Gas Accretion by Star Clusters and the Formation of Ultraluminous X-ray Sources from Cusps of Compact Remnants
DD RAFT VERSION N OVEMBER
9, 2018
Preprint typeset using L A TEX style emulateapj v. 08/22/09
GAS ACCRETION BY STAR CLUSTERS AND THE FORMATION OF ULTRALUMINOUS X-RAY SOURCES FROMCUSPS OF COMPACT REMNANTS
J. P. N
AIMAN , E NRICO R AMIREZ -R UIZ AND D OUGLAS
N. C. L IN Draft version November 9, 2018
ABSTRACTHere we show that the overabundance of ultra-luminous, compact X-ray sources (ULXs) associated withmoderately young clusters in interacting galaxies such as the Antennae and Cartwheel can be given an alterna-tive explanation that does not involve the presence of intermediate mass black holes (IMBHs). We argue thatgas density within these systems is enhanced by the collective potential of the cluster prior to being accretedonto the individual cluster members and, as a result, the aggregate X-ray luminosity arising from the neutronstar cluster members can exceed > ergs − . Various observational tests to distinguish between IMBHs andaccreting neutron star cusps are discussed. Subject headings: accretion;black hole physics; hydrodynamics; globular clusters: general INTRODUCTION
Over the years, the existence of two distinct populations ofblack holes has been established beyond a reasonable doubt.Supermassive black holes, M > M (cid:12) , are inferred in manygalactic centers (Kormendy & Richstone 1995; Magorrian etal. 1998), while stellar mass black holes, M ∼ − M (cid:12) , havebeen identified by their interaction with companion stars (Mc-Clintock & Remillard 2006). The situation at intermediatemasses, M ∼ − M (cid:12) , is still uncertain despite recentevidence for mass concentrations within the central regionsof some globular clusters (Gebhardt et al. 2005; Ulvestad etal. 2007; Noyola et al. 2008). This evidence remains contro-versial, partly because the velocity dispersion profiles can bereproduced without invoking the presence of an intermediatemass black hole (IMBH) (Baumgardt et al. 2003,?; Anderson& van der Marel 2009).Recently, some evidence has arisen for the presence ofIMBHs in moderately young star clusters, where ultra-luminous, compact X-ray sources (ULXs) have been prefer-entially found to occur (Fabbiano et al. 2001; Trinchieri etal. 2008). Their high luminosities have been interpreted asimprints of IMBHs (Portegies Zwart et al. 2004), rather thanbinaries containing a normal stellar mass black hole (Zezas etal. 2006). In this Letter , we present an alternative explanationfor the overabundance of ULXs associated with young clus-ters in galaxies such as the Antennae and Cartwheel. In thisnew paradigm, the accretion of gas by the collective star clus-ter potential moving through the merging medium is stronglyenhanced relative to the individual rates and, as a result, theaggregate X-ray luminosity arising from the neutron star clus-ter members can exceed > ergs − . Much of the effortherein will be dedicated to understanding the conditions bywhich the collective potential of a star cluster is able to accretegas with highly enhanced rates and its effect on the integratedaccretion luminosity of the neutron star cluster members. Theconditions found in systems such as the Antennae galaxy, aswe will argue, are favorable for this type of mechanism tooperate effectively and produce an overabundance of ULXs. ULX CUSPS FROM COMPACT STELLAR CLUSTER MEMBERS Department of Astronomy and Astrophysics, University of California,Santa Cruz, CA 95064; [email protected]
ULXs are seen in the star clusters of merging galaxies, suchas the Antennae and the Cartwheel (Trinchieri et al. 2008;Zezas et al. 2006). These sources are compact in nature andin general associated with super star clusters (SSCs) - young,compact, massive clusters of stars (Zezas et al. 2002). Manyof these sources have luminosities ≥ erg s − , which sug-gest that they could be IMBHs rather than binaries containinga normal stellar mass black hole.A compact star of mass M ∗ , moving with relative veloc-ity v through a gas of ambient density ρ and sound speed c s ,nominally accretes at the Bondi-Hoyle-Lyttleton rate: ˙ M (cid:104) π ( GM ∗ ) ρ ( v + c s ) − / (Edgar 2004). For a NS of mass M ∗ = M NS = 1 . M (cid:12) and radius R NS = 10 km, the correspond-ing X-ray luminosity is given by L X = (cid:15) GM NS ˙ MR − = 10 n (cid:15) (cid:18) V
10 km / s (cid:19) − erg / s , (1)where (cid:15) ≤ n = ρ/ m p is the hydrogen numberdensity in units of cm − and V = ( v + c s ) / . The integrated X-ray accretion luminosity of N NS neutron star cluster membersis then given by L X = 10 ( N NS / ) n (cid:15) ( V /
