The surprising Crab pulsar and its nebula: A review
The Crab nebula and its pulsar (referred to together as “Crab”) have historically played a central role in astrophysics. True to their legacy, several unique discoveries have been made recently. The Crab was found to emit gamma-ray pulsations up to energies of 400 GeV, beyond what was previously expected from pulsars. Strong gamma-ray flares, of durations of a few days were discovered from within the nebula, while the source was previously expected to be stable in flux on these time scales. Here we review these intriguing and suggestive developments. In this context we give an overview of the observational properties of the Crab and our current understanding of pulsars and their nebulae.
pacs:97.60.Bw, 97.60.Gb, 97.60.Jd
- 1 Introduction
- 2 Observational overview
- 3 Theory of pulsar wind nebulae
- 4 Pulsed very high-energy gamma-ray emission
- 5 Gamma-ray flux variations from the nebula
- 6 Outlook
On August 25, 1054 A.D., the Chinese astrologer Yang Wêlt reported “the appearance of a guest star, above which some yellow-colored light was faintly seen”. He goes on to interpret the observations as showing that “there is a person of great wisdom and virtue in the country. I beg that the Bureau of Historiography be given this message”111The term “guest star” was used by Chinese astronomers for new stars in the night sky, as novae or supernovae. [Peng-Yoke1972]. Yang Wêlt’s message was heard and today we know that the new star which emerged in July 1054 A.D. on the night sky was the Crab supernova [Breen1995]. Since then the remainder of this explosion, the Crab nebula and its pulsar, has been studied over the centuries. The source was rediscovered by an English amateur John Bevis who included it in a beautiful atlas which was never published because the publishers went bankrupt. He told his French colleague, Charles Messier about it. Messier was more interested in comets, to him the Crab Nebula was noise not signal. He included it in a famous catalog of celestial objects that could be confused with comets. The Crab is the first entry. The name of the nebula is due to an Irishman, the third Earl of Rosse, who thought it looked like a Crab.
Following observations from J C Duncan in 1921, Edwin Hubble noted that, not only the Universe, but also the Crab nebula is expanding [Hubble1928]. From the expansion velocity he correctly deduced that the nebula was the remainder of the 1054 A.D. star explosion, making the Crab the first historical supernova. In one of the most celebrated and concise conjectures in the history of astronomy, Baade and Zwicky in 1934 “advanced the view” that in a supernova “mass in bulk is annihilated”, “cosmic rays are produced” and that they “represent a transition from ordinary stars into neutron stars” [Baade1934]. In 1942, Minkowski correctly associated one of the two central stars in the nebula with the explosion and in 1967 Pacini proposed that this star was a highly magnetized, spinning neutron star and that it powered the nebula [PACINI1967]. The idea was put on a firmer footing by Gold who equated the rate of loss of rotational energy by the neutron star with the bolometric luminosity of the nebula [Gold1968]. Almost 1000 years after the explosion of the progenitor star, the Crab is far from being quiet. At photon energies above keV, it is typically one of the brightest sources in the sky.
Due to its high luminosity erg s [Hester2008] and its proximity of kpc [Trimble1973], the Crab can be studied in great detail. It is therefore one of our prime laboratories to study non-thermal processes in the Universe. Many discoveries have been made in the Crab and then been seen in other non-thermal sources (including active galactic nuclei, gamma ray bursts and X-ray binaries) such as polarized synchrotron radiation or pulsed optical emission [Shklovsky1953, Cocke1969]. True to this legacy two remarkable discoveries have been made in the last years. Very high-energy (VHE GeV) gamma-ray emission has been detected from the pulsar, and high-energy (HE MeV) gamma-ray flares have been discovered from the nebula. These phenomena have not been observed in any other pulsar wind nebula to date. As we will discuss, they challenge and extend our understanding of these systems.
This article is structured as follows: first we will summarize the observational properties of the Crab and our current theoretical understanding of pulsar wind nebulae (section 2 & 3). We will proceed to discuss the discovered gamma-ray pulsations and flares together with the ideas put forward so far to explain them (section 4 & 5). Finally, we conclude the article with an outlook on future observational and theoretical developments. We would like to note that, given the wealth of work done on this source, it is not possible for us to be exhaustive. We will therefore give references to related review articles whenever possible. A more detailed description of the observational properties of the Crab can for instance be found in \citeasnounHester2008. A more detailed discussion of the theory of pulsar wind nebulae can be found in \citeasnounKirk2009 and \citeasnounArons2012.
2 Observational overview
The Crab nebula can be seen in a composite image in Fig. 1. The point source at its center is the Crab pulsar, the energy source of the system (see \citeasnounRowan2004 and \citeasnounHarding2013a for reviews on neutron stars and pulsars). Its energy is in its largest part emitted in a relativistic flow of magnetized plasma. This pulsar wind is thought to be predominantly composed of electron-positron pairs (referred to together as electrons in the following), although some ions might be present [Gallant1994]. These pairs flow outwards and interact with the remaining ejecta of the progenitor star. As these particles spread out in the nebula, they loose energy due to synchrotron and inverse Compton radiation, creating the glowing pulsar wind nebula observed today. In the following we will describe the observations of the pulsar and the nebulae in more detail.
2.1 The Crab pulsar
The pulsar emits radiation across the electromagnetic spectrum with a period of ms, which is slowing down by [Manchester2005, Abdo2013]. The corresponding loss of rotational energy is erg s, assuming a moment of inertia of the neutron star of g cm. Only % of this energy is emitted in electromagnetic radiation. The radiation is thought to be collimated in beams of light, which sweep the field of view of the Earth, creating the observed pulsations. The phase-averaged spectral energy distribution (SED) is shown in Fig. 2. It is composed of three main components: the first one in the radio band, a second energetically dominant component peaking in the X-ray band and a third one emerging above energies of MeV.
The phase profile of the emission is shown in Fig. 3. As for the majority of pulsars detected in gamma rays by the Fermi Large Area Telescope (LAT), the radiation as a function of phase is concentrated in two peaks [Abdo2013]. The pulses arrive approximately simultaneously across the electromagnetic spectrum, only small shifts between energy bands are seen (; \citeasnounOosterbroek2008 and \citeasnounAbdo2010). The main pulse is located at and the inter-pulse at . A faint precursor to is detected at radio frequencies, and at frequencies above the optical bridge emission is found between and . A peculiarity of the pulse profile of the Crab is that it is unusually irregular on short time scales. Giant radio pulses with a flux 1000 times the average are seen randomly during and [Lundgren1995, Cordes2004, Popov2007]. Optical emission was seen to increase during such events [Shearer2003, Strader2013], but no such correlation has been found so far with higher energies [Bilous2011, Bilous2012, Aliu2012]. Pulsar glitches, during which for a limited time the spin-down frequency increases by up to Hz, are observed per year [LyneA.G.1993, Espinoza2011, Wang2012].
The pulsar emission is found to be polarized. The position angle of the linearly polarized component varies with pulse phase. The polarization properties in radio depend on frequency. Generally, the polarization degree and angle vary smoothly, with no abrupt changes during the main pulses [Moffett1999]. The Crab is one of the few pulsars for which polarization has also been detected at optical wavelength [Sowikowska2009, Moran2013]. The optical polarization angle swings from to during P1, decreases again during the bridge emission and swings from to during P2.
2.2 The Crab nebula
The appearance of the nebula in the sky is approximately ellipsoidal with a major axis of arc minutes and a minor axis of arc minutes. This corresponds to a projected length of pc and pc, respectively. As one observes the nebula at higher frequencies, a toroidal structure becomes increasingly apparent. Images of the inner region in X-rays and optical are shown in Fig. 4. A torus surrounding the pulsar and a jet emerging perpendicular to it are apparent. It is striking that there is no bright emission in the region within arc seconds of the pulsar [Hester1995, Hester2002, Mori2004a, Temim2006]. The pulsar wind is apparently radiationless (or “cold”), until interaction with the ambient medium happens. The first interaction is commonly thought to occur at the “inner ring” observed in the X-ray image [Weisskopf2000].
As can be seen in Fig. 4, the inner nebula is a highly dynamical place. Thin arcs of increased emission, so called “wisps”, are observed to move outwards from the inner ring into the body of the nebula [Scargle1969]. Wisps can be seen in radio, optical and X-rays, however their positions do not always coincide between frequencies. Typically, their inferred velocity is between 0.03 c and 0.5 c [Hester2002, SchweizerThomas2013], with indications for radio wisps to be slightly slower [Bietenholz2001, Bietenholz2004]. Additionally, several other structures on scales of a few arc seconds are seen close to the inner ring and along the jet. Most prominently the “Sprite” is seen as a fuzzy region at the base of the jet in the optical images, and the “inner knot”222There is some confusion with the nomenclature used in the literature. The “inner knot” is sometimes also referred to as “knot 1”, and the “Sprite” sometimes referred to as “Anvil”. is detected only arc second south east of the pulsar (the inner knot is too close to the pulsar to be visible in Fig. 4, see e.g. \citeasnounTziamtzis2009 or \citeasnounMoran2013). Sprite, wisps and the inner knot are known to be variable down to time scales of a few hours [Hester2002, Melatos2005].
Spectrally, the nebula shows a trend to softer spectra with increasing distance from the pulsar. This is interpreted as the radiative cooling of the highest energy electrons as they are convected and diffuse away from the inner nebula. Interestingly however, the spectrum in the inner region of the nebula is rather uniform. The torus, the jet and the small scale structures mentioned in the previous paragraph show no strong spectral variations among them from infrared to X-ray energies [Veron-Cetty1993, Willingale2001, Temim2006, Mori2004a, Tziamtzis2009]. At radio frequencies the picture is more complex. As radio emission originates from a larger volume in the nebula, it is generally more difficult to disentangle line of sight effects. However, also at radio frequencies the spectrum is harder in the inner nebula [Green2004a, Arendt2011].
