<abstract xmlns="http://www.w3.org/1999/xhtml">

The <italic>r</italic>-band of the Sloan Digital Sky Survey (SDSS) for 17,924 brightest cluster galaxies (BCGs) in clusters and groups within 0.02 ⩽ <italic>z</italic> ⩽ 0.20 are used to study possible environmental relations affecting the nature of these galaxies. We find a correlation between BCGs physical properties (the effective radius (<italic>Re</italic>), absolute magnitude and central velocity dispersion (<italic>σ</italic>0)) and their host groups and clusters velocity dispersion (<italic>σcl</italic>). This type of relations suggests that the most massive groups or clusters host larger central galaxies. On the other hand, the <italic>σ</italic>0/<italic>σcl</italic> ratio as a function of <italic>σcl</italic> is consistent with [<xref ref-type="bibr" rid="j_amns.2021.1.00002_ref_010">10</xref>].
</abstract>

The r-band of the Sloan Digital Sky Survey (SDSS) for 17,924 brightest cluster galaxies (BCGs) in clusters and groups within 0.02 ⩽ z ⩽ 0.20 are used to study possible environmental relations affecting the nature of these galaxies. We find a correlation between BCGs physical properties (the effective radius (Re), absolute magnitude and central velocity dispersion (σ0)) and their host groups and clusters velocity dispersion (σcl). This type of relations suggests that the most massive groups or clusters host larger central galaxies. On the other hand, the σ0/σcl ratio as a function of σcl is consistent with [10].

