Anticorrelation between X-ray luminosity and pulsed fraction in the Small Magellanic Cloud pulsar SXP 1323

Anticorrelation between X-ray luminosity and pulsed fraction in the Small Magellanic Cloud pulsar... ABSTRACT We report the evidence for the anticorrelation between pulsed fraction (PF) and luminosity of the X-ray pulsar SXP 1323, found for the first time in a luminosity range 1035–1037 erg s−1 from observations spanning 15 yr. The phenomenon of a decrease in X-ray PF when the source flux increases has been observed in our pipeline analysis of other X-ray pulsars in the Small Magellanic Cloud. It is expected that the luminosity under a certain value decreases as the PF decreases due to the propeller effect. Above the propeller region, an anticorrelation between the PF and the flux might occur either as a result of an increase in the unpulsed component of the total emission or a decrease of the pulsed component. Additional modes of accretion may also be possible, such as spherical accretion and a change in emission geometry. At higher mass accretion rates, the accretion disc could also extend closer to the neutron star surface, where a reduced inner radius leads to hotter inner disc emission. These modes of plasma accretion may affect the change in the beam configuration to fan-beam dominant emission. pulsars: individual: SXP 1323, X-rays: binaries 1 INTRODUCTION X-ray pulsars comprise two stars, a neutron star (NS, descended from a star with initial mass > 8 M⊙; Verbunt & van den Heuvel 1995), and a mass-losing companion star, also of large mass. The general picture of accretion on to X-ray pulsars consists of a flow in a wind or disc to the magnetosphere and then along the dipole field lines on to the magnetic poles of the NS. The pulsed fraction (PF), i.e. the relative amplitude of the emerging pulse profile, bears key information on the relation between X-ray emission from the accretion column (pulsed emission) and other regions of the accretion flow or NS surface (unpulsed emission), e.g. Beloborodov (2002). The Small Magellanic Cloud (SMC) pulsar SXP 5.05 was reported by Coe, Bartlett & Bird (2015) to show a positive correlation between the PF and luminosity, as shown in their fig. 11. Those data were taken while SXP 5.05 was undergoing high levels of accretion. At low-mass accretion rates, Cui (1997) reported two X-ray pulsars (GX 1+4 and GRO J1744−28) whose PF decreases as the X-ray flux drops below a certain threshold. This is an indication of the propeller effect (Illarionov & Sunyaev 1975) that takes place when the pulsar magnetosphere grows beyond the co-rotation radius, and the centrifugal force prevents accreting matter from reaching the magnetic poles. Tiengo, Mereghetti & Turolla (2005) observed an anticorrelation between PF and the corresponding flux of 1E 1048.1−5937 in the Milky Way. Spectral variations as a function of the pulse phase shows the hardest spectrum at pulse maximum. Lutovinov & Tsygankov (2009) presented marginal evidence for an anticorrelation of PF and energy in source 4U 0115+63 and Her X-1. Fig. 4 from Tsygankov et al. (2007) shows the increase of energy in 4U 0115+63 is not uniform but has local maximum near the cyclotron line. A positive and an anticorrelation is observed at low and high energy, respectively. Tsygankov, Lutovinov & Serber (2010) noted the PF of V 0332+53 increases with decreasing photon energy below 12–15 keV, which is difficult to explain. An anti and a positive correlation is observed at low and high luminosities, respectively (see their fig. 10). Below ∼1038 erg s−1 the anticorrelation is in accordance with a geometry model in which the PF is determined by the luminosity-dependent visible areas of the accretion columns. However, in the photon energy range 25–45  keV the observed correlation does not fully conform to the model. Parmar, White & Stella (1989) applied a geometric model to describe the pulse shape of X-ray pulsar EXO 2030+375 and showed that below a luminosity of 4 × 1036 erg s−1, the pencil beam becomes dominant compared to the fan-beam, along with an increase in the unpulsed component and a decrease in the luminosity. In Beloborodov (2002)’s classes of pulse profiles, visibility of the two polar caps depends on the angle between the magnetic rotation axis and dipole axis. If both poles are continuously visible, it is possible to have no pulsations. As shown in the modelled light curves of fig. 5 from Yang et al. (2017b), in classes 2 and 4 of the upper panel, and classes 3 and 4 of the middle panel, when both hot spots are visible, the observed pulse shows a plateau. We have collected and analysed the comprehensive archive of XMM–Newton (116), Chandra Advanced CCD Imaging Spectrometer (ACIS-I) (151), and RXTE (952) observations of the known pulsars in the SMC, spanning the years 1997–2014. Our pipeline generates a suite of products for each pulsar detection: spin period, flux, event list, high-time resolution light-curve, pulse-profile, periodogram, and spectrum. Combining all three satellites, we generated complete histories of the spin periods, pulse amplitudes, pulsed fractions, and X-ray luminosities (Yang et al. 2017a). Based on this archive, the relationship between the PF and luminosity of the SMC pulsars have drawn our attention. We find a surprising anticorrelation between PF and luminosity in SMC X-ray pulsars, for example, SXP 1323, SXP 893, SXP 756, SXP 726, SXP 701, SXP 348, and SXP 323. In this work, we show an example (SXP 1323) of this phenomenon and discuss the mechanism behind these results. We selected this source because it has the most data points compared to the other pulsars with anticorrelations. SXP 1323 (a.k.a. RX J0103.6-7201) was discovered by Haberl & Pietsch (2005) and shows one of the longest pulse periods known in the SMC. The names of the optical companion star are [MA93] 1393 (Meyssonnier & Azzopardi 1993) and [M2002] SMC 56901 (Massey 2002). Carpano et al (2017) found the orbital period of this Be/X-ray binary (BeXB) to be 26.2 d, which is very short for such a long spin period pulsar. It is located at RA = 01:03:37.5 and Dec. = −72:01:33 with a positional uncertainty of 1.1 arcsec (Lin, Webb & Barret 2012). The spectral type of this X-ray binary counterpart is B0 with a luminosity class of III–V (McBride et al. 2008). In this paper, we present the pulsed fraction dependence on luminosity from 15 yr of X-ray monitoring for SXP 1323. We aim to have a deeper understanding of the accretion process under the anticorrelation of the PFs and luminosities. 