Issue 
A&A
Volume 534, October 2011



Article Number  A85  
Number of page(s)  8  
Section  Stellar structure and evolution  
DOI  https://doi.org/10.1051/00046361/201117334  
Published online  07 October 2011 
Detailed study of the Xray and optical/UV orbital ephemeris of X1822–371
^{1}
Dipartimento di FisicaUniversità di Palermo, via Archirafi 36, 90123 Palermo, Italy
email: iaria@fisica.unipa.it
^{2}
Dipartimento di Fisica, Università degli Studi di Cagliari, SP MonserratoSestu, KM 0.7, 09042 Monserrato, Italy
^{3}
INAF, Istituto di Astrofisica Spaziale e Fisica cosmica di Palermo, via U. La Malfa 153, 90146 Palermo, Italy
^{4} INAF, Osservatorio Astronomico di Cagliari, Poggio dei Pini, Strada 54, 09012 Capoterra (CA), Italy
Received: 24 May 2011
Accepted: 21 July 2011
Aims. Recent studies of the optical/UV and Xray ephemerides of X1822371 have found some discrepancies in the value of the orbital period derivative. Because of the importance of this value in constraining the system evolution, we comprehensively analyse all the available optical/UV/X eclipse times of this source to investigate the origin of these discrepancies.
Methods. We collected all previously published Xray eclipse times from 1977 to 2008, to which we added the eclipse time observed by Suzaku in 2006. This point is very important to cover the time gap between the last RXTE eclipse time (taken in 2003) and the most recent Chandra eclipse time (taken in 2008). Similarly we collected the optical/UV eclipse arrival times covering the period from 1979 to 2006, adding a further eclipse time taken on 1978 and updating previous optical/UV ephemeris. We compared the Xray and the optical/UV ephemeris, and finally derived a new ephemeris of the source by combining the eclipse arrival times in the Xray and optical/UV bands.
Results. The Xray eclipse time delays calculated with respect to a constant orbital period model display a clear parabolic trend, confirming that the orbital period of this source constantly increases at a rate of Ṗ_{orb} = 1.51(7) × 10^{10} s/s. Combining the Xray and the optical/UV data sets, we find that Ṗ_{orb} = 1.59(9) × 10^{10} s/s, which is compatible with the Xray orbital solution. We also investigate the possible presence of a delay of the optical/UV eclipse with respect to the Xray eclipse, finding that this delay may not be constant in time. In particular, this variation is compatible with a sinusoidal modulation of the optical/UV eclipse arrival times with respect to the longterm parabolic trend. In this case, the optical/UV eclipse should lag the Xray eclipse and the timelag oscillate about an average value.
Conclusions. We confirm that the orbital period derivative is three orders of magnitude larger than expected from conservative mass transfer driven by magnetic braking and gravitational radiation.
Key words: stars: neutron / Xrays: binaries / Xrays: stars / stars: individual: X1822371
© ESO, 2011
1. Introduction
X1822371 is an eclipsing compact binary system with a period of 5.57 h hosting a 0.59 s Xray pulsar. Several authors have reported new orbital ephemeris of the source using observations performed in different energy bands. Burderi et al. (2010, hereafter BU10) analysed Xray data of X1822371 covering the period from 1996 to 2008 to determine the eclipse times of the source and improved the previous Xray ephemeris of X1822371 reported by Parmar et al. (2000, hereafter PA00) that covered the period from 1977 to 1996. BU10 added their data to those used by PA00 finding a positive derivative of the orbital period of (1.499 ± 0.071) × 10^{10} s/s that is compatible with the previous one given by PA00 but with a smaller associated error.
Bayless et al. (2010, hereafter BA10) obtained the optical/UV ephemeris of X1822371 using data covering the period from 1979 to 2006. They obtained a value of the orbital period derivative of (2.12 ± 0.18) × 10^{10} s/s, which is compatible with that reported by PA00 but slightly larger than the value proposed by BU10.
Ji et al. (2011, hereafter JI11), using the Xray eclipse arrival times reported by PA00 and the eclipse arrival times inferred by the two Chandra/HETG observations of X1822371 performed in 2000 (Obs ID: 671) and in 2008 (Obs ID: 9076 and 9858), already included in the work of BU10, estimated a value of the orbital period derivative of (0.83 ± 0.16) × 10^{10} s/s, with the error at the 90% confidence level, almost a factor of two smaller than the value reported by BU10.
We summarise the values of the eclipse reference time ${\mathit{T}}_{\mathrm{0}}^{\mathrm{e}}$, the orbital period P_{orb0}, and the orbital period derivative Ṗ_{orb} obtained by PA00, BU10, BA10, and JI11 in Table 1.
