Magnetic massive stars as magnetar progenitors

Ren-Yu HU and Yu-Qing LOUPhysics Department and Tsinghua Centre for Astrophysics (THCA), Tsinghua University

(Based on Hu & Lou 2009, MNRAS, in press, astro-ph/0902.3111)

23/4/19 Compact Stars in the QCD phase diagram II Beijing, China

2

Acknowledgments

This research was supported in part by Tsinghua Centre for Astrophysics (THCA), by the National Natural Science Foundation of China (NSFC) grants 10373009 and 10533020 and by the National Basic Science Talent Training Foundation (NSFC J0630317) at Tsinghua University, and by the SRFDP 20050003088 and 200800030071 and the Yangtze Endowment from the Ministry of Education and Tsinghua University.

23/4/19 Compact Stars in the QCD phase diagram II Beijing, China

3

Ultra-Intense Magnetic Fields

Two propositions on the origin of ultra-intense magnetic fields of magnetars (SGRs, AXPs) : Neutron Star Dynamo

“Fossil-fields”

(Duncan & Thompson 1992; Thompson & Duncan 1993)

Require fast-spining neutron stars at the beginning (Period~1-2 ms)

Based on magnetic flux conservation so far

Supported by population synthesis study (Ferrario & Wickramasinghe 2006, 2008)

23/4/19 Compact Stars in the QCD phase diagram II Beijing, China

4

Our purpose

Examine quantitatively the “fossil field” scenario

Study the conditions for magnetar formation.

Model magnetized massive stars with a quasi-spherical general polytropic magnetofluid under self-gravity

(Wang & Lou 2008; Lou & Hu 2009)

Our approach

23/4/19 Compact Stars in the QCD phase diagram II Beijing, China

5

General Polytropic Magnetofluid

A magnetofluid under self-gravity in quasi-spherical symmetry

Mass Conservation

Momentum Equation

Magnetic Induction Equation

General Polytropic EoS

Self-Similar Transformation

23/4/19 Compact Stars in the QCD phase diagram II Beijing, China

6

General Polytropic Magnetofluid

Several integrals

Nonlinear ODEs

nx-v=0 -> m=0 : a central cavity

h: magnetic parameter

q: self-similar parameter

q=2(γ+n-2)/(3n-2)

: singular surface

23/4/19 Compact Stars in the QCD phase diagram II Beijing, China

7

Progenitor Surface

We determine the self-similar parameters from density, temperature, magnetic field and mass loss rate on the surface of progenitor.

We proceed the integration inwards.

We should insert MHD shocks in the solutions to cross the singular surface.

Finite velocity solutions at large x,

Back to dimensional variables:

x-> ∞ means either t->0+ or r-> ∞

23/4/19 Compact Stars in the QCD phase diagram II Beijing, China

8

MHD Shock Jump Conditions

Quasi-static solutions can cross the singular surface by MHD shocks.

We consider different sound speed (temperature) across a shock front.

Entropy increases from upstream to downstream sides.

23/4/19 Compact Stars in the QCD phase diagram II Beijing, China

9

Quasi-Static Solutions

There exists a kind of asymptotic solutions v=LxK, α=A0x-2/n+NxK-1-2/n at small x.

When x->0, t->∞, v->0 (Quasi-Static).

The magnetic Lorentz force and the thermal pressure force are in the same order of magnitude at small x.

23/4/19 Compact Stars in the QCD phase diagram II Beijing, China

10

One numerical example

n=

0.673 q=0 γ=

1.327 h=

1.52×10-4

Rs=

109 cm at 1 s

23/4/19 Compact Stars in the QCD phase diagram II Beijing, China

11

The numerical example

On the surface of the progenitor (1012 cm):

On the surface of the neutron star (106 cm):

Density = 2.5×10-5 g cm-3, Temperature = 3×104 K,

Mass loss rate = 10-6 solar mass per year, Mass = 5.59 solar mass,

Magnetic field = 103 G ( may arise from dynamo or “fossil fields” from ISM).

Mass = 2.15 solar mass,

Magnetic field = 4.70×1014 G.

23/4/19 Compact Stars in the QCD phase diagram II Beijing, China

12

Mass Ratio and Magnetic Ratio

The ratio between the neutron star mass and the progenitor mass:

fM = Mi,ult/Mo,ini = (A0/A)λ2/n (ri/ro)3-2n

The ratio between the magnetic field on the neutron star surface and that on the progenitor surface:

fB = <B2i,ult>1/2/<B2

o,ini>1/2 = (A0/A)λ2/n(ri/ro)1-2n

23/4/19 Compact Stars in the QCD phase diagram II Beijing, China

13

Magnetar B-M Relation

Since we have fB/ fM = (ro/ri)2,

Considering the TOV limit of neutron star masses

23/4/19 Compact Stars in the QCD phase diagram II Beijing, China

14

The Amplification Factor

Magnetic enhancement across a shock

<B2t>1/2

1/<B2t>1/2

2 = ρ1/ρ2

= 2/[(γ+1)Mach12]+(γ+1)/(γ-1)

The final magnetic amplification factor depends on n, q, and shock properties.

23/4/19 Compact Stars in the QCD phase diagram II Beijing, China

15

The Amplification Factor

fB < 1012 =(ro/ri)2

Larger q, smaller fB

Median shock speed corresponds to smallest fB

Here we may resolve the difficulty posed by Petit et al. (2008)

23/4/19 Compact Stars in the QCD phase diagram II Beijing, China

16

Conclusions

If the progenitor is a magnetic massive star with a surface magnetic field strength of ~ 103 G, it would have a good chance to produce a magnetar at the center of its supernova remnant.

The magnetar magnetic field is proportional to the magnetar mass and the progenitor magnetic field. The TOV limit actually limits the magnetar magnetic field.

If the progenitor is extremely magnetized, the new born magnetar may power the short GRB.

We could naturally expect a continuum from dim isolated neutron stars to magnetars.

In this scenario, magnetars should be slowly rotating neutron stars.