<div xmlns="http://www.w3.org/1999/xhtml">
<sec id="j_amns.2021.1.00002_s_001"><label>1</label><div>Introduction</div>
Brightest cluster galaxies (BCGs) are considered as one from the interesting objects that can explain some unsolved problems in studying galaxies. They are large, bright early type galaxies lying at centers of most galaxies groups and clusters. There are several unanswered questions related to BCGs nature. The principal mechanism for BCGs evolution is feedback rather than merging [<a ref-type="bibr" href="#j_amns.2021.1.00002_ref_001">1</a>]. BCGs properties may also be affected by their clusters halo masses at low redshift. In general, BCGs follow the same fundamental plane (FP) of elliptical galaxies [<a ref-type="bibr" href="#j_amns.2021.1.00002_ref_006">6</a>], but they have different FP and other scaling relations than those of isolated galaxies and the FP is a waveband dependent [<a ref-type="bibr" href="#j_amns.2021.1.00002_ref_008">8</a>].
Previous studies found correlations between BCGs and their clusters properties such as cluster mass, richness and X-ray luminosity [<a ref-type="bibr" href="#j_amns.2021.1.00002_ref_002">2</a>, <a ref-type="bibr" href="#j_amns.2021.1.00002_ref_011">11</a>, <a ref-type="bibr" href="#j_amns.2021.1.00002_ref_012">12</a>]. Understanding BCGs nature needs to study well environmental effects which affect on their physical properties [<a ref-type="bibr" href="#j_amns.2021.1.00002_ref_006">6</a>, <a ref-type="bibr" href="#j_amns.2021.1.00002_ref_007">7</a>, <a ref-type="bibr" href="#j_amns.2021.1.00002_ref_009">9</a>].
In this work we present the sample and focus on investigating the relations between the physical properties of BCGs as the effective radii (<italic>Re</italic>), absolute magnitude, central velocity dispersions (<italic>σo</italic>) and the velocity dispersions of their host clusters and groups (<italic>σcl</italic>).
This paper is organized as follows; <a ref-type="sec" href="#j_amns.2021.1.00002_s_002">Section 2</a> describes the selection of our BCGs sample, while in <a ref-type="sec" href="#j_amns.2021.1.00002_s_003">Section 3</a> we introduce and discuss our results and in <a ref-type="sec" href="#j_amns.2021.1.00002_s_004">Section 4</a> our main conclusions are summarized. In this paper we will adopt the cosmological parameters Ω<italic>m</italic> = 0.3, ΩΛ = 0.7, and Hubble constant H<italic>o</italic> =70 km s−1 Mpc−1.
</sec>
<sec id="j_amns.2021.1.00002_s_002"><label>2</label><div>Galaxy Sample</div>
BCGs and Brightest Groups Galaxies (BGGs) are selected using the catalog of [<a ref-type="bibr" href="#j_amns.2021.1.00002_ref_013">13</a>] as it provides a huge list of galaxy clusters and groups in a broad redshift range. A sample of 17,924 elliptical galaxies in the <italic>r-</italic>band of the Sloan Digital Sky Survey (SDSS) in clusters and groups within 0.02 ⩽ <italic>z</italic> ⩽ 0.20 are constructed. All parameters in our sample are obtained and updated from the SDSS-DR16. Physical properties of BCGs and BGGs (the effective radius (<italic>Re</italic>), absolute magnitude and central velocity dispersion (<italic>σo</italic>)) are derived and corrected as in [<a ref-type="bibr" href="#j_amns.2021.1.00002_ref_008">8</a>]. The velocity dispersion of host groups and clusters (<italic>σcl</italic>) are taken from [<a ref-type="bibr" href="#j_amns.2021.1.00002_ref_013">13</a>].
</sec>
<sec id="j_amns.2021.1.00002_s_003"><label>3</label><div>Results and Discussions</div>
<sec id="j_amns.2021.1.00002_s_003_s_001"><label>3.1</label><div>Correlations between BCGs and environments</div>
In this section, we explore the relations between physical properties of the BCGs and their host clusters and groups. We consider absolute magnitude and central velocity dispersion as mass representatives of BCGs and BGGs. To measure the mass of cluster and group, we use <italic>σcl</italic>. <a ref-type="fig" href="#j_amns.2021.1.00002_fig_001">Figure 1</a> shows <italic>σcl</italic> of clusters and groups as a function of their redshifts (z). It is clear that most of clusters and groups have <italic>σcl</italic> higher than 300 km s−1.
<figure id="j_amns.2021.1.00002_fig_001" position="float" fig-type="figure"><h2>Fig. 1</h2>
<figCaption><italic>σcl</italic> - redshift relation.</figCaption>
<img xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_amns.2021.1.00002_fig_001.jpg" src="https://sciendo-parsed.s3.eu-central-1.amazonaws.com/6470a09471e4585e08aa1a55/j_amns.2021.1.00002_fig_001.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&amp;X-Amz-Date=20240728T073021Z&amp;X-Amz-SignedHeaders=host&amp;X-Amz-Expires=18000&amp;X-Amz-Credential=AKIA6AP2G7AKP25APDM2%2F20240728%2Feu-central-1%2Fs3%2Faws4_request&amp;X-Amz-Signature=b77c1429609c2602c64bef7745d3ef8251235f5e2b597f7c8119ca33fa7ee460" class="mw-100"/>
</figure>
In <a ref-type="fig" href="#j_amns.2021.1.00002_fig_002">Figure 2</a>, we plot the distribution of BCGs with their spectroscopic redshifts in the <italic>r</italic>-band.
<figure id="j_amns.2021.1.00002_fig_002" position="float" fig-type="figure"><h2>Fig. 2</h2>
<figCaption>BCGs distribution with their spectroscopic redshifts.</figCaption>
<img xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_amns.2021.1.00002_fig_002.jpg" src="https://sciendo-parsed.s3.eu-central-1.amazonaws.com/6470a09471e4585e08aa1a55/j_amns.2021.1.00002_fig_002.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&amp;X-Amz-Date=20240728T073021Z&amp;X-Amz-SignedHeaders=host&amp;X-Amz-Expires=18000&amp;X-Amz-Credential=AKIA6AP2G7AKP25APDM2%2F20240728%2Feu-central-1%2Fs3%2Faws4_request&amp;X-Amz-Signature=1262e988995e003f5da4147b11c8767981eee7d0cdb13b42928025e578ea04fb" class="mw-100"/>
</figure>