2 OBSERVATIONS AND METHODS Yang et al. (2017a) have collected and analysed 36 XMM–Newton and 108 Chandra X-ray observations up until 2014 for SXP 1323. XMM–Newton has detected this source 36 times and in 10 of these observations its pulsations are found. As for Chandra, we only used the ACIS-I detections: 63 out of 108 observations yield source detections and 14 observations have detected its pulsations. We are not including RXTE observations in this analysis since RXTE does not provide the required PF information. The RXTE Proportional Counter Array is a non-imaging detector and multiple sources are always in the field of view, so the unpulsed component cannot be reliably measured. The observations we used for SXP 1323 with pulsations detected are shown in Table 1. The pulsations are with a significance of s ≥ 99 per cent according to equation 2 of Yang et al. (2017a). Table 1. The XMM–Newton and Chandra ACIS-I X-ray observations in which the pulsations for SXP 1323 have been detected. The first column is the observation ID, the second and third columns show observing Modified Julian Date (MJD) and source flux, and the last two columns are the photon counts (for xmm, it is the medium value from the three EPIC instruments) and exposure time. XMM–Newton ID MJD Flux (erg s−1 cm−2) Photon counts Exposure time (ks) 135 722 401 53292.38 7.32 × 10−13 458 31.11 123 110 301 51651.15 1.50 × 10−12 2020 21.66 135 722 701 53845.10 4.29 × 10−12 5096 30.48 135 720 801 52268.75 2.10 × 10−12 2190 35.02 135 721 701 52959.26 1.41 × 10−12 3752 27.36 135 722 501 53477.93 4.69 × 10−12 9129 37.12 412 980 201 54215.52 2.50 × 10−12 2407 36.42 135 721 901 53123.30 3.21 × 10−13 1251 35.23 412 980 501 54575.39 3.44 × 10−12 3383 29.92 412 980 301 54399.41 1.80 × 10−12 2725 37.12 Chandra ID – – – – 1533 52065.27 2.33 × 10−12 984 7.42 1536 52065.57 2.04 × 10−12 860 7.42 1542 52065.76 1.69 × 10−12 699 7.42 1786 51728.55 1.66 × 10−12 738 7.58 2841 52249.09 1.62 × 10−12 686 7.46 6050 53352.15 8.25 × 10−13 336 7.16 6052 53353.37 8.96 × 10−13 358 7.54 6056 53356.31 5.064 × 10−13 253 8.01 6060 53534.55 9.00 × 10−13 1033 19.8 6749 53816.60 1.61 × 10−12 1830 19.51 6757 53891.55 5.24 × 10−13 582 19.8 8361 54136.10 1.14 × 10−12 1283 19.79 8364 54142.57 4.71 × 10−13 253 8.45 9693 54501.17 1.55 × 10−12 657 7.68 XMM–Newton ID MJD Flux (erg s−1 cm−2) Photon counts Exposure time (ks) 135 722 401 53292.38 7.32 × 10−13 458 31.11 123 110 301 51651.15 1.50 × 10−12 2020 21.66 135 722 701 53845.10 4.29 × 10−12 5096 30.48 135 720 801 52268.75 2.10 × 10−12 2190 35.02 135 721 701 52959.26 1.41 × 10−12 3752 27.36 135 722 501 53477.93 4.69 × 10−12 9129 37.12 412 980 201 54215.52 2.50 × 10−12 2407 36.42 135 721 901 53123.30 3.21 × 10−13 1251 35.23 412 980 501 54575.39 3.44 × 10−12 3383 29.92 412 980 301 54399.41 1.80 × 10−12 2725 37.12 Chandra ID – – – – 1533 52065.27 2.33 × 10−12 984 7.42 1536 52065.57 2.04 × 10−12 860 7.42 1542 52065.76 1.69 × 10−12 699 7.42 1786 51728.55 1.66 × 10−12 738 7.58 2841 52249.09 1.62 × 10−12 686 7.46 6050 53352.15 8.25 × 10−13 336 7.16 6052 53353.37 8.96 × 10−13 358 7.54 6056 53356.31 5.064 × 10−13 253 8.01 6060 53534.55 9.00 × 10−13 1033 19.8 6749 53816.60 1.61 × 10−12 1830 19.51 6757 53891.55 5.24 × 10−13 582 19.8 8361 54136.10 1.14 × 10−12 1283 19.79 8364 54142.57 4.71 × 10−13 253 8.45 9693 54501.17 1.55 × 10−12 657 7.68 View Large Table 1. The XMM–Newton and Chandra ACIS-I X-ray observations in which the pulsations for SXP 1323 have been detected. The first column is the observation ID, the second and third columns show observing Modified Julian Date (MJD) and source flux, and the last two columns are the photon counts (for xmm, it is the medium value from the three EPIC instruments) and exposure time. XMM–Newton ID MJD Flux (erg s−1 cm−2) Photon counts Exposure time (ks) 135 722 401 53292.38 7.32 × 10−13 458 31.11 123 110 301 51651.15 1.50 × 10−12 2020 21.66 135 722 701 53845.10 4.29 × 10−12 5096 30.48 135 720 801 52268.75 2.10 × 10−12 2190 35.02 135 721 701 52959.26 1.41 × 10−12 3752 27.36 135 722 501 53477.93 4.69 × 10−12 9129 37.12 412 980 201 54215.52 2.50 × 10−12 2407 36.42 135 721 901 53123.30 3.21 × 10−13 1251 35.23 412 980 501 54575.39 3.44 × 10−12 3383 29.92 412 980 301 54399.41 1.80 × 10−12 2725 37.12 Chandra ID – – – – 1533 52065.27 2.33 × 10−12 984 7.42 1536 52065.57 2.04 × 10−12 860 7.42 1542 52065.76 1.69 × 10−12 699 7.42 1786 51728.55 1.66 × 10−12 738 7.58 2841 52249.09 1.62 × 10−12 686 7.46 6050 53352.15 8.25 × 10−13 336 7.16 6052 53353.37 8.96 × 10−13 358 7.54 6056 53356.31 5.064 × 10−13 253 8.01 6060 53534.55 9.00 × 10−13 1033 19.8 6749 53816.60 1.61 × 10−12 1830 19.51 6757 53891.55 5.24 × 10−13 582 19.8 8361 54136.10 1.14 × 10−12 1283 19.79 8364 54142.57 4.71 × 10−13 253 8.45 9693 54501.17 1.55 × 10−12 657 7.68 XMM–Newton ID MJD Flux (erg s−1 cm−2) Photon counts Exposure time (ks) 135 722 401 53292.38 7.32 × 10−13 458 31.11 123 110 301 51651.15 1.50 × 10−12 2020 21.66 135 722 701 53845.10 4.29 × 10−12 5096 30.48 135 720 801 52268.75 2.10 × 10−12 2190 35.02 135 721 701 52959.26 1.41 × 10−12 3752 27.36 135 722 501 53477.93 4.69 × 10−12 9129 37.12 412 980 201 54215.52 2.50 × 10−12 2407 36.42 135 721 901 53123.30 3.21 × 10−13 1251 35.23 412 980 501 54575.39 3.44 × 10−12 3383 29.92 412 980 301 54399.41 1.80 × 10−12 2725 37.12 Chandra ID – – – – 1533 52065.27 2.33 × 10−12 984 7.42 1536 52065.57 2.04 × 10−12 860 7.42 1542 52065.76 1.69 × 10−12 699 7.42 1786 51728.55 1.66 × 10−12 738 7.58 2841 52249.09 1.62 × 10−12 686 7.46 6050 53352.15 8.25 × 10−13 336 7.16 6052 53353.37 8.96 × 10−13 358 7.54 6056 53356.31 5.064 × 10−13 253 8.01 6060 53534.55 9.00 × 10−13 1033 19.8 6749 53816.60 1.61 × 10−12 1830 19.51 6757 53891.55 5.24 × 10−13 582 19.8 8361 54136.10 1.14 × 10−12 1283 19.79 8364 54142.57 4.71 × 10−13 253 8.45 9693 54501.17 1.55 × 10−12 657 7.68 View Large In order to test the correlation with luminosities and make the results convincible, three different definitions of PF were calculated by integrating over the pulse profile. The simplified formulas are shown in equations (1)–(3). \begin{equation*}\mathrm{ PF}_\mathrm{A}=\frac{f_\mathrm{max}-f_\mathrm{min}}{f_\mathrm{max}}, \end{equation*} (1) here fmax is the maximum photon count rate in the pulse profile and fmin is the minimum value as demonstrated in an example of the pulsed profile in Fig. 1. PFA is also usually called modulation amplitude. \begin{equation*}\mathrm{ PF}_\mathrm{B}=\frac{f_\mathrm{mean}-f_\mathrm{min}}{f_\mathrm{mean}}, \end{equation*} (2)fmean is the average flux. \begin{equation*}\mathrm{ PF}_\mathrm{S}=\frac{\sqrt{2}f_\mathrm{rms}}{f_\mathrm{mean}}, \left(\mathrm{ and}\ f_\mathrm{rms}=\frac{\sqrt{\sum _i^{N}(f_i-f_\mathrm{mean})^2}}{N}\right) ,\end{equation*} (3) where frms is the root mean square (rms) flux, N is the number of bins for each folded light curve, and fi is the mean photon count rate in each bin. For a sinusoid wave, which is a good approximation to most accretion pulsars, the peak-to-peak pulsed flux fpulsed = fmean − fmin = $$\sqrt{2}f_\mathrm{rms}$$; for a square wave fpulsed = frms (Bildsten, Chakrabarty & Chiu 1997). Figure 1. View largeDownload slide An example of pulse profile for SXP 1323 shows the values used for the PF calculation in equations (1)–(3), and frms is the root mean square flux. It is an XMM–Newton Observation (ID 135 722 701), observed on 2006 April 20. Figure 1. View largeDownload slide An example of pulse profile for SXP 1323 shows the values used for the PF calculation in equations (1)–(3), and frms is the root mean square flux. It is an XMM–Newton Observation (ID 135 722 701), observed on 2006 April 20. The error of the PF is calculated as following. First get the error of the flux in each bin of the light curve, \begin{equation*}\mathrm{ error}_i=\frac{\sqrt{\sum _j^{n}(f_i-F_j)^2}}{{ \mathit{ n}}}, \end{equation*} (4) where Fj is the flux in the ith bin. n is the number of points in each bin. Then we could get the error of fmax (errormax) as well as the error from fmin (errormin). The error of PFA is \begin{equation*}\mathrm{ error}_\mathrm{PFA}=\sqrt{\frac{\mathrm{ error}_\mathrm{max}^2+\mathrm{ error}_\mathrm{min}^2}{(f_\mathrm{max}-f_\mathrm{min})^2}+\left(\frac{\mathrm{ error}_\mathrm{max}}{f_\mathrm{max}}\right)^2}\ \times\, \mathrm{ PF}_\mathrm{A} \end{equation*} (5) In order to calculate errorPFB and errorPFS, first calculate the error of the pulsed flux: \begin{equation*}e_\mathrm{pulse}=\frac{\sum _i^{N}\sqrt{\mathrm{ error}_\mathrm{max}^2+\mathrm{ error}_i^2}}{N}, \end{equation*} (6) \begin{equation*}\mathrm{ error}_\mathrm{PFB}=\frac{e_\mathrm{pulse}}{f_\mathrm{mean}}; \end{equation*} (7) \begin{equation*}\mathrm{ error}_\mathrm{PFS}=\sqrt{2}\frac{e_\mathrm{pulse}}{f_\mathrm{mean}}\ \times\,\mathrm{ PF}_ \mathrm{S}. \end{equation*} (8) Note, in Yang et al. (2017a) the pulsed fraction from XMM–Newton is PFB and the ones from Chandra are PFA. Here we used PFA and PFB for both XMM–Newton and Chandra observations. PFA has intuitive appeal, but it is more difficult to determine the fmin than fmean (Bildsten et al. 1997). People generally use PFA for light curves from long time exposures, where signal-to-noise ratio is large. PFB is smaller than PFA, but more stable as fmean is easier to be determined than fmax. PFS is used for relatively short time exposure. The PF as a function of luminosity for SXP 1323 is shown in Fig. 2. Although the light curves were extracted from the higher time resolution EPIC-PN data (Yang et al. 2017a), the luminosities used in Fig. 2 were obtained from the total XMM–Newton flux available in the three XMM–Newton catalogues since they are more complete than the instrument-specific fluxes. These fluxes are based on a spectral model of a power law of slope 1.7 absorbed by a Hydrogen column of 3 × 1020 cm−2 (0.2–12 keV).1 Figure 2. View largeDownload slide The PF as the function of luminosity for SXP 1323. Green circles are the XMM–Newton detections and blue square symbols present Chandra observations. The three panels show the PFs with different calculations which are in equations (1)–(3). Figure 2. View largeDownload slide The PF as the function of luminosity for SXP 1323. Green circles are the XMM–Newton detections and blue square symbols present Chandra observations. The three panels show the PFs with different calculations which are in equations (1)–(3). The trend between PFA and luminosity is \begin{equation*}\mathrm{ PF}_\mathrm{A}=-0.399\,\mathrm{ log }\left(\frac{L_\mathrm{X}}{10^{35}\,\text{erg s$^{-1}$}}\right)+0.850, \end{equation*} (9) The fit between PFB and luminosity is \begin{equation*}\mathrm{ PF}_\mathrm{B}=-0.350\,\mathrm{ log} \left(\frac{L_\mathrm{X}}{10^{35}\,\text{erg s$^{-1}$}}\right)+0.669. \end{equation*} (10) The anticorrelation of PFS and luminosity is fitted as \begin{equation*}\mathrm{ PF}_\mathrm{S}=-0.101\,\mathrm{ log} \left(\frac{L_\mathrm{X}}{10^{35}\,\text{erg s$^{-1}$}}\right)+0.173, \end{equation*} (11) where LX is in erg s−1. The trend with PFA is steeper than the one with PFB, and even more steeper than PFS. PFA is the most popular way to show the pulsed fraction of the X-ray pulse profiles, therefore, the linear regression is more convincing. However, all of them show the similar anticorrelation. Monte Carlo simulations are performed to estimate the false-positive detection rate for the correlation between these two observables, from which the significance level is estimated. For the correlation in each panel of Fig. 2, 4000 trial generates 4000 simulated data. Based on these data, the fitting is performed. One of the fitting parameters (slope) is shown in the histograms of Fig. 3. We interpret positive slopes as false positive detections of an anticorrelation in the real data. The number of false positives from Fig. 3 corresponds to a probability of 95.43, 93.28, and 92.68, for the anticorrelation found by using PFA, PFB, and PFS, respectively. Therefore, the fit of the correlations in Fig. 2 is around ∼2σ confidence. Figure 3. View largeDownload slide Frequency distribution of correlation slopes for PFA (upper), PFB (middle), and PFS (bottom) obtained using Monte Carlo method with 4000 simulations. The heights of bars indicate the number of parameter values in the equally spaced bins. The limit for false positive detections of an anticorrelation is shown as red solid lines at slope 0.0. The dashed lines are the slopes from Fig. 2. Figure 3. View largeDownload slide Frequency distribution of correlation slopes for PFA (upper), PFB (middle), and PFS (bottom) obtained using Monte Carlo method with 4000 simulations. The heights of bars indicate the number of parameter values in the equally spaced bins. The limit for false positive detections of an anticorrelation is shown as red solid lines at slope 0.0. The dashed lines are the slopes from Fig. 2. 3 THEORETICAL MECHANISMS Mukerjee, Agrawal & Paul (2000) observed a decrease in the pulsed fraction with decreasing luminosity of the X-ray pulsar Cepheus X-4 (GS 2138+56). However, they argued that the decrease in the pulsed fraction, depending on the accretion flow geometry with respect to line of sight, is not a consequence of propeller effect. They propose as a more likely scenario a different mode of accretion occurring below a certain luminosity. These additional entry modes of plasma may affect the emission geometry to be more fan-beam-like pattern, which will increase the unpulsed flux, and the pulsed fractions end up being smaller. However, for SXP 1323, the PF increases as the luminosity decreases. The critical luminosity mentioned in Mukerjee et al. (2000) is the maximum luminosity LX(min) at which the centrifugal inhibition dominates, resulting in the propeller effect (e.g. Shtykovskiy & Gilfanov 2005; Tsygankov et al. 2016; Christodoulou et al. 2016): \begin{eqnarray*}L_\mathrm{X} (\mathrm{min}) &=& 2 \times 10^{37}\left(\frac{R}{10^6 \rm \,{cm}}\right)^{-1}\left(\frac{M}{1.4\,\mathrm{ M}_{{{\odot }}}}\right)^{-\frac{2}{3}} \\&&\times \left(\frac{\mu }{10^{30}\, \mathrm{ G} \,\rm{cm}^{3}}\right)^{2}\left(\frac{P_\mathrm{s}}{1 \mathrm{ s}}\right)^{-\frac{7}{3}} \,{\rm erg\,s}^{-1}, \end{eqnarray*} (12) where R, M, μ, and Ps are the radius, mass, magnetic moment, and spin period of the NS, respectively. We use a surface polar magnetic field strength B = 2.6 × 1012 G (Mihara et al. 1991) and R = 10 km, for a dipole-like field configuration, μ = B × R3 = 2.6 × 1030 G cm3. Assuming M = 1.4M⊙, we calculate the minimum luminosity below which the propeller effect will occur in SXP 1323 to be LX(min) = 7.03 × 1030 erg s−1. In our analysis, all of the luminosities observed are higher than this critical value, therefore it is highly unlikely that the anticorrelation is the result of the propeller effect. We can see the PF drops quickly as the luminosity increases up to ∼1036 erg s−1. This is consistent with Campana, Gastaldello & Stella (2001)’s result above a certain critical luminosity of ∼1035 erg s−1 in the X-ray pulsar 4U 0115+63 in our Galaxy. Campana et al. (2001) expressed the source accretion luminosity as two components: the luminosity of the disc extending down to the magnetospheric boundary, Ldisc; and the luminosity released within the magnetosphere Lmag by the mass inflow rate that accretes on to the NS surface. They claimed that the pulsed fraction is expected to remain unaltered as long as Lmag dominates, while Ldisc is expected to be unpulsed, resulting in a decreasing pulsed fraction as its luminosity increases. It explains the PF trend only at the luminosities larger than ∼1035 erg s−1 in fig. 2 of Campana et al. (2001). Assuming