Reviews
X-ray studies of neutron stars and their magnetic fields
2016 Volume 92 Issue 5 Pages 135-155
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2016 Volume 92 Issue 5 Pages 135-155
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.
The present paper deals mainly with magnetic fields (MFs) of neutron stars (NSs). Let us, however, begin with a broader scope, and explain how the concept of stars is directly related to basic physics. This is because the paper is meant for readers from wide areas of physical science, rather than experts in astrophysics. For the same reason, we spare considerable pages to tutorial explanations of the basics of NSs, and use the International System Units.
Generally, a “star” means a celestial system, in which gravity is counter-balanced in a stable manner by some internal pressure. The gravity, which provides the inward pull force, is universal without any characteristic length scales. In contrast, the pressure p which tries to expand the star is versatile. It is indeed the variety of this p that allows the existence of stars of various types. More specifically, stars are characterized almost solely by the equation of state (EOS), which expresses p in terms of the mass density ρ of the constituent matter.
As illustrated in Fig. 1, the differences in the EOS are best distinguished by the relation between the mass M and radius R of the stars. Normal nuclear-burning stars are supported by the classical gas pressure of their interior. In contrast, planets are supported by Coulomb repulsion among constituent ions, which determines the mean particle separation d to be about the Bohr radius aB, and produces a scaling as R ∝ M1/3 (i.e., a constant density).
Mass-radius relations for various types of stars. Downward orange arrows illustrate the evolution of the core of normal stars (omitting their red-giant phase), which involves significant mass loss.
In brown dwarfs (stars too light to ignite hydrogen fusion) and white dwarfs (final form of low-mass stars), the gravity is counter-balanced by degenerate election pressure. Thus, d becomes comparable to the electron Compton wavelength, $\lambda _{\text{e}} = 2\pi \alpha _{\text{E}}a_{\text{B}} = 0.046a_{\text{B}}$, where $\alpha _{\text{E}} = e^{2}/4\pi \epsilon _{0}\hbar c = 1/137$ is the fine structure constant, with e the elementary charge, ε0 the vacuum dielectric constant, ħ the Dirac constant, and c the light velocity. In non-relativistic case, the mass-radius scaling becomes R ∝ M−1/3. When the degenerate Fermions become fully relativistic, the star becomes unstable. This sets an upper limit to these objects. For white dwarfs, the limit, called Chandrasekhar mass, is given as $ \sim m_{\text{p}}\alpha _{\text{G}}^{ - 2/3} \approx 1.4\ M_{ \odot }$, where mp is the proton mass, $\alpha _{\text{G}} \equiv Gm_{\text{p}}^{2}/\hbar c = 5.9 \times 10^{ - 39}$ is a dimensionless quantity called gravitational fine-structure constant, and G is the gravitational constant.
In Fig. 1, NSs appear as a class with by far the smallest radii. Since they are supported by degenerate pressure of neutrons, the neutron-neutron separation inside them is of the same order as the Compton wavelength of nucleons. As a result, the radius of an NS is ∼me/mn = 1/1840 times that of a white dwarf of the same mass, where me and mn are the electron mass and neutron mass, respectively. The upper-limit mass of NSs is considered to be ∼3 M⊙ or less, still with considerable uncertainties.
One interesting aspect of stars is their magnetism, because most of them are magnetized as summarized in Fig. 2. These MFs are in many cases interpreted as due to some electric currents flowing inside a plasma phase, e.g., a metallic-hydrogen core 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 electrons 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.
Typical surface MF intensities of various stars, plotted as a function of their density. Two lines indicate the expected MF intensities, when all electrons (dashed line) or nucleons (dotted line) are spin-aligned to form a ferromagnetic phase. The diagram also incorporates typical ferromagnetic materials.
The present paper reviews studies of magnetism of NSs,1) performed in the past quarter century mainly with Japanese X-ray satellites, Ginga launched in 1987 February,2) ASCA in 1983 February,3) and Suzaku in 2005 July.4) In addition, we incorporate results from the Monitor of All-sky 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.
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 (∼1046 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 M⊙. By bounced shocks, the remaining outer parts are ejected into the interstellar space to form an expanding shell structure known as a supernova remnant (SNR). If the progenitor star has a larger initial mass, e.g., >25 M⊙, the infalling core is considered to be heavier than the upper limit for NSs, and hence to collapse into a black hole.
Figure 3 shows the Crab Nebula6) which exploded in the year of 1054, and its central NS known as the Crab Plusar. It is the best-known example of NS-SNR association, even though it would not be a typical SNR because it lacks the blast-wave heated thermal remnant and has only the nonthermal pulsar-wind nebula. Here, the term “pulsar” generally means an NS of which the radiation intensity exhibits clear periodicity at its rotation period P. An NS is not called a pulsar if its P is unknown.
A composite image of the Crab Nebula, taken in the optical (purple) and X-rays (cyan). The Crab pulsar is seen at the center. The image size is about 6′ × 7′. Taken from the Chandra Photo Album.
In addition to the above canonical scenario, there can be yet another channel of NS formation, called “accretion induced collapse”.7) When a white dwarf in a binary system gradually gains its mass through accretion, it will hit the Chandrasekhar limit and ignite fusion reactions near the center. If the white dwarf has a composition which is rich in C and O, it will end up with a Type Ia supernova via thermonuclear runaway explosion. In contrast, the white dwarf will collapse into an NS if the composition is mainly of O, Ne, and Mg, because the electron capture takes over the nuclear burning and reduces the pressure. Details of this process wait for future investigation.
2.2. Major properties of neutron stars.Of all classes of stars, NSs are regarded as champions in three respects; the highest density, the fastest rotation, and the strongest MFs. Yet another characteristic of NSs is their strong gravity, although in this respect they are next to black holes.
Composition: An NS consists mostly of neutrons, and is sustained by their degenerate pressure against its extreme gravity. These neutrons are produced in the collapsing stellar core, via a process known as electron capture or neutronization. That is, a β-type reaction between two nuclear species A(N, Z) and A(N + 1, Z − 1),
| \begin{equation} \mathrm{A}(N,Z) + \text{e$^{-}$} \rightleftharpoons \mathrm{A}(N+1,Z-1) + \nu_{\text{e}}, \end{equation} | [1] |
Mass and radius: An NS is an extremely tiny object, with a typical mass MNS and radius RNS of
| \begin{equation} M_{\text{NS}} \approx 1.4\,M_{\odot},\quad R_{\text{NS}} \approx 11\,\text{km}. \end{equation} | [2] |
| \begin{equation} E_{\text{tot}} = - \frac{3}{5}G \frac{M_{\text{NS}}^{2}}{R_{\text{NS}}} + b\,p_{\text{d}} V \end{equation} | [3] |
The actual mass-radius relation of NSs is subject to special and general relativity, and nuclear interactions among neutrons which make the object a strongly-interacting Fermi gas. Because we still have limited knowledge of the nuclear interaction, or the “nuclear EOS” that replaces the above simplest EOS, theoretical MNS vs. RNS relations have not yet been accurately identified. Conversely, if we can measure MNS and RNS of a fair number of NSs with a sufficient accuracy, the results will give a valuable clue to the nuclear EOS.
Observationally, the values of MNS measured from about 50 NSs8) are concentrated in a narrow range around Eq. [2], with at most ±30% scatter: so are the measured values of RNS. On one hand, we need to explain how such narrow distributions are realized. On the other hand, these individual measurements must be made yet with higher accuracies, in order to constrain the nuclear EOS.
