Mon. Not. R. Astron. Soc. 364, 344–352 (2005) doi:10.1111/j.1365-2966.2005.09568.x Radio pulsars around intermediate-mass black holes in superstellar clusters A. Patruno,1,2 M. Colpi,2 A. Faulkner3 and A. Possenti4 1Astronomical Institute ‘A. Pannekoek’, University of Amsterdam, Kruislaan 403, 1098 SJ, the Netherlands 2Dipartimento di Fisica G. Occhialini, Universitadi` Milano Bicocca, Piazza della Scienza 3, I-20126 Milano, Italy 3University of Manchester, Jodrell Bank Observatory, Macclesfield, Cheshire 4INAF, Osservatorio Astronomico di Cagliari, Poggio dei Pini, Strada 54, Capoterra, Italy Downloaded from https://academic.oup.com/mnras/article/364/1/344/1153149 by guest on 30 September 2021 Accepted 2005 August 27. Received 2005 August 25; in original form 2005 July 8 ABSTRACT We study accretion in binaries hosting an intermediate-mass black hole (IMBH) of ∼1000 M, and a donor star more massive than 15 M. These systems experience an active X-ray phase characterized by luminosities varying over a wide interval, from <1036 erg s−1 up to a few 1040 erg s−1 typical of the ultraluminous X-ray sources (ULXs). Roche lobe overflow on the zero-age main sequence and donor masses above 20 M can maintain a long-lived accretion phase at the level required to feed a ULX source. In wide systems, wind transfer rates are magnified by the focusing action of the IMBH yielding wind luminosities 1038 erg s−1. These high-mass IMBH binaries can be identified as progenitors of IMBH–radio pulsar (PSR) binaries. We find that the formation of an IMBH–PSR binary does not necessarily require the transit through a ULX phase, but that a ULX can highlight a system that will evolve into an IMBH–PSR, if the mass of the donor star is constrained to lie within 15–30 M.Weshow that binary evolution delivers the pre-exploding helium core in an orbit such that after explosion, the neutron star has a very high probability to remain bound to the IMBH, at distances of 1– 10 au. The detection of an IMBH–PSR binary in the Milky Way has suffered, so far, from the same small number of statistics limit affecting the population of ULXs in our Galaxy. Ongoing deeper surveys or next-generation radio telescopes such as the Square Kilometre Array will have an improved chance to unveil such intriguing systems. The timing analysis of a pulsar orbiting around an IMBH would weigh the black hole in the still uncharted interval of mass around 1000 M. Keywords: accretion, accretion discs – black hole physics – X-rays: binaries – X-rays: galaxies. 2004; Zampieri et al. 2004), the properties of the optical and radio 1 INTRODUCTION counterparts (Kaaret et al. 2004; Liu, Bregman & Seitzer 2004; Recent high-resolution X-ray imaging and spectroscopic studies Zampieri et al. 2004; K¨ording,Colbert & Falcke 2005; Miller, with Chandra and XMM have led to the discovery of a large sample Mushotzky & Neff 2005; Soria et al. 2005) and the timing behaviour of a new class of compact sources with luminosities in the inter- of at least one source in the starburst galaxy M82 (Strohmayer & val between 3 × 1039 and 1041 erg s−1, which are in excess of the Mushotzky 2003; Fiorito & Titarchuk 2004) support this view. The Eddington limit of a stellar-mass black hole of 20 M (Fabbiano IMBH hypothesis however does not represent the only possibil- 1989; see Mushotzky 2004, for a critical review). These sources ity to explain the emission of ULXs, because mechanical beaming can find a simple interpretation in the hypothesis that intermediate- working in a thick disc around a conventional stellar-mass black mass black holes (IMBHs) exist with mass 102–104 M accreting hole, or Doppler boosting from a jet in a microblazar could pro- from a companion star in binary systems (Fabbiano 1989; Miller duce the same range of observed luminosities (King et al. 2001; & Colbert 2004; Mushotzky 2004). The detection of a cool-disc K¨ording, Falcke & Markoff 2002; Kaaret et al. 2003; Mushotzky thermal spectral component in a number of ultraluminous X-ray 2004). Moreover, in recent work, Rappaport, Podsiadlowski sources (ULXs; Miller et al. 2003; Cropper et al. 2004; Dewangan &Pfahl (2005) use binary evolution calculations to show how the et al. 2004; Kaaret, Ward & Zezas 2004; Miller, Fabian & Miller largest part of the ULX population may be explained with a stellar- mass black hole emitting at a super Eddington rate of ∼10 without E-mail: [email protected] the requirement of an IMBH (see also Podsiadlowski, Rappaport & C 2005 The Authors. Journal compilation C 2005 RAS Radio pulsars around IMBHs 345 Han 2003 and Pfahl, Podsiadlowski & Rappaport 2005 for an ex- hosted in the core of our Galaxy (Pfahl & Loeb 2004). Thus, the issue tended study on the evolution of stellar-mass black hole binaries). of