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Mon. Not. R. Astron. Soc. 364, 344Ð352 (2005) doi:10.1111/j.1365-2966.2005.09568.x

Radio 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, , 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 in binaries hosting an intermediate-mass (IMBH) of ∼1000 M, and a donor more massive than 15 M. These systems experience an active X-ray phase characterized by 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 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 IMBHÐradio (PSR) binaries. We find that the formation of an IMBHÐPSR binary does not necessarily require the transit through a ULX phase, but that a ULX can highlight a system that will evolve into an IMBHÐPSR, if the mass of the donor star is constrained to lie within 15Ð30 M.Weshow that binary evolution delivers the pre-exploding helium core in an orbit such that after explosion, the star has a very high probability to remain bound to the IMBH, at distances of 1Ð 10 au. The detection of an IMBHÐPSR binary in the has suffered, so far, from the same small number of statistics limit affecting the population of ULXs in our . Ongoing deeper surveys or next-generation radio telescopes such as the 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 Ð black hole physics Ð X-rays: binaries Ð X-rays: .

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 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 102Ð104 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 IMBHÐPSR system. In this alternatives to the IMBH hypothesis meet with strong difficulties framework, Hopman, Portegies Zwart & Alexander (2004) consid- when the 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. 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 , 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 undergoing fast dynamical segrega- important role. tion, in the core of a dense super (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 Population III star (Abel, Bryan & Portegies Zwart et al. (2004b) studied the evolution of an IMBH Norman 2000). In the first case, the 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, 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 at birth, will unbind the system? an IMBH. If ULXs are indeed accreting IMBHs in binaries, their (iv) On which orbits is the radio pulsar released after the super- evolution would end with a radio pulsar around the IMBH, if the explosion? Can Doppler effects hamper the detection of the mass of the donor star is in the range which avoids the formation of a radio signal? stellar-mass black hole or of a . The detection of a radio pulsar orbiting around an IMBH would provide, through timing, an In order to address these questions, we explore in Section 2 wind unambiguous measure of its mass. fed accretion (WFA) and accretion through Roche lobe overflow At present, no young radio pulsars have been seen orbiting a (RLOF), when considering donor stars with masses in excess of heavy invisible companion, but in the near future the search of these 15 M.Weinfer the typical luminosities of these high-mass IMBH hypothetical IMBHÐPSR systems can be extended to nearby galax- binaries and the fate of the mass transferring star. In Section 3 we ies, with the Low Array (LOFAR; R¬ottgering2003) and explore natal kicks in such exotic massive binaries, and determine the Square Kilometre Array (SKA; Cordes et al. 2004). An IMBHÐ the probabilities of survival of the binary. Taking into account the PSR system would lead to the discovery of black holes in the still effect of the natal kick, we also compute the typical eccentricity uninvestigated interval of masses between 100 and 104 M. Stellar- and semimajor axis of the neutron star orbit, after the mass black holes around pulsars have long been considered to be explosion in the binary. In Section 4 we simulate the observability the ‘holy grail’ of binaries. The systems studied here of an IMBHÐPSR in the Galaxy, considering the parameters of the are even more intriguing, given their importance in discovering a recent survey for radio pulsars in the Galactic disc using the Parkes new unexplored mass range crucial for cosmology (Madau & Rees . In Section 5 we discuss our results and outline our 2001). The discovery of a pulsar orbiting around a stellar-mass black conclusions. hole is expected in the next years, on the basis of theoretical consid- erations concerning their population, and on the observability of the 2ACCRETION ON TO INTERMEDIATE-MASS radio pulsar signal (Lipunov et al. 1994; Sigurdsson 2003; Lipunov, BLACK HOLES Bogomazov & Abubekerov 2005). On similar lines, there is also the hope of detecting, despite the large interstellar , a Here we explore the evolution of binaries with an IMBH of radio pulsar orbiting around the massive black hole of ∼3 × 106 M 1000 M and stars having mass M heavier than 15 M,sothat

C 2005 The Authors. Journal compilation C 2005 RAS, MNRAS 364, 344Ð352 346 A. Patruno et al. we can be confident that, despite mass loss, the donor star does may lead to an accretion rate Mú BH comparable to the wind mass- not evolve into a white dwarf. The helium core mass necessary to loss rate Mú w.Inparticular, if all the wind particles are deep in the < < 2 form a neutron star is in the range 2.8 M He 8M, although potential well of the IMBH, their total energy K + U = V rel /2 − some uncertainties exist in these upper and lower limits (Tauris & GMBH/a is negative. This implies a full wind gravitational focusing van den Heuvel 2006). In each evolutionary sequence, obtained by by the IMBH, and an X-ray luminosity at its highest value. The varying the mass and the initial orbital separation, the star is evolved limiting orbital separation for this to occur corresponds to the case until carbon ignition. The mass transfer episodes are either driven K + U = 0 for the most energetic√ wind particles, i.e. those having by RLOF during the main-sequence phase, by RLOF during the α = 0. This yields Vorb = (1 + 2)Vw and, accordingly, a binary rapid expansion of the star when ascending the giant branch, or by separation WFA when the system is detached. This third possibility has always GMBH MBH been overlooked in previous studies, although it seems relevant to amin = √  0.1 R. (6) + 2 2 M understand the different phases of an accreting IMBH. (1 2) Vw