10 km / s) − erg / s.In order for an aggregated accretion model to successfullydescribe ULXs, the predicted X-ray luminosity must naturallyspan the range of observed luminosities. This requires that theresulting speed V not be too large but more importantly thatthe external density be relatively high. Direct observationalsearches for cluster gas in the form of molecular, neutral, andionized hydrogen have yielded non-detections, implying up-per limits on the total gas content in the range of 0.1-10 M (cid:12) (Smith et al. 1995). In a search for ionized gas Knapp et al.(1996) found upper limits of 0.1 M (cid:12) within about one coreradius for the clusters, implying n H + ≤
50 cm − .A simple argument can be made to determine a lower limitto the density of the gas in the cores of globular clusters (GCs)in the absence of gas retention (Pfahl & Rappaport 2001).Suppose that the inner core of a GC contains N ∗ = 10 N ∗ , red giant stars, and so their mean separation is r ⊥ = 6 . × N − / ∗ , r c , − cm, where r c = 0 . r c , − pc. A lower limit on thewind density can be made by assuming that the wind of eachof the stellar member extends only to its closest neighbors. a r X i v : . [ a s t r o - ph . H E ] O c t Naiman et al.In this approximation, n > n w = 80 N / ∗ , r − , − v − , ˙ M w , − cm − ,where v w = 10 v w , km s − and ˙ M w = 10 − ˙ M w , − M (cid:12) yr − arethe velocity and mass loss rate of the stellar core members.When the cluster gravity and the interaction between stellarwinds is taken into account, we suspect that the gas densitycan be larger than this value.For clusters that are moving through a relatively densemedium, as in Antennae galaxy for which CO measurementsgive n ∼ cm − (Zhu et al. 2003), the collective externalmass accretion is likely to shape the luminosity function forthe accreting distribution of neutron stars. A density of 10 cm − , however, gives an aggregate neutron star luminosity ofabout L X = 10 ( N NS / ) ( (cid:15)/ . V /
10 km / s) − erg/s, whichis not high enough to explain ULXs (Kalogera et al. 2004;Maccarone et al. 2007; Pfahl & Rappaport 2001). If, however,the collective potential of the cluster was able to significantlyincrease the surrounding gas density prior to being accretedonto the individual neutron star members, the aggregate X-ray luminosity could exceed 10 erg/s. It is to this problemthat we now turn our attention. THE CLUSTER MODEL AND NUMERICAL METHOD
To test the gas density enhancement efficiency of a starcluster, we simulated a cluster potential moving through themerging galaxy medium at various typical velocities usingFLASH, a parallel, adaptive mesh refinement hydrodynam-ics code. This scheme, and tests of the code are described inFryxell et al. (2000). All star clusters are modeled here with aPlummer potential: Φ = GM c ( r + r ) / (2)Here, M c is the total cluster mass, taken to be 3 . × M (cid:12) (Zhang & Fall 1999; Gilbert & Graham 2007). We use sev-eral typical SSC cluster core radii, r c = 1 , , ±
1) pc. The core radius is expected to be significantlyless than the half-light radius.Our main goal is to examine the ability of a potential to ac-crete gas as a function of the relative speed of the potentialthrough the gas, and the gas temperature. Our star cluster,here modeled as a Plummer potential, has been therefore setin motion through an initially uniform medium. The speed ofsound far away from the cluster is taken to be c s ∼
10 km s − ,which is consistent with the inferred intracluster medium tem-perature ∼ K in the Antennae galaxy (Gilbert & Graham2007). Based on observations of several cluster knots in theAntennae galaxy, which indicate intracluster velocity disper-sions of order 10 km s − (Whitmore et al. 2005), the initialMach number of the cluster relative to the gas is varied be-tween µ ∞ = v ∞ / c s = 0 . .
0. Here, v ∞ and c s are the veloc-ity of the medium and the sound speed at infinity, respectively.The gas within the dense medium has a temperature selectedto give the desired value of c s and a density ρ ∞ = 10 − g cm − ,chosen to match the intracluster densities as derived from COmeasurements (Zhu et al. 2003).The effects of self gravity of the gas are ignored. This isadequate for most of our models, for which the accreted massis less than the mass responsible for the potential. To improvethe controlled nature of the models, we do not explicitly in-clude radiative heating or cooling. The gas, instead, evolves adiabatically. The effects of radiative equilibrium are approx-imated by having the gas evolve with an adiabatic constant γ = 1 .
