vela X-1

Pulse phase resolved spectroscopy of Vela X-1 with Suzaku

Abstract

We present a detailed pulse phase resolved spectral analysis of the persistent high mass X-ray binary pulsar Vela X-1 observed with Suzaku during June . The pulse profiles exhibit both intensity and energy dependence with multiple peaks at low energies and double peaks at higher energies. The source shows some spectral evolution over the duration of the observation and care has been taken to average over data with minimum spectral variability for the analysis. We model the continuum with a phenomenological partial covering high energy cutoff model and a more physical partial covering thermal comptonization model (CompTT) excluding the time ranges having variable hardness ratio and intensity dependence. For both the models we detect a cyclotron resonant scattering feature (CRSF) and its harmonic at keV and keV. Both the CRSF fundamental and harmonics parameters are strongly variable over the pulse phase, with the ratio of the two line energies deviating from the classical value of . The continuum parameters also show significant variation over the pulse phase and give us some idea about the changing physical conditions that is seen with the changing viewing angle at different pulse phases and obscuration by the accretion stream at some pulse phases.

X-rays: binaries– X-rays: individual: Vela X-1– stars: pulsars: general

1 Introduction

Vela X-1 (4U 0900-40) is a an eclipsing and persistently active high mass X-ray binary (HMXB) system consisting of a massive (; ) B0.5 1b supergiant HD 77581 (Brucato & Kristian, 1972; Nagase, 1989); and a neutron star (Rawls et al., 2011). It has an orbital period of 8.964 days (van Kerkwijk et al., 1995) with a slightly eccentric orbit (e 0.1). Being a closely spaced binary system (Quaintrell et al., 2003), the neutron star is deeply embedded in the strong stellar wind of the companion which has a mass loss rate in excess of (Nagase et al., 1986; Sako et al., 1999). It is a prototype candidate for accretion via stellar wind, and the typical X-ray luminosity is of the order of ergs . It exhibits pulsations with a period 283 s. The source is extremely variable undergoing giant flares (where flux increases by a factor of ), and abrupt off-states, where the source is almost undetectable for several pulse periods (Inoue et al., 1984; Kreykenbohm et al., 2008; Doroshenko et al., 2011).

The structure of the wind and hence the flaring behavior of Vela X-1 was investigated by Fürst et al. (2010) who also found a systematic trend in the change of column density of absorbing matter along the line of sight in different phase of the the orbit. The pulse profiles of Vela X-1 show a complex structure with multiple energy dependent dips. This has been explored before for other sources for example in GX 1+4 (Galloway et al., 2001), RX J0812.4-3114 (Corbet & Peele, 2000), 1A 1118-61 (Devasia et al., 2011a), GX 304-1 (Devasia et al., 2011) with RXTE, KS 1947+300 (Naik et al., 2006) with Beppo-SAX, GRO J1008-57 (Naik et al., 2011), and 1A 1118-61 (Maitra et al., 2012) with Suzaku. Dips in the pulse profile can be naturally explained due to the absorption in the accretion stream that is phase locked with the neutron star. The X-ray continuum spectrum of Vela X-1 has been modeled with a power law with an exponential cutoff (White et al., 1983; Tanaka, 1986), or with a Negative Positive EXponential model (NPEX) (Orlandini et al., 1998; Kreykenbohm et al., 1999, 2002). The continuum is further modified by a considerable amount of photoelectric absorption at low energies which varies erratically on short timescales and also with the orbital phase (Haberl & White, 1990). A strong iron fluorescence feature at 6.4 keV has also been reported (Watanabe et al., 2006).
An absorption like feature at 55 keV was first reported by Kendziorra et al. (1992) using data from HEXE. This was interpreted as a Cyclotron Resonance Scattering Feature (CRSF). CRSF arises due to resonant scattering of electrons in Landau levels in the presence of high magnetic fields. The energy of the CRSF is given by , where is the centroid energy, z is the gravitational redshift and B is the magnetic field strength of the neutron star. CRSF therefore gives us an estimate of the magnetic field strength of the neutron star. Pulse phase resolved spectroscopy of the CRSF parameters can provide crucial information on the magnetic field geometry and the emission region of the neutron star as we probe it at different viewing angles with spin phase. Makishima & Mihara (1992) and Choi et al. (1996) reported an absorption feature at 32 keV from the Ginga data. Mihara (1995) performed a detailed analysis of the Ginga observations and found that the CRSFs vary in strength over the pulse phase. Kretschmar et al. (1997) also confirmed the existence of two absorption features at 23 keV and 45 keV using the broadband data from the HEXE and TTM, and found similar variations with pulse phase as from the Ginga data. Subsequently more detailed pulse phase resolved analysis was performed by Kreykenbohm et al. (1999, 2002) using RXTE data who confirmed the existence of the two lines at 25 & 55 keV and also reported it’s variation with the pulse phase. Orlandini et al. (1998) and La Barbera et al. (2003) performed phase resolved analysis of Vela X-1 using BeppoSAX data but could only confirm the existence of the absorption line at 55 keV.