In this work, we comprehensively examine both Xray and optical/UV eclipse arrival times to give the most updated ephemeris of X1822371, adding to the eclipse arrival times reported by BU10 the one obtained from a Suzaku observation performed in 2006. We also include a data point from a Ginga observation performed in 1989, and a data point from a ROSAT observation performed in 1992. We critically examine the discrepancies that have emerged in calculating the orbital ephemeris in previous papers and, finally, show the ephemeris of the X1822371 by combining the optical/UV and Xray datasets.
Journal of the ephemerides of X1822371 discussed in this work.
2. Suzaku observation
Suzaku observed X1822371 on 2006 October 2 with an elapsed time of 88 ks, the start and stop times of the observation corresponding to 54010.48 and 54011.50 MJD, respectively. Both the Xray Imaging Spectrometer (0.2–12 keV, XIS; Koyama et al. 2007) and the Hard Xray Detector (10–600 keV, HXD; Takahashi et al. 2007) instruments were used during these observations. In this work, we used only the XIS data. There are four XIS detectors, numbered 0 to 3. The XIS0, XIS2, and XIS3 detectors use frontilluminated CCDs and have very similar responses, while XIS1 uses a backilluminated CCD.
We reprocessed the observation using the aepipeline tool included in the Suzaku FTOOLS Version 16 applying the latest calibration available as of 2011 March. During the observation, XIS0 and XIS1 were used adopting the quarter window option (frame time 2 s), while XIS2 and XIS3 worked in full window (frame time 8 s) mode. We barycentred the XIS data using the Suzaku tool aebarycen and adopting as the best estimate of the source coordinates those derived from the 2008 Chandra observations (RA: 18 25 46.81, Dec: –37 06 18.5, uncertainty: 0.6″).
We extracted the four XIS light curves in the 1–10 keV energy band selecting a circular region centred on the source. We adopted a radius of 130 pixels for XIS0 and XIS1 and 160 pixels for XIS2 and XIS3. The four light curves are quite similar and enclose four orbital periods of X1822371, thus we used the FTOOL lcmath to combine the four XIS light curves. The combined XIS light curve is shown in Fig. 1 adopting a bin time of 128 s.
Fig. 1 Combined XIS light curve of X1822371 in the 1–10 keV energy band. The adopted bin time is 128 s. 
Journal of all the available Xray eclipse times.
During only the third orbital passage of X1822371, the eclipse was fully covered by Suzaku at a time of 55 000 s from the start time. To estimate the eclipse arrival time, we folded the combined XIS light curve, adopting the ephemeris reported by BU10 and a bin time of 128 s. We fitted the orbital light curve to derive eclipse arrival times by adopting the same procedure described in BU10, obtaining an eclipse time passage at 54 010.6730 ± 0.0009 MJD_{⊙} with an associated error at the 68% confidence level.
3. The ephemeris of X1822371
For clarity’s sake, we show in Table 2 the Xray eclipse arrival times that we used to update the Xray ephemeris of X1822371. Most of these data points were included in the timing analysis of BU10. To their data set, we added eclipse arrival times from Ginga (1989), ROSAT (1992), and, most importantly, Suzaku (2006). The ephemerides showed in Table 1 and in the analysis now described are given in barycentric dynamical time. We note that the RXTE arrival times from 1998 to 2003 reported in Table 1 of BU10 (except for the second point corresponding to cycle 23 167) are not the eclipse arrival times, as erroneously stated, but the times of passage through the ascending node (which differs from the eclipse time by P_{orb}/4). Nevertheless, the corresponding RXTE time delays were correctly shown in Fig. 1 of BU10 and correctly used to derive the orbital ephemeris, which are therefore unaffected by this mistake. The correct RXTE eclipse arrival times are shown in our Table 2. The Xray ephemeris of X1822371 reported by BU10 and JI11 show a large discrepancy in the quadratic term by almost a factor of two. JI11 suggested that the discrepancy in the time delay associated with the last two Chandra observations is caused by BU10 not folding the Chandra light curves to estimate the eclipse arrival time, which instead was done by BU10. To understand the reason for this discrepancy, as a first step we tried to reproduce the results of JI11 by using the same data they used in their analysis. These consist of a total of 22 eclipsetimes, which are, respectively, those given by Hellier & Smale (1994), PA00, and three eclipse arrival times obtained from three Chandra observations corresponding to obsID 671, 9076, and 9058 derived by JI11 (see Table 2 in their paper).