<a ref-type="fig" href="#j_amns.2021.1.00002_fig_003">Figure 3(a)</a> shows the <italic>r</italic>-band <italic>Re</italic> of BCGs with respect to redshifts of their host clusters and groups. It is clear that galaxies are having larger <italic>Re</italic> as the redshift of their host environment increases. <a ref-type="fig" href="#j_amns.2021.1.00002_fig_003">Figure 3(b)</a> shows <italic>Re</italic> of BCGs as a function of <italic>σcl</italic> of their host clusters and groups. Error bars represent the average values of <italic>σcl</italic> in every <italic>Re</italic> bins with errors. There is a tight correlation between <italic>Re</italic> of BCGs and <italic>σcl</italic> of their clusters and groups. As a result, the most massive clusters and groups host central galaxies with larger values of <italic>Re</italic>.
<figure id="j_amns.2021.1.00002_fig_003" position="float" fig-type="figure"><h2>Fig. 3</h2>
<figCaption>BCGs <italic>r</italic>-band effective radii (<italic>Re</italic>) with (a) redshift and (b) <italic>σcl</italic> of host clusters and groups. Error bars represent the average values of <italic>σcl</italic> in every <italic>Re</italic> bin with errors.</figCaption>
<img xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_amns.2021.1.00002_fig_003.jpg" src="https://sciendo-parsed.s3.eu-central-1.amazonaws.com/6470a09471e4585e08aa1a55/j_amns.2021.1.00002_fig_003.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&amp;X-Amz-Date=20240728T073021Z&amp;X-Amz-SignedHeaders=host&amp;X-Amz-Expires=17999&amp;X-Amz-Credential=AKIA6AP2G7AKP25APDM2%2F20240728%2Feu-central-1%2Fs3%2Faws4_request&amp;X-Amz-Signature=89687c47898607ba30475ab1e0aa005946632a055a8f71b13af8c522c639f69a" class="mw-100"/>
</figure>
<a ref-type="fig" href="#j_amns.2021.1.00002_fig_004">Figure 4(a)</a> shows the <italic>r</italic>-band absolute magnitude of BCGs as a function of the redshift of their host clusters and groups. While BCGs are very bright (M<italic>r</italic> &lt; −22 mag) across redshift range, low redshift clusters and groups (z ≤ 0.04) host less luminous BCGs. These low redshift systems have also lower values of <italic>σcl</italic> as clear in <a ref-type="fig" href="#j_amns.2021.1.00002_fig_001">Figure 1</a>. <a ref-type="fig" href="#j_amns.2021.1.00002_fig_004">Figure 4(b)</a> shows the <italic>r</italic>-band absolute magnitude of BCGs as a function of <italic>σcl</italic>. It is clear from this figure that clusters or groups with higher velocity dispersions host the brighter central galaxies which is consistent with previous studies [<a ref-type="bibr" href="#j_amns.2021.1.00002_ref_004">4</a>, <a ref-type="bibr" href="#j_amns.2021.1.00002_ref_014">14</a>, <a ref-type="bibr" href="#j_amns.2021.1.00002_ref_015">15</a>].
<figure id="j_amns.2021.1.00002_fig_004" position="float" fig-type="figure"><h2>Fig. 4</h2>
<figCaption>BCGs <italic>r</italic>-band absolute magnitude with respect to (a) redshift and (b) <italic>σcl</italic> of host clusters and groups. Error bars represent the average values of <italic>σcl</italic> in every M<italic>r</italic> bin with errors.</figCaption>
<img xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_amns.2021.1.00002_fig_004.jpg" src="https://sciendo-parsed.s3.eu-central-1.amazonaws.com/6470a09471e4585e08aa1a55/j_amns.2021.1.00002_fig_004.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&amp;X-Amz-Date=20240728T073021Z&amp;X-Amz-SignedHeaders=host&amp;X-Amz-Expires=18000&amp;X-Amz-Credential=AKIA6AP2G7AKP25APDM2%2F20240728%2Feu-central-1%2Fs3%2Faws4_request&amp;X-Amz-Signature=486befc0185dab47730807c8bdfdda03f24e02c0d3909c4d27a469827621d023" class="mw-100"/>
</figure>
<a ref-type="fig" href="#j_amns.2021.1.00002_fig_005">Figure 5(a)</a> presents <italic>σo</italic> of BCGs in <italic>r</italic>-band with respect to the redshift of their host clusters and groups. In general, values of <italic>σo</italic> increase along the entire redsift range. In <a ref-type="fig" href="#j_amns.2021.1.00002_fig_005">Figure 5(b)</a>, we plot <italic>σo</italic> of BCGs as a function of <italic>σcl</italic> of their host clusters and groups. This figure shows that there is a correlation between <italic>σo</italic> of BCGs and <italic>σcl</italic> of their host environment. We can say that <italic>σo</italic> of BCG depends on its host cluster or group mass. The observed relation between <italic>σo</italic> and <italic>σcl</italic> provides an important test for the formation models of galaxies and clusters.
<figure id="j_amns.2021.1.00002_fig_005" position="float" fig-type="figure"><h2>Fig. 5</h2>
<figCaption><italic>σo</italic> of BCGs in <italic>r</italic>-band with respect to (a) redshift and (b) <italic>σcl</italic> of host clusters and groups. Error bars represent the average values of log10 <italic>σcl</italic> for log10 <italic>σo</italic> bins with errors.</figCaption>
<img xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_amns.2021.1.00002_fig_005.jpg" src="https://sciendo-parsed.s3.eu-central-1.amazonaws.com/6470a09471e4585e08aa1a55/j_amns.2021.1.00002_fig_005.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&amp;X-Amz-Date=20240728T073021Z&amp;X-Amz-SignedHeaders=host&amp;X-Amz-Expires=18000&amp;X-Amz-Credential=AKIA6AP2G7AKP25APDM2%2F20240728%2Feu-central-1%2Fs3%2Faws4_request&amp;X-Amz-Signature=66384482d15346ec72fd17ec0394ca7141dc4b7eca0783da6df9d4368db4ff88" class="mw-100"/>
</figure>
</sec>
<sec id="j_amns.2021.1.00002_s_003_s_002"><label>3.2</label><div>Comparison with simulations</div>