We present here a pulse phase resolved spectral analysis of Vela X-1 using Suzaku observation in June 2008. The same Suzaku observation has been analyzed by Doroshenko et al. (2011) who have mainly focused on the three off-states detected for a few pulses during the observation, and have detected pulsations for the first time in these “off-states“. They have also analyzed the energy dependent pulse profiles and the energy spectrum in both the off and normal states, and have confirmed the presence of the two CRSFs in the normal states. We have however probed the energy dependence of the pulse profiles in much more detail and carried out pulse phase resolved spectroscopy in narrow phase bins to explore its complex nature. The variations of the continuum spectral parameters as well as the CRSF fundamental and harmonic with pulse phase reported here are the most detailed results available so far. While performing pulse phase resolved analysis, care has also been taken to average over data having similar intensity and spectral hardness, to probe the variation solely due to the changing viewing angle with pulse phase. In section we describe the observation and data reduction, in section the pulse profiles including it’s energy and intensity dependence, in section spectroscopy, including phase averaged and phase resolved followed by discussions and conclusions in section .

2 Observations & Data Reduction

Vela X-1 has been observed with Suzaku (Mitsuda et al., 2007) on June 17-18 2008 (Obs. Id–403045010). The observation (exposure 103 ks) was performed at ’HXD nominal’ pointing position. Suzaku has two sets of instruments on board, the X-ray Imaging Spectrometer XIS (Koyama et al., 2007) covering the 0.2-12 keV range, the Hard X-ray Detector (HXD) having PIN diodes (Takahashi et al., 2007) covering the energy range of 10–70 keV, and GSO crystal scintillator detectors covering the 70–600 keV energy band. The XIS consists of four CCD detectors, three of which are front illuminated (FI : XIS0, XIS2, XIS3) and one back illuminated (BI: XIS1). Since the loss of XIS2 in 2006 November, only XIS 0, 1 & 3 are operational. For this observation, the XIS’s were operated in ’Normal’ clock mode in the ’ window’ option which gave a time resolution of 2 s.
HEASOFT 6.11 was used for the reduction and extraction. For the reduction and extraction of the XIS data, the unfiltered XIS events were reprocessed with the CALDB version 20100123 for XIS and 20091007 for HXD. The reprocessed XIS event files were then checked for the possible presence of photon pile-up. Pile-up estimation was performed by examining the Point Spread Function (PSF) of the XIS’s by checking the count rate per one CCD exposure at the image peak as given by Yamada & Takahashi. 2 Following their procedure, the value obtained was higher than that of Crab Nebula count rate of 36 ct/sq arcmin/s (CCD exposure), and the radius at which this value equals 36 in the PSF is about 15-16 arcsec. Thus the check performed showed a case of moderate photon pile up, and 15 pixels from the image center were removed to account for this effect. For the extraction of XIS light curves and spectra from the reprocessed XIS data, a circular region of diameter was selected around the source centroid with the central 15 ( ) pixels removed. Background light curves and spectra were extracted by selecting a region of the same size away from the source. The XIS count rate after the pile-up correction was around c with of the photons being lost due to the removal of the photons from the central region. Response files and effective area files were generated by using the FTOOLS task ’xisresp’. For extracting HXD/PIN light curves and spectra, cleaned event files were used (processing version 2.2.8.20). For HXD/PIN background, simulated ’tuned’ non X-ray background event files (NXB) corresponding to June 2008 were used to estimate the non X-ray background3, and the cosmic X-ray background was simulated as suggested by the instrument team4 applying appropriate normalizations for both cases. Response files of the respective observations were obtained from the Suzaku guest observatory facility.5

3 Timing Analysis

For the timing analysis, we applied barycentric corrections to the event data files using the FTOOLS task ’aebarycen’. Light curves with a time resolution of 2 s and 1 s were extracted from the XISs (0.2–12 keV) and the HXD/PIN (10–70 keV), respectively. Pulsations were searched in the data by applying pulse folding and maximization technique. The best estimate of the period was found to be s. We also checked for the correction of the pulse arrival times due to the orbital motion of the neutron star which showed that the filtered events corresponded to an orbital phase 0.17 to 0.36. The orbital motion curve however fitted well to a straight line in this phase range. This implies only a linear correction in the pulse arrival times which would not alter our results on pulse phase resolved spectroscopy significantly. Thus orbital correction for the pulse arrival times was not required. The pulse period has been determined for the same dataset to a greater precision by Doroshenko et al. (2011). Figure 1 shows the average pulse profile of Vela X-1 created by folding the light curve with the obtained pulse period.

