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The globular cluster NGC 6388 $XMM$-Newton and $Chandra$ observations_图文

Astronomy & Astrophysics manuscript no. nucita February 2, 2008

c ESO 2008

The globular cluster NGC 6388: XM M -Newton and Chandra observations
A.A. Nucita1 , F. De Paolis2 , G. Ingrosso2 , S. Carpano1 , and M. Guainazzi1

arXiv:0712.1134v2 [astro-ph] 17 Dec 2007


XMM-Newton Science Operations Centre, ESAC, ESA, PO Box 78, 28691 Villanueva de la Ca? ada, Madrid, Spain n Dipartimento di Fisica, Universit` del Salento, and INFN, Sezione di Lecce, CP 193, I-73100 Lecce, Italy a

Submitted: XXX; Accepted: XXX ABSTRACT Context. By studying the optical brightness surface density of the globular cluster NGC 6388, it has been recently proposed that it harbors a central intermediate-mass black hole with mass ? 5.7 × 103 M⊙ . Aims. We expect that the compact object in the center of NGC 6388 emits radiation in the X-ray band as a consequence of the accretion from the surrounding matter. We searched for XM M -Newton and Chandra observations towards NGC 6388 to test this hypothesis. Methods. We determine both the hardness ratios and luminosity with a minimum set of assumptions for each of the identi?ed ?eld sources. Results. The Chandra satellite disentangles several point-like X-ray sources, probably low mass X-ray binaries, well within the core radius of the globular cluster. However, three of them, coinciding with the cluster center of gravity, remain unresolved. Their total luminosity is LObs ? 2.7 × 1033 erg s?1 . If one of these sources is the X-ray counterpart X of the intermediate-mass black hole in NGC 6388, the corresponding upper limit on the accretion e?ciency, with respect to the Eddington luminosity, is 3 × 10?9 . This measurement could be tightened if moderately deep radio observations of the ?eld were performed. Key words. (Galaxy:) globular clusters: general – (Galaxy:) globular clusters: individual: NGC 6388

1. Introduction
Over the last few years, several pieces of evidence have been accumulated pointing to the presence of an intermediatemass black hole (hereafter IMBH) with mass ? 103 M⊙ in a globular cluster. The ?rst evidence comes from the extrapolation to globular clusters of the MBH ? MBulge relation found for super massive black holes in galactic nuclei (for details see Magorrian et al. 1998), which leads to the prediction of the existence of IMBHs. The second hint is related to the discovery of the so called ULXs, i.e. ultra-luminous, compact X-ray sources (with luminosity greater than ? 1039 erg s?1 ), which are believed to be IMBHs rather than binaries containing a normal stellar mass black hole (Miller & Colbert 2003). More indirect evidence of the existence of IMBHs comes from the study of the central velocity dispersion of stars in speci?c globular clusters. For example, by using the velocity dispersion measurements, Gerssen et al. (2002, 2003), and Gebhardt et al. (2002) (but see also Pooley & Rappaport 2006) proposed that IMBHs may exist in M15 and G1 (an M31 globular cluster) with masses about 103 -104 M⊙ 1
Send o?print requests to: A. A. Nucita 1 The observed brightness and the velocity dispersion pro?les of the G1 (Baumgardt et al. 2003) and M15 (Baumgardt et al. 2005a) globular clusters can be well ?tted by usual evolutionary King models. When the mass segregation e?ect is taken into account, a sharp increase in the mass-to-light ratio towards the cluster core is found, thus avoiding the necessity of a central IMBH.

Objects of the IMBH size are predicted by detailed Nbody simulations (see e.g. Portegies Zwart et al. 2004), according to which an IMBH forms as a consequence of merging of massive stars. Furthermore, at least for the cases of M 15 and 47 Tucane, the precise measurements of P and ˙ ˙ P of four millisecond pulsars (with negative P ) has allowed De Paolis et al. (1996) to put rather stringent upper limits to the mass of the central black hole of ? 103 M⊙ . In addition to the previous evidence, it is also expected that globular clusters with a central IMBH are characterized by a cusp in the inner stellar density pro?le (i.e. ρ ∝ r?7/4 ), so that the projected density pro?le, as well as the surface brightness, should also have a cusp with slope ?3/4. As shown by Miocchi (2007), the globular clusters that most likely harbor an IMBH are those having the projected photometry well ?tted by a King pro?le, except in the central part where a power law deviation (α ? ?0.2) from a ?at behavior is expected. However, as pointed out by Baumgardt et al. (2003, 2005a), a similar behavior is also expected in a constant core density King pro?le (α ? 0) when the mass segregation e?ect of stellar remnants is considered. This explanation, however, is uncertain because it depends on the assumption that all the neutron stars and/or stellar mass black holes are retained in the cluster so that the existence of a central IMBH cannot be completely ruled out (see Gebhardt et al. 2005). On the other hand, the errors with which the slopes of central densities can be determined are of the order 0.1 ? 0.2 (Noyola & Gebhardt 2006), so that surface density pro?les do not give clear ev-


