Hitomi X-ray studies of Giant Radio Pulses from the Crab pulsar
Hitomi Collaboration Felix Aharonian Hiroki Akamatsu Fumie Akimoto Steven W. Allen Lorella Angelini Marc Audard Hisamitsu Awaki Magnus Axelsson Aya Bamba Marshall W. Bautz Roger Blandford Laura W. Brenneman Gregory V. Brown Esra Bulbul Edward M. Cackett Maria Chernyakova Meng P. Chiao Paolo S. Coppi Elisa Costantini Jelle de Plaa Cor P. de Vries Jan-Willem den Herder Chris Done Tadayasu Dotani Ken Ebisawa Megan E. Eckart Teruaki Enoto Yuichiro Ezoe Andrew C. Fabian Carlo Ferrigno Adam R. Foster Ryuichi Fujimoto Yasushi Fukazawa Akihiro Furuzawa Massimiliano Galeazzi Luigi C. Gallo Poshak Gandhi Margherita Giustini Andrea Goldwurm Liyi Gu Matteo Guainazzi Yoshito Haba Kouichi Hagino Kenji Hamaguchi Ilana M. Harrus Isamu Hatsukade Katsuhiro Hayashi Takayuki Hayashi Kiyoshi Hayashida Junko S. Hiraga Ann Hornschemeier Akio Hoshino John P. Hughes Yuto Ichinohe Ryo Iizuka Hajime Inoue Yoshiyuki Inoue Manabu Ishida Kumi Ishikawa Yoshitaka Ishisaki Masachika Iwai Jelle Kaastra Tim Kallman Tsuneyoshi Kamae Jun Kataoka Satoru Katsuda Nobuyuki Kawai Richard L. Kelley Caroline A. Kilbourne Takao Kitaguchi Shunji Kitamoto Tetsu Kitayama Takayoshi Kohmura Motohide Kokubun Katsuji Koyama Shu Koyama Peter Kretschmar Hans A. Krimm Aya Kubota Hideyo Kunieda Philippe Laurent Shiu-Hang Lee Maurice A. Leutenegger Olivier O. Limousin Michael Loewenstein Knox S. Long David Lumb Greg Madejski Yoshitomo Maeda Daniel Maier Kazuo Makishima Maxim Markevitch Hironori Matsumoto Kyoko Matsushita Dan McCammon Brian R. McNamara Missagh Mehdipour Eric D. Miller Jon M. Miller Shin Mineshige Kazuhisa Mitsuda Ikuyuki Mitsuishi Takuya Miyazawa Tsunefumi Mizuno Hideyuki Mori Koji Mori Koji Mukai Hiroshi Murakami Richard F. Mushotzky Takao Nakagawa Hiroshi Nakajima Takeshi Nakamori Shinya Nakashima Kazuhiro Nakazawa Kumiko K. Nobukawa Masayoshi Nobukawa Hirofumi Noda Hirokazu Odaka Takaya Ohashi Masanori Ohno Takashi Okajima Kenya Oshimizu Naomi Ota Masanobu Ozaki Frits Paerels Stéphane Paltani Robert Petre Ciro Pinto Frederick S. Porter Katja Pottschmidt Christopher S. Reynolds Samar Safi-Harb Shinya Saito Kazuhiro Sakai Toru Sasaki Goro Sato Kosuke Sato Rie Sato Makoto Sawada Norbert Schartel Peter J. Serlemtsos Hiromi Seta Megumi Shidatsu Aurora Simionescu Randall K. Smith Yang Soong Ł ukasz Stawarz Yasuharu Sugawara Satoshi Sugita Andrew Szymkowiak Hiroyasu Tajima Hiromitsu Takahashi Tadayuki Takahashi Shiníchiro Takeda Yoh Takei Toru Tamagawa Takayuki Tamura Takaaki Tanaka Yasuo Tanaka Yasuyuki T. Tanaka Makoto S. Tashiro Yuzuru Tawara Yukikatsu Terada Yuichi Terashima Francesco Tombesi Hiroshi Tomida Yohko Tsuboi Masahiro Tsujimoto Hiroshi Tsunemi Takeshi Go Tsuru Hiroyuki Uchida Hideki Uchiyama Yasunobu Uchiyama Shutaro Ueda Yoshihiro Ueda Shiníchiro Uno C. Megan Urry Eugenio Ursino Shin Watanabe Norbert Werner Dan R. Wilkins Brian J. Williams Shinya Yamada Hiroya Yamaguchi Kazutaka Yamaoka Noriko Y. Yamasaki Makoto Yamauchi Shigeo Yamauchi Tahir Yaqoob Yoichi Yatsu Daisuke Yonetoku Irina Zhuravleva Abderahmen Zoghbi Toshio Terasawa Mamoru Sekido Kazuhiro Takefuji Eiji Kawai Hiroaki Misawa Fuminori Tsuchiya Ryo Yamazaki Eiji Kobayashi Shota Kisaka Takahiro Aoki
astro-ph.HE
 
