© ESO, 2016

1. Introduction

Radio pulses from pulsars undergo several kinds of transformation while traveling through the ionized interstellar medium, such as dispersion, pulse scatter broadening, scintillation, and delayed arrival of pulses; see Manchester & Taylor (1977) and Lyne & Smith (2006) for pedagogical reviews; see also Backer et al. (2000) and Lyne et al. (2001) and references therein for technical details. The Crab Pulsar in particular displays extreme forms of such activity from time to time (Smith & Lyne 2000). However, the event of late October 1997 in the Crab Pulsar stands out in that it was simultaneously accompanied by a dramatic slowing down of the Crab Pulsar (Backer et al. 2000; Smith & Lyne 2000; Lyne et al. 2001); it slowed down by ≈1.2 ms in ≈10 to 20 days. In comparison, the Crab Pulsar wanders in delay by about ≈0.3 ms over a month owing to timing noise (Backer et al. 2000), and is delayed by about ≈0.0007 ms over 20 days owing to systematic loss of rotational energy. Backer et al. (2000) and Smith & Lyne (2000) note the curious and confusing coincidence of the dramatic slowing down (which is presumed to be due to factors internal to the Crab Pulsar) with the dispersive, diffractive, and refractive phenomena (which are presumed to be due to factors related to the Crab Nebula). Both groups developed their respective models to explain the dispersive, diffractive, and refractive phenomena in terms of moving ionized screens within the Crab Nebula (Backer et al. 2000; Smith & Lyne 2000; Lyne et al. 2001.

More recently, however, Smith et al. (2011) have suggested that there was no intrinsic slowing down of the Crab Pulsar during the October 1997 event; they attribute the entire non-dispersive, frequency independent delay of 1.2 ms to ray paths in highly localized electron clouds in the Crab Nebula. A similar hint appears in the work of Wong et al. (2001), in the last sentence of their Sect. 3.4. A perspective of the problem is provided by Fig. 2a in Smith et al. (2011), which shows the variation of frequency independent timing residuals of the Crab Pulsar during the October 1997 event. The event being discussed here refers to the dramatic slowing down of the Crab Pulsar at around MJD 50 750 (29 October 1997), which manifests as increasing timing residuals. A glitch occurred at MJD 50 812.59 ± 0.01 (Espinoza et al. 2011), which is not believed to be connected to the October 1997 event (Backer et al. 2000; Smith et al. 2011).

This work attempts to verify, at least qualitatively, whether the Crab Pulsar intrinsically slowed down or not during late October 1997 by analyzing X-ray data for that epoch. X-ray propagation is not affected by passage through ionized media, unlike radio waves; so X-ray timing of the Crab Pulsar should show only the unusual intrinsic slowing down, if any, and not other delays. On the other hand, X-ray data is very sparse (i.e., poorly sampled in time) compared to radio data. Only four X-ray observatories capable of timing the Crab Pulsar observed it during that epoch. Out of the four, ROSAT and ASCA did not yield useful data. BeppoSAX provided useful data for only one epoch. All other data came from the RXTE observatory; however, these observations occurred on average once a week or once every two weeks, whereas the radio observations took place at least once every day. Therefore, quantitative comparison between the X-ray and radio results may not be constraining.

2. Observations

2.1. RXTE PCA observations

The RXTE data are obtained from the Proportional Counter Array (PCA; Jahoda et al. 1996) aboard the RXTE observatory. The PCA consists of five proportional counter units (PCUs) operating in the 2–60 keV range, having a field of view of 1° in the sky, and a time resolution of 1 μs (see “The ABC of XTE” guide on the RXTE website¹). The first observation was on 20 July 1997 (MJD 50 650, ObsID 10200-01-12-00) and the last observation was on 11 April 1998 (MJD 50 914, ObsID 30133-01-08-00); there were a totoal of 28 ObsIDs. The closest observation preceding this duration was on 9 May 1997 (MJD 50 577, ObsID 10200-01-13-00), which was not included in the analysis owing to the ≈73-day gap. The last observation for the analysis was chosen so as to sufficiently represent the glitch behavior. These data were obtained in the Generic Single Bit mode, having the configurations SB_250us_0_13_2s and SB_250us_14_249_2s. Both configurations accumulated photon events into time bins of size 244.14 μs; the former mode combined the first 14 energy channels into a single channel, while the latter combined the next 236 energy channels. Of the 28 ObsIDs, 22 had all five PCUs switched on, while 3 had four PCUs switched on, and 3 had only three PCUs switched on.

