arXiv:astro-ph/0502511v1 24 Feb 2005 o.Nt .Ato.Soc. Astron. R. Not. Mon. h ouaino lc io pulsars widow black of population The

cetd20 aur 7 eevd20 aur 6 norigi in 26; January 2005 Received 27. January 2005 Accepted eto trmgei edhsdcydt value recyclin a to decayed This when has place field companion. magnetic take star only binary neutron can close 1981) Srinivasan, a & from (Radhakrishnan accretion a (MSPs) by pulsars millisecond up most that believed widely is It INTRODUCTION 1 samlieodpla ihavr o pnonrt,a t l its as rate, weak. spindown very low radiation very dipole makes ap a field star with magnetic neutron pulsar the millisecond reason, a some as for stops subsequently tion ainit otc ihisRcelb h usri bet e to point able Lagrange is inner pulsar the the through lobe issuing Roche matter the its co with the companion contact bring dwarf into expansion nuclear panion white or helium loss momentum their angular Once eject mill and recycled (MSPs) containing turnoff–mas pulsars binaries which wide in into globulars favoure exchange a in stars identified BWPs We for field. mechanism hi the far mation in is than (BWPs) clusters pulsars globular widow black in of incidence the that out e the 2001). seeing al., us et prevent (Freire evapora which also inclinations are orbital these that with assume tems mass to natural lower is it systematically and tions, with pulsars millisecond binary ⋆ Fuhe ta. 98.Weee uhelpe r enthe seen extremel masses are are companion emission function implying mass eclipses pulsar pulsar such the the and Whenever by eccentricity nary 1988). way al., some fro et wind in intense (Fruchter driven an star, be companion must tha This the larger lobe. much Roche unde object star’s obscuring pulsars companion an these with Often eclipses, systems. wide binary very of members are sars hoeia srpyisGop nvriyo Leicester, of University Group, Astrophysics Theoretical c .R King R. A. -al [email protected] E-mail: 05RAS 2005 nln ihteeiesalrepooto fmlieodpu millisecond of proportion large a ideas these with line In narcn ae Kn ta.20;hratrKB epointed we KDB) hereafter 2003; al. et (King paper recent a In ⋆ .E er .J of,K cekradJ .Skipp M. J. and Schenker K. Rolfe, J. D. Beer, E. M. , 000 – 20)Pitd3 coe 08(NL (MN 2018 October 30 Printed (2005) 1–4 , M 2 ∼ < M ino l bevbepoete.W ugs httegroup the that suggest We masses properties. panion observable all app radiation of gravitational tion under loss mass consequent and vn.W on u htalbnr ilscn usr (MSP pulsars millisecond binary all that out point We event. htrcce Ssei ihri iefnba rapni be pencil a words: or Key o beam beam. 10 fan fan in wide a eclipses favour a the ideas in see evolutionary either Simple to emit us MSPs allows recycled sight that of line (our BWPs are ebr fgoua lses o iiu opno masses Th companion (BWPs). minimum For pulsars clusters. widow globular black of members of population the consider We ABSTRACT ⊙ hr saohrgopof group another is There . ∼ ecse,L17H UK 7RH, LE1 Leicester, 10 iais close binaries: L 1 ∼ > 8 hsmass Thus . .I accre- If G. a om20 pi 4 April 2004 form nal 0 . igsys- ting 1M small, y isecond espun re clipses for- d pears func- the n gher xpel ⊙ rgo the ow m- bi- m s. l- r ytm eaigt qiiru fe eaieyrece relatively a after equilibrium to relaxing systems are g s eeeaerdu ie by given radius degenerate and content, drogen oito h itiuino i.1pt h iiigln b line dividing the at puts BWPs low–mass 1 and t Fig. With high– inclination. of orbital distribution low the at seen sociation BWPs interp are The these systems. that eclipsing is the of those than smaller even ∼ > iayMP hc ontelpebtwoevle of values whose but oth eclipse groups not two do these which with 2004 associate MSPs January may binary we in way at Pulsars standard talk the Millisecond In Ransom, Binary Scott on (e.g. Meeting group Aspen low–mass the than eclipses R ihrflycnetv rdgnrt ecnmdlapproxim model an can as we it degenerate or convective adiabatically fully reacts either therefore star The los behaviour. mass BWP for ing timescale evolution binary the than longer much c ..Kn 98 o oeacrt ersnain e Ne see representations Here accurate 2003). more Rappaport, for & 1988; King e.g. (cf as(ls to (close mass Wsapa ofl notodsic ruswihw shall we which groups whether