that there are two X-ray components: the accretion column (Lcol) and the accretion disc (Ldisc), the luminosity of the accretion column should be relatively stable since it would be locally Eddington, and the luminosity of the disc changes because at high-mass accretion rate ($$\dot{M}$$) the magnetospheric radius (Rmag) gets smaller and the Ldisc increases. From the relation between Rmag and $$\dot{M}$$ (for a given Ps and magnetic field B) and feeding this through a standard Shakura–Sunyaev disc, we have that \begin{eqnarray*}T_\mathrm{{disc}} \propto \left\lbrace \frac{\dot{M}}{R^3}[1-\left(\frac{R_\mathrm{mag}}{R}\right)^{\frac{1}{2}}] \right\rbrace ^{\frac{1}{4}},\end{eqnarray*} (13) \begin{eqnarray*}L_\mathrm{{disc}} \propto T_\mathrm{{disc}}^{4} \times R^{2}\simeq \dot{M} \times R^{\frac{5}{4}}, \end{eqnarray*} (14) where Tdisk is the temperature. If luminosity from the accretion column Lcol is constant, Rmag decreases and Ldisc increases. The predicted PF should change with increasing luminosity due to the unpulsed disc emission. Our anticorrelation is still at odds with the trend reported for many other pulsars in the literature (e.g. Mukerjee et al. 2000; Coe et al. 2015). The possible reason is that the spin period matters, as the pulsars in Mukerjee et al. (2000) and Coe et al. (2015) have short spin periods of 66.27 and 5.05 s, respectively. It could be that the PF changes of the short period pulsars depend on their luminosities. In the following, we discuss the PF luminosity anticorrelation in the context of different models for X-ray emission in accreting pulsars. 3.1 Spherical accretion The flow of material towards the pulsar might not take place through an accretion disc but instead via a spherical accretion flow, a natural consequence of wind-fed accretion, as opposed to Roche lobe overflow. The spherical accretion should be outside the accretion column and would obscure it (unless highly ionized). Also at low luminosity, the magnetospheric radius should be large enough to truncate the accretion flow. This accretion model was applied to black holes by Nobili, Turolla & Zampieri (1991). The accretion of gas on to the compact object can be a very efficient way of converting gravitational potential energy into radiation. Traditional spherical accretion is thought of as a good approximation for isolated compact objects. Ikhsanov, Pustil’nik & Beskrovnaya (2005) has applied the spherical accretion model to High-Mass X-ray binaries (HMXBs), especially the long spin period pulsars. Zeldovich and Shakura (1969) presented a model to describe the gravitational energy of matter accreted on to an NS and released in a thin layer above the surface. Variations of this idea have also been applied in detailed models (e.g. Turolla et al. 1994, for spherical accretion). The deep layers of the NS atmosphere are heated by the outer layer and produce soft thermal photons (Cui et al. 1998). The hard X-ray photons are from the polar hot spots, which contribute to the pulsed flux observed. The soft X-ray photons from spherical accretion would mainly contribute to the unpulsed component of flux. Spherical accretion becomes more prominent as the luminosity and mass accretion rate increases, which leads to a smaller PF. 3.2 NS whole surface thermal emission Generally, there are two components of the X-ray emission from NSs: thermal emission and non-thermal emission. The non-thermal emission is caused by pulsar radiation in the magnetosphere and its own rotation activity, which is suppressed when accreting. Thermal emission is from the whole surface of a cooling NS and/or from the small hot spots around the magnetic poles on the star surface (Becker 2009). It is also heated by accretion. The thermal radiation from the entire stellar surface can dominate at soft X-ray energies for middle-aged pulsars (∼100 kyr) and younger pulsars (∼10 kyr). If thermal emission is a significant component of the X-rays from SXP 1323 and this component increases, it would represent and increase in unpulsed flux such that the PF becomes smaller. 3.3 Change in emission geometry Ghosh & Lamb (1979) found $$\dot{P}\propto L_\mathrm{X} ^{6/7}$$ assuming the effective inertial moment of the NS is constant, so a higher accretion rate and LX could cause the observed high spin-up rate of this pulsar. The accreted mass interacts with the magnetosphere, and the accretion disc extends inward to some equilibrium radial distance above the NS’s surface (Malina & Bowyer 1991). Yang et al. (2017a) has reported this pulsar’s average spin-up rate as 6 ± 3 ms d−1 based on data from three X-ray satellites from 1997–2014. Carpano et al (2017) has presented an even faster spin-up of ∼59.3 ms d−1 based on recent observations from 2006 to 2016. The higher spin period and mass accretion rate could build up a higher accretion column above the polar caps. As the height of the accretion column increases, scattering of photons off in-falling electrons gets more prominent. This increases the fraction of emission escaping the column to the side, i.e. a fan-beam emerges (e.g. Becker, Klochkov & Schönherr 2012). Fan-beam emission becomes dominant, which reduces the eclipse of the accretion column. Furthermore, the contribution of the flux reflected by the NS surface is significant (Mushtukov, Verhagen & Tsygankov 2018). It raises the unpulsed flux, therefore we see the luminosity increasing and the pulsed fraction decreasing. Romanova, Kulkarni & Lovelace (2008) used 3D magnetohydrodynamic simulations for a star that might be in the stable or unstable regime of accretion. In the unstable regime, matter penetrates into the magnetosphere and is deposited at random places on the surface of the star, which made the pulsations intermittent or with no pulsations. Therefore, the PF is reduced when the overall X-ray flux increases which may be also due to the transition to the unstable accretion regime. In this scenario, we predict that the slope of the PF versus the luminosity will decrease as the spin periods of the pulsars increase. We will further investigate all of the pulsars in our current library to test this prediction. 4 CONCLUSIONS The anticorrelation between the PF and luminosity in SXP 1323 reveals that different accretion modes are possible. This could be related to the puzzle of the existence of long period pulsars which are hard to explain (Ikhsanov, Beskrovnaya & Likh 2014) without invoking non-standard accretion modes (such as spherical accretion). However, the significance of the anticorrelation is not high enough to prove its existence. SXP 1323 is the best example within our sample and more high quality data from the future observations are still needed to check up on the anticorrelation. Footnotes 1 https://www.cosmos.esa.int/web/xmm–Newton/uls-userguide ACKNOWLEDGEMENTS We would like to thank the anonymous referee whose valuable suggestions and comments have significantly improved the quality of the paper. REFERENCES Becker P. A. et al. , 2012 , A&A , 544 , A123 CrossRef Search ADS Becker W. , 2009 ; , Neutron Stars and Pulsars, Astrophysics and Space Science Library, Vol. 357 , Springer , Berlin , p. 182 Beloborodov A. M. , 2002 , ApJ , 566 , 85 https://doi.org/10.1086/339511 CrossRef Search ADS Bildsten L. et al. , 1997 , ApJS , 113 , 367 https://doi.org/10.1086/313060 CrossRef Search ADS Campana S. , Gastaldello F. , Stella L. , Israel G. 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I. , 1969 , AZh , 46 , 225 (English transl. in Soviet Astron. 13, 175) © 2018 The Author(s) Published by Oxford University Press on behalf of the Royal Astronomical Society This article is published and distributed under the terms of the Oxford University Press, Standard Journals Publication Model (https://academic.oup.com/journals/pages/about_us/legal/notices) http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Monthly Notices of the Royal Astronomical Society: Letters Oxford University Press

