No. 5] Proc. Jpn. Acad., Ser. B 92 (2016) 135

Review X-ray studies of neutron stars and their magnetic fields

† By Kazuo MAKISHIMA*1,

(Communicated by Yasuo TANAKA, M.J.A.)

Abstract: Utilizing results obtained over the past quarter century mainly with Japanese X-ray astronomy satellites, a review is given to some aspects of neutron stars (NSs), with a particular emphasis on the magnetic fields (MFs) of mass-accreting NSs and magnetars. Measurements of electron cyclotron resonance features in binary X-ray pulsars, using the Ginga and Suzaku observatories, clarified that their surface MFs are concentrated in a narrow range of (1–7) # 108 T. Extensive studies of magnetars with Suzaku reinforced their nature as neutron stars with truly strong MFs, and revealed several important clues to their formation, evolution, and physical states. Taking all these results into account, a discussion is made on the origin and evolution of these strong MFs. One possible scenario is that the MF of NSs is a manifestation of some fundamental physics, e.g., neutron spin alignment or chirality violation, and the MF makes transitions from strong to weak states.

Keywords: neutron stars, pulsars, magnetars, magnetic fields, X-rays, scientific satellites

As illustrated in Fig. 1, the differences in the 1. Introduction EOS are best distinguished by the relation between The present paper deals mainly with magnetic the mass M and radius R of the stars. Normal fields (MFs) of neutron stars (NSs). Let us, however, nuclear-burning stars are supported by the classical begin with a broader scope, and explain how the gas pressure of their interior. In contrast, planets concept of stars is directly related to basic physics. are supported by Coulomb repulsion among constit- This is because the paper is meant for readers from uent ions, which determines the mean particle wide areas of physical science, rather than experts in separation d to be about the Bohr radius aB, and astrophysics. For the same reason, we spare consid- produces a scaling as R / M1/3 (i.e., a constant erable pages to tutorial explanations of the basics of density). NSs, and use the International System Units. In brown dwarfs (stars too light to ignite Generally, a “star” means a celestial system, in hydrogen fusion) and white dwarfs (final form of which gravity is counter-balanced in a stable manner low-mass stars), the gravity is counter-balanced by by some internal pressure. The gravity, which degenerate election pressure. Thus, d becomes com- provides the inward pull force, is universal without parable to the electron Compton wavelength, e ¼ 2 any characteristic length scales. In contrast, the 2EaB ¼ 0:046aB, where E ¼ e =40!c ¼ 1=137 is pressure p which tries to expand the star is versatile. the fine structure constant, with e the elementary It is indeed the variety of this p that allows the charge, C0 the vacuum dielectric constant, ! the Dirac existence of stars of various types. More specifically, constant, and c the light velocity. In non-relativistic stars are characterized almost solely by the equation case, the mass-radius scaling becomes R / M!1/3. of state (EOS), which expresses p in terms of the When the degenerate Fermions become fully rela- mass density ; of the constituent matter. tivistic, the star becomes unstable. This sets an upper limit to these objects. For white dwarfs, the limit, 2=3 *1 m MAXI Team, Global Research Cluster, The Institute of called Chandrasekhar mass, is given as p G 2 Physical and Chemical Research (RIKEN), Wako, Saitama, Japan. : M Gm = † 1 4 , where mp is the proton mass, G p Correspondence should be addressed: K. Makishima, !c ¼ 5:9 1039 is a dimensionless quantity called MAXI Team, Global Research Cluster, The Institute of Physical fi and Chemical Research (RIKEN), 2-1 Hirosawa, Wako, Saitama gravitational ne-structure constant, and G is the 351-0198, Japan (e-mail: [email protected]). gravitational constant. doi: 10.2183/pjab.92.135 ©2016 The Japan Academy 136 K. MAKISHIMA [Vol. 92,

in Jupiter, and an iron-rich molten interior of the Earth. On the other hand, the gross proportionality seen in Fig. 2, between the MF and the density, suggests alternatively that ferromagnetism (of elec- trons or nucleons) is contributing at least in some objects. In either case, the magnetism is expected to provide valuable information on the EOS. In particular, that of NS may potentially represent some physics in extreme conditions. The present paper reviews studies of magnetism of NSs,1) performed in the past quarter century mainly with Japanese X-ray satellites, Ginga Fig. 1. Mass-radius relations for various types of stars. Down- launched in 1987 February,2) ASCA in 1983 ward orange arrows illustrate the evolution of the core of normal February,3) and Suzaku in 2005 July.4) In addition, fi stars (omitting their red-giant phase), which involves signi cant we incorporate results from the Monitor of All-sky mass loss. X-ray Image (MAXI),5) placed onboard the Japan Experimental Module Kibo which comprises the International Space Station. Because of the page limitation, the paper rather poorly covers topics with radio pulsars, and theoretical aspects of the NS interior. 2. Neutron stars 2.1. Formation of neutron stars. In a lifetime of 105.5–107.5 years, a massive star reaches an endpoint of its evolution, where it makes a core- collapse supernova explosion. In this dramatic event with a huge energy release (91046 J), an inner part (“core”) of the star collapses by its own gravity towards the center, leading to the formation of an NS if the initial mass of the star is about 10–20 ME.By Fig. 2. Typical surface MF intensities of various stars, plotted as bounced shocks, the remaining outer parts are ejected a function of their density. Two lines indicate the expected MF into the interstellar space to form an expanding shell intensities, when all electrons (dashed line) or nucleons (dotted structure known as a supernova remnant (SNR). If line) are spin-aligned to form a ferromagnetic phase. The diagram also incorporates typical ferromagnetic materials. the progenitor star has a larger initial mass, e.g., >25 ME, the infalling core is considered to be heavier than the upper limit for NSs, and hence to collapse into a In Fig. 1, NSs appear as a class with by far the black hole. smallest radii. Since they are supported by degener- Figure 3 shows the Crab Nebula6) which ex- ate pressure of neutrons, the neutron-neutron sepa- ploded in the year of 1054, and its central NS known ration inside them is of the same order as the as the Crab Plusar. It is the best-known example of Compton wavelength of nucleons. As a result, the NS-SNR association, even though it would not be a radius of an NS is 9me/mn F 1/1840 times that of a typical SNR because it lacks the blast-wave heated white dwarf of the same mass, where me and mn are thermal remnant and has only the nonthermal the electron mass and neutron mass, respectively. pulsar-wind nebula. Here, the term “pulsar” generally The upper-limit mass of NSs is considered to be 93 means an NS of which the radiation intensity exhibits ME or less, still with considerable uncertainties. clear periodicity at its rotation period P.AnNSisnot One interesting aspect of stars is their mag- called a pulsar if its P is unknown. netism, because most of them are magnetized as In addition to the above canonical scenario, summarized in Fig. 2. These MFs are in many cases there can be yet another channel of NS formation, interpreted as due to some electric currents flowing called “accretion induced collapse”.7) When a white inside a plasma phase, e.g., a metallic-hydrogen core dwarf in a binary system gradually gains its mass No. 5] X-ray studies of neutron stars and their magnetic fields 137 through accretion, it will hit the Chandrasekhar limit is the stellar volume, and b is a numerical factor of and ignite fusion reactions near the center. If the order unity. In non-relativistic case, the EOS can be p ðeÞð=m Þ¼b0ðh2= m Þð= white dwarf has a composition which is rich in C and approximated as d F n 5 n 5=3 O, it will end up with a Type Ia supernova via mnÞ , with h the Planck constant, and bB yet thermonuclear runaway explosion. In contrast, the another numerical constant of order unity. Using this white dwarf will collapse into an NS if the compo- EOS, the solution to Eq. [3] is expressed as RNS 1=3 sition is mainly of O, Ne, and Mg, because the 10ðMNS=MÞ km. electron capture takes over the nuclear burning and The actual mass-radius relation of NSs is subject reduces the pressure. Details of this process wait for to special and general relativity, and nuclear inter- future investigation. actions among neutrons which make the object a 2.2. Major properties of neutron stars. Of all strongly-interacting Fermi gas. Because we still have classes of stars, NSs are regarded as champions in limited knowledge of the nuclear interaction, or the three respects; the highest density, the fastest “nuclear EOS” that replaces the above simplest EOS, rotation, and the strongest MFs. Yet another theoretical MNS vs. RNS relations have not yet been characteristic of NSs is their strong gravity, although accurately identified. Conversely, if we can measure in this respect they are next to black holes. MNS and RNS of a fair number of NSs with a sufficient Composition: An NS consists mostly of neu- accuracy, the results will give a valuable clue to the trons, and is sustained by their degenerate pressure nuclear EOS. against its extreme gravity. These neutrons are Observationally, the values of MNS measured produced in the collapsing stellar core, via a process from about 50 NSs8) are concentrated in a narrow known as electron capture or neutronization. That range around Eq. [2], with at most ’30% scatter: is, a O-type reaction between two nuclear species so are the measured values of RNS. On one hand, A(N, Z ) and A(N D 1, Z ! 1), we need to explain how such narrow distributions are realized. On the other hand, these individual AðN;ZÞþe AðN þ 1;Z 1Þþ ; ½1 e measurements must be made yet with higher where Z is the proton number and N is that of accuracies, in order to constrain the nuclear EOS. neutrons, would not proceed to the right any longer if High density: Because of the extremely small N > Z, because A(N D 1, Z ! 1) would have a larger RNS, NSs are by far the densest objects in the mass than the left hand side. However, when ; Universe. From Eq. [2], their volume-averaged den- becomes extremely high in the collapsing stellar core, sity becomes ; 9 5 # 1017 kg m!3, which is by >13 ðeÞ / the Fermi energy of electrons will increase as F orders of magnitude higher than those of the densest 1=3 (relativistic case), and make the rest-mass energy metals, and even exceeds those of atomic nuclei, 17 !3 of the left hand side higher than that of the right ;0 F 2.3 # 10 kg m . At the center of NSs, the hand side. Then, the electron to be emitted by density is expected to become as high as 910;0. D ! ðeÞ A(N 1, Z 1) has a lower energy than F , so that Rapid rotation: Among all celestial objects, the leftward reaction is forbidden by Pauli’s exclusion NSs (except mass-accreting ones) are by far the most principle. rapidly rotating class, with the fastest known record Mass and radius: An NS is an extremely tiny having a rotation period of P F 1.5 msec. This feature object, with a typical mass MNS and radius RNS of of NSs is a result of angular momentum inheritance from their progenitor stars, together with their M 1:4 M;R 11 km: ½2 NS NS extremely small radii. As a Gedanken experiment, Their radii are thus 95 orders of magnitude (just the let us compress the Sun into an NS (although the atom vs. nucleus size ratio) smaller than the Solar Sun would never evolve so). Then, the Solar rotation radius. When MNS is given, we can approximately period, about a month, would decrease to P 9 calculate RNS, by minimizing the overall energy 0.5 msec through angular momentum conservation, because the radius should decrease by a factor of 3 M2 E ¼ G NS þ bp V ½ 9 # 4 tot R d 3 7 10 . This happens to be the shortest period that 5 NS an NS can attain, as it would break up for P < with respect to RNS. Here, the first term on the right 0.5 msec due to centrifugal force. hand side represents self gravity (assuming a uniform Strong magnetic fields: Another outstanding density). The second term is the internal energy, feature of NSs is their strongest MFs among all where pd is the degenerate pressure of neutrons, V celestial objects (Fig. 2). As described later in § 2.3, a 138 K. MAKISHIMA [Vol. 92,

