Neutron stars serve as useful laboratories to study physics under conditions of extreme density, gravity, and magnetic fields. Magnetars represent a topical subclass of the neutron star family. The known magnetars 1 of our galaxy possess the longest spin periods among all isolated neutron stars, yet with large spin down rates. These temporal properties imply that they are young, with an average spin down age of a few thousand years, possess the highest magnetic fields in the Universe, with polar surface values of B p ∼ 10 13 -10 15 G, and exhibit weak spin-down power compared to their more numerous "cousins," the canonical rotationally-powered pulsars.
Magnetars spend much of their time in a quiescent state, where they are observed as persistent quasi-thermal hot X-ray emitters with kT ∼ 0.5 keV. Tellingly, their luminosities exceed their spindown power by as much as three orders of magnitude. Accordingly, magnetars cannot be powered by spin energy loss, but instead extract their power from the immense reservoir of magnetic energy, 10 46 -10 48 erg. They occasionally enter burst active episodes where they emit a few to hundreds of short (∼ 0.1 s), bright bursts in the 5-500 keV band with L γ ∼ 10 37 -10 42 erg s -1 . Following the onset of such bursting activity, magnetars enter an excited X-ray state where their quiescent flux increases by factors ranging from a few to 1000 times the quiescent flux 2;3 , phases named "magnetar outbursts". These phenomena are usually accompanied by strong spectral and temporal variations, e.g., hotter effective temperature, glitch and anti-glitch events, strong timing noise, and pulse profile evolution 4;5;6;7;8;9;10;11;12 . The outbursts may persist for months to years, during which the magnetar spectral and temporal properties recover to their pre-outburst behavior 2;13 .
Despite the relatively low number of magnetars (23 confirmed, 6 candidates), they possess an enormous topicality, as evidenced by the shear number of dedicated reviews in the last 10 years 14;15;16;17;18;19 . Moreover, magnetars have been invoked to explain some of the extreme phenomena in the Universe, such as super-luminous supernovae 20;21 , gamma-ray bursts 22;23 (GRBs), ultra-luminous X-ray sources 24;25;26;27 (ULXs), and the mysterious Fast Radio Bursts 28;29;30;31;32 (FRBs). In short, these fascinating objects remain at the forefront of astrophysics curiosity for the foreseeable future.
The last two decades have been the golden age for nascent magnetar science. Swift-BAT and Fermi-GBM have enabled the discovery of a large number of magnetars through the detection and localization of short magnetar-like bursts 33;34 , Swift-XRT and RXTE-PCA have permitted the detailed study of their temporal and spectral changes during outbursts 35;36 , and last but not least Chandra and XMM-Newton have deciphered the quasi-thermal nature of their persistent soft (0.5 -10 keV) X-ray emission in quiescence and during outbursts.
A remarkable discovery was reported in 2004 37 of a new persistent spectral component in 1E 1841-045 with RXTE HEXTE between 10 -150 keV, 100% pulsed at the highest energies. Similar detections followed for 1RXS J170849.0-400910, 4U 0142+61, and 1E 2259+586 using HEXTE and INTEGRAL IBIS ISGRI 38;39;40 . The higher sensitivity of NuSTAR enabled the detection of these hard X-ray tails in fainter magnetars; currently there are 7 magnetars that exhibit persistent hard tails during quiescence, and another 6 during outburst 3 . These hard X-ray tails exhibit spectra consistent with power laws (PL) of photon index Γ ≈ 1.0, demanding drastic spectral changes at ∼ 10 keV. Moreover, they dominate the energetics, with fluxes exceeding that of the soft components, often by factors of 10 or more. These hard power laws do not exhibit a break below 100 -200 keV, and in a few cases, INTEGRAL, CGRO-COMPTEL and Fermi-LAT upper limits at energies 300 -1000 keV imply that a break must exist in this soft γ-ray energy band.
Our understanding of magnetar energetics is incomplete. Given these upper limits, only a sensitive soft γ-ray observatory would ultimately uncover the peak energy of the magnetar spectral energy distributions, thereby determining their total persistent energy budget in quiescence and in outburst. Moreover, these observations would result in key observable parameters, such as the exact shape and energy of the high-energy cutoff and its variations with rotational phase. Equipped with polarization capabilities, such an observatory would also reveal the polarization degree and position angle signatures of the hard X-ray emission from magnetars. These key observables depend critically on the photon and particle interactions in one of the most extreme environments in the Universe, and may result in the first discovery of exotic quantum electrodynamic (QED) physics long thought to be operating in proximity of not only magnetars but also pulsars.