We found that <italic>σo</italic> of BCG correlates with <italic>σcl</italic>, which represents a cluster and group halo mass proxy. Here we compare the observed relation with predictions from numerical simulations by [<a ref-type="bibr" href="#j_amns.2021.1.00002_ref_003">3</a>] and [<a ref-type="bibr" href="#j_amns.2021.1.00002_ref_005">5</a>]. [<a ref-type="bibr" href="#j_amns.2021.1.00002_ref_003">3</a>] performed their simulation taking into account heating by a UV background, radiative cooling, star formation and feedback. With more than 20 satellite galaxies, they identified 44 clusters. Some star particles were identified which are not bound to any subhalo within the cluster potential. Those star particles are either a diffuse stellar component (DSC) or the BCGs stellar component (cD galaxies). They separated those two components and calculated velocity dispersions for them.
<figure id="j_amns.2021.1.00002_fig_006" position="float" fig-type="figure"><h2>Fig. 6</h2>
<figCaption><italic>σo</italic> of BCGs in <italic>r</italic>-band with respect to <italic>σcl</italic> of host clusters and groups as a function of <italic>σcl</italic>. Error bars represent the average values of <italic>σo</italic>/<italic>σcl</italic> in different <italic>σcl</italic> bins with errors. The blue solid line shows the best exponential fit to our sample. The black solid and dashed lines show the predicted relation and the 1<italic>σ</italic> deviation from simulation done by [<a ref-type="bibr" href="#j_amns.2021.1.00002_ref_003">3</a>], respectively. The green dotted line is the predicted relation from simulations done by [<a ref-type="bibr" href="#j_amns.2021.1.00002_ref_005">5</a>].</figCaption>
<img xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_amns.2021.1.00002_fig_006.jpg" src="https://sciendo-parsed.s3.eu-central-1.amazonaws.com/6470a09471e4585e08aa1a55/j_amns.2021.1.00002_fig_006.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&amp;X-Amz-Date=20240728T073021Z&amp;X-Amz-SignedHeaders=host&amp;X-Amz-Expires=18000&amp;X-Amz-Credential=AKIA6AP2G7AKP25APDM2%2F20240728%2Feu-central-1%2Fs3%2Faws4_request&amp;X-Amz-Signature=34968055f68373933d4c3d3d98de47a809655ba060c68dab231e6b31ecc70bfc" class="mw-100"/>
</figure>
<a ref-type="fig" href="#j_amns.2021.1.00002_fig_006">Figure 6</a> shows that the relation between <italic>σo</italic> and <italic>σcl</italic> decreases as a function of <italic>σcl</italic> which is also consistent with previous result from [<a ref-type="bibr" href="#j_amns.2021.1.00002_ref_010">10</a>]. They studied the relation between 227 BCGs and their host clusters in the redshift range 0.02 &lt; z &lt; 0.30. They found a tight relation between BCG velocity dispersion and cluster velocity dispersion. They found that the ratio of BCG velocity dispersion and cluster velocity dispersion decreases as a function of velocity dispersion of the host cluster. On the other side, the simulation of [<a ref-type="bibr" href="#j_amns.2021.1.00002_ref_003">3</a>] suggests a constant relation between <italic>σo</italic> and <italic>σcl</italic> along a wide range of <italic>σcl</italic>. Also numerical simulations of [<a ref-type="bibr" href="#j_amns.2021.1.00002_ref_005">5</a>] represents the same constant relation. In <a ref-type="fig" href="#j_amns.2021.1.00002_fig_006">Figure 6</a>, error bars represent the average values of <italic>σo</italic>/<italic>σcl</italic> in different <italic>σcl</italic> bins with errors. The black solid and dashed lines represent the relation and the 1<italic>σ</italic> deviation from simulation. In that simulation of [<a ref-type="bibr" href="#j_amns.2021.1.00002_ref_003">3</a>], the velocity dispersion of BCGs, DSC, and cluster galaxies are well correlated with virial mass of cluster halo. We can say that the observed <italic>σo</italic>/<italic>σcl</italic> ratio depends on cluster and group mass which suggests that the mass fraction associated with brightest central galaxies indicate the evolution of brightest central galaxies and their host halos.
</sec>
</sec>
<sec id="j_amns.2021.1.00002_s_004"><label>4</label><div>Summary and Conclusions</div>
The <italic>r</italic>-band of the SDSS for 17,924 BCGs in clusters and groups within 0.02 ⩽ <italic>z</italic> ⩽ 0.20 are used to study possible environmental relations that influence the formation of these galaxies. All parameters in our sample are obtained and updated from the SDSS-DR16. We find a tight relation between effective radii of BCGs and velocity dispersions of their host clusters and groups. As a result, the most massive clusters and groups host larger central galaxies. Also the <italic>r</italic>-band absolute magnitude of BCGs correlate with <italic>σcl</italic> of their host clusters and groups. This indicates that clusters and groups with higher velocity dispersions host the more bright central galaxies, that is in agreement with previous studies [<a ref-type="bibr" href="#j_amns.2021.1.00002_ref_004">4</a>,<a ref-type="bibr" href="#j_amns.2021.1.00002_ref_014">14</a>,<a ref-type="bibr" href="#j_amns.2021.1.00002_ref_015">15</a>]. We find that <italic>σo</italic> of BCGs depend on its host group or cluster mass and <italic>σo</italic> correlates tightly with <italic>σcl</italic>. This relation suggests that <italic>σo</italic> of BCGs can be used as a tracer for group or cluster mass, which is in agreement with [<a ref-type="bibr" href="#j_amns.2021.1.00002_ref_009">9</a>]. On the other hand, the <italic>σo</italic>/<italic>σcl</italic> ratio decreases as <italic>σcl</italic> increases which is consistent with [<a ref-type="bibr" href="#j_amns.2021.1.00002_ref_010">10</a>]. Also <italic>σo</italic>/<italic>σcl</italic> ratio is different than theoretical predictions of [<a ref-type="bibr" href="#j_amns.2021.1.00002_ref_003">3</a>], which suggests two different scenarios for BCGs growth in lower mass and massive host groups and clusters. More large scale simulating studies of <italic>σo</italic> and <italic>σcl</italic> is useful for studying the environmental dependence of BCGs.
</sec>
</div>