Anticorrelation between X-ray luminosity and pulsed fraction in the Small Magellanic Cloud pulsar SXP 1323

, Volume Advance Article (1) – May 14, 2018
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Abstract

ABSTRACT We report the evidence for the anticorrelation between pulsed fraction (PF) and luminosity of the X-ray pulsar SXP 1323, found for the first time in a luminosity range 1035–1037 erg s−1 from observations spanning 15 yr. The phenomenon of a decrease in X-ray PF when the source flux increases has been observed in our pipeline analysis of other X-ray pulsars in the Small Magellanic Cloud. It is expected that the luminosity under a certain value decreases as the PF decreases due to the propeller effect. Above the propeller region, an anticorrelation between the PF and the flux might occur either as a result of an increase in the unpulsed component of the total emission or a decrease of the pulsed component. Additional modes of accretion may also be possible, such as spherical accretion and a change in emission geometry. At higher mass accretion rates, the accretion disc could also extend closer to the neutron star surface, where a reduced inner radius leads to hotter inner disc emission. These modes of plasma accretion may affect the change in the beam configuration to fan-beam dominant emission. pulsars: individual: SXP 1323, X-rays: binaries 1 INTRODUCTION X-ray pulsars comprise two stars, a neutron star (NS, descended from a star with initial mass > 8 M⊙; Verbunt & van den Heuvel 1995), and a mass-losing companion star, also of large mass. The general picture of accretion on to X-ray pulsars consists of a flow in a wind or disc to the magnetosphere and then along the dipole field lines on to the magnetic poles of the NS. The pulsed fraction (PF), i.e. the relative amplitude of the emerging pulse profile, bears key information on the relation between X-ray emission from the accretion column (pulsed emission) and other regions of the accretion flow or NS surface (unpulsed emission), e.g. Beloborodov (2002). The Small Magellanic Cloud (SMC) pulsar SXP 5.05 was reported by Coe, Bartlett & Bird (2015) to show a positive correlation between the PF and luminosity, as shown in their fig. 11. Those data were taken while SXP 5.05 was undergoing high levels of accretion. At low-mass accretion rates, Cui (1997) reported two X-ray pulsars (GX 1+4 and GRO J1744−28) whose PF decreases as the X-ray flux drops below a certain threshold. This is an indication of the propeller effect (Illarionov & Sunyaev 1975) that takes place when the pulsar magnetosphere grows beyond the co-rotation radius, and the centrifugal force prevents accreting matter from reaching the magnetic poles. Tiengo, Mereghetti & Turolla (2005) observed an anticorrelation between PF and the corresponding flux of 1E 1048.1−5937 in the Milky Way. Spectral variations as a function of the pulse phase shows the hardest spectrum at pulse maximum. Lutovinov & Tsygankov (2009) presented marginal evidence for an anticorrelation of PF and energy in source 4U 0115+63 and Her X-1. Fig. 4 from Tsygankov et al. (2007) shows the increase of energy in 4U 0115+63 is not uniform but has local maximum near the cyclotron line. A positive and an anticorrelation is observed at low and high energy, respectively. Tsygankov, Lutovinov & Serber (2010) noted the PF of V 0332+53 increases with decreasing photon energy below 12–15 keV, which is difficult to explain. An anti and a positive correlation is observed at low and high luminosities, respectively (see their fig. 10). Below ∼1038 erg s−1 the anticorrelation is in accordance with a geometry model in which the PF is determined by the luminosity-dependent visible areas of the accretion columns. However, in the photon energy range 25–45  keV the observed correlation does not fully conform to the model. Parmar, White & Stella (1989) applied a geometric model to describe the pulse shape of X-ray pulsar EXO 2030+375 and showed that below a luminosity of 4 × 1036 erg s−1, the pencil beam becomes dominant compared to the fan-beam, along with an increase in the unpulsed component and a decrease in the luminosity. In Beloborodov (2002)’s classes of pulse profiles, visibility of the two polar caps depends on the angle between the magnetic rotation axis and dipole axis. If both poles are continuously visible, it is possible to have no pulsations. As shown in the modelled light curves of fig. 5 from Yang et al. (2017b), in classes 2 and 4 of the upper panel, and classes 3 and 4 of the middle panel, when both hot spots are visible, the observed pulse shows a plateau. We have collected and analysed the comprehensive archive of XMM–Newton (116), Chandra Advanced CCD Imaging Spectrometer (ACIS-I) (151), and RXTE (952) observations of the known pulsars in the SMC, spanning the years 1997–2014. Our pipeline generates a suite of products for each pulsar detection: spin period, flux, event list, high-time resolution light-curve, pulse-profile, periodogram, and spectrum. Combining all three satellites, we generated complete histories of the spin periods, pulse amplitudes, pulsed fractions, and X-ray luminosities (Yang et al. 2017a). Based on this archive, the relationship between the PF and luminosity of the SMC pulsars have drawn our attention. We find a surprising anticorrelation between PF and luminosity in SMC X-ray pulsars, for example, SXP 1323, SXP 893, SXP 756, SXP 726, SXP 701, SXP 348, and SXP 323. In this work, we show an example (SXP 1323) of this phenomenon and discuss the mechanism behind these results. We selected this source because it has the most data points compared to the other pulsars with anticorrelations. SXP 1323 (a.k.a. RX J0103.6-7201) was discovered by Haberl & Pietsch (2005) and shows one of the longest pulse periods known in the SMC. The names of the optical companion star are [MA93] 1393 (Meyssonnier & Azzopardi 1993) and [M2002] SMC 56901 (Massey 2002). Carpano et al (2017) found the orbital period of this Be/X-ray binary (BeXB) to be 26.2 d, which is very short for such a long spin period pulsar. It is located at RA = 01:03:37.5 and Dec. = −72:01:33 with a positional uncertainty of 1.1 arcsec (Lin, Webb & Barret 2012). The spectral type of this X-ray binary counterpart is B0 with a luminosity class of III–V (McBride et al. 2008). In this paper, we present the pulsed fraction dependence on luminosity from 15 yr of X-ray monitoring for SXP 1323. We aim to have a deeper understanding of the accretion process under the anticorrelation of the PFs and luminosities. 