01, giving nearly isothermal behavior, which is consis-tent with the presence of a large quantity of dust near theseclusters as inferred from infrared observations (Brandl et al.2005). In cases where sufficient gas is accreted for it to be-come self-shielded, cooling could decrease the temperature ofthe gas significantly, potentially enhancing the accretion ratebeyond the values computed here.We use inflow boundaries on one side of our rectangulargrid to simulate the cluster’s motion through the ambient me-dia. We run our simulations from initially uniform back-ground density until a steady density enhancement forms inthe cluster center, which usually takes a few 10-100 soundcrossing times. Several models were run longer to test conver-gence and density enhancements were found to change onlyslightly with longer run times. We further tested convergenceof our models for several resolutions and domain sizes. Alltests produced similar density enhancements to those shownhere. After hundreds of sound crossing times, the flow is rel-atively stable, and does not exhibit the “flip-flop” instabilityseen in two dimensional simulations (Blondin & Pope 2009). RESULTING MASS DENSITY PROFILES AND ULX CUSPS
The accretion of ambient gas by moving bodies is a clas-sical problem. Many studies have been focused on the flowaround compact stars with a point mass potential. Althoughclusters have much larger masses than individual stars, theirpotential is relatively shallow and the classical treatment de-rived for a point-mass potential is only a fair approxima-tion far from the cluster when GM c / r c (cid:29) c + v . When GM c / r c (cid:46) c + v , the collective potential alters the local gasproperties before the gas is accreted onto the individual starswithin the cluster.Figure 1 shows the resulting density profiles for star clus-ters with GM c / r c ∼ c + v for a variety of core radius andrelative motions with respect to the external medium combi-nations. For small r c , the potential starts to resemble that ofa point mass and, as a result, the density enhancement in thecentral regions is very significant. A density enhancement isobserved to persist as long as the sound speed or the rela-tive velocity of the ambient medium is greater than the cen-tral velocity dispersion of the cluster. The enhanced densityprofiles within the cluster differ from the classical Bondi so-lution, and, for low Mach numbers, are better described bythe cluster-Bondi analytic profiles derived by Lin & Murray(2007) as depicted in Figure 2. The profiles begin to deviatesignificantly from the cluster-Bondi solutions for high Machnumbers (inset in Figure 2).The flow pattern around a star cluster at large relative ve-locities is multi-dimensional and complex (Figure 1). In theframe of the potential, the gas streamlines are bent towardsthe cluster center. Some shall intersect the center, while oth-ers converge along a line behind it. The convergence speedof the gas determines the reduction in its velocity relative tothe potential due to shocks, and therefore whether or not thegas is accreted. In line with the conventional treatment, clus-ters moving with respect to the interstellar medium at increas-ing supersonic velocities will have density enhancements thatare progressively lower and significantly more offset from thecluster’s center. In these cases the aggregate mass accretionrate of the central neutron star is not significantly increasedand stars accrete gas as though they move through the exter-nal medium independently. Because several gas knots in theAntennae galaxy have velocities relative to the cluster of or-der the sound speed of the ambient medium, gas within thesecluster cores would achieve high densities. Within this en-vironment, accretion by the individual cluster members willbe enhanced greatly relative to their rate of accretion directlyfrom the ambient gas. X-ray Luminosities from Enhanced Accretion Rates
Accretion and emission from the neutron star clusterstrongly depends on the radial distribution of both compactremnants and gas. In this model, we calculate the expectedX-ray emission from the neutron star members in the clusterusing two extreme examples for the radial distribution of com-pact remnants. The first one is based on Fokker-Planck mod-els of a core collapsed (centrally condensed) globular cluster(Dull et al. 1997), and the second simply assumes that the neu-tron stars, containing 1% of the total mass, follow the radialstellar mass distribution. The absorption corrected X-ray lu-minosities and characteristic emission frequencies of the neu-tron star cusps are calculated assuming a neutral absorbingmedium with solar metallicity. Note that in this paper we con-sider neutron stars to be magnetic field free. If their fields arestrong enough, the propeller effect may reduce the X-ray lu-minosity of neutron stars (Menou et al. 1999).Figure 3 shows the aggregate X-ray luminosity of the ac-creting neutron star cluster as a function of the relative Machnumber for both centrally condensed and non-condensedcompact remnant distributions. The upper panel shows, forthe centrally condensed case, how the absorption correctedX-ray luminosities vary with both photon energy and radialposition within the cluster. As argued above, clusters mov-ing with increasing supersonic velocities will have densityenhancements that are progressively lower and significantlymore offset from the cluster’s center. As a result, the aggre-gate X-ray luminosity rapidly decreases with increasing Machnumber (although less sharply for more extended clusters).While the density enhancement increases monotonically withdecreasing relative velocity, so does the corresponding pho-toionization absorption. These two competing effects producea maximum in the X-ray luminosity of the cluster at about µ ∞ = 2. Most of the luminosity comes from 95% (60%) of allneutron stars in the condensed (non-condensed) distributionswith X-ray luminosities ranging between 2 × (10 ) and4 × (2 × ) erg s − . In this regime, the results dependweakly on the assumed radiation spectra of the individual ac-creting members. DISCUSSION