2017/07/21
2017/07/27










1Dublin Institute for Advanced Studies, 31 Fitzwilliam Place, Dublin 2, Ireland
2SRON Netherlands Institute for Space Research, Sorbonnelaan 2, 3584 CA Utrecht, The Netherlands
3Institute for Space-Earth Environmental Research, Nagoya University, Furo-cho, Chikusa-ku, Nagoya, Aichi 464-8601
4Kavli Institute for Particle Astrophysics and Cosmology, Stanford University, 452 Lomita Mall, Stanford, CA 94305, USA
5Department of Physics, Stanford University, 382 Via Pueblo Mall, Stanford, CA 94305, USA
6SLAC National Accelerator Laboratory, 2575 Sand Hill Road, Menlo Park, CA 94025, USA
7NASA, Goddard Space Flight Center, 8800 Greenbelt Road, Greenbelt, MD 20771, USA
8Department of Astronomy, University of Geneva, ch. d'Écogia 16, CH-1290 Versoix, Switzerland
9Department of Physics, Ehime University, Bunkyo-cho, Matsuyama, Ehime 790-8577
10Department of Physics and Oskar Klein Center, Stockholm University, 106 91 Stockholm, Sweden
11Department of Physics, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033
12Research Center for the Early Universe, School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033
13Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA
14Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138, USA
15Lawrence Livermore National Laboratory, 7000 East Avenue, Livermore, CA 94550, USA
16Department of Physics and Astronomy, Wayne State University,  666 W. Hancock St, Detroit, MI 48201, USA
17Department of Physics, Yale University, New Haven, CT 06520-8120, USA
18Department of Astronomy, Yale University, New Haven, CT 06520-8101, USA
19Centre for Extragalactic Astronomy, Department of Physics, University of Durham, South Road, Durham, DH1 3LE, UK
20Japan Aerospace Exploration Agency, Institute of Space and Astronautical Science, 3-1-1 Yoshino-dai, Chuo-ku, Sagamihara, Kanagawa 252-5210
21Department of Astronomy, Kyoto University, Kitashirakawa-Oiwake-cho, Sakyo-ku, Kyoto 606-8502
22The Hakubi Center for Advanced Research, Kyoto University, Kyoto 606-8302
23Department of Physics, Tokyo Metropolitan University, 1-1 Minami-Osawa, Hachioji, Tokyo 192-0397
24Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge, CB3 0HA, UK
25Faculty of Mathematics and Physics, Kanazawa University, Kakuma-machi, Kanazawa, Ishikawa 920-1192
26School of Science, Hiroshima University, 1-3-1 Kagamiyama, Higashi-Hiroshima 739-8526
27Fujita Health University, Toyoake, Aichi 470-1192
28Physics Department, University of Miami, 1320 Campo Sano Dr., Coral Gables, FL 33146, USA
29Department of Astronomy and Physics, Saint Mary's University, 923 Robie Street, Halifax, NS, B3H 3C3, Canada
30Department of Physics and Astronomy, University of Southampton, Highfield, Southampton, SO17 1BJ, UK
31Laboratoire APC, 10 rue Alice Domon et Léonie Duquet, 75013 Paris, France
32CEA Saclay, 91191 Gif sur Yvette, France
33European Space Research and Technology Center, Keplerlaan 1 2201 AZ Noordwijk, The Netherlands
34Department of Physics and Astronomy, Aichi University of Education, 1 Hirosawa, Igaya-cho, Kariya, Aichi 448-8543
35Department of Physics, University of Maryland Baltimore County, 1000 Hilltop Circle, Baltimore,  MD 21250, USA
36Department of Applied Physics and Electronic Engineering, University of Miyazaki, 1-1 Gakuen Kibanadai-Nishi, Miyazaki, 889-2192
37Department of Physics, Nagoya University, Furo-cho, Chikusa-ku, Nagoya, Aichi 464-8602
38Department of Earth and Space Science, Osaka University, 1-1 Machikaneyama-cho, Toyonaka, Osaka 560-0043
39Department of Physics, Kwansei Gakuin University, 2-1 Gakuen, Sanda, Hyogo 669-1337
40Department of Physics, Rikkyo University, 3-34-1 Nishi-Ikebukuro, Toshima-ku, Tokyo 171-8501
41Department of Physics and Astronomy, Rutgers University, 136 Frelinghuysen Road, Piscataway, NJ 08854, USA