Figure 1: In RICS, surface photons of energy kT ∼ 0.5 keV are upscattered by relativistic electrons which follow field lines. The observer samples a small portion of the magnetosphere owing to the kinematics of RICS. For misaligned magnetic μ and spin Ω axes, pulsations are observed.
The nonthermal nature of the persistent hard X-ray tails suggests that they are powered by a relativistic electron/positron population. Current models are still in their infancy but steadily developing. In contrast to normal pulsars, the persistent emission likely arises in the "closed" zone of the magnetosphere where particle acceleration proceeds in a magnetosphere that departs from ideal force-free magnetohydrodynamics. A quasi-equilibrium is established where particle acceleration, pair production and radiative losses are in counterbalance 41;42 .
At low altitudes where emission likely originates, resonant inverse Compton scattering (RICS) of the soft thermal surface photons is the dominant radiative process for electrons that is germane to the generation of hard X-ray tails 43;44;45;46;47;48;49;50 . The scattering cross section is greatly enhanced at the cyclotron fundamental, where the incoming photon energy is equal to the gyroenergy ω B in the electron rest frame. For the magnetar context, it is crucial to recognize that fields are in the QED domain where ω B ∼ m e c 2 ; this defines the critical field m 2 e c 3 /( q e ) ≡ B cr ≈ 4.413 × 10 13 G. Rapid cyclotron cooling restricts electrons to move parallel to the field (see Fig 1). Strong Doppler beaming anisotropy and flux (and photon energy) boosting then result from RICS, which is imprinted on light curves, and traces the field geometry (electron motion) and locales of the particles acceleration and cooling. RICS produces a relatively flat spectrum, with high linear polarization degree, which cuts off at a kinematically determined energy 50 .
Magnetar magnetospheres are also opaque for hard X-rays and γ rays. The measured spectral cutoffs may also be produced by attenuation of photons principally due to magnetic photon splitting (γ + B → γγ ) and pair production (γ + B → e + e -). These exotic QED propagation effects 51;52;53 which are as yet untested terrestrially, imprint telltale polarimetric signatures on magnetar spectra and pulsations that can be probed with updated telescope technology.
Extant models of the type discussed here provide an array of possible spectral and polarization predictions that serve as a toolkit for probing both geometry and physics of magnetars. Accordingly, an array of important advances to our understanding of these topical objects can be delivered with the deployment of a mission with Compton detection technology that has both improved continuum sensitivity and polarimetric capability above 100 keV. These deliverables include
• employing variations of spectra and polarization with pulse phase to constrain the locale for hard X-ray tail emission -Doppler boosting varies substantially for different sites of scattering. • phase-resolved spectroscopy to constrain the array of possible angles α between the rotational and magnetic axes of a magnetar. This can be determined for a variety of magnetars, and trends of α with magnetar age can be explored. Refinement of B p estimation then becomes possible. • fundamental QED physics can be probed by ascertaining whether photon splitting and/or pair creation impose upper limits to the emission energies. Polarimetry enhances this diagnostic.
(⊥-∥)/(⊥+∥)
(⊥-∥)/(⊥+∥)
Figure 2: Spin-phase resolved model RICS spectra of a generic magnetar (at arbitrary normalization) overlaid on phase-averaged data for 4U 0412+61 along with a PL with exponential cutoff at 350 keV in dotted green. The RICS emission is anticipated to be highly polarized and spinphase dependent. The model emission is computed for surface photons of temperature 5 × 10 6 K scattered by γ e = 10 -10 1.5 electrons uniformly populating field bundle from magnetic footpoint colatitudes 12 -45 • for B p = 10B cr . Left: Instantaneous observer impact angle (for a particular spin phase) of θ v = 30 • with respect to the magnetic axis μ; Right: θ v = 90 • . Bottom panels: Signed polarization degree, highlighting the spectropolarimetric signatures of resonant Compton scattering attenuated by magnetic photon splitting (PS) and/or magnetic pair production (PP).
• exploring activation of magnetar magnetospheres following burst-active episodes relative to long-term relaxed conditions, thereby informing magnetar energetics and wind properties.
Enabling these insights advances our understanding of magnetars and their relationship to other neutron star varieties. Yet the science reach extends to GRBs, ULXs and FRBs, each with possible magnetar connections.
2 Details: State-of-the-Art Magnetar Models & Pertinent QED Processes Soft X ray photon densities and magnetic field strengths are high at low altitudes, and so there the dominant energy loss mechanism for electrons is RICS, which may be regarded as cyclotron absorption followed by spontaneous re-emission, preserving the electron in the ground Landau state.