pulsars around black holes is becoming of paramount importance. This is also in agreement with another study of King & Dehnen In this paper we assume the hypothesis of the formation of IMBHs (2005) where the authors claim that the luminosities of a large sam- in young dense star clusters, and we start our evolution study just ple of ULXs could be explained using helium enriched matter and after the formation/capture of a high-mass star around the IMBH, mechanical beaming with a stellar-mass black hole. However, all the which could be the progenitor of an IMBH–PSR system. In this alternatives to the IMBH hypothesis meet with strong difficulties framework, Hopman, Portegies Zwart & Alexander (2004) consid- when the luminosity of a ULX is in excess of ∼1040 erg s−1, be- ered the possibility that a passing star is tidally captured by the cause, in this case, beaming under rather extreme conditions should IMBH in a stable, close, not plunging orbit. Mass transfer may ini- be at work to match with the observations, or super Eddington fac- tiate, after circularization, while the star is on the main sequence or tors greater than ∼10 could be difficult to achieve. On the other evolving away from it. Dynamical capture of a massive star by an hand, although the hypothesis of an IMBH explains naturally many IMBH is a further possibility, as shown by Baumgardt et al. (2004). of the observational clues, it clashes with the problem of provid- In an exchange interaction of a binary star, the IMBH can acquire Downloaded from https://academic.oup.com/mnras/article/364/1/344/1153149 by guest on 30 September 2021 ing a viable mechanism of formation. Until now, two possibilities a companion, likely a massive star, given that the IMBH forms in have been proposed: the formation of an IMBH through runaway a mass-segregated environment, where stellar encounters play an collisions among massive stars undergoing fast dynamical segrega- important role. tion, in the core of a dense super star cluster (see G¨urkan,Freitag & The observational appearance of binaries hosting an IMBH has Rasio 2004; Portegies Zwart et al. 2004a), or the wandering of an only been partly explored, and mainly in the context of ULXs. IMBH, relic of a zero metallicity Population III star (Abel, Bryan & Portegies Zwart et al. (2004b) studied the evolution of an IMBH Norman 2000). In the first case, the giant star that forms in the core of 1000 M accreting from a donor star of mass between 5 and of the dense star cluster, collapses into an IMBH. This can occur in 15 M (see also Kalogera et al. 2004 for another binary evolu- a star-forming region, and the result is based on very large detailed tionary study). Typically, light donors (5M)donot transfer N-body simulations (Portegies Zwart et al. 2004a). The case of a mass at a sufficiently sustained rate to produce sources as bright as wandering IMBH relic of the early assembly of haloes in a currently ULXs; only the high-mass stars (10 M)onthe main sequence star-forming galaxy is uncertain, in particular the capture of gas or or beyond can provide luminosities in excess of 1040 erg s−1. Thus, of a star to ignite accretion (Volonteri & Perna 2005). IMBHs cannot easily be identified on the basis of their X-ray activ- In order to solve the controversy on the real existence of IMBHs ity; they can display a rather wide range of luminosities, depending in ULXs, the only secure route would be the determination of the on the mass of the donor star, and on the mass transfer mechanism, optical mass function, similar to the procedure for the stellar-mass as will be shown in this paper. Only when they outshine as bright black holes in the Milky Way (Orosz et al. 2002). This is difficult ULXs can they become visible over the stellar-mass black holes. however, because ULXs are distant sources hosted in external (star- In this paper we address a number of issues, under the hypothesis burst) galaxies for which the optical identification of the companion that an X-ray and/or a ULX phase precedes that in which the system is troublesome, and even in the lucky circumstance of good identi- appears as an IMBH-PSR binary. fication (see Kaaret et al. 2004; Liu et al. 2004; Miller et al. 2004; (i) What are the characteristics of the X-ray phase and of mass Soria et al. 2005; Zampieri et al. 2004) the optical spectrum is too transfer when considering massive donors around an IMBH? noisy to allow a mass estimate of the black hole. (ii) Is the formation of a radio pulsar likely? In this paper we propose an alternative way to discover and weigh (iii) What is the probability that an asymmetric kick, imparted to a IMBH: it uses the detection of a young radio pulsar (PSR) around the neutron star at birth, will unbind the system? an IMBH.