RADIO CONTINUUM OBSERVATIONS OF 47 TUCANAE AND ω CENTAURI: HINTS FOR INTERMEDIATE-MASS BLACK HOLES?

Globular clusters are well-known exotic object factories because of their highly frequent dynamical interactions. It has been decades since the prediction was made that intermediate-mass black holes (IMBHs) might exist in globular clusters (e.g., Wyller 1970; Bahcall & Ostriker 1975; Frank & Rees 1976). IMBHs provide a possible connection between stellar-mass black holes and supermassive black holes, with their mass ranging from 10² to 10⁵ M_☉. There has been much conclusive evidence supporting the existences of stellar-mass black holes as in X-ray binaries and supermassive black holes as in active galactic nuclei (AGNs). However, the existence of IMBHs in globular clusters is still under debate. Although theoretical works provide possibilities of their existences, observational evidences are limited. There are many formation channels of IMBHs. One is that they may be the products of core collapses of population III stars (e.g., Fryer et al. 2001). IMBHs could also form through runaway merger processes in some young dense globular clusters (Portegies Zwart & McMillan 2002; Portegies Zwart et al. 2004). Moreover, it is possible that in globular clusters mergers of compact objects, such as stellar-mass black holes through interactions, would result in a central black hole with mass ∼0.001 times the mass of its host cluster, which falls in the mass regime of IMBHs (Miller & Hamilton 2002). As a result, searching for IMBHs in globular clusters is crucial for understanding formation histories of dense stellar clusters, and it may further help us study the stellar dynamics and construct cluster evolution scenarios.

There is an established "M–σ" relation between the supermassive black hole mass and velocity dispersion in the host galaxies based on observations (Tremaine et al. 2002; Ferrarese & Ford 2005; Gültekin et al. 2009). The correlation implies that the formation of a supermassive black hole is possibly related to the formation of a galaxy. If the M–σ relation extends to the regime of dense stellar cluster systems, globular clusters may host central IMBHs with masses ranging from 10² to 10³ M_☉. One of the formation scenarios of AGNs is that they may be grown from 10² to 10³ M_☉, formed from direct collapse of population III stars. If IMBHs do exist in globular clusters, the M–σ relation may link the formation mechanisms of IMBHs and AGNs.

As far as observations are concerned, detecting IMBHs is achievable through many methods. Farrell et al. (2009) identified an IMBH in the galaxy ESO243-49 by its extremely high X-ray luminosity and variability in the X-ray luminosity and spectra. For IMBHs in globular clusters, the most common way is measuring velocity dispersion of cluster stars and then applying a dynamical modeling technique to constrain the mass-to-light ratio of globular clusters. Another method is detecting possible radio emissions from the center of globular clusters expected from the fundamental plane of black hole (Merloni et al. 2003). The dynamical modeling technique can constrain the central "dark" mass in globular cluster, while it fails to distinguish whether the "dark" mass is contributed from a single IMBH or a group of neutron stars, white dwarfs, or stellar-mass black holes. Moreover, during the past decade, because of the improvement of the instruments, the detection of possible radio/X-ray emissions predicted by the black hole fundamental plane becomes possible. As a result, several deep radio continuum observations of globular clusters have been carried out to search for IMBHs in globular clusters.

To date, discoveries of IMBHs candidates in some globular clusters have been claimed with different observational techniques (Table 1). The reported dynamical mass of a possible IMBH in G1 (in M31) is M_BH = (1.8 ± 0.5) × 10⁴ M_☉ (Gebhardt et al. 2002, 2005), while in M15 (in our Milky Way) M_BH = 1.7^+2.7_−1.7 × 10³ M_☉ (Gerssen et al. 2003). Nevertheless, the claims of G1 and M15 based on the dynamical method have suffered subsequent challenges. Theoretical models suggest that it is not necessary to invoke an IMBH to explain the data (Baumgardt et al. 2003a, 2003b). Furthermore, the latest radio continuum observations on several globular clusters could only set an upper limit on the possible central IMBHs (e.g., Maccarone et al. 2005; de Rijcke et al. 2006; Bash et al. 2008; Maccarone & Servillat 2008; Cseh et al. 2010). The only radio detection is discovered in G1 (Ulvestad et al. 2007). Nevertheless, recent Chandra observation of G1 favors the idea that the central object in G1 is an X-ray binary (Kong et al. 2010). Evidences from different detection methods are still not so compelling. It is thus inconclusive if any IMBH exists in globular clusters.