Many studies have been focused on the flow around com-pact stars with a point mass potential. Although clusters havemuch larger masses than individual stars, their potential is rel-atively shallow. In this paper we consider the efficiency ofaccretion in these cluster potentials, and show that when thesound speed or the relative velocity of the ambient mediumis less than the central velocity dispersion of the cluster, thecollective potential alters the local gas flow before the gas isaccreted onto the individual stars within the cluster. Accretiononto these dense stellar cores at the inferred rate can lead tothe onset of ULX sources.While there are no stellar clusters observed in the Galac-tic disk which bear these anticipated properties (the relativevelocity of the halo clusters to the interstellar medium is inthe range of 100 km/s), observations of several cluster knotsin the Antennae indicate intracluster relative velocities that comparable to the central velocity dispersions (Whitmore etal. 2005). Based on the results of the current work, we showthat accretion by individual compact stars in the centers ofsuch systems is enhanced greatly relative to their rate of ac-cretion directly from the ambient gas, and conclude that thisprocess may be relevant for explaining the origin of ULXsources in these extraordinary clusters. Illumination of nearbygas clouds by these sources may also lead to reprocessed in-frared, optical and ultraviolet emission. Finally, the sourcesmay leave trails of denser and likely hotter gas behind themas they plough through the gas.A way to distinguish between an IMBH (Portegies Zwartet al. 2004) and an accreting neutron star cusp is via time-dependent observations. The emission from a relativistic re-gion of a IMBH might vary on time-scales of seconds. Theemission of a large number of statistically independent blackholes and neutron stars should be considerably less variable: ∆ t ≤ r c / c s ∼ yr. Observations find that a handful of theX-ray sources in the Antennae galaxy are indeed variable al-beit on timescales that are larger than a few years (Zezas et al.2006). Such variability might be explained if only a moderatefraction of the compact stars dominate the total luminosity.Such compact isolated accretors will probably have unusualtime-variability properties as their discs may be much largerthan the typical discs of X-ray binaries, and indeed they aremissing the perturbing influence of the secondary. On theother hand, accretion disc feeding in these sources will bevariable itself, leading to variability on variety of time-scales.Although accretion disk spectra are notoriously difficult tocalculate from first principles, an IMBH and a cluster coremay also have observably different spectra. It has been sug-gested that a cool multicolor disk spectral component, mightindicate the presence of an IMBH (Miller et al. 2003). Thisis understood as following. The larger mass of the BH accre-tor, the lower the temperature of the inner edge of the disk,which scales as T i ∝ ( M BH ˙ M / r i ) / ∝ ˙ M / M − / for a simplethin-disk model. Since for our model, individual neutron starsources have T i ∼ T i ∼
30 eV. Thus, an association of theULXs with an IMBH, as opposed to a accreting distributionof compact remnants, could be made on the basis of a verysoft observed spectral component. We know of no reportedobservations of such components.We thank Jason Kalirai and Glenn van de Ven for usefuldiscussions. The software used in this work was in part devel-oped by the DOE-supported ASCI/Alliance Center for Astro-physical Thermonuclear Flashes at the University of Chicago.Computations were performed on the Pleaides UCSC com-puter cluster. This work is supported by NSF: PHY-0503584(JN and ER), NASA: NNX08AL41G (JN and DL) and TheDavid and Lucile Packard Foundation (ER). Naiman et al. F IG . 1.— The flow pattern around a star cluster set in motion throughan initially uniform medium with varying core dimensions (r c ) and relativespeeds ( µ ∞ ). Color bars show density cuts through the xy -plane in units oflog(g / cm ). F IG . 2.— Density profile for a model with core radius r c = 1 pc and µ ∞ =2 .
0. Solid black line shows a cut along the x-axis for the simulated cluster.The the dotted line is the Bondi solution for a stationary point mass, while thedashed line gives the renormalized Bondi-Hoyle-Lyttleton solution modifiedfor a cluster potential as derived by Lin & Murray (2007). These modifiedsolutions provide a good description of the density profile for µ ∞ ≤ Inset:
The dotted line is the unnormalized cluster-Bondi solution while the lightpink, black and red lines show the numerical profiles for µ ∞ = 2 .
0, 3 .
0, and4 .
0, respectively.
Naiman et al. F IG . 3.— X-ray luminosities from enhanced accretion rates. Center:
Theabsorption corrected X-ray luminosities from an accreting neutron star mem-bers in a star cluster as a function of µ ∞ calculated using two extreme ex-amples for the radial distribution of compact remnants. Triangles are for r c = 2pc while diamonds are for r c = 1pc. Upper:
Spectral and luminositydecomposition as a function of distance from the cluster’s center for a modelwith µ ∞ = 0 . r c = 1pc. Right: