Grand unification of neutron stars

Rotation-Powered Pulsars

RPP rotation periods span the range of 1 ms through 8 s. Their magnetic field strengths range from 10⁸ to 9 × 10¹³ G. Their distribution in space is shown in Fig. 2. Those with P ≲ 20 ms and B ≲ 10¹⁰ G are usually called MSPs. The x-ray emission from RPPs falls into two broad classes, both of which are generally pulsed and steady (see ref. 6 for a review). First is thermal emission, which itself can be a result of residual cooling following formation in a core-collapse supernova (typically only observable for the first ∼10⁵ years or from surface reheating by return currents from the magnetosphere, common for MSPs. Thermal emission has received considerable attention owing to its potential for use in constraining the equation-of-state of dense matter, by comparing temperatures and luminosities with theoretical cooling curves, accounting for the spectrally distorting impact of the neutron-star atmosphere and also by detailed modeling of x-ray light curves (e.g., ref. 7). For reviews see, for example, refs. 8 or 9. Chandra highlights in this area include the detection of a surprisingly low temperature for the pulsar in the young SNR 3C 58 (10), interesting constraints on the equation-of-state from modeling millisecond pulsar thermal emission light curves (7). Major open questions in this area are the nature and impact of the neutron-star atmosphere and whether thermal-emission observations can strongly constrain the equation-of-state of dense matter.

Second is nonthermal, usually power-law emission originating from the magnetosphere, typically more highly pulsed than the thermal component and strongly correlated with the pulsar’s spin-down luminosity. The latter is defined as where I is the stellar moment of inertia. For a review of magnetospheric emission, see ref. 11, although thinking on this front is currently evolving thanks to recent interesting results from Fermi (3). Chandra’s primary strength in this field is its small background and ability to resolve the point source from its nebular surroundings (see below), allowing superior spectral studies. Major open questions on this subject include how the emission is generated and how is it related to observed nonthermal γ-rays and radio emission.

Chandra’s great angular resolution means it has been a superb tool for studying RPP surroundings, namely, pulsar wind nebulae (PWNe), the often spectacular result of the confinement of the relativistic pulsar wind by its environment (see ref. 12 for a review). Among Chandra’s greatest PWN legacies are the discovery of rapid time variability in the Crab and Vela PWNe (see ref. 13 and references therein) as well as of the surprisingly diverse morphologies these objects can have (see Fig. 1 for examples and the aforementioned reviews for more). Detailed modeling of the geometries (14) and emission mechanisms (15) constrain both the properties of the pulsar wind and shock acceleration mechanisms. Important open questions here are the nature and composition of the pulsar wind, specifically whether it consists of only e⁺/e^- pairs or also ions (e.g., ref. 16), what are the particle energy distributions, and what is the fraction of energy in particles versus magnetic fields? These have great relevance to our basic understanding of the neutron star as a rapidly rotating magnetic dipole converting rotational kinetic energy into such a powerful particle/field wind. The shock acceleration issues are interesting as well (e.g., ref. 17).

A subset of PWNe are the ram-pressure confined variety, showing bow-shock morphology that corresponds with the pulsar’s direction of motion through the interstellar medium, e.g., refs. 18 and 19. An example is shown in Fig. 1. These are additionally useful as they provide independent determinations of directions of motion, which are often difficult to determine otherwise, especially for young pulsars. Notably, the first-known PWN around an MSP, a ram-pressure confined structure with morphology in clear agreement with the measured proper motion, was found by Chandra, demonstrating unambiguously that MSPs have winds that are similar to those of their slower cousins (20).

From a grand-unification perspective, the properties of RPPs can be seen as the template against which all other classes are compared. Thermal emission, for example, is seen from all the other classes discussed below, demonstrating that it is generic to neutron stars, except the very cool ones for which it is unobservable. By contrast, RPP-type magnetospheric emission is only observable in high spin-down luminosity sources, as are PWNe. When considering any new neutron-star class, in the absence of telltale pulsations, the spectrum is therefore crucial to consider (thermal or nonthermal?) as is the presence or absence of associated nebulosity. This will be a recurring theme in the rest of this paper.