The two most massive and concentrated Galactic globular clusters, ω Centauri (ω Cen) and 47 Tucanae (47 Tuc), have been proposed to harbor a central IMBH. By using Hubble Space Telescope (HST) data, van der Marel & Anderson (2010) set a 1σ upper limit of 1.2 × 10⁴ M_☉ in ω Cen, while McLaughlin et al. (2006) put an upper limit of 1000–1500 M_☉ on the mass of a possible IMBH in 47 Tuc. In addition, previous radio observations set conservative upper limits of 1000 M_☉ and 2060 M_☉ for ω Cen and 47 Tuc, respectively (Maccarone et al. 2005; de Rijcke et al. 2006). As a consequence, our goal is to set a tighter upper limit on the mass of IMBHs in ω Cen and 47 Tuc to provide evidences for or against the existence of IMBHs in globular clusters.

Here, we show the results of our deep Australia Telescope Compact Array (ATCA) radio observations of ω Cen and 47 Tuc. We organize our searches of IMBHs in ω Cen and 47 Tuc in the following sections. In Section 2, we describe the accretion models we adopted to constrain the black hole mass. The radio observations, data analysis, and results are described in Section 3. We then constrain the masses of the possible IMBHs in both clusters based on the radio emission upper limits also in Section 3. Finally, we discuss the existence of IMBHs in globular clusters in Section 4.

Recent studies on correlations between X-ray and radio properties of both X-ray binaries and AGNs suggest that the ratio of radio-to-X-ray power increases with the black hole mass and decreases with the accretion rate (see, e.g., Falcke et al. 2004; Gallo et al. 2003; Maccarone et al. 2003; Merloni et al. 2003). The correlation found in Merloni et al. (2003) is shown in Equation (1), where $\mbox{\it F}_{\rm 5\, GHz}$ is the radio flux at 5 GHz, $\mbox{\it L}_{\rm X}$ is the X-ray luminosity, $\mbox{\it M}_{\rm BH}$ is the black hole mass, and $\mbox{\it d}$ is the cluster distance:

$$\begin{eqnarray} F_{\rm 5\, GHz} &=& 10\left(\frac{L_{\rm X}}{3 \times 10^{31}\, \thinspace \hbox{$\hbox{erg}\thinspace \hbox{s}^{-1}$}}\right)^{0.6} \left(\frac{M_{\rm BH}}{100\,{M_{\odot }}}\right)^{0.78} \nonumber \\ &&\times \left(\frac{d}{10\,{\rm kpc}}\right)^{-2}\;(\mu {\rm Jy}). \end{eqnarray} \tag{ 1 }$$

It is believed that the black holes in globular clusters are likely more massive than stellar-mass black holes and are accreting at low fractions of the Eddington luminosity (or we would have detect the X-ray emission from the cluster center). Consequently, the correlation of the fundamental plane may suggest that the detection of radio power would be an important indication of IMBHs existing in globular clusters.

Under the circumstances of uncertain X-ray luminosity based on observational constraints, Maccarone (2004) further assumes that the IMBH would accrete intracluster gas via a Bondi–Hoyle–Lyttleton (BHL) process (Hoyle & Lyttleton 1941; Bondi & Hoyle 1944; Bondi 1952). As shown by Ho et al. (2003) and Fender et al. (2003), the accretion efficiency () could be as low as 0.1% of the BHL accretion rate, assuming a radiative efficiency (η) of 10%. The BHL accretion rate, $\dot{M}_{\rm BHL}$, is described in Equation (2), where $\mbox{\it n}$ is the gas abundance, $\mbox{\it T}$ is the gas temperature of the globular cluster, and assuming a general value of 10⁴ K for all globular clusters. Given the fact that some globular clusters contain a substantial amount of gas measured from pulsars (e.g., Freire et al. 2001), one can adopt the gas abundance derived from these globular clusters in Equation (2) (see Table 1):