2 OBSERVATIONS AND METHODS Yang et al. (2017a) have collected and analysed 36 XMM–Newton and 108 Chandra X-ray observations up until 2014 for SXP 1323. XMM–Newton has detected this source 36 times and in 10 of these observations its pulsations are found. As for Chandra, we only used the ACIS-I detections: 63 out of 108 observations yield source detections and 14 observations have detected its pulsations. We are not including RXTE observations in this analysis since RXTE does not provide the required PF information. The RXTE Proportional Counter Array is a non-imaging detector and multiple sources are always in the field of view, so the unpulsed component cannot be reliably measured. The observations we used for SXP 1323 with pulsations detected are shown in Table 1. The pulsations are with a significance of s ≥ 99 per cent according to equation 2 of Yang et al. (2017a). Table 1. The XMM–Newton and Chandra ACIS-I X-ray observations in which the pulsations for SXP 1323 have been detected. The first column is the observation ID, the second and third columns show observing Modified Julian Date (MJD) and source flux, and the last two columns are the photon counts (for xmm, it is the medium value from the three EPIC instruments) and exposure time. XMM–Newton ID MJD Flux (erg s−1 cm−2) Photon counts Exposure time (ks) 135 722 401 53292.38 7.32 × 10−13 458 31.11 123 110 301 51651.15 1.50 × 10−12 2020 21.66 135 722 701 53845.10 4.29 × 10−12 5096 30.48 135 720 801 52268.75 2.10 × 10−12 2190 35.02 135 721 701 52959.26 1.41 × 10−12 3752 27.36 135 722 501 53477.93 4.69 × 10−12 9129 37.12 412 980 201 54215.52 2.50 × 10−12 2407 36.42 135 721 901 53123.30 3.21 × 10−13 1251 35.23 412 980 501 54575.39 3.44 × 10−12 3383 29.92 412 980 301 54399.41 1.80 × 10−12 2725 37.12 Chandra ID – – – – 1533 52065.27 2.33 × 10−12 984 7.42 1536 52065.57 2.04 × 10−12 860 7.42 1542 52065.76 1.69 × 10−12 699 7.42 1786 51728.55 1.66 × 10−12 738 7.58 2841 52249.09 1.62 × 10−12 686 7.46 6050 53352.15 8.25 × 10−13 336 7.16 6052 53353.37 8.96 × 10−13 358 7.54 6056 53356.31 5.064 × 10−13 253 8.01 6060 53534.55 9.00 × 10−13 1033 19.8 6749 53816.60 1.61 × 10−12 1830 19.51 6757 53891.55 5.24 × 10−13 582 19.8 8361 54136.10 1.14 × 10−12 1283 19.79 8364 54142.57 4.71 × 10−13 253 8.45 9693 54501.17 1.55 × 10−12 657 7.68 XMM–Newton ID MJD Flux (erg s−1 cm−2) Photon counts Exposure time (ks) 135 722 401 53292.38 7.32 × 10−13 458 31.11 123 110 301 51651.15 1.50 × 10−12 2020 21.66 135 722 701 53845.10 4.29 × 10−12 5096 30.48 135 720 801 52268.75 2.10 × 10−12 2190 35.02 135 721 701 52959.26 1.41 × 10−12 3752 27.36 135 722 501 53477.93 4.69 × 10−12 9129 37.12 412 980 201 54215.52 2.50 × 10−12 2407 36.42 135 721 901 53123.30 3.21 × 10−13 1251 35.23 412 980 501 54575.39 3.44 × 10−12 3383 29.92 412 980 301 54399.41 1.80 × 10−12 2725 37.12 Chandra ID – – – – 1533 52065.27 2.33 × 10−12 984 7.42 1536 52065.57 2.04 × 10−12 860 7.42 1542 52065.76 1.69 × 10−12 699 7.42 1786 51728.55 1.66 × 10−12 738 7.58 2841 52249.09 1.62 × 10−12 686 7.46 6050 53352.15 8.25 × 10−13 336 7.16 6052 53353.37 8.96 × 10−13 358 7.54 6056 53356.31 5.064 × 10−13 253 8.01 6060 53534.55 9.00 × 10−13 1033 19.8 6749 53816.60 1.61 × 10−12 1830 19.51 6757 53891.55 5.24 × 10−13 582 19.8 8361 54136.10 1.14 × 10−12 1283 19.79 8364 54142.57 4.71 × 10−13 253 8.45 9693 54501.17 1.55 × 10−12 657 7.68 View Large Table 1. The XMM–Newton and Chandra ACIS-I X-ray observations in which the pulsations for SXP 1323 have been detected. The first column is the observation ID, the second and third columns show observing Modified Julian Date (MJD) and source flux, and the last two columns are the photon counts (for xmm, it is the medium value from the three EPIC instruments) and exposure time. XMM–Newton ID MJD Flux (erg s−1 cm−2) Photon counts Exposure time (ks) 135 722 401 53292.38 7.32 × 10−13 458 31.11 123 110 301 51651.15 1.50 × 10−12 2020 21.66 135 722 701 53845.10 4.29 × 10−12 5096 30.48 135 720 801 52268.75 2.10 × 10−12 2190 35.02 135 721 701 52959.26 1.41 × 10−12 3752 27.36 135 722 501 53477.93 4.69 × 10−12 9129 37.12 412 980 201 54215.52 2.50 × 10−12 2407 36.42 135 721 901 53123.30 3.21 × 10−13 1251 35.23 412 980 501 54575.39 3.44 × 10−12 3383 29.92 412 980 301 54399.41 1.80 × 10−12 2725 37.12 Chandra ID – – – – 1533 52065.27 2.33 × 10−12 984 7.42 1536 52065.57 2.04 × 10−12 860 7.42 1542 52065.76 1.69 × 10−12 699 7.42 1786 51728.55 1.66 × 10−12 738 7.58 2841 52249.09 1.62 × 10−12 686 7.46 6050 53352.15 8.25 × 10−13 336 7.16 6052 53353.37 8.96 × 10−13 358 7.54 6056 53356.31 5.064 × 10−13 253 8.01 6060 53534.55 9.00 × 10−13 1033 19.8 6749 53816.60 1.61 × 10−12 1830 19.51 6757 53891.55 5.24 × 10−13 582 19.8 8361 54136.10 1.14 × 10−12 1283 19.79 8364 54142.57 4.71 × 10−13 253 8.45 9693 54501.17 1.55 × 10−12 657 7.68 XMM–Newton ID MJD Flux (erg s−1 cm−2) Photon counts Exposure time (ks) 135 722 401 53292.38 7.32 × 10−13 458 31.11 123 110 301 51651.15 1.50 × 10−12 2020 21.66 135 722 701 53845.10 4.29 × 10−12 5096 30.48 135 720 801 52268.75 2.10 × 10−12 2190 35.02 135 721 701 52959.26 1.41 × 10−12 3752 27.36 135 722 501 53477.93 4.69 × 10−12 9129 37.12 412 980 201 54215.52 2.50 × 10−12 2407 36.42 135 721 901 53123.30 3.21 × 10−13 1251 35.23 412 980 501 54575.39 3.44 × 10−12 3383 29.92 412 980 301 54399.41 1.80 × 10−12 2725 37.12 Chandra ID – – – – 1533 52065.27 2.33 × 10−12 984 7.42 1536 52065.57 2.04 × 10−12 860 7.42 1542 52065.76 1.69 × 10−12 699 7.42 1786 51728.55 1.66 × 10−12 738 7.58 2841 52249.09 1.62 × 10−12 686 7.46 6050 53352.15 8.25 × 10−13 336 7.16 6052 53353.37 8.96 × 10−13 358 7.54 6056 53356.31 5.064 × 10−13 253 8.01 6060 53534.55 9.00 × 10−13 1033 19.8 6749 53816.60 1.61 × 10−12 1830 19.51 6757 53891.55 5.24 × 10−13 582 19.8 8361 54136.10 1.14 × 10−12 1283 19.79 8364 54142.57 4.71 × 10−13 253 8.45 9693 54501.17 1.55 × 10−12 657 7.68 View Large In order to test the correlation with luminosities and make the results convincible, three different definitions of PF were calculated by integrating over the pulse profile. The simplified formulas are shown in equations (1)–(3). \begin{equation*}\mathrm{ PF}_\mathrm{A}=\frac{f_\mathrm{max}-f_\mathrm{min}}{f_\mathrm{max}}, \end{equation*} (1) here fmax is the maximum photon count rate in the pulse profile and fmin is the minimum value as demonstrated in an example of the pulsed profile in Fig. 1. PFA is also usually called modulation amplitude. \begin{equation*}\mathrm{ PF}_\mathrm{B}=\frac{f_\mathrm{mean}-f_\mathrm{min}}{f_\mathrm{mean}}, \end{equation*} (2)fmean is the average flux. \begin{equation*}\mathrm{ PF}_\mathrm{S}=\frac{\sqrt{2}f_\mathrm{rms}}{f_\mathrm{mean}}, \left(\mathrm{ and}\ f_\mathrm{rms}=\frac{\sqrt{\sum _i^{N}(f_i-f_\mathrm{mean})^2}}{N}\right) ,\end{equation*} (3) where frms is the root mean square (rms) flux, N is the number of bins for each folded light curve, and fi is the mean photon count rate in each bin. For a sinusoid wave, which is a good approximation to most accretion pulsars, the peak-to-peak pulsed flux fpulsed = fmean − fmin = $$\sqrt{2}f_\mathrm{rms}$$; for a square wave fpulsed = frms (Bildsten, Chakrabarty & Chiu 1997). Figure 1. View largeDownload slide An example of pulse profile for SXP 1323 shows the values used for the PF calculation in equations (1)–(3), and frms is the root mean square flux. It is an XMM–Newton Observation (ID 135 722 701), observed on 2006 April 20. Figure 1. View largeDownload slide An example of pulse profile for SXP 1323 shows the values used for the PF calculation in equations (1)–(3), and frms is the root mean square flux. It is an XMM–Newton Observation (ID 135 722 701), observed on 2006 April 20. The error