Possible Relations between Brightest Central Galaxies and Their Host Galaxies Clusters and Groups

Astronomy Department, National Research Institute of Astronomy and Geophysics (NRIAG)

Applied Mathematics and Nonlinear Sciences

This work is licensed under the Creative Commons Attribution 4.0 International License.

The r-band of the Sloan Digital Sky Survey (SDSS) for 17,924 brightest cluster galaxies (BCGs) in clusters and groups within 0.02 ⩽ z ⩽ 0.20 are used to study...

Possible Relations between Brightest Central Galaxies and Their Host Galaxies Clusters and Groups

Published Online: Jan 28, 2021

Page range: 395 - 400

Received: Nov 30, 2020

Accepted: Oct 27, 2020

DOI: https://doi.org/10.2478/amns.2021.1.00002

Keywords
brightest central galaxies, BCGs, galaxy clusters, galaxy groups

© 2021 R. M. Samir et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Possible Relations between Brightest Central Galaxies and Their Host Galaxies Clusters and Groups

Published Online: Jan 28, 2021

Page range: 395 - 400

Received: Nov 30, 2020

Accepted: Oct 27, 2020

DOI: https://doi.org/10.2478/amns.2021.1.00002

Keywordsbrightest central galaxies, BCGs, galaxy clusters, galaxy groups

© 2021 R. M. Samir et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Keywords
brightest central galaxies, BCGs, galaxy clusters, galaxy groups