Do Nuclear Star Clusters and Supermassive Black Holes Follow the Same Host-Galaxy Correlations?

Recent studies have suggested a strong correlation between the masses of nuclear star clusters and their host galaxies, an extension of the known correlations between supermassive black holes (SMBHs) and their host galaxies. By focusing on disk galaxies with well-determined black hole and nuclear cluster masses, we argue that there is not a universal"central massive object"correlation after all: careful analysis shows that while SMBHs correlate better with the stellar masses of the bulge components, nuclear star clusters clearly correlate better with total galaxy stellar mass.


INTRODUCTION
The past fifteen years have shown that essentially all massive galaxies in the local universe harbor supermassive black holes (SMBHs, with masses M • of ∼ 10 6 -10 9 M ). The same period has also shown that SMBH masses correlate quite strongly with several global properties of the host galaxies, especially central velocity dispersion [12,15] and bulge luminosity or mass [e.g., 23,18]. The implication is that the processes which drove galaxy growth and the processes which drove black hole growth were intimately linked, perhaps even the same processes.
The same period has also seen the discovery that many galaxies, particularly later-type spirals, host luminous nuclear star clusters [NSCs; e.g., 7,5]; see the review by Böker [6]. Recently, several authors have suggested that nuclear clusters and central SMBHs share the same host-galaxy correlations: in particular, that SMBHs and NSCs have the same correlation with bulge luminosity/mass [28,13,9,26,1].
There is, however, reason to be cautious about assuming a direct SMBH-NSC analogy. The samples of Wehner & Harris [28] and Ferrarese [13] were almost entirely early-type galaxies -ellipticals and dwarf ellipticals -which are essentially "pure bulge." But we know that SMBHs in spiral galaxies correlate better with the bulge, and not with the total galaxy mass or light [e.g., 21]. And there have been prior claims that nuclear star clusters correlate with total galaxy light [e.g. , 8]. So the question is: do nuclear clusters in spiral galaxies correlate with the bulge, or with the whole galaxy? arXiv:1002.1461v1 [astro-ph.CO] 7 Feb 2010

DATA SOURCES
For nuclear cluster masses, we prefer those which have been dynamically measured, both because this is the most direct analog to SMBH masses and because it circumvents any possible problems with multiple stellar populations, which can confound attempts to estimate stellar masses from broadband colors. The masses are drawn primarily from the sample of Walcher et al. [27], with additional data from Ho & Filippenko [19], Böker et al. [4], Matthews et al. [24] and Gebhardt et al. [16], and Barth et al. [2], along with preliminary measurements from L. Colina (private comm.). This yields a total of 14 galaxies, with Hubble types Sbc-Sm; the majority are Scd. We also include 15 galaxies from Rossa et al. [26], where the masses are estimated from spectroscopy; some of these are earlier spirals (Sa-Sb), but most are Sc and later.
Although current studies suggest that the M • -σ relation is tighter, with less intrinsic scatter, than the M • -M bulge relation [e.g., 17,11], velocity dispersion is not the ideal measure to use here, for the simple reason that the central velocity dispersion in nuclearcluster hosts is almost always that of the cluster itself, and is used in determining the cluster dynamical mass. So we compare nuclear cluster masses with the stellar mass of host galaxy bulge, and with that of the entire host galaxy. It is from these comparisons, after all, that we can most clearly see how SMBHs correlate with bulge mass and not with total galaxy mass ( Figure 1).
For comparison, we use the SMBH dataset and galaxy/bulge mass values compiled by Erwin & Gadotti [11]. Bulge masses in that study are determined by 2D image decomposition [via the BUDDA software package; 10,14] which incorporates bulge and disk components and optional bars and central point sources (accommodating both nuclear star clusters and AGN). Bulge/total ratios from the decompositions are combined with K-band total magnitudes from 2MASS to get bulge K-band luminosities; we then use optical colors from the literature to estimate stellar M/L ratios via Bell et al. [3] and thus determine bulge (and also total) M . Note that we explicitly define "bulge" to be the "photometric bulge" -that is, the excess light/stellar mass which is not part of the disk, bar, or nuclear star cluster. We defer questions of how SMBH (or nuclear cluster) mass relates to so-called "pseudobulges" versus "classical bulges" [e.g., 20, 25] to a later analysis.
We are currently working on 2D decompositions for the nuclear cluster galaxies, in cases where those are not already available; in the meantime, we present results from 1-D bulge/disk decompositions, always excluding the region dominated by the nuclear cluster itself (or, alternately, fitting it as an additional component). We use published 2D decompositions for some galaxies, such as those in Laurikainen et al. [22] and Barth et al. [2]. We do not expect the results to change significantly when 2D decompositions are used for the whole sample. Figure 1 plots SMBH mass versus total and bulge stellar mass. As is by now no surprise, the correlation of SMBH mass with bulge mass is much stronger than any correlation with total galaxy mass (Spearman correlation coefficients r S = 0.71 vs 0.29, with the FIGURE 1. Left: SMBH mass versus total galaxy stellar mass. Right: SMBH mass versus bulge stellar mass. The diagonal line is the best fit to the elliptical galaxies (squares); open symbols are galaxies without precise distances. It is clear that the SMBH masses of S0 and spiral galaxies (circles) correlate better with the bulge stellar mass than with total galaxy mass. Based on Erwin & Gadotti [11].  [26]. Arrows show nominal upper limits for four bulgeless spirals (assuming B/T ≤ 0.01). The situation is now the reverse of that for SMBHs: NSC masses clearly correlate better with total galaxy mass than they do with bulge mass.

COMPARING BLACK HOLES AND STAR CLUSTERS
latter not statistically significant).
The same plot for nuclear star clusters (Figure 2) shows the opposite: NSC mass clearly correlates better with total stellar mass than it does with bulge mass: r S = 0.76 versus 0.38, with the bulge-mass correlation lacking any statistical significance. The difference in correlation coefficients actually understates the contrast, because it assumes that bulgeless spirals have nominal bulges (B/T = 0.01). In reality, the existence of nuclear star clusters in bulgeless spirals is simply an unambiguous confirmation of the basic conclusion: nuclear star cluster masses scale with the total stellar mass of their host galaxies, not with the bulge mass, and are thus not following the same host-galaxy relation as SMBHs.
We have investigated whether other galaxy parameters might also correlate with nuclear cluster mass, or with residuals from the M NSC -M relation. In particular, we have compared nuclear cluster mass with rotation velocity and total baryonic mass. In both cases, correlations exist, but they are not as strong as the correlation with total stellar mass. So the latter appears to be the defining relation between nuclear star clusters and their host galaxies.