Neutron stars: Observational diversity and evolution

Ever since the discovery of the Crab and Vela pulsars in their respective Supernova Remnants, our understanding of how neutron stars manifest themselves observationally has been dramatically shaped by the surge of discoveries and dedicated studies across the electromagnetic spectrum, particularly in the high-energy band. The growing diversity of neutron stars includes the highly magnetized neutron stars (magnetars) and the Central Compact Objects shining in X-rays and mostly lacking pulsar wind nebulae. These two subclasses of high-energy objects, however, seem to be characterized by anomalously high or anomalously low surface magnetic fields (thus dubbed as ‘magnetars’ and ‘anti-magnetars’, respectively), and have pulsar characteristic ages that are often much offset from their associated SNRs’ ages. In addition, some neutron stars act ‘schizophrenic’ in that they occasionally display properties that seem common to more than one of the defined subclasses. I review the growing diversity of neutron stars from an observational perspective, then highlight recent and on-going theoretical and observational work attempting to address this diversity, particularly in light of their magnetic field evolution, energy loss mechanisms, and supernova progenitors’ studies.


Introduction: Brief history of the neutron stars zoo
This conference celebrates 50 years of neutron stars discovery.Neutron Stars were discovered as Pulsars (PSRs) by Jocelyn Bell and Antony Hewish in 1967 but predicted to exist back in 1934 by Baade and Zwicky, just two years following the discovery of the neutron by Chadwick.It is with the Crab and Vela pulsars discovery in their respective supernova remnants (SNRs) that Baade and Zwicky's 1934 prediction that supernovae (SNe) make neutron stars was confirmed.The launch of imaging X-ray telescopes, such as Einstein (1980's), followed by ROSAT and ASCA (1990's) then by Chandra, XMM-Newton and Suzaku (2000's), showed us how these rotation-powered pulsars (RPPs) power synchrotron-dominated pulsar wind nebulae (PWNe).
One of the neutron star subclasses introduced in the 1990's is the 'anomalous' X-ray pulsars (AXPs).It was recognized first by Mereghetti & Stella [1] as a new class of X-ray pulsars, since their spectra were much softer than those of accretion-powered pulsars and had no binary companions; furthermore their X-ray luminosity exceeds the energy available from spin-down power, so they can not be powered by rotation.Duncan & Thompson [2] suggested that these are 'magnetars', i.e. highly magnetized neutron stars with a magnetic field exceeding the socalled 'quantum critical field' value of B QED = 2π m 2 e c 3 /eh = 4.4×10 13 G.AXPs are now merged with the Soft Gamma-ray Repeaters (SGRs), as bursting high-energy sources whose powerful outbursts are believed to be powered by their magnetic field decay.Dubbed under the Figure 1.P -Ṗ diagram showing the diversity of neutron stars.Lines of constant dipole magnetic field (solid black) and characteristic age (dashed grey) are shown.The 4.4×10 13 G line corresponds to the QED value of the magnetic field that is traditionally used to separate magnetars from the rotation-powered pulsars.The 3 pulsars shown in cyan (diamond symbol) correspond to the 3 CCOs for which we have a measured P and Ṗ .The 6 starred objects correspond to the 5 HBPs and 1 magnetar associated with a PWN and/or SNR, with the youngest and fastest two being PSR J1846-0258 in Kes 75 and J1119-6127 in G292.2-0.5, both having now displayed magnetar-like activity.The blue triangles correspond to the 3 AXPs + 1 SGR in our Galaxy known to be securely associated with an SNR with known age.
'Magnetars' family, these objects are among the most extreme objects known in the universe (see, e.g., [3]).
In the past decade, other sub-classes of neutron stars have emerged, thanks to sensitive radio and X-ray observations.These subclasses include the X-ray Dim Isolated Neutron Stars (XDINSs) (or the Magnificent Seven [4]), the Rotating Ratio Transients (RRATs [5]), the high-B radio pulsars (HBPs) with B≥B QED [6], and the Central Compact Objects (CCOs), typified by the Cas A CCO [7,8].While we used to treat them as different classes, we are now into the era of unifying these sources thanks to a growing body of observational and theoretical works.This review will highlight these works, focusing on neutron stars with 'extreme' magnetic fields (i.e.much smaller or higher than the canonical value of ∼ 10 12 G for the 'classical' rotation-powered pulsars) and stressing the fact that their hosting SNRs provide an independent means to address their unification.