High density: Because of the extremely small RNS, NSs are by far the densest objects in the Universe. From Eq. [2], their volume-averaged density becomes ρ ∼ 5 × 1017 kg m−3, which is by >13 orders of magnitude higher than those of the densest metals, and even exceeds those of atomic nuclei, ρ0 = 2.3 × 1017 kg m−3. At the center of NSs, the density is expected to become as high as ∼10ρ0.
Rapid rotation: Among all celestial objects, NSs (except mass-accreting ones) are by far the most rapidly rotating class, with the fastest known record having a rotation period of P = 1.5 msec. This feature of NSs is a result of angular momentum inheritance from their progenitor stars, together with their extremely small radii. As a Gedanken experiment, let us compress the Sun into an NS (although the Sun would never evolve so). Then, the Solar rotation period, about a month, would decrease to P ∼ 0.5 msec through angular momentum conservation, because the radius should decrease by a factor of ∼7 × 104. This happens to be the shortest period that an NS can attain, as it would break up for P < 0.5 msec due to centrifugal force.
Strong magnetic fields: Another outstanding feature of NSs is their strongest MFs among all celestial objects (Fig. 2). As described later in § 2.3, a majority of NSs have Bd ∼ 108 T, where Bd refers to dipole MF intensity (more properly, magnetic flux density) measured at the magnetic poles on the NS surface. It is related to the object’s magnetic dipole moment $\mathcal{M}$ as
| \begin{equation} \mathcal{M} = 2 \pi R_{\text{NS}}^{3} B_{\text{d}}. \end{equation} | [4] |
Among several ways to classify NSs, a convenient one, shown in Fig. 4, is to use their values of P and Bd. There, the most dominant subclass is radio pulsars, i.e., isolated NSs with P of a few tens msec to several sec, and Bd = 107–109 T. Some of them are found in SNRs, like the case of Fig. 3. Since these NSs are considered to lose their rotational energies by radiating magnetic dipole radiation (§ 3.1), they will move to the right on Fig. 4 as they get older. Their age can be estimated using a quantity called characteristic age, defined as
| \begin{equation} \tau_{\text{c}} \equiv P/2\dot{P} \end{equation} | [5] |
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 τc of Eq. [5] are provided by dashed purple lines. “Death line” means that rotation-powered objects become unable to emit significant radiation when they cross this line. NSs residing in SNRs are also indicated.
The second subclass in Fig. 4 is binary X-ray pulsars (BXPs) extending horizontally at Bd = (1–7) × 108 T. They form binaries with (usually massive) companion stars, and capture their stellar winds to emit X-rays with strong pulsations, as the captured matter will fall to the two magnetic poles of the NS where it is shock heated to form X-ray emitting hot “accretion columns”. The wide scatter in P seen among BXPs, from 2 ms to ∼104 s, results from their interaction with the accreting matter (§ 3.2).
Yet another subclass is those at the low-Bd and short-P end, a mixture of millisecond pulsars (MSPs; isolated or in wide binaries) and Low-Mass X-ray Binaries (LMXBs). The latter class of NSs accrete matter from their low-mass companion stars, to emit X-rays with weak or almost no pulsation. Usually, these NSs are considered to be old (>109 yr).
Finally, a special subclass, located at the highest-MF region of Bd ∼ 1010–1011 T, is called “magnetars”. In § 4, we present more detailed descriptions of these objects, employing a working hypothesis that the values found in Fig. 4 represent their true surface MFs.
As indicated by Fig. 4, NSs exhibit not only very strong MFs, but also a remarkable scatter in Bd over 8 orders of magnitude. It is not known how the MF can scatter this much, given strong concentrations of the observed MNS and RNS around their canonical values [Eq. [2]]. It is unclear, either, whether NSs with strong and weak MFs differ systematically (but within the narrow scatter) in their masses. More fundamentally, we need to clarify how these strong MFs are held: is the magnetism driven by some electric currents (electric magnets), or sustained by some kind of ferromagnetism (permanent magnets)?
2.4. Energy sources of neutron stars.The NSs in Fig. 4 all emit electromagnetic radiation in some frequencies, with a typical luminosity of L = 1026–1031 W. From the energy sources of this radiation, the NS can be classified in a different manner into the following three categories. There is in fact yet another class, thermally radiating NSs. Although observations of their cooling provide valuable clues to the physical conditions inside NSs, the subject is beyond the scope of the present paper.
Rotation-powered NSs: radio pulsars and MSPs in Fig. 4 emit rather broad-band radiation (mainly radio but sometimes to optical or even higher frequencies) by consuming their rotational energies, which is given as
| \begin{equation} E_{\text{rot}} = \frac{I}{2} \left(\frac{2\pi}{P} \right)^{2} {}={} 2.0 \times 10^{40} I_{38} \left(\frac{P}{0.3\,\text{s}} \right)^{-2}\,\text{J} \end{equation} | [6] |
| \begin{align} L_{\text{rot}} & = -\frac{dE}{dt} = \frac{(2\pi)^{2}I}{P^{3}} \dot{P}\\ & = 1.5 \times 10^{26}\,I_{38} \left(\frac{P}{0.3\,\text{s}} \right)^{-3} \left(\frac{\dot{P}}{10^{-15}\,\text{s/s}} \right)\,\text{W}. \end{align} | [7] |
Rotation-powered NSs are a site of acceleration of particles and production of electron-positron pairs. These processes have been extensively studied9),10) since the discovery of pulsars in 1967.11) Instead of reviewing this subject in details, let us consider a simple exercise; why MSPs, in spite of their much weaker MFs than those of young radio pulsars, can still accelerate particles to very high energies and emit pulsed GeV gamma-rays, as discovered with the Fermi Gamma-Ray Space Telescope.12) The acceleration in rotation-powered NSs is likely to be caused by strong electric fields induced by their rotating MFs, at locations close to the “light cylinder”, RLC = cP/2π, where the velocity of co-rotation with the pulsar reaches c. Using the MF strength near RLC, i.e., BLC ∼ Bd(RNS/RLC)3), the induced electric potential therein will be estimated as $c\cdot B_{\text{LC}}\cdot R_{\text{LC}} \sim cB_{\text{d}}R_{\text{NS}}^{3}R_{\text{LC}}^{ - 2} \propto B_{\text{d}}/P^{2}$. MSPs have some 4 orders of magnitude lower Bd than representative radio pulsars, but typically 2 orders of magnitude shorter P, so that the induced potential is similar between these two subclasses. Thus, MSPs can accelerate particles to similarly high energies as radio pulsars, but with a much lower luminosity due to their much smaller volume available for the process.