Fig. 4. A schematic classification of NSs, in terms of P and Bd. Blue, green, and red indicate rotation-powered, accretion- powered, and magnetically-powered objects, respectively. Grids for =c of Eq. [5] are provided by dashed purple lines. “Death line” Fig. 3. A composite image of the Crab Nebula, taken in the means that rotation-powered objects become unable to emit optical (purple) and X-rays (cyan). The Crab pulsar is seen at significant radiation when they cross this line. NSs residing in the center. The image size is about 6B # 7B. Taken from the SNRs are also indicated. Chandra Photo Album.

8 majority of NSs have Bd 9 10 T, where Bd refers to companion stars, and capture their stellar winds to dipole MF intensity (more properly, magnetic flux emit X-rays with strong pulsations, as the captured density) measured at the magnetic poles on the NS matter will fall to the two magnetic poles of the NS surface. It is related to the object’s magnetic dipole where it is shock heated to form X-ray emitting hot moment M as “accretion columns”. The wide scatter in P seen among BXPs, from 2 ms to 9104 s, results from their M ¼ 2R3 B : ½4 NS d interaction with the accreting matter (§ 3.2). The above value of Bd can be understood through the Yet another subclass is those at the low-Bd and same Gedanken experiment as above; a typical Solar short-P end, a mixture of millisecond pulsars (MSPs; dipole field of Bd 9 0.02 T would be compressed, isolated or in wide binaries) and Low-Mass X-ray 8 during the core collapse, to Bd 9 10 T through Binaries (LMXBs). The latter class of NSs accrete conservation of magnetic flux. matter from their low-mass companion stars, to emit 2.3. Classification of neutron stars. Among X-rays with weak or almost no pulsation. Usually, several ways to classify NSs, a convenient one, shown these NSs are considered to be old (>109 yr). in Fig. 4, is to use their values of P and Bd. There, the Finally, a special subclass, located at the 10 11 most dominant subclass is radio pulsars, i.e., isolated highest-MF region of Bd 9 10 –10 T, is called NSs with P of a few tens msec to several sec, and “magnetars”. In § 4, we present more detailed 7 9 Bd F 10 –10 T. Some of them are found in SNRs, like descriptions of these objects, employing a working the case of Fig. 3. Since these NSs are considered to hypothesis that the values found in Fig. 4 represent lose their rotational energies by radiating magnetic their true surface MFs. dipole radiation (§ 3.1), they will move to the right on As indicated by Fig. 4, NSs exhibit not only very Fig. 4 as they get older. Their age can be estimated strong MFs, but also a remarkable scatter in Bd over using a quantity called characteristic age, defined as 8 orders of magnitude. It is not known how the MF can scatter this much, given strong concentrations c P=2P_ ½5 of the observed MNS and RNS around their canonical where P_ is the measured period derivative. values [Eq. [2]]. It is unclear, either, whether NSs The second subclass in Fig. 4 is binary X-ray with strong and weak MFs differ systematically (but pulsars (BXPs) extending horizontally at Bd F (1– within the narrow scatter) in their masses. More 7) # 108 T. They form binaries with (usually massive) fundamentally, we need to clarify how these strong No. 5] X-ray studies of neutron stars and their magnetic fields 139

MFs are held: is the magnetism driven by some pulsars, but typically 2 orders of magnitude shorter electric currents (electric magnets), or sustained by P, so that the induced potential is similar between some kind of ferromagnetism (permanent magnets)? these two subclasses. Thus, MSPs can accelerate 2.4. Energy sources of neutron stars. The particles to similarly high energies as radio pulsars, NSs in Fig. 4 all emit electromagnetic radiation in but with a much lower luminosity due to their much some frequencies, with a typical luminosity of L F smaller volume available for the process. 1026–1031 W. From the energy sources of this Accretion-powered NSs: In Fig. 4, BXPs and radiation, the NS can be classified in a different LMXBs accrete gas from their binary companions, manner into the following three categories. There is and emit X-rays powered by gravitational energies in fact yet another class, thermally radiating NSs. released by the accreting matter. The energy Although observations of their cooling provide available by this process is given as valuable clues to the physical conditions inside NSs, M M E ¼ G NS the subject is beyond the scope of the present paper. grav R NS Rotation-powered NSs: radio pulsars and M R 1 M ¼ : 42 NS NS MSPs in Fig. 4 emit rather broad-band radiation 3 4 10 J 1:4M 11 km 10 4M (mainly radio but sometimes to optical or even higher frequencies) by consuming their rotational energies, ½8 which is given as where "M is the overall mass accreted on the NS. M_ M I 2 P 2 Then, using the accretion rate /(accretion 2 40 M_ Erot ¼ ¼ 2:0 10 I38 J ½6 lifetime) which is typically of the order of P : 4 7 12 !1 2 0 3s 10 M=10 yr ¼ 0:6 10 kg s , the luminosity is where I38 is the moment of inertia in units of given as 1038 kg m2.Bydifferentiating this equation, the L ¼ 1:7 1028M=_ ð1 1012 kg s1Þ W ½9 luminosity available via spin down can be written as grav dE ð Þ2I where the dependence on MNS and RNS was omitted L ¼ ¼ 2 P_ rot dt P 3 for simplicity. This L has a clear upper limit, called P 3 P_ grav ¼ 1:5 1026 I W: ½7 Eddington limit, which is given as 38 0:3s 1015 s=s L ¼ 4cGM m f = fi F Edd NS p b T For reference, the ducial values of P 0.3 s and 31 15 !1 ¼ 2:1 10 ðMNS=1:4MÞðfb=1:16Þ W ½10 P_ ¼ 1 10 ss gives, via Eq. [5], =c F 4.8 Myr, !29 !2 which is a typical age of radio pulsars. How to where gamma-rays, as discovered with the with Eq. [2], gives 12) Fermi Gamma-Ray Space Telescope. The accel- L 1=4 L 1=4 eration in rotation-powered NSs is likely to be caused T ¼ grav ¼ 1:5 107 grav K ½11 bb 4R2 L by strong electric fields induced by their rotating NS Edd MFs, at locations close to the “light cylinder”, where < F 5.67 # 10!8 Wm!2 K!4 is the Stefan- RLC F cP/2:, where the velocity of co-rotation with Boltzmann constant. Thus, the heated NS surface the pulsar reaches c. Using the MF strength near has a temperature just corresponding to X-ray 3) RLC, i.e., BLC 9 Bd(RNS/RLC) , the induced electric energies. potential therein will be estimated as c BLC RLC Magnetically-powered NSs: As detailed later cB R3 R2 / B =P 2 d NS LC d . MSPs have some 4 orders in § 4, objects of the magnetar class in Fig. 4 radiate of magnitude lower Bd than representative radio mainly in X-rays. However, they cannot be rotation- 140 K. MAKISHIMA [Vol. 92, powered objects, since their X-ray luminosities and functional forms to Eq. [13],10) but without the largely exceed Lrot of Eq. [7]. As discussed in § 4, sin 3 dependence. Therefore, the spin-down behavior they are not likely to be accretion-powered objects, may not depend on 3 as strongly as implied by either. Instead, magnetars are considered to be Eq. [13]. magnetically-powered NSs, which emit X-rays by By solving Eq. [14] under a constant Bd, the consuming their magnetic energy given as pulse period and luminosity are predicted to evolve as B2 8 a function of time t as E ¼ d R3 = mag NS PðtÞ¼P ð þ t=t Þ1 2; ½ 20 3 0 1 1 15 2 1 B ErotðtÞ¼Erotð0Þð1 þ t=t1Þ ; ½16 40 d ¼ 4:4 10 J ½12 2 1011 T LrotðtÞ¼LM2ðtÞ¼L0ð1 þ t=t1Þ ; ½17 where 70 is the vacuum magnetic permeability. where subscript 0 specifies the value at the birth (t F 0), and t is a time constant over which the fi 1 3. Measurements of magnetic elds initial rotational energy is halved. From this P(t), the of neutron stars characteristic age of Eq. [5] can be expressed as In this section, we describe three representative ðtÞ¼t þ t : ½18 ways to estimate the MFs of NSs. The first one is for c 1 isolated NSs, while the latter two are applicable to Thus, =c can be identified with the true age t when accreting NSs. We have contributed to the third t1 can be neglected. Indeed, the Crab Pulsar has method, and partially to the second one as well. =c F 1250 yr, which is sufficiently close to its true age, 3.1. Pulse periods and period changes. The 962 yr as of 2016. Furthermore, by integrating the most widely used way to estimate Bd of isolated NSs above Lrot from t F 0tot FD1, we obtain is to assume that their spin-down energy release, L rot E ð0Þ¼L t : ½19 of Eq. [7], goes into magnetic dipole radiation,9) of rot 0 1 which the luminosity is written as Combining this with Eq. [13] and Eq. [6], we obtain ð = ÞðB R3 Þ2 4 t 3ðP= Þ2ðB = 8 Þ2 ½ L ¼ 2 3 d sin 2 ½ 1 7 10 10 ms 0 sin 10 T yr 20 M2 3 13 c 0 P where P0 9 10 msec is assumed. Thus, magnetars 11 where 3 is the angle between the rotational and with B0 9 10 T would lose half the initial rotational magnetic axes. Wep canffiffiffiffiffiffiffiffi equate this with Eq. [7], to energy in only a few days, while NSs with B 9 105 T 10 obtain Bd sin / PP_ . Using Eq. [2], the relation would have t1 9 10 yr, i.e., a cosmological time can be expressed more explicitly as scale. P 1=2 P_ 1=2 3.2. Accretion torque. To estimate MFs of B sin ¼ 0:32 108 T: mass-accreting NSs (those in binaries), which exhibit d : 15 = 0 3s 10 s s in Fig. 4 a large scatter in P, we must consider ½14 accretion torque, namely, angular momentum trans- This “P-P_ technique” has yielded the values of fer to/from the accreting matter. In this case, the NS Bd of all non-accreting NSs in Fig. 4, including radio can either spin up or spin down, unlike Eq. [13] which pulsars, MSPs, and magnetars. In particular, it yields always acts to spin down the NS. 8 Bd sin ¼ 2:8 10 T for the Crab pulsar, which The accretion torque formalism was developed 13 !1 14) has P F 0.0332 sec, P_ ¼ 4:22 10 ss , and Lrot F in the late 1970’s, and is being calibrated and 5.1 # 1031 erg s!1 employing I F 1.1 # 1038 kg m2.13) confirmed through MAXI monitoring of several While this method is convenient, it gives only a BXPs including GX 304–115) and 4U 1626–6716) in lower limit on Bd in the sense that 3 is usually particular. It assumes that the gravitational pull unknown. At the same time, it may be regarded working on the accreting matter becomes counter- as giving an upper limit, because the spin-down balanced by the magnetic presssure at a radius RA, may take place via other energy output channels, called Alfvén radius, which can be expressed as 2=7 4=7 including acceleration of particles via unipolar Lx Bd 10) R ¼ 106 induction mechanism (§ 2.4), and creation of A 1030 W 108 T plasma outflows. Thus, the estimates with Eq. [14] R 10=7 M 1=7 are considered rather crude. These additional energy NS NS m ½21 losses are considered to have very similar strengths 11 km 1:4M No. 5] X-ray studies of neutron stars and their magnetic fields 141 where 1 is a numerical factor of order unity, and This technique utilizes the basic physics that an L / M_ / R2 v v fi x 4 A ff is the X-ray luminosity with ff electron in a uniform magnetic eld B makes cyclo- being the radial free-fall velocity at RA. This Lx is tron gyration at an angular frequency of + F eB/me, essentially the same as Lgrav of Eq. [9]. At radii which translates to a photon energy of r > R , the matter is assumed to rotate with the A E ¼ !eB =m ¼ 11:6ðB =108 TÞ keV ½25 Keplerian angular frequency as a d e d pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ignoring special and general relativistic effects. In ! ðrÞ¼ GM =r3: ½22 K NS terms of quantum mechanics, this is identical to At r < RA, in contrast, the matter is assumed to be the Landau level intervals. As a result, an X-ray captured by the MF lines and fall to the accretion spectrum from a BXP often bears a noticeable columns with vff. The NS will receive momentum feature, called Cyclotron Resonance Scattering (positive torque) from the matter, and hence be spun Feature (CRSF),17),18) at the energy of Eq. [25] and up, if it is rotating slowly as + < BK(RA), where its higher harmonics; Fig. 5 shows two examples. + 2 P/2: is the angular frequency of the NS Evidently, detections of CRSFs provide the most rotation. (We implicitly assume that the accretion direct measurements of the surface dipole MFs of plane is nearly perpendicular to the pulsar’s spin axis BXPs through Eq. [25]. However, by the mid 1980’s, and the matter rotates in the same direction as the only two examples of CRSF were known; Her X-119) 20) pulsar.) In contrast, a fast rotator with + > BK(RA) at Ea F 35 keV and 4U 0115D63 at Ea F 11 keV. will give angular momentum to the accreting matter, Using Ginga launched in 1987,2) we have and expel it out. This “propeller effect” will spin-down drastically enlarged the number of CRSF detections. the NS. Beginning with a discovery at Ea F 21 keV from 4U Most of accreting NSs, including both BXPs and 1538–52,21) CRSFs have been detected one after LMXBs, are expected to be in a condition of near another, from X0331D53 at 28 keV,22) Cep X-4 at 23) 17) torque equilibrium, namely, + : BK(RA), because 29 keV, 4U 1907D09 at 20 keV, GX 301–2at their spin up/down time scales due to the accretion 36 keV,17) and Vela X-1 at 25 (or 50) keV.17) In torque are estimated to be shorter than their life addition, the previously known two CRSFs in Her 24) 25) times. Then, expressing the + : BK(RA) condition X-1 and 4U 0115D63 were reconfirmed. These using Eq. [21] and Eq. [22], we obtain so-called results have established that CRSFs are a common equilibrium rotation period as feature of BXPs, and provide their surface MFs in the L 3=7 B 6=7 most reliable way. The measured values of Ea were 3=2 x d – Peq 0:6 sec ½23 apparently concentrated in the range of 10 40 keV, 1030 W 108 T 8 which implies Bd F (1–4) # 10 T from Eq. [25]. where the dependence on MNS and RNS has again Although CRSFs can theoretically appear either in been suppressed. Thus, accreting NSs with stronger absorption or emission, and the Her X-1 result was at MFs and lower luminosities are expected to have first interpreted as an emission line,19) these Ginga- longer pulse periods. Conversely, by measuring P and detected CRSFs, including that of Her X-1, were all Lx of an accreting NS, and equating P with Peq,we found in absorption. can estimate its Bd as Through these observations, we showed that the L 1=2 P 7=6 BXP spectra with a CRSF can be described, as a B 1:8 108 7=4 x T: ½24 function of the X-ray energy E,as17),18),21),26) d 1030 W 1 sec fðEÞ¼ðEÞf ðEÞðEÞ: ½26 In Fig. 4, the MF strengths of LMXBs have been NPEX estimated in this manner, using their fast spins and Here, 9(E) is a factor for photoelectric absorption, high luminosities, although the results are rather and uncertain, reflecting uncertainties, e.g., in the numer- þ E 1 f ðEÞ¼ðA E 1 þ A E 2 Þ ½ ical factor in Eq. [21]. NPEX 1 2 exp E 27 3.3. Electron cyclotron resonances. Among cut accreting NSs, BXPs (§ 2.3; extending horizontally in is a continuum model called “NPEX” (Negative and 8 17),26) Fig. 4) have typically Bd 9 10 T, and allow partic- Positive power-law with EXponential cutoff), ularly accurate measurements of Bd based on electron with A1, A2, !1, !2,andEcut all positive free cyclotron resonances. In fact, the MF strengths of parameters. The first term E 1 expðE=EcutÞ these objects have all been determined in this way. represents unsaturated Comptonization within hot 142 K. MAKISHIMA [Vol. 92,