3.1 Light curves & hardness ratio

Figure 2 shows the light curves of Vela X-1 rebinned with the timebin equal to the pulse period as obtained from the XIS and PIN data respectively. The light curves show that the source is highly variable. Panel 3 of the same figure shows the hardness ratio (ratio of PIN counts to XIS counts) for the entire stretch. Except for the brief initial stretch at the beginning, the hardness ratio remains nearly constant upto the first 90000 s after which it is more variable with an increasing trend. For this above mentioned constant hardness ratio stretch, arrows in panel 1 also show the ”off-states” in the XIS light curve as is presented in Doroshenko et al. (2011). Since the main aim of this work is to perform pulse phase resolved spectroscopy to probe the spectral parameters with changing viewing angle, we took only this stretch of constant hardness ratio excluding the “off-states“ for further analysis. This would ensure that our results would be free from any systematic effects of phase average spectral variability.

3.2 Intensity dependence of the pulse profiles

As already mentioned earlier, since the main aim of this work is to probe the pulse phase dependence of the spectral parameters, we also checked for the intensity dependence of the pulse profiles to avoid averaging over data having different luminosity dependence. Intensity dependent pulse profiles were created using both XIS (0.3-12 keV) and PIN (10-70 keV) for the above mentioned stretch of the data having similar hardness ratio and excluding the ”off-states”. Pulse profiles were created in three intensity windows having characteristic XIS count rates 20 c , 20-50 c and 50 c by applying intensity filtering. Figure 3 shows the intensity dependent pulse profiles in the XIS and PIN energy band respectively. The XIS and the PIN profiles also show similar characteristics in all the intensity bands except for a slightly larger pulse fraction in XIS at low count rate ( 20) and in PIN at medium count rate (20-50). The XIS pulse profile created with counts greater than 50 however differs considerably, with the dips and peaks in some phases not coinciding as can be seen from the figure, the dip in the highest intensity profile at phase 0.6 coincides with a peak in the other intensity band profiles. To avoid this intensity dependence we averaged over data only in the intensity band of 50 c to perform spectral analysis.

3.3 Energy dependence of the pulse profiles

Energy resolved pulse profiles were created by folding the light curves in different energy bands with the obtained pulse period . In light of the issues discussed in the above sections, pulse profiles were created for the constant hardness ratio stretch excluding the ”off-states” and in the intensity band of 50 . This is different from that presented by Doroshenko et al. (2011) who have compared the energy resolved pulse profiles between the on and “off-states”. Our main goal is to avoid the systematic effects which might affect our results of pulse phase resolved spectroscopy described later in section 4.2. The energy dependence of the pulse profiles is shown in Figure 4. The pulse profiles from 0.3-12 keV are created using all the three XISs (0, 1 & 3). Higher energy profiles are created from the PIN data. The figure shows that the pulse profiles have complex energy dependent structures, with upto five peaks in the XIS energy band which merge to two asymmetric peaks in the PIN energy band. With a careful examination of the pulse profiles, the following characteristics can be observed (refer Figure 4 for the exact location of the low energy peaks)

  1. The first two peaks in the low energy profiles at phases 0.2 and 0.5 (henceforth termed peaks a and b) merge to become a single asymmetric peak (phase 0.3) at 12 keV. The next three peaks of the low energy profiles at phases 0.6, 0.8 and 1 (henceforth termed peaks c, d and e) merge to become the second high energy peak (phase 0.9) after 12 keV.

  2. The dip at phase 0.3 between the peaks a and b decreases with energy and disappears at 12 keV.

  3. The dip at phase 0.7 between the peaks c and d however increases with energy upto 5 keV after which it shows a decreasing trend and disappears at 14 keV.