We found the corresponding time delays following their procedure, namely we determined the time delays with respect to the bestfit linear ephemeris shown by Hellier & Smale (1994), that is
${\mathit{T}}_{\mathrm{ecl}}\mathrm{=}\mathrm{2}\hspace{0.17em}\mathrm{445}\hspace{0.17em}\mathrm{615.30942}\mathrm{\left(}\mathrm{14}\mathrm{\right)}\mathrm{J}{\mathrm{D}}_{\mathrm{\odot}}\mathrm{+}\mathrm{0.232109017}\mathrm{\left(}\mathrm{33}\mathrm{\right)}\mathit{N,}$and fitted the time delays with a quadratic function. We obtained bestfit values consistent with the ones reported in JI11. We showed in Fig. 2 the time delays in units of days associated with the eclipse arrival times shown by Hellier & Smale (1994) and PA00 with black open squares. The delay times associated with the Chandra eclipse arrival times showed by JI11 were plotted using red diamonds. The dashed line corresponds to the quadratic bestfit curve given by JI11.
Fig. 2 Time delays of the eclipse arrival times with respect to the linear ephemeris of Hellier & Smale (1994). The black open squares correspond to the eclipse arrival times shown by Hellier & Smale (1994) and PA00, the red diamonds to the Chandra eclipse arrival times given by JI11, the green filled squares to the Chandra eclipse arrival times reported in this paper (see Table 3), the blue open circles to the Chandra eclipse arrival times reported by BU10. The dashed and solid lines are the bestfit quadratic curve obtained by JI11 and in this paper (see text), respectively. (This figure is available in color in the electronic form.) 
After establishing the reproducibility of the parameter’s estimates of JI11, we explored the cause of the discrepancy in the fitting results given by BU10 extracting the eclipse arrival times from each Chandra barycentred and folded light curve (obsIDs 671, 9076, and 9858). We show the Chandra eclipse arrival times in Table 3. The corresponding delays were estimated as described above.
Eclipse arrival times of the three Chandra observations.
We found that the discrepancies of the eclipse arrival times between our analysis and JI11’s are −40 ± 140 s, 440 ± 70 s, and 440 ± 50 s for obsIDs 671, 9076, and 9858, respectively. Since the errors are at the 68% c.l., the eclipse arrival times corresponding to the obsIDs 9076 and 9858 are not compatible. We show our Chandra delays with green filled squares in Fig. 2. Only two eclipse times were derived by BU10 from the Chandra observations, because light curves of obsID 9076 and obsID 9058 were combined to obtain a single folded lightcurve and a single eclipsetime passage, with a smaller uncertainty, since the observations were sufficiently close in time to each other. We show the two corresponding time delays with blue open circles in Fig. 2. We note that our delays and those given by BU10 are widely compatible.
Fitting the time delays corresponding to the eclipse arrival times given by Hellier & Smale (1994), PA00, and our three eclipse arrival times reported in Table 3, for a total of 22 data points, we obtained $\begin{array}{ccc}{\mathit{T}}_{\mathrm{ecl}}\mathrm{=}\mathrm{45}\hspace{0.17em}\mathrm{614.80954}\mathrm{\left(}\mathrm{14}\mathrm{\right)}\mathrm{MJ}{\mathrm{D}}_{\mathrm{\odot}}\mathrm{+}\mathrm{0.2321088628}\mathrm{\left(}\mathrm{21}\mathrm{\right)}\mathit{N}& & \\ \mathrm{+}\mathrm{1.648}\mathrm{\left(}\mathrm{72}\mathrm{\right)}\mathrm{\times}{\mathrm{10}}^{11}{\mathit{N}}^{\mathrm{2}}\mathit{,}& & \end{array}$(1)with a χ^{2}/(d.o.f.) = 25.6/19 and the errors are at the 68% confidence level, the uncertainties in the parameters have been scaled by a factor $\sqrt{{\mathit{\chi}}_{\mathrm{red}}^{\mathrm{2}}}$ to take into account a ${\mathit{\chi}}_{\mathrm{red}}^{\mathrm{2}}$ of the bestfit model larger than 1. We note that the quadratic term is larger than that shown by JI11. The corresponding P_{orb0} and Ṗ_{orb} are 20 054.20574(17) s and 1.420(63) × 10^{10} s/s, respectively. These values are compatible within one σ with the ones given by BU10 (see Table 1).
3.1. Updated Xray ephemeris of X1822371
As a first step, we found the Xray ephemeris of X1822371 using the eclipse arrival times adopted by BU10 excluding the Chandra eclipse arrival times and including the eclipse arrival times taken with Ginga, ROSAT, and Suzaku (see Table 2) for a total of 28 available data points. The Suzaku datapoint is very important in this respect, since it was taken in 2006 and therefore precedes the last Chandra datapoints taken in 2008. This is very important to fill the time gap between the last RXTE arrival time taken in 2003 and the most recent Chandra observation taken in 2008, and therefore gives us the opportunity to discriminate more clearly between the Chandra eclipse arrival time as reported by JI11 and our measurement (which is compatible with the one reported by BU10).
