Accretion Induced Collapse of White Dwarfs as an Alternative Symbiotic Channel to Millisecond Pulsars

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1 Astron. Nachr. / AN 999, No. 88, (2006) / DOI please set DOI! Accretion Induced Collapse of White Dwarfs as an Alternative Symbiotic Channel to Millisecond Pulsars Ali Taani 1, Applied Science Department, Aqaba University College, Al-Balqa Applied University, Aqaba, Jordan Received 30 May 2005, accepted 11 Nov 2005 Published online later Key words pulsars: general, stars: neutron stars, white dwarfs, cataclysmic variables, x-ray binaries. The direct collapse of a white dwarf () to a neutron star (NS) was postulated by many authors in order to explain the origin of some low mass X-ray binary sources, as well as the existence of millisecond pulsars (s). The implication of accretion induced collapse (AIC) in accreting s for the s population is investigated in this paper. In addition, the number of AIC which are believed to occur in the Galaxy are estimated. We confirm that a significant fraction of s may originate from AICs, approximately 4 40%. Reaching the Chandrasekhar limit may lead to the the massive exploding as a Type Ia supernova (in case of a CO ) or to ignite the AIC process (in the case of an ONeMg ; and possibly also in some CO s) producing a NS. This scenario also suggests that some fraction of the isolated s in the Galactic disk could be formed through the same channel followed by a significant kick to the companion sufficient to completely disrupt the system. Finally, the implication and application of the contribution of AIC on the s papulation are discussed. 1 Introduction Millisecond pulsars (s) are remarkable objects born via type II supernovae (SNe) explosions and characterized by short spin periods (P spin 20 ms), weak magnetic fields (B 10 9 G) and being extremely old 10 9 yr, based on recycling process. They are often found in binaries with white dwarfs (s) of masses 0.15M 0.45M in circular orbits (see e.g., Alpar et al 1982; Bhattacharya & van den Heuvel 1991; Lorimer 2008). In spite of fact that our knowledge of s has grown tremendously in recent years, there is still a gap between observational data and underlying theory. This is attributable to the lack of compatibility behind standard population synthesis models and the data at hand. The origins of this mismatch stretch back to the first discovery of a, when it was suggested that s were formed in low-mass X- ray binary systems (LMXBs). This argument called for a recycling process in which the slowly rotating old NS may be spun-up into a via accretion from a binary companion (Alpar et al. 1982; Bhattacharya & van den Heuvel 1991; Taani et al. 2012a). In addition, observation of pulsations with a period of 2.4 ms in the accreting X-ray binary SAX J (Wijnands & van der Klis 1998) has confirmed this scenario. This link has been reinforced by the discovery of PSR J (Archibald et al. 2009), where radio emission is likely to have only switched on recently after the LMXB phase. Corresponding author: ali82taani@gmail.com An alternative proposal is the accretion induced collapse (AIC) of an ONeMg white dwarf () (Nomoto 1987; Hurley et al. 2010; Taani et al. 2012ab). In this scenario, mass transfer can increase the mass of a towards the Chandrasekhar mass. Close to this mass limit, degeneracy pressure can no longer support the star, where the supporting electron pressure is robbed by inverse β decays (Kitsikis et al. 2005), consequently losing energy through neutrinos. This causes it to collapse and violently release its gravitational energy, which might be observable by the gravitational wave observatories such as LIGO, VIRGO and GEO (Metzger et al. 2009; Darbha et al. 2010). It is noteworthy to mention here that the discovery of PSR J by Champion et al. (2008) and later, in more detail, by Freire et al. (2011) measuring M NS = 1.667±0.021M is about 30% larger than that of other binary NSs in the Galactic disk, further challenges the conventional formation scenarios. Not only because the pulsars companion is a main-sequence star M C = 1.05±0.015M, but the orbit is also highly eccentric (e = 0.44) with 95-d orbital period, neither of which are predicted by the standard formation scenarios. However, the standard model for producing s fails to explain the orbital characteristics of this extraordinary binary. Champion et al. (2008) proposed that the AIC of a massive and rapidly rotating could produce the observed orbital parameters of PSR J Recently, Freire et al. (2011) and Pijloo et al. (2012) have questioned the plausibility of the existence of such a --MS triple system and have pointed out several shortcomings associated with such a proposition. The purpose of this paper is to estimate