42Meisei University, 2-1-1 Hodokubo, Hino, Tokyo 191-8506
43Leiden Observatory, Leiden University, PO Box 9513, 2300 RA Leiden, The Netherlands
44Research Institute for Science and Engineering, Waseda University, 3-4-1 Ohkubo, Shinjuku, Tokyo 169-8555
45Department of Physics, Chuo University, 1-13-27 Kasuga, Bunkyo, Tokyo 112-8551
46Department of Physics, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8550
47Department of Physics, Toho University,  2-2-1 Miyama, Funabashi, Chiba 274-8510
48Department of Physics, Tokyo University of Science, 2641 Yamazaki, Noda, Chiba, 278-8510
49Department of Physics, Kyoto University, Kitashirakawa-Oiwake-Cho, Sakyo, Kyoto 606-8502
50European Space Astronomy Center, Camino Bajo del Castillo, s/n.,  28692 Villanueva de la Cañada, Madrid, Spain
51Universities Space Research Association, 7178 Columbia Gateway Drive, Columbia, MD 21046, USA
52National Science Foundation, 4201 Wilson Blvd, Arlington, VA 22230, USA
53Department of Electronic Information Systems, Shibaura Institute of Technology, 307 Fukasaku, Minuma-ku, Saitama, Saitama 337-8570
54Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218, USA
55Institute of Physical and Chemical Research, 2-1 Hirosawa, Wako, Saitama 351-0198
56Department of Physics, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku-ku, Tokyo 162-8601
57Department of Physics, University of Wisconsin, Madison, WI 53706, USA
58Department of Physics and Astronomy, University of Waterloo, 200 University Avenue West, Waterloo, Ontario, N2L 3G1, Canada
59Department of Astronomy, University of Michigan, 1085 South University Avenue, Ann Arbor, MI 48109, USA
60Okinawa Institute of Science and Technology Graduate University, 1919-1 Tancha, Onna-son Okinawa, 904-0495
61Faculty of Liberal Arts, Tohoku Gakuin University, 2-1-1 Tenjinzawa, Izumi-ku, Sendai, Miyagi 981-3193
62Department of Astronomy, University of Maryland, College Park, MD 20742, USA
63Faculty of Science, Yamagata University, 1-4-12 Kojirakawa-machi, Yamagata, Yamagata 990-8560
64Department of Physics, Nara Women's University, Kitauoyanishi-machi, Nara, Nara 630-8506
65Department of Teacher Training and School Education, Nara University of Education, Takabatake-cho, Nara, Nara 630-8528
66Frontier Research Institute for Interdisciplinary Sciences, Tohoku University,  6-3 Aramakiazaaoba, Aoba-ku, Sendai, Miyagi 980-8578
67Astronomical Institute, Tohoku University, 6-3 Aramakiazaaoba, Aoba-ku, Sendai, Miyagi 980-8578
68Department of Physics, Saitama University, 255 Shimo-Okubo, Sakura-ku, Saitama, 338-8570
69Astrophysics Laboratory, Columbia University, 550 West 120th Street, New York, NY 10027, USA
70Department of Physics and Astronomy, University of Manitoba, Winnipeg, MB R3T 2N2, Canada
71Department of Physics and Mathematics, Aoyama Gakuin University, 5-10-1 Fuchinobe, Chuo-ku, Sagamihara, Kanagawa 252-5258
72Astronomical Observatory of Jagiellonian University, ul. Orla 171, 30-244 Kraków, Poland
73Max Planck Institute for extraterrestrial Physics, Giessenbachstrasse 1, 85748 Garching , Germany
74Faculty of Education, Shizuoka University, 836 Ohya, Suruga-ku, Shizuoka 422-8529
75Faculty of Health Sciences, Nihon Fukushi University , 26-2 Higashi Haemi-cho, Handa, Aichi 475-0012
76MTA-Eötvös University Lendület Hot Universe Research Group, Pázmány Péter sétány 1/A, Budapest, 1117, Hungary
77Department of Theoretical Physics and Astrophysics, Faculty of Science, Masaryk University, Kotlářská 2, Brno, 611 37, Czech Republic
78Kashima Space Technology Center, National Institute of Information and Communications Technology, Kashima, Ibaraki 314-8501
79Planetary Plasma and Atmospheric Research Center, Tohoku University, Sendai, Miyagi 980-8578
80The Research Institute for Time Studies, Yamaguchi University, 1677-1 Yoshida, Yamaguchi 753-8511
terada@phy.saitama-u.ac.jp



