Updating the orbital ephemeris of the dipping source XB 1254–690 and the distance to the source
1 Introduction
XB 1254–690 is a persistent low mass Xray binary (LMXB) showing type I Xray bursts and dips. Coordinates of the source have been accurately derived from Iaria et al. ( 2007 ) who, using one Chandra observation, located the source at RA (J2000) = 194.4048° and Dec (J2000) = −69.2886° with a 90% confidence level error box with radius 0.6′′. The dipping activity was revealed during an EXOSAT observation in 1984 (Courvoisier et al. 1986 ) and consists of a periodic decrease in the countrate. This decrease is caused by photoelectric absorption in part of the Xray emission by the cold (and/or partially ionized) bulge of matter that forms as a consequence of the impact of transferred plasma from the companion star onto the outer accretion disk (White & Swank 1982 ). Although type I Xray bursts can be used to test the presence of a neutron star (NS) in the system (Mason et al. 1980 ), the presence of dips together with the absence of eclipses in the light curve constrains the inclination angle i of the system with respect to the line of sight to the observer between 60° and 80° (see Frank et al. 1987 ). The optical counterpart has been identified by Griffiths et al. ( 1978 ) to be the faint V≃19 star GR Mus.
Timing analysis of the periodic dips led to an estimation of the orbital period of the system. Courvoisier et al. ( 1986 ) estimated the orbital period of the system on the basis of the recurrence time of Xray dips, obtaining a period of 0.162(6)d. Motch et al. ( 1987 ) improved this estimate by giving a period of 0.163890(9)d obtained from optical data, while Díaz obtained an orbital period of 0.16388875(17)d, generating a periodogram from RXTE/All Sky Monitor (ASM) data. In their survey of the timing properties of several LMXB systems, instead, Levine et al. ( 2011 ) assigned an orbital period of 0.1638890(4) d to XB 1254–690. Observations, however, revealed that the dipping activity is not always present and that the dips are quite different in shape from one observation to another.
Bhattacharyya ( 2007 ) reported weak evidence of quasi periodic oscillations at about 95 Hz detected during one thermonuclear Xray burst. Díaz, Trigo et al. ( 2009 ), based on the results of their spectral analysis performed on the source using XMMNewton and INTEGRAL data, proposed the presence of a tilted accretion disk in the system. In this way they justified the disk temperature changes observed between the dip and nondip time intervals of XMM/INTEGRAL light curves, as well as optical modulation observed with data collected from the Optical Monitor (OM) on XMMNewton. The modulation of the optical light curve had already been observed by Motch et al. ( 1987 ) These authors observed that the optical light curve shows minima occurring 0.15 in phase after the Xray dips, suggesting that the modulation is due to the varying aspect of the Xray heated atmosphere of the donor star. They, however, did not rule out the presence of an asymmetric accretion disk that does not completely shadow the companion star. A further confirmation of the hypothesis of a tilted accretion disk was proposed by Cornelisse et al. ( 2013 ) They actually took advantage of the ephemeris from Díaz, revealing the presence of a negative superhump (i.e. a periodic photometric hump having a period shorter than the orbital period by a few percent). This supported the idea that XB 1254–690 could host a precessing accretion disk with a retrograde precession motion with a period of 6.74±0.07 d.
Cornelisse et al. ( 2013 ) proposed that the disk is tilted out of the orbital plane along its line of nodes, implying that a large fraction of matter transferred from the companion star to the NS overflows or underflows the accretion disk instead of hitting the disk’s rim. In their opinion this could explain the presence of absorption features observed by Iaria et al. ( 2007 ) and Boirin & Parmar ( 2003 ). They also found marginal evidence of a possible positive superhump suggesting that the accretion disk is possibly eccentric due to effects of tidal resonance. On the basis of these results they inferred the mass ratio of the system, q = M _{2}/M _{1} = 0.33 − 0.36, and constrained the mass of the NS, M _{1}, between 1.2 and 1.8 M _{⊙}.
A first estimate of the distance was advanced by Courvoisier et al. ( 1986 ). Using EXOSAT data, they inferred the distance to the source from two typeI bursts, assuming that the luminosity at the burst peak was the Eddington luminosity for a 1.4 M _{⊙} NS. They obtained a distance of 12±2 kpc and 11±2 kpc for the two bursts, respectively. Subsequently, Motch et al. ( 1987 ) constrained the distance to the source in the range 8−15 kpc from a modeling of the optical emission. Their modeling also showed that the optical brightness of the source is explained well when assuming that the donor star is near the main sequence. in’t Zand et al. ( 2003 ) reported an estimation of the distance to the source by analyzing data collected from BeppoSAX in 1999. The detection of a possible photospheric radius expansion (PRE) during one superburst precursor allowed them to estimate a distance of 13±3 kpc. A successive work by Galloway et al. ( 2008 ) allowed inferring an estimation of the distance, again on the basis of properties of type I Xray bursts from the source. Analyzing data collected from the proportional counter array (PCA) on board the RXTE mission, Galloway et al. ( 2008 ) found only marginal evidence of PRE during the observed type I Xray bursts, and estimated a distance to the source of 15.5±1.9 kpc in the case of a companion star with cosmic abundances, and of 20±2 kpc in the case of a pure helium donor star.
