Long term decay of the cyclotron line in Vela X-1

The Swift-BAT monitoring reveals a long term decay of the cyclotron line energy in Vela X-1

V. La Parola, G. Cusumano, A. Segreto , A. D’Aì
INAF, Istituto di Astrofisica Spaziale e Fisica Cosmica, Via U. La Malfa 153, I-90146 Palermo, Italy
Abstract

We study the behaviour of the cyclotron resonant scattering feature (CRSF) of the high mass X-ray binary Vela X-1 using the long-term hard X-ray monitoring performed by the Burst Alert Telescope (BAT) on board Swift. High statistics, intensity selected spectra were built along 11 years of BAT survey. While the fundamental line is not revealed, the second harmonic of the CRSF can be clearly detected in all the spectra, at an energy varying between keV and keV, directly correlated with the luminosity. We have further investigated the evolution of the CRSF in time, by studying the intensity selected spectra built along four 33-month time intervals along the survey. For the first time we find in this source a secular variation in the CRSF energy: independent of the source luminosity, the CRSF second harmonic energy decreases by keV/year between the first and the third time interval, corresponding to an apparent decay of the magnetic field of G/year. The intensity-cyclotron energy pattern is consistent between the third and the last time intervals. A possible interpretation for this decay could be the settling of an accreted mound that produces either a distortion of the poloidal magnetic field on the polar cap or a geometrical displacement of the line forming region. This hypothesis seems supported by the correspondance between the rate of the line shift per unit accreted mass and the mass accreted on the polar cap per unit area in Vela X-1 and Her X-1, respectively.

keywords:
X-rays: binaries – X-rays: individual: Vela X-1. Facility: Swift
pagerange: The Swift-BAT monitoring reveals a long term decay of the cyclotron line energy in Vela X-12pubyear:

1 Introduction

Vela X-1 is a wind-accreting neutron star with a spin period of  s (McClintock et al., 1976), rotating in an 8.9 d (van Kerkwijk et al., 1995) orbit around the B0.5Ib super-giant HD 77523 (Hiltner, Werner & Osmer, 1972), at a distance  kpc (Sadakane et al., 1985). The mean luminosity of the source is  erg s (Fürst et al., 2010), and the flux shows a great variability even at short time scales (hours), with the source going from off-states to giant flares up to a few Crab (Kreykenbohm et al., 2008).

Neutron stars in high mass X-ray binaries are characterized by intense magnetic fields ( G) that in several sources can be directly measured through the energy of characteristic absorption lines called cyclotron resonant scattering features (CRSF). A strong magnetic field causes the motion of the electrons perpendicular to the magnetic field in the accreting plasma to be quantized in discrete Landau levels and photons with energies corresponding to these levels undergo resonant scattering producing an absorption feature in their spectra.

In Vela X-1 an absorption line feature at 55 keV was first reported by Kendziorra et al. (1992) with data from the High Energy X-ray Experiment (HEXE), while Makishima & Mihara (1992); Choi et al. (1996) reported an absorption feature at lower energy ( keV) from Ginga data. Later observations failed to detect this low energy feature, revealing only one absorption line at keV (Orlandini et al., 1998; La Barbera et al., 2003; Kreykenbohm et al., 2008). Kretschmar et al. (1997), with HEXE, Kreykenbohm et al. (2002) with RXTE, Schanne et al. (2007) with INTEGRAL, and Maitra & Paul (2013) and Odaka et al. (2013) with Suzaku confirmed the presence of both features, with energies varying between keV and keV and between keV and keV, respectively. The low energy feature, interpreted as the fundamental CRSF, is considerably weaker than its second harmonic. Fürst et al. (2014) analysed two NuSTAR observations with different luminosity levels detecting both features, but while the harmonic is always highly significant, the fundamental is barely detectable in the observation at higher intensity. They also show that the depth of the two lines are anti-correlated and they interpret this result as due to photon spawning (see e.g. Schönherr et al., 2007), suggesting this as the likely explanation of the elusiveness of the fundamental. Moreover, Fürst et al. (2014) report for the first time in this source a correlation between the harmonic line energy and the flux, as expected in the sub-critical accretion regime (Becker et al., 2012).

In this paper we performed a detailed spectral analysis of Vela X-1 based on the eleven-year monitoring performed by the Burst Alert Telescope (BAT, Barthelmy et al., 2005) onboard Swift (Gehrels et al., 2004). The large BAT field of view (1.4 steradian half coded), together with the Swift observatory pointing strategy (several pointings per day towards different directions of the sky), allows BAT to have the source within its field of view nearly every day.