$$\begin{eqnarray} \dot{M}_{\rm BHL} &=& 3.2 \times 10^{17}\left(\frac{M_{\rm BH}}{2000\,{M}_{\odot }}\right)^{2}\left(\frac{n}{0.2 {\rm \,H\,cm^{-3}}}\right) \nonumber \\ &&\times \left(\frac{T}{10^{4}\,{\rm K}}\right)^{1.5}\;({\rm g\,s^{-1}}). \end{eqnarray} \tag{ 2 }$$

Based on the calculation in Maccarone & Servillat (2008, 2010), the radiative efficiency η is expressed as 0.5$\dot{m}$ c⁴/L_EDD. This relation is valid for the black holes in the low hard state and the X-ray luminosity $\mbox{\it L}_{\rm X}$ ∝ $\dot{m}^{2}$. Here $\dot{m}$ is the mass accretion rate. Thus, $\mbox{\it L}_{\rm X}$ could be estimated by the BHL accretion rate $\dot{M}_{\rm BHL}$, and expressed with the black hole mass $\mbox{\it M}_{\rm BH}$, the gas abundance $\mbox{\it n}$, and the gas temperature $\mbox{\it T}$ of the globular cluster, as shown in Equation (3). If we combine all the above information, the black hole mass could be constrained simply by radio flux and cluster properties:

$$\begin{eqnarray} &&L_{\rm X} = \eta \,\epsilon \,\dot{M}_{\rm BHL}\;(\hbox{$\hbox{erg}\, \hbox{s}^{-1}$}). \end{eqnarray} \tag{ 3 }$$

ω Cen was observed previously with ATCA simultaneously at 4.8 and 8.6 GHz over 12 hr, while 47 Tuc was observed briefly (3.5 hr) with ATCA at 1.4 GHz. Both observations failed to detect any central radio source and yielded 3σ rms noise levels of 96 μJy and 225 μJy for ω Cen and 47 Tuc, respectively (Maccarone et al. 2005; de Rijcke et al. 2006). With different combinations of BHL accretion fraction and gas abundance in globular clusters, the radio upper limits corresponding to the most probable estimation for the upper limit of the IMBH mass in ω Cen and 47 Tuc are 2000 M_☉ and 1000 M_☉, respectively (see Maccarone & Servillat 2008, 2010, and references therein). The results could not exclude the possibility that there is no IMBH in ω Cen or 47 Tuc, which motivated us to propose deeper radio observations on both targets.

3.1. Data Analysis

3.2. Results

Besides background quasars, we did not detect any radio sources at or near the central region of ω Cen and 47 Tuc with radio emissions higher than 3σ. In naturally weighted maps, the rms noise level for ω Cen is 7 (5.5 GHz) and 11 (9 GHz) μJy beam⁻¹; while for 47 Tuc, it is 17 (5.5 GHz) and 20 (9 GHz) μJy beam⁻¹. We combined the observations with different frequencies in order to obtain a lower rms noise level at frequency 6.8 GHz. As a result, the observations reached rms noise levels of 6.5 and 13.3 μJy beam⁻¹, giving a 3σ upper limit of 20 and 40 μJy beam⁻¹ for ω Cen and 47 Tuc, respectively. The brightest millisecond pulsar in 47 Tuc has a radio flux of ∼370 μJy at 1.4 GHz (McConnell et al. 2004). Assuming a spectral index α = −1.8 for pulsar spectrum (Kramer et al. 1998), it would have a flux of ∼21 μJy at 6.8 GHz. Thus, the millisecond pulsars in 47 Tuc are all under the detection threshold of our observation. We overlapped the positions of the X-ray sources detected in ω Cen (Haggard et al. 2009), and there is no any radio source with their signal-to-noise ratio higher than 3 matched to the 180 Chandra X-ray sources.