distinct on depending two low–mass, into and high–mass fall call to appear BWPs BWPS LOW–MASS OF POPULATION 2 n ria period orbital and rbto fBP ntepaeo iiu opno mass companion minimum of d plane the the understand in to BWPs is of aim tribution main Our BWPs. of evolution sequent hnti vlto n hstems osaeslow. are loss mass the thus and observab evolution are this BWPs timescale. when evolution binary the on lost is 2 A 0 T ≃ . E 1M tl l v2.2) file style X ecnie h o–asgopfis.Tesalsecondary small The first. group low–mass the consider We eew osdrtecneune fti itr o h sub the for picture this of consequences the consider we Here 10 ⊙ n 9 h ihms ru aentcal oeirregular more noticeably have group high–mass The . ( = 1 + 3 / X oyrp,wt radius with polytrope, 2 M ) 5 min / P 3 m Fg 1). (Fig. k o cisn ytm)ipisatemltime thermal a implies systems) eclipsing for 2 − ≥ 1 / 3 esrstedvainfo h fully– the from deviation the measures 1 k k m m(1) cm = a opoieachrn explana- coherent a provide to ear 2 M )wt ria periods orbital with s) .W sueta o–asBWPs low–mass that assume We 1. = fBP ihmnmmcom- minimum with BWPs of min < M to 6css.Ti implies This cases). 16 of ut ag aoiyo hs are these of majority large e . M 0.1 2 ≃ mcoet h pnplane. spin the to close am / M 0 . 05M ⊙ , ⊙ stefatoa hy- fractional the is X daai evolution adiabatic , ⊙ . tcapture nt M P M min si is it As . ∼ < retation etween min eonly le caus- s i as- his 0hr 10 M ∼ > ately lson min are the is- or er ). - 2 A.R. King et al.

Figure 1. A plot of log period in hours versus log minimum companion Figure 2. A plot of log period in hours versus log minimum companion mass for all the binary MSPs in globulars. Filled circles denote eclipsing mass for all the BWPs in globulars along with the evolutionary constraints systems and open circles non-eclipsing systems. as described in the text for the low-mass systems. Also labelled is the longest period BWP PSR J1740–5340 which has a sub-giant companion. < have a range 1 < k ∼ few for reasons we will discuss in the next section. Assuming a Roche-lobe filling donor gives the mass-period relation −2 5/2 3/2 −1 m2 = 1.5 × 10 (1 + X) k Ph (2) where Ph is the orbital period measured in hours. We assume further is plotted on Fig. 2 as ‘Visibility line’. that loss of orbital angular momentum via gravitational radiation In a similar way we can plot various other constraints on this (GR) drives orbital evolution, so that figure. For very small mass ratios q = M2/M1 the β term in the de- nominator of (3) becomes significant. This signals dynamical insta- M˙ 2 3(1 + q) J˙GR = (3) bility, as the Roche lobe moves inwards wrt the stellar surface (cf M2 2 − 3β + q J Stevens, Rees & Podsiadlowski, 1992). At such masses the com- β where q = M2/M1, M1 ≃ 1.4M⊙ is the pulsar mass, and is the panion must be broken up and sheared into a large disc surround- specific angular momentum of the lost mass relative to that of the ing the pulsar. This is presumably the origin of the planets observed secondary (van Teeseling & King 1998). Thus around PSR B1257+12 (Wolszczan & Frail 1992; Konacki & Wol- szczan 2003). Direct numerical calculation of b from Roche geom- b 2 β = (1 + q)2 (4) etry shows that dynamical instability occurs when M /M < 0.02 if  a  2 1 matter is ejected from the L1 point. However, matter can be ejected where a is the binary separation and b is the distance from the cen- from anywhere between the L1 point and the circularization radius tre of mass at which the matter is ejected from the binary. This is (which even for small mass ratios is not comparable with the dis- between the circularization radius of the infalling matter and the L1 tance to the L1 point). If matter reaches in 5 per cent of the distance point. As all BWPs have M2 ≪ M1, β ≪ 2/3 except for very small from the centre of mass to the L1 point this gives M2/M1 = 0.011 q (see below) the first term on the right hand side of (3) is 3/2 and i.e. m2 = 0.016. This line is labelled ‘Dynamical Instability’ on we can rewrite (3) as Fig. 2. We also plot the line (‘Hubble line’) on which the binary evolution has a characteristic timescale longer than a Hubble time. ˙ −10 −8/3 2/3 2 −1 M2 = −1.9 × 10 Ph m m0.1 M⊙yr (5) Finally we plot the binary evolution of a system whose secondary is fully degenerate (‘Degenerate’) and one whose radius is 3 times where m =(M1 +M2)/M⊙ and m0.1 = m2/0.1. According to KDB the system is only visible as a BWP if this rate is less than the as large for the same mass (k = 3) as given by equation (2). Arrows critical value on the degenerate sequences indicate the direction of evolution. 