The emission from the nebula is found to be linearly polarized from radio to hard X-rays [Wilson1974, Weisskopf1978, Bietenholz1991, Hester2008, Dean2008, Forot2008, Aumont2010]. Generally, the polarization angle is aligned with the symmetry axis of the nebula, indicating that the magnetic fields are predominantly azimuthal. A detailed study was recently performed in optical by \citeasnounMoran2013. They find that the polarization of the wisps, the inner knot and the torus are all within a few degrees of the aforementioned and have a high degree of polarization . While these structures are found to be variable in flux, their PA and PD show no significant variations.
The broad band SED of the nebula is shown in Fig. 2. One can see that the energy output of the nebula is a factor larger than the one for the pulsar (in addition, the isotropic pulsar flux is likely even lower due to the beaming of its emission). In the nebula, the peak of the emission is located in the UV. The emission from radio to X-rays is known to be due to synchrotron emission thanks to polarization measurements. At high energies ( MeV), a second emission component emerges due to inverse Compton emission of the same electrons. This component is energetically subordinate with respect to the synchrotron emission by a factor .
3 Theory of pulsar wind nebulae
To date pulsar wind nebulae have been detected, mostly at X-ray and TeV energies [Kargaltsev2013]. The pulsar wind evolves inside of the supernova remnant of its progenitor star. Its time evolution is therefore complex, and depends on the properties of the progenitor and the environment in which it exploded. A review on pulsar wind nebulae evolution can be found in \citeasnounGaensler2006. In the following, we will focus on only on young systems ( years), which have not yet been significantly disrupted by the reverse shock of their supernova remnant, or the proper motion of their pulsar. The Crab is the best studied of such systems.
In the common models of young pulsar wind nebula electrons and positrons are created in the magnetic fields of the pulsar and transported into the nebula. The electron density through most of the system is thereby expected to be large enough that magnetohydrodynamical conditions apply in good approximation. The pulsar wind is expected to carry most of the rotational energy lost by the pulsar into the nebula [Rees1974]. The wind is flowing radiationless until its momentum flux is balanced by the ambient nebula pressure at a termination surface. At this surface, particles are randomized and begin to loose energy, predominantly through synchrotron radiation. Following these ideas the Crab can be subdivided in three regions shown in Fig. 5: (i) The pulsar and its magnetosphere which extends out to the light cylinder radius cm (ii) The cold pulsar wind which is though to extend out to the inner ring. In the plane perpendicular to the symmetry axis of the nebula the latter is located at cm (iii) The synchrotron nebula, which extends from the inner ring into the outer nebula. We will discuss each of these regions in the following.
3.1 The pulsar magnetosphere
A pulsar can be seen in first order as a rotating, perfectly conducting sphere, with a dipole magnetic field. The magnetic moment is generally not aligned with the rotational axis (the so called “oblique rotator”). Compression of the magnetic field of the progenitor star onto a neutron star of km diameter results in magnetic fields of the order of G at the equatorial surface of the neutron star. The rotation of this field induces an electric potential of the order of V between the poles and the equator of the star. After obtaining vacuum solutions of the oblique rotator [Deutsch1955], it was realized that such strong potentials would remove particles from the neutron star surface and fill the magnetosphere with plasma. The magnetosphere becomes charge separated to compensate the electric potential [Goldreich1969]. This makes the calculation of the magnetosphere properties, as magnetic field structure and electric densities and currents, intrinsically non linear, and dependent on the microphysics of the neutron star surface and the magnetospheric plasma. We therefore still do not have a fully self-consistent description of the magnetosphere of pulsars.
Over the past decade however, there have been significant progress in our understanding of the magnetosphere using the force free electrodynamics (FFE) approximation. The FFE approximation can be derived from magnetohydrodynamics (MHD) in the limit of inertia-free plasma, where the transport of energy and momentum is purely electromagnetical [Komissarov2002, Blandford2002]. As in MHD, plasma is abundant and electric fields parallel to the magnetic fields are shortened out (). There is no particle acceleration or resistivity. This approach is supported by the fact that modeling of pulsar wind nebulae suggest that electrons are injected at high rates from the magnetosphere into the nebula , where s is the “Goldreich-Julian” current [Bucciantini2011]. Charge densities in the magnetosphere are therefore expected to significantly higher than the densities needed to compensate the electric potential due to pair creation within the magnetosphere (see \citeasnounArons2012 and references therein). Further supporting the FFE approximation is that only of the spin-down energy of pulsars is typically radiated in the form of pulsed emission, suggesting a low resistivity within the magnetosphere. Several simulations of magnetospheres in the FFE approximation have been made over the last years [Spitkovsky2006, Kalapotharakos2009, Bai2010]. The charge density and magnetic field structure in the plane of the angular moementum and magnetic moment vectors are shown in Fig. 6. The charge separation of the magnetosphere is apparent. A current sheet emerges in the equatorial plane, at the boundary between closed and open field lines333Field lines which return to the pulsar within the light cylinder are usually referred to as “closed”, others as “open”. and crosses the light cylinder.
The FFE approximation cannot be exact, as there must be some resistivity in the magnetosphere. The latter depends on the properties of the co-rotating plasma, and has not been derived from first principles to date. However, ad-hoc introduction of resistivity into FFE and MHD simulations have been performed over the last years [Li2012, Kalapotharakos2012a, Kalapotharakos2012b, Tchekhovskoy2013]. The basic magnetosphere properties, as e.g. the presence of the equatorial current sheet, are in agreement with the FFE approach. It was shown by \citeasnounLi2012 that the total spin-down luminosity and the potential drop over the open field lines transitions smoothly between the FFE approximation and the vacuum solution with increasing resistivity. The real magnetosphere of pulsars is therefore likely somewhere in between these two descriptions.
Neither MHD nor FFE simulations address the microphysics of the acceleration of particles within the magnetosphere. As currents flow out of the light cylinder on the open field lines, charge starved regions can emerge behind them (so called “gaps”). An electric potential drop can build up in these regions until it is discharged by electron pair cascades and particles are accelerated. A polar gap is thought to emerge up to a distance of cm above the magnetic poles [Sturrock1971, Ruderman1975, Holloway1975, Daugherty1982, Baring2004]. Gaps location have also been proposed out in the magnetosphere, along the last open field lines (slot gap [Arons1979, Muslimov2004]; annular gap [Qiao2004, Du2012]), reaching out to the light cylinder (outer gap [Cheng1976, Cheng1986, Romani1995, Cheng2004]). Alternatively, particles might also be accelerated in reconnecting magnetic fields at the equatorial current sheet [Li2012, Tchekhovskoy2013]. In either case, the particles loose their energy after leaving the acceleration region due to interaction with the magnetic and photon fields of the magnetosphere, and secondary particle cascades might be induced. As the direction of the particles is bound closely to the magnetic field lines, co-rotating cones of light are emitted around both magnetic poles. As one or both of them pass our line of sight, the observed electromagnetic pulsations are produced.
3.2 The cold pulsar wind
It was shown at the early days of pulsar studies, that the magnetic field lines become asymptotically radial beyond the light cylinder in the FFE approximation [Ingraham1973, Michel1974]. This justified studying the fields and flows outside of the light cylinder in the “split-monopole” approximation, where the field lines from the pulsar are thought to be a monopole which inverses its field direction at the equator. An analytic solution to the obliquely rotating split-monopole was found by \citeasnounBogovalov1999. Generally, plasma that flows outside of the magnetosphere on the open field lines begins to trail the pulsar rotation, creating a helical pattern. A current sheet emerges which undulates within an angle around the equatorial plane (the so called “striped wind”). The magnetic field lines become predominantly toroidal, and reverse their direction at the current sheet (see Fig. 5). Qualitative agreement with the split-monopole solutions has recently been found in FFE and MHD simulations out to a distance of [Kalapotharakos2012, Tchekhovskoy2013].
The Poynting flux per solid angle of the split monopole solution scales as , where is the angle with respect to the rotation axis of the pulsar. As most of the energy is emitted around the equatorial plane, the striped wind plays an important role in the dynamics of the nebula. The wind is thought to be magnetically dominated at its launch, with , where is the ratio of the magnetic to the kinetic energy of the flow. However, as we will discuss in the next section a low-sigma flow of was inferred at the termination of the wind from 1D MHD modeling of the synchrotron nebula. The emerging question how magnetic energy is transferred to particle energy in the flow is referred to as the “-problem”. In principle, at low latitudes the alternating magnetic fields of the striped wind make it susceptible to magnetic reconnection due to instabilities in the current flow [Coroniti1990]. However, it was realized that due to the relativistic motion of the wind, the time scales of these processes are likely too long [Lyubarsky2001, Kirk2003]. Recently, a new paradigm is emerging were magnetic energy is thought to be dissipated predominantly after the wind termination, as we will discuss in the next section.
3.3 The synchrotron nebula
As the cold pulsar wind can not be observed before it termination, its properties can only be inferred indirectly by observing the synchrotron nebula. Spherical symmetric MHD solution downstream of the termination surface were derived by \citeasnounKennel1984, predicting the magnetic field distribution in the nebula. The key parameter of this model is the magnetization of the wind just before its termination. In particular the distance of the termination surface from the pulsar in the Crab could only be reproduced if the magnetization at this point is low . The magnetic field strength is then expected to increase behind the shock and have values between 100-300 G in the synchrotron nebula [DeJager1992, AtoyanA.M.1996, Hillas1998, Meyer2010, Martin2012, Torres2013]. This field is lower than the one expected in the case of equipartition between particle energy and magnetic fields, indicating that of the internal energy in the nebula is in magnetic form [Hillas1998]. Similar magnetic field values are inferred by interpreting the hardening of the integrated spectrum of the nebula between the radio and the optical band due to electron cooling [Marsden1984].