Accretion-powered NSs: In Fig. 4, BXPs and LMXBs accrete gas from their binary companions, and emit X-rays powered by gravitational energies released by the accreting matter. The energy available by this process is given as
| \begin{align} E_{\text{grav}} & = G \frac{M_{\text{NS}} \Delta M}{R_{\text{NS}}}\\ & = 3.4 \times 10^{42} \left(\frac{M_{\text{NS}}}{1.4M_{\odot}} \right) \left(\frac{R_{\text{NS}}}{11\,\text{km}} \right)^{-1} \left(\frac{\Delta M}{10^{-4}M_{\odot}} \right)\,\text{J} \end{align} | [8] |
| \begin{equation} L_{\text{grav}} = 1.7 \times 10^{28} \dot{M}/(1 \times 10^{12}\,\text{kg\,s$^{-1}$})\,\text{W} \end{equation} | [9] |
This Lgrav has a clear upper limit, called Eddington limit, which is given as
| \begin{align} L_{\text{Edd}} & = 4 \pi c G M_{\text{NS}} m_{\text{p}} f_{\text{b}}/\sigma_{\text{T}}\\ & = 2.1 \times 10^{31} (M_{\text{NS}}/1.4M_{\odot}) (f_{\text{b}}/1.16)\,\text{W} \end{align} | [10] |
When Lgrav of Eq. [9] is emitted isotropically from the whole NS surface as blackbody radiation of temperature Tbb, the Stefan-Boltzmann law, together with Eq. [2], gives
| \begin{equation} T_{\text{bb}} = \left(\frac{L_{\text{grav}}}{4 \pi R_{\text{NS}}^{2} \sigma} \right)^{1/4} {}={} 1.5 \times 10^{7} \left(\frac{L_{\text{grav}}}{L_{\text{Edd}}} \right)^{1/4}\,\text{K} \end{equation} | [11] |
Magnetically-powered NSs: As detailed later in § 4, objects of the magnetar class in Fig. 4 radiate mainly in X-rays. However, they cannot be rotation-powered objects, since their X-ray luminosities largely exceed Lrot of Eq. [7]. As discussed in § 4, they are not likely to be accretion-powered objects, either. Instead, magnetars are considered to be magnetically-powered NSs, which emit X-rays by consuming their magnetic energy given as
| \begin{align} E_{\text{mag}} &= \left(\frac{B_{\text{d}}^{2}}{2\mu_{0}} \right) \left(\frac{8\pi}{3} R_{\text{NS}}^{3} \right) \\ &= 4.4 \times 10^{40} \left(\frac{B_{\text{d}}}{10^{11}\,\text{T}}\right)^{2}\,\text{J} \end{align} | [12] |
In this section, we describe three representative ways to estimate the MFs of NSs. The first one is for isolated NSs, while the latter two are applicable to accreting NSs. We have contributed to the third method, and partially to the second one as well.
3.1. Pulse periods and period changes.The most widely used way to estimate Bd of isolated NSs is to assume that their spin-down energy release, Lrot of Eq. [7], goes into magnetic dipole radiation,9) of which the luminosity is written as
| \begin{equation} L_{\text{M2}} = \frac{(2\pi/3) (B_{\text{d}} R^{3} \sin\theta)^{2}}{c^{3} \mu_{0}} \left(\frac{2\pi}{P} \right)^{4} \end{equation} | [13] |
| \begin{equation} B_{\text{d}} \sin\theta = 0.32 \times 10^{8} \left(\frac{P}{0.3\,\text{s}} \right)^{1/2}\left(\frac{\dot{P}}{10^{-15}\,\text{s/s}} \right)^{1/2}\,\text{T}. \end{equation} | [14] |
This “$P-\dot{P}$ technique” has yielded the values of Bd of all non-accreting NSs in Fig. 4, including radio pulsars, MSPs, and magnetars. In particular, it yields $B_{\text{d}}\sin\theta = 2.8 \times 10^{8}$ T for the Crab pulsar, which has P = 0.0332 sec, $\dot{P} = 4.22 \times 10^{ - 13}$ s s−1, and Lrot = 5.1 × 1031 erg s−1 employing I = 1.1 × 1038 kg m2.13) While this method is convenient, it gives only a lower limit on Bd in the sense that θ is usually unknown. At the same time, it may be regarded as giving an upper limit, because the spin-down may take place via other energy output channels, including acceleration of particles via unipolar induction mechanism (§ 2.4),10) and creation of plasma outflows. Thus, the estimates with Eq. [14] are considered rather crude. These additional energy losses are considered to have very similar strengths and functional forms to Eq. [13],10) but without the sin θ dependence. Therefore, the spin-down behavior may not depend on θ as strongly as implied by Eq. [13].
By solving Eq. [14] under a constant Bd, the pulse period and luminosity are predicted to evolve as a function of time t as
| \begin{equation} P(t) = P_{0} (1+t/t_{1})^{1/2}, \end{equation} | [15] |
| \begin{equation} E_{\text{rot}}(t) = E_{\text{rot}}(0) (1+t/t_{1})^{-1}, \end{equation} | [16] |
| \begin{equation} L_{\text{rot}}(t) = L_{\text{M2}}(t) = L_{0} (1+t/t_{1})^{-2}, \end{equation} | [17] |
| \begin{equation} \tau_{\text{c}}(t) = t + t_{1}. \end{equation} | [18] |
| \begin{equation} E_{\text{rot}}(0) = L_{0} t_{1}. \end{equation} | [19] |
| \begin{equation} t_{1} \sim 7\times 10^{3} (P/10\,\text{ms})^{2} (B_{0} \sin \theta/10^{8}\,\text{T})^{-2}\,\text{yr} \end{equation} | [20] |
To estimate MFs of mass-accreting NSs (those in binaries), which exhibit in Fig. 4 a large scatter in P, we must consider accretion torque, namely, angular momentum transfer to/from the accreting matter. In this case, the NS can either spin up or spin down, unlike Eq. [13] which always acts to spin down the NS.
The accretion torque formalism was developed in the late 1970’s,14) and is being calibrated and confirmed through MAXI monitoring of several BXPs including GX 304–115) and 4U 1626–6716) in particular. It assumes that the gravitational pull working on the accreting matter becomes counter-balanced by the magnetic presssure at a radius RA, called Alfvén radius, which can be expressed as
| \begin{align} R_{\text{A}} & = 10^{6}\,\zeta \left(\frac{L_{\text{x}}}{10^{30}\,\text{W}} \right)^{-2/7} \left(\frac{B_{\text{d}}}{10^{8}\,\text{T}} \right)^{4/7}\\ &\quad \times \left(\frac{R_{\text{NS}}}{11\,\text{km}} \right)^{10/7} \left(\frac{M_{\text{NS}}}{1.4 M_{\odot}} \right)^{1/7}\,\text{m} \end{align} | [21] |
| \begin{equation} \omega_{\text{K}} (r) = \sqrt{G M_{\text{NS}}/r^{3}}. \end{equation} | [22] |
Most of accreting NSs, including both BXPs and LMXBs, are expected to be in a condition of near torque equilibrium, namely, Ω ≈ ωK(RA), because their spin up/down time scales due to the accretion torque are estimated to be shorter than their life times. Then, expressing the Ω ≈ ωK(RA) condition using Eq. [21] and Eq. [22], we obtain so-called equilibrium rotation period as
| \begin{equation} P_{\text{eq}} \sim 0.6\,\zeta^{3/2} \left(\frac{L_{\text{x}}}{10^{30}\,\text{W}} \right)^{-3/7} \left(\frac{B_{\text{d}}}{10^{8}\,\text{T}} \right)^{6/7}\,\text{sec} \end{equation} | [23] |
| \begin{equation} B_{\text{d}} \sim 1.8 \times 10^{8}\,\zeta^{-7/4}\left(\frac{L_{\text{x}}}{10^{30}\,\text{W}} \right)^{1/2} \left(\frac{P}{1\,\text{sec}} \right)^{7/6}\,\text{T}. \end{equation} | [24] |
Among accreting NSs, BXPs (§ 2.3; extending horizontally in Fig. 4) have typically Bd ∼ 108 T, and allow particularly accurate measurements of Bd based on electron cyclotron resonances. In fact, the MF strengths of these objects have all been determined in this way. This technique utilizes the basic physics that an electron in a uniform magnetic field B makes cyclotron gyration at an angular frequency of Ω = eB/me, which translates to a photon energy of
| \begin{equation} E_{\text{a}} = \hbar e B_{\text{d}}/m_{\text{e}} = 11.6 (B_{\text{d}}/10^{8}\,\text{T})\,\text{keV} \end{equation} | [25] |
Examples of X-ray spectra (in νFν presentation) of two transient BXPs with CRSFs. (a) Deep harmonic CRSFs at 26 and 52 keV, observed from X0331+53 with RXTE.33) The best-fit model of Eq. [26] with double Ψ is superposed onto the data in a solid line, while the model after removing the factor Ψ 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 Ψ factor, while the bottom panel shows the data-to-model ratio. Prominent negative residuals at ∼80 keV indicate the highest-energy CRSF observed to date.38)
Using Ginga launched in 1987,2) we have drastically enlarged the number of CRSF detections. Beginning with a discovery at Ea = 21 keV from 4U 1538–52,21) CRSFs have been detected one after another, from X0331+53 at 28 keV,22) Cep X-4 at 29 keV,23) 4U 1907+09 at 20 keV,17) GX 301–2 at 36 keV,17) and Vela X-1 at 25 (or 50) keV.17) In addition, the previously known two CRSFs in Her X-124) and 4U 0115+6325) were reconfirmed. These results have established that CRSFs are a common feature of BXPs, and provide their surface MFs in the most reliable way. The measured values of Ea were apparently concentrated in the range of 10–40 keV, which implies Bd = (1–4) × 108 T from Eq. [25]. Although CRSFs can theoretically appear either in absorption or emission, and the Her X-1 result was at first interpreted as an emission line,19) these Ginga-detected CRSFs, including that of Her X-1, were all found in absorption.