Rotating Radio Transients

Recently, McLaughlin et al. (4) discovered brief radio bursts from galactic sources, but with no directly observed radio periodicities. The number of RRATs is now roughly a dozen and, in practically all cases, an underlying periodicity can be deduced thanks to the phase constancy of the bursts. At first thought to be possibly a truly unique class of neutron star, it now appears most likely that RRATs are just an extreme form of RPP, which have long been recognized as exhibiting sometimes very strong modulation of their radio pulses (21). Indeed several RRATs sit in unremarkable regions of the diagram (Fig. 2). Interesting though is the mild evidence for higher-than-average periods and B fields among the RRATs than in the general population, though the numbers are small (Fig. 2). In Chandra observations of the relatively high-B RRAT J1819 - 1458 (B = 5 × 10¹³ G), the source had a thermal x-ray spectrum typical of RPPs of the same age, arguing against any radical physical difference (22). Recently, a small apparently associated PWN was seen in Chandra data. It has a somewhat surprisingly high luminosity (though subject to substantial uncertainties), suggesting the presence of a possible additional source of energy beyond rotation power (23). If correct, it would argue for RRATs being somehow physically distinct from RPPs.

Regardless of whether or not RRATs are substantially physically different from RPPs, their discovery is important because it suggests a very large population of neutron stars that were previously missed by radio surveys that looked only for periodicities. This has potentially major implications for the neutron-star birthrate (4, 24).

Magnetars

Magnetars, which traditionally are seen as falling into two classes, the anomalous x-ray pulsars (AXPs) and the soft-gamma repeaters (SGRs), have been studied with practically every modern x-ray telescope, and Chandra is no exception. Today these long-P objects are thought to be powered by an intense magnetic field (25, 26), inferred via spin down to be in the range 10¹⁴–10¹⁵ G (see Fig. 2), well above the so-called quantum critical field (where QED stands for quantum electrodynamics). For a review of magnetars, see ref. 27. Magnetars have been argued to represent at most ∼10% of the neutron-star population, in part because of their apparent association with very massive progenitors, as very strongly demonstrated by the Chandra discovery of an AXP in the massive star cluster Westerlund 1 (28). However the discovery of the transient AXP XTE J1810–197 (29) suggests there could be a large, unseen population of quiescent magnetars, which would have important implications for understanding the formation of different types of neutron stars.

Chandra’s strengths for magnetar observations have been its spectral resolution, allowing searches for spectral features (none have been found; see refs. 30 and 31), and its angular resolution for searching for associated nebulae (none have been seen, with one possible exception; see ref. 32), and in some cases searching for a proper motion (none have been detected; see refs. 33 and 34). More fruitfully, Chandra has provided precise localizations for magnetars, crucial for multiwavelength follow up (e.g., refs. 29 and 35). In addition, Chandra’s superior viewing windows relative to XMM have allowed rapid target-of-opportunity (ToO) observations in response to magnetar outbursts, as triggered, for example, by RXTE monitoring. The latter telescope, with its excellent scheduling agility, is ideal for regular snapshot monitoring of magnetars, especially the generally bright AXPs (36–40). However, RXTE provides only pulsed fluxes above 2 keV, and spectroscopy of very limited quality in these short observations, hence the need for occasional high-sensitivity focusing telescope observations. For example, Chandra ToO observations of AXP 1E 1048.1–5937 revealed a clear correlation between pulsed fraction and flux as well as hardness and flux (see also ref. 41) during the relaxation following this source’s 2007 outburst. Such studies constrain models of magnetar outbursts, generally confirming the “twisted magnetosphere” picture (42, 43). Understanding the physics of magnetar outbursts is important not just for studying the behavior of matter in quantum critical magnetic fields, but also for constraining the burst recurrence rate, which is important for constraining the number of magnetars in the Galaxy. Chandra’s excellent point-source sensitivity has also been important for studying transient magnetars in quiescence (44), showing that they can have a huge dynamic range in flux and be very faint in quiescence, which further emphasizes the possibly large unseen population of quiescent magnetars, important for determining the magnetar birthrate (e.g., ref. 24).