The evolution equations for the binary systems are solved using Below amin the wind is entirely accreted. When α = π, the condition Downloaded from https://academic.oup.com/mnras/article/364/1/344/1153149 by guest on 30 September 2021 an updated version of the Eggleton code (Eggleton 1971; Pols et al. K + U = 0 corresponds to those particles having the minimum 1995) with a modified mass transfer rate for the WFA case, as ex- relative speed to remain bound√ to the IMBH. This defines a critical plained later in the text. All the stars considered have Population I orbital velocity Vorb = ( 2 − 1)Vw and in turn a limiting orbital chemical composition (Y = 0.28, Z = 0.02), radii R and wind losses separation Mú w obtained according to de Jager et al. (1988). The mixing length GMBH MBH parameter is set to α = 2.0, and the overshooting constant δ = 1.2 amax  √  3 R (7) ov − 2 2 M (Pols et al. 1998). Using general arguments, we then focus attention ( 2 1) Vw on the remnant left in the evolution to study the detectability of a above which all wind particles are unbound. In the interval a min < young neutron star revolving around an IMBH. a < a max wind particles with K + U > 0 escape the gravitational field of the IMBH and this defines a loss cone of solid angle  = π − α , α = −1 2 − 2 / 2.1 Wind fed accretion 2 (1 cos ˆ ) with ˆ cos [(Vorb Vw ) (2VwVorb)]. Under these conditions, the accretion rate on to the IMBH can be approximated Consider a donor main-sequence star of mass M above 15 M, as    moving on a circular orbit around an IMBH of mass MBH. Let a be  the relative separation, Mú ∼ Max 1 − Mú ; Mú SL . (8) BH 4π w BH   /   + 1 2 −1/2 MBH M a −1 For the mass transfer rate of equation (6) even a very high-mass Vorb  950 km s (1) 1015 M 1au star can provide the ULX luminosities during the main sequence, the relative orbital velocity, and without the requirement that the donor is crossing the supergiant     phase. In Fig. 1 we illustrate this effect, plotting accretion rates 1/2 −1/2 M R Mú and Mú SL for an IMBH of 1000 M and a donor star of V  1070 km s−1 (2) BH BH w 15 M 5R 30 M during the main sequence. The probability to observe this system is strongly increased due to the larger time spent by the star the velocity, set equal to the escape velocity from the on the main sequence. stellar surface. WFA dominates when the star is underfilling its Roche lobe ra- dius, i.e. when the binary separation a exceeds aRL, defined as R[0.6q2/3 + ln(1 + q1/3)] a = (3) RL 0.49q2/3 where q = M/M BH. In high-mass X-ray binaries, the mass of the donor usually ex- ceeds the mass of the black hole; hence, the wind particles mainly accrete on to the black hole from unbound orbits, because Vorb  V w. Capture occurs within a cylinder of radius comparable to a BH ∼ 2 2GMBH/V w ≈ (M BH/M) R.Inthe fluid approximation, this leads to an accretion rate on to the hole of ú SL ∼ / / 2 / ú MBH 1 4 (aBH a) (Vrel Vw)Mw (4)

(Shapiro & Lightman 1976; Shapiro & Teukolsky 1983), where V rel is the wind speed relative to the black hole 2 = 2 + 2 + α, Vrel Vw Vorb 2VorbVw cos (5) with α ∈ [0,π] the angle between the directions of V orb and V w. Equation (4) is valid when a  a BH and Vorb V w,sothat ∼ V rel V w. Figure 1. Mú (solid line) and Mú SL (dashed line) versus a for a donor of  BH BH In a binary with an IMBH, we may have aBH a (or equivalently 30 M and an IMBH of 1000 M. The mass transfer rates are in units of Vorb  V w), i.e. the particles released from the donor star surface the wind mass-loss rate. The accretion rate on to the IMBH is the highest can have kinetic energies such to be bound to the IMBH. This effect value between the two. The figure is explained in the text.