In this work, we update the orbital ephemeris of XB 1254–690 using pointed observations collected by different space missions during a total time span of about 26 yr. We constrain the orbital period derivative for the first time, and we give a revised estimate of the distance to the source. We also discuss mass transfer in the system, suggesting that the system experiences a conservative mass transfer driven by magnetic braking of the companion star. The paper is structured as follows: in Section
2 Observation and data reduction
To analyze the data on XB 1254–690, we take advantage of all the available pointed observations in Xray archival data. However, no dip could be found in BeppoSAX, ASCA, ROSAT, Swift or Chandra observations. We therefore analyzed only the data collected by EXOSAT, Ginga, RXTE and XMMNewton, which altogether span a temporal window of about 26 yr (from 1984 to 2010).
EXOSAT observed XB 1254–690 eight times between 1984 February 5 and 1985 April 15. We used the backgroundsubtracted data products of the EXOSAT Medium Energy experiment (ME) in the energy range between 1 and 8 keV. We binned the light curves at 6 s. In addition, we performed barycentric corrections using the ftool
XMMNewton observed the source five times between 2001 January 22 and 2007 March 9 with the EPICpn camera. The selected observations have been performed in fast timing mode. We processed the dataset with the
The available observations performed from RXTE/PCA are sparsely distributed in a temporal window of about 13 yr (from 1997 to 2010). We used backgroundsubtracted Standard 2 light curves covering the energy range 2 – 9 keV. The light curves have a bin time of 16 s and the barycentric corrections have been performed using the tool
Ginga observed the binary system with the Large Area Counter (LAC) experiment on 1989 July 17 (ObsID 900802113648) and on 1990 August 3 (ObsID 900803061648). We use the backgroundsubtracted light curves collected from the top layer of the detector covering the 2–17 keV energy band. The light curves have a bin time of 16 s and barycentric corrections have been applied with the ftool
3 Data analysis
To obtain the orbital ephemeris of XB 1254nnnnn–690 we need the arrival times of the dip as a function of time or of orbital cycle. For the first time we apply a timing technique to the arrival times of the dips in order to improve the ephemeris of the source. The ephemerides obtained so far for XB 1254–690 in the Xray band have been based on periodograms generated from ASM data that have lower statistical confidence than the pointed observations we use in our analysis, which altogether span a temporal period of 26 yr.
To obtain the dip arrival times we have to take into account the fact that XB 1254–690 shows dips varying in shape from one orbital cycle to another. For this reason, we cannot fit the dip with a specific function since this implies the assumption that the dip always has the same shape (see Gambino et al. 2016 ; Iaria et al. 2017 , in preparation).
To address this issue, we take advantage of the method developed by Hu et al. ( 2008 ) to parameterize the dipping behavior of XB 1916053, and to systematically study its variation. The method can be applied both to dippers and eclipsing sources, and represents a powerful tool to obtain the dip arrival time for sources showing dips that are strongly variable in width and depth during different orbital cycles. The only constraint required for this method is that the observation of at least a complete dip is required Hu et al. ( 2008 ).
Therefore we selected all the available pointed observations in which single dips appear to be complete, collecting a total of 14 dips to analyze. In addition to these dips, the Ginga observations (ObsIDs 900802113648 and 900803061648) show five incomplete dips. Similarly, three RXTE observations (ObsIDs 60044010103, 60044010105 and 60044010108) show a total of three partial dips close in time, and the other two incomplete dips are visible in two RXTE observations (ObsIDs 953240102000 and 95324010200). We will take into account all these incomplete dips in the second part of the data analysis.
We report all the selected observations in Table




The arrival times of the dips are then calculated as T
_{dip} = T
_{start} + t
_{dip}, where T
_{start} is the starting time of the specific observation (see Table


The error associated with the delays of the dip arrival times is determined by the standard deviation σ of the distribution of obtained phase delays associated with each dip. The σ of the distribution is equal to 0.04 which corresponds to 544 s according to the trial orbital period we used.
