Magnetars and Magnetic Energy Release

Magnetars are neutron stars whose persistent emission, bursts, and giant flares are powered substantially by magnetic energy and its rearrangement. A large spin-down-inferred dipole is common but not a definition: the external dipole is model dependent, while strong internal or higher-multipole fields can remain hidden from $P$ and $\dot P$. Connecting an observed fluence to a magnetic failure requires distance, beaming, bandpass, detector response, and a physical model of crustal yielding or magnetospheric reconnection. This page keeps the energy argument separate from that inference.

Required background. Frames, Coframes, and Anholonomy supplies local field strengths, particle energies, and measured fluxes.

Helpful background. Flat-Background Hilbert Stress-Energy from Metric Variation supplies electromagnetic energy and stress; The Einstein Equation supplies redshift and stellar structure; Relativistic Matter and Compact Objects supplies crust, superfluid, and transport physics; Computational Relativity supplies response and uncertainty checks.

The magnetic reservoir

In Gaussian units, a representative field filling a volume of radius $R$ has

$$E_B=\int\frac{B^2}{8\pi}\,dV \sim\frac{B^2R^3}{6}.$$

For $B=10^{15}\,\mathrm G$ and $R=10\,\mathrm{km}$, this scale is $1.7\times10^{47}\,\mathrm{erg}$. Geometry matters: a toroidal interior field, crust-confined field, and global dipole have different volumes and stresses. Only a fraction of the reservoir is free energy, and only a fraction of that emerges in a measured photon band. The scaling establishes plausibility; it does not locate the energy or predict an event rate.

Slow rotation makes another diagnostic. For many magnetars the standard comparison is $L_{\rm sd}=-dE_{\rm rot}/dt=-I\Omega\dot\Omega\lt L_{X,{\rm persistent}}$ for approximately constant $I$: rotational spin-down cannot sustain the persistent X-ray luminosity under the stated moment-of-inertia and torque estimate. Burst and flare energies are instead time-integrated quantities and must be compared separately with the available reservoir. Field decay and stress can supply both heating and bursts. Twisted magnetospheric currents resonantly scatter surface X-rays and can heat the footpoints. Stress accumulation may fracture or plastically deform the crust, or a magnetospheric instability may initiate reconnection. Kaspi and Beloborodov distinguish persistent emission, outbursts, short bursts, and giant flares and review these mechanisms in Kaspi and Beloborodov 2017, §§3.2 and 5.1–5.4.

Event classes are not one standard candle

Short bursts last from milliseconds upward and span broad fluence and spectral ranges. Outbursts raise persistent X-ray luminosity for days to years. Giant flares begin with a hard spike followed by a modulated tail and are rare enough that population rates remain uncertain. For a measured-band fluence $S_{\rm band}$ and distance $d$, $E_{{\rm iso},{\rm band}}=4\pi d^2S_{\rm band}$. A declared spectral model then gives $E_{{\rm iso},{\rm bol}}=C_{\rm bol}E_{{\rm iso},{\rm band}}$; the physical emitted energy has a separate angular-pattern or beaming correction.

Quasi-periodic oscillations in giant-flare tails motivate crustal and global magnetoelastic mode models. Frequency coincidence alone is not a unique mode identification: continuum structure, magnetic geometry, crust elasticity, rotation, window choice, trials, and changing pulse profile affect the result. The strongest inference compares a detector-level time-series likelihood under competing red-noise and oscillatory models, then propagates the surviving frequency posterior through several interior models.

Named catalogues and event data

Evidence cutoff: 2026-08-18. The named source dataset is the McGill Online Magnetar Catalog snapshot v201117, whose main table contains 30 confirmed or candidate objects and whose persistent-data page was last modified 2020-11-17. It is a historical snapshot relative to this page’s evidence cutoff. The classification flags, alternative values, bands, and associations are visible in the McGill Pulsar Group 2020, main table, Tables 2–7, frozen v201117 snapshot. The underlying compilation design and literature-reference policy are given in Olausen and Kaspi 2014, §2 and Tables 1–7. This page has not downloaded or checksummed the snapshot files. A reproducible selection must record the exact filename, access date, and SHA-256 checksum for every retained table.