C 2005 The Authors. Journal compilation C 2005 RAS, MNRAS 364, 344Ð352 Radio pulsars around IMBHs 347 Downloaded from https://academic.oup.com/mnras/article/364/1/344/1153149 by guest on 30 September 2021

Figure 2. aRL (dashed line), amin (lower solid line) and amax (upper solid Figure 3. From top to bottom, the lines denote WFA luminosity against line) versus MBH for a donor of 30 M on the ZAMS. WFA prevails time for donors with masses of 50, 30 and 20 M, respectively, and a black above the dashed line. If the donor star is inside the grey shaded area, hole mass of 1000 M. The initial orbital separation is 1 au. The dashed > WFA is enhanced by the of the IMBH. The black area (a min line is the limit to obtain a ULX. The mass transfer begin on the ZAMS a RL) corresponds to RLOF, while the heavy grey area is for accretion of and the integration is stopped when the star reaches the giant branch. At this the entire wind lost by the donor star. Mild grey refers to a partial focusing point a RLOF phase starts, producing the sharp spikes in the plot, with the of the wind, while light grey is the ShapiroÐLightman regime. The con- exception of the donor of 50 M for which the code is stopped at the end = dition a min a RL defines a minimum IMBH mass for which WFA oc- of the main sequence. curs under full capture of the stellar wind, giving maximum WFA lumi- nosities. For a 30-M donor, this minimum IMBH mass corresponds to ∼3000 M. the terminal-age main sequence. Only very massive stars can pro- vide mean luminosities in excess of 3 × 1039 erg s−1, the threshold defining ULX sources. In Fig. 2, we show amin and amax as a function of the mass of the IMBH, compared to a , i.e. the distance at which the donor RL 2.2 Accretion through Roche lobe overflow star overfills its Roche lobe. The light grey area corresponds to orbital separations where WFA is in the ShapiroÐLightman limit, Accretion via RLOF occurs during the main sequence when the star while in the middle grey area, the wind is enhanced by the action of is close enough to the IMBH to fill its Jacobi surface, or during the gravitational focusing by the IMBH, and in the heavy grey area, it rapid expansion of the star when ascending the giant or supergiant is fully captured, leading to a conservative system. The black area branch. In this section we explore the evolution for the former case, is the RLOF zone. i.e. for separations ranging between 0.18 and 0.25 au for a 1000-M In our WFA model, the possible formation of a circumbinary disc IMBH and 15Ð50 M companion stars. around the donor star might change the quantity of wind accreted, Roche lobe contact remains stable along the entire evolution and although the order of remains unchanged (see van den gives luminosities above 1039.5 erg s−1 when the donor star has a Heuvel 1994). We have followed the evolution of the binary under mass M  15 M. Luminosities of 1040 erg s−1, typical of the WFA, starting from a separation of 1 au, imposing angular mo- brightest ULXs, need a star at least as massive as 20 M,asil- mentum and mass loss from the fraction of the wind escaping from lustrated in Fig. 4. Adopting the Dubus criterion for assessing the the binary. The star is non-rotating and the wind leaves the donor stability of the disc against the thermal ionization instability (Dubus isotropically, carrying away, in the centre mass reference frame, a et al. 1999), we find that RLOF on to an IMBH is stable, under our specific Jú = h(Mú w − Mú BH) where h is the conditions. This ensures that high-mass IMBH binaries can remain specific angular momentum of the orbit (see Soberman, Phinney & bright for a relatively long time, between a few million to 10 mil- van den Heuvel 1997, for a detailed discussion). We have computed lion years. This is opposite to the case of IMBH binaries with donor the accretion rate on to the IMBH using equation (6) and a WFA stars having masses 10 M as pointed out by Portegies Zwart luminosity adopting an efficiency factor of ∼0.1 characteristic of et al. (2004b), for which the luminosities are transient and the X-ray disc accretion, because the captured wind has high enough angular phases last for a longer time, comparable with the donor lifetime. momentum to form a disc. Within the limits of the available time-span coverage of ULX ob- The run of the WFA luminosity as a function of time is shown servations, the apparent persistency in their emission may be an in Fig. 3 for an IMBH of 1000 M in a binary with a 20-, 30- indication that donor stars have masses in the range considered in and 50-M star, respectively. The luminosity is enhanced relative this paper. to the value that would be predicted from a stellar-mass black hole The high mass transfer rates that establish during RLOF dramat- under equivalent conditions. With time, the WFA luminosity rises ically change the mass of the star. Fig. 5 shows the donor mass mainly because of the intrinsic increase of the wind loss rate when as a function of time. At the end of the , the core the star is transiting from the zero-age main sequence (ZAMS) to mass is almost equal to the mass of the whole star, because the mass

C 2005 The Authors. Journal compilation C 2005 RAS, MNRAS 364, 344Ð352 348 A. Patruno et al.

could be considered the mass limit between the neutron star and the black hole formation, because its final core mass is ∼9M. The fate of the heaviest star here considered (M  30 M)istocollapse into a stellar-mass black hole. If RLOF is the mechanism leading to a ULX during the main sequence, the donor star is expected to lie at an initial distance of a  1aufrom the IMBH. After leaving the main sequence, the star ascends the giant branch, while continuing to overflow its Roche lobe. This generate the spikes in Fig. 4, giving very high luminosi- ties. The typical values of a reached at the end of the evolution are in the range of ∼2Ð5 au. If the initial orbital separation of a donor star is a  1 au, RLOF

is avoided on the main-sequence phase. The star, in exiting the Downloaded from https://academic.oup.com/mnras/article/364/1/344/1153149 by guest on 30 September 2021 terminal-age main sequence, may later overfill its Roche lobe due to the sizable increase of its radius when ascending the giant branch, initiating a phase of accretion. Mass transfer and angular momentum conservation will drive the star further away from the IMBH, up to typical distances of 8Ð10 au.

