Hitomi X-ray studies of Giant Radio Pulses from the Crab pulsar

Abstract

To search for giant X-ray pulses correlated with the giant radio pulses (GRPs) from the Crab pulsar, we performed a simultaneous observation of the Crab pulsar with the X-ray satellite Hitomi in the 2 – 300 keV band and the Kashima NICT radio observatory in the 1.4 – 1.7 GHz band with a net exposure of about 2 ks on 25 March 2016, just before the loss of the Hitomi mission. The timing performance of the Hitomi instruments was confirmed to meet the timing requirement and about 1,000 and 100 GRPs were simultaneously observed at the main and inter-pulse phases, respectively, and we found no apparent correlation between the giant radio pulses and the X-ray emission in either the main or inter-pulse phases. All variations are within the 2 sigma fluctuations of the X-ray fluxes at the pulse peaks, and the 3 sigma upper limits of variations of main- or inter-pulse GRPs are 22% or 80% of the peak flux in a 0.20 phase width, respectively, in the 2 – 300 keV band. The values become 25% or 110% for main or inter-pulse GRPs, respectively, when the phase width is restricted into the 0.03 phase. Among the upper limits from the Hitomi satellite, those in the 4.5–10 keV and the 70–300 keV are obtained for the first time, and those in other bands are consistent with previous reports. Numerically, the upper limits of main- and inter-pulse GRPs in the 0.20 phase width are about (2.4 and 9.3) ×10⁻¹¹ erg cm⁻², respectively. No significant variability in pulse profiles implies that the GRPs originated from a local place within the magnetosphere and the number of photon-emitting particles temporally increases. However, the results do not statistically rule out variations correlated with the GRPs, because the possible X-ray enhancement may appear due to a > 0.02% brightening of the pulse-peak flux under such conditions.

1. Introduction

Giant Radio Pulses (GRPs) consist of sporadic and short-lived radiation, during which time the radio flux density becomes 2–3 orders of magnitudes brighter than the regular, averaged pulse flux density. So far, this phenomenon has been discovered in ~14 radio pulsars (for a review, see Knight 2006 and references therein), including both “traditional” rotation-powered pulsars (e.g., the Crab pulsar) and millisecond pulsars (e.g., PSR B1937+21). Although the emission mechanism of the GRPs is still unknown, previous radio studies have shown some distinctive properties of the GRPs. The typical temporal width of individual GRPs is narrow, spanning a range from a few nanoseconds to a few microseconds (Hankins et al. 2003). GRPs occur in certain pulse phases with no clear periodicity. The energy spectrum of GRPs follows a power-law distribution (Popov & Stappers 2007; Mikami et al. 2016), different from the Gaussian or log-normal distribution of the normal pulses (Burke-Spolaor et al. 2012). Since studies of the ordinary pulses can only provide average information from the pulsar magnetosphere, observations of GRPs are imperative for furthering our understanding of the pulsar radiation mechanism. More recently, a hypothetical proposal of GRPs from young pulsars as candidates for the origin of fast radio bursts (FRBs; Cordes & Wasserman 2016) have been attracting more and more attention. These phenomena are extragalactic bright radio transients with ~1 msec duration (Lorimer et al. 2007; Thornton et al. 2013; Chatterjee et al. 2017). Seeking to reveal properties of known GRPs, such as identifying their counterparts in other wavelengths, is also a key line of investigation to examine the young pulsar model that could explain FRBs (e.g., Yamasaki et al. 2016; DeLaunay et al. 2016).

The Crab pulsar (PSR B0531+21) is one of the most intensively studied rotation-powered pulsars since the initial discovery of its GRPs (Staelin & Reifenstein 1968). This famous pulsar exhibits GRPs occurring both in the main pulse and the interpulse, which have been mainly studied at radio wavelengths (Popov & Stappers 2007). Since the pulsed energy spectrum of the Crab pulsar covers a wide range, from the coherent radio emission to the incoherent high-energy radiation at optical, X-rays, and gamma-rays, there have been multi-wavelength campaigns to attempt to search for enhancements at higher energy bands, simultaneous with the GRPs. In the optical band, a significant 3% optical enhancement was discovered with 7.2σ significance from the main pulse peak phase by the Westerbork Synthesis Radio Telescope and the 4.2-m William Herschel Telescope (Shearer et al. 2003). This result was further confirmed by the Green Bank Telescope and the Hale telescope (Strader et al. 2013). These detections imply that the coherent radio emission is somehow linked to the incoherent higher energy (optical) radiation. Despite intensive efforts to search at even higher energy bands, so far there are only upper-limits in soft X-rays and higher energy bands. Reports of these upper limits can be found for soft X-rays (Chandra, 1.5–4.5 keV; Bilous et al. 2012), for soft gamma-rays (CGRO/OSSE, 50–220 keV; Lundgren et al. 1995), for gamma-rays (Fermi/LAT, 0.1–5 GeV; Bilous et al. 2011), and for very high energy gamma-rays (VERITAS, >150 GeV; Aliu et al. 2012).

The X-ray astronomical satellite Hitomi (ASTRO-H) was launched on February 17, 2016 via a H-IIA launch vehicle from Tanegashima Space Center in Japan, and successfully entered into a low Earth orbit at an altitude of 575 km (Takahashi et al. 2016). The satellite is designed to cover a wide energy range from 0.3 keV up to 600 keV with four new X-ray instruments: the microcalorimeter (Soft X-ray Spectrometer, SXS; Kelley et al. 2016), a wide field-of-view X-ray CCD detector (Soft X-ray Imager, SXI; Tsunemi et al. 2010), two Si/CdTe hybrid hard X-ray imagers (Hard X-ray Imager, HXI; Sato et al. 2014), and a Compton telescope (Soft Gamma-ray Detector, SGD; Fukazawa et al. 2014). Such a wide energy coverage with high time resolution at a few microseconds (Terada et al. in prep) made Hitomi suitable for the search for X-ray enhancement simultaneously with the GRPs. After initial operations before opening the gate valve of the SXS, including successful observations of the Perseus cluster of galaxies (Hitomi Collaboration et al. 2016) and other supernova remnants (e.g., N132D and G21.5–0.9) the spacecraft lost communications with the ground stations on March 26, and eventually the mission was terminated. Therefore, the energy coverage below 2 keV was lost for the SXS.