Pulsars Characteristics and diversity
The diversity of pulsars is connected with their positions on the so-called P -Ṗ diagram.The period P and period derivative Ṗ determine their spin-down energy Ė=IΩ Ω (where I is their moment of inertia and Ω=2π/P ), their surface dipole field strength (at the magnetic equator) G, and their characteristic age τ c =P /2 Ṗ .For some pulsars, the braking index n=ν ν/ ν2 (where ν=1/P ) is measured (e.g, [15]).
Figure 1 shows the P -Ṗ diagram for the 2,613 currently known pulsars1 , revealing the growing diversity of neutron stars, and table 1 summarizes the secure PSR-SNR associations2 for the pulsars with 'extreme' magnetic fields.Below we briefly comment on these growing subclasses of neutron stars, and then address the blurring diversity and magnetic field evolution.

Magnetars and HBPs
There are currently 29 known magnetars (including 6 candidates) 3 .Magnetars are traditionally discovered as high-energy sources, with no PWNe around them.Only 3 AXPs and 2 SGRs (one of which is an extragalactic pulsar in the LMC SNR N49) are securely associated with SNRs (see figure 2).The High-B Pulsars (HBPs) are a growing class of radio-detected pulsars with an inferred magnetic field close to, or just above, the QED value.We know of approximately a dozen such objects, and they are believed to be powered primarily by rotational energy.The youngest  HBPs, PSR J1846-0258 and J1119-6127 in the SNRs Kes 75 and G292.2-0.5, respectively (figures 1 and 2), have recently displayed magnetar-like activity providing conclusive evidence for the connection between HBPs and magnetars (see §2.3).

CCOs
CCOs are X-ray emitting neutron stars found near SNR centres and typified by the compact object in the SNR Cas A (see figure 3).The term CCO was coined by Pavlov et al [7] following the first light Chandra discovery of the object. 4here are currently 14 CCOs5 (including 6 candidates) known in our Galaxy ( [8,19], SNRcat).These objects are X-ray emitters with no optical or radio counterparts, and with no evidence of PWNe surrounding them.X-ray pulsations have been discovered from 3 CCOs (see table 1).Their timing properties imply magnetic fields ∼10 10 -10 11 G, much lower than those of the traditional RPPs and magnetars, which led Gotthelf & Halpern [20] to dub them 'antimagnetars'.Spectroscopic studies support this interpretation through the discovery of spectral line features interpreted as cyclotron lines from a low B (e.g., [21][22][23][24]) or from modelling their thermal X-ray emission (e.g., [25,26]).
These objects are also known to be quiet X-ray emitters (except for the 'CCO' in RCW 103) with their X-ray emission described by two blackbodies and their X-ray luminosity (ranging from ∼ a few×10 32 -10 34 erg s −1 ) exceeding their spin-down energy.It is believed that their thermal spectra are derived from residual cooling and partly from accretion of supernova debris (e.g., [20]).One of their intriguing properties is their characteristic ages being orders of magnitude greater than their hosting SNRs' ages (see table 1 and figure 3).
The thermal X-ray luminosities of some of the HBPs and magnetars are systematically higher than those of the traditional radio pulsars, suggesting that magnetic fields affect their X-ray emission.Using 2D simulations of the fully-coupled evolution of both temperature and magnetic field in neutron stars, Viganò et al [42] unified the phenomenological diversity of magnetars, HBPs and isolated nearby neutron stars by varying their initial magnetic field, mass and envelope composition.Furthermore, the magnetic field topology was argued to play a key role in the observed properties of the bursting activity of neutron stars.Perna & Pons [43] showed that the toroidal component, particularly its strength with respect to the poloidal component, plays a significant role in the frequency of the bursting activity and its dependence on the age of the system.In addition, the role of fallback disks around young isolated neutron stars has been highlighted by Alpar et al [44] to unify different classes of neutron stars.

SNRs associations shedding light on magnetic field evolution
Generally it is assumed that neutron stars lose energy by spinning down due to the emission of magneto-dipole radiation.However, this simple model does not describe the neutron star population for the following reasons.First, it predicts a braking index n = 3, which has not been observed in young neutron stars; most of the measured indices are smaller than 3 (e.g., [15]).Second, the pulsars securely associated with SNRs show a remarkable disparity between their characteristic age and the SNR age, in some cases differing by several orders of magnitude (especially for the CCOs).Under the standard assumption of constant magnetic field, we have: 1) .Replacing τ with the SNR age (table 1), we are generally unable to explain the observed braking indices and enforce the SNR's age to be equal to the PSR's age with a constant n (see, e.g., figure 2 in [45]).Rogers & Safi-Harb [45,46] addressed magnetic field evolution focusing on the diverse population of neutron stars with 'anomalous' magnetic fields (i.e.much higher or lower than the canonical value of 10 12 Gauss).These objects include the AXPs, SGRs, HBPs and CCOs securely associated with SNRs of known ages and listed in table 1.

