Binary Millisecond Pulsars Research Articles

Helium core white dwarf evolution - including white dwarf companions to neutron stars

We present a detailed calculation of the evolution of low-mass helium white dwarfs. These white dwarfs are formed via long-term, low-mass binary evolution. After detachment from the Roche lobe, the hot helium cores have a rather thick hydrogen layer with masses between 0.001 to 0.06 M⊙. We found that the majority of our computed models experience one or two hydrogen shell flashes. The duration of the flashes is between a few ×106 y to a few ×107 y. In several flashes the white dwarf radius will increase so much that it forces the model to fill its Roche lobe again. Our calculations show that the cooling history of the helium white dwarf depends dramatically on the thickness of the hydrogen layer. The presence of low-mass helium white dwarf secondaries in millisecond pulsar binaries allows to determine the age of the systems independently of the rotational history of the pulsars. The same method may be applied to double degenerate systems. We discuss the cooling history of the low-mass, helium core white dwarfs in short orbital period millisecond pulsars.

Acceleration of close binaries in supernova explosions

We investigate the orientation of the orbital planes of X-ray binary systems relative to the direction of the additional velocity acquired by the binary in a supernova explosion or as a result of radiative acceleration. In the second case, the acceleration occurs due to X-ray radiation during a stage of intense accretion onto the neutron star, which has an asymmetric magnetic field. Observational consequences that could enable estimation of the role of each acceleration mechanism are discussed. The results are also applicable to binary millisecond radio pulsars, assuming that they have gone through an accretion stage.

Blue Stragglers, Young White Dwarfs, and UV‐Excess Stars in the Core of 47 Tucanae

We used a set of archived HST/WFPC2 images to probe the stellar population in the core of the nearby Galactic Globular Cluster (GGC) 47 Tuc. From the ultraviolet (UV) Color Magnitude Diagrams (CMDs) obtained for ~4,000 stars detected within the Planetary Camera (PC) field of view we have pinpointed a number of interesting objects: (i) 43 blue stragglers stars (BSSs) including 20 new candidates; (ii) 12 bright (young) cooling white dwarfs (WDs) at the extreme blue region of the UV-CMD; (iii) a large population of UV-excess (UVE) stars, lying between the BSS and the WD sequences. The WD candidates identified here define a clean pattern in the CMD, which define the WD cooling sequence. Moreover, both the location on the UV-CMDs and the number of WDs are in excellent agreement with the theoretical expectations. The UVE stars discovered here represent the largest population of anomalous blue objects ever observed in a globular cluster -- if the existence of such a large population is confirmed, we have finally found the long-searched population of interacting binaries predicted by the theory. Finally, we have investigated the feasibility of the optical identification of the companions of the binary X-ray sources recently detected by CHANDRA and of binary millisecond pulsars (MSPs) residing in the core of 47 Tuc. Unfortunately, the extreme faintness expected for the MSP companions together with the huge stellar crowding in the cluster center prevent statistically reliable identifications based only on positional coincidences.

Determination of the orbital parameters of binary pulsars

We present a simple novel method for determining the orbital parameters of binary pulsars. This method works with any sort of orbital sampling, no matter how sparse, provided that information on the period derivatives is available with each measurement of the rotational period of the pulsar, and it is applicable to binary systems with nearly circular orbits. We use the technique to precisely estimate the hitherto unknown orbital parameters of two binary millisecond pulsars in the globular cluster 47 Tucanae, 47 Tuc S and T. The method can also be used more generally to make first-order estimates of the orbital parameters of binary systems using a minimal amount of data.

Discovery of Short-Period Binary Millisecond Pulsars in Four Globular Clusters

We report the discovery, using the Parkes radio telescope, of binary millisecond pulsars in four clusters for which no associated pulsars were previously known. The four pulsars have pulse periods lying between 3 and 6 ms. All are in circular orbits with low-mass companions and have orbital periods of a few days or less. One is in a 1.7 hr orbit with a companion of planetary mass. Another is eclipsed by a wind from its companion for 40% of the binary period despite being in a relatively wide orbit. These discoveries result from the use of improved technologies and prove that many millisecond pulsars remain to be found in globular clusters.