2 790 Please give a shorter version with: \authorrunning and/or \titlerunning prior to \maketitle Table 1 Binary and Isolated s. Galactic Plane Ter 5 Globular Cluster 47 Tuc. Binary 64% 55% 69% Isolated 36% 45% 31% The data are taken from the ATNF catalogue (Manchester et al. 2005) Formation Routes in Binary Systems MS - MS Mass Transfer MS AIC MS - MS SN II Mass Transfer NS MS LMXB Fig. 1 The full-sky distribution of all known s, shown in Galactic coordinates in which the plane of the Galaxy is at the equator, and the Galactic center is at the origin. These data are taken from (Ritter & Kolb (2014). the contribution of the AIC process to the population which could influence the observed population of s. 2 AIC Process Recently, it has been pointed out that the Galactic core collapse SNe rate cannot sustain the complete NS population (van der Heuvel 2011), which implies that other mechanisms for forming NSs must exist. An ONeMg is considered more combustible and more massive than other types of s. Once nuclear ignition occurs in the core, the burning propagates through the entire star. As the burning deflagrates outwards, the central temperature and pressure rise enough according to the equation of state which describes the relationship between density and pressure in the material (Merloni & Ruffini 1998). The process of electron capture may induce gravitational collapse by 24 Mg and 20 Ne at a density of gcm 3 (Nomoto 1987) in the (Wickramasinghe 2009). The star contracts until it reaches the pressure limit and finally it collapses homogeneously to form a NS. Fig. 2 A diagram illustrating possible binary evolution scenarios leading to the formation of - systems in the Galactic disk. The AIC branch of binary evolution is an important channel by which NSs form. Thus this channel can contribute significantly to LMXB classification and evolution (Taani et al. 2012a). Of particular importance, the AIC of a can lead to the formation of a NS with larger angular momentum. This occurs in cataclysmic variable (CV) systems with main-sequence or red giant donors filling their Roche lobes or else in ultra-compact X-ray binary systems (UCXBs; (Breton et al. 2007). Depending on the strength of the s magnetic field, the matter flowing through the Lagrangian point can form either a full or partial accretion disk or else follow the magnetic field lines down to the surface at the magnetic poles. Thus it is important to monitor long-period CV systems in order to gain insight into the dynamics and binary evolution of those systems most likely to undergo AIC. Fig. 1 shows the multitude of known CV systems distributed throughout the Galaxy. 3 The Evolutionary Path from to Fig. 2 is a simple flow-chart of the currently favored model (Ferrario 2008ab; Lorimer 2009; Li 2010) used to explain the formation of the various types of systems. The left column illustrates a binary system in which the more massive star typically has a mass in the range 8 11M and produces a after exhausting its available thermonuclear

3 Astron. Nachr. / AN (2006) 791 fuel. Our major assumption is that the -MS channel for producing s is more common than the -NS channel, because (1) not all s have the right composition (O- Ne-Mg) and not all of them accrete sufficient mass ( m = M ) to undergo AIC. (2) in the -NS case the progenitor star of the NS is more massive and hence may bring the binary into Roche Lobe overflow from a larger original separation. Although the rate of AIC is uncertain, the expectation is about yr 1 per Milky Waytype galaxy (Darbha et al. 2010). In the right column of Fig. 2, the companion star is massive enough that it explodes directly as a type II SN, producing a NS. The binary does not stay intact if more than half the total pre-supernova mass is ejected from the system during the explosion 1 (Lorimer 2008), and then the NS may be observable as a normal radio pulsar spun-down to a period of