We found the delays of the eclipse arrival times by subtracting from our measurements the eclipse arrival times predicted by a constant orbital period model adopting the orbital period, P_{orb0}, and the reference time, ${\mathit{T}}_{\mathrm{0}}^{\mathrm{e}}$, given by PA00. The time delays were plotted versus the orbital cycle number N. The integer N is the exact number of orbital cycles elapsed since ${\mathit{T}}_{\mathrm{0}}^{\mathrm{e}}$; the cycle number N corresponding to each eclipse arrival time is shown in Col. 3 of Table 2. We then fitted the time delays using a parabolic function obtaining a χ^{2}/(d.o.f.) of 33.63/25. We found that ${\mathit{T}}_{\mathrm{0}}^{\mathrm{e}}\mathrm{=}\mathrm{45}\hspace{0.17em}\mathrm{614.80959}\mathrm{\left(}\mathrm{16}\mathrm{\right)}$ MJD_{⊙}, P_{orb0} = 20 054.2020(28) s, and Ṗ_{orb} = 1.626(90) × 10^{10} s/s with the associated errors at the 68% confidence level. All these values are compatible within one σ with those given by BU10 (see Col. 3 in Table 1), this suggests that the Chandra eclipse arrival times given by BU10 are in agreement with all the previous points.
To update the Xray ephemeris of X1822371, we then included the Chandra eclipse arrival times given by BU10 in our data set for a total of 30 available data points. We found the corresponding delays and cycle numbers as described above.
Fig. 3 Upper panel: eclipse time delays with respect to a constant orbital period model plotted versus the orbital cycle for all the available Xray eclipse time measures together with the bestfit parabola. Lower panel: residuals in units of σ with respect to the bestfit parabola. The black full squares points are from BU10, the red diamonds are the data added in this work. (This figure is available in color in the electronic form.) 
The time delays are shown in the upper panel of Fig. 3. We plotted the time delays used by BU10 with black full squares, while the time delays added in this work and corresponding to the Ginga, ROSAT, and Suzaku eclipse times are shown with red diamonds. We then fitted the time delays using a parabolic function, resulting in the ephemeris $\begin{array}{ccc}{\mathit{T}}_{\mathrm{ecl}}\mathrm{=}\mathrm{45}\hspace{0.17em}\mathrm{614.80953}\mathrm{\left(}\mathrm{16}\mathrm{\right)}\mathrm{MJ}{\mathrm{D}}_{\mathrm{\odot}}\mathrm{+}\mathrm{0.232108853}\mathrm{\left(}\mathrm{30}\mathrm{\right)}\mathit{N}& & \\ \mathrm{+}\mathrm{1.757}\mathrm{\left(}\mathrm{93}\mathrm{\right)}\mathrm{\times}{\mathrm{10}}^{11}{\mathit{N}}^{\mathrm{2}}\mathit{,}& & \end{array}$(2)where the associated errors are at the 68% confidence level. We obtained a χ^{2}/(d.o.f.) of 41.2/27, the bestfit curve is shown with a solid line in Fig. 3. We show the residuals in units of σ in the lower panel of Fig. 3 and report the obtained values of ${\mathit{T}}_{\mathrm{0}}^{\mathrm{e}}$, P_{orb0}, and Ṗ_{orb} in the second column of Table 4.
We found that the derivative of the orbital period, Ṗ_{orb}, is 1.514(80) × 10^{11} s/s, compatible with the value of 1.499(71) × 10^{11} s/s estimated by BU10.
Updated Xray and optical/UV ephemeris of X1822371.
3.2. Updated optical/UV ephemeris of X1822371
BA10 used 35 optical/UV eclipse arrival times shown in Table 1 of their paper to find the bestfit optical/UV ephemeris of X1822371 given by $\begin{array}{ccc}{\mathit{T}}_{\mathrm{ecl}}\mathrm{=}\mathrm{45614.81166}\mathrm{\left(}\mathrm{74}\mathrm{\right)}\mathrm{MJD}\mathrm{+}\mathrm{0.232108641}\mathrm{\left(}\mathrm{80}\mathrm{\right)}\mathit{N}& & \\ \mathrm{+}\mathrm{2.46}\mathrm{\left(}\mathrm{21}\mathrm{\right)}\mathrm{\times}{\mathrm{10}}^{11}{\mathit{N}}^{\mathrm{2}}\mathit{,}& & \end{array}$(3)where the errors are at the 68% confidence level (Bayless, priv. comm.). We added to their data the optical eclipse arrival time 2 443 629.841 ± 0.013 JD_{⊙} given by Hellier & Mason (1989) and not included in BA10.
