Evidence for an intermediate-mass black hole in the globular cluster NGC 6624

TL;DR

Over 25 years of pulsar timing data suggests the presence of an intermediate-mass black hole (>20,000 solar masses) at the center of globular cluster NGC 6624, based on orbital modeling of pulsar motion.

Contribution

This study provides the first evidence supporting an intermediate-mass black hole in a globular cluster through pulsar timing analysis.

Findings

Pulsar timing indicates a massive central object in NGC 6624.

Model-dependent black hole mass estimate is approximately 20,000 solar masses.

Results imply other globular clusters may also host central black holes.

Abstract

PSR B1820$-$30A is located in the globular cluster NGC 6624 and is the closest known pulsar to the centre of any globular cluster. We present more than 25 years of high-precision timing observations of this millisecond pulsar and obtain four rotational frequency time derivative measurements. Modelling these higher-order derivatives as being due to orbital motion, we find solutions which indicate that the pulsar is in either a low-eccentricity ($0.33\lesssim e\lesssim0.4$) smaller orbit with a low mass companion (such as a main sequence star, white dwarf, neutron star, or stellar mass black hole) or a high-eccentricity ($e\gtrsim0.9$) larger orbit with a massive companion. The cluster mass properties and the observed properties of 4U 1820$-$30 and the other pulsars in the cluster argue against the low-eccentricity possibility. The high-eccentricity solution reveals that the pulsar is most likely orbiting around an intermediate-mass black hole (IMBH) of mass $> 7,500$~M$_\odot$ located at the cluster centre. A gravitational model for the globular cluster, which includes such a central black hole (BH), predicts an acceleration that is commensurate with that measured for the pulsar. It further predicts that the model-dependent minimum mass of the IMBH is $\sim60,000$~M$_\odot$. Accounting for the associated contribution to the observed period derivative indicates that the $\gamma$-ray efficiency of the pulsar should be between 0.08 and 0.2. Our results suggest that other globular clusters may also contain central black holes and they may be revealed by the study of new pulsars found sufficiently close to their centres. Note that we found an erratum in Section 5 and thus, the $\sim$60,000~M$_\odot$ mass mentioned above has to be replaced by the correct model-dependent mass limit of $\sim$20,000~M$_\odot$. See the erratum appended.

Full text

The paper “Evidence for an intermediate-mass black hole in the globular cluster NGC 6624” was originally published in MNRAS 468, 2114$-$2127 (2017).

When estimating the model-dependent minimum mass of the IMBH of 60 000 M⊙ in Section 5, we used the separation of $0.15$ pc for PSR J1823$-$3021C from the globular cluster centre as given in Peuten et al. (2014) (see Table 2 therein). Unfortunately, this value is incorrect and the correct separation is $0.34$ pc based on the position given in Table 1 (also see Lynch et al., 2012). This correct distance measurement changes the result presented in Figure 9 in the published version and the modified figure based on the positions given in Table 1 is appended here. Note that this does not affect any other results presented in the paper in particular the IMBH mass estimation obtained through orbital dynamics given in Section 4.

If the measured accelerations (i.e. $\dot{\rm P}/{\rm P}$) of PSR J1823$-$3021B and C are assumed to be solely dynamically induced and the intrinsic spin-down contribution is negligible (see Equation 1), then the required mass of the IMBH to explain the acceleration of these sources becomes as massive as the cluster mass. This implies that the intrinsic spin-down of these two pulsars are important and their dynamically induced accelerations are smaller than the measured accelerations. Therefore, we exclude these two pulsars in the estimation of the IMBH mass limit in Section 5. Assuming that the dynamically induced acceleration of the LMXB is approximately equal to the observed value, as used in Peuten et al. (2014), we estimate the minimum model-dependent mass of the IMBH is $\sim$20 000 M⊙. Thus, the $\sim$60 000 M⊙ mass limit mentioned in Section 5 and Abstract in the published version has to be replaced by this correct model-dependent mass limit of $\sim$20 000 M⊙. We also note that the mass of the IMBH used to produce Figure 8 was $19\,000$ M⊙ and this mass is approximately equal to the correct mass limit given above. Therefore, the result presented in Figure 8 in the published version is valid.

Acknowledgments

We thank Mark Gieles and Federico Abbate for noticing this error in the separation of pulsar C used in the published version.