It is typically assume that particles are re-accelerated at the wind termination surface. However, it is unlikely that diffusive shock acceleration of particles takes place, as the emerging shock is expected to be relativistic and oblique [Sironi2011]. Instead, the turbulence downstream of the shock might trigger magnetic reconnection, which can lead to non-thermal particle acceleration [Lyubarsky2003]. Particle in cell (PIC) simulations show that, independent of the wind magnetization, the energy of the alternating field components of the striped wind is dissipated into kinetic energy downstream of the wind termination [Sironi2011a]. Assuming that electrons are accelerated into a power-law spectrum at the termination surface one dimensional MHD models reproduces the spectral energy distribution of the nebula qualitatively, with the exception of the radio band [AtoyanA.M.1996, Volpi2008]. As the life time of radio emitting electrons is much longer than the age of the nebula, these particles might have been injected in the past. Radio emission might therefore come from a separate electron population, which could have been injected during the high spin-down phase of the pulsar following the super novae explosion [AtoyanA.M.1996]. Alternatively, radio emitting electrons could be continuously accelerated throughout the nebula due to magnetic reconnection in MHD turbulence [Nodes2004]. Magnetic reconnection downstream of the wind termination can also reproduce the spectrum of radio emitting electrons, if electrons are injected at a rate of into the pulsar wind and the magnetization is high with [Sironi2011a]. The implications of high electron multiplicities therefore deserve further study.
While the one dimensional models of the Crab laid out our general picture, it was clear form the beginning that the asymmetry of the nebula needs to be taken into account for a more quantitative description of the nebula. The dynamics of the flow at and beyond the wind termination have therefore been studied with multidimensional MHD simulations over the past decade [Komissarov2004, Bucciantini2006, Porth2013]. The properties of the pulsar wind at its termination and the particle energy spectrum after the wind termination are free parameters of these simulations. Tracing the maximum particle energy in the flow makes it possible to compute synchrotron, inverse Compton and polarization maps of the nebula, which can be compared to observations [delZanna2006, Volpi2008, Volpi2009]. Axially symmetric models with an appropriately chosen azimuthal dependence of the wind qualitatively reproduce the Crab morphology: a torus emerges, and the flow is bend backwards due to the “hoop-stress” in the downstream, creating a jet (see Fig. 7). They explain the emergence of wisps and their dynamics. Their increased brightness is thought to be predominately due to Doppler beaming towards our line of sight [Camus2009]. The simulations predicted variability of a few percent per year in the overall X-ray emission of the nebula [Volpi2008], which has recently been discovered [Wilson-Hodge2011, Kouzu2013]. This is remarkable in high-energy astrophysics, where predictions and measurements are seldom done on this level of accuracy.
As the early 1D MHD solution, the 2D simulations show that a low-sigma wind with matches the observed morphology, and the location the shock at the observed . Recently, the first 3D simulations were performed [Mizuno2011, Porth2013, Porth2013b]. Interestingly, these simulations show that the morphology of the Crab can also be obtained at high magnetization (). As was pointed out by \citeasnounBegelman1998, 1D and 2D MHD solutions prevent the growth of turbulence due to current instabilities. Due to this turbulence, magnetic fields are randomized and remain predominantly axial only close to the wind termination (see Fig. 7), and pressure and magnetic field gradients in the nebula are reduced when compared to 1D or 2D models. The increased turbulence induces magnetic dissipation in the downstream, alleviating the -problem [Lyutikov2010]. While it might be too early for a final verdict, it appears that the origin of the latter lay in the simplifications made in 1D and 2D models.
The success of the MHD simulations in modeling many of the nebula’s properties shows that the general picture we have outlined is likely a good approximation of reality. However, several observational findings can not be explained or have not been studied yet. A quantitative comparison of the morphology obtained in the simulations to the observed one has not been performed to date. In particular, the inner ring does not seem to be found consistently in the simulations. At odds with the expectation from Doppler boosting, the Chandra observations show that the inner ring has similar brightness at the front and the receding side. We also do not have an explanation why the ring appears to be composed of a series of knots, which are highly variable in time [Weisskopf2000, Porth2013b]. The observation that the wisps at different wavebands are generally not aligned has not been studied in the simulations. If Doppler beaming is predominantly responsible for their enhanced brightness, one would naively expect radio, optical and X-ray wisps to be co-spatial. In addition, 2D MHD simulations with low magnetization overestimate the observed inverse Compton emission [Volpi2008]. It will be interesting to see if this discrepancy is reduced in 3D models of high-magnetization.
4 Pulsed very high-energy gamma-ray emission
After having discussed the observational properties of the Crab and our theoretical understanding of pulsar wind nebulae, we will turn to the recent discoveries and their implications in the following. We begin with the detection of pulsed emission in VHE gamma rays. The emission of pulsars is typically expected to fall close to exponentially above a cutoff energy . This cutoff is thought to be inherent to the emission mechanism, as we will discuss later. Indeed, all spectra of the pulsars detected to date at HE-gamma-rays are compatible with this expectation [Abdo2013]. Surprisingly, a significantly slower spectral decay is observed for the Crab pulsar.
4.1 Observational results
The high-energy end of the SED of the Crab pulsar is shown in Fig. 8. The best fit parametrizations of the Fermi-LAT measurement by a power-law function with an exponential cutoff () and a sub-exponential cutoff () are also displayed. The latter parametrization is preferred statistically at a confidence level, indicating a slower than exponential fall of the spectrum. This is not unusual for LAT detected pulsars [Abdo2013]. However, unexpectedly VHE gamma-ray measurements showed an enhanced emission above an extrapolation of both of these parametrizations [Aliu2008, Aliu2011, Aleksic2011, Aleksic2012] 444Statistically marginal experimental discrepancies can be seen between different measurements in Fig. 8. In particular, the MAGIC mono data have larger fluxes compared to the other measurements. However, within systematic errors these differences are not significant.. Considering systematic errors, the Fermi-LAT and VHE-gamma-ray data can be described by one power-law function above GeV [Aliu2011]. No indication of a spectral cutoff has been found up to photon energies of GeV.
The phase distribution of the VHE gamma-ray events is shown in Fig. 3. The peaks of the gamma-ray pulses coincide with the radio ones. Compared to the HE-gamma-ray pulsations, the VHE ones are narrower. This narrowing of the pulse width with increasing energy can also be seen in the HE and VHE data independently [Abdo2010, Aleksic2012]. Interestingly, a hardening of the spectrum of with respect to is observed in similar form in two components of the SED: the relative flux of increases with respect to from radio to hard X-rays, and from HE gamma-rays to the VHE gamma-rays.
4.2 The origin of the gamma-ray pulsations?
While radio emission from pulsars is usually attributed to coherent emission close to the polar gap, at higher frequencies the emission has to come from outer parts of the atmosphere. In particular the gamma-ray emission is expected to come from distance of [Romani1995, Qiao2004, Muslimov2004]. This is inferred from the phasograms and spectra of the population of gamma-ray detected pulsars [Abdo2013]. For the Crab pulsar, this expectation is confirmed in a model-independent way by the detection of emission beyond GeV. To avoid absorption of gamma rays due to pair production on the pulsars magnetic fields, the photons have to be emitted at a distance cm from the neutron star, a factor above the expected location of the polar gap (Eq. 1 in \citeasnounBaring2004).
The emission mechanism at the high-energy end of the SED of pulsars is expected to be dominated by curvature radiation of particles streaming along magnetic field lines. However, the high energy of the pulsations makes this unlikely for the Crab. Radiative losses due to curvature radiation would produce a cutoff in the spectrum above gamma-ray energies of GeV , where is the accelerating electric field [Aliu2011]. The latter is typically assumed to be in pulsar gaps. The absence of a cutoff in the spectrum up to energies GeV therefore implies . As particles stream along magnetic field lines only within the light cylinder, curvature radiation is likely not responsible for the VHE pulsations.
It was proposed by \citeasnounLyutikov2012 that the emission at the high-energy end of the SED is dominated by Inverse Compton scattering. Indeed, the pulsed emission can be explained by up-scattering of photons in particle cascades induced by outer gaps [Aleksic2011, Aleksic2012] or annular gaps [Du2012]. Alternatively, Inverse Compton emission can also occur in the striped wind [Bogovalov2000, Kirk2002]. As proposed by \citeasnounAharonian2012 and \citeasnounPetri2012, the VHE emission may result from the up-scatter of pulsed X-ray photons. If this is the case, the VHE observations are the first direct observational signature of the cold pulsar wind. In order to fit the observed pulse profile and spectrum of the VHE emission, the wind needs to be abruptly accelerated at . However, while the gamma-ray emission can be explained in this picture, the observed narrowing of the VHE pulses with increasing energy would not be expected.
5 Gamma-ray flux variations from the nebula
Flux variability on short time scales from structures within the Crab has been known for almost 100 years [Lampland1921]. However, the flux integrated over the volume of the nebula is varying only slowly over time: evidence for per year variations have been found in radio, optical and X-ray wavelength [Vinyaikin2007, Smith2003, Wilson-Hodge2011]. As this is small compared to the systematic errors of most high energy telescopes, the Crab was often used to cross-calibrate instruments, particularly in the X-ray and TeV domains. Stronger variability was generally expected to be found at the high end of the synchrotron component ( MeV), as this emission is expected to be emitted by particles with PeV energies in a mG magnetic field. The cooling time scales of these particles is year, and indeed indications for variability of over two years were found in this frequency range [Much1995, deJager1996]. Nevertheless, it came as a huge surprise when the Fermi-LAT and AGILE satellites detected strong gamma-ray flares, with increases of the unpulsed flux by a factor above 100 MeV on time scales down to hours [Abdo2011, Tavani2011, Balbo2011, Ackermann2013]. We will discuss the observational results on the HE gamma-ray variability of the nebula in the following and summarize the theoretical conclusions drawn so far afterwards.
5.1 Observational results
The gamma-ray flares are observed in the energy range between the synchrotron and inverse Compton component of the spectral energy distribution. The average photon flux of the synchrotron component is cm s and the one of the inverse Compton component is cm s above 100 MeV. For comparison, photon flux of the pulsar above this energy is cm s. The emission of the inverse Compton component of the nebula and the pulsar flux are found to be constant in time within measurement accuracies. However, in the synchrotron nebula is variable on all time scales which can be resolved. The power density spectrum as a function of frequency of the flux variations is compatible with a power-law [Buehler2012]. The flux can remain below the detection threshold of the Fermi-LAT for a month, with flux upper limits well below the average flux value [Abdo2010]. On the other hand, the flux can rapidly increase within a few hours during flares. Whether or not the flares are distinct events or the high-energy end of a continuous spectrum in variability is unclear. Time scales down to hours can be resolved in the PDS with no sign of a break in the spectrum. However, the flares are far outlayers in the flux distribution and the spectrum during the brightest flares clearly shows the emergence of a new spectral component in the SED.