Stellar Variability in the Metal‐rich, Obscured Globular Cluster Terzan 5

We present the results of a search for variability in and near the core of the metal-rich, obscured globular cluster Terzan 5, using the near-infrared camera and multiobject spectrometer (NICMOS) on board the Hubble Space Telescope. This extreme cluster has approximately solar metallicity and a central density that places it in the upper few percent of all clusters. It is estimated to have the highest interaction rate of any galactic globular cluster. The large extinction toward Terzan 5 and the severe stellar crowding near the cluster center present a substantial observational challenge. Using time-series analysis, we discovered two variable stars in this cluster. The first is an RRab Lyrae variable with a period of ~0.61 days, a longer period than that of field stars with similar high metallicities. This period is shorter, however, than the average periods of RR Lyraes found in the metal-rich globular clusters NGC 6441, NGC 6388, and 47 Tuc. The second variable is a blue star with a 7 hr period sinusoidal variation and a likely orbital period of 14 hr. This star is probably an eclipsing blue straggler or (less likely) the infrared counterpart to the low-mass X-ray binary known in Terzan 5. Because of the extreme crowding and overlapping Airy profile of the IR point-spread function, we fall short of our original goal of detecting cataclysmic variables via Paα emission and detecting variable infrared emission from the location of the binary millisecond pulsar in Terzan 5.

On a Theoretical Interpretation of the Period Gap in Binary Millisecond Pulsars

We reexamine evolutionary channels for the formation of binary millisecond pulsars in order to understand their observed orbital period distribution. The available paths provide a natural division into systems characterized by long orbital periods (> 60 d) and short orbital periods ( few days), early massive Case B evolution produces CO white dwarfs with orbital periods few days producing low mass He white dwarfs and periods > 30 d, and from stable Case C evolution producing CO white dwarfs. The lack of observed systems between 23 and 56 days probably reflects the fact that for comparable initial orbital periods (< few days) low mass Case B and early massive Case B evolution lead to very discrepant final periods. We show in particular that the lower limit (~ 23 d) cannot result from common-envelope evolution.

Formation of Short-Period Binary Pulsars in Globular Clusters.

We present a new dynamical scenario for the formation of short-period binary millisecond pulsars in globular clusters. Our work is motivated by the recent observations of 20 radio pulsars in 47 Tuc. In a dense cluster such as 47 Tuc, most neutron stars acquire binary companions through exchange interactions with primordial binaries. The resulting systems have semimajor axes in the range approximately 0.1-1 AU and neutron star companion masses approximately 1-3 M middle dot in circle. For many of these systems, we find that when the companion evolves off the main sequence and fills its Roche lobe, the subsequent mass transfer is dynamically unstable. This leads to a common envelope phase and the formation of short-period neutron star-white dwarf binaries. For a significant fraction of these binaries, the decay of the orbit due to gravitational radiation will be followed by a period of stable mass transfer driven by a combination of gravitational radiation and tidal heating of the companion. The properties of the resulting short-period binaries match well those of observed binary pulsars in 47 Tuc.

Formation of Millisecond Pulsars with Heavy White Dwarf Companions: Extreme Mass Transfer on Subthermal Timescales.

We have performed detailed numerical calculations of the nonconservative evolution of close X-ray binary systems with intermediate-mass (2.0-6.0 M middle dot in circle) donor stars and a 1.3 M middle dot in circle accreting neutron star. We calculated the thermal response of the donor star to mass loss in order to determine its stability and follow the evolution of the mass transfer. Under the assumption of the "isotropic reemission model," we demonstrate that in many cases it is possible for the binary to prevent a spiral-in and survive a highly super-Eddington mass transfer phase (1<<M&d2;&solm0;M&d2;Edd<105) on a subthermal timescale if the convective envelope of the donor star is not too deep. These systems thus provide a new formation channel for binary millisecond pulsars with heavy CO white dwarfs and relatively short orbital periods (3-50 days). However, we conclude that to produce a binary pulsar with a O-Ne-Mg white dwarf or Porb approximately 1 day (e.g., PSR B0655+64) the above scenario does not work, and a spiral-in phase is still considered the most plausible scenario for the formation of such a system.