Figure 4. Luminosity against time, for donors with masses of 15, 20, 25, 30 3 NEUTRON STAR KICKS AND THE and 50 M, respectively, and for an IMBH of 1000 M. The mass transfer SURVIVAL OF THE IMBH–PSR BINARY begins near the ZAMS and the integration is stopped before carbon ignition. In the RLOF case, the continuous increase of a, implied by conser- Stellar masses in excess of  20 M can produce luminosities above 1040 erg − vative mass transfer, would bring the donor to distances of several s 1 during the main sequence. All binaries appear to be persistent sources. The dashed line represents the ULX limit. Note that there is only one spike astronomical units. We may ask whether the explosion and the asym- for each donor, corresponding to the giant phase. The envelope of the donor metric kick that accompanies the formation of the neutron star can is almost completely depleted during this phase and the re-expansion after unbind the system. Given the high inertia of the IMBH, a neutron the helium burning is too small to produce another contact phase. star has a greater chance to remain bound than in the case of a lighter black hole companion. To keep a binary bound, we need a kick velocity below the limit given by the equation (Brandt & Podsiadlowski 1995; Willems, Kalogera & Henninger 2004)       1/2 1/2 G (MBH + M) MBH + MNS Vk,l = 1 + 2 , (9) a0 MBH + M

where MNS is the mass of the neutron star formed after the supernova explosion, and M and a0 are the mass of the donor star and binary separation, just prior the supernova explosion. In the presence of the IMBH, the total mass remains almost constant before and after the explosion, and so the most important parameter is the orbital separation a0.Toobtain a conservative estimate, we use our largest value of a0, which is about 10 au. The kick velocity limit is around 700 km s−1. To calculate the probability of survival of the IMBHÐPSR system, we adopt an analytical expression for the distribution of the kick magnitudes (HP distribution; Hansen & Phinney 1997)

2 2 Vk −V 2/σ 2 p(V ) = e k , (10) k π σ 3 Figure 5. Donor mass versus time during the whole life of the star for RLOF σ systems. The mass loss is very rapid for a high-mass star and decreases mildly where is the velocity of each of the components of the for a lighter star. The plot shows binaries with donor star masses of 15, 20, kick velocity. 25, 30 and 50 M orbiting around a 1000-M IMBH. The very rapid short Although there is not full agreement on the form of the kick decrease near the end of the curves is due to RLOF on the giant phase. magnitude distribution, it is rather well established that speeds larger Note that the initial mass corresponds to an age of 1 Myr as we are using than ∼700 km s−1 are attained only in extreme rare cases (see also logarithmic scale on the time axis. Lyne & Lorimer 1994; Arzoumanian, Chernoff & Cordes 2002; Hobbs et al. 2005). Therefore, we are confident that our calculations are not strongly affected by the particular choice of the distribution, transfer strips almost completely the entire stellar envelope during because what is interesting here is the existence of a cut-off at high the RLOF phase. Donors with mass between 15 and ∼25 M on velocities more than the specific form of the distribution itself. the ZAMS likely end their lives with a core mass between 3.3 and We use the following equation to calculate the probability of 7M, probably producing a neutron star. The case of a 30-M survival of our system, obtained by integrating the HP distribution

C 2005 The Authors. Journal compilation C 2005 RAS, MNRAS 364, 344Ð352 Radio pulsars around IMBHs 349 Downloaded from https://academic.oup.com/mnras/article/364/1/344/1153149 by guest on 30 September 2021

Figure 6. Distribution of post-supernova systems over α and e, normalized as in equation (14) of Kalogera (1996), calculated for β  1 and ξ = 0.3. between zero and our kick velocity limit:   Vk,l p (Vk )dVk V , 2V , − 2 /σ 2 0 k l k l 2V , ∞ = Erf − √ e k l . (11) p (V )dV σ πσ 0 k k Figure 7. Distribution of post-supernova systems over eccentricities, cal- −1 −1 culated for different values of ξ and for β  1. For ξ = 1, the systems are Using a value for V k,l of 700 km s and a value for σ of 152 km s highly eccentric, while they became less eccentric with decreasing ξ. (Hobbs et al. 2005), we infer a probability of survival greater than 99 per cent. Therefore, after the supernova explosion we can be confident that the system is still bound. After the explosion the orbital parameters change. To obtain the distribution of post-supernova orbital separations and eccentricities, we introduce, following Kalogera (1996), the three dimensionless parameters that are necessary to constrain the properties of the binary after the explosion:

α = af/a0 (12)