As of September 2013, six flares have been reported [Buehler2012, Ojha2012, Striani2013, Mayer2013]. Due to the statistical nature of the flux variations, the definition of a flare is somewhat arbitrary. In all flares reported to date the synchrotron component of the nebula had a peak flux cm s. Equally, the definition of a flare duration is not straight forward; typically, the flux is increased with respect to the monthly average flux for week. The SED around the peak of the flares is shown in Fig. 9. One can see that the spectral behavior differs strongly between flares. During the flare in February 2009, e.g. the flux increased with no measurable spectral changes with respect to the average nebula flux, while during the flare in April 2011 a new spectrum component with a rising flux was observed. Generally, all spectra show significant emission up to GeV.
The flare of April 2011 gave us the most detailed look into the flare phenomenon to date [Striani2011, Buehler2012]. The light curve of this flare is shown in Fig 10. Its high flux allowed flux measurements down to time scales of minutes. The flux doubled within hours at the rising edges of the two main bursts during the flare. The spectral evolution is shown in Fig. 11. Interestingly, the apparently complex evolution can be parametrized in a simple way: the emerging spectral component is well characterized by a power-law spectrum with an exponential cutoff. The spectral index remains constant within errors during the flare, whereas the cutoff energy and the total energy flux of the synchrotron component above 100 MeV vary as . At the maximum of the flare, the cutoff energy is MeV and the total isotropic luminosity in the synchrotron component is erg s, approximately 1% of the spin-down power of the pulsar.
The angular resolution of current HE instruments is arc minutes, not enough to determine the emission region of the flares within the nebula. From the beginning, it was clear that in order to pinpoint the emission region, correlated variability at radio, optical or X-rays is needed, making use of the arc second angular resolution achieved in these wavebands. However, to date, despite extensive efforts a detection of the flares outside of the HE gamma-ray band remains elusive. Strictly simultaneous observations were obtained during the September 2010, April 2011 and March 2013 flares [Vittorini2011, Morii2011, Lobanov2011, Weisskopf2013, Aliu2014]. Particularly dense observations with the Chandra and Hubble Space Telescopes and the Keck and VLA Observatories were carried out during the April 2011 flare. No increased emission was detected from radio to X-rays for any structure of the nebula above the usual levels. This finding was very unexpected. The inferred flux upper limits show that the SED of the HE gamma-ray flare steeply drops with decreasing frequency, as was already suggested by the hard spectral index of the flaring component in HE gamma-rays during the flare.
No pulsations are found in the gamma-ray emission of the flares. The pulsar properties remain unchanged during the outbursts, no change in the spin-down period or flux were found in radio, X-rays or gamma-rays [Abdo2011, Morii2011, Buehler2012]. The time scale of the recurrence of pulsar glitches is similar to the recurrence of the gamma-ray flares, however, there is no obvious correlation in time between these two events.
5.2 The origin of the gamma-ray flares?
To date, the Crab flares remain mysterious. We do not know what causes them and where they come from within the nebula. Several ideas have been proposed, but no definite answers can be given today. Any explanation will have to encompass all the presented observations, so far theoretical models have addressed different aspects of the problem. The rapid variability implies that, unless there is ultrarelativistic beaming, the flare emission comes from a small region within the nebula pc, small even when compared to nebula sub-structures as the Sprite, wisps or the inner knot with projected scales greater pc.
A puzzling observation is that flare emission is detected up to photon energies of GeV. Synchrotron emission appears to be the only radiation process which is efficient enough to account for the flare emission in the nebula environment [Abdo2011]. However, particles accelerated in MHD flows can only emit synchrotron emission up to a maximum energy MeV [Guilbert1983, Uzdensky2011]. Therefore, either MHD conditions are not valid in the flaring region, or the emission is relativistically boosted towards our line of sight 555Another alternative is that the flare emission is “jitter radiation”, which could e.g. be emitted in the striped wind if the length scale of magnetic turbulence is much smaller than the distance between stripes [Teraki2013]. Both scenarios are possibly interrelated: a breakdown of the MHD conditions occurs in magnetic reconnection events and beaming of particles naturally occurs in the reconnection layer [Zweibel2009, Uzdensky2011, Cerutti2012, Sturrock2012].
That magnetic reconnection process is responsible for the particle acceleration is also indicated by the fact that the proposed alternatives have severe difficulties: diffusive shock acceleration generally does not produce electron spectra which are hard enough to explain the emission during the April 2011 flare and is expected to be inefficient at the termination of the pulsar wind [Ellison2004, Sironi2011, Sironi2013], and the proposed acceleration due to absorption of ion cyclotron waves is expected to act on longer time scales [Amato2006]. Magnetic reconnection was studied with PIC simulation in the context of the flares by \citeasnounCerutti2013 and \citeasnounBaty2013. Cerutti et al. show that emission beyond is possible in such events. The variations in motion of the accelerated particle beams can explain the observed flux variations with a PDS compatible with the measured one. The spectrum of the April 2011 flare can be qualitatively reproduced, including its dynamical evolution and the observed correlation between cutoff energy and luminosity. The gamma-ray flares are therefore likely connected to explosive reconnection events triggered by current instabilities.
Regions with increased magnetic dissipation are the preferred emission sites, as e.g. downstream of the wind termination, near the inner ring [Bednarek2011, Lyutikov2012, Bykov2012]. In particular, at high latitudes the flow is expected to remain relativistic in the downstream and can be beamed into our line of sight. This produces increased emission from the so called “arch shock” of the wind termination, which was associated to the inner knot [Komissarov2011]. Another possibility is that the flares originate from the base of the jet. As pointed out by \citeasnounLyubarsky2012, turbulence and increased magnetic dissipation are expected in this region, which might be associated to the Sprite. However, no observational signatures related to the flares have been found for any of these regions to date.
The location of the emission region might in principle be different between flares. A distribution of flares throughout the nebula has been proposed, where the beamed gamma-ray emission from different regions randomly crosses our line of sight [Yuan2011, Clausen-Brown2012]. Such a process can produce PDS of flux variations compatible with the observed one, linking the flare phenomenon to the flux variations on longer time scales. The flares might therefore be responsible for a significant part of the magnetic dissipation in the nebula [Komissarov2012].
A review of the observations and theory of the Crab is bound to be outdated as it is written. New insights are gained continuously and building up on a long history of research. Nevertheless, key questions for our understanding remain unanswered. In particular, the structure of the magnetosphere, and related to it, the launch of the pulsar wind, remain to be understood in a quantitative way. The observed pulse profiles are sensitive probes of the magnetic field structure and of the sites particle acceleration in the magnetosphere [Bai2010a]. Pulsar emission models can be compared to a wealth of observational data, including phase profiles, spectra and polarization measurements of the pulsar population. The latter is continuously growing, in particular through the ongoing observations of the Fermi-LAT. At the same time, emission models can take advantage of the increasingly more realistic simulations of pulsar magnetospheres.
Such a broad modeling approach is currently being pursued by several groups, and bears large potential to increase our understanding of pulsars [Bai2010, Romani2010, Harding2011, Kalapotharakos2012]. The VHE gamma-ray pulsations of the Crab are a new constraint which needs to be addressed within this context. Experimentally, it remains to be seen whether VHE emission is typical for pulsars or only found in the Crab [Collaboration2013a]. Searches by current VHE instruments for pulsations from other pulsars are ongoing. The future Cherenkov Telescope Array (CTA) will allow to perform these searches at higher sensitivities [Hinton2013].
The understanding of the Crab synchrotron nebula has significantly increased with the help of MHD simulations in the last years. Quantitative comparisons of observations to these simulations can constrain the magnetization and angular dependence of the pulsar wind. First three dimensional simulations show that significant magnetic dissipation is expected to happen downstream of the wind termination [Porth2013]. The gamma-ray flares are an exciting discovery in this context, likely giving us a direct view into magnetic dissipation regions.
It is puzzling that flares have not been detected from any other pulsar wind nebula besides the Crab. The search of flares from other nebulae is ongoing in the HE-gamma-ray band [Ackermann2013]. Giving the unusually large magnetization of the Crab nebula, flare might be found at lower frequencies in other systems. In this case, all-sky X-ray instruments as MAXI are best suited to search for flares from other nebulae [Matsuoka2009]. The HE gamma-ray flares from the Crab have been recurring approximately once per year. Dense multi-waveband coverage in the radio, optical, X-ray and VHE gamma-ray bands was achieved during the last flare in March 2013 [Mayer2013]. The analysis of these observations is still ongoing and might already reveal correlated signatures to the HE-gamma-ray variability. Monitoring programs are already put in place for future flares. The continuous multi-wavelength coverage will enable more sensitive correlation studies and hopefully pinpoint the emission site in the coming years. Also, the detection of an inverse Compton component of the flares at VHE gamma-rays might be possible with CTA in the future, if the emission region is ultra-relativistically beamed towards our line of sight (Lorentz factor , \citeasnounKohri2012).
In a broader context, several phenomena observed in the Crab are ubiquitous in the non-thermal Universe. A better understanding of the Crab, and pulsar wind nebulae in general, is therefore interweaved with our understanding of other sources as active galaxies, microquasars, gamma-ray bursts or novae. The release of magnetic energy by a compact object, and the transfer of this energy into the acceleration of particles is common in these systems. Formation of jets is also ubiquitous in non-thermal sources. This process can be studied in detail in the synchrotron nebula of the Crab. As e.g., the study of the dynamics and formation of the wisps, the jet formation in the Crab allows us to study the behavior of relativistic magnetized plasma and the instabilities that govern its flow [Mignone2013]. The remainders of the “guest star” observed almost one thousand years ago will continue to be our companion in these endeavors.
\harvarditemAbdo et al.2011Abdo2011
Abdo et al. 2011 Science (New York, N.Y.)
