the early life of millisecond magnetars - pku · the early life of millisecond magnetars ian jones...
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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
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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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