Orbital evolution measurement of the accreting millisecond X-ray pulsar SAX J1808.4-3658

We present results from a pulse timing analysis of the accretion-powered millisecond X-ray pulsar SAX J1808.4-3658 using X-ray data obtained during four outbursts of this source. Extensive observations were made with the proportional counter array of the Rossi X-ray Timing Explorer (RXTE) during the four outbursts that occurred in 1998, 2000, 2002 and 2005. Instead of measuring the arrival times of individual pulses or the pulse arrival time delay measurement that is commonly used to determine the orbital parameters of binary pulsars, we have determined the orbital ephemeris during each observation by optimizing the pulse detection against a range of trial ephemeris values. The source exhibits a significant pulse shape variability during the outbursts. The technique used by us does not depend on the pulse profile evolution, and is therefore, different from the standard pulse timing analysis. Using 27 measurements of orbital ephemerides during the four outbursts spread over more than 7 years and more than 31,000 binary orbits, we have derived an accurate value of the orbital period of 7249.156862(5) s (MJD = 50915) and detected an orbital period derivative of (3.14 ± 0.21) × 10⁻¹² s s⁻¹. We have included a table of the 27 mid-eclipse time measurements of this source that will be valuable for further studies of the orbital evolution of the source, especially with ASTROSAT. We point out that the measured rate of orbital period evolution is considerably faster than the most commonly discussed mechanisms of orbital period evolution like mass transfer, mass loss from the companion star and gravitational wave radiation. The present time scale of orbital period change, 73 Myr is therefore likely to be a transient high value of period evolution and similar measurements during subsequent outbursts of SAX J1808.4-3658 will help us to resolve this.     

Optical spectroscopy and photometry of SAX J1808.4−3658 in outburst

We present phase resolved optical spectroscopy and photometry of V4580 Sagittarii, the optical counterpart to the accretion powered millisecond pulsar SAX J1808.4−3658, obtained during the 2008 September/October outburst. Doppler tomography of the N  iii λ4640.64 Bowen blend emission line reveals a focused spot of emission at a location consistent with the secondary star. The velocity of this emission occurs at  324 ± 15 km s⁻¹  ; applying a ' K -correction', we find the velocity of the secondary star projected on to the line of sight to be  370 ± 40 km s⁻¹  . Based on existing pulse timing measurements, this constrains the mass ratio of the system to be  0.044^+0.005_−0.004  , and the mass function for the pulsar to be  0.44^+0.16_−0.13 M_⊙  . Combining this mass function with various inclination estimates from other authors, we find no evidence to suggest that the neutron star in SAX J1808.4−3658 is more massive than the canonical value of  1.4 M_⊙  . Our optical light curves exhibit a possible superhump modulation, expected for a system with such a low mass ratio. The equivalent width of the Ca  ii H and K interstellar absorption lines suggest that the distance to the source is ∼2.5 kpc. This is consistent with previous distance estimates based on type-I X-ray bursts which assume cosmic abundances of hydrogen, but lower than more recent estimates which assume helium-rich bursts.     

The optical counterpart to SAX J1808.4−3658: observations in quiescence

We report the first extensive set of optical photometric observations of the counterpart to SAX J1808.4−3658 (V4580 Sagittarii) in quiescence. The source was detected at V ∼21 , 5 mag fainter than at the peak of its 1998 outburst. However, a comparable ∼6 per cent semi-amplitude 2-h modulation of its flux is revealed. This has the same phasing and approximately sinusoidal modulation as seen during outburst, and with photometric minimum when the pulsar is behind the companion. The lack of a double-humped morphology rules out an ellipsoidal origin, implying that the bulk of the optical flux does not arise from the companion. Moreover, applying crude modelling to the disc and X-ray irradiated face of the donor shows that the internal energy release of a remnant disc (with mass transfer driven by gravitational radiation) is sufficient to explain most of the optical emission, and with the modulation because of the varying contribution of the heated face of the star. We note that this model is also consistent with the much lower X-ray to optical flux ratio in quiescence versus outburst, and with the phasing of the optical modulation.     

A weak outburst of the millisecond X-ray pulsar SAX J1808.4-3658 in October 1996 as detected from RXTE slew data

Analysis of the RXTE slew data in October 1996 revealed a weak X-ray burst from the millisecond pulsar SAX J 1808.4-3658. The 3–20-keV energy spectrum of the source can be described by a power law with an index of 2.0 and a(3-to 20 keV) luminosity of ～1.4×10³⁵ erg s^?1 (the distance to the source was taken to be 2.5 kpc). Because of the short exposure time, we failed to detect weak pulsations at a frequency of 401 Hz in the source. The (2σ) upper limit of the pulse fraction is ～13%.     

Physics of accretion in the millisecond pulsar XTE J1751 − 305

We have undertaken an extensive study of X-ray data from the accreting millisecond pulsar XTE J1751 − 305 observed by RXTE and XMM–Newton during its 2002 outburst. In all aspects this source is similar to the prototypical millisecond pulsar SAX J1808.4 − 3658, except for the higher peak luminosity of 13 per cent of Eddington, and the optical depth of the hard X-ray source, which is larger by a factor ∼2. Its broad-band X-ray spectrum can be modelled by three components. We interpret the two soft components as thermal emission from a colder  ( kT ∼ 0.6 keV)  accretion disc and a hotter (∼1 keV) spot on the neutron star surface. We interpret the hard component as thermal Comptonization in plasma of temperature ∼40 keV and optical depth ∼1.5 in a slab geometry. The plasma is heated by the accretion shock as the material collimated by the magnetic field impacts on to the surface. The seed photons for Comptonization are provided by the hotspot, not by the disc. The Compton reflection is weak and the disc is probably truncated into an optically thin flow above the magnetospheric radius. Rotation of the emission region with the star creates an almost sinusoidal pulse profile with an rms amplitude of 3.3 per cent. The energy-dependent soft phase lags can be modelled by two pulsating components shifted in phase, which is naturally explained by a different character of emission of the optically thick spot and optically thin shock combined with the action of the Doppler boosting. The observed variability amplitude constrains the hotspot to lie within 3°–4° of the rotational pole. We estimate the inner radius of the optically thick accreting disc to be about 40 km. In that case, the absence of emission from the antipodal spot, which can be blocked by the accretion disc, gives the inclination of the system as ≳70°.     