Through these observations, we showed that the BXP spectra with a CRSF can be described, as a function of the X-ray energy E, as17),18),21),26)
| \begin{equation} f(E) = \xi(E) \times f_{\text{NPEX}} (E) \times \Psi(E). \end{equation} | [26] |
| \begin{equation} f_{\text{NPEX}}(E) = (A_{1} E^{-\Gamma_{1}} + A_{2}E^{+\Gamma_{2}}) \exp \left(-\frac{E}{E_{\text{cut}}} \right) \end{equation} | [27] |
| \begin{equation} \Psi(E) = \exp \left\{-\frac{D(WE/E_{\text{a}})^{2}}{(E-E_{\text{a}})^{2}+W^{2}} \right\} \end{equation} | [28] |
Following the Ginga achievements, observations with the BeppoSAX, RXTE, and INTEGRAL satellites increased the number of detected CRSFs.28),29) From a fair number of these objects, higher harmonic absorptions were detected (e.g., Fig. 5a), up to the 4th harmonic in the most extreme case.30) Another interesting effect which we discovered with Ginga and RXTE is luminosity-dependent changes (up to ∼50%) in the resonance energy in a few BXPs.31)–33) Possibly the standing shocks which form in the accretion columns change their heights as $\dot{M}$ varies, so that the value of Bd changes to some extent under the dipolar field configuration.
Suzaku,4) launched in 2005, allowed us to search CRSFs in the 30–100 keV energy range, which had poorly been explored by previous missions. Thanks to the Hard X-ray Detector (HXD)34) onboard, this attempt has been successful, as we detected CRSFs from A0535+26 at ∼45 keV,35) from GX 304–1 at 50–54 keV,36) from 1A 118–61 at ∼55 keV,37) and the highest record of Ea ∼ 76 keV from GRO J1008–57.38) Although some of these CRSFs had been suggested by previous studies, the Suzaku detections are much more convincing. These new results somewhat expanded the MF distribution of BXPs towards the higher side, to Ea = 10–80 keV and hence
| \begin{equation} B_{\text{d}} = (1{-}7) \times 10^{8}\,T. \end{equation} | [29] |
Using Suzaku, we also discovered that 4U 1822–37, which has a low-mass companion and was so far classified as an LMXB, is in reality a BXP with Ea ∼ 33 keV.40) Including these and other firm examples, the CRSF has been detected to date from about 20 objects, out of the ∼50 BXPs that are securely catalogued in the Local Universe. They are subdivided into about 10 objects with Be-type primary stars, about 7 objects capturing stellar winds from their OB-type companions, and 3 examples (Her X-1, 4U 1626–67 and 4U 1822–37) accreting from their low-mass companions presumably via Roche-lobe overflow.
3.4. Distributions of MF strengths.Figure 6 shows distribution histograms of the values of Bd of NSs, determined with the P-$\dot{P}$ method (§ 3.1) and the CRSF technique (§ 3.3). There, MF determinations using the accretion-torque method of Eq. [24] are not included, because of large uncertainties involved. However, we are left with a freedom of adjusting the value of ζ in Eq. [21]. Empirically, we found that ζ ∼ 1 can consistently explain the behavior of disk-fed short-period (P < 100 sec) BXPs, while ζ ∼ 5 is favored by the data of long-period (P > 100 sec) objects.41) By thus calibrating ζ, the accurately measured MF strengths of the CRSF-bearing BXPs have been reproduced with Eq. [24] within a factor of a few. In this sense, the two independent measurements of MF of BXPs are consistent with each other.
Distribution histograms of the surface dipole MF, Bd, of NSs. Blue indicates radio pulsars and MSPs, and red shows magnetars, both utilizing Eq. [14]. Green shows BXPs with confirmed CRSFs, for which Eq. [25] is utilized. The blue histograms refer to the left ordinate, while the red and green ones to the right. The data refer to the ATNF Pulsar Catalogue,76) available online at http://www.atnf.csiro.au/research/pulsar/psrcat for updated versions.
Figure 6 is approximately equivalent to the projection of Fig. 4 onto the Bd axis. It exhibits three broad peaks; one at Bd = 107–109 T covering BXPs and the majority of radio pulsars, another for magnetars at Bd = 1010–1011 T, and the other at Bd = 104–105 T for MSPs (and LMXBs). It is important to search for clues to this wide scatter in the MF strength, and to the origin of the three apparent peaks. Another interesting point in Fig. 6 is that the MF distribution of BXPs (in green), determined with the CRSF technique via Eq. [29], is much narrower than the main peak formed by radio pulsars. At present, it is unclear whether the two distributions are different, or can be consistent if considering various selection effects.
So far, the search for CRSFs have been unsuccessful on more than half the known BXPs. Some of these objects may have Bd > 7 × 108 T, and hence exhibit CRSFs in higher energies (e.g., >80 keV) than was explored with Suzaku. Promising candidates include BXPs with long pulse periods (P > 103 s)41) as inferred from Eq. [24], and/or with very hard spectra as suggested by the Ea vs. Ecut correlation (§ 3.3). This pertains to the issue of whether the apparent gap in the MF distribution between BXPs and magnetars is intrinsic or due to selection effects.
We have now come to the stage of describing magnetars, by far the most enigmatic of all NS subclasses. Historically, the concept of magnetars emerged from two populations of high-energy objects. One is Soft Gamma Repeaters, known since 1979, which emit sporadic gamma-ray bursts with softer spectra than the classical (hence cosmological) gamma-ray burst sources. The other is Anomalous X-ray Pulsars, peculiar X-ray pulsars without binary evidence, of which several were known from the 1980’s. Based on observations with, e.g., ASCA3),42) launched in 1993, these two populations have gradually been found to represent two different aspects of the essentially identical population, and they have come to be collectively called “magnetars”.43),44)
At present, about 30 magnetars are known in the Milky Way and the Magellanic clouds. Furthermore, new magnetars are being discovered typically one per year or so, mainly by the Swift mission which detects short bursts from (re-)activated transient magnetars. Including both these transients and persistent sources, major observational properties of magnetars are summarized as follows.