For a burst or outburst analysis, the catalogue is only a source list. Primary Swift BAT or XRT event data and observation identifiers come from the HEASARC Swift Archive. The archive distinguishes quick-look from archived products and directs users to mission calibration histories in NASA High Energy Astrophysics Science Archive Research Center, “Swift Data Availability” and “Swift Calibration Data Archive,” accessed 18 August 2026. That landing page does not itself designate a versioned event dataset: an analysis must pin the ObsID, event-file checksums, HEASoft version, and exact CALDB components. A published spectrum or catalog flux is a derived product, not a replacement for event data and its response matrix.

Selection, calibration, and likelihood

A persistent-source sample should state whether candidates and transient-only objects are included, the time interval taken to represent quiescence, required band and exposure, and treatment of upper limits. A burst sample needs a trigger algorithm, energy band, significance threshold, good-time intervals, dead-time cuts, occultation and detector-quality selections, and a rule for merging burst episodes. Selecting only events that triggered an instrument misses faint, off-axis, or occulted bursts.

For Swift, freeze observation and trigger identifiers, raw and processed-file checksums, HEASoft version, CALDB snapshot and component files, coded-mask weighting, detector-quality map, gain correction, dead time, pileup treatment, source and background regions, and generated ancillary and response matrices. Cross-instrument work must retain each instrument’s calibration and clock version rather than fitting all counts through one nominal bandpass.

The forward model folds an absorbed atmosphere, blackbody-plus-tail, or burst spectrum through the response. Low-count spectra require a Poisson likelihood with background handled explicitly; Gaussian grouping is a choice that must be justified. Priors on distance, absorption $N_{\rm H}$, emitting area, temperature, spectral shape, beaming, and cross-normalization propagate into luminosity and energy. For a QPO search, the likelihood or periodogram null must include red noise, nonstationarity, windowing, and the searched-frequency trials.

Important systematic alternatives are distance and association, spectral model, dust-scattering halo, absorption, pileup or saturation in bright events, dead time, background, bandpass extrapolation, anisotropy, and calibration drift. The catalog’s inferred $B_{\rm surf}$ also inherits a torque model and should not be used as an independent measured covariate without that dependence.

Reproduction boundary and physical claims

This page does not download the McGill files, query HEASARC, reprocess Swift events, or form a new likelihood. A reproduction package would contain the versioned source tables, exact selection query, ObsID and trigger list, raw-data checksums, software environment, calibration files, event-screening commands, responses, spectral and timing models, priors, posterior samples, and scripts for fluence and trials corrections.

The inference chain should preserve distinct claims. A detected burst shows transient energy release. A magnetic reservoir can energetically accommodate it. A crustal fracture, magnetospheric reconnection, or interior instability is a model for the trigger. A QPO can favor a response family only after its significance and mode degeneracies are controlled. None of these steps alone measures the hidden internal field.

Check your understanding

Use the uniform-field estimate for $B=10^{15}\,\mathrm G$ and $R=10\,\mathrm{km}$. What magnetic energy is available, and what fraction would an isotropic-equivalent $10^{44}\,\mathrm{erg}$ flare represent?

Solution

With $R=10^6\,\mathrm{cm}$,

$$E_B\sim\frac{(10^{15}\,\mathrm G)^2(10^6\,\mathrm{cm})^3}{6} =1.7\times10^{47}\,\mathrm{erg}.$$

The ratio is

$$\frac{10^{44}}{1.7\times10^{47}} \simeq5.9\times10^{-4}.$$

Energetically the event uses less than a thousandth of this representative reservoir. The result is not an efficiency measurement because the real field geometry, free-energy fraction, beaming, distance, and bolometric correction are unspecified.

References

• Kaspi, Victoria M., and Andrei M. Beloborodov. “Magnetars.” Annual Review of Astronomy and Astrophysics 55 (2017): 261–301. arXiv:1703.00068.
• McGill Pulsar Group. “McGill Online Magnetar Catalog.” Snapshot v201117, main table last modified 17 November 2020. Frozen official snapshot.
• NASA High Energy Astrophysics Science Archive Research Center. “Swift Archive.” Archive and calibration access documentation, accessed 18 August 2026. Official archive.
• Olausen, Scott A., and Victoria M. Kaspi. “The McGill Magnetar Catalog.” The Astrophysical Journal Supplement Series 212 (2014): 6. DOI.