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. .