High-B Rotation-Powered Pulsars

A potentially pivotal class of objects are the high-B RPPs. There are now 7 RPPs (including one RRAT, J1819–1458) that have spin down inferred B > 4 × 10¹³ G, a somewhat arbitrary limit but comparable to B_QED, and very close to the lowest B field yet seen in a bona fide magnetar (6 × 10¹³ G in AXP 1E 2259+586). There is clear overlap between high-B RPPs and magnetars, as is evident in the diagram (Fig. 2). There have been multiple efforts to look for magnetar-like emission from high-B RPPs (45–50). The bottom line thus far is that, in spite of very similar spin parameters, the high-B RPPs show x-ray properties that are approximately consistent within uncertainties with those of lower-B RPPs of comparable age (but see ref. 49), though also consistent with spectra of transient magnetars in quiescence (48). The latter point suggested that high-B RPPs could be quiescent magnetars. The radio detections of two transient magnetars lend some support to this idea, although in those cases the radio emission appears temporarily following an outburst, and the radio spectra are distinctly harder than those of most RPPs (51, 52).

Recently, a major breakthrough occurred. The well-established young, high-B (B = 4 × 10¹³ G) RPP PSR J1846–0258 at the center of the SNR Kes 75 exhibited a sudden, few-week x-ray outburst in 2006, as detected by RXTE monitoring (53). The outburst included a large pulsed flux enhancement, magnetar-like x-ray bursts (53), and, intriguingly, a coincidental unusual spin-up glitch (54). This source had been monitored regularly with RXTE since 1999 (55) and had shown no other activity. Chandra had observed this source twice: once in 2000 when the RPP was in its usual state and, by amazing coincidence, once in 2006, in the few-week period of activity. These Chandra observations showed that the RPP x-ray spectrum softened significantly, with a thermal component emerging from a previously purely power-law spectrum, and that the associated PWN showed likely changes too, though possibly unassociated with the event (53, 56, 57). Overall, this event demonstrates unambiguously a connection between high-B RPPs and magnetars, further supporting the possibility that high-B RPPs could in general be quiescent magnetars, as speculated in ref. 48.

Isolated Neutron Stars

The seven confirmed INSs are characterized, as mentioned earlier, by quasi-thermal x-ray spectra, relative proximity (distances ≲500 pc), lack of radio or other counterpart, and relatively long spin periods (3–11 s). For past reviews of INSs, see refs. 58, 59. Recently, another possible example of INS was identified, in part thanks to Chandra (60, 61). These objects are potentially very interesting for constraining the unknown equation-of-state (EOS) of dense matter, because proper modeling of their x-ray spectra, which are thought to be uncontaminated by magnetospheric processes, could constrain the stellar masses and radii for comparison with different EOS models. Also, INSs may represent an interestingly large fraction of all galactic neutron stars (24). Timing observations of several objects, done in part by Chandra, have revealed that they are spinning down regularly, with inferred dipolar surface magnetic fields of typically ∼1–3 × 10¹³ G (59, 62) and characteristic ages of ∼1–4 Myr (see Fig. 2). Such fields are somewhat higher than the typical RPP field. This raises the interesting question of why the closest neutron stars should have preferentially higher B fields.

The favored explanation for INS properties is that they are actually RPPs viewed well off from the radio beam. Their x-ray luminosities are thought to be from initial cooling and they are much less luminous than younger thermally cooling RPPs because of their much larger ages. However, their luminosities are too large for conventional cooling, which suggests an additional source of heating, such as magnetic field decay, which may explain their surprisingly high magnetic fields (discussed further below).

Particularly noteworthy in the INSs are puzzling broad and occasionally time-variable absorption features in their x-ray spectra (63–66). The Chandra low-energy transmission grating has contributed significantly to this work (which is also being done using the XMM reflection grating spectrometer). The features have been suggested to be proton cyclotron lines, neutral hydrogen transitions, but the time variability is puzzling, suggesting precession (67) or accretion episodes (65). This remains an open issue.

