The early life of millisecond magnetars

IanJones

Figurecredit:NationalScienceFoundation/LIGO/SonomaStateUniversity/A.Simonnet.

SorryIoverslept!

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LeonMestel:1927– 2017

Pioneerinthemodellingofstellarmagneticfields.

Developedmodelforprecessingmagneticstar.

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Whathappenstospinandmagneticaxesinearlylifeofapulsar?

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Basedon:• Lander&DIJMNRAS4564343(2017)• Lander&DIJMNRAS4814169(2018)

Relevantfor:1. Gravitationalwave

emissionfollowingbirth(e.g.PaulLasky’s talk)

2. Determiningtheinclinationangleoftheobservedpulsarpopulation.

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Millisecondmagnetar birthWillassumestarsareborn:

1. Spinningfast2. Withstrongmagneticfield

Rotationmayitselfwind-upthemagneticfield.

Couldgetastronginternaltoroidalmagneticfield.

Figurecredit:J.J.Love

Poloidal Toroidal

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Magneticdistortions

Poloidal field

Oblatedistortion

Toroidal field

Prolate distortion

BasicpictureMagneticfield distortsstar,givingellipticity:

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Unlessrotationandmagneticaxesexactlyaligned,starwillthenundergofreeprecession.

Freeprecessionconsistsofrapidspinofmagneticaxisaboutfixedangularmomentumaxis…

…plusslowsuperimposedrotationaboutmagneticaxis.

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Spin-flipmechanism

PointedoutbyP.B.Jones(1976)Mestel+(1981).

Kineticenergyofarigidprecessing biaxialbody:

𝐸 =𝐽%

2𝐼( 1 − 𝜖,cos%𝜒

Ifoneallowsforinternaldissipation,�̇� < 0, 𝐽̇ = 0,so:• Oblate:𝜖, > 0, �̇� < 0,⇒ 𝑎𝑙𝑖𝑔𝑛𝑚𝑒𝑛𝑡• Prolate:𝜖, < 0, �̇� > 0,⇒ 𝑜𝑟𝑡ℎ𝑜𝑔𝑜𝑛𝑎𝑙𝑖𝑠𝑎𝑡𝑖𝑜𝑛

Cutler(2002):Prolate optimalforgravitationalwaveemission

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Magnetictorques

Magnetictorquescausespin-down.

Theyalsotendtomake𝜒 decrease (Davis&Goldstein1970,Michel&Goldwire 1970,Goldreich 1970).

Canthereforegetcompetition between:

ORTHOGONALISATION

Duetointernaldissipationinprolate state

ALIGNMENT

Duetoelectromagnetictorques.

Internaldissipation:Non-rigidresponse

Spinaxistracesoutaconeofhalf-angle𝜒asviewedfromrotatingstar.

Butspinaxisdefinescentrifugalbulge,ofsize:

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⟹ havedensitywavepropagatingaroundstar

Time-varying densityperturbationwillinducedisplacementmotioninthestellarfluid,Mestel’s “xi-motions”.

Crucialforcalculatingdissipationrates(e.g.duetoshear&bulkviscosities),andhenceevolutioninwobbleangle.

Mustsatisfycontinuityequation:

Butthisisn’tsufficienttocompute𝜉.

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Non-rigidresponse:“xi-motions”

Solution:Lander&DIJ2017TakefullsetofPDEs,andexploitsmallnessof𝜖E and𝜖,:

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• Zerothorder:sphericalstar• Order𝜖E:rotationaldeformed star• Order𝜖,:magneticallydeformed star• Order𝜖E𝜖,:xi-motions!

Application:newlybornNSsImagineNSbornwithsomenon-zeroinclinationangle.

SetofcoupledODEs(Lander&DIJ2018):

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Temperature:FGFH= −𝑛𝑒𝑢𝑡𝑟𝑖𝑛𝑜𝑐𝑜𝑜𝑙𝑖𝑛𝑔

Spin frequency:FEFH= −𝐸𝑀𝑠𝑝𝑖𝑛𝑑𝑜𝑤𝑛

Inclinationangle:FOFH= ±𝑣𝑖𝑠𝑐𝑜𝑢𝑠𝑑𝑖𝑠𝑠𝑖𝑝𝑎𝑡𝑖𝑜𝑛 − 𝐸𝑀𝑎𝑙𝑖𝑔𝑛𝑚𝑒𝑛𝑡

Oblate(𝜖, > 0): alignment Prolate(𝜖, < 0):counteralignment,aka“Mestel-Jonesspin-flip”

Inter-dependenceofparameters

Dominantviscousdampingmechanismisprobablybulkviscosity.

Bulkviscosityfrequencydependent(Lindblom&Owen2002):

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𝜏~𝑇WX,microphysicalreactionrate𝜔~𝑓𝜖,~𝑓𝐵% ,precessionfrequency

EMtorque~𝑓\𝐵%Complexinterplay

“Orthogonalisation”curveCanuseback-of-the-envelopeformulaetoestimatecurvein(𝑓, 𝑇) planeabovewhichspin-flipactive:

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3a

1a

3b

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1b

B=1016 G

TimeevolutionsofcoupledODEsshowrichstructure.

CanclassifyasAligned,Orthogonalised,orUnevolved.

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Timeevolutions

Figure:Lander&DIJ(2018)

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Currentwork:improvingtorquemodel

ActualEMtorquesonmillisecondmagnetars morecomplex.

Needtoaccountforangularmomentumtransportbyoutwardmatterflux.

Currentlyunderinvestigation.

Summary

• Newlybornmillisecondmagnetar maybesusceptible

tospin-flipinstability.

• Dependsuponcompetitionbetweenelectromagnetic

torquesandinternaldissipation.

• ImportantforpulsarphysicsandGWemission.

• Standtolearnaboutbothinteriorandexteriorofstar.

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