pulsar:individual:B0531+21 — radio continuum:stars – X-rays:stars – Giant radio pulses 


















































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

Corresponding authors are
Yukikatsu Terada,
Teruaki Enoto,
Shu Koyama,
Aya Bamba,
Toshio Terasawa,
Shinya Nakashima, 
Tahir Yaqoob,
Hiromitsu Takahashi,
and
Shin Watanabe.


    Hitomi Collaboration,
Felix Aharonian1,
Hiroki Akamatsu2,
Fumie Akimoto3,
Steven W. Allen4,5,6,
Lorella Angelini7,
Marc Audard8,
Hisamitsu Awaki9,
Magnus Axelsson10,
Aya Bamba11,12,
Marshall W. Bautz13,
Roger Blandford4,5,6,
Laura W. Brenneman14,
Gregory V. Brown15,
Esra Bulbul13,
Edward M. Cackett16,
Maria Chernyakova1,
Meng P. Chiao7,
Paolo S. Coppi17,18,
Elisa Costantini2,
Jelle de Plaa2,
Cor P. de Vries2,
Jan-Willem den Herder2,
Chris Done19,
Tadayasu Dotani20,
Ken Ebisawa20,
Megan E. Eckart7,
Teruaki Enoto21,22,
Yuichiro Ezoe23,
Andrew C. Fabian24,
Carlo Ferrigno8,
Adam R. Foster14,
Ryuichi Fujimoto25,
Yasushi Fukazawa26,
Akihiro Furuzawa27,
Massimiliano Galeazzi28,
Luigi C. Gallo29,
Poshak Gandhi30,
Margherita Giustini2,
Andrea Goldwurm31,32,
Liyi Gu2,
Matteo Guainazzi33,
Yoshito Haba34,
Kouichi Hagino20,
Kenji Hamaguchi7,35,
Ilana M. Harrus7,35,
Isamu Hatsukade36,
Katsuhiro Hayashi20,
Takayuki Hayashi37,
Kiyoshi Hayashida38,
Junko S. Hiraga39,
Ann Hornschemeier7,
Akio Hoshino40,
John P. Hughes41,
Yuto Ichinohe23,
Ryo Iizuka20,
Hajime Inoue42,
Yoshiyuki Inoue20,
Manabu Ishida20,
Kumi Ishikawa20,
Yoshitaka Ishisaki23,
Masachika Iwai20,
Jelle Kaastra2,43,
Tim Kallman7,
Tsuneyoshi Kamae11,
Jun Kataoka44,
Satoru Katsuda45,
Nobuyuki Kawai46,
Richard L. Kelley7,
Caroline A. Kilbourne7,
Takao Kitaguchi26,
Shunji Kitamoto40,
Tetsu Kitayama47,
Takayoshi Kohmura48,
Motohide Kokubun20,
Katsuji Koyama49,
Shu Koyama20,
Peter Kretschmar50,
Hans A. Krimm51,52,
Aya Kubota53,
Hideyo Kunieda37,
Philippe Laurent31,32,
Shiu-Hang Lee21,
Maurice A. Leutenegger7,
Olivier O. Limousin32,
Michael Loewenstein7,
Knox S. Long54,
David Lumb33,
Greg Madejski4,
Yoshitomo Maeda20,
Daniel Maier31,32,
Kazuo Makishima55,
Maxim Markevitch7,
Hironori Matsumoto38,
Kyoko Matsushita56,
Dan McCammon57,
Brian R. McNamara58,
Missagh Mehdipour2,
Eric D. Miller13,
Jon M. Miller59,
Shin Mineshige21,
Kazuhisa Mitsuda20,
Ikuyuki Mitsuishi37,
Takuya Miyazawa60,
Tsunefumi Mizuno26,
Hideyuki Mori7,
Koji Mori36,
Koji Mukai7,35,
Hiroshi Murakami61,
Richard F. Mushotzky62,
Takao Nakagawa20,
Hiroshi Nakajima38,
Takeshi Nakamori63,
Shinya Nakashima55,
Kazuhiro Nakazawa11,
Kumiko K. Nobukawa64,
Masayoshi Nobukawa65,
Hirofumi Noda66,67,
Hirokazu Odaka6,
Takaya Ohashi23,
Masanori Ohno26,
Takashi Okajima7,
Kenya Oshimizu68,
Naomi Ota64,
Masanobu Ozaki20,
Frits Paerels69,
Stéphane Paltani8,
Robert Petre7,
Ciro Pinto24,
Frederick S. Porter7,
Katja Pottschmidt7,35,
Christopher S. Reynolds62,
Samar Safi-Harb70,
Shinya Saito40,
Kazuhiro Sakai7,
Toru Sasaki56,
Goro Sato20,
Kosuke Sato56,
Rie Sato20,
Makoto Sawada71,
Norbert Schartel50,
Peter J. Serlemtsos7,
Hiromi Seta23,
Megumi Shidatsu55,
Aurora Simionescu20,
Randall K. Smith14,
Yang Soong7,
Łukasz Stawarz72,
Yasuharu Sugawara20,
Satoshi Sugita46,
Andrew Szymkowiak17,
Hiroyasu Tajima3,
Hiromitsu Takahashi26,
Tadayuki Takahashi20,
Shiníchiro Takeda60,
Yoh Takei20,
Toru Tamagawa55,
Takayuki Tamura20,
Takaaki Tanaka49,
Yasuo Tanaka73,
Yasuyuki T. Tanaka26,
Makoto S. Tashiro68,
Yuzuru Tawara37,
Yukikatsu Terada68,
Yuichi Terashima9,
Francesco Tombesi7,62,
Hiroshi Tomida20,
Yohko Tsuboi45,
Masahiro Tsujimoto20,
Hiroshi Tsunemi38,
Takeshi Go Tsuru49,
Hiroyuki Uchida49,
Hideki Uchiyama74,
Yasunobu Uchiyama40,
Shutaro Ueda20,
Yoshihiro Ueda21,
Shiníchiro Uno75,
C. Megan Urry17,
Eugenio Ursino28,
Shin Watanabe20,
Norbert Werner76,77,26,
Dan R. Wilkins4,
Brian J. Williams54,
Shinya Yamada23,
Hiroya Yamaguchi7,
Kazutaka Yamaoka3,
Noriko Y. Yamasaki20,
Makoto Yamauchi36,
Shigeo Yamauchi64,
Tahir Yaqoob35,
Yoichi Yatsu46,
Daisuke Yonetoku25,
Irina Zhuravleva4,5,
Abderahmen Zoghbi59,
Toshio Terasawa55,
Mamoru Sekido78,
Kazuhiro Takefuji78,
Eiji Kawai78,
Hiroaki Misawa79,
Fuminori Tsuchiya79,
Ryo Yamazaki71,
Eiji Kobayashi71,
Shota Kisaka71,
Takahiro Aoki80,