This Paper is organized as follows. Section 2 describes the data reduction and the calibration procedures applied to the BAT data. In Sect. 3 we describe the spectral analysis and in Sect. 4 we discuss our results.

2 Data Reduction

The BAT survey data collected between 2004 December and 2015 November were retrieved from the HEASARC public archive111http://heasarc.gsfc.nasa.gov/docs/archive.html and processed with the bat_imager code (Segreto et al., 2010), a software built for the analysis of data from coded mask instruments that performs screening, mosaicking and source detection and produces scientific products of any revealed source.

Figure 1 shows the light curve of Vela X-1 in the 15–100 keV band, with a bin time equal to the orbital period (8.964 d). The intensity of the source shows large fluctuations, up to one order of magnitude.

The spectral analysis is aimed to investigate the behaviour of the cyclotron features with luminosity. We produced background subtracted spectra of the source at several count rate levels. The appropriate good time intervals (GTIs) for each count rate interval were selected based on the source 15–150 keV light curve with a bin time of 90 minutes, in the count rate range between 0.001 and 0.05 counts s pixel, corresponding to an observed 15-150 keV luminosity range between and erg s. To define the boundaries of each count rate bin, we started from the lower count rate limit, and we increased the upper count rate limit with a step of 0.001 counts s pixel until a satisfactory signal-to-noise ratio (SNR) of is reached, allowing for enough statistics for an adequate modeling of the second harmonic). Since a Crab spectrum with similar statistics shows the presence of systematic deviations with respect to a power law, we have applied to each Vela X-1 spectrum a systematic error to be added in quadrature to the statistical one. The systematic errors were derived fitting the Crab spectrum extracted from the entire survey monitoring with a power law and evaluating for each energy channel the values , where is the rate derived with the best fitting powerlaw model in the i channel and R is the Crab count rate in the same channel. We have verified that this correction (amounting to 2% on average) is negligible with respect to the statistical errors for the channels above 40 keV. We used the official BAT spectral redistribution matrix222http://heasarc.gsfc.nasa.gov/docs/heasarc/caldb/data/swift/bat/index.html. We report errors on spectral parameters at 68 % confidence level.

3 Spectral analysis

Figure 1: BAT 15-100 keV light curve of Vela X-1. The bin time is equal to the orbital period (8.964 d). The vertical dashed lines mark the four time-selected intervals used to probe the line ennergy vs luminosity relation.

To model the continuum emission of Vela X-1 we tested different spectral shapes. A simple power law modified with an exponential cut-off (cutoffpl) is not adequate to describe the data. Both an optically thick Comptonization (comptt) and a Fermi-Dirac cutoff provide an acceptable fit for the continuum emission, while the CRSF is well described with a Gaussian absorption profile (gabs in Xspec). We verified that the choice between the two continuum models does not affect the best fit line parameters. The results presented in this Paper refer to a continuum described with an optically thick Comptonization. The results of the spectral analysis are reported in Table 1. In all the spectra we detect with high significance the second harmonic, while the fundamental cannot be detected in any of the spectra. Figure 2 shows two representative spectra at different levels of intensity, and their residuals with respect to the relevant best fit model. Figure 3 shows the best fit line parameters (energy, width, strength and equivalent width in panels A, B, C, D, respectively) as a function of the intrinsic source luminosity. The equivalent width was evaluated according to the definition:

(1)

where represents the intensity of the continuum and is the intensity of the best fit model, evaluated in the 15–100 keV energy range. The line energy shows a clear direct correlation with the luminosity, ranging from keV at low luminosity to keV at high luminosity. The other line parameters also show a positive correlation with the luminosity. Panel E of figure 3 shows the Comptonization parameter, defined as . We observe that is positively correlated with the luminosity, indicating a hardening of the continuum at higher luminosity, as already reported by Odaka et al. (2013) and Fürst et al. (2014) for Vela X-1 and by Klochkov et al. (2011) for other accreting pulsars in subcritical accretion regime.

Figure 2: Data, best fit model, and residuals for two representative spectra (spectra 2 and 21 in Table 1). In the top panel, the black line represents the best fit model (continuum and CRSF), while the grey line represents the best fit continuum model.

Figure 3: Best fit parameters vs source luminosity for the spectra extracted along the entire survey interval. From top to bottom: line energy, width, strength, equivalent width, Comptonization parameter. The solid line in the top panel is the theoreticical prediction for E=29.56 keV (see Eq. 2).