On March 25, just before the satellite loss, we observed the Crab pulsar with Hitomi for onboard instrumental calibration activity. The requirement and goal of the absolute timing accuracy of the Hitomi satellite are 350 μs and 35 μs, respectively (Terada et al. in prep). In order to verify the timing tag accuracy, we compared arrival times of the main pulse peak of the Crab pulsar with the radio or X-ray ephemeris provided by other observatories (Terada et al. 2008). The archival monthly radio ephemeris of the Crab pulsar has been regulary provided by the Jodrell-Bank observatory¹ on every 15th monitoring (Lyne et al. 1993). Interpolating from this, the predicted ephemeris of the Crab pulsar timing in Barycentric Dynamical Time (TDB) is tabulated in table 1.

Table 1.

Crab ephemeris in Radio

Parameter	Value
Main pulse	MJD 57472.0000002874260532
Period	0.0337204396077250 s
Pediod derivative	4.1981605 × 10−13 s s−1

Ephemeris of the Crab pulsar determined by the radio observations on 25 March 2016. The ‘Main pulse’ represents the arrival time of the main pulse in the radio band. All values are in TDB.

Arrival times of the radio pulses are known to be delayed from X-rays in proportion to the interstellar dispersion measure (DM). The long-term, averaged DM of the Crab pulsar is ~56.8 pc cm⁻³, corresponding to ~120 ms delay of the 1.4 GHz radio pulses relative to X-rays. Although this radio delay is corrected via radio analyses (de-dispersion), this DM is known to show fluctuation in time with ~0.028 pc cm⁻³ (1σ) of a Gaussian distribution. This corresponds to an intrinsic uncertainty of ~60 μs timing accuracy, higher than our goal for the timing accuracy (35 μs). Therefore, we coordinated follow-up radio observations simultaneous with our X-ray observations to reduce uncertainties due to this fluctuating DM. In this paper, we report X-ray studies of GRPs from the Crab pulsar based on simultaneous X-ray and radio observations. Detailed investigations of the instrumental timing calibration will be summarized in a different paper (Koyama et al. in prep).

2. Observation and Data Reduction

2.1. X-ray and radio simultaneous observation of the Crab pulsar

The X-ray observation of the Crab pulsar was made with all the instruments on board the Hitomi satellite, starting from 12:17 on March 25, 2016 until 18:01 (UT) [TDB] with a total on-source duration of 9.7 ks. The radio observations of the Crab pulsar were made in two frequency bands, (a) 1.4 – 1.7GHz at the Kashima observatory from 03:00:00 to 14:00:00 UTC, and (b) 323.1 – 327.1MHz at the Iitate observatory from 09:30:00 to 13:00:00 UTC. The locations of the observatories are listed in table 1 of Mikami et al. (2016). After the start time of the X-ray observation we idenfitied 3350 GRPs (section 2.2.4) for (a), but only 94 GRPs for (b). In terms of the occurence probability (number of GRPs per minute), the ratio between (a) and (b) was ~19:1. Mikami et al. (2016) reported, on the other hand, that the ratio was ~3:1 on 6 – 7 September 2014. The marked difference between these ratios seems to be caused by refractive interstellar scintilation (RISS; e.g. Lundgren et al. (1995)): While the RISS condition for 1.4 – 1.7GHz would have corresponded to a phase of the intensity larger than the average, the RISS condition for 325MHz would have corresponded to a phase of the intensity smaller than the average. Therefore we concentrate on observation (a) in what follows.

2.2. Data Reduction of Radio observations

2.2.1. Frequency assignment

The radio observation in the 1.4 – 1.7GHz band was made with the 34m telescope at the Kashima Space Technology Center (Takefuji et al. 2016) operated by the NICT (National Institute of Information and Communications Technology). We used the ADS3000+ recorder (Takefuji et al. 2010) which has a capability of 8 individual channels with 4-bit 64MHz Nyquist-rate sampling. (The sampling time step δt is 1/64 MHz=15.625ns, and the data rate 2Gbit/s.) table 2 shows the frequency assignment for 8 channels. Channel 7, the backup for channel 6 with a slight frequency shift, was not used for the following data analysis.

Table 2.

Frequency bands of the Kashima observatory

channel k	frequency (MHz) minimum-maximum	original bandwidth (MHz)	effective bandwidth (MHz) after filterization (Δvk)
ch0	1404–1436	32	20.48
ch1	1570–1602	32	16.00
ch2	1596–1628	32	-
ch3	1622–1654	32	-
ch4	1648–1680	32	24.83
ch5	1674–1706	32	21.82
ch6	1700–1732	32	23.23
(ch7)	(1702–1734)	(32)	-

The frequency range between ch0 and ch1, 1436–1570MHz, is avoided so as to minimize the radio frequency interference (RFI) from cellphone base stations. Only the right-hand circular polarized signals were received. In the coherent dedispersion process for each channel, the timing of the voltage data is adjusted to that for the maximum frequency of the channel.

2.2.2. Determination of DM

We first determined the dispersion measure (DM) appropriate for the epoch of the observation, 25 March 2016 (MJD 57472). While the Jodrell Bank Crab pulsar monthly ephemeris reports the values of 56.7657 pc cm⁻³ (=DM_JB) for 15 March 2016 (MJD 57462), and 56.7685 pc cm⁻³ for 15 April 2016 (MJD 57493), we should take into account possible intra-month variations of DM which are sometimes very erratic (e.g., Kuzmin et al. 2008). With DM_JB as a trial value, we coherently dedispersed (Hankins & Ricket 1975; Lorimer & Kramer 2004) the ch0 data and found several bright GRPs. We then extended the dedispersion analysis to all the channels for ~50 ms intervals including these GRPs. The best value of DM, 56.7731±0.0001 pc cm⁻³ (=DM_best), was obtained so as to get the alignment of the substructures of these GRPs (e.g., Sallmen et al. 1999) in all channels with ~ 0.1μs accuracy. An example of a successful alignment can be seen in Figure 2 of Mikami et al. (2016). The frequency bands LL and LH approximately correspond to ch1 and ch4–6 here.