Fig. 5. Examples of X-ray spectra (in 8F8 presentation) of two transient BXPs with CRSFs. (a) Deep harmonic CRSFs at 26 and 52 keV, observed from X0331D53 with RXTE.33) The best-fit model of Eq. [26] with double * is superposed onto the data in a solid line, while the model after removing the factor * is indicated by a dashed curve. (b) A hard X-ray spectrum of GRO J1008–57, obtained with the HXD onboard Suzaku. Histograms in the top panel show a fit with Eq. [26], but without the * factor, while the bottom panel shows the data-to-model ratio. Prominent negative residuals at 980 keV indicate the highest-energy CRSF observed to date.38) plasmas in the accretion columns of BXPs, while the changes (up to 950%) in the resonance energy in a þ2 31)–33) 2nd term E expðE=EcutÞ, often with !2 F 2.0 few BXPs. Possibly the standing shocks which fixed, describes Wien hump produced by the Comp- form in the accretion columns change their heights as tonization. Finally, a multiplicative factor M_ varies, so that the value of Bd changes to some () fi fi DðWE=E Þ2 extent under the dipolar eld con guration. ðEÞ¼exp a ½28 Suzaku,4) launched in 2005, allowed us to search ðE E Þ2 þ W 2 a CRSFs in the 30–100 keV energy range, which had models the CRSF after the classical cross section of poorly been explored by previous missions. Thanks cyclotron resonance, where D is the depth and W is to the Hard X-ray Detector (HXD)34) onboard, this the width of the resonance. This model typically attempt has been successful, as we detected CRSFs 35) yields D F 0.3–1.5 and W F (0.2–0.3) # Ea. The from A0535D26 at 945 keV, from GX 304–1at latter may reflect various effects in the accretion 50–54 keV,36) from 1A 118–61 at 955 keV,37) and column, including thermal Doppler effects, MF the highest record of Ea 9 76 keV from GRO J1008– intensity gradients, Compton scattering, and even 57.38) Although some of these CRSFs had been induced emission27) as a speculative possibility. We suggested by previous studies, the Suzaku detections also found clear positive correlation between Ea and are much more convincing. These new results some- Ecut. This suggests that the electron temperature what expanded the MF distribution of BXPs towards of the accretion column, approximated by Ecut in the higher side, to Ea F 10–80 keV and hence Eq. [27], is determined mainly by cyclotron cooling.26) B ¼ð1{7Þ108 T: ½29 Following the Ginga achievements, observations d with the BeppoSAX, RXTE, and INTEGRAL In addition, a possible cyclotron emission feature was satellites increased the number of detected obtained from 4U 1626–67.39) CRSFs.28),29) From a fair number of these objects, Using Suzaku, we also discovered that 4U 1822– higher harmonic absorptions were detected (e.g., 37, which has a low-mass companion and was so far Fig. 5a), up to the 4th harmonic in the most extreme classified as an LMXB, is in reality a BXP with 30) 40) case. Another interesting effect which we discov- Ea 9 33 keV. Including these and other firm ered with Ginga and RXTE is luminosity-dependent examples, the CRSF has been detected to date from No. 5] X-ray studies of neutron stars and their magnetic fields 143 about 20 objects, out of the 950 BXPs that are securely catalogued in the Local Universe. They are 4. Challenging the mysteries of magnetars subdivided into about 10 objects with Be-type 4.1. Basic properties. We have now come to primary stars, about 7 objects capturing stellar winds the stage of describing magnetars, by far the most from their OB-type companions, and 3 examples (Her enigmatic of all NS subclasses. Historically, the con- X-1, 4U 1626–67 and 4U 1822–37) accreting from cept of magnetars emerged from two populations of their low-mass companions presumably via Roche- high-energy objects. One is Soft Gamma Repeaters, lobe overflow. known since 1979, which emit sporadic gamma-ray 3.4. Distributions of MF strengths. Figure 6 bursts with softer spectra than the classical (hence shows distribution histograms of the values of Bd of cosmological) gamma-ray burst sources. The other NSs, determined with the P-P_ method (§ 3.1) and is Anomalous X-ray Pulsars, peculiar X-ray pulsars the CRSF technique (§ 3.3). There, MF determina- without binary evidence, of which several were tions using the accretion-torque method of Eq. [24] known from the 1980’s. Based on observations with, are not included, because of large uncertainties e.g., ASCA3),42) launched in 1993, these two popula- involved. However, we are left with a freedom of tions have gradually been found to represent two adjusting the value of 1 in Eq. [21]. Empirically, different aspects of the essentially identical popula- we found that 1 9 1 can consistently explain the tion, and they have come to be collectively called behavior of disk-fed short-period (P < 100 sec) BXPs, “magnetars”.43),44) while 1 9 5 is favored by the data of long-period At present, about 30 magnetars are known in (P > 100 sec) objects.41) By thus calibrating 1, the the Milky Way and the Magellanic clouds. Further- accurately measured MF strengths of the CRSF- more, new magnetars are being discovered typically bearing BXPs have been reproduced with Eq. [24] one per year or so, mainly by the Swift mission which within a factor of a few. In this sense, the two detects short bursts from (re-)activated transient independent measurements of MF of BXPs are magnetars. Including both these transients and consistent with each other. persistent sources, major observational properties of Figure 6 is approximately equivalent to the magnetars are summarized as follows. projection of Fig. 4 onto the Bd axis. It exhibits 1. Some magnetars are persistent X-ray sources 7 9 27 28 three broad peaks; one at Bd F 10 –10 T covering with a luminosity of Lx F 10 –10 W, while BXPs and the majority of radio pulsars, another for others are transients which are much dimmer 10 11 magnetars at Bd F 10 –10 T, and the other at during quiescence. They are all very dim in 4 5 Bd F 10 –10 T for MSPs (and LMXBs). It is other wavelengths. important to search for clues to this wide scatter in 2. During active periods, magnetars emit sporadic the MF strength, and to the origin of the three bursts lasting for 90.1 to 9103 sec. The burst apparent peaks. Another interesting point in Fig. 6 energy scatters widely over 1030–1039 J, and is that the MF distribution of BXPs (in green), the emission often extends to soft gamma-ray determined with the CRSF technique via Eq. [29], is energies. much narrower than the main peak formed by radio 3. Several magnetars reside near the center of pulsars. At present, it is unclear whether the two SNRs. distributions are different, or can be consistent if 4. All magnetars show clear X-ray pulsations considering various selection effects. due to their spin, at periods which cluster in a So far, the search for CRSFs have been narrow range of P F 2–12 sec. They also show unsuccessful on more than half the known BXPs. rather high spin-down rates as P_ 1013 to 8 !11 !1 Some of these objects may have Bd >7# 10 T, 10 ss . and hence exhibit CRSFs in higher energies (e.g., 5. None of them show evidence for binary com- >80 keV) than was explored with Suzaku. Promising panions or mass accretion. candidates include BXPs with long pulse periods 6. Compared to those of typical BXPs (e.g., (P >103 s)41) as inferred from Eq. [24], and/or with Fig. 5), their persistent spectra in the 1–10 keV very hard spectra as suggested by the Ea vs. Ecut range are often very soft, typically equivalent to correlation (§ 3.3). This pertains to the issue of a blackbody temperature of 95 # 106 K. whether the apparent gap in the MF distribution From item 4 above, magnetars are considered as between BXPs and magnetars is intrinsic or due to magnetized NSs, and are rather young from item 3, selection effects. in spite of their long P (item 4); in fact, Eq. [5] gives 144 K. MAKISHIMA [Vol. 92,

2 9 =c F 1–100 kyr. From items 5 and 6, they are unlikely quantum critical field Bc F (mec) /!e F 4.4 # 10 T 2 to be accretion-powered NSs. Furthermore, they at which the energy of Eq. [25] reaches mec .Asa cannot be rotation-powered objects, either, since result, magnetars have been regarded as magneti- 43) their long P makes Erot much lower than those of cally-powered NSs (§ 2.4). This is supported by the radio pulsars, and hence their Lrot of Eq. [7] falls, in fact that the values of Bd of magnetars calculated via spite of the large P_ (item 4), 1–3 orders of magnitude Eq. [13] clearly decrease as a function of =c of Eq. [5], below the observed Lx (item 1). At the same time, as we see later in Fig. 12. Then, item 2 can be Eq. [14] indicates that magnetars have extremely explained as sudden releases of magnetic energies,43) 10 11 strong MF as Bd F 10 –10 T, which exceeds the either inside or outside the stars. Finally, items 1 and 6 can be understood by presuming that magnetars emit soft X-rays as thermal emission from the NS surface heated by these magnetic activities. Besides the above standard scenario, there are BXPs alternative explanations of magnetars, including the idea that they are fed by accretion from fossil disks.45) However, this possibility is less likely, because the characteristic two-component spectra of magnetars (Fig. 7b) are not observed from BXPs (cf. Fig. 5), even when they become rather dim35) down to the typical luminosity of magnetars (< a few times 1028 W). 4 5 6 7 8 9 10 11 The strong-MF interpretation of magnetars43),44) (T) has thus been generally successful. Nevertheless,