Using the 36 optical/UV data points and following the procedure described in the previous section we found the corresponding time delays. Fitting them with a parabola, we obtained the following optical/UV ephemeris $\begin{array}{ccc}{\mathit{T}}_{\mathrm{ecl}}\mathrm{=}\mathrm{45614.8116}\mathrm{\left(}\mathrm{11}\mathrm{\right)}\mathrm{MJ}{\mathrm{D}}_{\mathrm{\odot}}\mathrm{+}\mathrm{0.23210865}\mathrm{\left(}\mathrm{12}\mathrm{\right)}\mathit{N}& & \\ \mathrm{+}\mathrm{2.44}\mathrm{\left(}\mathrm{31}\mathrm{\right)}\mathrm{\times}{\mathrm{10}}^{11}{\mathit{N}}^{\mathrm{2}}\mathit{,}& & \end{array}$(4)with a χ^{2}/(d.o.f.) of 71.38/33 and the errors are at the 68% confidence level. The uncertainties have been scaled by a factor $\sqrt{{\mathit{\chi}}_{\mathrm{red}}^{\mathrm{2}}}$ to take into account a ${\mathit{\chi}}_{\mathrm{red}}^{\mathrm{2}}$ of the bestfit model larger than 1. This explains why the uncertainties in the optical/UV ephemeris we have shown are larger than the ephemeris shown by BA10. The updated optical/UV ephemeris are consistent with those given by BA10. We report the corresponding values of ${\mathit{T}}_{\mathrm{0}}^{\mathrm{e}}$, P_{orb0}, and Ṗ_{orb} in the third column of Table 4. In the upper panel of Fig. 4, we show the time delays for each eclipse arrival time of X1822371 for the Xray (red full squares) and optical/UV bands (black full squares) for a total of 66 data points. The solid and dashed lines correspond to the bestfit parabolas reproducing the Xray and optical/UV ephemerides showed in Eqs. (2) and (4), respectively.
Fig. 4 Top panel: the optical/UV (black filled squares) and Xray (red filled squares) time delays. The dashed and solid lines correspond to the optical/UV and Xray bestfit parabolic curve. Middle panel: residuals with respect to the Xray bestfit parabolic curve. Bottom panel: residuals with respect to the optical/UV bestfit parabolic curve. (This figure is available in color in the electronic form.) 
We compare the Xray and optical/UV residuals with the Xray bestfit parabola in Fig. 4 (middle panel). Although we plot the residuals for the bestfit parabola obtained from the Xray time delays, we note that almost all of the optical/UV data are close to the bestfit curve. The largest discrepancies are associated with the last two optical eclipse times shown by Hellier & Mason (1989) corresponding to orbital cycles 7243 and 7600 and the two UV eclipse arrival times obtained with HST and reported by BA10; these last two data points are at orbital cycles 35 387 and 35 395, respectively. All the other optical/UV points are within two σ of the corresponding values of the bestfit Xray ephemeris.
In Fig. 4 (bottom panel), we show the Xray and optical/UV residuals with respect to the optical/UV bestfit curve. In this case, the Xray data are mainly below the bestfit optical/UV parabola.
3.3. Timelag between optical/UV and Xray eclipse times
To our knowledge, there are only two simultaneous Xray and optical observations of the eclipse of X1822371 reported by Hellier & Mason (1989) and Hellier et al. (1990); these authors showed that the optical eclipse times lag the Xray eclipse times by 3.0 ± 3.4 min, and 180 ± 50 s, respectively.
The optical eclipses are also wider than the Xray eclipses; the different width suggests a different origin for the optical and Xray eclipses, respectively. Hellier & Mason (1989) proposed that the Xray emission comes from an accretion disc corona (ADC) with a radius half of the outer accretion disc radius, while the optical emission is produced by a more extended disk structure. Furthermore, the optical eclipse lags the Xray eclipse because of the asymmetric disk structure probably caused by the stream impact onto the outer accretion disk. Hellier & Mason (1989), modelling the Xray and optical light curves of X1822371, found an optical eclipse timelag of ~0.01 in units of orbital phase, corresponding to a timelag of 200 s. BA10 discussed a marginally significant timelag between the optical/UV and Xray ephemeris of 100 ± 65 s and 122 s with respect to the Xray ephemeris reported by PA00 and BU10, respectively.
Since we have used an unprecedentedly large amount of optical/UV and Xray eclipse times, we can estimate the average timelag along 50 000 orbital cycles with good accuracy. We fitted simultaneously the Xray and optical/UV time delays allowing the constant terms of each parabola free to vary and constraining the values of the linear and quadratic parameters of each parabola to the same value, since the orbital period of X1822371 and its derivative cannot depend on the considered waveband.