2.2. BeppoSAX PDS observation

The BeppoSAX observatory observed the Crab Pulsar on 8 October 1997 (MJD 50 729, ObsID 20795004) using, among other narrow field instruments (NFIs), the Phoswich Detector System (PDS; Frontera et al. 1997). The PDS consists of four NaI(Tl)/CsI(Na) phoswich scintillation photon counters grouped into two pairs, which rock on and off the source in the sky, similar to the HEXTE instrument of RXTE. It covers the energy range 15–300 keV and has a time resolution of 16 μs (see the “Cookbook for BeppoSAX NFI Spectral Analysis” guide on the BeppoSAX website²). This lone BeppoSAX observation was considered important since its epoch is close to the dramatic slowdown of the Crab Pulsar. BeppoSAX also observed the Crab Pulsar on 6 April 1998 (MJD 50 909), which falls in the glitch part of the data in Fig. 1; this data could not be analyzed owing to the lack of housekeeping files.

3. Analysis

Vivekanand (2015) has described in comprehensive detail the timing analysis for the Crab Pulsar using the HEXTE instrument. The method of analysis differs from instrument to instrument mainly up to the stage of referring the photon arrival times to the solar system barycenter.

When combining data from different instruments, the keyword TIMEPIXR is important. All data used in this work have TIMEPIXR = 0. The pulse arrival epochs determined by the tool efold have been corrected by the values + 122μs and + 8μs for the instruments PCA/SB and PDS, respectively, as per the prescription in the document “RXTE Absolute Timing Accuracy” on the RXTE website³.

3.1. RXTE PCA analysis details

Data for each of the two configurations were analyzed separately until the very end. It was found that in 25 of the 28 ObsIDs, there was negligible difference in arrival times of the two configurations (less than a milliperiod), so their average was used for the final analysis. The same was done for two of the three remaining ObsIDs, in which the difference was −477.9994 periods, which is very close to an even number of periods. In the third ObsID, the difference was −89.0000 periods, which is an odd number of periods, so averaging the two arrival times will result in an error of half a period; so the arrival time of one of the configurations was used in this case. For more details of analysis for this instrument see Vivekanand (2015).

3.2. BeppoSAX PDS analysis details

BeppoSAX PDS data was analyzed using FTOOLS version 5.0 and SAXDAS version 2.3.1. The following data was downloaded for ObsID 20795004: the cleaned and linearized event file, the GTI file, and the housekeeping file. Using the housekeeping file, an additional system related GTI was created using the following selections: (a) Earth occultaion angle, EARTH_ANG > 14°; (b) time since the peak of the last South Atlantic Anomaly passage, TIME_SINCE_SAA > 30 min or TIME_SINCE_SAA < 0 min; (c) star tracker configuration, ID STR_CONF >= 4 and STR_CONF <= 6; see the “Aspect Reconstruction” section of “BeppoSAX Cookbook” on the BeppoSAX website⁴. In summary, GTI selection criteria are as per standard procedures, with additional constraints on the three parameters mentioned above. After selecting photons based on this GTI, the light curve was obtained using the tool lcurve; based on this light curve, the data beyond 70 ks from the start of the data file were excluded from further analysis. Then photons were selected in the energy range 15 to 220 keV. Finally the tool baryconv was used to refer photon arrival times to the solar system barycenter. Further analysis was similar to that of the PCA instrument of RXTE.

4. Results for the October 1997 event using the radio reference timing model

In this section the X-ray data are analyzed using the reference timing model of Backer et al. (2000), given in their Table 1; this is used to check that the same phenomenon is being observed that was observed by radio astronomers. The Jodrell group have not published their reference timing model. Figure 1 shows the result of using TEMPO2 along with the parameters in Table 1 of Backer et al. (2000) as constant input (i.e., without any fitting) for the X-ray data from the PCA/HEXTE and from PDS/BeppoSAX. This figure is remarkably similar to Fig. 2a in Smith et al. (2011). The slowing down of the 1997 event and the glitch behavior are clearly evident, including the negative slope in residuals between the two epochs. In Fig. 1, the Crab Pulsar slowed down by ≈0.7 ± 0.1 ms over a duration of ≈30 days around MJD 50 750. This is smaller than, but consistent with, the findings of Backer et al. (2000), Smith & Lyne (2000), and Lyne et al. (2001). Furthermore, the delay observed here is about half of that observed at radio frequencies. We therefore conclude that the Crab Pulsar indeed slowed down intrinsically during the 1997 event.