Fig. 6. Distribution histograms of the surface dipole MF, Bd,of it still remains a sort of conjecture, to be called NSs. Blue indicates radio pulsars and MSPs, and red shows magnetar hypothesis, and leaves us with a number of magnetars, both utilizing Eq. [14]. Green shows BXPs with challenges. First of all, it must be proven whether confirmed CRSFs, for which Eq. [25] is utilized. The blue magnetars really harbor such strong MFs, and are histograms refer to the left ordinate, while the red and green ones to the right. The data refer to the ATNF Pulsar Catalogue,76) indeed powered by magnetic energies. Even if these available online at http://www.atnf.csiro.au/research/pulsar/ basic questions are answered affirmatively, we must psrcat for updated versions. clarify how the magnetic energies are consumed to

(a) Cyg X-1 (b) 10 The Crab Nebula Her X-1

Cyg X-1 SGR 1806-20 (0.22 kyr) 1 1E 1547.0-5408 (1.4 kyr) (a.u.) Aql X-1 (high) ν F ν RXS J1708-40 (9.0 kyr) GC plasma 0.1 Aql X-1 (low)

4U 0142+61 (70 kyr) 0.01 V2400 Oph 1 10 100 1 10 100 Energy (keV) Energy (keV)

Fig. 7. (a) Suzaku spectra of various Galactic X-ray sources, in their 8F8 forms. The <10 keV and >10 keV data are from the XIS and the HXD, respectively. Cyg X-1 is an accreting black hole, Her X-1 is a BXP with a CRSF at 35 keV, Aql X-1 is an LMXB, V2400 Oph is an accreting white dwarf, “GC plasma” with strong emission lines represents thin-thermal emission from diffuse hot plasmas surrounding our Galactic center, and the Crab Nebula (in its model form rather than real data) refers to synchrotron emission from the entire nebula shown in Fig. 3. Vertical positions of these spectra are arbitrary. (b) Suzaku spectra of four magnetars in the same form as panel (a), and all normalized at 2.0 keV. The number in parenthesis after the name indicates =c of Eq. [5]. No. 5] X-ray studies of neutron stars and their magnetic fields 145 power the persistent and burst emissions, and what up of low-energy electrons/photons towards higher is the relation between these two X-ray emission energies.49) Details are explained below. channels. It also needs to be answered whether While magnetars have 2 orders of magnitude the apparent gap in the MF distribution in Fig. 4 slower spins than typical radio pulsars, they have between BXPs and magnetars are real or due to 2 orders of magnitude higher MF. Therefore, the some selection effects, and what is special about the induced electric field in their magnetosphere up to formation scenario of magnetars compared to those of RLC should be comparable to those in pulsars. Then, NSs of the other subclasses. Hoping to obtain clues to as discussed in § 2.4, electrons in the magnetars’ these questions, we have been studying magnetars magnetosphere will be accelerated and emit abundant with Suzaku. gamma-rays (via, e.g., curvature radiation) which in 4.2. Emission spectra. Just before the launch turn produce electron-positron pairs. However, these of Suzaku, a European group used INTEGRAL to particles would not freely escape out from magneto- discover that a fair fraction of magnetars emit a sphere, because the centrifugal force of magnetars is separate hard X-ray component,46),47) in addition to 94 orders of magnitude weaker than that of pulsars. the well known soft X-rays (item 6 in § 4.1). This Then, the particles will fall onto the magnetar surface, novel spectral component has such a hard slope, where the positrons annihilate to emit 511 keV approximated by a power-law of photon index ! 9 1, gamma-rays. In radio pulsars, these photons would that it cannot be readily explained in terms of again initiate electron-positron cascades. However, in ordinary high-energy radiation processes, such as magnetars with Bd > Bcr, an energetic photon has a synchrotron radiation, inverse Compton scattering, finite probability of colliding with the MF that acts as or (non-)thermal Bremsstrahlung. a virtual photon, and splitting into two real photons. Our magnetar study with Suzaku utilizes its By a repetition of this “photon splitting” process, the wide-band capability, realized by the HXD34) and the input gamma-rays will increase in number, and X-ray Imaging Spectrometer (XIS). Figure 7a shows decrease in individual photon energy, thus forming a a compilation of Suzaku spectra of representative hard X-ray continuum from 511 keV downwards. In Galactic X-ray sources, while Fig. 7b presents those older magnetars with weaker MFs, this process will of 4 magnetars. Thus, we have reconfirmed the soon stop, while it will continue to softer photon reported two-component spectral characteristic of energies in younger ones with stronger MFs, because magnetars, because the spectra in panel (b) all exhibit this process, unlike the eDe! pair creation, has no very hard emission rising from 910 keV towards particular energy threshold. This scenario,49) fully higher energies, in addition to the long known soft based on the magnetar hypothesis, can consistently component (item 6 in § 4.1). This property is explain the properties of the hard component, generally not seen in other known classes of compact including its evolution revealed with Suzaku. X-ray sources [e.g., those presented in panel (a)], The above hypothesis provides a nice research except young rotation-powered pulsars of which the subject for future observations in the 0.1–1 MeV X-ray spectrum often consists of a soft thermal range. If we can detect a steep cutoff of the continuum component and a hard non-thermal tail.48) However, above 9511 keV, our scenario, as well as the magnetar the hard component of these objects usually have hypothesis itself, will be significantly reinforced. ! 9 2, not as hard as those of magnetars. Thus, the 4.3. Bursts and persistent signals. As unusual spectral shape alone would considerably explained in § 4.1 (item 2), the X-ray/gamma-ray reinforce the peculiar nature of magnetars. bursts emitted from an activated magnetar scatter In Fig. 7b, the hard component of the four over many orders of magnitude in their size (energy magnetars are seen to become weaker (relative to the content). Among these bursts, very energetic and soft component), but harder in slope, as the objects rare ones have been detected and studied by instru- get older. This is an important discovery by Enoto ments with a wide sky coverage (but with a low et al. (2010)49) of a clear evolution in the magnetar sensitivity), because their occurrence is totally spectra, which suggests as if there is a pivot point unpredictable. In contrast, little has been known at several hundreds keV. We have hence proposed a about broad-band properties of smaller bursts that new explanation of the hard component, that it may are undetectable by these wide-field instruments. We be due to energy degradation of some energetic have successfully carried out this challenge with input gamma-rays, possibly the 511 keV annihilation Suzaku, through Target of Opportunity observations photons, rather than a result of successive boosting- (triggered by Swift) of two activated magnetars; the 146 K. MAKISHIMA [Vol. 92, new magnetar SGR 0501D451650) which suddenly combined without difficulty with our new interpre- appeared in 2008 August, and the fastest-spinning tation of the hard component (§ 4.2). In fact, known magnetar 1E 1547.0–540851) which became individual bursts are likely to be a manifestation of active in 2009 January. sudden release of magnetic energies44) somewhere Figure 8 shows the results on SGR 0501D in the system. This will lead to intense particle 4516,50),52),53) where we compare wide-band spectra acceleration, and to the hard-tail formation via the of (i) one big burst (which caused an automatic proposed photon-splitting process. The scenario is shut-off of the HXD), (ii) stacked small bursts, (iii) hence attractive, but it requires that the number vs. persistent emission during the activity, and (iv) that size distribution of bursts should steepen consider- after the activity decreased. Thus, the spectra of (ii) ably towards smaller bursts. and (iii) both consist of the soft and hard compo- As already mentioned, the soft component of nents, and the upper limit in (iii) is also consistent. magnetars, with a luminosity comparable to that of In (i), the two components appear to be merged the hard component, can be naturally regarded as together. Thus, the two-component nature of the thermal emission from the NS surface, heated either magnetar emission has been found to be a basic directly by the magnetic energy release, or indirectly property common to both their persistent and burst by the accelerated particles. Actually, the soft- emissions. In addition, over more than 4 orders of component spectra can be approximated by a black- magnitude, the luminosities of the two components body model, as inferred from Fig. 7b and Fig. 8. are approximately proportional to each other. These However, the data often require two temperatures, results strongly suggest that the persistent and burst with the hotter one 93 times higher than the emissions are produced essentially by the same other. Because this universal scaling applies to both mechanism. We obtained similar results from 1E persistent and burst spectra,56),57) the two-temper- 1547.0–5408.51),54),55) ature property is considered to represent some physics Incorporating data from a small satellite HETE- specific to the strong MF. One possibility is that 2, Nakagawa et al.56) proposed that the persistent electrons under such strong MF have quite different emission from magnetars is an assembly of numerous scattering cross sections to the two X-ray polarizasion “micro bursts” that are individually too small to modes, O-mode and X-mode with respect to the MF detect. (Evidently, this was inspired by the well direction. As a result, the two modes may have known view that solar coronae can be composed different photospheres with different temperatures. of numerous micro flares.) This conjecture can be If this interpretation is correct, we expect the soft component to be strongly polarized. The verification of this idea must await the advent of X-ray polar- imetry missions, including in particular PRAXyS being proposed under US-Japan collaboration. 4.4. Relation to supernova remnants. Usu- ally, stars with the initial mass >25 ME are thought to leave black holes, rather than NSs, in their collapse (§ 2). However, if the star is rapidly rotating, and/or is strongly magnetized, excess energies in the rotation and/or MF can expel out a larger amount of mass, and can lead to the formation of an NS rather than a black hole. It has hence been proposed that magnet- ars can be produced in supernova explosions of very massive (e.g., initial mass >20 ME) and rapidly- rotating stars.58) Using Suzaku, we examined the above predic- tion, since past observations were not very informa- tive. For this purpose, we chose the SNR called CTB109, which hosts at its center a relatively aged Fig. 8. Four spectra of the transient magnetar SGR 0501D4516, D obtained with Suzaku. A big burst,50) a stack of small bursts,53) magnetar, named 1E 2256 586. As shown in Fig. 9, the persistent emission during the acivity,52) and that after the this is actually one of the most typical magnetar- activity diminished. SNR associations. By analyzing soft X-ray spectra No. 5] X-ray studies of neutron stars and their magnetic fields 147