3 4 If this is a viable picture of the evolution of low–mass BWPs, M˙ = 1.5 × 10−12 P T / M yr−1 (6) crit h 6 ⊙ we expect them to have combinations of P,M2 lying inside the for free–free absorption at typical (400 – 1700 MHz) observing various constraints shown in Fig. 2. Given that eclipsing systems (solid circles) have M ≃ M , while non–eclipsing systems have frequencies, where T6 ∼ 1 is the temperature of the lost mass near 2 min 6 M > M , we see that the data plotted on Fig. 2 are indeed rea- L1 in units of 10 K. The resulting constraint 2 min sonably consistent with adiabatic evolution under mass loss driven > −9/44 2/11 6/11 Ph ∼3.7T6 m m0.1 (7) by gravitational radiation.

c 2005 RAS, MNRAS 000, 1–4 The population of black widow pulsars 3

3 HIGH–MASS BWPS origin of the range of radii (k–values) inferred for low–mass BWPs above. We now consider the remaining systems on Fig. 2, i.e. those with Grindlay (talk at Aspen Meeting on Binary Millisecond Pul- > Mmin ∼0.05M⊙. Nelson (talk at the Aspen Meeting on Binary Mil- sars in January 2004) has found 108 X-ray sources in the globular lisecond Pulsars in January 2004) has studied the evolution of the cluster 47 Tuc. A number of these are claimed to be quiescent low- long–period system J1740–5340, which has a subgiant compan- mass X-ray binaries (LMXBs) and have measured periods from X- ion (D’Amico et al. 2001; Ferraro et al. 2001) and shown that it ray dips/eclipses (eg W37 at 3 hrs), power law components (pos- is consistent with a location near a bifurcation point, at which nu- sibly from a wind) and variable absorption. These may be BWPs, clear evolution and angular momentum loss are comparable. The rather than quiescent LMXBs, where the absorption is too large to < < remaining 4 systems have P∼5 hr and Mmin ∼0.13M⊙. Except observe the radio emission and the stellar wind is responsible for for implausibly small orbital inclinations these companions have the X-ray emission. main–sequence radii far too small to fill their Roche lobes. There are various ways around this difficulty, including competition be- tween nuclear and orbital evolution, or attributing the eclipses to strong stellar winds of detached companions. However the most 4 FANOR PENCIL BEAM? likely explanation appears to us to follow from the turbulent his- Fig. 1 reveals the striking fact that all binary MSPs with orbital tory these binaries must have had. < periods P∼10 hr are BWPs: 10 out of 16 actually eclipse. There The process of gaining a new companion must involve con- are two obvious possible explanations for this: siderable disturbance to that star, probably leading to extensive (a) Fan beam. The pulsar beam of a recycled MSP is so wide mass loss. This is clearly indicated for tidal capture (Podsiadlowski that it always includes the orbital plane, whatever the relative ori- 1996), but is probably true in any picture. For an exchange en- entation of spin and orbit. For a wide fan beam such systems are counter to give a short period system a large post-exchange ec- detectable at any spin inclination. Then all binary MSPs become centricity is required (see section 5). When this eccentric system BWPs as soon as their companions fill their Roche lobes. circularizes the tidal effects on the secondary can in some cases (b) Pencil beam. The beam of a recycled MSP is narrowly be similar to tidal capture if the periastron distance is compara- confined. Clearly the only plausible geometry for making BWPs ble to the stellar radii. The globular–cluster X–ray binary AC211 has the beam axis orthogonal to the spin, with the latter roughly (van Zyl et al. 2004; Charles, Clarkson & van Zyl 2002, and ref- aligned with the binary orbit. erences therein) may be an example where the companion star is It is quite difficult to break the degeneracy between these two oversized because of the capture process, the only difference being possibilities. However the pencil