M + M β = BH NS (13) MBH + M σ ξ = (14) Vorb where a0 is the pre-explosion binary separation, af is its post- explosion value, and β ∼ 1isthe binary total mass ratio, after and prior to explosion. Typicalpulsar one-dimensional speeds peak at 152 km s−1 (Hobbs et al. 2005). Given the high relative orbital velocity (equation 1) σ ξ  Figure 8. Distribution of post-supernova systems over dimensionless or- with respect to , 1inour case. Fig. 6 shows the probability ξ β  ξ = α bital separation, calculated for different values of and for 1. For distribution over and post-encounter eccentricity e, computed for 1, the most probable post-supernova semimajor axis is about 0.5a , while β ∼ ξ = 0 1 and 0.3, while Figs 7 and 8 give the distribution over for ξ  1 the most probable semimajor axis is similar to the pre-supernova e (integrated over α) and α (integrated over e), respectively, for orbital separation. selected values of ξ. Post-supernova binaries populate only a restricted area of the cluster tend to decrease the orbital separation of the system, although αÐe plane giving minimum acceptable post-supernova separations there are some uncertainties in the real effect of this process as stated a f = (1/2)a 0 for ξ  1 and a f = a 0 for ξ  1 according to the by Hopman & Portegies Zwart (2005). fact that the post-supernova orbit must include the position of the Neglecting this uncertain effect, the production of gravitational two stars just prior to explosion. Because we have found in Sec- waves seems to be unimportant, because the pulsar is revolving on tion 2.2 that the likely pre-supernova orbital separation falls in the a mildly eccentric orbit at a large separation. The in-spiral time range 2Ð10 au, the final values of af range between ∼1 and 10 au. for emission of gravitational waves is extremely large: t GW  3 × The small eccentricity of these systems is a direct consequence 1010 yr for e = 0.4, and only for very high eccentric systems (e = 7 of the very high mass of the IMBH, which produces higher orbital 0.9) it is t GW ∼ 6 × 10 yr. velocities than in normal binaries, and a value of ξ<1 also for the The lifetime of a super star cluster is about 108 yr (see Hopman largest orbital separations. Another consequence of the large mass & Portegies Zwart 2005), which is comparable to the lifetime of the of the black hole is that the binary can be always defined as a hard binary even if the eccentricity produced by dynamical interactions binary (Heggie 1975) and thus the dynamical interactions in the star becomes ∼0.9. Thus, we have a very small probability of a merger in