Figure 1 shows the HST optical images overlaid with ATCA radio map contours of 47 Tuc and ω Cen. The radio position of 47 Tuc and ω Cen has an estimated error of ∼14 by 06 and 11 by 07, respectively, derived by dividing the beam size by the signal-to-noise ratio. Although we did not find any statistically significant radio emission, there is a 2.5σ detection near the center of both globular clusters (∼04 from 47 Tuc center and ∼07 from ω Cen center). We calculated the average source number within the error ellipse of the globular cluster center by computing the area ratios of the error ellipse to the field of the 10'' × 10'' region and also the total number of the sources (with their signal-to-noise ratio larger than 2.5) inside the field of view of the 10'' × 10'' region. With the assumption of the Poisson distribution, we obtained the probabilities of finding one or more radio sources inside the error circle, which is ∼2% for both 47 Tuc and ω Cen. That is to say, the probability of chance coincidence is quite low and the nearby source could really be the central radio source.

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3.3. Constraints on IMBH Masses

To date, several radio continuum observations have been performed on a few globular clusters in order to detect possible IMBHs in the cluster center. There is a radio source detected in G1. However, whether the radio source in G1 is related to an IMBH or an LMXB is still under debate (Kong et al. 2010). Except for G1, no central radio source has been detected in the other globular clusters. Nevertheless, the non-detections did not rule out the existence of IMBHs in globular clusters. The radio flux upper limits are used to constrain the IMBH masses, regarding certain assumptions of gas properties in globular clusters and accretion model. Based on Pfahl & Rappaport (2001), the gas abundance in globular clusters could vary from 0.1 to 1 H cm⁻³. The accretion efficiency of the putative IMBH in G1 is just below 1% (Ulvestad et al. 2007). Moreover, according to the standard accretion disk theory, the IMBH in globular clusters would be in an extremely low state, while as suggested in Cseh et al. (2010) both the accretion efficiency and radiative efficiency could vary in a wide range. The scatter in the black hole fundamental plane correlation would also contribute errors in IMBH mass estimates. Combined with all of these uncertainties, the estimation of IMBH masses is actually model dependent and under strong model assumptions.

Despite the large uncertainties in the estimation of IMBH masses based on radio observations, there are discrepancies between the IMBH masses estimated from accretion model constraints and dynamically inferred IMBH masses, especially for the case of ω Cen (see Table 1). The measurement of IMBH masses based on stellar dynamics is limited to the instrument ability, which could not achieve high enough spatial resolution, although it provides a more accurate estimation on the IMBH masses. We further compare the upper limits of IMBH masses of some globular clusters to the M–σ relation of galaxies (Figure 2). The upper limit for the mass of the IMBH in 47 Tuc is consistent with the M–σ relation of Gültekin et al. (2009), while for ω Cen the upper limit of the IMBH mass is within the region of the M–σ relation of Ferrarese & Ford (2005). As the true masses of IMBHs must be lower than the upper limits, ω Cen, 47 Tuc, and M15 do not show inconsistency of the M–σ relation. There is no reason that globular clusters should obey the same relation that is confirmed to exist in massive galaxies. However, the consistency may suggest similar formation mechanisms or similar content between globular clusters and galaxies. If we could lower the upper limits of the IMBH masses in globular clusters, it may provide evidences of different formation mechanisms between globular clusters and galaxies.

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In summary, we estimate the 3σ upper limit for the mass of the central IMBH in ω Cen of 1100–5200 M_☉, and for 47 Tuc we estimate the 3σ upper limit of 520–4900 M_☉. The estimations strongly depend on the accretion model and the gas properties of globular clusters. We detect a 2.5σ radio emission near the center of both globular clusters. Future radio observations with a sensitivity improvement to ∼5 μJy may be able to confirm whether the sources are real or further constrain the parameters of the accretion model.

This project is supported by the National Science Council of Republic of China (Taiwan) through grants NSC 96-2112-M-007-037-MY3 and NSC 99-2112-M-007-004-MY3. The Australia Telescope is funded by the Commonwealth of Australia for operation as a National Facility managed by CSIRO.