The early life of millisecond magnetars Ian Jones Melbourne, March - - PowerPoint PPT Presentation

The early life of millisecond magnetars

Ian Jones

Melbourne, March 2019

Figure credit: National Science Foundation/LIGO/Sonoma State University/A. Simonnet.

Leon Mestel: 1927 – 2017

Pioneer in the modelling of stellar magnetic fields. Developed model for precessing magnetic star.

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What happens to spin and magnetic axes in early life of a pulsar?

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Based on:

• Lander & DIJ MNRAS 456 4343 (2017)
• Lander & DIJ MNRAS 481 4169 (2018)

Relevant for:

• 1. Gravitational wave

emission following birth.

• 2. Light curves of short GRBs,

maybe!

• 3. Determining the

inclination angle of the

• bserved pulsar

population.

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Millisecond magnetar birth

Will assume stars are born:

• 1. Spinning fast
• 2. With strong magnetic field

Rotation may itself wind-up the magnetic field. Could get a strong internal toroidal magnetic field.

Figure credit: J. J. Love

Poloidal Toroidal

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Magnetic distortions

Poloidal field Oblate distortion Toroidal field Prolate distortion

Basic picture

Magnetic field distorts star, giving ellipticity:

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Unless rotation and magnetic axes exactly aligned, star will then undergo free precession. Free precession consists of rapid spin of magnetic axis about fixed angular momentum axis… …plus slow superimposed rotation about magnetic axis.

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Geometry of the precession

𝐾 = angular momentum Angle 𝜓 𝑛 = magnetic axis Angular momentum vector fixed in space. Magnetic deformation assumed axisymmetric about axis 𝑛. ⟹ biaxial free precession. [We consider early stages, before crust formation.] Centrifugal distortion not shown in picture! 𝜓 = 0 ∶ no gravitational wave emission 𝜓 = )

* : optimal gravitational wave emission

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Spin-flip mechanism

Pointed out by P. B. Jones (1976) Mestel+ (1981). Kinetic energy of a rigid precessing biaxial body: 𝐹 = 𝐾* 2𝐽/ 1 − 𝜗3 cos*𝜓 If one allows for internal dissipation, 𝐹̇ < 0, 𝐾̇ = 0, so:

• Oblate: 𝜗3 > 0, 𝜓̇ < 0, ⇒ 𝑏𝑚𝑗𝑕𝑜𝑛𝑓𝑜𝑢
• Prolate: 𝜗3 < 0, 𝜓̇ > 0, ⇒ 𝑝𝑠𝑢ℎ𝑝𝑕𝑝𝑜𝑏𝑚𝑗𝑡𝑏𝑢𝑗𝑝𝑜

Cutler (2002): Prolateoptimal for gravitational wave emission

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Magnetic torques

Magnetic torques cause spin-down. They also tend to make 𝜓 decrease (Davis & Goldstein 1970, Michel & Goldwire 1970, Goldreich 1970). Can therefore get competition between:

ORTHOGONALISATION Due to internal dissipation in prolate star ALIGNMENT Due to electromagnetic torques.

Internal dissipation: Non-rigid response

Spin axis traces out a cone of half-angle 𝜓 as viewed from rotating star. But spin axis defines centrifugal bulge, of size:

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⟹ have density wave propagating around star

Time-varying density perturbation will induce displacement motion in the stellar fluid, Mestel’s “xi-motions”. Crucial for calculating dissipation rates (e.g. due to shear & bulk viscosities), and hence evolution in wobble angle. Must satisfy continuity equation: But this isn’t sufficient to compute 𝜊.

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Non-rigid response: “xi-motions”

Solution: Lander & DIJ 2017

Take full set of PDEs, and exploit smallness of 𝜗H and 𝜗3:

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• Zeroth order: spherical star
• Order 𝜗H: rotational deformed star
• Order 𝜗3: magnetically deformed star
• Order 𝜗H𝜗3: xi-motions!

Application: newly born NSs

Imagine NS born with some non-zero inclination angle. Set of coupled ODEs (Lander & DIJ 2018):

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Temperature: IJ

IK = −𝑜𝑓𝑣𝑢𝑠𝑗𝑜𝑝 𝑑𝑝𝑝𝑚𝑗𝑜𝑕

Spin frequency: IH

IK = −𝐹𝑁 𝑡𝑞𝑗𝑜𝑒𝑝𝑥𝑜

Inclination angle: IR

IK = ±𝑤𝑗𝑡𝑑𝑝𝑣𝑡 𝑒𝑗𝑡𝑡𝑗𝑞𝑏𝑢𝑗𝑝𝑜 − 𝐹𝑁 𝑏𝑚𝑗𝑕𝑜𝑛𝑓𝑜𝑢

Oblate (𝜗3 > 0): alignment Prolate (𝜗3 < 0):counteralignment, aka “Mestel-Jones spin-flip”

Inter-dependence of parameters

Dominant viscous damping mechanism is probably bulk viscosity. Bulk viscosity frequency dependent (Lindblom & Owen 2002):

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𝜐 ~ 𝑈YZ, microphysical reaction rate 𝜕 ~ 𝑔𝜗3 ~ 𝑔𝐶* , precession frequency EM torque ~𝑔^ 𝐶* Complex interplay

“Orthogonalisation” curve

Can use back-of-the-envelope formulae to estimate curve in (𝑔, 𝑈) plane above which spin-flip active:

15 3a 1a 3b 2 1b

B = 1016 G

Time evolutions of coupled ODEs show rich structure. Can classify as Aligned, Orthogonalised, or Unevolved.

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Time evolutions

Figure: Lander & DIJ (2018)

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Current work: improving torque model

Actual EM torques on millisecond magnetars more complex. Need to account for angular momentum transport by

• utward matter flux.

Bulk viscosity may be suppressed in very young (hot) stars, and also in older (cooler) stars. Currently under investigation.

Summary

• Newly born millisecond magnetar may be susceptible

to spin-flip instability.

• Depends upon competition between electromagnetic

torques and internal dissipation.

• Important for pulsar physics and GW emission.
• Stand to learn about both interior and exterior of star.

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