Fig. 1 Result of using TEMPO2 on all data with the parameters given in Table 1 of Backer et al. (2000) as constant input (i.e., without any fitting). The lone BeppoSAX data point is at epoch ≈–21 days with a larger error bar. We note that no artificial phase jumps (using PHASE ±1 in the input file to TEMPO2) are required, pointing to the robustness of the radio reference timing model used.

5. Results for the October 1997 event using the reference timing model derived from X-rays

In this section the X-ray data are analyzed using reference timing models that are derived self-consistently from the X-ray data itself. These data are not expected to be as accurate as the radio reference timing model owing to sparse X-ray timing data.

The first step is to identify precisely the “post-event and pre-glitch” duration in Fig. 1; this duration will be used to obtain the reference timing model for the entire data. Based on the independent identifications by Backer et al. (2000), Lyne et al. (2001), and Smith et al. (2011), which differ marginally from each other, for our purposes the post-event and pre-glitch duration can be safely identified as being from MJD 50 758 to MJD 50 812.

The second step is to fit the X-ray data in the above post-event and pre-glitch duration to a pulsar slowdown model (using TEMPO2 Hobbs et al. (2006)), which is conventionally taken as consisting of three parameters: rotation frequency ν, its derivative , and its second derivative ; see Eq. (1) of Espinoza et al. (2011). Two such models are derived, which are shown as models 1 and 2 in Table 1. Model 1 is obtained by a fit of the X-ray data in the post-event and pre-glitch duration using TEMPO2. Model 2 is an arbitrary but minor modification of model 1, for reasons explained later. The rms residuals of the fit in the two models is 21 μs and 68 μs, respectively. Within the errors both models are similar. The corresponding parameters from the Jodrell Bank monthly timing ephemeris of the Crab Pulsar⁵ (Lyne et al. 1993), referring to the reference epoch in Table 1, are 29.870335055 Hz and −3.75274 × 10^-10 s^-2, which compare very well with the estimates in Table 1.

The final step is to use TEMPO2 along with the parameters in Table 1 as constant input (i.e., without any fitting) for the entire data; the results are presented in the two panels of Fig. 2. The glitch behavior is clearly seen using both models, although it is not shown in the figure; qualitatively they are similar to the glitch behavior seen in Fig. 2a in Smith et al. (2011), while quantitative comparison is done in the following section. The occurrence of a glitch soon after the event of October 1997 in the Crab Pulsar is fortuitous, since its analysis in the current X-ray data validates the method of analysis for the event as well.

Unfortunately, the X-ray data analysis of this section is not unequivocal regarding the October 1997 event. Using Model 1, the pre-event X-ray timing residuals can be interpreted as a speeding up of the Crab Pulsar (top panel of Fig. 2), while using Model 2 they can be interpreted as a slowing down (bottom panel of Fig. 2). The most probable reason for this is the sparse (i.e., poorly sampled in time) X-ray data. Model 2 was obtained by trial and error, in the effort to ascertain whether the X-ray data could show an event behavior contrary to that obtained using Model 1. We therefore conclude from the above analysis that the X-ray data by itself cannot categorically determine whether the Crab Pulsar intrinsically slowed down during the event of October 1997.

Fig. 2 Top panel: result of using TEMPO2 on the X-ray data with the parameters of model 1 in Table 1 as constant input (i.e., without any fitting). The plot is restricted to the post-event and pre-glitch duration, along with four data points before this duration, to better view the event itself. Bottom panel: same as top panel, but using the parameters of model 2 in 1.

However, a closer look at Fig. 2 reveals a detail. In both panels of Fig. 2, the first data point before the post-event and pre-glitch duration at epoch ≈−1.43 days is lower than the reference data (i.e., data later than this epoch in Fig. 2). In the bottom panel of Fig. 2 it is expected to be so anyway, but in the top panel of Fig. 2 it is lower by 0.30 ± 0.04 ms. Therefore, it appears that even Model 1 indicates a slowing down of the Crab Pulsar around the epoch −1.43 days, or equivalently at round MJD 50 750–1.43 = MJD 50 748.57. It can therefore be concluded from the above analysis that although the X-ray data analysis of this section cannot categorically determine whether the Crab Pulsar slowed down during the event of October 1997, it offers reasonable support for that hypothesis.