Cooling curves and initial models for low-mass white dwarfs (&lt;0.25 M ) with helium cores

We present a detailed calculation of the evolution of low-mass (<0.25 M⊙) helium white dwarfs. These white dwarfs (the optical companions to binary millisecond pulsars) are formed via long-term, low-mass binary evolution. After detachment from the Roche lobe, the hot helium cores have a rather thick hydrogen layer with mass between 0.01 and 0.06 M⊙. As a result of mixing between the core and outer envelope, the surface hydrogen content (Xsurf) is 0.5–0.35, depending on the initial value of the heavy element Z and the initial secondary mass. We found that the majority of our computed models experience one or two hydrogen shell flashes. We found that the mass of the helium dwarf in which the hydrogen shell flash occurs depends on the chemical composition. The minimum helium white dwarf mass in which a hydrogen flash takes place is 0.213 M⊙ (Z=0.003), 0.198 M⊙ (Z=0.01), 0.192 M⊙ (Z=0.02) or 0.183 M⊙ (Z=0.03). The duration of the flashes (independent of chemical composition) is between a few ×106 and a few ×107 yr. In several flashes the white dwarf radius will increase so much that it forces the model to fill its Roche lobe again. Our calculations show that the cooling history of the helium white dwarf depends dramatically on the thickness of the hydrogen layer. We show that the transition from a cooling white dwarf with a temporarily stable hydrogen-burning shell to a cooling white dwarf in which almost all residual hydrogen is lost in a few thermal flashes (via Roche lobe overflow) occurs between 0.183 and 0.213 M⊙ (depending on the heavy element value).

Low–Mass He WDs and Millisecond Pulsars Age Determination

It is accepted that the formation of a millisecond binary pulsar (MBP) with a low–mass companion may be explained as the end–point of close binary evolution in which an old pulsar is spun–up by accretion from the red giant (Bhattacharaya &amp;amp; van den Heuvel 1991). In this paper we shall discuss the cooling properties of the helium white dwarfs (WD) in short orbital period MBP systems PSR J0437–4715, PSR J0751+1807 and PSR J1012+5307, without referring to the rotational history of neutron stars (NS).Below we discuss observational data for several system for which the results of our calculations (Sarna, Antipova, &amp;amp; Muslimov 1998; Sarna, Ergma, &amp;amp; Antipova 1999) may be applied, by taking into account the orbital parameters of the system, the pulsar spin-down time, and the WD cooling time-scale.

Helium white dwarf cooling in PSR J0751+1807 and PSR J1012+5307

It is accepted that formation of a binary millisecond (or recycled) pulsar with a low–mass companion may be explained as the end–point of close binary evolution in which an old pulsar is spun–up by accretion from the secondary (Alpar et al., 1982). After detachment from the Roche lobe, the pulsar spin period starts to change due to magneto–dipole radiation and the white dwarf begins to cool down. In this paper we shall discuss the cooling history of helium core low–mass white dwarfs in the short orbital period millisecond binary pulsars PSR J0751+1807 and PSR J1012+5307 (Ergma, Sarna, &amp;amp; Antipova 1999).

Cygnus X-2, super-Eddington mass transfer, and pulsar binaries

We consider the unusual evolutionary state of the secondary star in Cygnus X-2. Spectroscopic data give a low mass ($M_2 \simeq 0.5 - 0.7\msun$) and yet a large radius ($R_2 \simeq 7\rsun$) and high luminosity ($L_2 \simeq 150\lsun$). We show that this star closely resembles a remnant of early massive Case B evolution, during which the neutron star ejected most of the $\sim 3\msun$ transferred from the donor (initial mass $M_{\rm 2i}\sim 3.6\msun$) on its thermal time-scale $\sim 10^6$ yr. As the system is far too wide to result from common-envelope evolution, this strongly supports the idea that a neutron star efficiently ejects the excess inflow during super--Eddington mass transfer. Cygnus X-2 is unusual in having had an initial mass ratio $q_{\rm i} = M_{\rm 2i}/M_1$ in a narrow critical range near $q_{\rm i}\simeq 2.6$. Smaller $q_{\rm i}$ lead to long-period systems with the former donor near the Hayashi line, and larger $q_{\rm i}$ to pulsar binaries with shorter periods and relatively massive white dwarf companions. The latter naturally explain the surprisingly large companion masses in several millisecond pulsar binaries. Systems like Cygnus X-2 may thus be an important channel for forming pulsar binaries.