    December 30, 2023
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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. 






§ 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 <cit.> 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 <cit.>.
GRPs occur in certain pulse phases with no clear periodicity. 
The energy spectrum of GRPs follows
	a power-law distribution <cit.>, 
	different from the Gaussian or log-normal distribution of the normal pulses
	<cit.>.
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; <cit.>)
        have been attracting more and more attention.
	These phenomena are  extragalactic bright radio transients with ∼1 msec duration 
	<cit.>.
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., <cit.>). 

The Crab pulsar (PSR B0531+21)
	is one of the most intensively studied rotation-powered pulsars 
	since the initial discovery of its GRPs <cit.>. 
This famous pulsar exhibits GRPs
	occurring both in the main pulse and the interpulse,
	which have been mainly studied at radio wavelengths	
	<cit.>.	
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
	 <cit.>.
This result was further confirmed 
	by the Green Bank Telescope and 
	the Hale telescope <cit.>. 
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; <cit.>), 
	for soft gamma-rays (CGRO/OSSE, 50–220 keV; <cit.>), 
	for gamma-rays (Fermi/LAT, 0.1–5 GeV; <cit.>), 
	and for very high energy gamma-rays (VERITAS, >150  GeV; <cit.>). 

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 <cit.>.
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; <cit.>),
	a wide field-of-view X-ray CCD detector (Soft X-ray Imager, SXI; <cit.>),
	two Si/CdTe hybrid hard X-ray imagers (Hard X-ray Imager, HXI; <cit.>),
	and a Compton telescope (Soft Gamma-ray Detector, SGD; <cit.>).
Such a wide energy coverage with high time resolution at a few microseconds <cit.> 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 
        <cit.> 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 <cit.>.
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
	<cit.>.
The archival monthly radio ephemeris of the Crab pulsar has been regulary provided 	
	by the Jodrell-Bank observatory[http://www.jb.man.ac.uk/ pulsar/crab/crab2.txt]
	on every 15th monitoring 
	 <cit.>.
Interpolating from this,
	the predicted ephemeris of the Crab pulsar timing 
        in Barycentric Dynamical Time (TDB)
        is tabulated in table <ref>.





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 <cit.>.















§ OBSERVATION AND DATA REDUCTION








 §.§ 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 <cit.>. 
After the start time of the X-ray observation
we idenfitied 3350 GRPs (section <ref>) 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.
<cit.> 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.






 §.§ Data Reduction of Radio observations


 

















































Data reduction radio (TBA).
Table <ref> is prepared here.

comment(YT-20170419): Section 2.2 and 2.3 were swapped.
- how the radio data were cleaned up?
- how the GRPs are identified?
- statistics of GRPs of main pulse / inter pulse.
- (A/I) ask Terasawa-san et al to fill this section.










  §.§.§ Frequency assignment

The radio observation in the 1.4 – 1.7GHz band was made with the 34m telescope
at the Kashima Space Technology Center <cit.>
operated by the NICT (National Institute of Information and Communications Technology).
We used the ADS3000+ recorder <cit.>
which has a capability of 8 individual channels
with 4-bit 64MHz Nyquist-rate sampling.
(The sampling time step δ t is 1/64 MHz=15.625ns,
and the data rate 2Gbit/s.)
table <ref> 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.





  §.§.§ 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., <cit.>).
With DM_ JB as a trial value, we coherently dedispersed 
<cit.> 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., <cit.>)
in all channels with ∼0.1μs accuracy.
An example of a successful alignment can be seen in Figure 2 of 
<cit.>.
The frequency bands LL and LH approximately correspond to ch1 and ch4-6 here.



  §.§.§ 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 <ref>
gives the resultant effective bandwidths after filtering.
The total effective bandwidth, Δν_ sum  =Δν_0 + Δν_1 + ...+ Δν_6,
is 106.36MHz.





  §.§.§ GRP selection


In the main panel of figure <ref>
dots show all GRP candidates with a S/N (signal to noise ratio) >5.5
(or pulse energy >∼2.2 kJy μs, 
see Appendix <ref>),
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 φ respectively. 
The top panel of figure <ref>
shows the time intervals subjected to
the time-domain RFI rejection (see Appendix <ref>) 
in black (OFF), and the time intervals kept, in red (ON).
In total, 571s (5729s) in time intervals were rejected (kept).