Nucita et al.: XM M -Newton and Chandra observation of NGC 6388

idence of the existence of IMBH in globular clusters, thus requiring observations in di?erent bands. Among all the known globular clusters in our Galaxy, NGC 6388 is one of the best candidates to host an IMBH (Baumgardt et al. 2005b). NGC 6388 is a globular cluster at distance d ? 11.5 kpc (with center at coordinates 0 ′ ′′ A.R.= 17h 36m 17.6s , DEC= ?44 44 08.2 ) and with an es6 timated mass of 2.6 × 10 M⊙ (Lanzoni et al. 2007). By using a combination of high resolution (HST ACS-HCR, ACS-WCS and WFPC2) and wild-?eld (ESO-WFI) observations, Lanzoni et al. (2007) derived the center of gravity, the projected density pro?le and the central surface brightness pro?le of NGC 6388. While the overall projected pro?le is well ?tted by a King model (with concentration parameter c = 1.8 and core radius rc ? 7.2′′ ), a signi?cant power law (with slope α ? ?0.2) deviation from a ?at core behavior has been detected within ? 1′′ . This was interpreted as the signature of the existence of an IMBH with mass ? 5.7 × 103 M⊙ at the center of NGC 6388. We expect that the central IMBH emits signi?cant radiation in the X-ray band as a consequence of the accretion of the surrounding matter. Thus, we searched for both XM M -Newton and Chandra observations towards the globular cluster NGC 6388. The paper is structured as follows: In Sect. 2, we brie?y describe the XM M -Newton and Chandra observations and data reduction. In Sect. 3, we describe the main characteristics of the sources detected within a few core radii of the globular cluster and in Sect. 4 we address our main results and conclusions.

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17:36:00.0 35:55.0

Fig. 1. The XMM-Newton ?eld of view (PN camera) centered on NGC 6388. The green circle has a radius comparable to the half mass radius (? 0.67′ ) of the globular cluster. 2.7+0.3 ×1021 cm?2 , Γ = 2.4+0.1 and N = 2.2+0.2 ×10?4 for ?0.3 ?0.1 ?0.2 the column density2 , power law index and normalization, respectively. The ?ux in the 0.5-7 keV is F0.5?7 = 4.0+0.2 × 10?13 erg ?0.2 ?2 ?1 cm s which, for the globular cluster distance of ? 11.5 kpc, corresponds to a luminosity of L0.5?7 ? 6.31 × 1033 erg s?1 . Note that all the uncertainties quoted above are given at a 90% con?dence level.

46:00.0 47:00.0
20 40 60 80

2. XMM-Newton and Chandra observation and data reduction
The globular cluster NGC 6388 was observed in March 2003 (observation ID 0146420101) with both the EPIC MOS and PN cameras (Turner et al. 2001; Str¨ der et al. 2001) operu ating with the medium ?lter mode. The EPIC observation data ?les (ODFs) were processed using the XMM-Science Analysis System (SAS version 7.0.0). Using the latest calibration constituent ?les currently available, we processed the raw data with the emchain and epchain tools to generate calibrated event lists. After screening with standard criteria, as recommended by the Science Operation Centre technical note XMM-PS-TN-43 v3.0, we rejected any time period a?ected by soft proton ?ares. The remaining time intervals resulted in e?ective exposures of ? 2.5 × 104 ks, ? 2.4 × 104 ks, and ? 1.3 × 104 ks for MOS 1, MOS 2, and PN, respectively. In Fig. 1, the XMM-Newton observed ?eld of view (PN camera) is shown. The green circle is centered on NGC 6388 and has a radius equal to the half mass radius of the globular cluster. The source spectra were extracted in a circular region centered on the nominal position of the target in the three EPIC cameras, while the background spectra were accumulated in annuli around the same coordinates. The resulting spectra were rebinned to have at least 25 counts per energy bin. The spectra were simultaneously ?tted with XSPEC (version 12.0.0). In Fig. 2, we show the MOS 1, MOS 2, and PN spectra for NGC 6388 and the respective ?ts. The best-?tting model was an absorbed power law (χ2 /ν=1.14 for ν = 147). We left all the parameters free, yielding NH =

normalized counts s?1 keV?1





?S χ2


?2 0.5 1 2 5

Energy (keV)

