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Register a new userExploring the Mass Segregation Effect of X-ray Sources in Globular Clusters. IV. Evidence of Black Hole Burning in $omega$ Centauri
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Using X-ray sources as sensitive probes of stellar dynamical interactions in globular clusters (GCs), we study the mass segregation and binary burning processes in $omega$ Cen. We show that the mass segregation of X-ray sources is quenched in $omega$ Cen, while the X-ray source abundance of $omega$ Cen is much smaller than other GCs, and the binary hardness ratio (defined as $L_{rm X}/(L_{rm K}f_{b})$, with $f_{b}$ the binary fraction, $L_{rm X}$ and $L_{rm K}$ the cumulative X-ray and K band luminosity of GCs, respectively) of $omega$ Cen is located far below the $L_{rm X}/(L_{rm K}f_{b})-sigma_{c}$ correlation line of the dynamically normal GCs. These evidences suggest that the binary burning processes are highly suppressed in $omega$ Cen, and other heating mechanisms, very likely a black hole subsystem (BHS), are essential in the dynamical evolution of $omega$ Cen. Through the black hole burning processes (i.e., dynamical hardening of the BH binaries), the BHS is dominating the energy production of $omega$ Cen, which also makes $omega$ Cen a promising factory of gravitational-wave sources in the Galaxy.
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Using archival {it Chandra} observations with a total exposure of 510 ks, we present an updated catalog of point sources for Globular Cluster 47 Tucanae. Our study covers an area of $sim 176.7$ arcmin$^{2}$ (i.e., with $Rlesssim7.5arcmin$) with 537 X-ray sources. We show that the surface density distribution of X-ray sources in 47 Tuc is highly peaked in cluster center, rapidly decreases at intermediate radii, and finally rises again at larger radii, with two distribution dips at $Rsim 100arcsec$ and $Rsim 170arcsec$ for the faint ($L_{X}lesssim 5.0times 10^{30} {rm erg,s^{-1}}$) and bright ($L_{X}gtrsim 5.0times 10^{30} {rm erg,s^{-1}}$) groups of X-ray sources, separately. These distribution features are similar to those of Blue Straggler Stars (BSS), where the distribution dip is located at $Rsim 200arcsec$ citep{ferraro2004}. By fitting the radial distribution of each group of sources with a generalized King model, we estimated an average mass of $1.51pm0.17 M_{odot}$, $1.44pm0.15 M_{odot}$ and $1.16pm0.06 M_{odot}$ for the BSS, bright and faint X-ray sources, respectively. These results are consistent with the mass segregation effect of heavy objects in GCs, where more massive objects drop to the cluster center faster and their distribution dip propagates outward further. Besides, the peculiar distribution profiles of X-ray sources and BSS are also consistent with the mass segregation model of binaries in GCs, which suggests that in addition to the dynamical formation channel, primordial binaries are also a significant contributor to the X-ray source population in GCs.
Using archival {it Chandra} observations with a total effective exposure of 734 ks, we derive an updated catalog of point sources in the massive globular cluster Terzan 5. Our catalog covers an area of $58.1, rm arcmin^{2}$ ($Rleq 4.3 , rm arcmin$) with 489 X-ray sources, and more than $75%$ of these sources are first detected in this cluster. We find significant dips in the radial distribution profiles of X-ray sources in Terzan 5, with the projected distance and width of the distribution dips for bright ($L_{X} gtrsim 9.5times 10^{30} {rm erg ,s^{-1}}$) X-ray sources are larger than that of the faint ($L_{X} lesssim 9.5times 10^{30} {rm erg ,s^{-1}}$) sources. By fitting the radial distribution of the X-ray sources with ageneralized King model, we estimated an average mass of $1.48pm0.11,M_{odot}$ and $1.27pm0.13,M_{odot}$ for the bright and faint X-ray sources, respectively. These results are in agreement with that observed in 47 Tuc, which may suggest a universal mass segregation effect for X-ray sources in GCs. Compared with 47 Tuc, we show that the two-body relaxation timescale of Terzan 5 is much smaller, but its dynamical age is significantly younger than 47 Tuc. These features suggest that the evolution of Terzan 5 is not purely driven by two-body relaxation, and tidal stripping effect also plays an important role in accelerating the dynamical evolution of this cluster.