We have also investigated the long-term behaviour of this trend in time selected intervals. To this aim we have split the survey monitoring into four time intervals of the same length (33 months, see dashed lines in Fig. 1), selecting the spectra in eight flux intervals for each of them. The results of the spectral analysis are plotted in Figure 4. We find that the line energy shows a systematic decrease between the first and the second time interval and between the second and the third one, while there is no significant change between the third and the fourth interval.

Figure 4: Energy of the second harmonic vs source luminosity for the four 33-month time intervals. The continuous lines in the top panel are theoretical predictions (see Eq. 2) for E=28.25, 29.42, 31.12 keV (bottom to top, respectively). The E values were obtained fitting each set of data with Equation 2. Data sets p3 and p4 were fitted together.

4 Discussion and conclusions

We report on the analysis of the Swift-BAT spectral data of Vela X-1, focussing on the on the relation between the CRSF energy and luminosity in the overall timespan covered by BAT and in time-selected intervals.

The energy of the second harmonic is directly correlated with the luminosity (with a correlation coefficient of 0.89, and a corresponding probability of no correlation of ) , confirming the results reported by Fürst et al. (2014) from the analysis of two NuSTAR observations. This correlation, observed for the first time in Her X-1 (Staubert et al., 2007) is expected in the sub-critical accretion regime (, see Becker et al., 2012), where the deceleration of the material to rest at the stellar surface is accomplished by a shock dominated by Coulomb interactions. The ram pressure of the infalling plasma increases with the accretion rate driving the shock region down to regions of higher magnetic field intensity. Using equations (51) and (58) in Becker et al. (2012), we can derive the energy/luminosity correlation for the fundamental CRSF:

(2)

where is the Thomson optical depth ( for typical HMXB parameters, Becker et al., 2012), is the radius of the NS, is the mass of the NS, is the energy of the fundamental cyclotron line at the NS surface and is a constant related to the interaction between the magnetic field and the surrounding medium (Lamb et al., 1973). We adopt the values , suitable for spherical accretion, km and (Rawls et al., 2011) as in Fürst et al. (2014). The energy of the CRSF depends on the accretion rate in good agreement with theoretical predictions: a fit of the data using as best fit model Equation 2 yields , with , assuming a harmonic ratio of 2 (solid line in the top panel of Fig 3).

Mushtukov et al. (2015) have proposed an alternative theory to explain the positive correlation between CRSF energy and luminosity in subcritical sources: the bulk of the radiation, emitted by the hotspot on the polar cap, travels upwards through the accretion channel interacting with the infalling matter and producing the CRSF at the resonant energies. The line appears redshifted by Doppler effect to the observer due to the velocity profile of the plasma falling towards the NS surface. The higher the luminosity, the lower is the velocity of plasma, slowed by the radiation pressure, and the smaller is the Doppler shift of the line. At the limit of the critical luminosity that marks the balance between radiation pressure and ram pressure of the matter, no Doppler shift is observed and the line energy corresponds to the value defined by the surface magnetic field. In this framework, the width of the line is also expected to correlate positively with the luminosity, since an increase of the radiation pressure produces a layer of infalling matter at lower velocity, extending blueward the line profile. These trends are indeed observed in our results (Fig 3)

We have investigated if this correlation evolves on a yearly time scale, splitting the survey data into four 33-month intervals. We observe a significant shift in energy of this correlation along the time, except for the last two intervals, where the measurements overlap. The correlation coefficient for each data set are 0.83 (p-value=0.010), 0.99 (p-value=), 0.47 (p-value=0.066) for p1, p2 and p3+p4, respectively. The theoretical correlation matches the observed data for different values of the energy of the fundamental at the stellar surface ( keV, keV and keV, with of 2.3, 1.2, and 2.4, respectively, solid lines in the top panel of Figure 4). This translates into a decrease of the fundamental line of keV/year along the first three time intervals, corresponding to a decay of the surface magnetic field intensity of G/year.

We have checked if this shift could be due to a systematic drift of the instrumental energy/channel gain. Such a drift would produce a significant variation in the slope of the Crab spectrum along the time. Therefore we accumulated the Crab spectra in the four time intervals and fitted them with a power-law. The variation of the Crab power-law photon index between the last and the first time interval is . If this was due to a variation in the channel/energy gain, this would correspond to an uncertainty in the energy determination of only keV, negligible with respect to the statistical uncertainty on the line position.

