Magnetic Field Decay and Core Temperature of Magnetars, Normal and MS pulsars

Shuang-Nan Zhang 张双南 1

Yi Xie 谢祎 2

1. Institute of High Energy Physics

2. National Astronomical Observatories of China

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Evolutionary study of pulsars on p-pdot diagram

Han, J.L, 1997, A&A

B decay required?

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Indirect Evidence for B decay?

Han, J.L. (1997): power-law decay with “gene”: t0~B0 dependence

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Direct Evidence for B Decay

Best fits

magnetars

Normal pulsars

ms pulsars

Magnetars do not cross death line: normal radio pulsar mechanism works here? Consistent with recent detection of radio magnetars (talks by Manchester and Yuan in this meeting).

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P-Pdot or B-Age?

Direct observables: But all tracks calculated using B-dipole radiation model, and indirect comparison with B-decay model.

Derived quantities using B-dipole radiation model (OK if not overwhelmed by pulsar wind loss), but direct comparison with B-decay model.

P

Pdo

t

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Inclination angle decay?

Magnetic-Dipole radiation model:

0 d obs NS dIf sin sin exp( ), then exp( )t t B B t t

• Then the observed B-decay may be in fact an illusion of inclination angle decay (Faucher-Giguère & Kaspi 2006; Weltevrede & Johnston 2008).

• However, B-decay by 100 times for each kind of pulsars is difficult for inclination angle decay alone.– A better and more physical model required.

3 32 2 0 2

2 6 2 6

3 3sin , assume 90 , then

8 8

c I c IB PP B PP

r r

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B Decay Model: Heyl & Kulkarni, 1998, ApJL

The dominant term

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~ Constant Core Temperatures of NSs

magnetars

normal pulsarsms pulsars

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Best fits of real pulsars

All observed P and Pdot paired randomly

All observed P

All observed Pdot

General trend of the observed distributions!

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Each class of observed P and Pdot paired randomly

Very similar to the observed distributions!

Model for real pulsars

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Completely simulated data: Gaussian distributions

Still very similar to the observed distributions!

Model for real pulsars

logPP (s)

M σ M σ

8 2 -11 0.5

0.8 0.8 -16 0.2

0.002 0.001 -20 0.5

Input parameters

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Completely simulated data: Not a surprise!logPP (s)

M σ M σ

8 0.2 -11 0.5

0.8 0.1 -16 0.2

0.002 0.0001 -20 0.5

Model for real pulsars

Simulated data follow model precisely!

& = 2B PP P P -1 2B P

-1 2B P=const

B-Dipole radiation:

For each type of pulsars

2 3 1 2B T B B T Ambipolar B-Decay model (T=const):

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Why is the Pdot so small for all pulsars?

• B-dipole radiation

– But why the observed Pdot is so small?

• Ambipolar diffusion B-decay with constant core

temperature P~constant Pdot must be very small!

• This is a natural prediction of the above ambipolar

diffusion B-decay model.

2 3 1 2 1 2B T B B T B

1 2 & = 2B PP P P B P

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Evidence for Hot Magnetars

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Evidence for Equilibrium between Heating & Cooling?

?

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Summary and Open Questions• No magnetar cross the pulsar’s death line

– Normal pulsar radiation mechanism?• All NSs show clear evidence for B-deday

– Agrees with ~constant Tcore ambipolar diffusion B-decay model well• Heating by B-decay energy and NS cooling by

neutrino and emission in ~equilibrium for all pulsars?• The model naturally predicts very small Pdot as observed

– Core temperature: Magnetars 2x108 K, Normal pulsars 2x107 K, ms pulsars 1x105 K• Different populations at birth?