Fig. 2. The simultaneous ?t to the MOS 1 (red), MOS 2 (black), and PN (green) data with a model based on an absorbed power law (see text for more details). The information that we can get from XM M -Newton data are important in obtaining an overall description of
2 Within the error, the column density obtained from the ?t procedure is compatible with that due to gas in our Galaxy along the line-of-sight to NGC 6388, i.e. NH ? 2.5 × 1021 cm?2 (Dickey & Lockman 1990).

Nucita et al.: XM M -Newton and Chandra observation of NGC 6388


Table 1. We report some useful parameters for the globular cluster NGC 6388 as given in Harris (1996). The columns represent the distance to NGC 6388, the core radius, the half mass radius, the central luminosity density, the concentration as derived by a King ?t to the photometric data, the total magnitude and mass.
D(kpc) 11.5 Rc (arcmin) 0.12 RH (arcmin) 0.67 log(ρc )(L⊙ /pc3 ) 5.29 c 0.17 Vt 6.72 M (×106 M⊙ ) 2.6

Table 2. Properties of the observed discrete sources in NGC 6388 (see text for the source 14*).
Source 1 2 ....... 3 ....... 4 ....... 5 ....... 6 ....... 7 ....... 8 ....... 9 ....... 10 ..... 11 ..... 12 ..... 13 ..... 14* ... Net (counts) (0.5-7 keV) 172.0 ± 13.3 195.1 ± 14.2 527.1 ± 23.0 37.0 ± 6.3 125.1 ± 11.4 41.9 ± 6.8 134.7 ± 11.9 87.0 ± 9.8 109.0 ± 10.6 355.0 ± 19.1 78.1 ± 8.8 108.1 ± 10.7 127.8 ± 11.7 789.6 ± 28.8 HR1 (S ? M)/(S + M) 0.26 ± 0.09 -0.18 ± 0.11 0.53 ± 0.04 -0.12 ± 0.20 0.80 ± 0.06 -0.04 ± 0.19 0.66 ± 0.07 0.30 ± 0.13 0.25 ± 0.11 0.54 ± 0.05 -0.23 ± 0.13 -0.18 ± 0.13 0.14 ± 0.10 0.38 ± 0.04 HR2 (M ? H)/(M + H) 0.20 ± 0.09 -0.52 ± 0.07 0.96 ± 0.01 -0.04 ± 0.21 0.95 ± 0.03 -0.07 ± 0.20 0.89 ± 0.04 0.18 ± 0.13 0.27 ± 0.11 0.97 ± 0.02 0.02 ± 0.15 -0.11 ± 0.14 0.30 ± 0.11 0.58 ± 0.03 HR3 (S ? H)/(S + H) -0.06 ± 0.10 -0.38 ± 0.07 0.86 ± 0.04 0.08 ± 0.20 0.60 ± 0.21 -0.03 ± 0.20 0.57 ± 0.16 -0.12 ± 0.16 0.02 ± 0.13 0.91 ± 0.03 0.25 ± 0.13 0.07 ± 0.12 0.17 ± 0.12 0.26 ± 0.06
Abs Cor Fx (Fx ) (×10?14 cgs) 2.9 (3.7) 3.3 (4.2) 8.9 (11.2) 0.6 (0.8) 2.1 (2.7) 0.7 (0.9) 2.3 (2.9) 1.4 (1.8) 1.8 (2.3) 6.0 (7.6) 1.3 (1.6) 1.8 (2.3) 2.2 (2.7) 13.4 (16.8)