several seconds. During the accretion phase, X-rays are emitted by the frictional heating of infalling matter to the NS. This makes the system visible as an X-ray binary. At the end of this spin-up phase, the secondary sheds its outer layers to become a in orbit around a now rapidly spinning. We suggest that the right branch is far more probable based on the observed abundance of s being quite large compared to NSs. 4 Discussions Standard stellar evolution predicts that more than 97% of all stars with a main-sequence mass lower than 8M end their lives as a (Kitsikis et al. 2005). We can use the total number of s (N W D ) to investigate the expected contribution of AIC to the measured population. However the prevalence of AIC is still a matter of heated debate both observationally and theoretically (Wickramasinghe et al.2009: Hurley et al. 2010; Taani et al. 2012b). Based on a survey of the local population within 20 pc of the sun by Holberg et al. (002) and Holberg et al. (2008), the estimated number of s in the Galaxy is about They predicted that 25% of s are in binary systems (N Binary ) and that 6% of those binaries are doubly degenerate binary systems (N Degenerate ), so that the total number of binary degenerate systems in the population N (W D Binary Degenerate) = % 6% can be expressed as Ω W D. Let us start with a back-of-the-envelope calculation of the double degenerate systems. Their two branches are, - and -NS. The number of -NS systems in our galaxy is given by: Ω W D N W D NS N W D NS + N W D W D. (1) It is suggested that the - model is more likely to lend to an AIC than a SN Ia (Wang & Han 2010), from an observational point of view (Holberg et al. 2008; Ritter & Kolb 2014). There has recently been a significant increase in the number of new + binaries with M W D 0.7M ( 1 For simplicity, we assume the explosion is symmetric. Log P orbital (D) Log P orbital (D) Log Mass sun Fig. 3 The correlations between mass and orbital period, showing that a massive is recycled to an. The orbital periods of the binary systems show a clear difference (over two orders of magnitude). It should be noticed that the AIC process leads to dynamical interactions for systems during the conversion of a to an. The data of s and s are taken from the ATNF catalogue (Manchester et al. 2005) and Ritter & Kolb (2014), respectively. Ferrario & Wickramsinghe 2005; Rebassa-Mansergas et al. 2012), with several having total masses close to the Chandrasekhar limit M ch 1.4M. In either AIC or a - merger, the star will be rapidly rotating prior to collapse and must eject a sizable fraction of its mass into a disk during the collapse in order to conserve angular momentum. Hence, Equation1 becomes: Ω W D N W D NS. (2) N W D W D Since there is a firm evidence that many newborn NSs receive a momentum kick at birth ( Podsiadlowski et al. 2004; van der Heuvel 2011) raises the observed high velocities (typically 400 kms 1 ), so the supernova kicks to disrupt binary systems. That is why most massive stars known today reside in binary systems while most NSs are single. Solely for illustrative purpose, we expect that the ratio of the denominator is less than the numerator in the expressions of Eq. 1, and hence (N W D NS )/(N W D W D ) << N NS /N W D. There is a large of the systems that are close enough that mass is transferred from one star to the other which changes the structures of both stars and their subsequent evolution. While the exact numbers are

4 792 Please give a shorter version with: \authorrunning and/or \titlerunning prior to \maketitle somewhat uncertain, binary surveys suggest that the range of interacting binaries, is in the range of 30 % to 50 % (see, e.g., Duquennoy & Mayor 1991; Kobulnicky & Fryer 2007) equation 2 can be rewritten as: N W D N W D+NS Ω W D N NS (3) It is noteworthy to mention here that the s are also kicked at their birth with a velocity of a few km s 1 (Davis et al. 2008). However, the kick is too small to be seen in single stars because their Galactic velocities are much larger, but in binaries with orbital velocities of the same order of magnitude such kicks will impact the binary dynamics (Izzard et al. 2010). By using measurements of the local surface density of pulsars and integrating over the full Galaxy, such as 10 5 < N P SR < 10 6 (Lyne & Smith 2007; Lorimer 2008), and substituting