Neutron Star Mass Measurements. I. Radio Pulsars

There are now about 50 known radio pulsars in binary systems, including at least five in double neutron star binaries. In some cases, the stellar masses can be directly determined from measurements of relativistic orbital effects. In others, only an indirect or statistical estimate of the masses is possible. We review the general problem of mass measurement in radio pulsar binaries and critically discuss all current estimates of the masses of radio pulsars and their companions. We find that significant constraints exist on the masses of 21 radio pulsars and on five neutron star companions of radio pulsars. All the measurements are consistent with a remarkably narrow underlying Gaussian mass distribution, m=1.35?0.04 M. There is no evidence that extensive mass accretion (?m0.1 M) has occurred in these systems. We also show that the observed inclinations of millisecond pulsar binaries are consistent with a random distribution, and thus find no evidence for either alignment or counteralignment of millisecond pulsar magnetic fields.

The Characteristics of Millisecond Pulsar Emission. I. Spectra, Pulse Shapes, and the Beaming Fraction

The extreme physical conditions in millisecond pulsar magnetospheres, as well as an evolutionary history that differs from that of normal pulsars, raise the question whether these objects also differ in their radio emission properties. We have monitored a large sample of millisecond pulsars for a period of 3 yr using the 100 m Effelsberg radio telescope in order to compare the radio emission properties of these two pulsar populations. Our sample comprises a homogeneous data set of very high quality. With some notable exceptions, our findings suggest that the two groups of objects share many common properties. A comparison of the spectral indices between samples of normal and millisecond pulsars demonstrates that millisecond pulsar spectra are not significantly different from those of normal pulsars. This is contrary to what has previously been thought. There is evidence, however, that millisecond pulsars are slightly less luminous and less efficient radio emitters than normal pulsars. We confirm recent suggestions that a diversity exists among the luminosities of millisecond pulsars, with the isolated millisecond pulsars being less luminous than the binary millisecond pulsars, implying that the different evolutionary history has an influence on the emission properties. There are indications that old millisecond pulsars exhibit somewhat flatter spectra than the presumably younger ones. We present evidence that, contrary to common belief, the millisecond pulsar profiles are only marginally more complex than those found among the normal pulsar population. Moreover, the development of the profiles with frequency is rather slow, suggesting very compact magnetospheres. The profile development seems to anticorrelate with the companion mass and the spin period, again suggesting that the amount of mass transfer in a binary system might directly influence the emission properties. The angular radius of radio beams of millisecond pulsars does not follow the scaling predicted from a canonical pulsar model applicable for normal pulsars. Instead, they are systematically smaller, supporting the concept of a critical rotational period below which such a scaling ceases to exist. The smaller inferred luminosity and narrower emission beams will need to be considered in future calculations of the birthrate of the Galactic population.

The two-hour orbit of a binary millisecond X-ray pulsar

Typical radio pulsars are magnetized neutron stars that are born rapidly rotating and slow down as they age on time scales of 10 to 100 million years. In contrast, millisecond radio pulsars spin very rapidly even though many are billions of years old1. The most compelling explanation is that they have been ‘spun up’ by the transfer of angular momentum during the accretion of material from a companion star in so-called low-mass X-ray binary systems, LMXBs. (LMXBs consist of a neutron star or black hole accreting matter from a companion with mass less than one solar mass2.) The recent detection of coherent X-ray pulsations with a millisecond period from a suspected low-mass X-ray binary system appears to confirm this link3. Here we report observations showing that the orbital period of this binary system is two hours, which establishes it as an LMXB. We also find an apparent modulation of the X-ray flux at the orbital period (at the two per cent level), with a broad minimum when the pulsar is behind the low-mass companion star. This system seems closely related to the ‘black-widow’ millisecond radio pulsars, which are evaporating their companions through irradiation4,5,6,7,8. It may appear as an eclipsing radio pulsar during periods of X-ray quiescence.

Stellar forensics — II. Millisecond pulsar binaries

We use the grid of models described in paper~I to analyse those millisecond pulsar binaries whose secondaries have been studied optically. In particular, we find cooling ages for these binary systems that range from $< 1 \rm Gyr$ to $\sim \rm 15 Gyr$. Comparison of cooling ages and characteristic spin down ages allows us to constrain the initial spin periods and spin-up histories for individual systems, showing that at least some millisecond pulsars had sub-Eddington accretion rates and long magnetic field decay times.

