Abstract
Two classes of X-ray/gamma-ray sources, the Soft Gamma Repeaters and the Anomalous X-ray Pulsars have been identified with isolated, slowly spinning magnetars, neutron stars whose emission draws energy from their extremely strong magnetic field (∼1015–1016 G). Magnetars are believed to form with millisecond spin period and to represent an important fraction of the whole young neutron star population. Newborn magnetars can convert very quickly their rotational energy into electromagnetic and/or gravitational waves, by virtue of their magnetic field strength and fast spins. This chapter provides a brief summary of astrophysical problems and scenarios in which millisecond magnetars are believed to play a key role: these include Gamma Ray Bursts, Supernovae, Gravitational Wave events and Fast Radio Bursts.
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Notes
- 1.
For the lower limit of this range see [49].
- 2.
For a basic tutorial see http://solomon.as.utexas.edu/magnetar.html.
- 3.
Note that the virial limit of \({\lesssim } 10^{17}\) G holds for NS interior B-fields (e.g. [171]).
- 4.
- 5.
This holds when the magnetic symmetry axis is orthogonal to the rotation axis. In general, when they are misaligned by a tilt angle χ, the rhs of Eq. 8.3 must be multiplied by \(\left (1+ 15 \sin ^2 \chi \right )/16\).
- 6.
They may release magnetic energy as well, though this channel involves a smaller reservoir and there is no simple prescription for the power that can be liberated; this possibility has been discussed in relation to FRBs and the low-luminosity end of the short-GRB population.
- 7.
We note in passing that the two classical magnetars for which a progenitor mass of ∼(30–45) M⊙ has been derived are associated to young open clusters (< 8 Myr) hosting WR stars.
- 8.
During this short time, the enhanced spin down luminosity can be expressed as [137]
$$\displaystyle \begin{aligned} L_{\mathrm{wind}} = L_{\mathrm{EM}} \left(R_L/R_Y\right)^2 \times {\mathrm{max}}\left[\sigma_0^{-/1/3}, 1\right]\, . \end{aligned} $$(8.5)Here R L = c∕ Ω is the light cylinder, R Y ≤ R L the equatorial radius of the closed magnetosphere and \(\sigma _0 = \phi ^2 \Omega ^2/(\dot {M} c^3)\) the magnetization parameter of the wind, where \(\dot {M}\) is the neutrino-driven mass loss from the NS surface and ϕ the magnetic flux threading the NS surface and linked to open B-field lines. In the early stages the closed magnetosphere is small, i.e. a large fraction of the NS magnetic flux is linked to open B-field lines, hence R Y ≪ R L. In addition, the neutrino-driven wind is strongest, carrying a sufficiently large mass outflow to ensure a low magnetization (σ 0 ≪ 1): as a result, L wind ≫ L EM. Later, as the mass loss rate drops, σ 0 grows quickly and the wind approaches a force-free condition (σ 0 →∞) while the closed magnetosphere expands, R Y → R L. Thus L wind → L EM and the classic magneto-dipole spindown kicks in.
- 9.
Secular instabilities arise from the fact that lower-energy states are accessible to the fluid if it can get rid of its excess energy, e.g. via GW-emission or viscosity on timescales ≫ the dynamical time.
- 10.
Indeed, for a constant L = I Ω, the spin energy T = L 2∕2I is minimised by maximising I.
- 11.
At these early times the NS temperature is T ∼ (3–10) × 109 K ([40, 42, 91]), implying the main dissipative term should be bulk viscosity. The latter requires a periodic pressure perturbation in the fluid NS to activate out-of-equilibrium chemical reactions. The precessional motion of the fluid NS provides such a perturbation, the amplitude of which is still debated (e.g. [42, 90, 91]).
- 12.
For this estimate, we adopt a minimum magnetar birth rate of one per 10 CCSNe. .
- 13.
As long as viscosity can be neglected.
- 14.
Λ is the angular frequency of internal motions in the frame co-rotating with the elliptical pattern.
- 15.
Normalized to the spindown power of the Crab pulsar and an acceleration potential φ ∼ 1012 V.
- 16.
Israel et al. [77].
- 17.
NS glitches represent an example of this kind of processes.
- 18.
The same result is obtained using VLA or Green Bank data ([99]).
- 19.
The spectral peak at ν ∼ 10 GHz and the luminosity L ν ∼ 1029 erg s−1 Hz−1 below the peak lead to the conclusion that the energy of the emitting particles peaks at γ e ∼ 102∕B 1∕2, where B (in gauss) is the magnetic field strength in the emitting region, and that \({\mathcal {N}} B \sim 2 \times 10^{50}\) G ([80]). Moreover, the constraint that the particle cooling break \(\nu _c = 10 e m_e c/\left (\sigma ^2_T B^3 t^2\right )\) be > 10 GHz implies \(B < 0.03 \left (t_{\mathrm {age}}/30~{\mathrm {yr}}\right )^{-2/3} (\nu _{c,9}/10)^{-1/3}\) G, from which \({\mathcal {N}} > 7 \times 10^{51} t^{2/3}_9 (\nu _{c, 9}/10)^{1/3}\) is derived. Particles are accelerated at the NS surface to relativistic energies, giving rise to an electrical current i = μ Ω2∕c and leading to copious pair-production in the magnetosphere. Pairs are produced at the rate \(\dot {N}^{\pm } \sim 2 {\mathcal {M}} i/e\), where the multiplicity \({\mathcal {M}}\) is the number of e ± pairs per accelerated particle, and typically \({\mathcal {M}} \lesssim 10^3\) in PWNe. Because LEM ∼ i 2∕c, the NS in FRB121102 should produce pairs with a multiplicity \({\mathcal {M}} \sim 10^7\mbox{--}10^{10}\) in order to inject 1052 particles, given the spindown luminosity ∼1039 erg s−1. This is several orders of magnitude larger than typical in PWNe, pointing to a different mechanism or to very different conditions existing in this source.
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Acknowledgements
We wish to thank G. Ghisellini, B. Margalit, B. Metzger and A. Papitto for careful reading of the manuscript and helpful comments and suggestions. LS acknowledges financial contributions from ASI-INAF agreements 2017-14-H.O and I/037/12/0 and from “iPeska” research grant (P.I. Andrea Possenti) funded under the INAF call PRIN-SKA/CTA (resolution 70/2016).
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Dall’Osso, S., Stella, L. (2022). Millisecond Magnetars. In: Bhattacharyya, S., Papitto, A., Bhattacharya, D. (eds) Millisecond Pulsars. Astrophysics and Space Science Library, vol 465. Springer, Cham. https://doi.org/10.1007/978-3-030-85198-9_8
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