Using archival {it Chandra} observations with a total effective exposure of 323 ks, we derive an updated catalog of point sources in the bulge globular cluster M28. The catalog contains 502 X-ray sources within an area of $sim475, rm arcmin^{2}$, and more than $90%$ of these sources are first detected in this cluster. We find significant dips in the radial distribution profiles of X-ray sources in M28, with the projected distance and width of the distribution dip for bright ($L_{X} gtrsim 4.5times 10^{30} {rm erg ,s^{-1}}$) X-ray sources are larger than the faint ($L_{X} lesssim 4.5times 10^{30} {rm erg ,s^{-1}}$) sources. The generalized King model fitting give a slightly larger average mass for the bright sources ($1.30pm0.15,M_{odot}$) than the faint sources ($1.09pm0.14,M_{odot}$), which support a universal mass segregation delay between heavy objects in GCs. Compared with 47 Tuc and Terzan 5, we show that the dynamical age of M28 is comparable to Terzan 5 and much smaller than 47 Tuc, but it is evolving more fast (i.e., with smaller two-body relaxation timescale) than 47 Tuc. These features may suggest an acceleration effect of cluster dynamical evolution by tidal shock in M28. Besides, we find an abnormal deficiency of X-ray sources in the central region ($R lesssim 1.5 rm~arcmin$) of M28 than its outskirts, which indicate that M28 may have suffered an early phase of primordial binary disruption within its central region, and mass segregation effect will erase such a phenomenon as cluster evolve to older dynamical age.
A calibration is made for the correlation between the X-ray Variability Amplitude (XVA) and Black Hole (BH) mass. The correlation for 21 reverberation-mapped Active Galactic Nuclei (AGN) appears very tight, with an intrinsic dispersion of 0.20 dex. The intrinsic dispersion of 0.27 dex can be obtained if BH masses are estimated from the stellar velocity dispersions. We further test the uncertainties of mass estimates from XVAs for objects which have been observed multiple times with good enough data quality. The results show that the XVAs derived from multiple observations change by a factor of 3. This means that BH mass uncertainty from a single observation is slightly worse than either reverberation-mapping or stellar velocity dispersion measurements; however BH mass estimates with X-ray data only can be more accurate if the mean XVA value from more observations is used. Applying this relation, the BH mass of RE J1034+396 is found to be $4^{+3}_{-2} times 10^6$ $M_{odot}$. The high end of the mass range follows the relationship between the 2$f_0$ frequencies of high-frequency QPO and the BH masses derived from the Galactic X-ray binaries. We also calculate the high-frequency constant $C= 2.37 M_odot$ Hz$^{-1}$ from 21 reverberation-mapped AGN. As suggested by Gierlinski et al., $M_{rm BH}=C/C_{rm M}$, where $C_{rm M}$ is the high-frequency variability derived from XVA. Given the similar shape of power-law dominated X-ray spectra in ULXs and AGN, this can be applied to BH mass estimates of ULXs. We discuss the observed QPO frequencies and BH mass estimates in the Ultra-Luminous X-ray source M82 X-1 and NGC 5408 X-1 and favor ULXs as intermediate mass BH systems (abridged).
Recent discoveries of black hole (BH) candidates in Galactic and extragalactic globular clusters (GCs) have ignited interest in understanding how BHs dynamically evolve in a GC and the number of BHs ($N_{rm{BH}}$) that may still be retained by todays GCs. Numerical models show that even if stellar-mass BHs are retained in todays GCs, they are typically in configurations that are not directly detectable. We show that a suitably defined measure of mass segregation ($Delta$) between, e.g., giants and low-mass main-sequence stars, can be an effective probe to indirectly estimate $N_{rm{BH}}$ in a GC aided by calibrations from numerical models. Using numerical models including all relevant physics we first show that $N_{rm{BH}}$ is strongly anticorrelated with $Delta$ between giant stars and low-mass main-sequence stars. We apply the distributions of $Delta$ vs $N_{rm{BH}}$ obtained from models to three Milky Way GCs to predict the $N_{rm{BH}}$ retained by them at present. We calculate $Delta$ using the publicly available ACS survey data for 47 Tuc, M 10, and M 22, all with identified stellar-mass BH candidates. Using these measured $Delta$ and distributions of $Delta$ vs $N_{rm{BH}}$ from models as calibration we predict distributions for $N_{rm{BH}}$ expected to be retained in these GCs. For 47 Tuc, M 10, and M 22 our predicted distributions peak at $N_{rm{BH}}approx20$, $24$, and $50$, whereas, within the $2sigma$ confidence level, $N_{rm{BH}}$ can be up to $sim150$, $50$, and $200$, respectively.
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