  4. The dip at phase 0.9 between the peaks d and e also decreases with energy and disappears at 7 keV.

  5. There is also an indication of a dip like structure at the lowest energies ( 5 keV) between phase 0.5-0.6.

4 Spectroscopy

4.1 Pulse phase averaged spectroscopy

We performed pulse phase averaged spectral analysis of Vela X-1 using spectra from the front illuminated CCDs spectrum (XISs-0 and 3), back illuminated CCD spectrum (XIS 1) and the PIN spectrum. As discussed earlier we extracted spectra only for the above mentioned stretch of the data having similar hardness ratio, excluded the ”off-states”, and further applied intensity filtering to choose the time within it having count rates 50 c . Spectral fitting was performed using XSPEC v12.7.0. The energy ranges chosen for the fits were 0.8-10 keV for the XISs and 12-70 keV for the PIN spectrum respectively. Due to an artificial structure in the XIS spectra around the Si edge and Au edge, the energy range of 1.75-2.23 keV was neglected. After appropriate background subtraction we fitted the spectra simultaneously with all parameters tied, except the relative instrument normalizations which were kept free. The XIS spectra were rebinned by a factor of 6 from 0.8-6 keV and 7-10 keV, and by a factor of 2 between 6-7 keV. The PIN spectra were rebinned by a factor of 2 upto 22 keV, by 4 upto 45 keV, and 6 upto 70 keV.
The continuum was fitted with both a phenomenological high-energy cutoff ’highecut’ model and a more physical comptonization model ’CompTT’ assuming a spherical geometry for the Comptonizing region (Titarchuk, 1994). In both the cases along with the Galactic line of sight absorption, a partial covering absorption model ’pcfabs’ was applied to take into account the intrinsic absorption local to the neutron star. A gaussian line was also used to model the narrow Fe k feature found at 6.4 keV.
In addition, two absorption features were found at 25 and 50 keV, which are the CRSF fundamental and harmonic as found previously for this source. These were modeled with Lorentzian profiles. Figure 5 shows the best-fitting spectra along with the residuals. Since the energy spectrum has a strong pulse phase dependence, we do not expect the pulse phase averaged spectrum to fit well to a simple continuum model. The best-fitting parameters for the high energy cutoff ’highecut’ model and the ’CompTT’ model are given in Table 1. The best fit had a reduced of 2.03 for 831 d.o.f for the ’highecut’ model and 1.92 for 832 d.o.f for the ’CompTT’ model respectively. The value of the additional absorption component () and the covering fraction () are higher for the ’CompTT’ model. The fundamental CRSF has similar parameters for both the models except for a slightly wider line in the case of the ’CompTT’ model. The harmonic is however much deeper and wider in the case of ’CompTT’ model. The continuum model used by Doroshenko et al. (2011) is slightly different from ours since they used a combination of powerlaw and CompTT model while we have used a partial covering CompTT model. As a result, the Galactic line of sight absorption () value obtained in our analysis is lower, and the comptonization parameters are also different. The cyclotron parameters however match well and are consistent with each other within error bars. Keeping in mind that Ecycl from the Lorentzian description does not define the minimum of the line profile (Nakajima et al., 2010) , from the values of and we obtained with the Lorentzian (cyclabs) model, the corresponding minimum of the line profile are calculated to be at 26.8 keV and 56.3 keV which are consistent with the values obtained by Doroshenko et al. (2011) within error bars. The depth and width of the cyclotron lines are also consistent.

Confidence contours were plotted to check the inter dependence between some of the parameters for both the models. Figure 6 shows the confidence contours between several pairs of model parameters for the phase averaged spectra. Among the continuum parameters when both were allowed to vary, the partial covering parameters and could be constrained well within 14 % and 8 % of the respective parameter values for the ’highecut’ model. There were however limitations in this model like the break energy ’E-cut’ and the fundamental CRSF were found to be correlated and could not be well constrained independently. The contour between and the powerlaw photon index () showed that although could be constrained very well, could not be. The fundamental being very shallow, and possibly because of the correlation with the break energy and inability to constrain against in the ’highecut’ model, the energy and depth of the fundamental could not be constrained completely independent of these parameters. However, similar trend of the variation of the fundamental line energy obtained with pulse phase for both the models give us an added confidence on our results. and for the ’CompTT’ model also could be constrained well (11 % and 6 % of their values). The optical depth and electron temperature ’’ and ’’ showed some correlation but could be constrained between 18 % and 4 % of their values. The interdependence between the parameters discussed above were also evident from the results of the pulse phase resolved spectroscopy of the parameters discussed later. For the cyclotron line parameters, both the CRSFs could be constrained well in the case of the ’CompTT’ model and showed no dependence both among themselves or with the continuum parameters like ’’ and ’’. In the case of ’highecut’ model although parameters of the CRSF harmonic could be constrained well, the and contour maps showed dependency and difficulty in constraining both the parameters simultaneously. However the similar trend of variation of the parameters obtained with both the spectral models as discussed above gives us confidence on our obtained results. Because of some of the limitations discussed here, the errors quoted and plotted henceforth are assuming variation of only one parameter, with the other parameters allowed to vary independently to find the minimum .

4.2 Pulse phase resolved spectroscopy

Strong energy dependence of the pulse profiles, as shown in Figure 4 implies dependence of the energy spectrum on the pulse phase. The narrow energy dependent dips in the pulse profiles can also be explained by a partial covering absorption model in which the absorber is phase locked with the neutron star. To investigate this we performed pulse phase resolved spectroscopy, applying phase filtering in the FTOOLS task XSELECT. For the phase resolved analysis we used the same background spectra and response matrices as was used for the phase averaged spectrum for both the XIS’s and the PIN data. We also fitted the spectra in the same energy range and rebinned them by the same factor as in phase averaged case. The value of the Galactic absorption () and the Fe line width were frozen to the phase averaged values for the two respective models.

