The Luminosity Function of Galaxies in Some Nearby Clusters

1. INTRODUCTION

Galaxies come in a diversity of sizes and cover a very wide range of luminosities, extending from the faintest dwarfs to the most luminous giant ellipticals. To know how these galaxies are distributed with respect to their luminosities, the luminosity function (LF) is used. It is one of the most important techniques used for studying galaxy formation and evolution. A suitable approximation to this function was given by Paul Schechter in 1976 [1]. It can be written as

where, L* is a characteristic luminosity, indicating the change from power law (L < L*) to exponential law (L > L*), α is the faint-end slope, and Ф* is a normalization constant for the distribution. These parameters may take different values for different morphological types and also for different environments. Considering an interval dL in luminosity, Ф(L)dL gives the number density of galaxies.

Galaxy clusters are ideal systems for studying the galaxy LF due to the existence of a large number of galaxies at almost the same distance. Many studies have thus been devoted to the LF of cluster galaxies to discover the influence of environment on their evolution. After the earlier works on the LF, carried out by Hubble (1936) [2], [3], Zwicky (1942) [4], Oemler (1974) [5], and others, Schechter (1976) [1] proposed the analytic expression given by Equation (1), which is called the Schechter function. He suggested that the cluster LF is universal in shape. This universality has been supported by various studies [6], [7], [8]. However, studies carried out by others [9], [10], [11] have demonstrated that the shape of the cluster LF is not universal.

The LF of cluster galaxies has been compared to that of field galaxies through several studies. Some of these studies found them to be identical [12], [13], [14], while others found them to be different [8], [15], [16]. The cluster LF has been found to vary with cluster-centric radius [11], [17]. This is because different galaxy morphological types have different LFs [18] and that the mixture of these morphological types varies with cluster-centric radius, according to the morphology-density relation [19]. In fact, studying the variation of the cluster LF with such characteristics as cluster-centric radius, galaxy morphologies, and, also, galaxy colors is very important in constraining theories of galaxy formation and evolution.

In the present work, we study the LF of a sample of seven Abell-type galaxy clusters having redshifts in the range (0.0 ≲ z ≲ 0.1). A detailed description of the sample is given in Section 2, and the results and discussion are presented in Section 3. Our conclusions are outlined in Section 4. Throughout the work, ɅCDM parameters (Ω_M = 0.27, Ω_Ʌ = 0.73, H₀ = 73 km s⁻¹ Mpc⁻¹) are used.

2. SAMPLE AND DATA

In this work, we consider a sample of seven nearby galaxy clusters, selected from Abell catalogue [20] within the redshift range (0.0 ≲ z ≲ 0.1). Their basic data are given in Table 1. All possible member galaxies within Abell radius (R_A= 1.5 h⁻¹ Mpc) of each cluster were taken into account. For membership confirmation, redshift data were obtained from the Sloan Digital Sky Survey (SDSS-DR9) [21] database (for A1656, A2199, and A2147) and the NASA/IPAC Extragalactic Database (NED) (for A2255 and A2144). For the other two clusters A85 and A2029, redshift data were obtained from Agulli et al. (2016) [22] and Sohn et al. (2017) [23], respectively. Petrosian magnitudes, taken from the SDSS database, were used for calculating the absolute magnitudes in the five bands u (3551Å), g (4686Å), r (6166Å), i (7480Å), and z (8932Å). These magnitudes were then corrected for galactic foreground extinction, using values given by Schlafly and Finkbeiner (2011) [24], and, also, K-corrected, using a method given by Chilingarian et al. 2010 [25] and Chilingarian and Zolotukhin (2012) [26].

TABLE 1: The basic data of the cluster sample.

With both of these corrections taken into consideration, the relation between absolute and apparent magnitudes for any passband can be written as:

where, D_L is the luminosity distance, K(z) is the K correction, A_l is the galactic foreground extinction, and b is the galactic latitude.

