Some Theoretical Aspects of Magnetars

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Some Theoretical Aspects of Magnetars Some theoretical aspects of Magnetars Monika Sinha Indian Institute of Technology Jodhpur Collaborator Armen Sedrakian (Frankfurt Institute of Advanced Studies) Structure of Neutron star Outer crust: ions + electrons a few hundred meters Inner crust: electrons + neutrons + neutron rich nuclei about one kilometer Outer core: neutrons + protons + electrons + muons Inner core: ? number of possibilities Structure of Neutron star Nuclear matter Hyperon matter Pion condensate Kaon condendate Quark matter Neutrons in the core could also be in superfluid state. Theoretical model predicts . Pulsating stars discovered – . Typical radius of NS is ~ 10 km and PULSARS with pulse period ~ ms – s. mass ~ 1.4 Msun: very compact. As NSs are very compact in size, . Radiation from such object is they can withstand fast rotation: emitted in some particular P ~ ms – s. direction. The object is rotating What is the cause of directional radiation? . When radiation comes into Magnetic field our line of sight we observe the radiation. • Hence, pulsars are soon identified as magnetized rotating NS • Pulsars are believed to be rotating NS with surface magnetic field 108 – 1012 G. • Later on NSs were discovered with much higher surface magnetic field 1014 – 1015 G: MAGNETAR Introduction Soft Gamma Repeaters (SGRs) and Anomalous X-ray Pulsars (AXPs) : Very different from ordinary X-ray bursters and pulsars 45 35 • Lpeak ~ 10 ergs/s, Lx ~ 10 ergs/s. • Rotational period ~ 5 – 10 s, spin down rate ~ 10-11 s/s • No evidence of binary companions: sometime association with supernova remnants: Increasing number of common properties: Close relationship between SGRs and AXPs Introduction Soft Gamma Repeaters (SGRs) and Anomalous X-ray Pulsars (AXPs) : Very different from ordinary X-ray bursters and pulsars • No correlation between energy and time interval since the previous burst: Trigger of the bursts is not accretion. • AXPs: Softer spectrum: Neither accretion powered, nor rotation powered. • Current model: Magnetar – Neutron stars with strong surface magnetic field ~ 1014 - 1015 G. • The field in the interior of the NS may have higher value. Effect of magnetic field on matter Energy momentum tensor of the system: Matter energy density Thermodynamic pressure Magnetization tensor Effect of magnetic field on matter • In the rest frame of matter, with the choice of magnetic field Magnetic field Magnetization Effect of magnetic field on matter k p p contribution from potential energy pF In absence of E d 3 p E p2 m2 magnetic field k p p 0 In presence of magnetic field Superconductivity inside neutron stars 14 15 • Bs = 10 -10 G • Interior field even greater Superconductivity inside magnetar Quenched? Superconductivity inside neutron stars Type-II superconductivity London’s penetration δ퐿 depth 1 휅 = κ > ξ푝 √2 Coherence length Type-II superconductivity exists if Φ0 퐻푐2 = 2 Quantum 퐻푐1 < 퐵 < 퐻푐2 2πξ푝 of flux 푛ℎ Φ = 0 2푒 From virial theorem 퐵 > 퐻 18 푚푎푥 푐2 퐵푚푎푥 = 10 G Inputs… 퐸 퐴 = −16.14 MeV 퐸푠 = 32.20 MeV 퐾0 = 250.90 MeV -3 푛0 = 0.152 fm Wambach et al. NPA 555, 128 (1993) Baldo et al. PRC 58, 1921 (1998) Superconductivity inside neutron stars ΦΦ00 퐻푐2 = 2 1 + 푓 2πξ푝 푘푝 ξ푝 = π푚푒푓푓Δ푝 2 2 2 27π 푛푛 Δ푝 푓 = 퐺푛푝 2 2 8 μ푝 μ푛 푚푝푘퐹푝 16 max 퐻푐2 ≅ 6.25 × 10 G Implications… Field Rotational Neutrino decay dynamics emissivity glitch cooling Reheating Heat capacity Electrical conductivity Emissivity 풌푭풏 푛 → 푝 + 푒 + ν 푒 풌푭풑 풌푭풆 푘 2 − (푘 + 푘 )2 Direct Urca 퐹푛 퐹푝 퐹푒 2/3 푥 = 2 푁퐹푝 process 푘퐹푛 Pair-breaking process Neutrino emissivity Neutrino dUrca emissivity −(Δ +Δ ) 푇 푒 푛 푝 푥 > 0 푥 < 0 Pair-breaking emissivity 4퐺 2 ϵ = =푎 푆/푃(퐵) 퐹 푇7퓘 푛/푝 푛/푝 15π2 Summary • Presence of magnetic field introduces the anisotropic pressure in the system. • Negative contribution from field pressure of from interaction of matter with field to pressure leads to instability above a critical field. • Magnetars are fully of partially free of proton superconductivity depending on strength of field inside the magnetars. • Neutrino emissivity is affected due to unpairing effect. • Detailed cooling simulations are needed to confront the theory of magnetar with quenched superconductivity with the observations. • Heat capacity, reheating due to field decay are to be addressed under this condition. • Electrical conductivity, field decay, rotational dynamic, coupling of normal matter to superfluid matter should be revisited with this result. .
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