From item 4 above, magnetars are considered as magnetized NSs, and are rather young from item 3, in spite of their long P (item 4); in fact, Eq. [5] gives τc = 1–100 kyr. From items 5 and 6, they are unlikely to be accretion-powered NSs. Furthermore, they cannot be rotation-powered objects, either, since their long P makes Erot much lower than those of radio pulsars, and hence their Lrot of Eq. [7] falls, in spite of the large $\dot{P}$ (item 4), 1–3 orders of magnitude below the observed Lx (item 1). At the same time, Eq. [14] indicates that magnetars have extremely strong MF as Bd = 1010–1011 T, which exceeds the quantum critical field Bc = (mec)2/ħe = 4.4 × 109 T at which the energy of Eq. [25] reaches mec2. As a result, magnetars have been regarded as magnetically-powered NSs (§ 2.4).43) This is supported by the fact that the values of Bd of magnetars calculated via Eq. [13] clearly decrease as a function of τc of Eq. [5], as we see later in Fig. 12. Then, item 2 can be explained as sudden releases of magnetic energies,43) 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 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).
The strong-MF interpretation of magnetars43),44) has thus been generally successful. Nevertheless, it still remains a sort of conjecture, to be called magnetar hypothesis, and leaves us with a number of challenges. First of all, it must be proven whether magnetars really harbor such strong MFs, and are indeed powered by magnetic energies. Even if these basic questions are answered affirmatively, we must clarify how the magnetic energies are consumed to power the persistent and burst emissions, and what is the relation between these two X-ray emission channels. It also needs to be answered whether the apparent gap in the MF distribution in Fig. 4 between BXPs and magnetars are real or due to some selection effects, and what is special about the formation scenario of magnetars compared to those of NSs of the other subclasses. Hoping to obtain clues to these questions, we have been studying magnetars with Suzaku.
4.2. Emission spectra.Just before the launch of Suzaku, a European group used INTEGRAL to discover that a fair fraction of magnetars emit a separate hard X-ray component,46),47) in addition to the well known soft X-rays (item 6 in § 4.1). This novel spectral component has such a hard slope, approximated by a power-law of photon index Γ ∼ 1, that it cannot be readily explained in terms of ordinary high-energy radiation processes, such as synchrotron radiation, inverse Compton scattering, or (non-)thermal Bremsstrahlung.
Our magnetar study with Suzaku utilizes its wide-band capability, realized by the HXD34) and the X-ray Imaging Spectrometer (XIS). Figure 7a shows a compilation of Suzaku spectra of representative Galactic X-ray sources, while Fig. 7b presents those of 4 magnetars. Thus, we have reconfirmed the reported two-component spectral characteristic of magnetars, because the spectra in panel (b) all exhibit very hard emission rising from ∼10 keV towards higher energies, in addition to the long known soft component (item 6 in § 4.1). This property is generally not seen in other known classes of compact X-ray sources [e.g., those presented in panel (a)], except young rotation-powered pulsars of which the X-ray spectrum often consists of a soft thermal component and a hard non-thermal tail.48) However, the hard component of these objects usually have Γ ∼ 2, not as hard as those of magnetars. Thus, the unusual spectral shape alone would considerably reinforce the peculiar nature of magnetars.
In Fig. 7b, the hard component of the four magnetars are seen to become weaker (relative to the soft component), but harder in slope, as the objects get older. This is an important discovery by Enoto et al. (2010)49) of a clear evolution in the magnetar spectra, which suggests as if there is a pivot point at several hundreds keV. We have hence proposed a new explanation of the hard component, that it may be due to energy degradation of some energetic input gamma-rays, possibly the 511 keV annihilation photons, rather than a result of successive boosting-up of low-energy electrons/photons towards higher energies.49) Details are explained below.
While magnetars have 2 orders of magnitude slower spins than typical radio pulsars, they have 2 orders of magnitude higher MF. Therefore, the induced electric field in their magnetosphere up to RLC should be comparable to those in pulsars. Then, as discussed in § 2.4, electrons in the magnetars’ magnetosphere will be accelerated and emit abundant gamma-rays (via, e.g., curvature radiation) which in turn produce electron-positron pairs. However, these particles would not freely escape out from magnetosphere, because the centrifugal force of magnetars is ∼4 orders of magnitude weaker than that of pulsars. Then, the particles will fall onto the magnetar surface, where the positrons annihilate to emit 511 keV gamma-rays. In radio pulsars, these photons would again initiate electron-positron cascades. However, in magnetars with Bd > Bcr, an energetic photon has a finite probability of colliding with the MF that acts as a virtual photon, and splitting into two real photons. By a repetition of this “photon splitting” process, the input gamma-rays will increase in number, and decrease in individual photon energy, thus forming a hard X-ray continuum from 511 keV downwards. In older magnetars with weaker MFs, this process will soon stop, while it will continue to softer photon energies in younger ones with stronger MFs, because this process, unlike the e+e− pair creation, has no particular energy threshold. This scenario,49) fully based on the magnetar hypothesis, can consistently explain the properties of the hard component, including its evolution revealed with Suzaku.
The above hypothesis provides a nice research subject for future observations in the 0.1–1 MeV range. If we can detect a steep cutoff of the continuum above ∼511 keV, our scenario, as well as the magnetar hypothesis itself, will be significantly reinforced.
4.3. Bursts and persistent signals.As explained in § 4.1 (item 2), the X-ray/gamma-ray bursts emitted from an activated magnetar scatter over many orders of magnitude in their size (energy content). Among these bursts, very energetic and rare ones have been detected and studied by instruments with a wide sky coverage (but with a low sensitivity), because their occurrence is totally unpredictable. In contrast, little has been known about broad-band properties of smaller bursts that are undetectable by these wide-field instruments. We have successfully carried out this challenge with Suzaku, through Target of Opportunity observations (triggered by Swift) of two activated magnetars; the new magnetar SGR 0501+451650) which suddenly appeared in 2008 August, and the fastest-spinning known magnetar 1E 1547.0–540851) which became active in 2009 January.
Figure 8 shows the results on SGR 0501+4516,50),52),53) where we compare wide-band spectra of (i) one big burst (which caused an automatic shut-off of the HXD), (ii) stacked small bursts, (iii) persistent emission during the activity, and (iv) that after the activity decreased. Thus, the spectra of (ii) and (iii) both consist of the soft and hard components, and the upper limit in (iii) is also consistent. In (i), the two components appear to be merged together. Thus, the two-component nature of the magnetar emission has been found to be a basic property common to both their persistent and burst emissions. In addition, over more than 4 orders of magnitude, the luminosities of the two components are approximately proportional to each other. These results strongly suggest that the persistent and burst emissions are produced essentially by the same mechanism. We obtained similar results from 1E 1547.0–5408.51),54),55)
(a) Suzaku spectra of various Galactic X-ray sources, in their νFν 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 τc of Eq. [5].
Incorporating data from a small satellite HETE-2, Nakagawa et al.56) proposed that the persistent emission from magnetars is an assembly of numerous “micro bursts” that are individually too small to detect. (Evidently, this was inspired by the well known view that solar coronae can be composed of numerous micro flares.) This conjecture can be combined without difficulty with our new interpretation of the hard component (§ 4.2). In fact, individual bursts are likely to be a manifestation of sudden release of magnetic energies44) somewhere in the system. This will lead to intense particle acceleration, and to the hard-tail formation via the proposed photon-splitting process. The scenario is hence attractive, but it requires that the number vs. size distribution of bursts should steepen considerably towards smaller bursts.