Central Compact Objects

CCOs are neutron-star-like objects at the centers of supernova remnants, but which have puzzling properties which have at some point precluded them from being classified among one of the classes discussed above. Common properties to CCOs are absence both of associated nebulae and of counterparts at other wavelengths.

The poster-child CCO, discovered in the Chandra first-light observation, is the central object in the young oxygen-rich supernova remnant Cas A. This mysterious object has been very well studied, especially with Chandra. Particularly puzzling is its lack of x-ray periodicity, lack of associated nebulosity, and unusual x-ray spectrum (68–71). Recently, Ho and Heinke (72) suggested that the Cas A CCO has a carbon atmosphere, showing that its Chandra-observed spectrum is fit well by such a model, and implies a stellar radius consistent with expectations for a neutron star, in contrast to hydrogen or helium atmosphere models. With the entire surface radiating, the absence of pulsations would not be surprising.

Three other previously mysterious sources classified as CCOs are today, thanks largely to Chandra, known to be pulsars with interesting properties. PSR J1852 + 0040 is at the center of the SNR Kes 79 (73, 74). This pulsar, observed only in x-rays, has period 105 ms yet very small spin-down-inferred magnetic field strength, B = 3.1 × 10¹⁰ G and large characteristic age, τ = 192 Myr (75). This age is many orders of magnitude larger than the SNR age, and much older than would be expected for an object of this x-ray luminosity (which greatly exceeds the spin-down luminosity). The B value is also the smallest yet seen in young neutron stars, prompting Halpern and Gotthelf (75) to call this an “antimagnetar.” Interestingly, the object sits in a sparsely populated region of the diagram (Fig. 2), among mostly recycled binary pulsars. A similar case is the CCO in the SNR PKS 1209–52, 1E 1207.4–5209. Discovered in ROSAT observations (76), pulsations were detected at 0.4 s in Chandra data (77, 78). Spectral absorption features were seen using Chandra (79) and XMM (80) but as of yet are not well explained. Interestingly, the source has an unusually small (as yet undetectable) period derivative, implying B < 3.3 × 10¹¹ G and τ > 27 Myr, again, orders of magnitude greater than the SNR age and inconsistent with so large an x-ray luminosity (81). Yet another such low-B CCO is RX J0822–4300 in Puppis A (82). Although its properties are not as well constrained (B < 9.8 × 10¹¹ G), it seems likely to be of similar ilk. Halpern and Gotthelf (75) present a synopsis of other sources they classify as CCOs and argue that these antimagnetars are x-ray bright thanks to residual thermal cooling following formation, with the neutron star having been born spinning slowly (consistent with some recent population synthesis studies, e.g., ref. 83) and with low B. In this case, the origin of the nonuniformity of the surface thermal emission remains puzzling.

Arguably the most bizarre CCO is 1E 161348–5055 in SNR RCW 103. Discovered with Einstein (84), this CCO showed no pulsations or a counterpart at other wavelengths. Unusually large variability was reported a decade ago (85) and, more recently, a strong 6.6-h periodicity was seen from the source in an XMM observation (86). No infrared counterpart has been detected in spite of deep observations enabled by a precise Chandra position (87). The nature of this source is currently unknown, with suggestions ranging from an unusual binary (88, 89) to a neutron star and a fallback disk (90).