Phase resolved spectroscopy of the cyclotron parameters

To investigate the pulse phase resolved spectroscopy of the two CRSFs we generated phase resolved spectra with the phases centered around as in the case of 25 independent bins but at thrice their widths. This resulted in 25 overlapping bins out of which only 8 were independent. Due to limited statistics we were unable to constrain all the parameters, and froze the width of the CRSF harmonic to the phase averaged value of the respective models and varied the rest of the parameters with pulse phase. For phases close to or at the off pulse regions, the CRSFs are weak and sometimes cannot be detected in the spectra for either or both of the continuum models. Confidence contours were created for the pairs of parameters as shown in panels ’B’, ’C’, ’D’, ’E’, ’H’, ’I’, ’J’, ’K’ in Figure 6 for some of the phase resolved spectra. The fundamental , when paired with the parameters , E-cut or could not be constrained simultaneously as was the case with the phase averaged spectrum. For all the other pairs, the parameters could be constrained fairly well with the errors being 1.5 times the corresponding errors with the phase averaged spectrum. Refer section 4.1

Figure 7 shows the variation of the cyclotron parameters for both the models as a function of pulse phase. Despite statistical limitations in the data to constrain the CRSF fundamental energy and depth independent of the cutoff energy in the ’highecut’ model, the variation of the CRSF parameters have very similar pattern for both the ’highecut’ and the ’CompTT’model. This gives us reasonable amount of confidence on the obtained results. The results also follow the trend as obtained previously by Kreykenbohm et al. (2002) using RXTE but they did not have enough sensitivity to probe these features in detail. The following features can be seen from the Figure 7. The variation is compared with respect to the high energy PIN pulse profile shown in panel two of the same figure and the peaks and the dips refer to the peaks and dips in the same.

  1. The energy of the fundamental () vary by a large amount with pulse phase, with the values varying between 22 keV in the off pulse region to 28 keV in the ascending phase of the second pulse. It has a decreasing trend with phase for the first pulse with nearly constant values for the second pulse, except for the ascent of the second pulse at phase 0.7 where E1 peaks in value.

  2. The depth of the fundamental () varies almost by a factor of three with the pulse phase, with the deepest lines near the pulse peaks and shallowest in the off pulse regions. Its value peaks near the ascending edges of the first pulse (phase 0.2-0.4) and the ascending edge of the second pulse (phase 0.7). The lines are in general deeper for the first pulse.

  3. The width () of the fundamental varies almost by a factor of two. The width is maximum at the rising edges of the two pulse peaks at phases 0.1 and 0.7.

  4. The energy of the second harmonic () varies between values of 48 keV to 62 keV. The values are maximum at the descending phase of both the pulses.

  5. The depth of the second harmonic () varies by a factor of 2 with the deepest harmonics found at the same phases as the phases having maximum .

  6. The ratio of the two line energies / has significant pulse phase dependence (Figure 8) with an average value of 2.1, maximum of 2.6 near the pulse peaks at phase 0.4 and 0.9 and minimum of 1.7 near the off pulse regions at phase 0.8.

Phase resolved spectroscopy of the continuum parameters

To investigate the pulse phase resolved spectroscopy of the continuum parameters we generated the phase resolved spectra with 25 independent phase bins. We froze the cyclotron parameters of the corresponding phase bins to the best-fit values obtained for the investigation of the cyclotron line parameters using 25 overlapping phase bins as described in section 4.2.1. Figure 9 shows the best-fit phase resolved continuum parameters for both the models as a function of the pulse phase. Confidence contours were created for the pairs of parameters as shown in panels ’A’, ’F’ and ’G’ in Figure 6 for some of the phase resolved spectra. For all the pairs, the parameters could be constrained well with the errors being 1.3 times the corresponding errors with the phase averaged spectrum. Refer section 4.1 The results obtained as seen from the figure from both the models are as follows:

  1. At the dips between peak a and b (phase 0.3) and peak d and e (phase 0.9) of the low energy XIS profile, there is a sudden increase in the value of the local absorption component (). The dip being larger at phase 0.3 the corresponding value of is also larger.

  2. At the main dip of the XIS profile between phase 0.5-0.6, there is also an indication of an increase of with a high covering fraction ().

  3. The dip between c and d (phase 0.7) of the XIS profile has somewhat different characteristics and extends upto 20 keV. The ’highecut’ model shows a very high value and a very small at this phase. The ’CompTT’ model however does not show any significant change in the values of or , but a very high optical depth ().

  4. The value of shows somewhat different pattern of variation for the two models. For the ’highecut’ model, the phases where is high usually has a small , but for the ’CompTT’ model there is an indication of correlation between the two parameters.

  5. In general the optical depth () increases and the low-energy seed temperature falls at the dips of the XIS pulse profile.

  6. The powerlaw photon index () shows a strong dependence on the pulse profile. It is hardest at high energy PIN pulse profile peaks and softest at the off pulse phases. Similar spectral hardening at the pulse peaks was found for this source previously by Kreykenbohm et al. (1999).

  7. The folding energy () varies with the pulse phase with the values peaking at the ascending and descending phases of the PIN pulse profile, and their minimum at the pulse peaks. The Cutoff-energy also varies with the pulse phase.