Fitting the time delays, we obtained a large χ^{2}/(d.o.f.) of 124.04/62 and found that the bestfit values of the linear and quadratic terms are (3.7 ± 2.8) × 10^{3} s and (1.595 ± 0.086) × 10^{6} s, respectively. The constant terms are 121 ± 36 s and − 6 ± 16 s for the optical/UV and Xray datasets, respectively. Using these values, we obtained the ephemerides for the Xray and optical/UV data $\begin{array}{ccc}{\mathit{T}}_{\mathrm{ec}{\mathrm{l}}_{\mathrm{X}\mathrm{}\mathrm{ray}}}& \mathrm{=}& \mathrm{45}\hspace{0.17em}\mathrm{614.80957}\mathrm{\left(}\mathrm{19}\mathrm{\right)}\mathrm{MJ}{\mathrm{D}}_{\mathrm{\odot}}\mathrm{+}\mathrm{0.232108828}\mathrm{\left(}\mathrm{32}\mathrm{\right)}\mathit{N}\\ & & \mathrm{+}\mathrm{1.847}\mathrm{\left(}\mathrm{99}\mathrm{\right)}\mathrm{\times}{\mathrm{10}}^{11}{\mathit{N}}^{\mathrm{2}}\mathit{,}\end{array}$(5)$\begin{array}{ccc}{\mathit{T}}_{\mathrm{ec}{\mathrm{l}}_{\mathrm{opt}\mathit{/}\mathrm{UV}}}& \mathrm{=}& \mathrm{45}\hspace{0.17em}\mathrm{614.81104}\mathrm{\left(}\mathrm{42}\mathrm{\right)}\mathrm{MJ}{\mathrm{D}}_{\mathrm{\odot}}\mathrm{+}\mathrm{0.232108828}\mathrm{\left(}\mathrm{32}\mathrm{\right)}\mathit{N}\\ & & \mathrm{+}\mathrm{1.847}\mathrm{\left(}\mathrm{99}\mathrm{\right)}\mathrm{\times}{\mathrm{10}}^{11}{\mathit{N}}^{\mathrm{2}}\mathit{.}\end{array}$(6)The corresponding orbital period derivative is 1.591(86) × 10^{10} s/s, and the reference time T_{0} is 45 614.80957(19) and 45 614.81104(42) MJD_{⊙} for Xray and optical/UV datasets, respectively; all the errors are at the 68% c.l. For clarity’s sake, the values of ${\mathit{T}}_{\mathrm{0}}^{\mathrm{e}}$, P_{orb0}, and Ṗ_{orb} are showed in Table 5. In the upper panel of Fig. 5, we show the Xray (red points) and the optical/UV (black points) time delays; the dashed and solid curves are the optical/UV and Xray bestfit parabolas, respectively.
From our analysis, we found a timelag of 127 ± 52 s, which is significant at a confidence level of 2.4σ. In the bottom panel of Fig. 5, we show the residuals of the Xray (red points) and optical/UV (black points) delays with respect to the Xray bestfit parabola.
Ephemeris of X1822371 fitting simultaneously Xray and optical/UV data.
Fig. 5 Upper panel: the optical/UV (black filled squares) and Xray (red filled squares) time delays fitted with two parabolas having the same linear and quadratic terms. The solid and dashed parabolas correspond to the Xray and optical/UV bestfit curves. Lower panel: residuals in units of σ with respect to the bestfit parabola describing the Xray ephemeris shown in Eq. (5). (This figure is available in color in the electronic form.) 
The values of the optical/UV timelags with respect to the bestfit parabola describing the Xray ephemeris given by Eq. (5) are shown in Table 6. We note that the largest optical timelags are associated with the last two optical eclipse times shown by Hellier & Mason (1989) corresponding to orbital cycles 7243 and 7600 and with the recent two UV eclipse arrival times obtained with HST and reported by BA10; the corresponding timelags are 433 ± 86 s, 282 ± 86 s, 364 ± 86 s, and 452 ± 86 s, respectively. These values are larger than 200 s, in disagreement with that predicted by Hellier & Mason (1989) modelling the Xray and optical light curves of X1822371.
Journal of the optical/UV timelags.
Fig. 6 Upper panel: the optical/UV (red filled squares) timelags fitted with a constant (dashed line) and a sinusoidal function f(t) (solid line) with a period of 18 yr (see text). Lower panel: residuals in units of σ with respect to the bestfit sinusoidal function. (This figure is available in color in the electronic form.) 
We fitted the optical/UV timelags with a constant obtaining a large χ^{2}(d.o.f.) of 81.25(35); the constant value was 127 s, which is similar to the averaged timelag previously discussed. In Fig. 6 (top panel), we show the optical/UV timelags as a function of time in units of days, the dashed line being the constant function. We note that if we remove the four optical/UV points mentioned above, we find no significant timelag between the optical/UV and Xray eclipse times, with a bestfit value of 31 ± 46 s.