Stellar forensics — I. Cooling curves

The presence of low-mass, degenerate secondaries in millisecond pulsar binaries offers the opportunity to determine an age for the binary system independently of the rotational properties of the pulsar. To this end, we present here a detailed calculation of the evolution of a grid of low-mass (< 0.5 M⊙) helium core white dwarfs. We investigate the effects of different hydrogen layer masses and provide results for well-known optical bandpasses. We supplement the OPAL opacity calculations with our own calculations for low effective temperatures (Teff < 6000 K) and also provide fitting formulae for the gravity as a function of mass and effective temperature. In Paper II we apply these results to individual cases.

FORMATION OF LOW-MASS X-RAY BINARIES

ABSTRACT Low-mass X-ray binaries (LMXBs) are bright X-ray sources that consist of a compact object (neutron star or black hole) accreting from a low-mass companion that fills its Roche lobe and tidally loses mass. A study of the origin and properties of such systems formed in the Galactic disk is presented, involving the statistical modeling of the evolution of a primordial ensemble of binaries through evolutionary stages until the onset of the X-ray phase. For the completion of this study, understanding of the effects of supernova explosions on orbital dynamics, as well as knowledge of the binary characteristics of nascent LMXBs are required. Observational evidence exists in support of the idea that kicks are imparted to neutron stars at their birth. An analytical method is developed for studying the effect of supernova explosions on the orbital dynamics of a binary population with initially circular orbits. Expressions for the distribution of systems over post-SN orbital separations, eccentricities, and center-of-mass velocities are derived, and their dependence on the kick and binary characteristics is studied. This analysis is a necessary tool for population studies of binaries that experience supernova explosions (see Kalogera 1996). The binary properties of LMXBs at the onset of the X-ray phase are studied, and the donor masses and orbital separations are found to be constrained by the requirement that mass transfer be stable and the age of the systems be shorter than the age of the Galaxy. It is also shown that super-Eddington mass transfer allows relatively massive donors to remain in hydrostatic and thermal equilibrium, and that observed long-period LMXBs with evolved donors as well as ultra-short-period LMXBs with hydrogen deficient donors must have survived a phase of super-Eddington mass transfer (see Kalogera & Webbink 1996). Formation of LMXBs has been suggested to occur when primordial binaries with extreme mass ratios evolve through a common envelope phase and the exposed helium core subsequently explodes as a supernova. The complete set of structural and evolutionary constraints on the properties of LMXB progenitors is identified, and it is shown that (i) their orbital separations are restricted to a narrow range, and (ii) short-period LMXBs are formed only if kicks are imparted to neutron stars at birth. Population synthesis calculations are performed with the use of a semi-analytical method which offers major advantages in terms of statistical accuracy and computational efficiency. The results of an extensive parameter study indicate that the predicted birth rates essentially reflect the choice of the -- mostly unknown -- characteristics of the primordial binary population, while the properties of the nascent LMXBs are primarily determined by stability and age constraints and the efficiency of angular momentum losses. The random natal kicks imparted to neutron stars weaken the dependence of the results on pre-SN evolution and hamper the distinction between formation paths that involve a common-envelope phase (see Kalogera & Webbink 1997). In light of the importance of neutron stars kicks in LMXB formation, a new evolutionary path is proposed, the direct-supernova mechanism, which does not invoke common-envelope evolution. Instead, the required small post-SN binary orbits are achieved because of a kick velocity of appropriate magnitude and direction relative to the pre-SN orbital velocity. The efficiency of this new mechanism strongly depends on the average kick magnitude, and can account for one third of the LMXB population for kicks of ~ 100kms-1 . More importantly, the direct-supernova path provides the only natural way for the formation of binary millisecond pulsars in very-long-period orbits (see Kalogera 1997).

Stellar forensics - I. Cooling curves

The presence of low-mass, degenerate secondaries in millisecond pulsar binaries offers the opportunity to determine an age for the binary system independently of the rotational properties of the pulsar. To this end, we present here a detailed calculation of the evolution of a grid of low-mass (< 0.05 M⊙) helium core white dwarfs. We investigate the effects of different hydrogen layer masses and provide results for well-known optical bandpasses. We supplement the OPAL opacity calculations with our own calculations for low effective temperatures (Teff < 6000 K) and also provide fitting formulae for the gravity as a function of mass and effective temperature. In Paper II we apply these results to individual cases.