  8. The electron temperature () is highest at the ascending and descending phases of the PIN pulse profile at phases 0.1, 0.5, 0.7 and 1. It is lower in the off pulse regions.

  9. The optical depth () and however shows strong anti-correlation with each other throughout the pulse phase. This may imply that the statistics of the data are not good enough to determine the variation of these two parameters independently as was already indicated in the confidence contour maps.

  10. Both the power law normalizations () and the CompTT normalizations () shows a variability pattern with the values peaking at the peaks of the XIS pulse profile.

5 Discussions & Conclusions

In the present work, we have performed a detailed pulse phase resolved analysis of a long Suzaku observation of Vela X-1. Data from the same Suzaku observation has been analyzed by Doroshenko et al. (2011). They have probed the energy dependence of the pulse profile in four energy bands and have confirmed the presence of the two CRSFs in the energy spectrum. We have however investigated the complex energy dependence of the pulse profiles and probed the narrow dips of the same in much more detail by performing pulse phase resolved spectroscopy. Pulse phase resolved spectral analysis have been performed previously by Kreykenbohm et al. (1999, 2002) using RXTE data. Apart from the variations in the continuum spectra with the pulse phase they also confirmed the existence of the two lines at 25 & 55 keV and reported their variation with the phase. In the present work, we have used a long observation of Vela X-1 with Suzaku, and the high sensitivity of Suzaku over a broad energy band allows us to carry the same with much finer phase bins. Orlandini et al. (1998); La Barbera et al. (2003) performed phase resolved analysis of Vela X-1 using BeppoSAX data but could only confirm the existence of the absorption line at 55 keV. The results in all these previous works are more or less in agreement with us. But we have been able to bring out these variations in more detail specially for the two CRSF features for which this is the most detailed result obtained so far.

5.1 Energy resolved pulse profiles

Vela X-1 is a highly variable source and shows strong pulse to pulse variations. The low and high energy profiles have a very complex upto five peaked structure at lower energies which eventually merges to become a double peaked profile at higher energies. The strong energy dependence of the pulse profiles have been probed previously by Doroshenko et al. (2011) using data from the same Suzaku observation in four energy bands which show the structure of the complex pulse profiles. Their main emphasis was on comparing the pulse profiles between the on and “off-states“. We have however investigated the complex energy dependence of the pulse profiles and probed the narrow dips of the same in much more detail. Presence of double peaked pulses at high energies have been found previously in some sources for example in XTE J1946+274 (Paul et al., 2001), 4U 1538-52 (Bildsten et al., 1997), GX 301-2 (Koh et al., 1997) etc. They can either be interpreted due to a fan beam pattern of the emission geometry, or that due to the contribution from both the magnetic poles. The low energy complex pulse profiles are however more difficult to interpret since they are affected due to scattering and absorption in the local environment of the neutron star. The dips in the low energy profiles can be explained due to an additional absorption component in our line of sight, probably by the passage of a phase locked accretion stream or the accretion column itself. This aspect is discussed in more detail below.

5.2 Phase resolved spectroscopy of the continuum spectrum

We have performed pulse phase resolved spectroscopy to probe the complex energy dependence of the pulse profiles. The dips in the pulse profiles at phases 0.3, 0.5-0.6, 0.7 and 0.9 can be explained due to an increase in the additional absorption column density with a corresponding change in the covering fraction at that phase. The changes in the value of and covering fraction with pulse phase can act as a tracer for the properties of the plasma in the accretion stream, which may be a clumpy structure having different values of opacities and optical depths. The fitted parameters of the ’highecut’ model shows an abrupt increase in the value of at the dips at phases 0.3 and 0.9. The dip at phase 0.3 extends upto somewhat higher energies, the value of of the former being higher than that at phase 0.9. Both of the dips have similar strength in agreement with similar values of covering fraction in both the cases. The main dip at phase 0.5-0.6 may be indicated by a slight increase in with a high value of the covering fraction. The dip at phase 0.7 is different from the others since it increases in strength upto 5 keV and then decreases and disappears after 20 keV, being relatively shallower than the other dips in the pulse profile. This dip is in agreement with a large increase in and a very small covering fraction, with the value of peaking at this particular phase. This would indicate the presence of a very dense clump of matter (a narrow and dense stream), with the high value of responsible for the dip extending upto higher energies. In general the covering fraction decreases at the dips in the profile where is larger, which may indicate a clumpy structure of the accretion stream. The ’highecut’ model is thus able to explain the energy dependence of the pulse profiles very well. The parameters obtained by fitting the spectra with the ’CompTT’ model on the other hand, does not show a similar pattern of variation of the partial covering model specially for the case of the covering fraction parameter. The dip at phase 0.7 also does not show any significant increase in , although the optical depth () parameter of the ’CompTT’ model increases at all phases corresponding to the dips. We would however like to point out that the ’CompTT’ model may not be a good description of the low energy part of the pulsar spectra keeping in mind that the N and the covering fraction were found to have some dependence (mentioned earlier in section 4.2.2). In addition, it is a highly simplified model with a spherical shape of the Comptonizing cloud whereas the emission region in accreting pulsars are likely to have a slab or cylindrical geometry. The ’highecut’ model inspite of being a phenomenological model and having a divergent property at low energies when paired with a powerlaw, is able to explain the complex energy dependence of the pulse profile better.
Another interesting result found is the spectral hardening at the high energy pulse peaks. The power law index () reaches it’s minima at these phases, more so for the phase corresponding to the second peak (phase 0.9). Similar regions of pulse hardening have been observed previously in other sources like Her X-1 (Pravdo et al., 1977, 1978), 4U 0115+63 (Johnston et al., 1978; Rose et al., 1979) & GX 1+4 (Doty et al., 1981) & 1A 1118-61 (Maitra et al., 2012). Assuming the spectral formation by the comptonization of photons by the thermal electrons, the Compton parameter can be used as a measure for the degree of comptonization. It is given by , where is the electron temperature and the optical depth. (Rybicki & Lightman, 1986). The higher is the degree of comptonization the larger is the ”y” parameter, and hence harder is the spectrum. ”y” can be easily found since and are the parameters of the ’CompTT’ model. Calculating it shows that the ”y” values also peak at more or less the same phase as the hardest , i.e at the pulse peaks with the phase corresponding to the second peak having a higher value of ”y”. at all the phases, which is indicative of saturated comptonization being prevalent in the the spectrum. We also checked for the correspondence between ““ and ”y” at all other phases. The parameters seem to be correlated with each other with the Spearman rank correlation coefficient equal to -0.89. Figure 10 shows the interdependence between the two parameters. We would like to caution however that the ’CompTT’ model assumes spherical geometry for the plasma region which is a crude approximation for the accretion column which has a cylindrical or slab geometry in most cases. Hence this may give rise to some systematic errors in the results.

