New Limits on an Intermediate-Mass Black Hole in Omega Centauri. Ii. Dynamical Models

Abstract

We present a detailed dynamical analysis of the projected density and kinematical data available for the globular cluster ω Centauri. We solve the spherical anisotropic Jeans equation for a given density profile to predict the projected profiles of the RMS velocityσ(R), in each of the three orthogonal coordinate directions (line of sight, proper motion radial, and proper motion tangential). The models allow for the presence of a central dark mass, such as a possible intermediate-mass black hole (IMBH). We fit the models to new HST star count and proper motion data near the cluster center presented in Paper I, combined with existing ground-based measurements at larger radii. The projected density profile is consistent with being flat near the center, with an upper limit γ 0.07 on the central logarithmic slope. The RMS proper motion profile is also consistent with being flat near the center. The velocity anisotropy profile, distance, and stellar mass-to-light ratio are all tightly constrained by the data, and found to be in good agreement with previous determinations by van de Ven et al.To fit the kinematics we consider anisotropic models with either a flat core (γ = 0) or a shallow cusp (γ = 0.05). Core models provide a good fit to the data with M BH = 0; cusp models require a dark mass. If the dark mass in cusp models is an intermediate-mass black hole (IMBH), then M BH = (8.7 ± 2.9) × 10 3 M ⊙ ; if it is a dark cluster, then its extent must be 0.16 pc. Isotropic models do not fit the observed proper motion anisotropy and yield spuriously high values for any central dark mass. These models do provide a good fit to the Gauss-Hermite moments of the observed proper motion distributions (h 4 = −0.023 ± 0.004, h 6 = 0.001 ± 0.004). There are no unusually fast-moving stars observed in the wings of the proper motion distribution, but we show that this does not strongly constrain the mass of any possible IMBH. The overall end-result of the modeling is an upper limit to the mass of any possible IMBH in ω Centauri: M BH 1.2 × 10 4 M ⊙ at ∼ 1σ confidence (or 1.8 × 10 4 M ⊙ at ∼ 3σ confidence). The 1σ limit corresponds to M BH /M tot 0.43%. We combine this with results for other clusters and discuss the implications for globular cluster IMBH demographics. Tighter limits will be needed to rule out or establish whether globular clusters follow the same black hole demographics correlations as galaxies. The arguments put forward by Noyola et al. to suspect an IMBH in ω Centauri are not confirmed by our study; the value of M BH they suggested is firmly ruled out.

N-body modelling of globular clusters: masses, mass-to-light ratios and intermediate-mass black holes

“…7 for example shows that their isotropic no-IMBH model is already in very good agreement with the observed velocity dispersion profile, while it provides a very poor fit in our case. It is therefore not clear if the inclusion of radial anisotropy would change the velocity dispersion profile by a large enough amount to bring our models without IMBHs into agreement with the observations, especially since van der Marel & Anderson (2010) and the proper motion data of Watkins et al show that ω Cen is essentially isotropic in its center and only mildly radially anisotropic beyond 200 arcsec. It seems more likely that ω Cen contains either a dark cluster of compact remnants or a population of low-mass stars in its center on top of what mass segregation is already producing in our models, or a ∼ 40,000 M⊙ IMBH.…”

“…Noyola et al (2010) and Jalali et al (2012) reported evidence for a 50000 M⊙ IMBH in the globular cluster ω Cen based on VLT-FLAMES integrated spectra of the central parts of the cluster and detailed N -body models. In contrast, van der Marel & Anderson (2010) found that the velocity dispersion increase in the center can be explained by a radially anisotropic velocity dispersion profile and derived a 1σ upper limit of only 12000 M⊙ for any possible IMBH.…”

“…have argued that radially anisotropic velocity dispersion profiles could create a similar increase in the velocity dispersion profile as a central IMBH. In addition, van der Marel & Anderson (2010) found that anisotropic models provided a better fit to the velocity dispersion profile of ω Cen than isotropic models with central IMBHs. While the models of van der Marel & Anderson (2010) took mass segregation of stars into account, it is not clear how realistic their approach was.…”

Low-mass black holes as the remnants of primordial black hole formation

“…These most massive clusters also tend to show a wider range of stellar ages and chemical compositions than is seen in typical globular clusters, suggesting that they were formed gradually rather than as a single unit. The three prominent stripped galaxy candidates that are in our own local neighbourhood all show dynamical evidence for a central 10 4 M } black hole [90][91][92] , although the detections are still controversial 93 . Radiation from these putative black holes has not yet been detected 75,94 .…”

TheGaia-ESO Survey: Kinematics of seven Galactic globular clusters

“…Internal rotation may also play an indirect role in the open question of whether there are intermediate-mass black holes (IMBH) in some GCs. In fact, the detection of strong gradients in the velocity dispersion profile toward the cluster core is often interpreted as a hint of the presence of an IMBH (Baumgardt et al 2005), but the evidence gathered so far in support of the existence of IMBHs is inconclusive and controversial, and none of the published studies (van der Marel & Anderson 2010;Lützgendorf et al 2011;Lanzoni et al 2013) did consider differential rotation, which, together with anisotropy, can yield gradients in the velocity dispersion profiles Bianchini et al 2013). Finally, recent investigations indicate that rotation could be a key ingredient in the formation of multiple generations of stars in GCs (Bekki 2010;Mastrobuono-Battisti & Perets 2013).…”