Because we found a large value of ${\mathit{\chi}}_{\mathrm{red}}^{\mathrm{2}}$, after a visual inspection of the fit residuals, we decided to fit the timelags with the function f(t) = A − Bsin[2π/P(t − t_{0})]. In this case, we largely improved the fit for two different sets of parameters. For the first set, we obtained a χ^{2}(d.o.f.) = 34.52(32) and a probability of chance improvement with respect to the fit with a constant of 4.03 × 10^{6}. The values of the bestfit parameters are A = 161 ± 24 s, B = 194 ± 29 s, P = 6593 ± 452d (18.1 ± 1.2 yr), and t_{0} = −1180 ± 481 d, the errors being at the 68% c.l. For the second set of parameters, we obtained a χ^{2}(d.o.f.) = 35.57(32) and a probability of chance improvement with respect to the fit with a constant of 6.45 × 10^{6}; in this case, A = 105 ± 24 s, B = −267 ± 43 s, P = 283.1 ± 0.6 d, and t_{0} = 239 ± 16 d, the errors being at the 68% c.l. The bestfit values of both the fits are shown in Table 7.
Bestfit parameters of the sinusoidal modulation fitting the optical/UV timelags.
The bestfit curve corresponding to the first set of parameters (hereafter bestfit 1) is shown in Fig. 6 (top panel) with a solid line. In the bottom panel of Fig. 6, we show the residuals with respect to the sinusoidal modulation in units of σ. The values of the residuals corresponding to the first set of parameters are shown in the third column of Table 6. The bestfit curve corresponding to the second set of parameters (hereafter bestfit 2) is shown in Fig. 7 (top panel) with a solid line. In the bottom panel of Fig. 7, we show the residuals with respect to the sinusoidal modulation in units of σ. The values of the residuals corresponding to the second set of parameters are shown in the fourth column of Table 6. We checked our results fitting the Xray timelags with respect to the bestfit parabola giving the Xray ephemeris. In this case, the residuals do not show any sinusoidal modulation, as expected. Fitting them with a constant, we found a χ^{2}(d.o.f.) = 42.8(29).
The two bestfit sinusoidal functions indicate that the optical/UV eclipse lags the Xray eclipse with a time shift of either 161 ± 24 s or 105 ± 24, which are significant at a confidence level of 6.7σ and 4.4σ, respectively. These values are compatible with the timelag predicted by Hellier & Mason (1989), of ~200 s. Our most intriguing result, never previously detected, is that the optical/UV eclipse times may oscillate in time with an amplitude of either 194 ± 29 s (bestfit 1) or 267 ± 43 s (bestfit 2), these values being significant at a confidence level of 6.7σ and 6.2σ, respectively. The detected periods are ~18 yr (bestfit 1) and ~283 days (bestfit 2). Both the detected periods are very long and difficult to explain by invoking a superhump phenomenon (see Wang & Chakrabarty 2010, and reference therein). The superhump excess ϵ is defined as P_{sh}/P_{orb} − 1, where P_{sh} is the superhump period, and also as ϵ = 0.18q + 0.29q^{2} (Patterson et al. 2005), where q is the mass ratio m_{2}/m_{1} with m_{1} the neutronstar mass. Since the mass function and inclination angle of X1822371 is well known (Jonker & van der Klis 2001), assuming a neutronstar mass of 1.4 M_{⊙} and an inclination angle of 87° we find that q ≃ 0.29 and ϵ ~ 0.077. Consequently the superhump period should be P_{sh} = 1.077P_{orb} = 21 598.38 s. A possible beat phenomenon between the superhump period and the orbital period could produce a period given by (1/P_{orb} − 1/P_{sh})^{1} ≃ 3.25 days. This value is shorter than the two periodicities that we reported.
Fig. 7 Upper panel: the optical/UV (red filled squares) timelags fitted with a sinusoidal function f(t) (solid line) with a period of 283 days (see text). Lower panel: residuals in units of σ with respect to the bestfit sinusoidal function. (This figure is available in color in the electronic form.) 
We found that the lag changes with time and that this variation is compatible with a sinusoidal modulation at two different periods of 18 yr and 283 days, respectively. However, we cannot exclude shorter periodicities, but our data set of only 36 optical/UV eclipse times spanning a time of 10 000 days do not allow a rigorous study. To investigate this aspect, long optical/UV observations of X1822371 covering several contiguous orbital periods of the source would be necessary.
Finally we note that both these bestfit curves are strongly driven by the optical measures corresponding to orbital cycles 7243 and 7600 and by the recent two UV eclipse arrival times obtained with HST and reported by BA10; these last two points are at orbital cycle 35 387 and 35 395.