As can be seen in figure <ref>
there are two clusters of GRP candidates in φ.
We adjusted the initial value of φ at 00:00:00TDB
(y_0 in (<ref>)) 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 <ref>
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.










 §.§ 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; <cit.>) 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 <ref>.
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.  <ref> 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 <cit.>. 
The target position for the barycentric correction was 
(R.A., DEC) = (83D.633218, +22D.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 <ref>.
As described in <cit.> and <cit.>,
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.  <ref> (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 10^3 GRP cycles were exposed among (5 – 6)× 10^4 cycles 
by each instrument, as summarized in table <ref>.

















§ ANALYSES AND RESULTS

































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





 §.§ Variation of the Pulse Profiles in GRPs








Most significant MP- and IP-GRPs, shown as large circles in figure <ref>, 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 <ref> 
to see the pulse profiles of MP-GRP and NORMAL cycles. 
As shown in the top panels of the left-hand plots in figure <ref>, 
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 <ref>).

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 <ref> (right).
The statistical errors were very high on the Hitomi datasets, both in MP- and IP-GRPs.










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 <ref>.
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 <ref>, 
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.





 §.§ Pulse peak enhancement at GRPs 












Since no significant enhancement found in five cycles before/after GRPs (section <ref>), 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 ξ(Δφ) ≡C_ grp(Δφ) - C_ nor(Δφ)/C_ nor(Δφ). 
The table <ref> 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.










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 <ref>.
Therefore, a possible enhancement at φ= was within the 
fluctuations of ξ(Δφ) in other cycles 
to within 2 σ 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 <ref>) 
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 <cit.>, 
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 <ref>.




















 §.§ 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 <cit.>) 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 <cit.>, the X-ray spectra of the pure-pulsed components were clearly demonstrated in figure <ref>.














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 χ^2 of 305.85 and 301.18 for 250 degrees of freedom, respectively, as shown in the figure <ref>.
The pulsed flux obtained with Hitomi accumulated within the time interval of Δφ phase was summarized in table <ref>.

Therefore, the 3 σ upper limit values of enhancement in terms of flux
can be obtained by multiplying the values in table <ref> (section <ref>) with those in table <ref>. 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.






§ 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 <ref>). 
No significant changes in the X-ray pulse profiles were detected along all the phase bins at the GRP cycles (Section <ref>), 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 <ref>.
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 <cit.> as shown in Fig.  <ref>.
Our result constitutes the second case of a study in the hard X-ray band 
where the flux (in ν F_ν space) of the pulsed component of the Crab pulsar became the highest, 
following a previous report of a marginal detection at the 2.7 σ level with Suzaku <cit.>.
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 <cit.>, 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.








As described in section <ref>,
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 <cit.>.
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 <cit.>). 
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 <cit.> resulting a higher density plasma than the Goldreich-Julian density in the GRP region <cit.>.
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. <ref>) 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 <ref>, the enhancement at the pulse peak ξ were within the 2 σ 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 <ref>), 
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 <cit.>.
Interestingly, the optical enhancement of ξ_ opt(0.003  phase) = 3% reported by <cit.> 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. <cit.>) 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 <cit.>.
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 <cit.>, 
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. 






§ ACKNOWLEDGEMENTS


We thank the support from the JSPS Core-to-Core Program.

We acknowledge all the JAXA members who have contributed to the ASTRO-H (Hitomi)
project.

All U.S. members gratefully acknowledge support through the NASA Science Mission
Directorate. Stanford and SLAC members acknowledge support via DoE contract to SLAC
National Accelerator Laboratory DE-AC3-76SF00515. Part of this work was performed under
the auspices of the U.S. DoE by LLNL under Contract DE-AC52-07NA27344.

Support from the European Space Agency is gratefully acknowledged.

French members acknowledge support from CNES, the Centre National d'Études Spatiales.

SRON is supported by NWO, the Netherlands Organization for Scientific Research.  Swiss
team acknowledges support of the Swiss Secretariat for Education, Research and
Innovation (SERI).

The Canadian Space Agency is acknowledged for the support of Canadian members.  

We acknowledge support from JSPS/MEXT KAKENHI grant numbers 15J02737,
15H00773, 15H00785, 15H02090, 15H03639, 
15K05088, 
15K05069, 
15H05438, 15K05107, 15K17610,
15K17657, 16J00548, 16J02333, 
16J06773, 
16H00949, 16H06342, 16K05295, 16K05296,
16K05300, 16K13787, 16K17672, 16K17673, 21659292, 23340055, 23340071,
23540280, 24105007, 24244014, 24540232, 25105516, 25109004, 25247028,
25287042, 25400236, 25800119, 26109506, 26220703, 26400228, 26610047,
26800102, JP15H02070, JP15H03641, JP15H03642, JP15H06896,
JP16H03983, JP16K05296, JP16K05309, JP16K17667, and JP16K05296.