As already mentioned, the soft component of magnetars, with a luminosity comparable to that of the hard component, can be naturally regarded as thermal emission from the NS surface, heated either directly by the magnetic energy release, or indirectly by the accelerated particles. Actually, the soft-component spectra can be approximated by a blackbody model, as inferred from Fig. 7b and Fig. 8. However, the data often require two temperatures, with the hotter one ∼3 times higher than the other. Because this universal scaling applies to both persistent and burst spectra,56),57) the two-temperature property is considered to represent some physics specific to the strong MF. One possibility is that electrons under such strong MF have quite different scattering cross sections to the two X-ray polarizasion modes, O-mode and X-mode with respect to the MF direction. As a result, the two modes may have different photospheres with different temperatures. 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 polarimetry missions, including in particular PRAXyS being proposed under US-Japan collaboration.
4.4. Relation to supernova remnants.Usually, stars with the initial mass >25 M⊙ 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 magnetars can be produced in supernova explosions of very massive (e.g., initial mass >20 M⊙) and rapidly-rotating stars.58)
Using Suzaku, we examined the above prediction, since past observations were not very informative. For this purpose, we chose the SNR called CTB109, which hosts at its center a relatively aged magnetar, named 1E 2256+586. As shown in Fig. 9, this is actually one of the most typical magnetar-SNR associations. By analyzing soft X-ray spectra of CTB109 obtained with the Suzaku XIS, Nakano (2015)59) found that the X-ray emitting plasma involves two temperatures (∼7 × 106 K and ∼2 × 106 K). He identified the hotter and cooler components to the stellar ejecta and shock-heated inter-stellar matter, respectively, and estimated the former to have a mass of ∼40 M⊙. This provides one of the first observational confirmations of the theoretical prediction described above.
As seen in Fig. 9, 1E 2259+586 resides at the center of the half-moon-shaped CTB109. Nevertheless, their mutual association was plagued with a serious puzzle called “age problem”: the characteristic age of 1E 2259+586, τc = 230 kyr, is much longer than the estimated age of CTB109, ∼13 kyr. This puzzle has been successfully solved60) by considering that τc calculated via Eq. [5] assuming a constant Bd systematically overestimates the true system age when the MF strength is decreasing with time as postulated in the magnetar hypothesis. Specifically, they mathematically modeled the spin down and the MF decay of 1E 2259+586, and constructed the following scenario for this magnetar-SNR association.60)
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 2259+586 (and possibly other magnetars as well) is indeed a magnetically-powered NS, because its MF must have been decreasing significantly as indicated by the age 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 considered to be systematically and considerably younger than is indicated by their face values of τc. This last point is of the largest importance, because it further implies that magnetars must be produced with a much higher rate than thought previously, possibly more frequently than radio pulsars. The produced magnetars will fade off very quickly by exhausting Emag, and become invisible, because they can no longer be rotation-powered objects. These results altogether reinforce the magnetar hypothesis significantly, and suggest that magnetars are in fact one of major forms of new-born NSs, instead of being a rare and special population.
4.5. Free precession of magnetars.In addition to the dipole MFs which we have considered so far, magnetars can also harbor strong toroidal MF, Bt, which is confined inside the stars. In fact, a few magnetars which were discovered recently have Bd < Bcr,61),62) so that the burst activity which led to their discovery is likely to be powered by much stronger Bt hidden inside them. Such toroidal MFs could be produced in the final collapse of a stellar core, wherein the field lines will be wound up by differential rotation.63) Although it is intrinsically difficult to observationally estimate Bt which is invisible from outside, we have successfully overcome this difficulty, by utilizing the idea that strong internal MFs will deform the star up to an “asphericity” of64)
| \begin{equation} \epsilon \equiv (I_{1}-I_{3})/I_{3} \sim 1 \times 10^{-4} (B_{\text{t}}/10^{12}\,\text{T}). \end{equation} | [30] |
Let us consider dynamics of such an axisymmetric rigid body, under no external torque. If $\hat{x}_{3}\parallel \vec{L}$, where $\vec{L}$ is the angular momentum, the body would simply rotate around $\vec{L}$ with a constant rotation period Prot = 2πI3/L (with $L \equiv |\vec{L}|$). However, if $\hat{x}_{3}$ is titled from $\vec{L}$ by a finite “wobbling angle” α (which can take any value regardless of ϵ or |L|), the $\hat{x}_{3}$ axis will rotate, or wobble, around $\vec{L}$ with a slightly different “precession period” Pprec = 2πI1/L. This condition is illustrated in Fig. 10. As seen from an observer located on the $\vec{L}$-$\hat{x}_{3}$ plane, the body will slowly rotates at a “slip period”,
| \begin{equation} T \equiv P_{\text{prec}}/\epsilon = (1/P_{\text{rot}} - 1/P_{\text{prec}})^{-1}, \end{equation} | [31] |
A mosaic Suzaku image (0.5–4 keV) of the SNR CTB109, hosting the magnetar 1E 2258+586 at its center.60)
Even when the free precession is taking place, (i.e., ϵ ≠ 0 and α ≠ 0), we can detect only Pprec, and cannot observe Prot, as long as NS’s radiation pattern is symmetric around $\hat{x}_{3}$. (In this sense, the regular pulsations of radio pulsars and BXPs should be considered as precession, rather than rotation.) However, if the radiation pattern is asymmetric around $\hat{x}_{3}$, it becomes possible to observe the slip period T in addition to Pprec. Suppose that the emission hotspot (an orange circle in Fig. 10) is displaced from $\hat{x}_{3}$ by a finite angle γ, or the radiation beam is tilted by an angle ξ from $\hat{x}_{3}$. Then, depending on the phase in T, the emission reaching us will become maximum slightly before or after the timing when the $\vec{L}$-$\hat{x}_{3}$ plane points to us every precession cycle.65) As a result, the regular pulsation at Pprec becomes periodically phase modulated, at the period T and with a certain modulation amplitude Ap ≪ Pprec. This Ap is expected to depend positively on α, γ, and ξ.
The persistently bright X-ray source 4U 0142+61, pulsing at P = 8.689 sec, is one of the magnetars with the strongest hard component, showing a clearcut two-component spectrum (blue in Fig. 7b).66) We analyzed 4 Suzaku data sets of this object, taken in 2007, 2009, 2011, and 2013. Clear evidence of periodic modulation in the 8.689 sec pulse phase was discovered in the 15–40 keV data from the latter 3 observations, at a consistent modulation period (to be identified with the slip period) of T = 55 ± 4 ksec.67) The modulation amplitude in 2009, 2011, and 2013 was Ap = 0.7 ± 0.3 sec, 0.9 ± 0.5 sec, and 1.1 ± 0.4 sec, respectively, while the 2007 data gave an upper limit as Ap < 0.8. Interestingly, the phase modulation was always absent (Ap < 0.3 sec) in signals below 10 keV, where the soft component dominates (Fig. 7b). These novel results on 4U 0142+61 can be consistently interpreted by assuming that this magnetar is axisymmetric, and is undergoing free precession with a slip period of T = 55 ksec. From Eq. [31], the asphericity is constrained as ϵ = 1.6 × 10−4, which in turn translates to Bt ∼ 1012 T via Eq. [30] if the deformation is attributed to internal magnetic pressure. The absence of this phase modulation in the soft component can be understood if the soft X-ray emission region is symmetric (γ = ξ = 0 in Fig. 10) around $\hat{x}_{3}$, while the possible year-to-year variation in Ap in the hard component is likely to result from secular changes in γ (≠ 0) and/or ξ (≠ 0) of the hard X-ray emission region; α should not change on such short time scales. The data however constrained neither α, γ, nor ξ uniquely.