Fig. 2.

Light curve of the Crab with from Hitomi SXS, HXI within region a, HXI within region b, and SGD-1, from top to bottom panels, respectively. The black croses represent the entire clened events of the Crab with Hitomi, and red shows the same but within the simultaneous intervals with radio observatories.

2.2.3. Frequency-domain RFI rejection

During the process of finding DM_best, we noticed that two channels, ch2 and ch3, were severly contaminated by radio frequency interferences (RFI). Since RFI occurred intermittently, we could still use these channels for the bright GRP search. However, for weaker GRPs search, we excluded ch2 and ch3 from the following analysis. We further noticed that other channels were weakly contaminated by RFI in some limited frequency ranges. To minimize the effect of RFI, we filtered out these contaminated frequency ranges. The numerical filter was applied at the first stage of the coherent dedispersion process, where the time series of antenna voltage data are subjected to FFT (fast Fourier transformation) and decomposed into Fourier components. For the RFI-contaminated frequency ranges, we set their Fourier components to zero. The overlapping frequency ranges for ch4-ch5 and ch5-ch6 are also filtered out at this stage. The rightmost column of table 2 gives the resultant effective bandwidths after filtering. The total effective bandwidth, Δv_sum = Δv₀ + Δv₁ + … + Δv₆, is 106.36MHz.

2.2.4. GRP selection

In the main panel of figure 1 dots show all GRP candidates with a S/N (signal to noise ratio) >5.5 (or pulse energy >~2.2 kJy μs, see Appendix 1), where dots are sized and color-coded with the values of S/N. The abscissa and ordinate of the panel represent the time in TDB and the pulsar rotation phase ‘ respectively. The top panel of figure 1 shows the time intervals subjected to the time-domain RFI rejection (see Appendix 1) in black (OFF), and the time intervals kept, in red (ON). In total, 571s (5729s) in time intervals were rejected (kept).

Fig. 1.

In the main panel GRP candidates (S/N>5.5) are shown in the (TDB, φ) plane, where two clusters in φ are of main pulse and interpulse GRPs (see text). Scatterd points show the remaining noise contribution. The threshold S/N=5.5 corresponds to the minimum pulse energy 2.2 kJy μs. The strongest main pulse occurred at 13:07:25.645TDB had the peak S/N~ 659. It spreaded over ~40μs interval having the total pulse energy 358 kJy μs.

As can be seen in figure 1 there are two clusters of GRP candidates in φ. We adjusted the initial value of φ at 00:00:00TDB (y₀ in (A6)) so as to locate the peak of the main cluster at φ=0, which is the main pulse GRPs (hereafter we call them the “MP-GRP”). The second cluster found around φ =0.4056 corresponds to the inter-pulse GRPs (hereafter “IP-GRP”). Scattered points also seen in figure 1 are due to the noise component. With the selection criteria, (1) −0.0167 ≤ φ ≤ +0.0167 for the MP-GRPs and (2) 0.3889 ≤ φ ≤ 0.4222 for the IP-GRPs, we identified 3090 MP-GRPs and 260 IP-GRPs during the interval between 12:15:00TDB and 14:00:00TDB. We estimated the noise contributions in terms of fake GRPs to be 11 ± 3 (0.4±0.1% and 4±1% for the MP- and IP-GRPs, respectively.) The pulse energy distributions of GRPs have power-law shapes with the spectral indices −2.88 ± 0.52 for the MP-GRPs and − 2.91 ± 1.13 for the IP-GRPs.

2.3. Data Reduction of Hitomi observation

The X-ray data obtained with the Hitomi satellite were processed by the standard Hitomi pipeline version 03.01.005.005 (Angelini et al 2016) with the pre-pipeline version 003.012.004p2.004 using the hitomi ftools in the HEAsoft version 6.20, with CALDB versions gen20161122, hxi20161122, sgd20160614, sxi20161122, and sxs20161122. In the timing analyses of Hitomi data in the following sections, the SXI and SGD-2 data were not used, because the timing resolution of the SXI was insufficient for the analyses and the SGD-2 was not in the nominal operation mode during the simultaneous epoch with the radio observation.

The standard cleaned events were used for the SXS and HXI analyses; the low resolution events (ITYPE == 3 or 4; Kelley et al. 2016) of the SXS events were not excluded in order to maximize the statistics, although the time resolution of the low resolution events was worse (80 μs) than those of high or med resolution events (5 μs). The HXI data were extracted using a sky image region around the Crab pulsar, out to 70 arcsec radius from the image centroid. On the analyses of the SGD-1 data, the photo-absorption events were extracted as described in Appendix 2. At this stage, the total exposure times of the Hitomi Crab observation were 9.7, 8.0, and 8.6 ksec for the SXS, HXI, and SGD, respectively. The background-inclusive light curves of these data were shown in Fig. 2 black. Note that no energy selection were applied to the events; the rough energy band for the SXS, HXI, and SGD-1 photo absorption events were 2 – 10 keV, 2 – 80 keV, and 10 – 300 keV, respectively.

The TIME columns of all the event lists of SXS, HXI, and SGD-1 were converted into a barycentric position using the “barycor” ftool in the hitomi package of HEAsoft 6.20 and the hitomi orbital file (Terada et al. in prep). The target position for the barycentric correction was (R.A., DEC) = (83.°633218, +22.°014464) for this analyses. The period and period derivatives determined only with the Hitomi data were consistent with the ephemeris from the radio summarized in table 1. As described in Terada et al. (in prep) and Koyama et al. (in prep), the time differences between instruments were negligible for the timing analyses of the giant radio pulses reported here.

Finally, all the good time intervals of the radio observation were applied to the Hitomi Crab data, which then results in a shorter duration, as shown in Fig. 2 (red). Consequently, the total exposure times for the SXS, HXI, and SGD-1 that were simultaneously observed with the radio observatories become 2.7, 1.7, and 2.1 ks, respectively. About 10³ GRP cycles were exposed among (5 – 6)×10⁴ cycles by each instrument, as summarized in table 3.