3. Because of the strong initial MF, 1E 2259D586 quickly [Eq. [20]] dumped out most of its rotational energy and became a slow rotator. Meantime, the MF decayed by dissipating Emag, to make P_ smaller and smaller. 4. As a result, 1E 2259D586 has achieved the present values of P F 6.98 s and P_ ¼ 4:8 13 !1 10 ss in a much shorter time, than =c calculated backwards from the present-day values ignoring the MF decay. The above scenario, derived from the particular SNR-magnetar pair, does not conflict with observed properties of other magnetar-SNR associations, and have three important and more general implications for magnetars. First, it implies that 1E 2259D586 (and possibly other magnetars as well) is indeed a magnetically-powered NS, because its MF must have fi Fig. 9. A mosaic Suzaku image (0.5–4 keV) of the SNR CTB109, been decreasing signi cantly as indicated by the age hosting the magnetar 1E 2258D586 at its center.60) problem. Second, the scenario can also explain why the values of P of magnetars are concentrated in the narrow range of 2–12 sec. Finally, magnetars are thus of CTB109 obtained with the Suzaku XIS, Nakano considered to be systematically and considerably 59) (2015) found that the X-ray emitting plasma younger than is indicated by their face values of =c. involves two temperatures (97 # 106 K and 92 # This last point is of the largest importance, because it 106 K). He identified the hotter and cooler compo- further implies that magnetars must be produced nents to the stellar ejecta and shock-heated inter- with a much higher rate than thought previously, stellar matter, respectively, and estimated the former possibly more frequently than radio pulsars. The to have a mass of 940 ME. This provides one of the produced magnetars will fade off very quickly by first observational confirmations of the theoretical exhausting Emag, and become invisible, because they prediction described above. can no longer be rotation-powered objects. These As seen in Fig. 9, 1E 2259D586 resides at the results altogether reinforce the magnetar hypothesis center of the half-moon-shaped CTB109. Neverthe- significantly, and suggest that magnetars are in fact less, their mutual association was plagued with a one of major forms of new-born NSs, instead of being serious puzzle called “age problem”: the characteristic a rare and special population. age of 1E 2259D586, =c F 230 kyr, is much longer than 4.5. Free precession of magnetars. In the estimated age of CTB109, 913 kyr. This puzzle addition to the dipole MFs which we have considered 60) has been successfully solved by considering that =c so far, magnetars can also harbor strong toroidal calculated via Eq. [5] assuming a constant Bd system- MF, Bt, which is confined inside the stars. In fact, a atically overestimates the true system age when the few magnetars which were discovered recently have 61),62) MF strength is decreasing with time as postulated in Bd < Bcr, so that the burst activity which led the magnetar hypothesis. Specifically, they mathe- to their discovery is likely to be powered by much matically modeled the spin down and the MF decay of stronger Bt hidden inside them. Such toroidal MFs 1E 2259D586, and constructed the following scenario could be produced in the final collapse of a stellar for this magnetar-SNR association.60) core, wherein the field lines will be wound up by 1. CTB109 and 1E 2259D586 were born together, differential rotation.63) Although it is intrinsically 913 kyr (not 230 kyr) ago, by the supernova difficult to observationally estimate Bt which is explosion of a progenitor of which the initial invisible from outside, we have successfully overcome mass was 940 ME. this difficulty, by utilizing the idea that strong 2. At the birth, 1E 2259D586 was rapidly rotating internal MFs will deform the star up to an 64) (e.g., P 9 10 msec), and had a higher Bd (e.g., “asphericity” of 91011 T) than the present value of B F 5.9 # d ðI I Þ=I 1 104ðB =1012 TÞ: ½30 109 T. 1 3 3 t 148 K. MAKISHIMA [Vol. 92,