of the PF is calculated as following. First get the error of the flux in each bin of the light curve, \begin{equation*}\mathrm{ error}_i=\frac{\sqrt{\sum _j^{n}(f_i-F_j)^2}}{{ \mathit{ n}}}, \end{equation*} (4) where Fj is the flux in the ith bin. n is the number of points in each bin. Then we could get the error of fmax (errormax) as well as the error from fmin (errormin). The error of PFA is \begin{equation*}\mathrm{ error}_\mathrm{PFA}=\sqrt{\frac{\mathrm{ error}_\mathrm{max}^2+\mathrm{ error}_\mathrm{min}^2}{(f_\mathrm{max}-f_\mathrm{min})^2}+\left(\frac{\mathrm{ error}_\mathrm{max}}{f_\mathrm{max}}\right)^2}\ \times\, \mathrm{ PF}_\mathrm{A} \end{equation*} (5) In order to calculate errorPFB and errorPFS, first calculate the error of the pulsed flux: \begin{equation*}e_\mathrm{pulse}=\frac{\sum _i^{N}\sqrt{\mathrm{ error}_\mathrm{max}^2+\mathrm{ error}_i^2}}{N}, \end{equation*} (6) \begin{equation*}\mathrm{ error}_\mathrm{PFB}=\frac{e_\mathrm{pulse}}{f_\mathrm{mean}}; \end{equation*} (7) \begin{equation*}\mathrm{ error}_\mathrm{PFS}=\sqrt{2}\frac{e_\mathrm{pulse}}{f_\mathrm{mean}}\ \times\,\mathrm{ PF}_ \mathrm{S}. \end{equation*} (8) Note, in Yang et al. (2017a) the pulsed fraction from XMM–Newton is PFB and the ones from Chandra are PFA. Here we used PFA and PFB for both XMM–Newton and Chandra observations. PFA has intuitive appeal, but it is more difficult to determine the fmin than fmean (Bildsten et al. 1997). People generally use PFA for light curves from long time exposures, where signal-to-noise ratio is large. PFB is smaller than PFA, but more stable as fmean is easier to be determined than fmax. PFS is used for relatively short time exposure. The PF as a function of luminosity for SXP 1323 is shown in Fig. 2. Although the light curves were extracted from the higher time resolution EPIC-PN data (Yang et al. 2017a), the luminosities used in Fig. 2 were obtained from the total XMM–Newton flux available in the three XMM–Newton catalogues since they are more complete than the instrument-specific fluxes. These fluxes are based on a spectral model of a power law of slope 1.7 absorbed by a Hydrogen column of 3 × 1020 cm−2 (0.2–12 keV).1 Figure 2. View largeDownload slide The PF as the function of luminosity for SXP 1323. Green circles are the XMM–Newton detections and blue square symbols present Chandra observations. The three panels show the PFs with different calculations which are in equations (1)–(3). Figure 2. View largeDownload slide The PF as the function of luminosity for SXP 1323. Green circles are the XMM–Newton detections and blue square symbols present Chandra observations. The three panels show the PFs with different calculations which are in equations (1)–(3). The trend between PFA and luminosity is \begin{equation*}\mathrm{ PF}_\mathrm{A}=-0.399\,\mathrm{ log }\left(\frac{L_\mathrm{X}}{10^{35}\,\text{erg s$^{-1}$}}\right)+0.850, \end{equation*} (9) The fit between PFB and luminosity is \begin{equation*}\mathrm{ PF}_\mathrm{B}=-0.350\,\mathrm{ log} \left(\frac{L_\mathrm{X}}{10^{35}\,\text{erg s$^{-1}$}}\right)+0.669. \end{equation*} (10) The anticorrelation of PFS and luminosity is fitted as \begin{equation*}\mathrm{ PF}_\mathrm{S}=-0.101\,\mathrm{ log} \left(\frac{L_\mathrm{X}}{10^{35}\,\text{erg s$^{-1}$}}\right)+0.173, \end{equation*} (11) where LX is in erg s−1. The trend with PFA is steeper than the one with PFB, and even more steeper than PFS. PFA is the most popular way to show the pulsed fraction of the X-ray pulse profiles, therefore, the linear regression is more convincing. However, all of them show the similar anticorrelation. Monte Carlo simulations are performed to estimate the false-positive detection rate for the correlation between these two observables, from which the significance level is estimated. For the correlation in each panel of Fig. 2, 4000 trial generates 4000 simulated data. Based on these data, the fitting is performed. One of the fitting parameters (slope) is shown in the histograms of Fig. 3. We interpret positive slopes as false positive detections of an anticorrelation in the real data. The number of false positives from Fig. 3 corresponds to a probability of 95.43, 93.28, and 92.68, for the anticorrelation found by using PFA, PFB, and PFS, respectively. Therefore, the fit of the correlations in Fig. 2 is around ∼2σ confidence. Figure 3. View largeDownload slide Frequency distribution of correlation slopes for PFA (upper), PFB (middle), and PFS (bottom) obtained using Monte Carlo method with 4000 simulations. The heights of bars indicate the number of parameter values in the equally spaced bins. The limit for false positive detections of an anticorrelation is shown as red solid lines at slope 0.0. The dashed lines are the slopes from Fig. 2. Figure 3. View largeDownload slide Frequency distribution of correlation slopes for PFA (upper), PFB (middle), and PFS (bottom) obtained using Monte Carlo method with 4000 simulations. The heights of bars indicate the number of parameter values in the equally spaced bins. The limit for false positive detections of an anticorrelation is shown as red solid lines at slope 0.0. The dashed lines are the slopes from Fig. 2. 3 THEORETICAL MECHANISMS Mukerjee, Agrawal & Paul (2000) observed a decrease in the pulsed fraction with decreasing luminosity of the X-ray pulsar Cepheus X-4 (GS 2138+56). However, they argued that the decrease in the pulsed fraction, depending on the accretion flow geometry with respect to line of sight, is not a consequence of propeller effect. They propose as a more likely scenario a different mode of accretion occurring below a certain luminosity. These additional entry modes of plasma may affect the emission geometry to be more fan-beam-like pattern, which will increase the unpulsed flux, and the pulsed fractions end up being smaller. However, for SXP 1323, the PF increases as the luminosity decreases. The critical luminosity mentioned in Mukerjee et al. (2000) is the maximum luminosity LX(min) at which the centrifugal inhibition dominates, resulting in the propeller effect (e.g. Shtykovskiy & Gilfanov 2005; Tsygankov et al. 2016; Christodoulou et al. 2016): \begin{eqnarray*}L_\mathrm{X} (\mathrm{min}) &=& 2 \times 10^{37}\left(\frac{R}{10^6 \rm \,{cm}}\right)^{-1}\left(\frac{M}{1.4\,\mathrm{ M}_{{{\odot }}}}\right)^{-\frac{2}{3}} \\&&\times \left(\frac{\mu }{10^{30}\, \mathrm{ G} \,\rm{cm}^{3}}\right)^{2}\left(\frac{P_\mathrm{s}}{1 \mathrm{ s}}\right)^{-\frac{7}{3}} \,{\rm erg\,s}^{-1}, \end{eqnarray*} (12) where R, M, μ, and Ps are the radius, mass, magnetic moment, and spin period of the NS, respectively. We use a surface polar magnetic field strength B = 2.6 × 1012 G (Mihara et al. 1991) and R = 10 km, for a dipole-like field configuration, μ = B × R3 = 2.6 × 1030 G cm3. Assuming M = 1.4M⊙, we calculate the minimum luminosity below which the propeller effect will occur in SXP 1323 to be LX(min) = 7.03 × 1030 erg s−1. In our analysis, all of the luminosities observed are higher than this critical value, therefore it is highly unlikely that the anticorrelation is the result of the propeller effect. We can see the PF drops quickly as the luminosity increases up to ∼1036 erg s−1. This is consistent with Campana, Gastaldello & Stella (2001)’s result above a certain critical luminosity of ∼1035 erg s−1 in the X-ray pulsar 4U 0115+63 in our Galaxy. Campana et