it into 4, we get the total number of AIC cases as follows: N AIC = (4) This provides a rough estimate of the total number of AIC which could potentially occur in our Galaxy. To place this into context we consider the observed population of s, they were estimated to have a Galactic population of about (Lorimer 2008). Using this estimation, we can approximate the possible contribution of AIC (α AIC ) to the population in the Galaxy as follows: < α AIC < = 4 40%. (5) In this approach, the total number of potential AIC host systems are estimated with values show that their events are able to contribute significantly to the total population of s. In this case the AIC-formed s are produced from an accreting in a binary system which reaches the Chandrasekhar limit to form a NS. Thereafter it forms a binary with long orbital period (P orb 2 d), according to the observed data shown in Fig. 3, or in some cases produces an isolated if the companion undergoes a powerful SNe and unbinds the binary. Further, if quark stars do exist, the AIC could be invoked to produce submillisecond pulsing quark stars, a regime which otherwise may be unattainable by the normal channels that produce NSs (Chen et al. 2011). Knowledge of the SNe Ia rate is necessary to include these effects in galaxy evolution models. However, an accurate prediction of the SNe Ia rate in galaxies of varying ages, masses, and star formation histories requires a good understanding of the nature of the progenitor. This is particularly true for higher redshifts where direct SNe rate constraints are unavailable. From a cosmological perspective, the progenitor has become a central concern following the use of SNe Ia as standardizable candles in the discovery of dark energy (Riess et al. 1998; Perlmutter et al. 199). If we now begin from the opposite end of the problem and note that the observed rate of SNe Ia is r SNeIa = 4 ± yr 1 per (Milky Way-type) galaxy (Barbary et al. 2012), then the total number of SNe Ia can be estimated as N SNeIa = r SNeIa τ = , (6) where τ is the age of universe. We therefore find that the potential contribution of the AIC to the total number of SNe Ia is roughly 1 %. This confirms the predictions of (Darbha et al. 2010), with the caveat that the precise nature of the progenitors involved and the physics of the explosion mechanisms are still not well understood. It is noteworthy to mention here that the AIC process leads to with mass less than Chandrasekhar limit (Zhang et al. 2011) When a gains mass by accreting matter from its companion, its binding energy also increases, this effect is significant in the estimation of the amount of mass accretion. However, unfortunately most of the studies argued that the binding energy of the NS is not commonly considered (Bagchi 2011). One can consider an estimate of the amount of gravitational binding energy (mass loss), due to the conversion from ONeMg matter to. Let s begin with the gravitational energy in NS (Shapiro & Teukolsky 1983) E = GM 2 R Where G is the gravitational constant, M the mass companion, R the NS radius E = ( 2GM c 2 ) Mc2 2R R SMc 2 2R where R S is Schwartz radius (R S = 2GM c 3 km for 2 (1M/M ) (7) E = ηmc 2 (8) where η = R S 2R, thus E 0.1Mc 2 (9) As a result, around 10% of mass will goes as binding energy and reduce the mass below 1.4M with about 0.14M, where the total energy is Mc 2 (1 η) (10) In sum-up, the AIC decreases the mass of the compact object and increases the orbital period so that the further evolution can no longer be compared to that of systems without an AIC. 5 Summary and Conclusions We have studied the AIC process and its contribution to the s population. As such, an understanding of the nature of s, s and SNs Ia depends critically on our knowledge of stellar evolutionary process responsible for their formation and evolution. The following conclusions can be drawn from the present study.

