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 Neutrino emissivity 푛

Pair → Direct Urca process process 푝 - breaking + 푒 Emissivity +

ν

푒

푥 = 푘 퐹푛 풌

풌 2 푭풆 푭풏 −

( 푘

푘 퐹푛 퐹푝 2 풌 + 푭풑 푘 퐹푒

) 2 푁 퐹 푝 2 / 3 dUrca emissivity 푒−(Δ푛+Δ푝) 푇

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.