C 2005 The Authors. Journal compilation C 2005 RAS, MNRAS 364, 344Ð352 350 A. Patruno et al. a by emission, and the observ- and eccentricities even for 10-ms pulsars. In summary, only the ability in the radio band of our system is not compromised by this combination of very extreme eccentricities e > 0.9, unfavourable effect. This is in agreement with the results of Hopman & Portegies orbital phases (longitude of periastron ∼180◦ and an observation Zwart (2005) which found that with an IMBH of ∼1000 M, only performed at about the epoch of periastron) and orbital separations a fraction around 2 per cent would merge in a Hubble time. in the lower end of the assumed range decrease the sensitivity of the search below η = 0.5. Foradisc structure with thickness much smaller than its radial 4 SIMULATING PULSARS AROUND extension, η roughly represents the ratio between the galactic vol- INTERMEDIATE-MASS BLACK HOLES umes explored to search for the two types of sources; thus, assum- The search for pulsars in binary systems is more difficult than for ing a disc-like and uniform distribution for both pulsars, i.e. those isolated pulsars, because of changes in the line-of-sight velocity in IMBHÐPSR systems and the isolated pulsars, η indicates ap- due to orbital motion cause varying observed pulse periods. Most proximately the relative detection efficiency. In summary, given the of the algorithms for searching for periodicities in a time series use orbital parameters of the putative pulsars orbiting IMBHs, under Downloaded from https://academic.oup.com/mnras/article/364/1/344/1153149 by guest on 30 September 2021 afast Fourier transform (FFT) to produce a frequency spectrum; the conditions explored, we conclude that their detectability by the avarying received pulsation frequency spreads the detection over Parkes Multibeam Pulsar survey has only been modestly affected many spectral bins. This reduces the signal-to-noise ratio (S/N) of by their orbital motion. Other biases related to large-scale pulsar a detection with respect to that of an isolated pulsar with the same surveys (discussed in Section 5.2) play a major role in selecting the intrinsic flux and rotational period. observed population from the intrinsic population of IMBHÐPSR We have investigated the consequences of this effect on the prob- systems. ability of detecting a pulsar orbiting an IMBH during the Parkes Pulsar Multibeam survey (Manchester et al. 2001), i.e. the deepest and most successful large-scale survey for pulsars in the Galactic 5 DISCUSSION disc completed so far, resulting in the discovery of more than 700 new sources (Faulkner et al. 2004). We have generated many sets 5.1 Formation of an IMBH–PSR and its X-ray luminosity of simulated time series containing a pulsating signal (with a duty The formation of an IMBHÐPSR binary system relies mainly on cycle of 5 per cent, as statistically appropriate for non-recycled pul- four working hypotheses: that an IMBH (i) forms in a young core- sars) of a pulsar of 1.4 M orbiting an IMBH of 1000 M. The collapsed dense star cluster, (ii) acquires, preferentially, a massive other binary parameters have been chosen to span the most likely companion star (with M > 15 M), given the dense environment values of the distribution plotted in Fig. 6, i.e. orbital separations in in which it is expected to form and live, (iii) experiences a phase ∼ the range 1Ð10 au (corresponding to orbital periods from 10dto of wind fed or RLOF accretion that terminates when the donor star ∼1 yr) and eccentricity from 0 to 1 in steps of 0.05. The sampling 23 ends its life, and (iv) that the donor star is sufficiently massive to time (0.25 ms) and the total number of samples (2 ) are the same explode leaving behind a radio pulsar, as a remnant. as the observations of the Parkes Pulsar Multibeam survey. Spin pe- Hypothesis (iii) implies that an X-ray active phase precedes the riods have been chosen to be 1000, 100 and 10 ms (the latter being formation of the IMBHÐPSR binary. Thus, IMBHÐPSR progenitors a rather extreme case for typical non-recycled pulsars, which would can be identified as X-ray sources. The X-ray active phase is found be expected to be hosted in a binary with an IMBH). For each of to be characterized by luminosities that spread over a broad range, the parameters, we have produced eight time series, spanning four depending on the mass of the companion star and the initial orbital different values of the longitude of the periastron of the elliptical separations. Two possibilities may occur, as follows. orbit (0◦,90◦, 180◦ and 270◦) and two values of the orbital phase (quadrature or conjunction) for simulated observation. (i) If the star on the ZAMS is underfilling its Roche lobe, WFA 39 −1 After creating this large set of time series, we first applied the luminosities in excess of L ULX ∼ 3 × 10 erg s are found only standard search (which maximizes the sensitivity for detecting iso- in the presence of donors as massive as 30 M.With lighter stars, lated pulsars) and, later, the ‘stack search’, which involves splitting WFA luminosities fall typically in the range between 1037 and 1039 each time series into 16 segments, performing an FFT on each of erg s−1, with the highest values coming from transfer rates magni- them. Then the resulting spectra are summed applying a constant fied by the focusing action of the gravitational field of the heavy shift between frequency bins of adjacent spectra, the shift corre- IMBH on wind particles. At separations up to several au, typical sponding to the change in the apparent spin frequency between one WFA luminosities fall short below 1038 erg s−1 so that, based on segment of observation and the next (Faulkner et al. 2004). Many luminosity arguments, it would be impossible to distinguish an ac- different bin shifts are explored in order to find those that maximize creting IMBH from a stellar-mass black hole, under WFA. WFA the spectral S/N of a given periodicity in the whole time series. At can last as long as the entire time spent by the star on the main the sacrifice of a certain loss of sensitivity (due to the incoherent sequence, τ MS ∼ 1Ð10 Myr. Expansion of the massive star during sum of spectra) this algorithm considerably improves the possibility nuclear evolution leads inevitably to a phase where the star fills its of detecting Doppler distorted signals at a reasonable computational Roche lobe. This occurs when the binary separation a  10 au at cost. the time the star is transiting the Hertzsprung gap and/or ascending For each simulated time series, we finally compared the signal- the giant branch. At this moment, one expects a dramatic increase to-noise ratio (S/N)obs at which the simulated pulsation period has of the mass transfer rate (see the spikes in Figs 3 and 4, and also been recovered by the search analysis with the signal-to-noise ratio Portegies Zwart et al. 2004b). This is a short-lived phase of a few 4 5 (S/N)sol of the same signal if it were been emitted by a solitary pulsar. 10 Ð10 yr that accounts only for ∼5 per cent of τ MS,inwhich the 40 −1 For spin period P > 100 ms, it results that η = (S/N)obs/(S/N)sol > binary can emit luminosities in excess of 10 erg s , characteristic 0.8 for all cases but those involving e  0.7 and the closest orbital of those bright ULXs in which we can be confident to find an IMBH. separations. The application of the stack search allows us to main- Thus, the lifetime of a ULX, progenitor of an IMBHÐPSR system, 4 tain a relatively good sensitivity (η  0.6) at most orbital phases τ ULX, can be as short as a few 10 yr.