\harvardurlhttp://adsabs.harvard.edu/abs/2011Sci…331..739A \harvarditemAbdo et al.2010Abdo2010 Abdo et al. 2010 The Astrophysical Journal 708(2), 1254–1267.
\harvardurlhttp://adsabs.harvard.edu/abs/2010ApJ…708.1254A \harvarditemAbdo et al.2013Abdo2013 Abdo et al. 2013 The Astrophysical Journal Supplement Series 208(2), 17.
\harvardurlhttp://adsabs.harvard.edu/abs/2013ApJS..208…17A \harvarditemAcharya et al.2013Hinton2013 Acharya et al. 2013 Astroparticle Physics 43, 3–18.
\harvardurlhttp://www.sciencedirect.com/science/article/pii/S0927650513000169 \harvarditemAckermann et al.2013Ackermann2013 Ackermann et al. 2013 The Astrophysical Journal 771(1), 57.
\harvardurlhttp://iopscience.iop.org/0004-637X/771/1/57/article/ \harvarditemAharonian et al.2012Aharonian2012 Aharonian et al. 2012 Nature 482(7386), 507–9.
\harvardurlhttp://adsabs.harvard.edu/abs/2012Natur.482..507A \harvarditemAleksic et al.2012Aleksic2012 Aleksic et al. 2012 Astronomy & Astrophysics 540, A69.
\harvardurlhttp://www.aanda.org/10.1051/0004-6361/201118166 \harvarditemAleksic et al.2011Aleksic2011 Aleksic et al. 2011 The Astrophysical Journal 742(1), 43.
\harvardurlhttp://adsabs.harvard.edu/abs/2011ApJ…742…43A \harvarditemAliu et al.2008Aliu2008 Aliu et al. 2008 Science (New York, N.Y.) 322(5905), 1221–4.
\harvardurlhttp://adsabs.harvard.edu/abs/2008Sci…322.1221A \harvarditemAliu et al.2012Aliu2012 Aliu et al. 2012 The Astrophysical Journal 760(2), 136.
\harvardurlhttp://adsabs.harvard.edu/abs/2012ApJ…760..136A \harvarditemAliu et al.2014Aliu2014 Aliu et al. 2014 The Astrophysical Journal 781(1), L11.
\harvardurlhttp://adsabs.harvard.edu/abs/2014ApJ…781L..11A \harvarditemAliu et al.2011Aliu2011 Aliu et al. 2011 Science (New York, N.Y.) 334(6052), 69–72.
\harvardurlhttp://adsabs.harvard.edu/abs/2011Sci…334…69V \harvarditemAmato \harvardand Arons2006Amato2006 Amato \harvardand Arons 2006 The Astrophysical Journal 653(1), 325–338.
\harvardurlhttp://adsabs.harvard.edu/abs/2006ApJ…653..325A \harvarditemArendt et al.2011Arendt2011 Arendt et al. 2011 The Astrophysical Journal 734(1), 54.
\harvardurlhttp://adsabs.harvard.edu/abs/2011ApJ…734…54A \harvarditemArons2012Arons2012 Arons 2012 Space Science Reviews 173(1-4), 341–367.
\harvardurlhttp://adsabs.harvard.edu/abs/2012SSRv..173..341A \harvarditemArons \harvardand Scharlemann1979Arons1979 Arons \harvardand Scharlemann 1979 The Astrophysical Journal 231, 854.
\harvardurlhttp://adsabs.harvard.edu/abs/1979ApJ…231..854A \harvarditemAtoyan \harvardand Aharonian1996AtoyanA.M.1996 Atoyan \harvardand Aharonian 1996 Monthly Notices of the Royal Astronomical Society 278(2), 525–541.
\harvardurlhttp://adsabs.harvard.edu/abs/1996MNRAS.278..525A \harvarditemAumont et al.2010Aumont2010 Aumont et al. 2010 Astronomy and Astrophysics 514, A70.
\harvardurlhttp://adsabs.harvard.edu/abs/2010A&A…514A..70A \harvarditemBaade \harvardand Zwicky1934Baade1934 Baade \harvardand Zwicky 1934 Physical Review 46(1), 76–77.
\harvardurlhttp://adsabs.harvard.edu/abs/1934PhRv…46…76B \harvarditemBai \harvardand Spitkovsky2010aBai2010 Bai \harvardand Spitkovsky 2010a The Astrophysical Journal 715(2), 1282–1301.
\harvardurlhttp://iopscience.iop.org/0004-637X/715/2/1282/fulltext/ \harvarditemBai \harvardand Spitkovsky2010bBai2010a Bai \harvardand Spitkovsky 2010b The Astrophysical Journal 715(2), 1270–1281.
\harvardurlhttp://iopscience.iop.org/0004-637X/715/2/1270/fulltext/ \harvarditemBalbo et al.2011Balbo2011 Balbo et al. 2011 Astronomy & Astrophysics 527, L4.
\harvardurlhttp://adsabs.harvard.edu/abs/2011A&A…527L…4B \harvarditemBaring2004Baring2004 Baring 2004 Advances in Space Research 33(4), 552–560.
\harvardurlhttp://adsabs.harvard.edu/abs/2004AdSpR..33..552B \harvarditemBaty et al.2013Baty2013 Baty et al. 2013 Monthly Notices of the Royal Astronomical Society 436(1).
\harvardurlhttp://adsabs.harvard.edu/abs/2013arXiv1308.0906B \harvarditemBednarek \harvardand Idec2011Bednarek2011 Bednarek \harvardand Idec 2011 Monthly Notices of the Royal Astronomical Society 414(3), 2229–2234.
\harvardurlhttp://adsabs.harvard.edu/abs/2011MNRAS.414.2229B \harvarditemBegelman1998Begelman1998 Begelman 1998 The Astrophysical Journal 493(1), 291–300.
\harvardurlhttp://iopscience.iop.org/0004-637X/493/1/291/fulltext/ \harvarditemBietenholz et al.2001Bietenholz2001 Bietenholz et al. 2001 The Astrophysical Journal 560(1), 254–260.
\harvardurlhttp://iopscience.iop.org/0004-637X/560/1/254/fulltext/ \harvarditemBietenholz et al.2004Bietenholz2004 Bietenholz et al. 2004 The Astrophysical Journal 615(2), 794–804.
\harvardurlhttp://adsabs.harvard.edu/abs/2004ApJ…615..794B \harvarditemBietenholz et al.1991Bietenholz1991 Bietenholz et al. 1991 The Astrophysical Journal 373, L59.
\harvardurlhttp://adsabs.harvard.edu/abs/1991ApJ…373L..59B \harvarditemBilous et al.2011Bilous2011 Bilous et al. 2011 The Astrophysical Journal 728(2), 110.
\harvardurlhttp://adsabs.harvard.edu/abs/2011ApJ…728..110B \harvarditemBilous et al.2012Bilous2012 Bilous et al. 2012 The Astrophysical Journal 749(1), 24.
\harvardurlhttp://adsabs.harvard.edu/abs/2012ApJ…749…24B \harvarditemBlandford2002Blandford2002 Blandford 2002 Lighthouses of the Universe: The Most Luminous Celestial Objects and Their Use for Cosmology ESO ASTROPHYSICS SYMPOSIA
\harvardurlhttp://adsabs.harvard.edu/abs/2002luml.conf..381B \harvarditemBogovalov1999Bogovalov1999 Bogovalov 1999 Astronomy and Astrophysics 349, 1017.
\harvardurlhttp://adsabs.harvard.edu/abs/1999A&A…349.1017B \harvarditemBogovalov \harvardand Aharonian2000Bogovalov2000 Bogovalov \harvardand Aharonian 2000 Monthly Notices of the Royal Astronomical Society 313(3), 504–514.
\harvardurlhttp://adsabs.harvard.edu/abs/2000MNRAS.313..504B \harvarditemBreen \harvardand McCarthy1995Breen1995 Breen \harvardand McCarthy 1995 Vistas in Astronomy 39(3), 363–379.
\harvardurlhttp://dx.doi.org/10.1016/0083-6656(95)96619-S \harvarditemBucciantini et al.2011Bucciantini2011 Bucciantini et al. 2011 Monthly Notices of the Royal Astronomical Society 410(1), 381–398.
\harvardurlhttp://adsabs.harvard.edu/abs/2011MNRAS.410..381B \harvarditemBucciantini et al.2006Bucciantini2006 Bucciantini et al. 2006 Monthly Notices of the Royal Astronomical Society 368(4), 1717–1734.
\harvardurlhttp://adsabs.harvard.edu/abs/2006MNRAS.368.1717B \harvarditemBuehler et al.2012Buehler2012 Buehler et al. 2012 The Astrophysical Journal 749(1), 26.
\harvardurlhttp://iopscience.iop.org/0004-637X/749/1/26/ \harvarditemBykov et al.2012Bykov2012 Bykov et al. 2012 Monthly Notices of the Royal Astronomical Society: Letters 421(1), L67–L71.
\harvardurlhttp://adsabs.harvard.edu/abs/2012MNRAS.421L..67B \harvarditemCamus et al.2009Camus2009 Camus et al. 2009 Monthly Notices of the Royal Astronomical Society 400(3), 1241–1246.
\harvardurlhttp://adsabs.harvard.edu/abs/2009MNRAS.400.1241C \harvarditemCerutti et al.2012Cerutti2012 Cerutti et al. 2012 The Astrophysical Journal 746(2), 148.
\harvardurlhttp://adsabs.harvard.edu/abs/2012ApJ…746..148C \harvarditemCerutti et al.2013Cerutti2013 Cerutti et al. 2013 eprint 1302.6247.
\harvardurlhttp://adsabs.harvard.edu/abs/2013arXiv1302.6247C \harvarditemCheng et al.1976Cheng1976 Cheng et al. 1976 The Astrophysical Journal 203, 209.
\harvardurlhttp://adsabs.harvard.edu/abs/1976ApJ…203..209C \harvarditemCheng2004Cheng2004 Cheng 2004 Advances in Space Research 33(4), 561–570.
\harvardurlhttp://adsabs.harvard.edu/abs/2004AdSpR..33..561C \harvarditemCheng et al.1986Cheng1986 Cheng et al. 1986 The Astrophysical Journal 300, 500.