Using the same technique performed in Gambino et al. ( 2016 ) and in Iaria et al. ( 2015 ), we fit the delays with a linear function


However, we expect that, due to the orbital evolution of the binary system, a quadratic term has to be included in the orbital ephemeris. For this purpose, our method easily allows us to evaluate the orbital period derivative of the system by taking into account the possibility that delays follow a quadratic trend. Then, we fitted the delays with the quadratic function
Nevertheless, this quadratic fit gives a χ ^{2}(d.o.f.) = 10.73(11) and the estimated Ftest probability of chance improvement with respect to the previous linear fit is 82%. This suggests that adopting the quadratic ephemeris does not significantly improve the fit.
The delays as a function of number of orbital cycles are shown in the upper panels of Figure
In order to increase the statistics describing the timing technique, we can also take advantage of observations acquired by RXTE and Ginga (sequential numbers 5, 8 and 12 in Table
We folded each group of these observations using the updated ephemeris given in Equation (
The dip arrival times are estimated, starting from the obtained phases, as T
_{dip} = T
_{0} + (N + ϕ
_{dip})P
_{0}, where T
_{0} and P
_{0} are the reference epoch and the orbital period evaluated with the updated ephemeris of Equation (
In Table
To integrate the delays evaluated in the first part of the analysis with those evaluated just now, we rescaled the delays obtained in the first iteration with respect to the new T
_{0} and P
_{0} of the updated ephemeris in Equation (
Nevertheless, the quadratic fit gives a χ ^{2}(d.o.f.) = 17.20(14) and the estimated Ftest probability of chance improvement with respect to the previous linear fit is 63%. This suggests that by adopting the quadratic ephemeris we do not significantly improve the fit.
Again, we ran the same fits using the postfit standard deviation as error for each delay, obtaining compatible results.
Even though the new ephemeris of Equation (
4 Discussion
We derived and improved the orbital ephemeris for XB 1254–690 by taking advantage of the whole Xray data archive, which consists of pointed observations spanning 26 yr. The direct measurement of the dip arrival times allowed us to increase the accuracy of the orbital period of the system by a factor of 10 with respect to the previous estimation of Levine et al. ( 2011 ), and by a factor of 4 with respect to the value estimated by D´ıaz Trigo et al. ( 2009 ). Furthermore, we evaluated, for the first time, a constraint on the orbital period derivative of  Ṗ  < 1.4 × 10^{−10} s s^{−1}. This value is compatible with zero and includes both positive and negative values and for this reason should be considered an upper limit on the modulus of the orbital period derivative. However, the result represents the first evaluation of this orbital parameter so far in the literature for this source and will be certainly improved by including future observations when these become available.
In the following, using the equations for secular evolution of the source, we discuss the mass transfer for XB 1254–690 in order to get more information on the system. As a first step, we evaluate the observed mass accretion rate onto the NS surface.
Iaria et al. ( 2001 ), modeling the spectrum of XB 1254–690 collected by BeppoSAX in 0.1–100 keV, estimated an averaged unabsorbed flux of 1.4×10^{−9} erg cm^{−2} s^{−1}. Taking into account the value of distance of 15.5±1.9 kpc proposed by Galloway et al. ( 2008 ) and the value of flux inferred by Iaria et al. ( 2001 ), and assuming an NS radius RNS of 10 km, we can estimate the observed mass accretion rate onto the NS as
To understand in which evolutive scenario the system has to be located, we compare the observed mass accretion rate with that predicted by the theory of secular evolution for LMXB systems. As mechanisms of angular momentum loss, we take into account the emission of gravitational waves (gravitational radiation), as well as magnetic braking. We do not rule out the possibility that the magnetic braking term plays a role as a mechanism of angular momentum loss, owing to the fact that the mass of the companion star, inferred assuming the condition of thermal equilibrium (see eq. (25) in Verbunt 1993 ), is large enough to generate the dynamo effect resulting in a net magnetic field anchored into the companion star surface (see Nelson & Rappaport 2003 ).
The mass accretion rate predicted by the theory of secular evolution, under the assumed hypothesis, is given by the relation of Burderi et al. ( 2010 ) (see also di Salvo et al. 2008 )
We can compare the theoretical mass accretion rate predicted by Equation (
Adopting a distance to the source of d = 15.5±1.9 kpc (Galloway et al.
2008
), and setting the parameter f in Equation (
This value of distance, however, as well as the distance of d = 13±3 kpc derived by in’t Zand et al. ( 2003 ), has been inferred by the analysis of Xray typeI bursts, assuming that they show PRE, and thus that the peak luminosity of the bursts is the Eddington luminosity for an NS of 1.4M _{⊙}. However, as the same authors reported in their works, the observations they analyzed do not have enough statistics to be sure if a PRE occurred, and as a consequence of this their distances could be overestimated.