LAbs (LCor ) x x (×1032 cgs) 4.6 (5.8) 5.2 (6.6) 14.0 (17.6) 0.9 (1.2) 3.3 (4.2) 1.1 (1.4) 3.6 (4.6) 2.2 (2.8) 2.8 (3.6) 9.4 (11.9) 2.0 (2.5) 2.8 (3.6) 3.4 (4.2) 21.1 (26.5)

the X-ray radiation coming from NGC 6388. However, the Chandra satellite has a much better angular resolution than the XM M -Newton telescope and therefore it is worth using Chandra to verify whether the emission detected by XM M Newton is due to a single source rather than superpositions of several bright X-ray sources. The globular cluster was observed by Chandra with the ACIS-S camera (for ? 45 ks, observation ID 5505). In our analysis, we used the event 2-type ?les and followed the standard procedures for analysis of Chandra data using the CIAO version 3.4 tool suite. The background level during the observation was nominal. We created images in the full (F=0.5-7 keV), soft (S=0.5-1.5 keV), medium (M=1.5-2.5 keV) and hard (H=2.5-7 keV) bands, and created a true color X-ray image of the globular cluster (given in Fig. 3). The X-ray emission towards NGC 6388 detected by the XM M -Newton satellite is associated with several discrete sources. We searched in the images in each band for discrete sources by using the CIAO celldetect tool with a threshold signal-to-noise detection value of 3. In the following, we will treat only the sources detected within ? 2 core radii from the NGC 6388 center. This resulted in the detection of 16 discrete sources well within the half mass radius (? 40′′ ) of NGC 6388. Of the detected sources, 9 are contained within the globular cluster core radius (? 7′′ ), while 3 are close to the NGC 6388 center of gravity, which is 0 ′ ′′ located at A.R.= 17h 36m 17.23s and DEC= ?44 44 07.1 (Lanzoni et al. 2007) with an uncertainty of ? 0.3′′ in both coordinates. The absolute errors associated with Chandra astrometry is ? 1′′ . The detected X-ray sources appear to be associated with the globular cluster NGC 6388. Based on the Log NLog S relationship of Giacconi et al. (2001), the estimated number of the background sources (with ?ux greater than

the minimum detected ?ux, i.e. ? 8 × 10?15 erg cm?2 s?1 ) contained within the cluster half mass radius is ? 10?2 . In Fig. 4, we show the detected discrete sources in the Chandra 0.5-7 keV image (right panel) as the encircled ones (each source being labeled with an increasing number). In left panel of the same ?gure, we show a 29.1′′ × 28.4′′ HST ACS-HRC image (?lter V F555W) of the same ?eld of view. The red solid circle represents the NGC 6388 core, while the dashed circle is centered on the globular cluster center of gravity and has a radius of ? 1.3′′ as the sum of the uncertainties of the center of gravity and the absolute position error of Chandra. We estimated the counts of each source from an aperture including most of the observed emission3 . The background has been estimated by using annuli around each source when possible, or circles with the same extraction region radius otherwise (excluding any encompassed source). For each source, we extracted the net number of counts in the full band and evaluated the hardness ratios HR1 = (S ? M)/(S + M), HR2 = (M ? H)/(M + H) and HR3 = (S ? H)/(S + H), where S, M and H correspond to the net counts in the soft, medium and hard bands, respectively. We give the results of the analysis in Table 2, where the counts in the 0.5-7 keV band, the hardness raAbs Cor tios and the absorbed (Fx ) and corrected (Fx ) ?uxes are shown. In the last column, the absorbed (LAbs ) and x corrected luminosity (LCor ) of each source (in the 0.5x 7 keV) has been determined assuming a Γ = 1.7 power law absorbed by the Galactic line-of-sight column density NH ? 2.5 × 1021 cm?2 . The three sources (labeled as 14*) present in the globular cluster center should be viewed cautiously: since we
In the case of point-like sources, the aperture radius was ? 1.3′′ , which corresponds to an encircled energy of ? 90% at 1.4 keV.


Nucita et al.: XM M -Newton and Chandra observation of NGC 6388

Fig. 3. Chandra/ACIS images in the soft, medium and hard bands. From the left to the right, the soft, soft+medium and soft+medium+hard images are shown.