\harvardurlhttp://adsabs.harvard.edu/abs/1986ApJ…300..500C \harvarditemClausen-Brown \harvardand Lyutikov2012Clausen-Brown2012 Clausen-Brown \harvardand Lyutikov 2012 Monthly Notices of the Royal Astronomical Society 426(2), 1374.
\harvardurlhttp://adsabs.harvard.edu/abs/2012arXiv1205.5094C \harvarditemCocke et al.1969Cocke1969 Cocke et al. 1969 Nature 221(5180), 525–527.
\harvardurlhttp://adsabs.harvard.edu/abs/1969Natur.221..525C \harvarditemCollaboration2013Collaboration2013a Collaboration 2013 eprint 1306.6772.
\harvardurlhttp://adsabs.harvard.edu/abs/2013arXiv1306.6772T \harvarditemCordes et al.2004Cordes2004 Cordes et al. 2004 The Astrophysical Journal 612(1), 375–388.
\harvardurlhttp://adsabs.harvard.edu/abs/2004ApJ…612..375C \harvarditemCoroniti1990Coroniti1990 Coroniti 1990 The Astrophysical Journal 349, 538.
\harvardurlhttp://adsabs.harvard.edu/abs/1990ApJ…349..538C \harvarditemDaugherty \harvardand Harding1982Daugherty1982 Daugherty \harvardand Harding 1982 The Astrophysical Journal 252, 337.
\harvardurlhttp://adsabs.harvard.edu/abs/1982ApJ…252..337D \harvarditemde Jager \harvardand Harding1992DeJager1992 de Jager \harvardand Harding 1992 The Astrophysical Journal 396, 161.
\harvardurlhttp://adsabs.harvard.edu/abs/1992ApJ…396..161D \harvarditemde Jager et al.1996deJager1996 de Jager et al. 1996 The Astrophysical Journal 457, 253.
\harvardurlhttp://adsabs.harvard.edu/abs/1996ApJ…457..253D \harvarditemDean et al.2008Dean2008 Dean et al. 2008 Science (New York, N.Y.) 321(5893), 1183–5.
\harvardurlhttp://adsabs.harvard.edu/abs/2008Sci…321.1183D \harvarditemDel Zanna et al.2006delZanna2006 Del Zanna et al. 2006 Astronomy and Astrophysics 453(2), 621–633.
\harvardurlhttp://dx.doi.org/10.1051/0004-6361:20064858 \harvarditemDeutsch1955Deutsch1955 Deutsch 1955 Annales d’Astrophysique 18(1).
\harvardurlhttp://adsabs.harvard.edu/abs/1955AnAp…18….1D \harvarditemDu et al.2012Du2012 Du et al. 2012 The Astrophysical Journal 748(2), 84.
\harvardurlhttp://adsabs.harvard.edu/abs/2012ApJ…748…84D \harvarditemEllison \harvardand Double2004Ellison2004 Ellison \harvardand Double 2004 Astroparticle Physics 22(3-4), 323–338.
\harvardurlhttp://adsabs.harvard.edu/abs/2004APh….22..323E \harvarditemEspinoza et al.2011Espinoza2011 Espinoza et al. 2011 The Astronomer’s Telegram 3777.
\harvardurlhttp://adsabs.harvard.edu/abs/2011ATel.3777….1E \harvarditemForot et al.2008Forot2008 Forot et al. 2008 The Astrophysical Journal 688(1), L29–L32.
\harvardurlhttp://adsabs.harvard.edu/abs/2008ApJ…688L..29F \harvarditemGaensler \harvardand Slane2006Gaensler2006 Gaensler \harvardand Slane 2006 Annual Review of Astronomy and Astrophysics 44(1), 17–47.
\harvardurlhttp://adsabs.harvard.edu/abs/2006ARA&A..44…17G \harvarditemGallant \harvardand Arons1994Gallant1994 Gallant \harvardand Arons 1994 The Astrophysical Journal 435, 230.
\harvardurlhttp://adsabs.harvard.edu/abs/1994ApJ…435..230G \harvarditemGold1968Gold1968 Gold 1968 Nature 218(5143), 731–732.
\harvardurlhttp://adsabs.harvard.edu/abs/1968Natur.218..731G \harvarditemGoldreich \harvardand Julian1969Goldreich1969 Goldreich \harvardand Julian 1969 The Astrophysical Journal 157, 869.
\harvardurlhttp://adsabs.harvard.edu/abs/1969ApJ…157..869G \harvarditemGreen et al.2004Green2004a Green et al. 2004 Monthly Notices of the Royal Astronomical Society 355(4), 1315–1326.
\harvardurlhttp://adsabs.harvard.edu/abs/2004MNRAS.355.1315G \harvarditemGuilbert et al.1983Guilbert1983 Guilbert et al. 1983 Monthly Notices of the Royal Astronomical Society (ISSN 0035-8711) 205, 593–603.
\harvardurlhttp://adsabs.harvard.edu/abs/1983MNRAS.205..593G \harvarditemHarding2013Harding2013a Harding 2013 Frontiers of Physics 8(6), 679.
\harvardurlhttp://adsabs.harvard.edu/abs/2013arXiv1302.0869H \harvarditemHarding et al.2011Harding2011 Harding et al. 2011 eprint 1111.0828.
\harvardurlhttp://adsabs.harvard.edu/abs/2011arXiv1111.0828H \harvarditemHarding et al.2008Harding2008 Harding et al. 2008 The Astrophysical Journal 680(2), 1378–1393.
\harvardurlhttp://adsabs.harvard.edu/abs/2008ApJ…680.1378H \harvarditemHester2013Hester Hester 2013 webpage .
\harvardurlhttp://chandra.harvard.edu/photo/2002/0052/more.html \harvarditemHester2008Hester2008 Hester 2008 Annual Review of Astronomy and Astrophysics 46(1), 127–155.
\harvardurlhttp://adsabs.harvard.edu/abs/2008ARA&A..46..127H \harvarditemHester et al.2002Hester2002 Hester et al. 2002 The Astrophysical Journal 577(1), L49–L52.
\harvardurlhttp://adsabs.harvard.edu/abs/2002ApJ…577L..49H \harvarditemHester et al.1995Hester1995 Hester et al. 1995 The Astrophysical Journal 448, 240.
\harvardurlhttp://adsabs.harvard.edu/abs/1995ApJ…448..240H \harvarditemHillas et al.1998Hillas1998 Hillas et al. 1998 The Astrophysical Journal 503(2), 744–759.
\harvardurlhttp://iopscience.iop.org/0004-637X/503/2/744/fulltext/ \harvarditemHolloway1975Holloway1975 Holloway 1975 Monthly Notices of the Royal Astronomical Society 171, 619–635.
\harvardurlhttp://adsabs.harvard.edu/abs/1975MNRAS.171..619H \harvarditemHubble1928Hubble1928 Hubble 1928 Astronomical Society of the Pacific Leaflets 1(14), 55.
\harvardurlhttp://adsabs.harvard.edu/abs/1928ASPL….1…55H \harvarditemIngraham1973Ingraham1973 Ingraham 1973 The Astrophysical Journal 186, 625.
\harvardurlhttp://adsabs.harvard.edu/abs/1973ApJ…186..625I \harvarditemKalapotharakos \harvardand Contopoulos2009Kalapotharakos2009 Kalapotharakos \harvardand Contopoulos 2009 Astronomy and Astrophysics 496(2), 495–502.
\harvardurlhttp://adsabs.harvard.edu/abs/2009A&A…496..495K \harvarditemKalapotharakos et al.2012Kalapotharakos2012 Kalapotharakos et al. 2012 Monthly Notices of the Royal Astronomical Society 420(4), 2793–2798.
\harvardurlhttp://mnras.oxfordjournals.org/content/420/4/2793 \harvarditemKalapotharakos et al.2012bKalapotharakos2012a Kalapotharakos et al. 2012b The Astrophysical Journal 754(1), L1.
\harvardurlhttp://adsabs.harvard.edu/abs/2012ApJ…754L…1K \harvarditemKalapotharakos et al.2012cKalapotharakos2012b Kalapotharakos et al. 2012c The Astrophysical Journal 749(1), 2.
\harvardurlhttp://adsabs.harvard.edu/abs/2012ApJ…749….2K \harvarditemKargaltsev et al.2013Kargaltsev2013 Kargaltsev et al. 2013 eprint 1305.2552.
\harvardurlhttp://adsabs.harvard.edu/abs/2013arXiv1305.2552K \harvarditemKennel \harvardand Coroniti1984Kennel1984 Kennel \harvardand Coroniti 1984 The Astrophysical Journal 283, 694.
\harvardurlhttp://adsabs.harvard.edu/abs/1984ApJ…283..694K \harvarditemKirk \harvardand Lyubarsky2009Kirk2009 Kirk \harvardand Lyubarsky 2009 in ‘Neutron Stars and Pulsars’ Vol. 357 Springer Berlin Heidelberg pp. 421–450. \harvarditemKirk \harvardand Skjaraasen2003Kirk2003 Kirk \harvardand Skjaraasen 2003 The Astrophysical Journal 591(1), 366–379.
\harvardurlhttp://adsabs.harvard.edu/abs/2003ApJ…591..366K \harvarditemKirk et al.2002Kirk2002 Kirk et al. 2002 Astronomy and Astrophysics 388(2), L29–L32.
\harvardurlhttp://adsabs.harvard.edu/abs/2002A&A…388L..29K \harvarditemKohri et al.2012Kohri2012 Kohri et al. 2012 Monthly Notices of the Royal Astronomical Society 424(3), 2249–2254.
\harvardurlhttp://adsabs.harvard.edu/abs/2012MNRAS.424.2249K \harvarditemKomissarov2002Komissarov2002 Komissarov 2002 Monthly Notices of the Royal Astronomical Society 336(3), 759–766.
\harvardurlhttp://adsabs.harvard.edu/abs/2002MNRAS.336..759K \harvarditemKomissarov2012Komissarov2012 Komissarov 2012 Monthly Notices of the Royal Astronomical Society 428(3), 2459–2466.