Here, I3 is the moment of inertia around the become maximum slightly before or after the timing ~ magnetar’s symmetry axis x^3, which we identify with when the L-x^3 plane points to us every precession 65) its dipole MF axis, and I1 is that around the axes cycle. As a result, the regular pulsation at Pprec orthogonal to x^3. The deformation is expected to be becomes periodically phase modulated, at the period prolate (C >0)if Bt > Bd as assumed below, while T and with a certain modulation amplitude Ap = oblate (C <0)ifBd dominates. Pprec. This Ap is expected to depend positively on ,, Let us consider dynamics of such an axisym- ., and 9. ~ metric rigid body, under no external torque. If x^3 k L, The persistently bright X-ray source 4U where L~ is the angular momentum, the body would 0142D61, pulsing at P F 8.689 sec, is one of the simply rotate around L~ with a constant rotation magnetars with the strongest hard component, ~ period Prot F 2:I3/L (with L jLj). However, if x^3 showing a clearcut two-component spectrum (blue is titled from L~ by a finite “wobbling angle” , (which in Fig. 7b).66) We analyzed 4 Suzaku data sets of this can take any value regardless of 0 or |L|), the x^3 object, taken in 2007, 2009, 2011, and 2013. Clear axis will rotate, or wobble, around L~ with a slightly evidence of periodic modulation in the 8.689 sec pulse different “precession period” Pprec F 2:I1/L. This phase was discovered in the 15–40 keV data from the condition is illustrated in Fig. 10. As seen from an latter 3 observations, at a consistent modulation ~ observer located on the L-x^3 plane, the body will period (to be identified with the slip period) of T F slowly rotates at a “slip period”, 55 ’ 4 ksec.67) The modulation amplitude in 2009, 2011, and 2013 was A F 0.7 ’ 0.3 sec, 0.9 ’ 0.5 sec, T P = ¼ð1=P 1=P Þ 1; ½31 p prec rot prec and 1.1 ’ 0.4 sec, respectively, while the 2007 data which is just the beat between Pprec and Prot. This is gave an upper limit as Ap < 0.8. Interestingly, the the most basic behavior of a torque-free rigid body phase modulation was always absent (Ap < 0.3 sec) with axial symmetry, and is called “free precession”.65) in signals below 10 keV, where the soft component Even when the free precession is taking place, dominates (Fig. 7b). These novel results on 4U (i.e., 0 º 0and, º 0), we can detect only Pprec, and 0142D61 can be consistently interpreted by assuming cannot observe Prot, as long as NS’s radiation pattern that this magnetar is axisymmetric, and is under- is symmetric around x^3. (In this sense, the regular going free precession with a slip period of T F 55 ksec. pulsations of radio pulsars and BXPs should be From Eq. [31], the asphericity is constrained as 0 F !4 12 considered as precession, rather than rotation.) 1.6 # 10 , which in turn translates to Bt 9 10 T However, if the radiation pattern is asymmetric via Eq. [30] if the deformation is attributed to around x^3, it becomes possible to observe the slip internal magnetic pressure. The absence of this phase period T in addition to Pprec. Suppose that the modulation in the soft component can be understood emission hotspot (an orange circle in Fig. 10) is if the soft X-ray emission region is symmetric displaced from x^3 by a finite angle ., or the radiation (. F 9 F 0 in Fig. 10) around x^3, while the possible beam is tilted by an angle 9 from x^3. Then, depending year-to-year variation in Ap in the hard component is on the phase in T, the emission reaching us will likely to result from secular changes in . (º 0) and/or 9 (º 0) of the hard X-ray emission region; , should not change on such short time scales. The data however constrained neither ,, ., nor 9 uniquely. Although we cannot tell from the data alone whether the suggested deformation of 4U 0142D61 is prolate or oblate, we may obtain a clue to this issue from basic Newtonian dynamics. When L~ is con- served and some energy dissipation takes place, an oblate rigid body will reach its energy minimum at , F 0 (no precession), while a prolate body will do so at , F 90° (flat spin). Since internal dissipation in an NS is considered to be relatively fast, the wobbling angle of an oblate NS (e.g., due to centrifugal force Fig. 10. An illustration of free precession of an axisymmetric when the rotation is fast) would soon decay even if rigid body. Three angles, ,, ., and 9 are of importance. See text free precession is once excited by some perturbation. for details. Since 4U 0142D61 definitely has , º 0 as evidence No. 5] X-ray studies of neutron stars and their magnetic fields 149 by its clear pulsation, a prolate shape is favored, in evidence for free precession in the two magnetars which case , would gradually increase with time. (§ 4.5). As a result, our confidence in the magnetar The same pulse-phase modulation effects, as hypothesis has been significantly reinforced, and observed from 4U 0142D61, have also been discov- evidence is accumulating to believe that magnetars 68) 10 11 ered in Suzaku data of 1E 1547.0–4516, the fastest- really have strong MFs as Bd F 10 –10 T or higher, spinning (P F 2.0721 sec) magnetar which became and are powered by the magnetic energies. Further- active in 2009 January (§ 4.3; orange in Fig. 7b).51) more, we have shown that magnetars can be one of T ¼ : þ4:5 In this case, we obtained 36 02:5 ksec, which the most major subclasses of new-born NSs, besides yields 0 F 0.6 # 10!4. This is somewhat smaller than, radio pulsars and BXPs. As a natural consequence of but still of the same order, as the case of 4U 0142D61. these results, NSs are now considered to have a wide Figure 11 visualizes the phase modulation of the 15– range of scatter in Bd from their birth, at least over 40 keV pulse profiles of this magnetar at the 36 ksec 108–11 T. slip period. Again, the pulse-phase modulation was Can a new-born NS, then, have a very weak MF 7 seen only in the hard component, and absent in the as Bd <10 T? The answer is probably yes, from the soft component. following two pieces of evidence. One is a handful The study of free precession has opened a totally young SNRs (with age <10 kyr; including Cas A in new window on the estimation of toroidal MFs of particular) that contain rather inactive central NSs magnetars. We are now searching Suzaku data of called CCOs (Central Compact Objects). Some of other magnetars for similar effects. In addition, CCOs are weakly pulsing at sub-second periods, archival data from the NuSTAR mission will greatly and their values of P_ is extremely small, implying 6 7 accelerate the study. An increased number of detec- Bd sin 3 F 10 –10 T. Even if sin 3 9 0, we would tions of the free precession will allow us to address expect strong particle acceleration and associated 8 10) such issues as; whether the magnetic deformation is activities as long as Bd 9 10 T. Thus, CCOs are common among magnetars; what is the distribution considered to have truly weak Bd. The other is a of Bt; and whether Bt is proportional to Bt. peculiar accreting NS called Cir X-1. It has a rather massive (910 ME) companion, of which the lifetime 5. Discussion is <107.5 year, and could even be associated with the As described so far, our understanding of the NS SNR G321.9–0.3. Therefore, this NS is definitely very magnetism has made a large progress owing to the young, but it it known to emit Type I X-ray bursts, 6 extensive studies over the last quarter century. which are considered to take place only if Bd <10 T Nevertheless, we are still left with several fundamen- or so. Therefore, this particular NS is also considered tal questions to be solved, as we already mentioned in young and weakly magnetized. These two examples § 2.3, § 3.4, and several places in § 4. These include; suggest that some NSs are born with weak dipole why the MF of NSs exhibits such a large scatter as MFs (although they could have high Bt). seen in Fig. 4 even though their masses and radii Based on these considerations, we conclude that show narrow distributions; are there intermediate NSs are born with a variety of dipole MF strengths, 11 7 objects between magnetars and ordinary radio ranging from >10 T down to Bd <10. Objects like pulsars; how the MF of NSs evolve after their birth; the Crab Pulsar can no longer be considered as and, what hold the MFs inside NSs. In an attempt typical young NSs. The information on Bt is still very to answer some of these questions, let us conduct poor, however. discussion from several aspects. 5.2. Evolution of MFs above Bcr. When 5.1. Initial MFs of NSs. In the last decade, trying to understand the MF distribution in Fig. 6, significant new facts about magnetars have been three factors must be considered; the initial MF unveiled (§ 4). These include our own achievements; spread as discussed in § 5.1, the MF evolution the universal two-component nature of their persis- over the life times of respective NSs, and various tent and short-burst spectra (§ 4.2); the new scaling observational selection effects. Here, let us consider law for the hard component (§ 4.2); the microburst the second factor, incorporating some aspects of the hypothesis to explain the persistent emission (§ 4.3); third one. For this purpose, Fig. 12 summarizes all the two-temperature quantification of their soft the currently known non-accreting pulsars (including component (§ 4.3); the estimated progenitor mass magnetars) on the plane of =c and Bd. Several of 1E 2259D586 (§ 4.4); the solution to the age remarks may be added to this figure. (i) As long as problem in terms of MF decay (§ 4.4); and the non-accreting pulsars are concerned, this plot can be 150 K. MAKISHIMA [Vol. 92,

12 Folded at 36 ks 11 1E 2259 10 Bcr 9 Crab 8

7 6 Isolated 5 Binaries Magnetars 4 In SNRs

Log Dipole Magnetic Field (T) 3 2 3 4 5 6 7 8 9 10 11 Log Characteristic Age (yr)

Fig. 12. The dipole magnetic fields and the characteristic ages of all known pulsars, including magnetars but excluding mass- accreting objects such as BXPs and LMXBs. Black crosses, green squares, and red hexagons indicate isolated pulsars, pulsars in binaries, and magnetars, respectively. Magenta circles indicate Pulse Phase Bin those in SNRs. The plot was made by T. Nakano, making use of the information from the ATNF Pulsar Catalogue76) in the same – fi Fig. 11. The 15 40 keV pulse pro les of the magnetar 1E way as Fig. 6. Cyan and blue lines indicate possible evolutionary – 1547.0 4516, folded at a barycentric period of 2.07214 sec, in 6 tracks of 1E 2259D586 (see text § 5.1). different phases of the T F 36 ksec slip period.68) Their average is shown in black at the middle. halved. The condition of a constant MF (non-decay) is expressed as =d !1. obtained by changing the plotting axes in Fig. 4, and In the case of 1E 2259D586, one possible solution its projection onto the Bd axis gives Fig. 6 (except (among many possibilities) to Eq. [32] is given as 11 60) the green histogram). (ii) The green squares indicate B0 F 1.8 # 10 T, =d F 160 yr, and O F 1.4, which pulsars in binaries, but they have relatively wide imply that the MF decreased to 0.033B0 in the 13 ky orbits so that mass accretion does not take place. of life time. This particular evolutionary track is (iii) The values of =c of magnetars are likely to be shown in Fig. 12 by a cyan curve, in which abscissa is systematically overestimated as we described in § 4.4, redefined as the true elapsed time. After converting but the plot employs the uncorrected =c. (iv) A few this true age to the apparent (heavily over-estimated) 6 9 SNR-hosted pulsars with =c F 10 –10 yr and Bd F =c to match with the plot, the track becomes as 5 6 10 –10 T are CCOs, of which =c is likely to be heavily indicated by a blue curve. Thus, Eq. [32] can explain overestimated, because we cannot ignore in this case the behavior of not only 1E 2259D586, but also of t1 in Eq. [18]. With these remarks in mind, let us other magnetars. Furthermore, the magnetic energy investigate into Fig. 12. release rate, !dEmag/dt, calculated from Eq. [12] and In Fig. 12, magnetars define a clear negative Eq. [32] using these parameters, become 97.5 # 27 dependence of Bd on =c. This behavior is likely to be 10 W at present, which is in a good agreement free from selection effects, since persistent magnetars with the observed bolometric X-ray luminosity of 1E and newly discovered transients line up on the same 2259D586, 6 # 1027 W. From these considerations, line. The trend agrees with the magnetar hypothesis, the MFs of magnetars are concluded to decay over and our results on 1E 2259D586 and CTB109 (§ 4.4). time scales of 10–100 kyr, down to values below Bcr. More quantitatively, we can model the decay of Bd They would soon become undetectable, unless some of magnetars as60),69) revival mechanisms operate.  B t 1= 5.3. Evolution of MFs below cr. Hereafter, BdðTÞ¼B0 1 þ ; ½32 we limit the discussion to those NS which were born d with B0 < Bcr. In Fig. 12, radio pulsars are distri- B / 0:4 where t is the time since the birth, B0 is the initial buted approximately along a slope of d c . The (t F 0) field, O is a positive parameter, and =d/O simplest interpretation, which in fact used to be a describes a time scale on which the initial B0 is standard one till the 1990’s, is to consider that the No. 5] X-ray studies of neutron stars and their magnetic fields 151