beam requires alignment, and thus > that the neutron star in this system accretes the overflowing matter that the pulsar has accreted ∼0.1M⊙ from its current companion. rather than expelling it, presumably because no previous partner re- This requires it to have been an LMXB and then somehow broken cycled it. For an exchange encounter the lowest mass star is ejected contact, and seems harder to reconcile with the picture of high– and so the captured star, in a high-mass BWP formed through this mass BWP evolution we have sketched above. We thus tentatively route, must have lost a significant portion of its initial mass. This conclude that a fan beam offers a simple explanation for the univer- mass loss, however, occurs during the tidal circularization (not af- sality of eclipsing behaviour in MSPs with short orbital periods. terwards) and so the companion could still be thermally bloated. After the tidal disturbance and consequent mass loss, the com- panion attempts to reach its new main–sequence radius on a thermal 5 DISCUSSION timescale. This process competes with orbital shrinkage via GR and reduces the mass loss (already weak – cf equation (5) for the rel- It is generally agreed that dynamical encounters must be invoked atively long orbital periods of most of this group). It is therefore to explain the overproduction of BWPs in globular clusters (KDB; plausible that BWPs ultimately emerge from the tidally induced Rasio et al. 2000). Rappaport, Putney & Verbunt (1989) consid- mass loss with the parameters of the high–mass BWPs. The ther- ered the problem of exchanging out the white dwarf companion mal timescale of some of these BWPs may be less than the GR of the neutron star in a binary MSP. Their Fig. 1 shows that the timescale and so eventually these would shrink from contact with timescale (in 47 Tuc) for ejecting the white dwarf from systems their Roche lobes. However, they would still be observed as high- with periods of 10, 100 and 1000 days is ∼10, 3, and 1 Gyr, respec- mass BWPs for the length of their thermal timescale. tively. Thus an exchange encounter is likely only for orbital peri- > ods ∼30 days. The post–exchange period is generally not substan- If the companion has a sufficiently strong stellar wind, this tially shorter, and most of these systems would not become BWPs. can produce orbital eclipses through free–free absorption. This ap- However the post–exchange eccentricity e is evenly distributed in pears to happen in PSR 1718–19 (Wijers & Paczy´nski 1993; Bur- e2 (Heggie 1975). For large e2 tides circularize the orbit at much deri & King 1994). Here P ≃ 6 hr, and modelling of the absorp- tighter separations than the initial post-exchange value. The post- tion light curve (Burderi & King 1994) shows that M2 ∼ 0.2M⊙. exchange period after tidal circularization can thus be much shorter We note that PSR 1718–19 is probably a cluster member (Wijers (hours) in a few cases, producing a BWP. & Paczy´nski 1993) and that the stellar wind must be the eclipsing The need for the exchange into the binary MSP is set by the agent as the pulsar is not an MSP, and thus incapable of driving assumption that radio pulsars do not turn on as long as there is a mass loss. binary companion in near contact; thus the need for removing it al- Although the companion must relax towards the main se- together after the initial recycling. Burgay et al. (2003), however, quence, its radius ultimately shrinks only slowly, whereas orbital claim that the lack of detection of radio pulsations from quiescent shrinkage via GR accelerates. Depending on the initial separation, LMXBs could result from pulsar radiation driving a large outflow the binary reaches contact with the companion somewhat oversized from the system which then attenuates the radio emission. A prob- compared with its thermal–equilibrium radius. This is probably the lem with this scenario is that the pulsar must remove the accretion