Fig. 4. A comparison of the Chandra and HST ACS-HRC ?elds of view towards NGC 6388 is given. The red solid circles represent the globular cluster core with radius ? 7.2′′ , while the red dashed circles (? 1.3′′ ) are centered on the center of gravity (see text for more details). LOW RESOLUTION IMAGE (see the published version of the paper). cannot resolve them in a better way we refer to the cumulative net counts and luminosity. and HRhard = (H ? M )/(S + M + H) are given. In the same plot, we give the expected set of color-color contours for bremsstrahlung (grey region) and power law (black region) components, respectively. In both the two regions, the equivalent hydrogen column NH (taken varying between 1020 cm?2 and 1022 cm?2 ) is associated with almost horizontally-oriented lines. The temperature kT of the bremsstrahlung models (taken in the range 0.1-2.5 keV) is associated with primarily vertical-lines. In the case of the power law region, vertical orientation is associated with values of the parameter Γ in the range 0.1-2.5. According to the classi?cation scheme of Jenkins et al. (2005), to which we refer for more details, most of the sources with HRsoft > ?0.2 seem to be low mass X-ray bi? naries, with the source 2 possibly being a high mass X-ray binary containing a neutron star. The source labeled as 14* is positioned in a region of the color-color diagram where its spectral properties are not well ?tted by a single spectral component (represented

3. The inner X-ray cluster in NGC 6388
As we have seen in the previous Section, the better angular resolution of the Chandra satellite with respect to that of XM M -Newton, allowed us to detect several discrete sources within a few core radii of NGC 6388. The main properties of the detected sources are given in Table 2. Any classi?cation of the detected sources requires an understanding of their spectral shapes. Due to the low count rates of most of the detected sources, formal spectral modeling is only possible for the brightest ones (namely those with more than 300 counts and labeled as 3, 10 and 14*). For the other sources, a rough classi?cation can be done by using a color-color diagram (see Fig. 5) in which the two hardness ratios HRsoft = (M ? S)/(S + M + H)

Nucita et al.: XM M -Newton and Chandra observation of NGC 6388


by the two shaded regions), even if it seems marginally consistent with power law models with large exponents (Γ greater than 2.5, typical of X-ray emission from IMBHs, which are expected to be soft sources). This was expected since we extracted the cumulative spectrum of what appeared to be the superposition of three di?erent sources (possibly LMXRBs), each of which has di?erent spectrum properties. Finally, note the existence of four soft sources corresponding to HRsoft < ?0.5. ? Interestingly, the cumulative luminosity of the sources detected in the Chandra ?eld of view (see Table 2) is fully consistent with that derived by the XMM-Newton observation of NGC 6388. For the three sources with more than

The derived ?ux in the 0.5-7 keV is 5.1+0.2 × 10?14 erg ?3.6 cm?2 s?1 . As discussed above, the source labeled as 14* seems to be the superposition of three di?erent sources: one very soft and the other two harder, which lie close to the center of gravity of the globular cluster. With the present observations there is no way to discriminate whether one of these X-ray sources is associable with the IMBH hosted in NGC 6388. Nevertheless, if this is the case, the observed ?ux in the 0.5-7 keV can be considered as the present upper limit to the IMBH X-ray signal. The source appears to be soft since the best ?t absorbed power law (χ2 /ν=0.81 0.05 for ν = 26) has parameters NH = 2.7?0.1 × 1021 cm?2 , +0.3 +1.4 ?5 Γ = 2.4?0.2 and N = 4.7?0.6 × 10 for the column density, power law index and normalization, respectively. In this case, the ?ux in the 0.5-7 keV would be 1.02×10?13 erg cm?2 s?1 corresponding to an X-ray luminosity of 2.7×1033 erg s?1 .

4. Results and conclusions
Intermediate-mass black holes may represent the link between the stellar mass black holes present throughout the Milky Way and the super-massive black hole thought to exist in the center of the Galaxy and in external galaxies. Recent theoretical works have suggested that all the globular clusters may have central black holes with masses of the order 10?3 times the stellar mass in the cluster, as a consequence of merging processes of stellar mass black holes (Miller & Hamilton 2002). Present observational campaigns seem to con?rm this hypothesis. In the particular case of NGC 6388, numerical simulations (see e.g. Baumgardt et al. 2005b) have shown that it is a good candidate to host an IMBH of a few 103 M⊙ . Interestingly, the optical HST observations of the globular cluster and the detailed study of the brightness surface pro?le down to a distance of ? 1′′ from the center, revealed a signi?cant power law (with slope α ? ?0.2) deviation from a ?at core behavior (Lanzoni et al. 2007). This was explained assuming the existence of an IMBH with mass 5.7 × 103 M⊙ in the center of the globular cluster. As a consequence of matter accretion, we expect that the putative IMBH should accrete and emit radiation in the X-ray band, so we searched for such a signature in the observations available in both XM M -Newton and Chandra archives. The study of the central region of NGC 6388 in the 0.57 keV energy band reveals the existence of several discrete X-ray sources (see Sect. 3 for a detailed discussion) among which three of them seem to be overlapped and close to the center of gravity of NGC 6388. Although we can not obtain the spectrum of each of the three sources separately, we have speculated that if one of these is the putative NGC 6388 IMBH, the observed X-ray signal can be thought as an upper limit to the IMBH ?ux. Hence, with reference to Table 2, the unabsorbed X-ray Obs ?ux (in the 0.5-7 keV band) of the IMBH is FX < 1.6 × ? ?13 ?2 ?1 10 erg cm s , corresponding to a luminosity of LObs < 2.7 × 1033 erg s?1 for the NGC 6388 distance of X ? 11.5 kpc. At this point one can evaluate the IMBH radiative e?ciency η = LX /LEdd with respect to the maximum allowed