Although we cannot tell from the data alone whether the suggested deformation of 4U 0142+61 is prolate or oblate, we may obtain a clue to this issue from basic Newtonian dynamics. When $\vec{L}$ is conserved and some energy dissipation takes place, an oblate rigid body will reach its energy minimum at α = 0 (no precession), while a prolate body will do so at α = 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 when the rotation is fast) would soon decay even if free precession is once excited by some perturbation. Since 4U 0142+61 definitely has α ≠ 0 as evidence by its clear pulsation, a prolate shape is favored, in which case α would gradually increase with time.
The same pulse-phase modulation effects, as observed from 4U 0142+61, have also been discovered in Suzaku data of 1E 1547.0–4516,68) the fastest-spinning (P = 2.0721 sec) magnetar which became active in 2009 January (§ 4.3; orange in Fig. 7b).51) In this case, we obtained $T = 36.0_{ - 2.5}^{ + 4.5}$ ksec, which yields ϵ = 0.6 × 10−4. This is somewhat smaller than, but still of the same order, as the case of 4U 0142+61. Figure 11 visualizes the phase modulation of the 15–40 keV pulse profiles of this magnetar at the 36 ksec slip period. Again, the pulse-phase modulation was seen only in the hard component, and absent in the soft component.
An illustration of free precession of an axisymmetric rigid body. Three angles, α, γ, and ξ are of importance. See text for details.
The study of free precession has opened a totally new window on the estimation of toroidal MFs of magnetars. We are now searching Suzaku data of other magnetars for similar effects. In addition, archival data from the NuSTAR mission will greatly accelerate the study. An increased number of detections of the free precession will allow us to address such issues as; whether the magnetic deformation is common among magnetars; what is the distribution of Bt; and whether Bt is proportional to Bt.
As described so far, our understanding of the NS magnetism has made a large progress owing to the extensive studies over the last quarter century. Nevertheless, we are still left with several fundamental questions to be solved, as we already mentioned in § 2.3, § 3.4, and several places in § 4. These include; why the MF of NSs exhibits such a large scatter as seen in Fig. 4 even though their masses and radii show narrow distributions; are there intermediate objects between magnetars and ordinary radio pulsars; how the MF of NSs evolve after their birth; and, what hold the MFs inside NSs. In an attempt to answer some of these questions, let us conduct discussion from several aspects.
5.1. Initial MFs of NSs.In the last decade, significant new facts about magnetars have been unveiled (§ 4). These include our own achievements; the universal two-component nature of their persistent and short-burst spectra (§ 4.2); the new scaling law for the hard component (§ 4.2); the microburst hypothesis to explain the persistent emission (§ 4.3); the two-temperature quantification of their soft component (§ 4.3); the estimated progenitor mass of 1E 2259+586 (§ 4.4); the solution to the age problem in terms of MF decay (§ 4.4); and the evidence for free precession in the two magnetars (§ 4.5). As a result, our confidence in the magnetar hypothesis has been significantly reinforced, and evidence is accumulating to believe that magnetars really have strong MFs as Bd = 1010–1011 T or higher, and are powered by the magnetic energies. Furthermore, we have shown that magnetars can be one of the most major subclasses of new-born NSs, besides radio pulsars and BXPs. As a natural consequence of these results, NSs are now considered to have a wide range of scatter in Bd from their birth, at least over 108–11 T.
Can a new-born NS, then, have a very weak MF as Bd < 107 T? The answer is probably yes, from the following two pieces of evidence. One is a handful young SNRs (with age <10 kyr; including Cas A in particular) that contain rather inactive central NSs called CCOs (Central Compact Objects). Some of CCOs are weakly pulsing at sub-second periods, and their values of $\dot{P}$ is extremely small, implying Bd sin θ = 106–107 T. Even if sin θ ∼ 0, we would expect strong particle acceleration and associated activities as long as Bd ∼ 108 T.10) Thus, CCOs are considered to have truly weak Bd. The other is a peculiar accreting NS called Cir X-1. It has a rather massive (∼10 M⊙) companion, of which the lifetime is <107.5 year, and could even be associated with the SNR G321.9–0.3. Therefore, this NS is definitely very young, but it it known to emit Type I X-ray bursts, which are considered to take place only if Bd < 106 T or so. Therefore, this particular NS is also considered young and weakly magnetized. These two examples suggest that some NSs are born with weak dipole MFs (although they could have high Bt).
Based on these considerations, we conclude that NSs are born with a variety of dipole MF strengths, ranging from >1011 T down to Bd < 107. Objects like the Crab Pulsar can no longer be considered as typical young NSs. The information on Bt is still very poor, however.
5.2. Evolution of MFs above Bcr.When trying to understand the MF distribution in Fig. 6, three factors must be considered; the initial MF spread as discussed in § 5.1, the MF evolution over the life times of respective NSs, and various observational selection effects. Here, let us consider the second factor, incorporating some aspects of the third one. For this purpose, Fig. 12 summarizes all the currently known non-accreting pulsars (including magnetars) on the plane of τc and Bd. Several remarks may be added to this figure. (i) As long as non-accreting pulsars are concerned, this plot can be obtained by changing the plotting axes in Fig. 4, and its projection onto the Bd axis gives Fig. 6 (except the green histogram). (ii) The green squares indicate pulsars in binaries, but they have relatively wide orbits so that mass accretion does not take place. (iii) The values of τc of magnetars are likely to be systematically overestimated as we described in § 4.4, but the plot employs the uncorrected τc. (iv) A few SNR-hosted pulsars with τc = 106–109 yr and Bd = 105–106 T are CCOs, of which τc is likely to be heavily overestimated, because we cannot ignore in this case t1 in Eq. [18]. With these remarks in mind, let us investigate into Fig. 12.
The 15–40 keV pulse profiles of the magnetar 1E 1547.0–4516, folded at a barycentric period of 2.07214 sec, in 6 different phases of the T = 36 ksec slip period.68) Their average is shown in black at the middle.
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 those in SNRs. The plot was made by T. Nakano, making use of the information from the ATNF Pulsar Catalogue76) in the same way as Fig. 6. Cyan and blue lines indicate possible evolutionary tracks of 1E 2259+586 (see text § 5.1).
In Fig. 12, magnetars define a clear negative dependence of Bd on τc. This behavior is likely to be free from selection effects, since persistent magnetars and newly discovered transients line up on the same line. The trend agrees with the magnetar hypothesis, and our results on 1E 2259+586 and CTB109 (§ 4.4). More quantitatively, we can model the decay of Bd of magnetars as60),69)
| \begin{equation} B_{\text{d}}(T) = B_{0} \left\{\left(1 + \frac{\beta t}{\tau_{\text{d}}} \right) \right\}^{-1/\beta}, \end{equation} | [32] |
In the case of 1E 2259+586, one possible solution (among many possibilities) to Eq. [32] is given as B0 = 1.8 × 1011 T, τd = 160 yr, and β = 1.4,60) which imply that the MF decreased to 0.033B0 in the 13 ky of life time. This particular evolutionary track is shown in Fig. 12 by a cyan curve, in which abscissa is redefined as the true elapsed time. After converting this true age to the apparent (heavily over-estimated) τc to match with the plot, the track becomes as indicated by a blue curve. Thus, Eq. [32] can explain the behavior of not only 1E 2259+586, but also of other magnetars. Furthermore, the magnetic energy release rate, −dEmag/dt, calculated from Eq. [12] and Eq. [32] using these parameters, become ∼7.5 × 1027 W at present, which is in a good agreement with the observed bolometric X-ray luminosity of 1E 2259+586, 6 × 1027 W. From these considerations, the MFs of magnetars are concluded to decay over time scales of 10–100 kyr, down to values below Bcr. They would soon become undetectable, unless some revival mechanisms operate.
