphological studies have been carried out in the following years, demonstrating that the fraction of spiral galaxies increases with increasing redshift, and that this increase appears approximately balanced by a decrease in the fraction of the lenticular galaxies since z ∼ 0.5. Over the same redshift range, the fraction of elliptical galaxies is approximately constant (Dressler et al. 1997; Fasano et al. 2000). In more recent years, detailed morphological  E-mail: studies have been pushed to lower mass ranges (Wilman et al. 2009), and to higher redshift, where the mean fraction of different morphological types does not appear to evolve significantly (Postman et al. 2005; Desai et al. 2007). At a given redshift, clusters with similar mass (measured from either X-ray luminosity or velocity dispersion) exhibit a nonnegligible scatter in their morphological composition (e.g. Poggianti et al. 2009). In the context of the currently accepted paradigm for structure formation [the Lambda cold dark matter (CDM) model], it is logical to relate this cluster-to-cluster variance to the dynamical history of the cluster. Although difficult to test quantitatively, this expectation is confirmed by early observations that centrally concentrated clusters have typically large populations of ellipticals and lenticulars and relatively low numbers of spirals, while irregular, unrelaxed clusters are more spiral-rich and show weaker radial gradients in their morphological mix (e.g. Butcher & Oemler 1978b). In this paper, we will address this issue by considering two different semi-analytic models of galaxy formation, and by relating the predicted fraction of elliptical galaxies to the accretion history of the simulated cluster haloes. 2 T H E G A L A X Y F O R M AT I O N M O D E L S In this paper, we take advantage of two independently developed galaxy formation models: the ‘Munich’ model, with the implementation discussed in De Lucia & Blaizot (2007) and applied to the  C 2011 The Authors C 2011 RAS Monthly Notices of the Royal Astronomical Society  We study the correlation between the morphological mix of cluster galaxies and the assembly history of the parent cluster by taking advantage of two independently developed semi-analytic models for galaxy formation and evolution. In our models, both the number of cluster members and that of elliptical members increase as a function of cluster mass, in such a way that the resulting elliptical fractions are approximately independent of cluster mass. The population of cluster ellipticals exhibits a marked bimodal distribution as a function of galaxy stellar mass, with a dip at masses ∼1010 M . In the framework of our models, this bimodality originates from the combination of a strongly decreasing number of galaxies with increasing stellar mass, and a correspondingly increasing probability of experiencing major mergers. We show that the correlation between the measured elliptical fraction and the assembly history of the parent cluster is weak, and that it becomes stronger in models that adopt longer galaxy merger times. We argue that this results from the combined effect of a decreasing bulge production due to a reduced number of mergers, and an increasing survival probability of pre-existing ellipticals, with the latter process being more important than the former. The fraction of ellipticals in clusters 1 The most important difference between WMAP first- and third-year data is a lower value for the amplitude of matter fluctuations on 8 h−1 Mpc scales (σ 8 ), which leads to a delay in structure formation (e.g. Wang et al. 2008).  C 2011 The Authors, MNRAS 419, 1324–1330 C 2011 RAS Monthly Notices of the Royal Astronomical Society  The treatment of disc instability differs significantly in the two models considered: both adopt the same stability criterion proposed in Efstathiou, Lake & Negroponte (1982) but use different definitions for the relevant physical quantities, and make different assumptions about the outcome of instabilities. DLB07 only transfer to the bulge a fraction of the stellar disc that is enough to restore stability. In the MORGANA model, half of the disc baryonic mass (both gas and stars) is transferred to the bulge. As discussed and shown in De Lucia et al. (2011), this translates into a more relevant contribution of disc instability to bulge formation. In the framework of our models, most of the elliptical galaxies acquire their morphology through major mergers. Disc instability can contribute significantly for low and intermediate mass galaxies, depending on the adopted treatment for galaxy mergers and instabilities. As mentioned above, bulge-dominated galaxies can later grow a new disc, if they are fed by an appreciable cooling flow. We have shown that the rates of disc regrowth are negligible for massive galaxies and at low redshift. They represent, however, a non-negligible component of the evolution of low and intermediate mass galaxies, particularly at high redshift (see section 6 of De Lucia et al. 2011). As we focus on galaxy clusters, the model ellipticals considered in this paper are almost all satellite galaxies (with the exclusion of central cluster galaxies). For these galaxies, the bulge-to-total ratio is not affected after accretion on to a more massive halo in the MORGANA model. DLB07 accounts for mergers between satellites (that are, however, rare) so that the bulges of satellite galaxies can sti (...truncated)