MF of NSs decay gradually and ubiquitously, on such a low-mass star formed a binary with a massive typical e-folding time scales of 9108 yr.70) This was progenitor of the NS. However, if the capture process also motivated to explain MSPs and LMXBs: a dominates, we would observe even larger number of standard view is that they were born as isolated radio strong-MF NS with low-mass companions (in con- 8 pulsars with Bd 9 10 T, became slow rotators by trast to the only known three), because higher MFs losing Erot, and weak-Bd objects due to the MF decay, of NSs will enhance the extraction of orbital angular and captured by a low-mass star to become LMXBs, momentum73) which is necessary in their capture wherein they were spun up (“recycled”) by accretion process. Even if the accretion induced collapse as described by Eq. [14]. After the accretion ceased or dominates, a small fraction (10–25%) of white dwarfs 71) 2 8 the binary dissociated, the NS were left as MSPs. with Bd >10 T would become NSs with Bd >10 T The above scenario of MF decay, however, via the magnetic flux compression; again, we should became obsolete for the following two reasons. One observe more aged NSs with strong MFs than are is selection effects, combined with the initial scatter observed. Therefore, the MF below 9109 is unlikely in B0 (§ 5.1). Pulsars born with relatively high B0, to be constant with time. hence with shorter lifetimes [Eq. [20]], will fade away A third explanation of the MF evolution below 9 more quickly than those with weaker B0. Further- Bd 9 10 T is to invoke a kind of “transition” from 7 9 4 5 more, those with weak B0 have large values of t1 Bd F 10 –10 Tto10–10 T, at a certain timing of so that their =c will be overestimated. These two the evolution of individual NSs. As a toy model, we artifacts suppress, in Fig. 12, the numbers of old/ may assume that the transition occurs in 9109 yr, high-Bd pulsars and young/low-Bd ones, respectively, and that the timing scatters considerably from object to mimic the apparent negative correlation. Actually, to object for some unspecified reasons. This is indeed a reanalysis of the radio pulsar statistics had already what is apparently suggested by Fig. 12. Then, the shown in the middle 1990’s that a constant MF strong concentration of the MF of BXPs at Eq. [29] model is consistent with the observations.72) can be explained because their life times are <108 yr The other evidence is the very narrow distribu- or so. The abundance of MSPs and LMXBs can be tion of Bd of BXPs [Fig. 6 (green) and Eq. [29]], explained by considering that the dominant NS 7 9 which is considered complete on the lower-field subclass born with Bd F 10 –10 T would have side17),18) (although still incomplete towards the mostly completed their transition in 9109 yr. The higher-field side). Considering typical lifetimes of three outliers, Her X-1, 4U 1626–67, and 4U 1822– the primary stars of BXPs (105.5–107.5 yr), any field 37, can be interpreted as those which have not decay on time scales of <108 yr would make the MF yet completed their transition. Thus, this simple distribution of BXPs much broader towards the view17),18) can explain the observations in a consistent lower field side. Furthermore, the presence of the way, although it is not yet widely accepted. three BXPs with low-mass companions stars (§ 3.3), 5.4. How the MF is held. The final and the which have estimated system ages of >109 yr, cannot most fundamental issue is how the MFs of NSs are be reconciled with the MF decay even on a time held, and how the strong-to-weak MF transition 9 8 scale of 10 yr. Therefore, the MF below Bd 9 10 Tis suggested in § 5.3 takes place. The simplest idea is unlikely to decay smoothly on time scales of <109 yr, so-called fossil-MF view; during the core collapse, the 8 8 although the behavior at 10 T

A contrasting scenario is to assume that the MF tion of NSs) and fundamental physics. The results is sustained by ferromagnetism in nuclear matter, obtained in these studies can be summarized into the produced by quantum alignment of magnetic mo- following points. ment of neutrons.17),18) This view had already been 1. Magnetars are indeed likely to be magnetically- proposed in the late 1960’s,75) immediately after the powered objects, with truly super-critical dipole 11) 10 11 discovery of pulsars. If a fraction f of the total fields of Bd F 10 –10 T and possibly even 57 12 Nn F MNS/mn F 1.7 # 10 neutrons in an NS be- stronger toroidal fields of Bt 9 10 T. come spin-aligned, we obtain from Eq. [4] a MF 2. NSs are born with a wide range of initial dipole strength of fields, from 1011 to <105 T. In addition, mag- netars are likely to occupy a relatively large B fN =2R3 2:5 f 1012 T ½33 0 n n NS fraction of NSs that are born in core-collapse !27 !1 where 7n F 1.91 7N F 9.7 # 10 JT is the neu- supernovae. tron magnetic moment, with 7N 2 e!/2mp F 5.05 # 3. The MFs of magnetars (>Bcr) decay, in 10– 10!27 JT!1 the nuclear magneton and 1.91 being the 100 kyr, as postulated in the original magnetar neutron’s g-factor halved. Thus, as illustrated in hypothesis. Fig. 2, we can explain the strongest MFs of magnet- 4. The CRSF technique has provided a very ars if f 9 1, and those of ordinary pulsars if only 0.1% important probe to the MF strengths of BXPs, of the neutrons form a ferromagnetic phase. The MF and has reinforced the view that the MF is transition postulated in § 5.3 can be readily ex- unlikely to make gradual decays except at >Bcr. plained as ferromagnetic to paramagnetic state 5. The overall dipole-MF distributions of NSs, transitions of the nuclear matter, in response to, below Bcr, can be understood as combination e.g., slight changes in the internal temperature, of the initial MF scatter (item 2) and some possibly during high-accretion-rate phase as LMXBs. kind of transition from strong-MF to weak-MF However, a weak point of this idea is that quantum states. exchange force between two neutrons prefers singlet- 6. The MF of NSs could be a manifestation of S state, wherein the wave function is symmetric ferromagnetism in the nuclear matter, or more against positional exchange of the two neutrons and interestingly, a result of some symmetry braking anti-symmetric with respect to their spin factor, than in fundamental physics. triplet-P state wherein the two spins become aligned. Yet another possibility is that the electrons Acknowledgements remaining in the NS becomes spin-aligned to form a The author would like to thank Prof. Yasuo ferromagnetic phase,77) due to some quantum mech- Tanaka, Prof. Naoki Onishi, Prof. Toshikazu anisms, including the neutrino’s chirality violation,78) Shigeyama, Dr. Tatehiro Mihara, Dr. Teruaki Enoto, or “chiral plasma instability” through which toroidal and Dr. Toshio Nakano, for their inspiring discussion. and poloidal electron currents are successively His thanks are also due to his colleagues at the amplified.79) Thus, MFs close to Eq. [33] could be University of Tokyo and RIKEN. This work was produced, because the very small number (e.g., supported by the MEXT KAKENHI on Innovative 910!3 of neutrons) of the remaining electrons can Areas, Area No. 2404, Grant No. 25105507, and be compensated by the Bohr magneton, 7 F e!/2me, MEXT KAKENHI Grant No. 15H03653. which is 91840 times larger than 7N. These new ideas are attractive, and should be extensively pursued, References because they try to explain the NS magnetism in terms of symmetry in fundamental physics, including 1) Makishima, K. (2013) From Sco X-1 to magnetars: the electron-to-proton mass difference, the chirality Past, present, and future of X-ray studies of neutron stars. Mem. Soc. Astron. Ital. 84, 547– violation by neutrinos, and the overall parity and 553. charge asymmetry. 2) Turner, M.J.L. et al. (1989) The large area counter on Ginga. Publ. Astron. Soc. Jpn. 41, 345–372. 6. Conclusion 3) Tanaka, Y., Inoue, H. and Holt, S.S. (1994) The Over the past quarter century, we have been X-ray astronomy satellite ASCA. Publ. Astron. Soc. Jpn. 46, L37–L41. using several (mainly Japanese) X-ray observatories 4) Mitsuda, K. et al. (2007) The X-ray observatory towards understanding the NS magnetism in the Suzaku. Publ. Astron. Soc. Jpn. 59,1–7. context of both astrophysics (formation and evolu- 5) Matsuoka, M. et al. (2009) The MAXI mission on the No. 5] X-ray studies of neutron stars and their magnetic fields 153

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Kazuo Makishima, born in Tokyo in 1949, graduated from the University of Tokyo in 1972, and entered the research field of experimental astrophysics, mainly using scientific satellites to observe X-rays from various celestial objects. He became in 1978 Associate Professor at the Institute of Space and Astronautical Science, the University of Tokyo, and was promoted in 1986 to Associate Professor at the Department of Physics of the same university. After further promoted to Professor in 1995, he worked there till 2015. Meantime, he contributed, both in hardware developments and scientific observations, to all the 6 Japanese X-ray astronomy satellites, Hakucho (launched in 1979), Tenma (1983), Ginga (1987), ASCA (1993), Suzaku (2005), and Hitomi (just launched in 2016). Furthermore, he contributed to two solar satellites, Hinotori (1981) and Yohkoh (1991). From 2001 onwards, he was also jointly appointed as Chief Scientist (Group Director since 2009) at RIKEN, or The Institute of Physical and Chemical Research, where he supported the MAXI (Monitor of All-sky X-ray Image) instrument placed on the Japanese experimental module comprising the International Space Station. Using these space missions, he has so far achieved a number of new observational discoveries that allow us to better understand, e.g., magnetism of neutron stars, accretion processes onto black holes, and plasma-physics aspects of clusters of galaxies. At least for a decade since 1991, the Hard X-ray Telescope onboard Yohkoh, developed by him and his co-workers, held the record of the highest angular resolution, 5 arcseconds, in hard X-rays up to 100 keV.