Table 3.

Statistics of GRPs during the simultaneous observation

Instrument	Exposure	# of cycles	MP-GRPs	IP-GRPs
SXS	2.2 ks	64,701	1,171	103
HXI	1.7 ks	50,705	945	85
SGD	2.1 ks	63,197	1,144	98

Total exposures, number of cycles of pulsar pulses, and number of GRPs for main and inter pulses, during the simultaneous observation between radio observatories and Hitomi instruments.

3. Analyses and Results

In this section, we used the cleaned events of Hitomi SXS/HXI/SGD instruments obtained at the end of the section 2.3 and the pulsar ephemeris in table 1.

3.1. Variation of the Pulse Profiles in GRPs

Most significant MP- and IP-GRPs, shown as large circles in figure 1, were detected at 12:46:44 and 12:54:10 (TDB) on 25 May 2016, respectively, but no significant variations were seen in the X-ray photons before and after the GRPs. Therefore, we then try to stack X-ray events which were correlated with MP-or IP-GRPs to see a possible enhancement in the X-ray band. X-ray events within one cycle of each MP-GRP (hereafter we call them the “MP-GRP cycles”) were accumulated between φ = −0.5 to +0.5 phases from the arrival time of the main pulse of the radio-defined MP-GRPs (i.e., φ = 0). The events outside the MP-GRP cycles were defined as “NORMAL cycles” and were accumulated for comparison. Both groups of events were folded by the radio ephemeris in table 1 to see the pulse profiles of MP-GRP and NORMAL cycles. As shown in the top panels of the left-hand plots in figure 3, no major enhancements could be seen between the two profiles. The difference between the two, shown in the bottom panels, was consistent with being statistically constant among all the instruments and along all of the phases (−0.5 ≤ φ ≤ 0.5). Note that the pulse profile of the Crab pulsar with the SXS is free from a possible distortion by the dead time, which occurs in > 5 s on the SXS. Similarly, the distortion of the profiles of the HXI and SGD can be also ignored in comparison between the GRP and NORMAL shapes, although the absolute fractions of the dead to live times were about 75% (Section 3.3). The same analyses were performed for the inter-pulse GRPs (hereafter, “IP-GRP cycles”), and no significant enhancement between pulse profiles at IP-GRP and another NORMAL cycles was found, as seen in figure 3 (right). The statistical errors were very high on the Hitomi datasets, both in MP- and IP-GRPs.

Fig. 3.

Comparison of Crab pulse profiles between the NORMAL and the GRP cycles, which were shown in blue and red, respectively, and the green croses in the each bottom panel show the difference between them. The left and right panels were the plots of the MP-GRPs and IP-GRPs, respectively, and from the top to the bottom, the data taken by the SXS, HXI, SGD-1, and combined data were plotted, respectively.

In order to see some possible enhancements in several cycles around the GRPs in a wider time range, we then accumulated the events from 2 cycles before, to 2 cycles after the MP-GRPs; i.e., five pulses −2.5 < φ < 2.5 were plotted where − 0.5 ≤ φ ≤ 0.5 corresponds to the MP-GRP cycle. Similar to the previous single-pulse analyses, the NORMAL cycles, here, were defined outside the 5 cycles around the MP-GRPs. The results were shown in figure 4. According to the time intervals between GRPs, about 0.7 % and 2.4% of MP-GRPs were contaminated within ±1 or ±2 cycles from the GRP, respectively. To estimate the statistical errors on the pure-pulsed components, the non-pulsed counts accumulated from the OFF phase (φ = 0.6 – 0.8) were subtracted from the pulse profiles of the MP-GRP and NORMAL cycles. Several possible enhancements could be seen in several main pulses in the soft energy band by the SXS in the top panels of figure 4, however, the significance was all below 2 σ as indicated in the bottom panels, and no corresponding enhancement was seen in the hard X-ray band by the HXI. The same study could be performed for IP-GRPs but the statistical errors were very high and the results were the same as for the MP-GRP cases. Therefore, no enhancements were detected in all phases among five cycles around GRPs from the Hitomi data.

Fig. 4.

The top plots in each panel show the same pulse profiles of NORMAL and on/near GRP cycles represented by blue and red lines, respectively. The counts in off-phase (φ = 0.6 – 0.8) of the NORMAL cycles were subtracted from these pulse profiles. The bottom plots in each panel represent the ratio of the enhancement of near GRP data relative to the NORMAL cycles, which was shown in green. The data during the OFF phase were not plotted here. The statistical uncertainties of each phase bin at 1 and 2 sigma were shown in thick and thin black lines, respectively. The SXS, HXI, SGD-1, and combined data were shown from top to bottom panels, respectively.

3.2. Pulse peak enhancement at GRPs

Since no significant enhancement found in five cycles before/after GRPs (section 3.1), we then concentrated on the statistical tests of possible enhancements at the peak of pulses. Here, we compared the non-pulse subtracted peak-counts (C_grp) of main- or inter-pulses of MP-GRP or IP-GRPs with those of corresponding NORMAL cycles (C_nor). In this comparison, we defined four types of phase widths (Δφ) to accumulate the peak counts; i.e., Δφ = 0.20 phases (covering main- or inter pulses), 1/11, 1/31, and 1/128 phases. The enhancement of C_grp from C_nor accumulated within Δφ can be defined as $\xi (\mathrm{\Delta }\phi )\equiv \frac{C_{\text{grp}}(\mathrm{\Delta }\phi )-C_{\text{nor}}(\mathrm{\Delta }\phi )}{C_{\text{nor}}(\mathrm{\Delta }\phi )}$. The table 4 summarize ξ(Δφ) of each Δφ, shown in the percentage, for each instrument, with the significance to the statistical errors. As a result, no larger than a 2 sigma enhancement was detected around GRPs in all cases. The fluctuation got smaller when we restricted the phase width for MP-GRPs due to the sharp pulse profile of the main pulse, except for the Δφ = 1/128 ~ 0.008 phase-width cases with poorer photon statistics, although such a trend could not be seen for the inter-pulses that had a shallower shape.