al. (2001) expressed the source accretion luminosity as two components: the luminosity of the disc extending down to the magnetospheric boundary, Ldisc; and the luminosity released within the magnetosphere Lmag by the mass inflow rate that accretes on to the NS surface. They claimed that the pulsed fraction is expected to remain unaltered as long as Lmag dominates, while Ldisc is expected to be unpulsed, resulting in a decreasing pulsed fraction as its luminosity increases. It explains the PF trend only at the luminosities larger than ∼1035 erg s−1 in fig. 2 of Campana et al. (2001). Assuming that there are two X-ray components: the accretion column (Lcol) and the accretion disc (Ldisc), the luminosity of the accretion column should be relatively stable since it would be locally Eddington, and the luminosity of the disc changes because at high-mass accretion rate ($$\dot{M}$$) the magnetospheric radius (Rmag) gets smaller and the Ldisc increases. From the relation between Rmag and $$\dot{M}$$ (for a given Ps and magnetic field B) and feeding this through a standard Shakura–Sunyaev disc, we have that \begin{eqnarray*}T_\mathrm{{disc}} \propto \left\lbrace \frac{\dot{M}}{R^3}[1-\left(\frac{R_\mathrm{mag}}{R}\right)^{\frac{1}{2}}] \right\rbrace ^{\frac{1}{4}},\end{eqnarray*} (13) \begin{eqnarray*}L_\mathrm{{disc}} \propto T_\mathrm{{disc}}^{4} \times R^{2}\simeq \dot{M} \times R^{\frac{5}{4}}, \end{eqnarray*} (14) where Tdisk is the temperature. If luminosity from the accretion column Lcol is constant, Rmag decreases and Ldisc increases. The predicted PF should change with increasing luminosity due to the unpulsed disc emission. Our anticorrelation is still at odds with the trend reported for many other pulsars in the literature (e.g. Mukerjee et al. 2000; Coe et al. 2015). The possible reason is that the spin period matters, as the pulsars in Mukerjee et al. (2000) and Coe et al. (2015) have short spin periods of 66.27 and 5.05 s, respectively. It could be that the PF changes of the short period pulsars depend on their luminosities. In the following, we discuss the PF luminosity anticorrelation in the context of different models for X-ray emission in accreting pulsars. 3.1 Spherical accretion The flow of material towards the pulsar might not take place through an accretion disc but instead via a spherical accretion flow, a natural consequence of wind-fed accretion, as opposed to Roche lobe overflow. The spherical accretion should be outside the accretion column and would obscure it (unless highly ionized). Also at low luminosity, the magnetospheric radius should be large enough to truncate the accretion flow. This accretion model was applied to black holes by Nobili, Turolla & Zampieri (1991). The accretion of gas on to the compact object can be a very efficient way of converting gravitational potential energy into radiation. Traditional spherical accretion is thought of as a good approximation for isolated compact objects. Ikhsanov, Pustil’nik & Beskrovnaya (2005) has applied the spherical accretion model to High-Mass X-ray binaries (HMXBs), especially the long spin period pulsars. Zeldovich and Shakura (1969) presented a model to describe the gravitational energy of matter accreted on to an NS and released in a thin layer above the surface. Variations of this idea have also been applied in detailed models (e.g. Turolla et al. 1994, for spherical accretion). The deep layers of the NS atmosphere are heated by the outer layer and produce soft thermal photons (Cui et al. 1998). The hard X-ray photons are from the polar hot spots, which contribute to the pulsed flux observed. The soft X-ray photons from spherical accretion would mainly contribute to the unpulsed component of flux. Spherical accretion becomes more prominent as the luminosity and mass accretion rate increases, which leads to a smaller PF. 3.2 NS whole surface thermal emission Generally, there are two components of the X-ray emission from NSs: thermal emission and non-thermal emission. The non-thermal emission is caused by pulsar radiation in the magnetosphere and its own rotation activity, which is suppressed when accreting. Thermal emission is from the whole surface of a cooling NS and/or from the small hot spots around the magnetic poles on the star surface (Becker 2009). It is also heated by accretion. The thermal radiation from the entire stellar surface can dominate at soft X-ray energies for middle-aged pulsars (∼100 kyr) and younger pulsars (∼10 kyr). If thermal emission is a significant component of the X-rays from SXP 1323 and this component increases, it would represent and increase in unpulsed flux such that the PF becomes smaller. 3.3 Change in emission geometry Ghosh & Lamb (1979) found $$\dot{P}\propto L_\mathrm{X} ^{6/7}$$ assuming the effective inertial moment of the NS is constant, so a higher accretion rate and LX could cause the observed high spin-up rate of this pulsar. The accreted mass interacts with the magnetosphere, and the accretion disc extends inward to some equilibrium radial distance above the NS’s surface (Malina & Bowyer 1991). Yang et al. (2017a) has reported this pulsar’s average spin-up rate as 6 ± 3 ms d−1 based on data from three X-ray satellites from 1997–2014. Carpano et al (2017) has presented an even faster spin-up of ∼59.3 ms d−1 based on recent observations from 2006 to 2016. The higher spin period and mass accretion rate could build up a higher accretion column above the polar caps. As the height of the accretion column increases, scattering of photons off in-falling electrons gets more prominent. This increases the fraction of emission escaping the column to the side, i.e. a fan-beam emerges (e.g. Becker, Klochkov & Schönherr 2012). Fan-beam emission becomes dominant, which reduces the eclipse of the accretion column. Furthermore, the contribution of the flux reflected by the NS surface is significant (Mushtukov, Verhagen & Tsygankov 2018). It raises the unpulsed flux, therefore we see the luminosity increasing and the pulsed fraction decreasing. Romanova, Kulkarni & Lovelace (2008) used 3D magnetohydrodynamic simulations for a star that might be in the stable or unstable regime of accretion. In the unstable regime, matter penetrates into the magnetosphere and is deposited at random places on the surface of the star, which made the pulsations intermittent or with no pulsations. Therefore, the PF is reduced when the overall X-ray flux increases which may be also due to the transition to the unstable accretion regime. In this scenario, we predict that the slope of the PF versus the luminosity will decrease as the spin periods of the pulsars increase. We will further investigate all of the pulsars in our current library to test this prediction. 4 CONCLUSIONS The anticorrelation between the PF and luminosity in SXP 1323 reveals that different accretion modes are possible. This could be related to the puzzle of the existence of long period pulsars which are hard to explain (Ikhsanov, Beskrovnaya & Likh 2014) without invoking non-standard accretion modes (such as spherical accretion). However, the significance of the anticorrelation is not high enough to prove its existence. 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Monthly Notices of the Royal Astronomical Society: LettersOxford University Press

Published: May 14, 2018

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