C 2005 The Authors. Journal compilation C 2005 RAS, MNRAS 364, 344Ð352 Radio pulsars around IMBHs 351

(ii) If, instead, the massive star overfills its Roche lobe near the This shows that the IMBHÐPSR binaries whose progenitor experi- zero age, contact is maintained stably in the binary, and mean trans- enced a ULX phase may well represent only the tip of the iceberg fer rates as large as 10−7Ð10−5 M yr−1 are found. These rates are of the whole population of IMBHÐPSR binaries. However, we note large enough to guarantee the stability of the disc against thermal- that the estimate of is strongly affected by the uncertainty of the ionization perturbations. For donors more massive than ∼15 M maximum orbital separation allowed by an exchange interaction the mass transfer rate is higher than the Dubus critical value so that [which corresponds to the cut-off of the distribution P(a)], and also we argue in favour of persistent emission in binaries with an IMBH by the real form of the distribution P(a). Detailed stellar dynamical and massive donors. The accretion luminosities inferred at an aver- simulations are required to improve the knowledge of the crucial aged efficiency of 0.1 all exceed 1039 erg s−1,but only stars more factor . massive than 20 M can guarantee luminosities above 1040 erg s−1 Provided is known, we can estimate the number of IMBHÐPSR during the main sequence. RLOF with massive donors (>20 M) binaries, from the simple formula (τ PSR/τ X) fN ULX where τ PSR ∼ at the ULX level lasts for a time τ ULX of few million years, while 10 Myr is the lifetime of a radio pulsar, N ULX is the observed num- − lighter donors are found to brighten at the level of a few 1039 erg s 1 ber of bright ULX sources and f  1isafudge factor to compute Downloaded from https://academic.oup.com/mnras/article/364/1/344/1153149 by guest on 30 September 2021  PSR = for a time of 10 Myr. N ULX fNULX from the known number of ULXs. In order to calcu- late the number of potentially observable radio pulsars N − Concerning the ultimate fate of the donor star, we have seen that IMBH PSR orbiting an IMBH, one must also account for the strong anisotropy RLOF on the ZAMS causes significant mass losses, so one can in pulsar emission. Introducing the pulsar beaming factor b ∼ 10 estimate that only stars heavier than 15 M and lighter than 30 M (Lorimer 2001), and scaling the others quantities to the reference may end their lives as neutron stars and thus turn on as radio pulsars. values, it turns out Lighter donors probably end their life as white dwarfs. These can    still produce ULX activity under transient conditions. τPSR 10 Myr 10 NIMBH−PSR  20 f NULX. (16) With hypothesis (iv), the formation of an IMBHÐPSR system 10 Myr τX 200 b requires that the supernova explosion of the companion to the IMBH In Section 4 we have shown that Doppler distortion of the radio does not end with the disruption of the binary. Symmetric mass signal should not have hampered the detection of a putative IMBHÐ loss would not unbind the system given the large inertia of the PSR system by the Parkes Multibeam survey of the Galactic disc IMBH, but the occurrence of an asymmetric natal kick can place (Manchester et al. 2001). However, other selection effects influence the neutron star in an unbound orbit. Considering the pre-explosion the detectability of a given radio pulsar during a survey, the most rel- orbital parameters from our binary evolution models, we find that evant being the pulsar intrinsic luminosity and the survey sensitivity the probability of survival is very high, around 99 per cent. The limit for a source at the given position in the Galaxy, in turn depend- IMBHÐPSR binary that survives disruption would have preferential ing on the pulsar spin period, duty cycle, dispersion measure and separations between 1 and 10 au, and a mild eccentricity. the amount of smearing. A population synthesis analysis combined with a simulation, for the given survey, is necessary (e.g. 5.2 Perspectives of detection of the radio pulsar Lorimer et al. 1993) for assessing the ratio χ  1 between the num- ber of expected detections and the number of potentially observable In our study we have shown that binaries hosting an IMBH and radio pulsars (i.e. those having the radio beam sweeping the line a donor star, massive enough to leave a pulsar as a relic, likely of sight to the Earth). Putative pulsar companions to the IMBH and experience an X-ray phase characterized by accretion luminosities typical isolated pulsars are populations of non-recycled pulsars born ranging from well below the of a 1-M star, and still residing in the Galactic disc. Assuming, in the first approxi- up to values characterizing the bright tail of the ULX window. The mation, that the two populations both share the galactic distribution lifetime, τ , over which a ULX phase is observed falls in the range ULX and the same intrinsic properties (such as the luminosity function), between 0.05 and 10 Myr, whereas τ  10 Myr is the characteristic X we can apply to the pulsars orbiting an IMBH the ‘average’ value of lifetime of an accreting IMBH as a ‘normal’ X-ray source. While χ properly calculated for the Parkes Multibeam survey (Manchester the formation of a binary IMBHÐPSR system does not necessarily et al. 2001). In particular, χ is in the range 0.050Ð0.075 for pulsars require a transit through a ULX phase, a ULX phase can inversely with luminosity greater than 1 mJy kpc2 (Vranesevic et al. 2004), highlight a system that will evolve into an IMBHÐPSR binary. From and is ∼ three times smaller, when including fainter sources having the knowledge of the distribution function P(a)ofthe initial orbital minimum luminosity ∼0.2 mJy kpc2. separations, we can calculate the ratio > 1 between the number of Correcting for this factor, and adopting the reference values of binaries hosting an IMBHÐmassive ending as a IMBHÐ equation (16), we expect that the Parkes Multibeam survey should PSR, to the number of binaries N PSR which experience a bright ULX have detected ULX phase before becoming an IMBHÐPSR. is