Table 4.

Summary of enhancements in X-ray flux at GRPs

Instrument	pulse	0.0078 phase†	0.0322 phase†	0.091 phase†	0.200 phase†
SAS	main pulse	1% (0.0σ)	10% (0.7σ)	1% (0.1σ)	7% (0.6σ)
SXS	inter pulse	310% (1.6σ)	93% (1.3σ)	55% (1.1σ)	31% (0.6σ)
HXI	main pulse	11% (0.5σ)	−2% (−0.2σ)	−5% (−0.6σ)	6% (0.7σ)
HXI	inter pulse	136% (1.4σ)	78% (1.3σ)	29% (0.9σ)	49% (1.5σ)
SGD	main pulse	−116% (1.2σ)	−39% (0.7σ)	−43% (−1.0σ)	−59% (−1.4σ)
SGD	inter pulse	310% (1.6σ)	93% (1.3σ)	55% (1.1σ)	31% (0.6σ)
Combined	main pulse	8.9% (0.5σ)	5.1% (0.6σ)	−0.8% (−0.1σ)	13.2% (1.8σ)
Combined	inter pulse	195% (2.2σ)	45% (1.2σ)	50% (1.8σ)	66.5% (2.4σ)

^†the phase width (Δφ).

The values represent the enhancement ξ(Δφ) (%) and values in parentheses show the significance in the standard deviation of each to the statistical errors.

To test the enhancement ξ(Δφ) at the snapshot on GRP (φ = 0), same trials were repeated for 29 cycles around the GRP, i.e. the 14 cycles before to the 14 cycles after the MP-GRP or IP-GRPs (−14.5 ≤ φ ≤ 14.5) as plotted in figure 5. Therefore, a possible enhancement at φ = was within the fluctuations of ξ(Δφ) in other cycles to within 2σ variations for 28+1 cycles. Numerically, the 3 σ upper limits of the variations at the MP-GRP during the main-pulse phases (i.e., φ = −0.1 – 0.1, with 0.200 phase-width in figure 5) will be ξ_MPGRP(0.200 phase) = 40, 30, and 110 % of the X-ray flux in the NORMAL cycles, with the SXS, HXI, and SGD, corresponding roughly to the 2 – 10, 2 – 80, 10 – 300 keV bands. Similarly, the 3 σ upper limits for the IP-GRP during inter-pulse phases (φ = 0.3 – 0.5) were ξ_IPGRP(0.200 phase) = 130, 90, and 420 % in the same energy bands listed above, respectively. When all of the instruments (i.e., the SXS, HXI, and SGD-1) were used for this study, the upper-limit values become tighter at ξ(0.200 phase) = 22% and 80% of the NORMAL cycles for the MP- and IP-GRPs, respectively. In addition, in order to see a possible enhancement on a short-time scale around the peaks of pulses, as had been seen in the optical observations (Shearer et al. 2003; Strader et al. 2013), the enhancements of MP- and IP-GRPs accumulated within the Δφ = 1/31 ~ 0.03 phase-width were also numerically checked, ξ(0.03 phase) = 25% and 110% for MP- and IP-GRPs were obtained. The 3-σ upper limits of ξ from the 29-cycles study were summarized in table 5.

Fig. 5.

The enhancement of inter or main pulses on the MP-GRP or IP-GRP were shown in the left and right plots, respectively. From the top to bottom panels, the SXS, HXI, SGD-1, and combined data were shown, respectively. The enhancements of GRP relative to normal cycles were measured at the corresponding pulse peaks (i.e., inter pulse of main pulse) with 0.0078, 0.0322, 0.0909, and 0.200 phase widths, which were shown from top to bottom in each plot. The enhancement, as a percentage, was shown in red, and statistical uncertainties of 1 and 2 sigma were shown in blue and green colors, respectively.

Table 5.

Upper limit of enhancement of GRP (3σ)

Instrument	Energy band	MP-GRP	IP-GRP
Δφ = 0.2000 phase
SXS	2 – 10 keV	40%	130%
HXI	5 – 80 keV	30%	90%
SGD	10 – 300 keV	110%	420%
all	2 – 300 keV	22%	80%
Δφ = 0.0322 phase
SXS	2 – 10 keV	90%	180%
HXI	5 – 80 keV	40%	200%
SGD	10 – 300 keV	200%	1100%
all	2 – 300 keV	25%	110%

The “all” represents the sum of SXS, HXI, and SGD instruments.

3.3. Upper limit of Enhanced Peak flux

To convert the enhancement of GRP in count rate into an X-ray flux, the X-ray spectra of purely pulsed components (i.e., main and inter pulses) were numerically tested. First, the SXS and HXI events were extracted by phases, φ = −0.1 – 0.1, φ =0.3 E 0.5, and φ = 0.6 -E0.8, corresponding to the main-pulse (MP), inter-pulse (IP), and off (OFF) phases, respectively, and the pulse-height distributions were accumulated. The dead time correction was applied to the HXI data with the Hitomi ftools, hxisgddtime; the live time of the HXI-1 and HXI-2 were 73.9 % and 76.6 % for this observation. Only the high-primary and the medium-primary grades (Hp and Mp grades, respectively, defined in Kelley et al. 2016) were accumulated in the SXS spectral analyses here in order to reduce systematic errors in the response matrix. The X-ray spectra of the pure pulsed components were calculated by subtraction of the OFF-phase spectrum from the MP or IP spectra. Thanks to the fine timing resolutions of the SXS, HXI, and SGD (Terada et al. in prep), the X-ray spectra of the pure-pulsed components were clearly demonstrated in figure 6.

Fig. 6.

Left and right panels show the X-ray spectra during the main and inter pulses, respectively. The spectra with the SXS and the HXI are shown in black and red crosses, respectively. The best-fit power-law models are shown in red and black lines for the SXS and HXI, respectively. The bottom panels represent the ratio between the data and the model.