\harvardurlhttp://adsabs.harvard.edu/abs/2013MNRAS.428.2459K \harvarditemKomissarov \harvardand Lyubarsky2004Komissarov2004 Komissarov \harvardand Lyubarsky 2004 Monthly Notices of the Royal Astronomical Society 349(3), 779–792.
\harvardurlhttp://mnras.oxfordjournals.org/content/349/3/779 \harvarditemKomissarov \harvardand Lyutikov2011Komissarov2011 Komissarov \harvardand Lyutikov 2011 Monthly Notices of the Royal Astronomical Society 414(3), 2017–2028.
\harvardurlhttp://adsabs.harvard.edu/abs/2011MNRAS.414.2017K \harvarditemKouzu et al.2013Kouzu2013 Kouzu et al. 2013 Publications of the Astronomical Society of Japan 65(4), 74.
\harvardurlhttp://adsabs.harvard.edu/abs/2013arXiv1303.7109K \harvarditemKuiper et al.2001Kuiper2001 Kuiper et al. 2001 Astronomy and Astrophysics 378(3), 918–935.
\harvardurlhttp://adsabs.harvard.edu/abs/2001A&A…378..918K \harvarditemLampland1921Lampland1921 Lampland 1921 Publications of the Astronomical Society of the Pacific 33, 79.
\harvardurlhttp://adsabs.harvard.edu/abs/1921PASP…33…79L \harvarditemLi et al.2012Li2012 Li et al. 2012 The Astrophysical Journal 746(1), 60.
\harvardurlhttp://iopscience.iop.org/0004-637X/746/1/60/fulltext/ \harvarditemLobanov et al.2011Lobanov2011 Lobanov et al. 2011 Astronomy & Astrophysics 533, A10.
\harvardurlhttp://adsabs.harvard.edu/abs/2011A&A…533A..10L \harvarditemLundgren et al.1995Lundgren1995 Lundgren et al. 1995 The Astrophysical Journal 453, 433.
\harvardurlhttp://adsabs.harvard.edu/abs/1995ApJ…453..433L \harvarditemLyne et al.1993LyneA.G.1993 Lyne et al. 1993 Monthly Notices of the Royal Astronomical Society 265.
\harvardurlhttp://adsabs.harvard.edu/abs/1993MNRAS.265.1003L \harvarditemLyubarsky2003Lyubarsky2003 Lyubarsky 2003 Monthly Notices of the Royal Astronomical Society 345(1), 153–160.
\harvardurlhttp://adsabs.harvard.edu/abs/2003MNRAS.345..153L \harvarditemLyubarsky2012Lyubarsky2012 Lyubarsky 2012 Monthly Notices of the Royal Astronomical Society 427(2), 1497–1502.
\harvardurlhttp://mnras.oxfordjournals.org/content/427/2/1497 \harvarditemLyubarsky \harvardand Kirk2001Lyubarsky2001 Lyubarsky \harvardand Kirk 2001 The Astrophysical Journal 547(1), 437–448.
\harvardurlhttp://adsabs.harvard.edu/abs/2001ApJ…547..437L \harvarditemLyutikov2010Lyutikov2010 Lyutikov 2010 Monthly Notices of the Royal Astronomical Society 405(3), 1809.
\harvardurlhttp://adsabs.harvard.edu/abs/2010MNRAS.405.1809L \harvarditemLyutikov et al.2012Lyutikov2012 Lyutikov et al. 2012 Monthly Notices of the Royal Astronomical Society 422(4), 3118–3129.
\harvardurlhttp://adsabs.harvard.edu/abs/2012MNRAS.422.3118L \harvarditemManchester et al.2005Manchester2005 Manchester et al. 2005 The Astronomical Journal 129(4), 1993–2006.
\harvardurlhttp://adsabs.harvard.edu/abs/2005AJ….129.1993M \harvarditemMarsden et al.1984Marsden1984 Marsden et al. 1984 The Astrophysical Journal 278, L29.
\harvardurlhttp://adsabs.harvard.edu/abs/1984ApJ…278L..29M \harvarditemMartin et al.2012Martin2012 Martin et al. 2012 Monthly Notices of the Royal Astronomical Society 427(1), 415–427.
\harvardurlhttp://adsabs.harvard.edu/abs/2012MNRAS.427..415M \harvarditemMatsuoka et al.2009Matsuoka2009 Matsuoka et al. 2009 Publications of the Astronomical Society of Japan 61(5), 999.
\harvardurlhttp://adsabs.harvard.edu/abs/2009PASJ…61..999M \harvarditemMayer et al.2013Mayer2013 Mayer et al. 2013 The Astrophysical Journal 775(2), L37.
\harvardurlhttp://iopscience.iop.org/2041-8205/775/2/L37/article/ \harvarditemMelatos et al.2005Melatos2005 Melatos et al. 2005 The Astrophysical Journal 633(2), 931–940.
\harvardurlhttp://adsabs.harvard.edu/abs/2005ApJ…633..931M \harvarditemMeyer et al.2010Meyer2010 Meyer et al. 2010 Astronomy & Astrophysics 523, A2.
\harvardurlhttp://adsabs.harvard.edu/abs/2010A&A…523A…2M \harvarditemMichel1974Michel1974 Michel 1974 Astrophysical Journal 187, 585–588.
\harvardurlhttp://adsabs.harvard.edu/abs/1974ApJ…187..585M \harvarditemMignone et al.2013Mignone2013 Mignone et al. 2013 Monthly Notices of the Royal Astronomical Society 436(2), 1102.
\harvardurlhttp://adsabs.harvard.edu/abs/2013MNRAS.436.1102M \harvarditemMizuno et al.2011Mizuno2011 Mizuno et al. 2011 The Astrophysical Journal 728(2), 90.
\harvardurlhttp://iopscience.iop.org/0004-637X/728/2/90/fulltext/ \harvarditemMoffett et al.1999Moffett1999 Moffett et al. 1999 The Astrophysical Journal 522(2), 1046.
\harvardurlhttp://adsabs.harvard.edu/abs/1999ApJ…522.1046M \harvarditemMoran et al.2013Moran2013 Moran et al. 2013 Monthly Notices of the Royal Astronomical Society 433(3), 2564–2575.
\harvardurlhttp://adsabs.harvard.edu/abs/2013MNRAS.433.2564M \harvarditemMori et al.2004Mori2004a Mori et al. 2004 The Astrophysical Journal 609(1), 186–193.
\harvardurlhttp://iopscience.iop.org/0004-637X/609/1/186/fulltext/ \harvarditemMorii et al.2011Morii2011 Morii et al. 2011 Journal of Physics: Conference Series 302(1), 012062.
\harvardurlhttp://adsabs.harvard.edu/abs/2011JPhCS.302a2062M \harvarditemMuch et al.1995Much1995 Much et al. 1995 Astronomy and Astrophysics 299, 435.
\harvardurlhttp://adsabs.harvard.edu/abs/1995A&A…299..435M \harvarditemMuslimov \harvardand Harding2004Muslimov2004 Muslimov \harvardand Harding 2004 The Astrophysical Journal 606(2), 1143–1153.
\harvardurlhttp://adsabs.harvard.edu/abs/2004ApJ…606.1143M \harvarditemNg \harvardand Romani2004Ng2004 Ng \harvardand Romani 2004 The Astrophysical Journal 601(1), 479–484.
\harvardurlhttp://adsabs.harvard.edu/abs/2004ApJ…601..479N \harvarditemNodes et al.2004Nodes2004 Nodes et al. 2004 Astronomy and Astrophysics 423(1), 13–19.
\harvardurlhttp://adsabs.harvard.edu/abs/2004A&A…423…13N \harvarditemOjha et al.2012Ojha2012 Ojha et al. 2012 The Astronomer’s Telegram 4239.
\harvardurlhttp://adsabs.harvard.edu/abs/2012ATel.4239….1O \harvarditemOosterbroek et al.2008Oosterbroek2008 Oosterbroek et al. 2008 Astronomy and Astrophysics 488(1), 271–277.
\harvardurlhttp://adsabs.harvard.edu/abs/2008A&A…488..271O \harvarditemPacini1967PACINI1967 Pacini 1967 Nature 216(5115), 567–568.
\harvardurlhttp://adsabs.harvard.edu/abs/1967Natur.216..567P \harvarditemPeng-Yoke et al.1972Peng-Yoke1972 Peng-Yoke et al. 1972 Vistas in Astronomy 13(null), 1–13.
\harvardurlhttp://dx.doi.org/10.1016/0083-6656(72)90002-5 \harvarditemPetri2012Petri2012 Petri 2012 Monthly Notices of the Royal Astronomical Society 424(3), 2023–2027.
\harvardurlhttp://mnras.oxfordjournals.org/cgi/doi/10.1111/j.1365-2966.2012.21350.x \harvarditemPopov \harvardand Stappers2007Popov2007 Popov \harvardand Stappers 2007 Astronomy and Astrophysics 470(3), 1003–1007.
\harvardurlhttp://adsabs.harvard.edu/abs/2007A&A…470.1003P \harvarditemPorth et al.2013aPorth2013 Porth et al. 2013a Monthly Notices of the Royal Astronomical Society: Letters 431, L48–L52.
\harvardurlhttp://adsabs.harvard.edu/abs/2013MNRAS.431L..48P \harvarditemPorth et al.2013bPorth2013b Porth et al. 2013b Monthly Notices of the Royal Astronomical Society 438(1), 278–306.
\harvardurlhttp://adsabs.harvard.edu/abs/2014MNRAS.438..278P \harvarditemQiao et al.2004Qiao2004 Qiao et al. 2004 The Astrophysical Journal 606(1), L49–L52.
\harvardurlhttp://adsabs.harvard.edu/abs/2004ApJ…606L..49Q \harvarditemRees \harvardand Gunn1974Rees1974 Rees \harvardand Gunn 1974 Monthly Notices of the Royal Astronomical Society 167, 1–12.
\harvardurlhttp://adsabs.harvard.edu/abs/1974MNRAS.167….1R \harvarditemRickett \harvardand Lyne1990Rickett1990 Rickett \harvardand Lyne 1990 Monthly Notices of the Royal Astronomical Society (ISSN 0035-8711) 244, 68–75.