Magnetic Field Decay
Magnetic field decay has been invoked to describe the evolution of AXPs and SGRs (e.g., [47][48][49]).Magnetic field decay channels depend on a variety of effects including Ohmic dissipation, ambipolar diffusion and the Hall drift.While for the low-B pulsars with ages ∼10-100 kyr the Ohmic dissipation is expected to dominate the magnetic field evolution, for magnetar-strength-B pulsars, the Hall effect provides the dominant mechanism for the field evolution on timescales comparable to their associated SNR ages.

Empirical model for magnetic field evolution
In Rogers & Safi-Harb [45,46], both magnetic field growth and decay are described within the same basic framework, using empirical models for magnetic field evolution developed for various classes of neutron stars.In this approach the braking index is time-dependent: n = 3 − 4τ ḟj /f j , where the function f j (t) carries the time-dependence of the field.Thus, field decay gives n > 3 since ḟ D < 0, and field growth gives n < 3 since ḟ G > 0 .The sample shown in table 1 (plus other RPPs with a measured braking index) gives solutions to the field evolution in neutron stars, some of which are shown in figure 4 (see [45] and figure 5 therein for a more detailed and complete description of the sample and fits considered).Magnetic field growth has been used to fit the 3 CCOs (cyan), the 2 SGRs (red) and the HBP J1846-0258 in Kes 75 (green).AXPs have been fit with magnetic field decay models highlighted by the grey area in figure 4 [47].It is worth noting that the time evolution of the CCOs' characteristic age explains the apparent large discrepancy between the pulsars' ages (appearing very old) and the ages of the associated young SNRs.In particular, for the three systems shown, the PSR and SNR ages match at times ≥10 4.5 yr, by which time the SNR would have mostly dissipated.Therefore, the characteristic age for these pulsars does not reflect their true age as long as they are within their SNRs.This property, along with their inferred low asymptotic field strength, lead to the suggestion that CCOs could be ancestors of old isolated radio pulsars as long as they overcome the accretion phase (which would explain their X-ray dominant emission) and their surface field grows to the critical limit required for radio emission.The late time evolution of the CCOs may also link them to the class of objects known as XDINS; radio-quiet X-ray pulsars with long periods and no apparent SNR associations, with some of these objects having magnetic fields ≥10 13 G, similar to the HBPs.Pulsar age versus SNR age shown with evolutionary tracks for evolving magnetic fields in PSR-SNR pairs.
The solid black diagonal line corresponds to equal PSR and SNR ages.The colours/symbols match those used in figure 1, with the cyan, red and green curves showing field growth fits to 3 CCOs, 2 SGRs and 1 HBP, respectively.See §3.3 for details.

Magnetar progenitors
Which stars make magnetars?Two scenarios of interest have been proposed in the literature.
(1) The proto-neutron star model where the neutron star is born with a few milliseconds period [2], which predicts that the initial kinetic energy of the supernova would be reflected in a superenergetic hosting SNR.However, studies of magnetar SNRs and HBP SNRs (albeit limited to a very small sample and subject to low-resolution, CCD-type, X-ray spectroscopy) yield a 'typical' kinetic energy of the order of a few×10 50 -10 51 ergs (e.g., [14,65]).Furthermore, the inferred ratio of initial to current spin-period (P 0 /P ) for the magnetars and HBPs is not much smaller than 1, unlike what is predicted by the proto-neutron star model.(2) The fossil field hypothesis where magnetars are born from the most massive, most magnetic, main-sequence stars [66].Studies of magnetar SNRs point towards massive progenitors (see, e.g., [67]), supporting the fossil field hypothesis.However, this is not conclusive given that a few other studies point to lower mass progenitors [68,69].