Attempts at Unification

In spite of the obviously great diversity in young neutron-star observational x-ray properties, some interesting ideas for grand unification are emerging. A theory of magnetothermal evolution in neutron stars has recently been developed in a series of papers (91–94). Motivated largely by an apparent correlation between inferred B field and surface temperature in a wide range of neutron stars, including RPPs, INSs, and magnetars (91) (but see ref. 50), a model has recently been developed in which thermal evolution and magnetic field decay are inseparable. Temperature affects crustal electrical resistivity, which in turn affects magnetic field evolution, while the decay of the field can produce heat that then affects the temperature evolution. In this model, neutron stars born with large magnetic fields (> 5 × 10¹³ G) show significant field decay, which keeps them hotter longer. The magnetars are the highest B sources in this picture, consistent with observationally inferred fields; the puzzling fact that INSs, in spite of their great proximity, all appear to have high inferred Bs relative to the RPP population is explained nicely as the highest B sources remain hottest, hence most easily detected, longest. A recent attempt at population synthesis modeling of RPPs, INSs, and magnetars using the magnetothermal evolutionary models (95) followed closely a previous analysis of RPPs (83) but found that the populations of RPPs, INSs, and magnetars (though they admit the latter two classes are few in number) can be explained if the birth magnetic field distribution of nascent neutron stars has mean B of 10^13.25 G. This is significantly higher than has been previously thought (83).

If this unification picture is correct, then RPPs, INSs, and magnetars can be roughly understood as having such disparate properties simply because of their different birth magnetic fields and their present ages. Unifying further, RRATs are likely just an extreme form of RPP, with MSPs being binary-recycled RPPs with quenched B fields, as has been believed for many years (2).

The low-B CCOs could be understood in the above picture as being the lowest birth B neutron stars, x-ray bright only because of their true young ages, which are much smaller than their characteristic ages (75). This however presents an interesting quandary. The Kes 79 pulsar (see above) with its small B = 3.1 × 10¹⁰ G spins down very slowly. It is widely believed that RPPs, as they spin down, eventually cross a “death line” beyond which their radio emission shuts off, in keeping with the absence of pulsars at long P and small in the diagram (Fig. 2). There have been many theory-motivated suggestions for the exact location of the death line which is highly constrained by observations; one possibility is shown in Fig. 2 and is given by B/P² = 0.17 × 10¹² Gs^-2 (see ref. 83 and references therein). For the Kes 79 pulsar, in the absence of B-field decay (reasonable for so low a field in the magnetothermal evolutionary model) and assuming dipolar spin down, it will have P ∼ 0.43 s at death, which will occur in ∼3 Gyr. Assuming the other CCOs have similar properties, and noting that their parent SNRs all have ages ≲7 kyr, we estimate a birthrate of such low-B objects of ∼0.0004 yr^-1. For this birthrate and estimated lifetime, we expect to find ≳1 × 10⁶ of these objects in the galaxy! This is comparable to, or greater than, the expected number of higher-B sources, which though born more often, do not live as long. Yet—and here is the quandary—the Kes 79 pulsar sits in a greatly underpopulated region of the diagram (see Fig. 2). Selection effects cannot explain this lack of pulsars; only preferentially low radio luminosities could. The latter is consistent with models in which radio luminosity depends on spin-down parameters, as opposed to being only dependent on viewing geometry (see ref. 83).

Next Chandra Decade

There is no shortage of ideas for future tests of the above theory of neutron-star grand unification, and Chandra is likely to play a major role. The high-B RPPs are a crossroads class. X-ray observations of these objects, both deep to determine precise spectra and fluxes for comparison with the predictions of magnetothermal evolutionary models, as well as shallow monitoring to permit searches for magnetar-like variations, could be helpful. ToO observations of high-B RPPs at glitch epochs could reveal generic associated magnetar-like behavior, which would be a major breakthrough in our understanding of glitches and, possibly, neutron-star structure (40). Continuing ToO observations of magnetars in outburst will continue to constrain detailed models of magnetars and help understand crucial parameters like outburst recurrence rate, central to understanding how many magnetars there are in the galaxy, hence their birthrate. Continued monitoring of INSs, both to study their intriguing spectra and their variations, as well as their timing properties, is also important. Systematic timing and spectral studies of newly discovered members of any of the classes discussed in this review, particularly CCOs, are clearly very important for making progress, given the paucity of sources in most of the classes. With so many possibilities, the future of this field is very bright. I look forward with high hopes to reading the next Chandra decade’s neutron-star review.