A long-term decay in the magnetic field, unrelated to the source luminosity, was recently assessed in the persistent accreting pulsar Her X-1 (Staubert et al., 2014; Staubert et al., 2016), where the cyclotron line energy decreased on average by 0.26 keV/year between 1996 and 2012. This long term decay is most likely a local effect confined to the magnetic polar cap: it could be related to the accreted matter that accumulates into a magnetically supported mound and causes either a distortion of the magnetic field lines (Brown & Bildsten, 1998) or a geometrical displacement of the emission region. The observed break in the decay after the third time interval could be explained if this mound has reached a maximum size for a stable structure (Mukherjee & Bhattacharya, 2012; Litwin, Brown, & Rosner, 2001) and the plasma settling on it is balanced by the plasma leaking out from its base. A similar interpretation was adopted to explain the drop of the magnetic field in V0332+53 during the 2015 outburst, where a difference of keV in the CRSF fundamental line energy was observed between the start and the end of the outburst (Cusumano et al., 2016).

With an average luminosity of erg/s Vela X-1 accretes at per year, while the average luminosity of erg/s in Her X-1 corresponds to per year (Klochkov et al., 2015). If the accreted matter is the cause of the decay of the magnetic field along the accretion column, this mechanism is a factor of more efficient in Vela X-1 than in Her X-1. This difference could be related to a narrower accretion column in Vela X-1, that, following Eq. 23 in Becker et al. (2012), is km with respect to km in Her X-1 and allows for a faster growth of the height of the mound. Indeed, the accreted mass per unit surface is km year in Vela X-1, a factor of higher than km year in Her X-1.

As shown in Figure 4 in Staubert et al. (2014), the CRSF energy in Her X-1 was constant before 1991. Between 1991 and 1995 a drop of kev was observed, followed by a more linear decay after 1995. One explanation might be a cyclic behaviour of the CRSF energy, and the jump could be induced by a destructive event that destroys the mound and resets the line emission region to the pre-mound configuration. Vela X-1 could have entered a stable configuration in the last time interval. An abrupt recovery of the line energy to a higher value in the next years could be therefore expected if the same restoring mechanism observed in Her X-1 works also in Vela X-1.

Sp
keV keV keV erg s
1 1.73 1.27
2 2.74 1.10
3 3.06 1.26
4 3.40 1.44
5 3.74 1.12
6 4.02 1.15
7 4.27 0.78
8 4.45 0.99
9 5.03 0.70
10 5.10 1.24
11 5.60 1.04
12 6.00 1.15
13 6.04 1.33
14 6.23 1.38
15 6.71 1.36
16 6.79 1.34
17 7.15 1.04
18 7.63 1.77
19 8.12 0.80
20 8.67 1.09
21 8.92 1.92
22 9.84 1.48
23 10.10 1.26
24 10.31 1.37
25 10.76 1.47
26 13.21 1.01
Table 1: Spectral fit results from the count-rate selected spectra extracted along the entire survey monitoring. E, and D are the energy, width and depth of the CRSF second harmonic, respectively. kT and are the plasma temperature and optical depth, respectively. The input photon temperature attains to the soft X-ray energy range and it is not well constrained by the BAT data. Therefore, it has been kept fixed to 0.82 keV for all the spectra, which is the average value obtained in a pre-analysis of the spectra. is the luminosity of the continuum evaluated in the 1-150 keV energy range in units of erg s. The quoted reduced is evaluated for 32 degrees of freedom.

Acknowledgments

This work was supported by contract ASI I/004/11/0. We thank the anonymous referee for comments that helped improve the paper.

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Sp
keV keV keV erg s
p1-1 2.05 1.66
p1-2 3.46 1.42
p1-3 4.22 1.30
p1-4 4.99 1.21
p1-5 5.63 1.19
p1-6 6.29 1.80
p1-7 7.73 1.66
p1-8 9.31 1.48
p2-1 2.14 1.19
p2-2 3.71 1.71
p2-3 4.60 0.77
p2-4 5.30 0.92
p2-5 5.93 0.96
p2-6 7.17 1.00
p2-7 8.30 0.72
p2-8 10.83 1.12
p3-1 2.14 1.53
p3-2 3.91 1.11
p3-3 4.87 0.67
p3-4 5.70 1.27
p3-5 6.41 1.40
p3-6 7.47 0.77
p3-7 9.11 1.22
p3-8 10.92 1.23
p4-1 2.15 1.53
p4-2 3.78 1.08
p4-3 4.62 0.57
p4-4 5.63 1.18
p4-5 6.39 1.22
p4-6 7.26 0.94
p4-7 8.88 0.97
p4-8 10.27 1.38
Table 2: Spectral fit results from the count-rate selected spectra extracted along the four 33-month time intervals. The columns are described in Table 1.
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