3. RESULTS AND DISCUSSION

It is convenient to write the LF in terms of absolute magnitude, M, rather than luminosity [27]. These two quantities are related through the expression

Hence, the LF becomes [28]

where, M* is the characteristic absolute magnitude corresponding to L*.

Figures 1-5 show the absolute magnitude distributions of galaxies in the ugriz bands, within R_A= 1.5 h⁻¹ Mpc, for the whole cluster sample, each fitted with a Schechter function. The fitting is done using the χ² – minimization method, and for each case, we vary the magnitude bins until we get the best χ² that gives the optimal values of Schechter parameters. Table 2 summarizes the results of the best-fitting Schechter parameters ɸ*, M*, and α, for the whole clusters, in all passbands.

Fig. 1. The luminosity distributions (histograms) of the cluster sample in the u-band, fitted with Schechter functions (solid curves).

Fig. 2. The luminosity distributions (histograms) of the cluster sample in the g-band, fitted with Schechter functions (solid curves).

Fig. 3. The luminosity distributions (histograms) of the cluster sample in the r-band, fitted with Schechter functions (solid curves).

Fig. 4. The luminosity distributions (histograms) of the cluster sample in the i-band, fitted with Schechter functions (solid curves).

Fig. 5. The luminosity distributions (histograms) of the cluster sample in the z-band, fitted with Schechter functions (solid curves).

TABLE 2: The best-fitting Schechter parameters for the cluster sample in the ugriz bands.

Since ɸ* is just a normalization constant which defines the overall density of galaxies, we focus our attention only on the characteristic absolute magnitude, M*, and the faint-end slope α, as the shape of the LF is defined by these two parameters [29]. No remarkable variations are seen in both of these parameters, for all clusters, in each band, within the redshift range considered in this work. Furthermore, by noting the basic data listed in Table 1, we conclude that, in each band, the LF does not vary with such cluster characteristics as velocity dispersion (in agreement with Propis et al. [8]), richness (in agreement with Colless [6], Propis et al. [8]), and Bautz–Morgan morphology (in agreement with Colless [6], Propis et al. [8], Lugger [30]). The above results confirm the universality of the cluster LF, in agreement with several other works (for example, Colless [6]). For this reason, we can deal with the mean values of the Schechter parameters M* and α, for the whole clusters. These values are listed in Table 3.

TABLE 3: The mean values of the Schechter parameters M* and α for the cluster sample in the ugriz bands.

It is obvious from Table 3 that the characteristic absolute magnitude, M*, becomes brighter towards redder bands, while no remarkable change is noted in the value of the faint-end slope with passband. The reason for this variation of galaxy LF with passband is the contribution of different mechanisms in galaxy evolution. At ultraviolet, for example, the shape of the LF is strongly influenced by star formation since most of the flux is generated by young stars [31]. On the other hand, the LF in the red bands determines the typical stellar distribution [28]. The results in the present work are in good agreement with the previous works [32], [33]. The flat faint-end slope (α~−1) obtained in the present work (Table 3) agrees well with the one obtained by Blanton et al. (2003) [32]. This flat faint-end slope is a result of the disruption of a large number of dwarf galaxies inside clusters during the first stages of cluster formation [10]. At the bright end of the LF, the exponential decrease of the number density of galaxies is caused by various feedback processes quenching star formation in massive galaxies. The mechanisms proposed for this quenching are either the effect of supernova explosions or an accreting supermassive black hole. In either case, the gas content is heated and then ejected out of the galaxy, quenching star formation process.

4. CONCLUSIONS

The galaxy LFs of some nearby clusters were studied in all of the SDSS passbands ugriz. In each case, a Schechter function was fitted to the bright end of the distribution, using the χ² – minimization technique, to obtain the best-fitting Schechter parameters, Ф*, M*, and α. For each passband, no noticeable variations were observed in the values of M* and α in any cluster. Further, it was found that the LF does not change with such cluster parameters as richness, velocity dispersion, and Bautz–Morgan morphology. From the mean values of M* and α, it was found that M* becomes brighter toward redder bands, whereas no remarkable change was noted in the value of α with passband, being about (−1.00).