In the Thomson limit, the maximum upscattered photon energy (in units of m e c 2 ) is γ e (B/B cr ) ∼ γ 2 e s while it is γ e in the Klein-Nishina regime, for electron Lorentz factor γ e , and surface thermal photon energy s m e c 2 ∼ 0.1 -3 keV. The conditions for resonance are always satisfied in a thermal photon bath 47 . In high B B cr fields, a full QED treatment is necessary for cyclotron lifetimes, RICS cross sections and scattering kinematics 50;54;55;56 . As in Thomson scattering, RICS generates distributions of photons with high linear polarization degree. The field direction (and electron momentum distribution) breaks spatial symmetry and acts as an optical axis. The ⊥ (X, extraordinary) and (O, ordinary) mode are defined as the electric field vector or ⊥ to the plane containing the outgoing photon k f and magnetic field B loc vectors, respectively. There is an associated energy-dependent Doppler beaming cone for electrons in the magnetosphere; the highest energy RICS photons are sampled for electrons viewed head-on by an observer, corresponding to lines of sight that are tangent to local field lines. Therefore, different viewing angles with respect to the magnetic axis sample different electron populations and beaming geometry. The upshot is spin modulation, i.e. (polarized) pulsations, if the spin and magnetic moments are misaligned. QED Propagation Effects: Magnetar magnetospheres are opaque to high energy photons, so that above the pair threshold around 1 MeV, pair creation strongly dominates the photon opacity. Dis-persive influences of the magnetized quantum vacuum introduce birefringence, i.e. different refractive indices for the elliptical polarization eigenstates 53 ; dispersion is small for ∼ 1 keV photons. Below pair threshold, photon splitting is the dominant attenuation mechanism in a strong magnetic field; this is a 3 rd order QED process arising from vacuum polarization (virtual pairs) radiating when interacting with the field. The rate of splitting is a strong function of photon energy ∝ 5 B 6 where B is the projection of the local magnetic field B loc onto the direction of the photon momentum. In the weakly dispersive limit, only ⊥-mode photons may split due to kinematic selection rules 57 . However, splitting of both photon polarizations (modes) does not violate charge-parity (CP) symmetry; it is still an open question if both modes may split in the strongly dispersive nonlinear regime of QED. If both polarizations are permitted to split, then the shape of the spectral cutoff ought to follow a super-exponential shape.
In Fig. 2 we depict selected RICS model spectra (Wadiasingh et al., in prep). For comparison, INTEGRAL data and COMPTEL bounds for 4U 0142+61 39 are plotted along with a power law with exponential cutoff at 350 keV in dotted green. Hu et al. (2019, MNRAS submitted) provide a convenient parameterization of photon splitting and pair creation escape energies we use to compute photon-trajectory-dependent opacities in our code for RICS emission in Fig. 2. As is typical of scattering processes, the ⊥ mode dominates for most energies except near the unknown cutoff -see the bottom panels. Without inclusion of QED opacities, the cutoff is kinematically attained and exponential in character; this is illustrated in the brown and cyan polarization-summed curves. In contrast, if the ⊥ mode photon splitting and the mode pair creation attenuates the spectrum, a regime of very high polarization degree is exhibited in the cutoff as depicted in the red curves. Finally, if both ⊥ and modes of splitting operate as represented by the blue curves, then a depolarization effect in the cutoff is apparent, yet with a cutoff that is no longer exponential but super-exponential. Therefore, spectropolarimetric diagnostics of the cutoff regime of magnetars offer a powerful path to probing photon splitting. Also, the sensitivity exhibited in Fig. 2 to θ v indicates that phase-resolved spectropolarimetry will strongly constrain the angle α between the rotational and magnetic axes of individual magnetars (Wadiasingh et al., in prep). There are currently 7 magnetars that exhibit a hard X-ray tail in quiescence out of 8 observed with sensitive hard X-ray instruments such as Suzaku and NuSTAR 3 . These are depicted in Fig. 3. The energy scale covers 3 × 10 -3 -40 MeV, hence partially displays the soft X-ray quasi-thermal model (dashed-lines) and also hard power-law tails (dottedlines). Our knowledge of these spectra extends up to ∼ 100 -200 keV (where it is 100% pulsed) beyond which our observational picture is completely missing. We extrapolated the observed phaseaveraged hard tails of these magnetars and adopted an 0.5 MeV exponential cutoff for all the sources. These mock soft γ-ray spectra are well below the 2σ CGRO-COMPTEL upper-limits for 4U 0142+61 and 1RXS J170849.0-400910 depicted in blue and yellow, respectively. Planned Compton telescope technology furnishes wide-field and polarization capabilities, enabling compelling time-domain and spectropolarimetric studies. The red curve of Fig. 3 denotes the 1-year sensitivity curve to the proposed probe-class mission AMEGO 58 (similar in capabilities to its proposed European kin e-ASTROGAM 59 ) and demonstrates that all seven magnetars are well