c 2005 RAS, MNRAS 000, 1–4 4 A.R. King et al. disc before it can blow away matter flowing through the inner La- Ferraro F. R., Possenti A., D’Amico N., Sabbi E., 2001, ApJ, 561, L93 grangian point. Burderi et al. (2001) show that this can only occur Freire, P. C.; Camilo, F. C.; Kramer, M.; Lorimer, D. R.; Lyne, A. G.; in some wide systems, and only then when the magnetic pressure Manchester, R. N.; D’Amico, N., 2001, AAS Abstract 199, #159.04 due to the neutron star overcomes the disc’s internal pressure. Con- Fruchter, A.S., Stinebring, D.R., Taylor, J.H., 1988, Nat. 312, 255 sequently it is unlikely that the companion in a BWP is the one that Grindlay J. E., 2004, in Rasio F. A., Stairs I. H., eds, Binary Radio Pulsars, ASP Conf. Ser., San Francisco spun the pulsar up, unless the latter has somehow contracted well Heggie D. C., 1975, MNRAS, 173, 729 inside its Roche lobe. If this occurs through evolutionary loss of the King A. R., 1988, QJRAS, 29, 1 envelope one then has the problem of bringing the system to short King A. R., Davies M. B., Beer M. E., 2003, MNRAS, 345, 678 periods in a reasonable time. Konacki M., Wolszczan A., 2003, ApJ, 591, L147 Converting wide orbits to narrow ones was the main motiva- Nelson L. A., 2004, in Rasio F. A., Stairs I. H., eds, Binary Radio Pulsars, tion for Rasio et al. (2000) in considering an alternative scenario. ASP Conf. Ser., San Francisco This invokes binary formation through exchange interactions, pro- Nelson, L. A., Rappaport, S. A. 2003, ApJ 598, 431 ducing neutron star systems with companions which are more mas- Podsiadlowski Ph., 1996, MNRAS, 279, 1104 sive. This must occur in a relatively short interval of 1 − 2 Gyr be- Radhakrishnan, V. & Srinivasan, G., 1981, paper presented at 2nd Asian– fore all the potential extended companions with masses larger than Pacific Regional IAU Meeting, Bandung Ransom S. M., 2004, in Rasio F. A., Stairs I. H., eds, Binary Radio Pulsars, that of the neutron star have finished their evolution. Given such ASP Conf. Ser., San Francisco a system, a common envelope phase results once the companion Rappaport S., Putney A., Verbunt F., 1989, ApJ, 345, 210 evolves and overfills its Roche lobe. The envelope of the red giant Rasio F. A., Pfahl E. D., Rappaport S., 2000, ApJ, 532, L47 is ejected and the core spirals in, leaving a He–rich white dwarf Stevens I. R., Rees M. J., Podsiadlowski Ph., 1992, MNRAS, 254, 19 in a relatively close orbit with the neutron star. If contact is estab- van Zyl L., Charles P.A., Arribas S., Naylor T., Mediavilla E., Hellier C., lished, the pulsar could presumably begin to evaporate the compan- 2004, MNRAS, 350, 649 ion. However because the donor star has no hydrogen, the orbital van Teeseling A., King A. R., 1998, A&A, 338, 957 periods of systems made this way are much shorter than those of Wijers R. A. M. J., Paczy´nski B., 1993, ApJ, 415, L115 observed BWPs (see equation 1 and Fig. 2). Wolszczan A., Frail D. A., 1992, Nat, 355, 145 The evolutionary outcome for BWPs depends on whether they have evolved to a period where they have become dynamically This paper has been typeset from a T X/ LAT X file prepared by the author. unstable. A number of BWPs exist which have reached or are E E evolving towards the ‘Hubble line’ and so are not yet old enough to have been dynamically disrupted. The systems which have undergone dynamical instability are observed as isolated MSPs. In the globular 47 Tuc 7 out of 21 of MSPs are isolated (see http://www.naic.edu/∼pfreire/GCpsr.html for an up to date list of pulsars in globular clusters) while 5 out of 21 are low-mass BWPs. Objects may undergo evolution through the low-mass evolution- ary route and disruption of the companion. However, the num- ber of resulting isolated MSPs should not be significantly greater than the number of BWPs unless there is a process which strongly favours short periods (less bloated secondaries). The similar num- ber of low-mass BWPs and isolated pulsars in 47 Tuc supports this conclusion.

ACKNOWLEDGEMENTS We thank the referee Saul Rappaport for comments which have im- proved this paper. We are also grateful to the organisers of the As- pen Meeting on Binary Millisecond Pulsars in January 2004 which provided much stimulus for this work. DR and KS are supported by the Leicester PPARC rolling grant for theoretical astrophysics, and JS by a PPARC studentship. ARK gratefully acknowledges a Royal Society Wolfson Research Merit Award. MEB acknowledges the support of a UKAFF fellowship.

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c 2005 RAS, MNRAS 000, 1–4