Fig. 5. Color-color diagram of the sources (data points) detected within a few core radii in NGC 6388 and colorcolor contours for bremsstrahlung (grey region) and power law (black region) components, respectively. On the horizontal and vertical axes, the two hardness ratios HRhard = (H ? M )/(S + M + H) and HRsoft = (M ? S)/(S + M + H) are given (see text for details).

300 counts (3, 10 and 14*) detected within the NGC 6388 globular cluster, we extracted the spectrum from a circular aperture centered on each of the three sources. Note that the source labeled as 14* seems to be the superposition of three distinct sources (see also the true color images in Fig. 3), for which it was not possible to extract the single spectra. In this case we refer to the cumulative spectrum. The spectra (shown in Fig. 6) were rebinned with 25 counts per bin and ?tted using the XSPEC spectral ?tting package. All the errors given below are at a 90% con?dence level. The spectrum of the source 3 is well ?tted (χ2 /ν=0. 76 for ν = 15) by an absorbed black-body model with temperature kT = 0.26+0.03 keV, hydrogen column density NH = ?0.10 +0.1 3.1?0.1 × 1021 cm?2 , and normalization N = 1.2+0.6 × 10?7 ?0.3 corresponding to a ?ux (in the 0.5-7 keV) of 4.5 × 10?14 erg cm?2 s?1 . Source 10 is characterized by a power law whose best ?t parameters (χ2 /ν=0. 76 for ν = 9) are NH = 1.6+1.7 × 1021 ?1.6 cm?2 , Γ = 2.4+1.3 , and N = 2.0+0.3 × 10?5 for the column ?1.0 ?0.9 density, power law index and normalization, respectively.


Nucita et al.: XM M -Newton and Chandra observation of NGC 6388

normalized counts s?1 keV?1

normalized counts s?1 keV?1

normalized counts s?1 keV?1








2×10?3 10?3

2×10?3 10?3 1
?S χ2 ?S χ2

1 1 0.5 0 ?0.5
?S χ2

0 ?1 1 2


?1 1

?1 1 2

Energy (keV)

Energy (keV)

Energy (keV)