4. Conclusions
We have revisited and discussed the Xray and optical/UV ephemerides of X1822371. Fitting simultaneously the optical/UV and Xray time delays, we have found that the optical/UV eclipses of X1822371 lag the Xray eclipses by 127 ± 52 s with a significance level of 2.4σ. However, this timelag may not be constant in time. Fitting the optical/UV timelags, we have found a statistically significant variation, which is compatible with a sinusoidal modulation at two different periods, ~18 yr and 239 d. In the first case, the optical/UV eclipses lag the Xray eclipse by an average time of 161 s (significance 6.7σ) and this delay oscillates in time around this value with an amplitude of 194 s (significance 6.7σ). In the second case, the optical/UV eclipses lag the Xray eclipse by an average time of 105 s (significance 4.4σ), and this delay oscillates in time around this value with an amplitude of 267 s (significance 6.2σ).
Owing to the relatively small number of points over a longtime span of 30 yr, we cannot be sure of the period of this modulation, because we cannot exclude much shorter periods. Long and relatively continuous optical/UV observations are necessary to prove or disprove the presence of this periodicity in the optical/UV eclipse timelags.
Our results confirm the value of the orbital solution derived by the Xray eclipse times given by BU10 and that the orbital period derivative is three orders of magnitude larger than expected on the basis of the conservative mass transfer driven by magnetic braking and gravitational radiation. We have also confirmed this result by combining the Xray data and the optical/UV data of X1822371.
Acknowledgments
We thank the anonymous referee for the useful suggestions and A. Bayless for the fruitful interaction. authors acknowledge financial contribution from the agreement ASIINAF I/009/10/0. A.P. acknowledges financial support from the Autonomous Region of Sardinia through a research
grant under the program PO Sardegna ESF 20072013, L.R.7/2007, Promoting scientific research and technological innovation in Sardinia. L.B. and T.D. acknowledge support from the European Community’s Seventh Framework Program (FP7/20072013) under grant agreement number ITN 215212 Black Hole Universe.
References
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All Tables
Bestfit parameters of the sinusoidal modulation fitting the optical/UV timelags.
All Figures
Fig. 1 Combined XIS light curve of X1822371 in the 1–10 keV energy band. The adopted bin time is 128 s. 

In the text 
Fig. 2 Time delays of the eclipse arrival times with respect to the linear ephemeris of Hellier & Smale (1994). The black open squares correspond to the eclipse arrival times shown by Hellier & Smale (1994) and PA00, the red diamonds to the Chandra eclipse arrival times given by JI11, the green filled squares to the Chandra eclipse arrival times reported in this paper (see Table 3), the blue open circles to the Chandra eclipse arrival times reported by BU10. The dashed and solid lines are the bestfit quadratic curve obtained by JI11 and in this paper (see text), respectively. (This figure is available in color in the electronic form.) 

In the text 
Fig. 3 Upper panel: eclipse time delays with respect to a constant orbital period model plotted versus the orbital cycle for all the available Xray eclipse time measures together with the bestfit parabola. Lower panel: residuals in units of σ with respect to the bestfit parabola. The black full squares points are from BU10, the red diamonds are the data added in this work. (This figure is available in color in the electronic form.) 

In the text 
Fig. 4 Top panel: the optical/UV (black filled squares) and Xray (red filled squares) time delays. The dashed and solid lines correspond to the optical/UV and Xray bestfit parabolic curve. Middle panel: residuals with respect to the Xray bestfit parabolic curve. Bottom panel: residuals with respect to the optical/UV bestfit parabolic curve. (This figure is available in color in the electronic form.) 

In the text 
Fig. 5 Upper panel: the optical/UV (black filled squares) and Xray (red filled squares) time delays fitted with two parabolas having the same linear and quadratic terms. The solid and dashed parabolas correspond to the Xray and optical/UV bestfit curves. Lower panel: residuals in units of σ with respect to the bestfit parabola describing the Xray ephemeris shown in Eq. (5). (This figure is available in color in the electronic form.) 

In the text 
Fig. 6 Upper panel: the optical/UV (red filled squares) timelags fitted with a constant (dashed line) and a sinusoidal function f(t) (solid line) with a period of 18 yr (see text). Lower panel: residuals in units of σ with respect to the bestfit sinusoidal function. (This figure is available in color in the electronic form.) 

In the text 
Fig. 7 Upper panel: the optical/UV (red filled squares) timelags fitted with a sinusoidal function f(t) (solid line) with a period of 283 days (see text). Lower panel: residuals in units of σ with respect to the bestfit sinusoidal function. (This figure is available in color in the electronic form.) 

In the text 
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