To perform spectral fitting of the MP and IP spectra, the spectral response matrices were generated with the Hitomi ftools sxsmkrmf and aharfgen, with the exposure map calculated for the HXI and SXS using the ftools sxsregext and ahexpmap, respectively. The result was that the MP and IP spectra were well reproduced by a single power-law model with a photon indices of 1.94 ± 0.02 and 1.87 ± 0.02 and X-ray fluxes of (4.7±0.1)×10⁻⁹ and (4.4±0.5)×10⁻⁹ ergs cm⁻² s⁻¹ in the 2 – 10 keV band with the reduced χ² of 305.85 and 301.18 for 250 degrees of freedom, respectively, as shown in the figure 6. The pulsed flux obtained with Hitomi accumulated within the time interval of Δφ phase was summarized in table 6. Therefore, the 3 σ upper limit values of enhancement in terms of flux can be obtained by multiplying the values in table 5 (section 3.1) with those in table 6. The upper limits of enhancements of MP-GRPs in the X-ray flux in the 2 – 300 keV band within the phases of 0.20 or 0.03 become (24 or 3.3)×10⁻¹² erg cm⁻², respectively, and the same for IP-GRPs were (93 or 9.9) × 10⁻¹² erg cm⁻², respectively.

Table 6.

Pulsed flux of Crab pulsar

Instrument	Energy band	Δφ	Main pulse†	Inter pulse†
SXS	2 – 10 keV	0.20	31 ± 5	30 ± 4
HXI	5 – 80 keV	0.20	${59}_{-8}^{+9}$	62 ± 9
SGD	10 – 300 keV	0.20	${76}_{-10}^{+11}$	87 ± 13
all	2 – 300 keV	0.20	${108}_{-16}^{+15}$	116 ± 17
SXS	2 – 10 keV	0.03	4.0 ± 0.6	2.7 ± 0.4
HXI	5 – 80 keV	0.03	7.0 ± 1.0	5.0 ± 0.8
SGD	10 – 300 keV	0.03	10 ± 2	6.9±1.5
all	2 – 300 keV	0.03	13 ± 2	9.0 ±1.5

^†X-ray flux in 10⁻¹² erg cm⁻² at the energy band accumulated within the phase-with (Δφ).

4. Discussion

With the simultaneous observations of the Crab with Hitomi and Kashima radio observatory, the correlation studies in the X-ray band with about 1,000 GRPs have been performed (Section 2). No significant changes in the X-ray pulse profiles were detected along all the phase bins at the GRP cycles (Section 3), and the 3-σ upper-limit values for the MP-GRPs in the 2 – 300 keV band with Hitomi were ξ = 22% and 80% within the time interval of Δφ = 0.200 phase, as summarized in table 5. The upper limits in the 4.5 – 10 keV and the 70 – 300 keV were obtained for the first time with Hitomi, and those in other bands were consistent with previous works (Mikami et al. 2014; Bilous et al. 2012) as shown in Fig. 7. Our result constitutes the second case of a study in the hard X-ray band where the flux (in vF_v space) of the pulsed component of the Crab pulsar became the highest, following a previous report of a marginal detection at the 2.7σ level with Suzaku Mikami et al. (2014). Our results were mainly limited by the photon numbers in the X-ray band, and the statistical errors dominated the results. The pulse shape in the X-ray band was observationally confirmed to be stable with the 1 σ fluctuation of ~ 0.7 % level by RXTE showing about-two-times intensive pulses (Patt et al. 1999; Vivekanand 2001), which could be shallow “giant X-ray pulses” (GXPs) but the timing correlations between these shallow GXPs and the GRPs were unknown. In our X-ray correlation study using the Hitomi satellite, we could not identify such GXPs due to a poor effective area.

Fig. 7.

The enhancement of MP-GRPs of Crab pulsar in various energy bands obtained by the Hilliam Herschel Telescope (Shearer et al. 2003), Hale telescope (Strader et al. 2013), Chandra (Bilous et al. 2012), Suzaku (Mikami et al. 2014), Hitomi (this work), CGRO (Lundgren et al. 1995; Ramanamurthy & Thompson 1998), Fermi (Bilous et al. 2011), and VERITAS (Aliu et al. 2012) All the upper limits shown in arrows represent 3 σ values. The red and blue cases indicate the enhancement measured in a short-phase width (Δφ = 0.02 – 0.03 phase) and wider-phase width (Δφ > 0.1), respectively. Note that the thresholds of GRP detections in the radio band were different among them.

As described in section 3.1, no significant variabilities were detected in the X-ray pulse profiles of 14 cycles before and after the GRPs. Similarly, in the optical band, the enhancements related to the GRPs only happen in narrow time intervals (~ 100 μs) at the pulse peak, and the pulse profiles in other phases were stable (Shearer et al. 2003). These facts indicated that the magnetosphere is stable during the GRPs, which should originate from a local place within the magnetosphere.

What happens during the GRP on the pulsar, when the structure of the magnetosphere does not change? Here, we assumed the emission mechanism of the optical pulses is synchrotron emission, like X-ray pulses, because the optical emission seems to have the same origin as that of the X-rays from the multi-wavelength spectrum of the pulsed component of the pulsar (e.g. see Bühler & Blandford 2014). To increase the synchrotron emission temporarily on a short time scale of μs, whilst maintaining the structure of the magnetosphere, only two candidates can be considered; a) an increase in the number of particles for radiation, or b) a change in the local magnetic field strength. However, case b) would be considered difficult to achieve normally, and the pulse phase needs not be aligned to the main or inter pulses, and therefore it is straightforward to think that the case a) is the origin of the optical enhancement at GRPs. Such occasion might occur after a magnetic reconnection near the light cylinder (Istomin, Y. N. 2004) resulting a higher density plasma than the Goldreich-Julian density in the GRP region (Lyutikov, M. 2007). In the Crab pulsar, the emission regions for the radio, optical, and X-rays are normally considered to be close to each other because the pulses are well aligned in these energy bands, although the pulse profile in the X-ray band is wider than that in radio. If the number of particles for synchrotron emission increases in a local region that emits very short GRPs, a possible X-ray enhancement should also occur very shortly, within about 10 μs just on the pulse peak, like the optical and radio cases. If such short enhancement will be detected in the X-ray band, we are able to reinforce the idea a), but the fine pulse profiles divided by 1/128 phases with Hitomi (Fig. 3) do not show such enhancement at the peak statistically.