CCOs' progenitors
Progenitor studies have been performed on the CCOs-hosting SNRs: Cas A, Puppis A, Kes 79, RCW 103 and RX J1713.7-3946.It is interesting to note that these studies point to progenitor masses around 20 M (although inconclusively).Below we summarize these studies.
• Cas A, the youngest historical type SNR in our Galaxy, harbours the CCO CXOU J232327.9+584842.It is commonly believed that Cas A results from a SN IIb event with a progenitor mass of ∼15-25 M and may have lost its H envelope to binary interaction (e.g., [70]), although a slightly higher mass (up to ∼30 M ) progenitor has been also discussed in the literature (e.g., [71]).• Puppis A is a ∼4.5 kyr-old SNR harbouring the 112 ms CCO RX J0822-4300.Spatially resolved spectroscopic studies of SNR ejecta using Suzaku, Chandra and XMM-Newton point to a 15-25 M progenitor [72,73].
• Kes 79 is a ∼5 kyr-old SNR harbouring the CCO CXOU J185238.6+004020(PSR J1852+0040).A multi-wavelength study, together with an X-ray spectroscopic study of the ejecta compared to nucleosynthesis model yields, suggest a 15-20 M progenitor [17]).• RX J1713.7-3946(G347.7-0.5) is a ∼1-2 kyr-old SNR harbouring the CCO 1WGA J1713.4-3949.The measured metal abundance ratios suggest that the progenitor star was a relatively low-mass star (≤20 M ), However, based on the inferred blast wave velocity of ∼6,000 km/s which is considered fast for such a core-collapse SNR, Katsuda et al [74] propose that RX J1713.7-3946results from a SN Ib/c and that its progenitor is a member of an interacting binary.• RCW 103 is a ∼2 kyr-old SNR hosting near its centre the unusual CCO 1E 161348-5055 which had been recently proposed to be a magnetar [36,37].Comparison of the ejecta abundances inferred from X-ray spectra with supernova nucleosynthesis yields models suggests a progenitor mass of ∼18-20 M [75].

The Crab
Going back to the 'poster' outcome of a core-collapse SN, the Crab's progenitor is known to be an ∼8-10 M progenitor star.However, it has a low visible mass of ∼5 M and a small kinetic energy of <10 50 erg for a young core-collapse SNR.Two scenarios have been discussed: (1) a massive undetected shell beyond the visible PWN [76], (2) an electron-capture SN, an endothermic reaction of electrons captured in an O-Ne-Mg core of a super AGB star with a low energy (∼10 50 erg) explosion [77].This puzzle has been most recently addressed with the Hitomi X-ray satellite [78].One of the science goals for Hitomi was to search for thermal X-ray emission from the synchrotrondominated SNRs, thanks to its unprecedented spectral resolution and sensitivity to the thermal X-ray emission with the Soft X-ray Spectrometer.A brief observation took place just before the end of the Hitomi mission [79].The gate valve was still closed, which hampered the sensitivity below 2 keV.While no thermal X-rays were detected, as in previous dedicated searches (e.g., with Chandra [80]), a more constrained upper limit on the X-ray emitting plasma has been established with Hitomi and past Chandra and XMM-Newton studies.Furthermore, while a low-energy supernova explosion has been favoured [81,82], a higher energy Fe core-collapse explosion could not be ruled out but implies, depending on the environment, a very stringent upper limit on the ambient density or mass loss rate [79].

Future prospects
Despite significant advances in neutron stars physics in the past 50 years, many questions remain to be answered.We hope the answers will be obtained with the planned X-ray missions.
• The sample of PSR-SNR associations has been limited by sensitivity and resolution.
Furthermore, the X-ray emission from CCO descendants and old radio pulsars would benefit from deep X-ray observations and/or a sensitive X-ray survey.The upcoming eRosita X-ray satellite (Germany/Russia), expected to be launched in 2018, will allow us to expand our sample and probe the X-ray emission from the different classes of neutron stars.• To date, we do not have braking index measurement of magnetars (SGRs and AXPs) and other neutron stars subclasses, and most measurements done to-date point to an index n<3.Timing studies of the different classes of neutron stars is needed to shed light on their braking indices, which in turn addresses magnetic field evolution.The recently launched ASTROSAT (India/Canada), NICER (NASA), and the HXMT (China) X-ray satellites will provide a new window into timing studies of pulsars.
• X-ray polarimetry is still lacking in the field, but is crucial as it provides a direct measurement of the neutron star's magnetic field and sheds light on its topology (particularly for the magnetars and PWNe).XIPE (ESA), IXPE (NASA) and XTP (China) are currently being planned for the near future.• High-resolution X-ray spectroscopy is needed to (a) provide an accurate measurement of SNR ages, (b) probe SN progenitors and (c) provide a direct measurement of the neutron star's magnetic field.Powerfully demonstrated by the glimpse of the Hitomi satellite on a few targets before its loss, high-resolution X-ray spectroscopy is now planned for the X-ray recovery mission (XARM, JAXA/NASA; 2021 timescale) and in the more distant future for Athena (ESA; 2028 timescale) and Lynx (NASA; beyond 2030).
Figure 4.Pulsar age versus SNR age shown with evolutionary tracks for evolving magnetic fields in PSR-SNR pairs.The solid black diagonal line corresponds to equal PSR and SNR ages.The colours/symbols match those used in figure1, with the cyan, red and green curves showing field growth fits to 3 CCOs, 2 SGRs and 1 HBP, respectively.See §3.3 for details.

Table 1 .
Pulsars with very high or very low magnetic field securely associated with SNRs with known ages.