5.3. Evolution of MFs below Bcr.Hereafter, we limit the discussion to those NS which were born with B0 < Bcr. In Fig. 12, radio pulsars are distributed approximately along a slope of $B_{\text{d}} \propto \tau _{\text{c}}^{ - 0.4}$. The simplest interpretation, which in fact used to be a standard one till the 1990’s, is to consider that the MF of NSs decay gradually and ubiquitously, on typical e-folding time scales of ∼108 yr.70) This was also motivated to explain MSPs and LMXBs: a standard view is that they were born as isolated radio pulsars with Bd ∼ 108 T, became slow rotators by losing Erot, and weak-Bd objects due to the MF decay, and captured by a low-mass star to become LMXBs, wherein they were spun up (“recycled”) by accretion as described by Eq. [14]. After the accretion ceased or the binary dissociated, the NS were left as MSPs.71)
The above scenario of MF decay, however, became obsolete for the following two reasons. One is selection effects, combined with the initial scatter in B0 (§ 5.1). Pulsars born with relatively high B0, hence with shorter lifetimes [Eq. [20]], will fade away more quickly than those with weaker B0. Furthermore, those with weak B0 have large values of t1 so that their τc will be overestimated. These two artifacts suppress, in Fig. 12, the numbers of old/high-Bd pulsars and young/low-Bd ones, respectively, to mimic the apparent negative correlation. Actually, a reanalysis of the radio pulsar statistics had already shown in the middle 1990’s that a constant MF model is consistent with the observations.72)
The other evidence is the very narrow distribution of Bd of BXPs [Fig. 6 (green) and Eq. [29]], which is considered complete on the lower-field side17),18) (although still incomplete towards the higher-field side). Considering typical lifetimes of the primary stars of BXPs (105.5–107.5 yr), any field decay on time scales of <108 yr would make the MF distribution of BXPs much broader towards the lower field side. Furthermore, the presence of the three BXPs with low-mass companions stars (§ 3.3), which have estimated system ages of >109 yr, cannot be reconciled with the MF decay even on a time scale of 109 yr. Therefore, the MF below Bd ∼ 108 T is unlikely to decay smoothly on time scales of <109 yr, although the behavior at 108 T < Bd < Bcr is still uncertain.
An alternative view to the above MF decay scenario is to assume that the MF of NSs remain relatively constant except in magnetars, and the scatter in Fig. 6 and Fig. 12 below Bd ∼ 109 T is at least partially natal, i.e., determined by distributions in B0. Then, can we explain the larger populations of non-accreting binary MSPs (green squares in Fig. 12) and accreting LMXBs (∼200 known)? These aged NSs in binaries are likely to have been produced via capture of NSs by non-degenerate stars, or via the accretion-induced collapse7) of white dwarfs, because they all have low-mass companions: it is unlikely that such a low-mass star formed a binary with a massive progenitor of the NS. However, if the capture process dominates, we would observe even larger number of strong-MF NS with low-mass companions (in contrast to the only known three), because higher MFs of NSs will enhance the extraction of orbital angular momentum73) which is necessary in their capture process. Even if the accretion induced collapse dominates, a small fraction (10–25%) of white dwarfs with Bd > 102 T would become NSs with Bd > 108 T via the magnetic flux compression; again, we should observe more aged NSs with strong MFs than are observed. Therefore, the MF below ∼109 is unlikely to be constant with time.
A third explanation of the MF evolution below Bd ∼ 109 T is to invoke a kind of “transition” from Bd = 107–109 T to 104–105 T, at a certain timing of the evolution of individual NSs. As a toy model, we may assume that the transition occurs in ∼109 yr, and that the timing scatters considerably from object to object for some unspecified reasons. This is indeed what is apparently suggested by Fig. 12. Then, the strong concentration of the MF of BXPs at Eq. [29] can be explained because their life times are <108 yr or so. The abundance of MSPs and LMXBs can be explained by considering that the dominant NS subclass born with Bd = 107–109 T would have mostly completed their transition in ∼109 yr. The three outliers, Her X-1, 4U 1626–67, and 4U 1822–37, can be interpreted as those which have not yet completed their transition. Thus, this simple view17),18) can explain the observations in a consistent way, although it is not yet widely accepted.
5.4. How the MF is held.The final and the most fundamental issue is how the MFs of NSs are held, and how the strong-to-weak MF transition suggested in § 5.3 takes place. The simplest idea is so-called fossil-MF view; during the core collapse, the progenitor’s MF was compressed (§ 2.2) to ∼108 T, and is sustained presumably by toroidal electric current, carried by protons and/or electrons that remain in the NS interior (mainly in so-called inner crust). The protons are possibly in a superfluid state, and are considered to gyrate around digitized “vortices” which thread the superfluid.74) These current-carrying vortices are considered to be gradually transported outwards, leading to the MF decay. However, as argued in § 5.3, this classical view can no longer explain the MF evolution. Furthermore, the ultra-strong MFs of magnetars may not be explained by such a fossil view. We are hence urged to explore alternative explanations.
A contrasting scenario is to assume that the MF is sustained by ferromagnetism in nuclear matter, produced by quantum alignment of magnetic moment of neutrons.17),18) This view had already been proposed in the late 1960’s,75) immediately after the discovery of pulsars.11) If a fraction f of the total Nn = MNS/mn = 1.7 × 1057 neutrons in an NS become spin-aligned, we obtain from Eq. [4] a MF strength of
| \begin{equation} B \sim \mu_{0}\,\mu_{\text{n}}\,f\,N_{\text{n}}/2\pi R_{\text{NS}}^{3} \sim 2.5\,f \times 10^{12}\,\text{T} \end{equation} | [33] |
Yet another possibility is that the electrons remaining in the NS becomes spin-aligned to form a ferromagnetic phase,77) due to some quantum mechanisms, including the neutrino’s chirality violation,78) or “chiral plasma instability” through which toroidal and poloidal electron currents are successively amplified.79) Thus, MFs close to Eq. [33] could be produced, because the very small number (e.g., ∼10−3 of neutrons) of the remaining electrons can be compensated by the Bohr magneton, μ = eħ/2me, which is ∼1840 times larger than μN. These new ideas are attractive, and should be extensively pursued, because they try to explain the NS magnetism in terms of symmetry in fundamental physics, including the electron-to-proton mass difference, the chirality violation by neutrinos, and the overall parity and charge asymmetry.
Over the past quarter century, we have been using several (mainly Japanese) X-ray observatories towards understanding the NS magnetism in the context of both astrophysics (formation and evolution of NSs) and fundamental physics. The results obtained in these studies can be summarized into the following points.
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.
The author would like to thank Prof. Yasuo Tanaka, Prof. Naoki Onishi, Prof. Toshikazu Shigeyama, Dr. Tatehiro Mihara, Dr. Teruaki Enoto, and Dr. Toshio Nakano, for their inspiring discussion. His thanks are also due to his colleagues at the University of Tokyo and RIKEN. This work was supported by the MEXT KAKENHI on Innovative Areas, Area No. 2404, Grant No. 25105507, and MEXT KAKENHI Grant No. 15H03653.