5.3 Phase resolved spectroscopy of the cyclotron parameters

We also performed pulse phase resolved spectral analysis of the two CRSF features. Pulse phase resolved spectroscopy of the cyclotron parameters have been performed for some sources previously, for example in Her X-1 (Soong et al., 1990; Enoto et al., 2008; Klochkov et al., 2008), 4U 1538-52 (Robba et al., 2001), 4U0115+63 (Heindl et al., 2000), Vela X-1 (Kreykenbohm et al., 1999, 2002; La Barbera et al., 2003), Cen X-3 (Suchy et al., 2008), and more recently in GX 301-2 (Suchy et al., 2012), 1A 1118-61 (Suchy et al., 2011; Maitra et al., 2012) and 4U 1626-67 (Iwakiri et al., 2012). We have obtained detailed results on the variation of both the CRSF’s of Vela X-1 with the pulse phase. Both the ’highecut’ and ’CompTT’ models used by us to fit the spectra give comparable results. This gives us more confidence on the obtained pattern of variation. The results are also very similar to that obtained by Kreykenbohm et al. (2002) with RXTE but they did not have enough sensitivity to probe these variations in detail.
There have also been attempts to model the CRSF features analytically by assuming certain physics and geometry of the line forming region by Araya & Harding (1999); Araya-Góchez & Harding (2000); Schönherr et al. (2007) and more recently by Nishimura (2008, 2011); Mukherjee & Bhattacharya (2012). All these models predict significant variations in the depth, width and the centroid energy of the CRSF features with the changing viewing angle at different pulse phases. They also predict possible deviation or distortion from the simple dipole geometry of the magnetic field, and deviation of the line ratios from the classical value of two. Vela X-1 has a shallow and narrow fundamental, and a deep and wide harmonic (refer Table 1). This may happen due to photon spawning by Raman Scattering at higher harmonics (refer (Schönherr et al., 2007)), or the superposition of a large number of lines from different sites in the line forming region (Nishimura, 2008, 2011) may also make the fundamental CRSF appear shallower. Nishimura (2011) further predicts a shallow and narrow fundamental and a deeper and wider second harmonic would imply large viewing angle w.r.t the magnetic field. A fan like beam would be expected for Vela X-1 in this case. As is mentioned in section the ratio of the two line energies is at many phases. According to Nishimura (2011), This would favor a line forming region with a large polar cap or of a greater height. The fundamental would be formed at a higher site and second harmonic primarily around the bottom. As a result is expected.
The electron temperature ”” is high at the phases corresponding to the wider CRSFs, specially at the ascending edges of the high energy PIN pulse peaks. For a Maxwell-Boltzmann distribution of electrons the observed CRSF FWHM is given as : (Mészáros, 1992) ,
where is the electron temperature, the CRSF energy, and the viewing angle w.r.t the magnetic field. This implies a higher would result into a higher as is obtained. The fundamental line is deepest at the ascending edge of the pulse phase. The deepest second harmonic is also in the descending edge of the main pulse and very shallow outside the pulses. Nishimura (2011) predicts these signatures would imply looking at a very large viewing angle w.r.t the magnetic field at those phases and hence a fan beam like emission pattern would be expected. All these are however assuming the contribution from one of the magnetic poles of the neutron star, and results may be complicated further with the contribution from the other pole.