\harvardurlhttp://adsabs.harvard.edu/abs/1990MNRAS.244…68R \harvarditemRomani \harvardand Watters2010Romani2010 Romani \harvardand Watters 2010 The Astrophysical Journal 714(1), 810–824.
\harvardurlhttp://adsabs.harvard.edu/abs/2010ApJ…714..810R \harvarditemRomani \harvardand Yadigaroglu1995Romani1995 Romani \harvardand Yadigaroglu 1995 The Astrophysical Journal 438, 314.
\harvardurlhttp://adsabs.harvard.edu/abs/1995ApJ…438..314R \harvarditemRowan \harvardand Coontz2004Rowan2004 Rowan \harvardand Coontz 2004 Science 304(5670), 531.
\harvardurlhttp://www.sciencemag.org/content/304/5670/531.short \harvarditemRuderman \harvardand Sutherland1975Ruderman1975 Ruderman \harvardand Sutherland 1975 The Astrophysical Journal 196, 51.
\harvardurlhttp://adsabs.harvard.edu/abs/1975ApJ…196…51R \harvarditemScargle1969Scargle1969 Scargle 1969 The Astrophysical Journal 156, 401.
\harvardurlhttp://adsabs.harvard.edu/abs/1969ApJ…156..401S \harvarditemSchweizer et al.2013SchweizerThomas2013 Schweizer et al. 2013 Monthly Notices of the Royal Astronomical Society 433(4), 3325.
\harvardurlhttp://adsabs.harvard.edu/abs/2013arXiv1301.1321S \harvarditemShearer et al.2003Shearer2003 Shearer et al. 2003 Science (New York, N.Y.) 301(5632), 493–5.
\harvardurlhttp://adsabs.harvard.edu/abs/2003Sci…301..493S \harvarditemShklovsky1953Shklovsky1953 Shklovsky 1953 Doklady Akademii Nauk SSSR 90, 983. \harvarditemSironi \harvardand Spitkovsky2011aSironi2011a Sironi \harvardand Spitkovsky 2011a The Astrophysical Journal 741(1), 39.
\harvardurlhttp://adsabs.harvard.edu/abs/2011ApJ…741…39S \harvarditemSironi \harvardand Spitkovsky2011bSironi2011 Sironi \harvardand Spitkovsky 2011b The Astrophysical Journal 726(2), 75.
\harvardurlhttp://adsabs.harvard.edu/abs/2011ApJ…726…75S \harvarditemSironi et al.2013Sironi2013 Sironi et al. 2013 The Astrophysical Journal 771(1), 54.
\harvardurlhttp://iopscience.iop.org/0004-637X/771/1/54/article/ \harvarditemSlowikowska et al.2009Sowikowska2009 Slowikowska et al. 2009 Monthly Notices of the Royal Astronomical Society 397(1), 103–123.
\harvardurlhttp://adsabs.harvard.edu/abs/2009MNRAS.397..103S \harvarditemSmith2003Smith2003 Smith 2003 Monthly Notices of the Royal Astronomical Society 346(3), 885–889.
\harvardurlhttp://adsabs.harvard.edu/abs/2003MNRAS.346..885S \harvarditemSollerman et al.2000Sollerman2000 Sollerman et al. 2000 The Astrophysical Journal 537(2), 861–874.
\harvardurlhttp://adsabs.harvard.edu/abs/2000ApJ…537..861S \harvarditemSpitkovsky2006Spitkovsky2006 Spitkovsky 2006 The Astrophysical Journal 648(1), L51–L54.
\harvardurlhttp://adsabs.harvard.edu/abs/2006ApJ…648L..51S \harvarditemStrader et al.2013Strader2013 Strader et al. 2013 The Astrophysical Journal Letters 779(1), L12.
\harvardurlhttp://adsabs.harvard.edu/abs/2013arXiv1309.3270S \harvarditemStriani et al.2011Striani2011 Striani et al. 2011 The Astrophysical Journal 741(1), L5.
\harvardurlhttp://adsabs.harvard.edu/abs/2011ApJ…741L…5S \harvarditemStriani et al.2013Striani2013 Striani et al. 2013 The Astrophysical Journal 765(1), 52.
\harvardurlhttp://adsabs.harvard.edu/abs/2013ApJ…765…52S \harvarditemSturrock1971Sturrock1971 Sturrock 1971 The Astrophysical Journal 164, 529.
\harvardurlhttp://adsabs.harvard.edu/abs/1971ApJ…164..529S \harvarditemSturrock \harvardand Aschwanden2012Sturrock2012 Sturrock \harvardand Aschwanden 2012 The Astrophysical Journal 751(2), L32.
\harvardurlhttp://adsabs.harvard.edu/abs/2012ApJ…751L..32S \harvarditemTavani et al.2011Tavani2011 Tavani et al. 2011 Science (New York, N.Y.) 331(6018), 736–9.
\harvardurlhttp://adsabs.harvard.edu/abs/2011Sci…331..736T \harvarditemTchekhovskoy et al.2013Tchekhovskoy2013 Tchekhovskoy et al. 2013 Monthly Notices of the Royal Astronomical Society: Letters 435, L1–L5.
\harvardurlhttp://adsabs.harvard.edu/abs/2013MNRAS.435L…1T \harvarditemTemim et al.2006Temim2006 Temim et al. 2006 The Astronomical Journal 132(4), 1610–1623.
\harvardurlhttp://adsabs.harvard.edu/abs/2006AJ….132.1610T \harvarditemTeraki \harvardand Takahara2013Teraki2013 Teraki \harvardand Takahara 2013 The Astrophysical Journal 763(2), 131.
\harvardurlhttp://adsabs.harvard.edu/abs/2013ApJ…763..131T \harvarditemThompson et al.1999Thompson1999 Thompson et al. 1999 The Astrophysical Journal 516(1), 297–306.
\harvardurlhttp://adsabs.harvard.edu/abs/1999ApJ…516..297T \harvarditemTorres et al.2013Torres2013 Torres et al. 2013 Monthly Notices of the Royal Astronomical Society 436(4), 3112.
\harvardurlhttp://adsabs.harvard.edu/abs/2013arXiv1309.5291T \harvarditemTrimble1973Trimble1973 Trimble 1973 Publications of the Astronomical Society of the Pacific 85, 579.
\harvardurlhttp://adsabs.harvard.edu/abs/1973PASP…85..579T \harvarditemTziamtzis et al.2009Tziamtzis2009 Tziamtzis et al. 2009 Astronomy and Astrophysics 508(1), 221–228.
\harvardurlhttp://dx.doi.org/10.1051/0004-6361/200912031 \harvarditemUzdensky et al.2011Uzdensky2011 Uzdensky et al. 2011 The Astrophysical Journal 737(2), L40.
\harvardurlhttp://adsabs.harvard.edu/abs/2011ApJ…737L..40U \harvarditemVeron-Cetty \harvardand Woltjer1993Veron-Cetty1993 Veron-Cetty \harvardand Woltjer 1993 Astronomy and Astrophysics (ISSN 0004-6361) 270, 370–378.
\harvardurlhttp://adsabs.harvard.edu/abs/1993A&A…270..370V \harvarditemVinyaikin2007Vinyaikin2007 Vinyaikin 2007 Astronomy Reports 51(7), 570–576.
\harvardurlhttp://adsabs.harvard.edu/abs/2007ARep…51..570V \harvarditemVittorini et al.2011Vittorini2011 Vittorini et al. 2011 The Astrophysical Journal 732(2), L22.
\harvardurlhttp://adsabs.harvard.edu/abs/2011ApJ…732L..22V \harvarditemVolpi et al.2008Volpi2008 Volpi et al. 2008 Astronomy and Astrophysics 485(2), 337–349.
\harvardurlhttp://adsabs.harvard.edu/abs/2008A&A…485..337V \harvarditemVolpi et al.2009Volpi2009 Volpi et al. 2009 eprint 0903.4120.
\harvardurlhttp://adsabs.harvard.edu/abs/2009arXiv0903.4120V \harvarditemWang et al.2012Wang2012 Wang et al. 2012 Astrophysics and Space Science 340(2), 307–315.
\harvardurlhttp://adsabs.harvard.edu/abs/2012Ap&SS.340..307W \harvarditemWeisskopf et al.2000Weisskopf2000 Weisskopf et al. 2000 The Astrophysical Journal 536(2), L81–L84.
\harvardurlhttp://adsabs.harvard.edu/abs/2000ApJ…536L..81W \harvarditemWeisskopf et al.2013Weisskopf2013 Weisskopf et al. 2013 The Astrophysical Journal 765(1), 56.
\harvardurlhttp://iopscience.iop.org/0004-637X/765/1/56/article/ \harvarditemWeisskopf et al.1978Weisskopf1978 Weisskopf et al. 1978 The Astrophysical Journal 220, L117.
\harvardurlhttp://adsabs.harvard.edu/abs/1978ApJ…220L.117W \harvarditemWillingale et al.2001Willingale2001 Willingale et al. 2001 Astronomy and Astrophysics 365(1), L212–L217.
\harvardurlhttp://adsabs.harvard.edu/abs/2001A&A…365L.212W \harvarditemWilson-Hodge et al.2011Wilson-Hodge2011 Wilson-Hodge et al. 2011 The Astrophysical Journal 727(2), L40.
\harvardurlhttp://adsabs.harvard.edu/abs/2011ApJ…727L..40W \harvarditemWilson1974Wilson1974 Wilson 1974 Monthly Notices of the Royal Astronomical Society 166, 617–632.
\harvardurlhttp://adsabs.harvard.edu/abs/1974MNRAS.166..617W \harvarditemYuan et al.2011Yuan2011 Yuan et al. 2011 The Astrophysical Journal 730(2), L15.
\harvardurlhttp://adsabs.harvard.edu/abs/2011ApJ…730L..15Y \harvarditemZweibel \harvardand Yamada2009Zweibel2009 Zweibel \harvardand Yamada 2009 Annual Review of Astronomy and Astrophysics 47(1), 291–332.