In Figs. 1 and 2, the lone BeppoSAX timing residual differs by about ≈ 0.17 ± 0.20 ms with respect to RXTE/PCA data, which is consistent with the formal error of ≈0.2 ms on this timing residual (Mineo et al. 2000). See also Cusumano (2003) and Nicastro et al. (2004) for details of the accuracy of the onboard clock of BeppoSAX. The lone BeppoSAX data point used in this work follows the RXTE timing residual variation in both Figs. 1 and 2, without having to artificially insert phase cycle corrections in TEMPO2. We believe that the lone BeppoSAX data point significantly enhances the confidence of the fits to the RXTE data since it is obtained from an entirely independent observatory.

6. Results for the December 1997 glitch

The results of the previous section depend critically upon the post-event and pre-glitch solutions of TEMPO2, which are listed in Table 1. An independent verification of these is to use them to derive the parameters of the glitch that soon followed the October 1997 event, and compare them with results obtained at radio frequencies. For this glitch, Wong et al. (2001) have publish more detailed parameters than Espinoza et al. (2011); therefore, their method of glitch analysis has been followed. We used their glitch epoch (MJD 50 812.9) and their decay time scale (2.9 days) since the X-ray data is too sparse to derive these parameters independently. The X-ray data beyond the glitch epoch were analyzed using the model of Backer et al. (2000), and models 1 and 2 of Table 1. The results are shown in Table 2; for comparison the corresponding values derived by Wong et al. (2001) are also shown (see their Table 3).

The errors on t_g and τ_n in Col. 2 of Table 2 cannot be used to estimate the errors in Cols. 3 to 5, because the parameters of the fit are highly correlated, and the covariance matrix is obtained only when t_g and τ_n are also fit. The actual uncertainties are larger than those quoted in Cols. 3 to 5 of Table 2. However, the mean values of the derived X-ray parameters can be compared with the corresponding radio parameters and their errors.

From Table 2 it is clear that the glitch parameters derived using the three models are broadly consistent with each other. It can therefore be concluded that the post-event and pre-glitch solutions of Table 1 are fairly robust, and enhance the confidence in the results of the previous section.

7. Discussion

We conclude from this work that, strictly speaking, the X-ray data by itself cannot unequivocally discriminate between the two hypotheses, but offers reasonable evidence for intrinsic slowing down of the Crab Pulsar during the October 1997 event. However, when coupled with the very accurate radio reference timing model, the X-ray data strongly supports the intrinsic slowing down hypothesis. It may be worthwhile to check the Jodrell data for other occurrences of such slowing down in the Crab Pulsar.

Assuming that the Crab Pulsar indeed slowed down, the implications are the following:

• 1.

  The effect of such extreme events in pulsars with plerions mustbe taken into account while deriving their glitch parameters.

• 2.

  This is probably a slow version of the anti-glitch observed by Archibald et al. (2013) in a magnetar.

• 3.

  The explanation of Akbal et al. (2015) for the observed slowing down of PSR J1119-6127 after a glitch in May 2007 could be the mechanism driving the slowing down in the Crab Pulsar.

Acknowledgments

I thank Francis Graham-Smith for useful and encouraging discussion, and Andrew Lyne for verifying the X-ray timing residual behavior. I thank the referee for useful comments. This research made use of data obtained from the High Energy Astrophysics Science Archive Research Center Online Service, provided by the NASA-Goddard Space Flight Center. It has also made use of data provided by the BeppoSAX satellite.

References

All Tables

All Figures

	Fig. 1 Result of using TEMPO2 on all data with the parameters given in Table 1 of Backer et al. (2000) as constant input (i.e., without any fitting). The lone BeppoSAX data point is at epoch ≈–21 days with a larger error bar. We note that no artificial phase jumps (using PHASE ±1 in the input file to TEMPO2) are required, pointing to the robustness of the radio reference timing model used.
In the text

	Fig. 2 Top panel: result of using TEMPO2 on the X-ray data with the parameters of model 1 in Table 1 as constant input (i.e., without any fitting). The plot is restricted to the post-event and pre-glitch duration, along with four data points before this duration, to better view the event itself. Bottom panel: same as top panel, but using the parameters of model 2 in 1.
In the text