5 Astron. Nachr. / AN (2006) 793 The observed sample of s indicates refinement regarding the picture of the distribution of populations all over the sky. The existence of these objects has expanded the possible evolutionary channels for the formation of near Chandrasekhar-mass type Ia SNe models and s via the AIC process. The build-up of the depends critically on the accumulation efficiency of matter in the presence of unstable He burning shells. More extensive studies of this phase over wide range of masses are argued. The AIC of a is able to produce a significant portion (up to about 40%) of the population. Further, the process by which AIC occurs directly predicts systems with a long orbital period of a few days, like those found in roughly half of the population. We also show that, in extreme cases in which a powerful supernova occurs, the resulting kick and ejection of material can often unbind the binary and produce an isolated. Therefore, AIC scenario is rectified to reconcile the apparent discrepancy in the birthrate of LMXBs and s, and provide the missing evolutionary links which can possibly unify the observed populations of X-ray binaries, CVs, LMXBs and s under a common evolutionary pattern. AIC does not contribute significantly to the standard event rate for SNe Ia simply because comparatively AIC events are relatively rare. This result agrees with?. This is supported by the fact that an AIC has yet to be definitively observed. In summary, research into the AIC process could prove fruitful to explain the formation of s while simultaneously enabling astrophysicists to test the theories of LMXB evolution and both and NS formation. In forthcoming work we shall continue this research with studies aimed at tackling these questions in greater depth. Acknowledgements We are grateful for the discussions with Chengmin Zhang. References Alpar, M. A., Cheng, A. F. & Ruderman, M. A. et al.: 1982, Nature 300, 728 Archibald A. M., Stairs I. H., Ransom S. M., et al. 2009, Science, 324, 1411 Bagchi M., 2011, Revealing Their Structure, Formation, Evolution and Dynamic History. Pulsars: Theory, Categories and Applications. Nova Science Publishers arxiv: v2 Bhattacharya, D. & van den Heuvel, E. P. J.: 1991, Phys. Rep. 203 Breton R. P., Roberts M. S. E. & Ransom, S. M. et al. 2007, ApJ, 661, 1073 Champion, D. J., et al.: 2008, Sci, 320, 1309 Chen W.-C., Lui X.-W., Xu R.-X. & Li X.-D., 2010, MNRAS, 410, 1441 Darbha, S., Metzger, B. D. & Quataert, E. et al.: 2010 MNRAS, 409, 846 Davis D. S., Richer H. B., King I. R., et al. 2008, MNRAS, 383, L20 Ferrario, L. & Wickramasinghe, D. T., 2008, AIP Con. series, 968, 188 Ferrario, L. & Wickramasinghe, D. T., 2008, AIP Con. series, 968, 188 Freire P. C. C., Bassa C. G., Wex N., et al., MNRAS, 412, 2763, Holberg J. B., Oswalt T. D., & Sion E. M. 2002, ApJ, 571, 512 Holberg J. B., Sion E. M., Oswalt T. et al. 2008, AJ, 135, 1225 Hurley, J. R., Tout, C. A. & Wickramasinghe, D. T. et al.: 2010, MNRAS 402, 1437 Izzard R. G., Dermine T., & Church R. P., 2010, A&A, 523, A10 Kitsikis A., Fontaine G., & Brassard P., 2005, ASPC series, 334, 65 Lorimer D. R. 2008, Living Rev. Relativity, 11, 8 Lorimer D. R. 2009, Astrophysics and Space Science Library, Neutron Stars and Pulsars, 357, 1 Li, X.D.: 2010, Sience in China 53, 9 Lyne A. G. & Graham-Smith, F., 2007, Cambridge astrophysics Series, Cambridge University Press, Pulsar astronomy, 3ed Edit. Manchester, R. N., Hobbs, G. B. & Teoh, A. et al.: 2005, AJ 129, 1993 Merloni A. & Ruffini R., 1998, Journal of Korean Physical Society 33, 554 Metzger, B. D., Piro, A. & Quataert, E., MNRAS 396, 304 Nomoto, K.: 1987, ApJ 322, 206 Podsiadlowski Ph., Langer N., Poelarends A., et al. 2004, ApJ, 612, 1044 Perlmutter S., Aldering G., Goldhaber G., et al. 1998, Astrophys. J. 517, 565 Pijloo J. T., Caputo D. P., & Zwart S. P., 2012, MNRAS, 424, 2914 Rebassa-Mansergas A., Nebot Gmez-Moran A., Schreiber M. R., et al. 2012, MNRAS, 419, 806 Riess A. G., Filippenko A. V., Challis P., et al. 1998, Astronom. J. 116, 1009, Ritter, H. & Kolb, U.: 2014, Catalogue of Cataclysmic Binaries, Low-Mass X-Ray Binaries and Related Objects, Shapiro S. L. & Teukolsky S. A., 1983, Journal of the British Astronomical Association 93, 276 Taani A., Zhang C.M., Al-Wardat M. et al., 2012a, AN, 333, 53 Taani A., Zhang C.M., Al-Wardat M. et al., 2012b, Ap&SS, 338, 295 van den Heuvel E. P. J., 2011, Bulletin of the Astronomical Society of India 39, 1 Wang B. & Han Z., 2010, Astrophys Space Sci, 329, 293 Wickramasinghe D. T., Hurley J. R., Ferrario L., Tout C. A. & Kiel P. D. 2009, JPhCS., 172, 2037 Wijnands R. & van der Klis M., 1998, Nature, 394, 344 Zhang C. M., Wang J., Zhao Y. H. et al. 2011, A&A, 527, A83 Zwart S. P., van den Heuvel E. P. J., van Leeuwen J. et al. 2011, Astrophys. J. 734, 55