Finally, we discuss the energy balance between the X-ray upper limit of the pulse-peak flux (ξ) and the radiation energy of GRP in the radio band, E_radio. As described in section 3.2, the enhancement at the pulse peak ξ were within the 2 ˙ fluctuation among the 29 cycles around GRPs, and the upper limit of ξ in flux were obtained at about 3.3 × 10⁻¹² erg cm⁻² accumulated in the time interval of Δφ = 0.03 phase. The threshold of detection of GRPs in our radio observation was 2.2 kJy·μs (Section 2.2.4), which corresponds to a total emission-energy par area of E_radio > 2.2 × 10⁻¹⁷ erg cm⁻² in a 10 μs accumulation under the assumption that the GRP pulses emit with 1 GHz-width in the radio (Mikami et al. 2016). Interestingly, the optical enhancement of ξ_opt(0.003 phase) = 3% reported by Shearer et al. (2003) within 100 μs bin corresponds to a roughly-equivalent energy with E_radio. Therefore, here we assume that the radiation energy of possible X-ray enhancement is almost equivalent to E_radio, although the pulsed energy spectrum of Crab (e.g. Bühler & Blandford 2014) indicates that the optical light and X-rays have different origins. If an X-ray detection is performed with rather wide phase-bins (Δφ= 0.20 phase around the peak), it appears at ξ_X(0.20 phase) = 2× 10⁻⁵ % of the X-ray normal pulses in the 2 – 300 keV band within the same phase-bins. This enhancement appears better at the ξ_X(0.0003 phase) = 0.02 % of normal pulse flux when the X-ray observation can resolve the 10 μs time-bin at the pulse peak. But the value is still undetectable under the poor statistics of our Hitomi data and the timing accuracy (Terada et al. in prep). Therefore, the results did not statistically rule out variations correlated with the GRPs, because the possible X-ray enhancement may appear as > 0.02% brightening of the pulse peak under such conditions. We can expect future X-ray missions with larger effective area and better timing capability, such as the recently-launched NICER mission (Gendreau et al. 2016), for continuing the X-ray correlation studies of GRPs. If the GXPs appears in short-phase bins and are correlated with GRPs, NICER may detect the enhancement in X-ray band, althoufh the sensitivity peak of NICER is at a softer energy band than that of the previous, larger area mission RXTE, so the count rate expected for Crab pulses is comparable.

Appendix 1. Details for radio data reduction

A.1.1. TEMPO2 timing package

The pulsar timing package TEMPO2 (Hobbs et al., 2006) gives the function $\tilde{f}\left(t_{\text{UTC}}\right)$ to convert the observation time in UTC, t_UTC, to the time at the solar system barycenter (TDB), ${\tilde{t}}_{\text{TDB}}$. TEMPO2 also gives the signal frequency v_ISM in the rest frame of the interstellar matter (ISM) corresponding to the observation frequency v_obs, which is Doppler shifted by the revolutionary+rotationary motion of the earth with respect to the solar system barycenter. We defined the Doppler factor η ≡ v_obs/v_ISM.

A.1.2. Calculations of S/N

We dedispersed the raw antenna voltage data of the channel k, $V_k^{\text{raw}}(t)$, to obtain V_k(t). We integrated² |V_k(t)|² over the time interval of Δt=10 μs,

$${\mathcal{E}}_k\left(t_n\right)=\frac{1}{\mathrm{\Delta }t}{\int }_{t_n}^{t_{n+1}}{|V_k\left(t^{\prime }\right)|}^{2}d{t}^{\prime }$$ (A1)

where we defined the binned times as t_n = t_start + nΔt (Here we represent t and t_n by UTC. t_start=12:15:00 UT.) Between the channel k and 6, there is an arrival time difference owing to the propagation group delay,

$${\tau }_{k,6}=\frac{e^2}{2\pi m_{e}c}DM\left\{\frac{1}{{\nu }_k^2}-\frac{1}{{\nu }_6^2}\right\}\eta$$ (A2)

where (e, m_e, c) are usual physical quantities, DM the dispersion measure, and v_k and v₆ the highest frequencies of the bands k and 6. The Doppler factor η appears in equation (A2) since τ_k,6, v_k, and v₆ are defined in the observer’s frame. We combined incoherently ${\mathcal{E}}_0\left(t_n\right),{\mathcal{E}}_1\left(t_n\right),..,{\mathcal{E}}_6\left(t_n\right)$, as,

$${\mathcal{E}}_{\text{sum}}\left(t_n\right)=\sum _{k=0,1,4,5,6}{\mathcal{E}}_k\left(t_n-{\tau }_{k,6}\right)$$ (A3)

where appropriate interpolations were taken to calculate the RHS of equation (A3).

We calculated the average ${\overline{\mathcal{E}}}_{\text{sum}}$ and standard deviation σ_sum of ${\mathcal{E}}_{\text{sum}}\left(t_n\right)$ over an appropriate longer time interval (ΔT, for which we take 1s). Ideally ${\overline{\mathcal{E}}}_{\text{sum}}$ and σ_sum are constant in time. In reality, however, they showed slight and gradual variations in time T_M(= t_start +MΔT; M = 0,1,2…). We calculate the signal-to-noise ratio (S/N) at t_n for T_M ≤ t_n < T_M+1 as

$${\mathcal{S}}_{\text{sum}}\left(t_n\right)=\frac{1}{{\sigma }_{\text{sum}}\left(T_M\right)}\left({\mathcal{E}}_{\text{sum}}\left(t_n\right)-{\overline{\mathcal{E}}}_{\text{sum}}\left(T_M\right)\right)$$ (A4)

With a given threshold ${\mathcal{S}}_{\text{sum,}\text{thr}}$ we selected ‘GRP candidates’ for each one in which there was an enhancement³, ${\mathcal{S}}_{\text{sum}}\left(t_n\right)>={\mathcal{S}}_{\text{sum,}\text{thr}}$.