The following NASA grants are acknowledged: NNX15AC76G, NNX15AE16G, NNX15AK71G,
NNX15AU54G, NNX15AW94G, and NNG15PP48P to Eureka Scientific.

H. Akamatsu acknowledges support of NWO via Veni grant.  

C. Done acknowledges STFC funding under grant ST/L00075X/1.  

A. Fabian and C. Pinto acknowledge ERC Advanced Grant 340442.

P. Gandhi acknowledges JAXA International Top Young Fellowship and UK Science and
Technology Funding Council (STFC) grant ST/J003697/2. 

Y. Ichinohe, K. Nobukawa, and H. Seta are supported by the Research Fellow of JSPS for Young
Scientists.

N. Kawai is supported by the Grant-in-Aid for Scientific Research on Innovative Areas
“New Developments in Astrophysics Through Multi-Messenger Observations of Gravitational
Wave Sources”.

S. Kitamoto is partially supported by the MEXT Supported Program for the Strategic
Research Foundation at Private Universities, 2014-2018.

B. McNamara and S. Safi-Harb acknowledge support from NSERC.

T. Dotani, T. Takahashi, T. Tamagawa, M. Tsujimoto and Y. Uchiyama acknowledge support
from the Grant-in-Aid for Scientific Research on Innovative Areas “Nuclear Matter in
Neutron Stars Investigated by Experiments and Astronomical Observations”.

N. Werner is supported by the Lendület LP2016-11 grant from the Hungarian Academy of
Sciences.

D. Wilkins is supported by NASA through Einstein Fellowship grant number PF6-170160,
awarded by the Chandra X-ray Center, operated by the Smithsonian Astrophysical
Observatory for NASA under contract NAS8-03060.

We thank contributions by many companies, including in particular, NEC, Mitsubishi Heavy
Industries, Sumitomo Heavy Industries, and Japan Aviation Electronics Industry. Finally,
we acknowledge strong support from the following engineers.  JAXA/ISAS: Chris Baluta,
Nobutaka Bando, Atsushi Harayama, Kazuyuki Hirose, Kosei Ishimura, Naoko Iwata, Taro
Kawano, Shigeo Kawasaki, Kenji Minesugi, Chikara Natsukari, Hiroyuki Ogawa, Mina Ogawa,
Masayuki Ohta, Tsuyoshi Okazaki, Shin-ichiro Sakai, Yasuko Shibano, Maki Shida, Takanobu
Shimada, Atsushi Wada, Takahiro Yamada; JAXA/TKSC: Atsushi Okamoto, Yoichi Sato, Keisuke
Shinozaki, Hiroyuki Sugita; Chubu U: Yoshiharu Namba; Ehime U: Keiji Ogi; Kochi U of
Technology: Tatsuro Kosaka; Miyazaki U: Yusuke Nishioka; Nagoya U: Housei Nagano;
NASA/GSFC: Thomas Bialas, Kevin Boyce, Edgar Canavan, Michael DiPirro, Mark Kimball,
Candace Masters, Daniel Mcguinness, Joseph Miko, Theodore Muench, James Pontius, Peter
Shirron, Cynthia Simmons, Gary Sneiderman, Tomomi Watanabe; ADNET Systems: Michael
Witthoeft, Kristin Rutkowski, Robert S. Hill, Joseph Eggen; Wyle Information Systems:
Andrew Sargent, Michael Dutka; Noqsi Aerospace Ltd: John Doty; Stanford U/KIPAC: Makoto
Asai, Kirk Gilmore; ESA (Netherlands): Chris Jewell; SRON: Daniel Haas, Martin Frericks,
Philippe Laubert, Paul Lowes; U of Geneva: Philipp Azzarello; CSA: Alex Koujelev, Franco
Moroso.


Y. Terada led this study in data analysis and writing drafts,
in addition to the Hitomi timing Calibration and software preparation.
X-ray data analyses and calibrations were done with 
T. Enoto, S. Koyama, A. Bamba S. Nakashima, T. Yaqoob, 
H. Takahashi, S. Watanabe, and K. Oshimizu.
T. Terasawa led the radio data analysis
with M. Sekido, K. Takehuji, E. Kawai, H. Misawa,
F. Tsuchiya, R. Yamazaki, E. Kobayashi, S. Kisaka, and T. Aoki.

T. Dotani, L. Gallo, R. Mushotzky, C. Ferrigno, K. Pottschmidt, M. Loewenstein, 
M. Tsujimoto, and S. Safi-Harb improved the draft.











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§ DETAILS FOR RADIO DATA REDUCTION





 §.§ TEMPO2 timing package


The pulsar timing package TEMPO2 (Hobbs et al., 2006)
gives the function f̃(t_ UTC) to convert the observation time in UTC, t_ UTC, to 
the time at the solar system barycenter (TDB), t̃_ TDB.
TEMPO2 also gives the signal frequency ν_ ISM 
in the rest frame of the interstellar matter (ISM)
corresponding to the observation frequency ν_ 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≡ν_ obs/ν_ ISM.