Fig. 6. The spectra of the sources labeled as 3, 10 and 14* from the left to the right (see text for details on the ?t). black hole accretion rate given by the Eddington luminosity LEdd ? 1.38 × 1038 (M/M⊙ ) erg s?1 . For the IMBH at the center of NGC 6388 one gets LEdd ? 7.87 × 1041 erg s?1 , so that we can conclude that it is accreting with e?ciency η < 3 × 10?9. Note that this accretion e?ciency is in ? agreement with the e?ciency estimates for black hole accretion in quiescent galaxies and ultra-low luminous AGNs, for which η is typically in the range 4 × 10?12 ? 6 × 10?7 (Bagano? et al. 2003). The bolometric luminosity of the NGC 6388 IMBH can be inferred from the broadband spectral energy distributions of galactic nuclei (see Elvis et al. 1994 for details). In this case, it is found that the bolometric correction for the X-ray band corresponds to a factor ? 7 ? 20, so that Lbol /LEdd <(2 ? 6) × 10?8 (or Lbol <(2 ? 5) × 1034 erg s?1 ). ? ? It could be also interesting to estimate the expected accretion luminosity (Lacc ) of the IMBH as a consequence of the accretion of the surrounding gas, and compare it to the bolometric luminosity (Lbol ) above. It is indeed expected that post-main-sequence stars continuously lose mass that is injected both in the cluster and intracluster medium. Dispersion measurements derived from radio observations of pulsars give the most sensitive probe of the gas content in globular clusters. Studying the population of millisecond pulsars in the globular clusters M 15 and 47 Tuc, Freire et al. (2001) ?nd indications of the presence of a plasma with electron density ne ? 0.2 atoms cm?3 and temperature T ? 104 K (see also Ho at al. 2003 for a detailed study of the M 15 globular cluster). In common with other authors (Maccarone 2004), we assume in the following that the gas density in NGC 6388 is ? 0.2 atoms cm?3 . If the IMBH at the center of NGC 6388 accretes spherically through the Bondi accretion process, the gravitational potential of the IMBH dominates the dynamics of the gas within the accretion radius de?ned as Ra ? GMbh /c2 , where cs ? 0.1T 1/2 s km s?1 is the sound speed in a plasma at temperature T . For T = 104 K and Mbh = 5.7×103 M⊙ , one obtains cs ? 10 km s?1 and Ra ? 0.3 pc. The accretion mass rate in the 2 ˙ Bondi mechanism is MB = 4πRa ρa cs , where ρa is the gas density at Ra . Assuming that the e?ciency in converting the accreted mass into energy is the standard ? = 10%, the ˙ expected luminosity due to accretion is Lacc = ?MB c2 , i.e. Lacc = 2.4 × 1038 × Mbh 5.7 × 103 M⊙ ? × 0.1

n 0.2 cm?3

cs 10 kms?1


(1) cgs.

Hence, in the case of the NGC 6388 IMBH, the accretion luminosity is clearly larger than the bolometric luminosity quoted above by a factor of at least ? 104 , leading us to conclude that the accretion e?ciency is ? < 8 × 10?5 ? 2 × ? 10?4 . In recent years it has also been proposed that a relationship between black hole mass, X-ray luminosity and radio luminosity does exist (see e.g. Merloni et al. 2003 and Maccarone 2004). In this context, IMBHs at the center of many globular clusters, such as NGC 6388, may be easily identi?able objects in deep radio observations. In particular, the expected radio ?ux at 5 GHz from the putative IMBH in NGC 6388 would be F5 = 10 LX 3 × 1031 cgs

Mbh 100M⊙


10kpc d



Assuming that it is a quiescent and stable accreting black hole, we can be more predictive about its radio luminosity. In Fig. 7, the expected radio emission (solid oblique line) from the IMBH at the center of NGC 6388 is shown. The solid vertical line represents the maximum allowed X-ray luminosity for an Eddington limited accreting black hole. As one can see, depending on the accretion e?ciency (dotted and dashed lines are for η = 3×10?9 and η = 3×10?10, respectively) the radio ?ux at 5 GHz is < 3 mJy, which is ? within the detection possibilities of the Australia Telescope Compact Array (ATCA). Deep radio observations within the core radius of NGC 6388 would also be important for the possibility of discovering millisecond pulsars nearby the cluster center that may allow a further and independent

Nucita et al.: XM M -Newton and Chandra observation of NGC 6388


constraint on the IMBH mass and position with respect to the cluster center 4 .

Noyola, E., & Gebhardt, K., 2006, AJ, 132, 447. Pooley, D., & Rappaport, S., 2006, ApJ, 644, L45. Portegies Zwart, S. F., et al., 2004, Nature, 428, 724. Str¨der , L., et al., 2001, A&A, 365, 18. u Turner, M. J. L., et al., 2001, A&A, 365, 27.

Fig. 7. The expected radio emission (solid oblique line) from the IMBH at the center of NGC 6388 as a function of the IMBH X-ray luminosity. Present X-ray observations can put only an upper limit of ? 3 mJy to the black hole radio luminosity.

Acknowledgements. This paper is based on observations from XM M Newton, an ESA science mission with instruments and contributions directly funded by ESA member states and NASA. We are grateful to G. Trincheri and L. Bello for useful discussions. We are grateful to the anonymous referee for the suggestions that improved the manuscript.

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Indeed, one expects that an IMBH randomly moves, within the globular cluster core, due to the interaction with the other stars (assumed to have the same mass m) with an amplitude ? rc (m/Mbh ) (see e.g. Bahcall & Wolf 1976, Gurzadyan 1982 and Merritt et al. 2006).


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