a N = χ N −  fN (17) max P(a)da obs IMBH PSR ULX = rt , aULX (15) pulsars orbiting an IMBH. This estimate implies that the detection P(a)da rt of a radio pulsar orbiting an IMBH in the Galaxy is subjected to where rt is the tidal disruption radius of the IMBH, amax is the or- the same small number statistics of the ULX population (whose bital separation at which an X-ray phase (of arbitrary low intensity) detection in the X-ray band is free from biases), even for the most occurs, ending with the formation of a pulsar bound to the IMBH, favourable case f = 1. In particular, it is compatible with the current and aULX is the initial orbital separation at which a ULX phase sets lack of observed pulsars of this type. More sensitive surveys of the in during binary evolution. If we suppose P(a)isuniform, and take Galactic disc (such as the ongoing P-Alpha survey at Arecibo) or a max  200 au as the limiting distance above which a natal kick targeted surveys (searching deeply for pulsars in the directions of would unbind the system (for a chance probability of 50 per cent), young star clusters) may result in an improved value of χ, enhancing and a ULX  1au(the distance for a RLOF phase during the main the possibility of unveiling a pulsar orbiting an IMBH within a few sequence), then we obtain an approximate estimate of ∼200. years. However, another possibility is that the number of ULXs

C 2005 The Authors. Journal compilation C 2005 RAS, MNRAS 364, 344Ð352 352 A. Patruno et al. hosting an IMBH is not so high as supposed, because, as previously Hopman C., Portegies Zwart S. F., Alexander T., 2004, ApJ, 604, L101 discussed, these sources may be explained by simple stellar-mass Kaaret P., Corbel S., Prestwich A. H., Zezas A., 2003, Sci, 299, 365 black holes, leaving only a few ULXs with a true IMBH. In this case, Kaaret P., Ward M. J., Zezas A., 2004, MNRAS, 351, L83 we must rescale the value of equation (16) to the unknown number Kalogera V., 1996, ApJ, 471, 352 Kalogera V., Henninger M., Ivanova N., King A. R., 2004, ApJ, 603, L41 N < N ULX of ULXs with a real IMBH, diminishing our chance of ULX King A. R., Dehnen W., 2005, MNRAS, 357, 275 a successful detection. Next-generation radio telescopes will be able King A. R., Davies M. B., Ward M. J., Fabbiano G., Elvis M., 2001, ApJ, to go well beyond the Magellanic Clouds and eventually reach all 552, L109 the galaxies in the Local Group (e.g. M31 with LOFAR; R¬ottgering K¬ording E., Falcke H., Markoff S., 2002, A&A, 382, L13 2003) or nearby galaxies (e.g. M82 with SKA; Cordes et al. 2004). K¬ording E., Colbert E., Falcke H., 2005, A&A, 436, 427 The much larger volume of space explored will enclose some known Lipunov V. M., Postnov K. A., Prokhorov M. E., Osminkin E. Y., 1994, ApJ, bright ULXs.1 If these future instruments will be able to sample a 423, L121 sizeable fraction of the total pulsar population in nearby external Lipunov V. M., Bogomazov A. I., Abubekerov M. K., 2005, MNRAS, 359, galaxies, they will greatly increase the chance of discovering objects 1517 Downloaded from https://academic.oup.com/mnras/article/364/1/344/1153149 by guest on 30 September 2021 belonging to the very intriguing class of binaries presented in this Liu J., Bregman J. N., Seitzer P., 2004, ApJ, 602, 249 paper. Lorimer D. R., 2001, Living Reviews in Relativity, 4, 5 Lorimer D. R., Bailes M., Dewey R. J., Harrison P. A., 1993, MNRAS, 263, 403 ACKNOWLEDGMENTS Lyne A. G., Lorimer D. R., 1994, Nat, 369, 127 Madau P., Rees M. J., 2001, ApJ, 551, L27 We would like to thank Onno Pols and Jasinta Dewi for the kind Manchester R. N. et al., 2001, MNRAS, 328, 17 support in the use of the Eggleton code, and Simon Portegies Zwart Miller M. C., Colbert E. J. M., 2004, Int. J. Mod. Phys. D, 13, 1 for a useful discussion on several aspects of this work. The contri- Miller J. M., Fabbiano G., Miller M. C., Fabian A. C., 2003, ApJ, 585, bution of AP has been partially supported by the Italian Ministry L37 for Education, University and Research (MIUR) under grant PRIN- Miller J. M., Fabian A. C., Miller M. C., 2004, ApJ, 607, 931 2004023189. Miller N. A., Mushotzky R. F., Neff S. G., 2005, ApJ, 623, L109 Mushotzky R., 2004, Prog. Theor. Phys. Suppl., 155, 27 Orosz J. 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C 2005 The Authors. Journal compilation C 2005 RAS, MNRAS 364, 344Ð352