A.1.3. Time-domain RFI rejection

To eliminate RFI further, we conducted the following auxiliary process: We calculated the squared antenna voltages ${\mathcal{E}}_k^{\text{raw}}\left(t_n\right)$ following equation (A1) except that we used $V_k^{\text{raw}}(t)$ instead of V_k(t). From ${\mathcal{E}}_k^{\text{raw}}\left(t_n\right)$ we then calculated

$${\mathcal{E}}_{\text{sum}}^{\text{raw}}\left(t_n\right)\equiv \sum _{k=0,1,4,5,6}{\mathcal{E}}_k^{\text{raw}}\left(t_n\right)$$ (A5)

and their average and standard deviation, ${\overline{\mathcal{E}}}_{\text{sum}}^{\text{raw}}\left(T_M\right)$ and ${\sigma }_{\text{sum}}^{\text{raw}}\left(T_M\right)$. We watched the behaviors of σ_sum(T_M) and ${\sigma }_{\text{sum}}^{\text{raw}}\left(T_M\right)$ throughout the observation interval. When ${\sigma }_{\text{sum}}\left(T_M\right)<{\sigma }_{\text{sum}}^{\text{raw}}\left(T_M\right)$, we reject the data ${\mathcal{S}}_{\text{sum}}\left(t_n\right)$ for T_M ≤ t_n < T_M+1, as affected by RFIs.

A.1.4. Rotation phase and GRP identification

We calculated the phase φ_n of a GRP candidate at the time in UTC t_n,

$${\phi }_n=\mathit{frac}(y)\text{ with }y=y_0+{\nu }_{\text{rot}}{\tilde{t}}_n+0.5{\dot{\nu }}_{\text{rot}}{\tilde{t}}_n^2,$$ (A6)

where ${\tilde{t}}_n=\tilde{f}\left(t_n\right)$ is the time in TDB, frac(y) the fractional part of y, y₀ the initial phase at 00:00:00 TDB, v_rot and ${\dot{v}}_{\text{rot}}$ the rotation frequency and its time derivative from the Jodrell bank monthly ephemeris (table 2). In the operation of equation (A6), we also recorded the integer part of y as the sequential pulse number of the day, N_pulse, which is to be used for the GRP and X-ray photon comparison.

As discussed in section 2.2.4 we classify the GRP candidates according to their values of φ by setting two selection ranges, (φ_MP,1, φ_MP,2) for main pulse GRPs, and (φ_IP,1, φ_IP,2) for interpulse GRPs. With the choice of Δt=10μs, two thirds of GPR candidates in the 1.4–1.7GHz band are isolated in the φ space. However, for the remaining one third of (stronger) GRPs, 2~4 GRP candidates of the same N_pulse are found in the same selection range for φ. For such cases, we count them as one GRP, either main pulse or interpulse.

For a GRP occurring near the binned time boundary t = t_n, its contribution is divided into ${\mathcal{E}}_{\text{sum}}\left(t_n\right)$ and ${\mathcal{E}}_{\text{sum}}\left(t_{n+1}\right)$, and the corresponding ${\mathcal{S}}_{\text{sum}}\left(t_n\right)$ and ${\mathcal{S}}_{\text{sum}}\left(t_{n+1}\right)$ are artificially lowered (sometimes both are less than ${\mathcal{S}}_{\text{sum,}\text{thr}}$). To avoid mal-counting of GRPs caused by this effect, we repeated the procedure from equation (A1) to equation (A4) for the binned time with a shift of Δt/2: Firstly, we calculate

$${\mathcal{E}}_k\left(t_{n+\frac{1}{2}}\right)=\frac{1}{\mathrm{\Delta }t}{\int }_{t_n+\frac{\mathrm{\Delta }t}{2}}^{t_{n+1}+\frac{\mathrm{\Delta }t}{2}}{|V_k\left(t^{\prime }\right)|}^{2}d{t}^{\prime }$$

If the resultant ${\mathcal{S}}_{\text{sum}}\left(t_{n+\frac{1}{2}}\right)$ exceeds ${\mathcal{S}}_{\text{sum},\text{thr}}$, this GRP is ‘rescued from the sea of the noise’. We found that about 10% of GRPs are thus rescued.

A.1.5. Radiometer equation

The flux density $\mathcal{F}$ is calculated as C × (S/N) with C given by the radiometer equation (Dicke, 1946; Lorimer and Kramer, 2004),

$$C=\frac{\text{SEFD}+S_{\text{CN}}}{\sqrt{\mathrm{\Delta }{\nu }_{\text{sum}}\mathrm{\Delta }t}}[\text{Jy}]$$ (A7)

where SEFD is the system equivalent flux density, and S_CN is the flux density of the Crab nebula. With the representative values, SEFD = 500Jy and S_CN = 810Jy (Mikami et al., 2016), we get C = 40.2Jy for Δv_sum=106.36MHz (section 2.2.3) and Δt=10μs. The GRP threshold S/N = 5.5 used in section 2.2 corresponds to a flux density threshold of $\mathcal{F}=220\text{Jy}$, or a pulse energy threshold $\mathcal{F}\mathrm{\Delta }t=2.2\text{kJy}$ μs.

Appendix 2. Extraction of the SGD photo absorption mode

On the timing analyses of the SGD-1 data in section 2.3, the photo-absorption events were extracted from the un-screened event files to have more effective areas than those of the standard Compton scattered events; an expression that ”FLAG LCHKMIO==b0 && FLAG CCBUSY[1]==b0 && FLAG CCBUSY[2]==b0 && FLAG CCBUSY[3]==b0 && FLAG HITPAT[1]==b0 && FLAG HITPAT[2]==b0 && FLAG HITPAT[3]==b0 && FLAG HITPAT[4]==b0 && FLAG FASTBGO[1]==b0 && FLAG FASTBGO[2]==b0 && FLAG FASTBGO[3]==b0 && FLAG FASTBGO[4]==b0 && FLAG SEU==b0 && FLAG LCHK==b0 && FLAG CALMODE==b0 && FLAG TRIGPAT[29]==b0 && CATEGORY==85 && MATTYPE==1 && NUMSIGNAL==1 ” were applied to the ufa event and standard GTI in the 2nd extension of the cleaned events were also applied.