This research has made use of data obtained through the High Energy Astrophysics Science Archive Research Center On line Service, provided by NASA/Goddard Space Flight Center.
Figure 1: Average pulse profile of Vela X-1 folded with the best obtained period. The top panel shows the pulse profiles (0.3-12 keV) using XIS data & the bottom panel shows the pulse profile (10-70 keV) using PIN data.
Figure 2: The first panel shows the light curve of Vela X-1 obtained with Suzaku for one of the XIS in the energy band of 0.3-12 keV. The second panel shows the same obtained in the PIN energy band(10-70 keV). The time binning is equal to the pulse period. The bottom panel shows the hardness ratio. The arrows and the dash indicates the time range of the data which were selected on the basis of constant hardness ratio for further analysis.
Figure 3: Intensity dependent pulse profiles of Vela X-1. The left panel shows the pulse profiles (0.3-12 keV) using XIS data & the right panel shows the pulse profile (10-70 keV) using PIN data. The pulse profiles in red shows the profile with XIS count rate 20 c , the one in green with 20-50 c , and the one in blue 50 c
Figure 4: Energy dependent pulse profiles of Vela X-1 using XIS & PIN data. The energy range for the pulse profiles are specified inside the panels.
Figure 5: The pulse-phase averaged spectrum of Vela X-1 using high-energy cutoff model (left panel) and ’CompTT’ model (right panel). The upper panel shows the best-fit spectra. The residuals are given in the bottom panels.

Figure 6: confidence contours between several pairs of continuum and line parameters for the two models, obtained from the phase averaged spectra. The innermost to outermost contours represent respectively 68, 90 and 99 confidence levels. The upper two panels separated with a horizontal line show the contour plots for the ’highecut’ model and the lower panels for the ’CompTT’ model. The plots show the confidence contours between A) and B) E-cut energy and C) PowIndex and D) and & E) and , for the ’highecut’ model, and F) and G) and H) and I) and J) and & K) and for the ’CompTT’ model.
Figure 7: Variation of the cyclotron line parameters as is obtained with the two models. The black points with ’circle’ denotes the parameters as obtained with the highecut model The red points denote the points as obtained with the CompTT model. Only 8 of the 25 bins are indepenent. Although the parameters for the two models match reasonably well, the fundamental line energy for the Highecut model cannot be constrained well and depends on the continuum parameters, specially the cutoff energy as shown in the contour plots in Figure 6.
Figure 8: Variation of the ratio of the two cyclotron lines E2/E1 as is obtained by fitting the two models. The variation of the parameter as obtained from the high energy cutoff model is denoted by the symbol ’circle’. Variation of the parameter as obtained from the CompTT model is denoted by the symbol ’star’.
Figure 9: Variation of the spectral parameters with phase along with the pulse profile (0.3-12 keV for XIS and 10-70 keV for PIN). The left panel shows the variation using the model ’highecut’ and the right panel shows the same using the model ’CompTT’. For the ’highecut’ model, the real uncertainty in the value the cutoff energy is bigger than shown in the plot considering it’s dependence on the fundamental line energy as seen in the contour plots (Figure 6)
Figure 10: Plot showing the interdependence between the power law index () and the Compton parameter. The error bars are plotted as seen within the symbols.
Parameter Highecut model values CompTT model values
( atoms )
( atoms )
PowIndex
E-folding energy (keV)
E-cut energy (keV)
(keV)
CompTT (keV)
CompTT
(keV)
(keV)
(keV)
(keV)
Iron line energy (keV) 6.41 0.01 6.41 0.01
Iron line eqwidth (eV) 56.8 2.3 56.7 2.2
Flux (XIS) (0.3-10 keV)
Flux (PIN) (10-70 keV)
reduced /d.o.f 2.03/831 1.92/832



Flux is in units of and are in 99 % confidence range.
Flux is in units of and are in 99 % confidence range.

Table 1: Best fitting spectral parameters of Vela X-1 with a partial covering high-energy cutoff model. Errors quoted are for 99 per cent confidence range.

Footnotes

  1. affiliation: Joint Astronomy Programme, Indian Institute of Science, Bangalore-560012, India
  2. http://www-utheal.phys.s.u-tokyo.ac.jp/ yuasa/wiki/index.php
    /How_to_check_pile_up_of_Suzaku_XIS_data
  3. http://heasarc.nasa.gov/docs/suzaku/analysis/pinbgd.html
  4. http://heasarc.nasa.gov/docs/suzaku/analysis/pin_cxb.html
  5. http://heasarc.nasa.gov/docs/heasarc/caldb/suzaku/ and used for the HXD/PIN spectrum

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