On the other hand, Cornelisse et al. ( 2013 ) obtained an estimation of the range of q and of M_{NS}, totally independent from assumptions about distance to the source. This allows us to obtain a range of masses for the donor star of 0.46–0.50M _{⊙} assuming a mass of the NS of 1.4M _{⊙}
To sketch the most probable evolutive scenario, as well as to constrain the distance of XB 1254–690, we need to evaluate the companion star mass using the results of our timing analysis. For this purpose, we assume that the companion star is a main sequence star in thermal equilibrium. The selfconsistency of this hypothesis will be tested in a subsequent part of this discussion. All the available Xray data of XB 1254–690 clearly demonstrate that the source is a persistent Xray emitter over a temporal window of about 26 yr. As a consequence of this, we can properly assume that the companion star fills its Roche lobe, continuously transferring part of its mass to the NS. Thus, we impose that the companion star radius R _{2} has to be equal to the Roche lobe radius R _{ L2}, given by the expression of Paczyǹnski ( 1971 )
Our estimation of the donor star mass of 0.42±0.04 M⊙ is in accordance with the values of Cornelisse et al. (
2013
) and as a consequence of this, we guess that the donor is probably a main sequence star in thermal equilibrium. With this assumption, we can estimate the maximum distance that the system can have, assuming that the KelvinHelmholtz timescale τ
_{KH} (i.e. the characteristic time that a star spends to reach thermal equilibrium) is equal to the mass transfer timescale
The KelvinHelmholtz timescale is given by the relation
On the other hand, the mass transfer timescale is given by
Imposing the similarity between τ
_{KH} and
The distance to the source for XB 1254–690 can be obtained by the flux inferred by Iaria et al. ( 2001 ) in the band 0.1–100 keV and from the Xray luminosity just obtained as
In this case we observe that when assuming β = 1 (conservative mass transfer) there is no agreement between theory and observation adopting the parameter f = 0.73 in Equation (
For completeness, we also explore the nonconservative mass transfer scenario for both distances considered above, adopting the same f parameters used for the conservative case and assuming n = 0.8. For a distance of 15.5±1.9 kpc the observation is in agreement with the theory for a value of β ~0.9, i.e. 90% of the mass of the companion star is accreted onto the NS surface. On the other hand, adopting a distance of 7.6±0.8 kpc we find a lower limit for β of about 0.92. This actually means that most of the mass transferred bythe donor star is accreted onto the NS.
In order to have a further confirmation of the scenario just depicted for XB 1254–690, and to understand the temporal evolution that the orbital separation of the system will undergo, we use the relation
The theoretical value of Ṗ we inferred for this system is indeed compatible with the upper limit of the orbital period derivative obtained through the quadratic ephemeris: Ṗ < 1.4× 10^{−10} s s^{−1}.
5 Conclusions
In this work we update the existent orbital ephemerides for XB 1254–690, taking advantage of about 26 yr of Xray data and performing direct measurements of the dip arrival times on different pointed observations. We further increase the accuracy reached by Levine et al. ( 2011 ) by one order of magnitude.
The quadratic ephemeris, even though not statistically significant with respect to the linear ephemeris, allows us to constrain the orbital period derivative of the system for the first time. Assuming that the companion star is in thermal equilibrium, we infer a donor star mass of 0.42±0.04 M _{⊙}, which is in agreement with the range of masses estimated by Cornelisse et al. ( 2013 ), assuming that the mass of the NS is 1.4 M _{⊙}. In our analysis, we propose a different estimate of the distance to the source with respect to those obtained by in’t Zand et al. ( 2003 ) and Galloway et al. ( 2008 ). These authors provided estimates of the distance to the source that, as they state, should be considered as upper limits to the distance to the source, owing to the relatively poor statistics of the data they analyzed. We suggest a new distance of 7.6±0.8 kpc that represents the distance for which the companion star has a KelvinHelmholtz timescale that is similar to the mass transfer timescale in this system. For larger distances, the inferred mass accretion rate would be higher, implying a mass transfer timescale shorter than the KelvinHelmholtz timescale of the donor, bringing the companion star out of thermal equilibrium.
These results, as well as the assumption of an NS of 1.4 M _{⊙}, allow us to state that the most probable scenario for this system is the one in which the companion star is in thermal equilibrium and that most of (if not all) the mass transferred by the companion is accreted onto the NS in a conservative way through the inner Lagrangian point, regardless of whether we assume a distance of 15.5±1.9 kpc or of 7.6±0.8 kpc. Moreover, the analysis strongly supports the idea that the magnetic braking plays an important role in the angular momentum loss in this binary system. In the hypothesis that the companion star is in thermal equilibrium with a massradius index of about 0.8, we also predict that the binary orbit is shrinking at a rate of about −5 × 10^{−13} s s^{−1}. This prediction can be easily tested with future observations, when the uncertainty on the orbital period derivative we have now will be greatly reduced.
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