Timing of the accreting millisecond pulsar XTE J1814−338

We present a precise timing analysis of the accreting millisecond pulsar XTE J1814−338 during its 2003 outburst, observed by RXTE . A full orbital solution is given for the first time; Doppler effects induced by the motion of the source in the binary system were corrected, leading to a refined estimate of the orbital period,   P _orb= 15 388.7229(2)  s, and of the projected semimajor axis,   a sin  i / c = 0.390633(9)  light-second. We could then investigate the spin behaviour of the accreting compact object during the outburst. We report here a refined value of the spin frequency  (ν= 314.356 108 79(1) Hz)  and the first estimate of the spin frequency derivative of this source while accreting     . This spin-down behaviour arises when both the fundamental frequency and the second harmonic are taken into consideration. We discuss this in the context of the interaction between the disc and the quickly rotating magnetosphere, at accretion rates sufficiently low to allow a threading of the accretion disc in regions where the Keplerian velocity is slower than the magnetosphere velocity. We also present indications of a jitter of the pulse phases around the mean trend, which we argue results from movements of the accreting hotspots in response to variations of the accretion rate.     

Optical photometry and spectroscopy of the accretion-powered millisecond pulsar HETE J1900.1 − 2455

We present phase resolved optical photometry and spectroscopy of the accreting millisecond pulsar HETE J1900.1−2455. Our R -band light curves exhibit a sinusoidal modulation, at close to the orbital period, which we initially attributed to X-ray heating of the irradiated face of the secondary star. However, further analysis reveals that the source of the modulation is more likely due to superhumps caused by a precessing accretion disc. Doppler tomography of a broad Hα emission line reveals an emission ring, consistent with that expected from an accretion disc. Using the velocity of the emission ring as an estimate for the projected outer disc velocity, we constrain the maximum projected velocity of the secondary to be 200 km s⁻¹, placing a lower limit of  0.05 M_⊙  on the secondary mass. For a  1.4 M_⊙  primary, this implies that the orbital inclination is low, ≲20°. Utilizing the observed relationship between the secondary mass and the orbital period in short-period cataclysmic variables, we estimate the secondary mass to be ∼0.085  M_⊙  , which implies an upper limit of  ∼2.4 M_⊙  for the primary mass.     

Chandra and XMM–Newton observations of the low-luminosity X-ray pulsators SAX J1324.4−6200 and SAX J1452.8−5949

We present results from our Chandra and XMM–Newton observations of two low-luminosity X-ray pulsators  SAX J1324.4−6200  and  SAX J1452.8−5949  which have spin periods of 172 and 437 s, respectively. The XMM–Newton spectra for both sources can be fitted well with a simple power-law model of photon index,  Γ∼ 1.0  . A blackbody model can equally well fit the spectra with a temperature,   kT ∼  2 keV, for both sources. During our XMM–Newton observations,  SAX J1324.4−6200  is detected with coherent X-ray pulsations at a period of 172.86 ± 0.02 s while no pulsations with a pulse fraction greater than 18 per cent (at 95 per cent confidence level) in 0.2–12 keV energy band are detected in  SAX J1452.8−5949  . The spin period of  SAX J1324.4−6200  is found to be increasing on a time-scale of     which would suggest that the accretor is a neutron star and not a white dwarf. Using subarcsec spatial resolution of the Chandra telescope, possible counterparts are seen for both sources in the near-infrared images obtained with the son of infrared spectrometer and array camera (SOFI) instrument on the New Technology Telescope. The X-ray and near-infrared properties of  SAX J1324.4−6200  suggest it to be a persistent high-mass accreting X-ray pulsar at a distance  ≤8 kpc  . We identify the near-infrared counterpart of  SAX J1452.8−5949  to be a late-type main-sequence star at a distance ≤10 kpc, thus ruling out  SAX J1452.8−5949  to be a high-mass X-ray binary. However, with the present X-ray and near-infrared observations, we cannot make any further conclusive conclusion about the nature of  SAX J1452.8−5949  .     

The quiescent light curve and the evolutionary state of GRO J1655–40

We present ellipsoidal light-curve fits to the quiescent B , V , R and I light curves of GRO J1655–40 (Nova Scorpii 1994). The fits are based on a simple model consisting of a Roche-lobe-filling secondary and an accretion disc around the black hole primary. Unlike previous studies, no assumptions are made concerning the interstellar extinction or the distance to the source; instead these are determined self-consistently from the observed light curves. In order to obtain tighter limits on the model parameters, we used the distance determination from the kinematics of the radio jet as an additional constraint. We obtain a value for the extinction that is lower than was assumed previously; this leads to lower masses for both the black hole and the secondary star of  5.4±0.3  and  1.45±0.35 M_⊙  , respectively. The errors in the determination of the model parameters are dominated by systematic errors, in particular arising from uncertainties in the modelling of the disc structure and uncertainties in the atmosphere model for the chemically anomalous secondary in the system. A lower mass of the secondary naturally explains the transient nature of the system if it is in either a late case A or early case B mass-transfer phase.