 §.§ Calculations of S/N

We dedispersed the raw antenna voltage data of the channel k, V^ raw_k(t), 
to obtain V_k(t). 
We integrated[
For simplicity we use the term, 'integrate'.
In reality, of course, we calculated equation (<ref>)
as finite sums over t_n ≤ t <t_n+1 with an original sampling time step δ t =15.625ns.
] 
|V_k(t)|^2 over the time interval of Δ t=10 μs,

    E_k (t_n) = 1/Δ t∫_t_n^t_n+1 |V_k(t')|^2 dt'

where we defined
the binned times as t_n=t_ start + n Δ t
(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,

    τ_k,6 = e^2/2π m_e c DM
      {1/ν_k^2 - 1/ν_6^2}η

where (e, m_e, c) are usual physical quantities, DM the dispersion measure,
and ν_k and ν_6 the highest frequencies of the bands k and 6.
The Doppler factor η 
appears in equation (<ref>)
since τ_k,6, ν_k, and ν_6 are defined in the observer's frame.
We combined incoherently
E_0 (t_n), E_1 (t_n),..,

E_6 (t_n),
as,

    E_ sum (t_n) = ∑_k=0,1,4,5,6 E_k (t_n-τ_k,6)

where appropriate interpolations were taken to calculate the RHS of equation (<ref>).

We calculated the average E̅_ sum and standard deviation σ_ sum
of E_ sum(t_n) over an appropriate longer time interval (Δ T, for which we take 1s).


Ideally E̅_ sum and σ_ sum are constant in time.
In reality, however, they showed slight and gradual variations in time T_M (= t_ start + M Δ T; 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 

    S_ sum(t_n) = 1/σ_ sum(T_M) ( E_ sum(t_n) - E̅_ sum(T_M))

With a given threshold S_ sum,  thr,
we selected `GRP candidates' for each one in which there was an enhancement[
A strong GRP gives enhancements of the average and standard deviation,
so that the S/N obtained by equation (<ref>) is reduced.
To avoid this effect, we replace 
the average and standard deviation in equation (<ref>)
with the values interpolated from those
obtained in the surrounding time intervals that are unaffected by GRPs.
],
S_ sum(t_n) >= S_ sum,  thr.




 §.§ Time-domain RFI rejection

To eliminate RFI further,
we conducted the following auxiliary process:
We calculated the squared antenna voltages E^ raw_k (t_n) 
following equation (<ref>)
except that we used V^ raw_k(t) instead of V_k(t).
From E^ raw_k (t_n) we then calculated

    E^ raw_ sum (t_n) ≡∑_k=0,1,4,5,6 E^ raw_k (t_n)

and their average and standard deviation, E̅^ raw_ sum(T_M) and σ^ raw_ sum(T_M).
We watched the behaviors of σ_ sum(T_M) and σ^ raw_ sum(T_M)
throughout the observation interval.
When σ_ sum(T_M) < σ^ raw_ sum(T_M),
we reject the data 
S_ sum(t_n) for T_M ≤ t_n <T_M+1, as affected by RFIs.



 §.§ Rotation phase and GRP identification

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

    φ_n = frac(y)
        with   
    y         = y_0 + ν_ rott̃_n + 0.5 ν̇ _ rott̃_n^2,

where 
t̃_n = f̃(t_n) is the time in TDB,
frac(y) the fractional part of y,
y_0 the initial phase at 00:00:00 TDB, 
ν_ rot and ν̇_ rot the rotation frequency and its time derivative from 
the Jodrell bank monthly ephemeris (table <ref>).
In the operation of equation (<ref>), 
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 <ref>
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 Δ t=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 E_ sum (t_n) and E_ sum (t_n+1),
and the corresponding S_ sum(t_n) and S_ sum(t_n+1)
are artificially lowered (sometimes both are less than S_ sum ,thr).
To avoid mal-counting of GRPs caused by this effect,
we repeated the procedure from equation (<ref>) to equation (<ref>)
for the binned time with a shift of Δ t/2:
Firstly, we calculate

    E_k (t_n+1/2) = 1/Δ t∫_t_n+Δ t/2^t_n+1+Δ t/2 |V_k(t')|^2 dt'
                                                                                  equation (<ref>')

If the resultant S_ sum(t_n+1/2) exceeds S_ sum, thr,
this GRP is `rescued from the sea of the noise'.
We found that about 10% of GRPs are thus rescued.





 §.§ Radiometer equation

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

    C=SEFD+S_ CN/√(Δν_ sumΔ t)     [Jy]

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 Δν_ sum=106.36MHz (section <ref>)
and Δ t=10μs.
The GRP threshold S/N=5.5 used in section <ref>
corresponds to a flux density threshold of F= 220Jy,
or a pulse energy threshold FΔ t=2.2kJy μs.




§ EXTRACTION OF THE SGD PHOTO ABSORPTION MODE



On the timing analyses of the SGD-1 data 
in section <ref>, 
the photo-absorption events were extracted 
from the unscreened 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. 



