Magnetic field during the birth of a neutron star
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1 Magnetic field during the birth of a neutron star Jon Braithwaite Bonn University 6th neutron star workshop Bonn, 27th Oct 2014
2 Contents - Flux conservation hypothesis - Proto neutron stars - Dynamo - Post-dynamo relaxation - Progenitor field - Types of equilibrium - Summary
3 Contents - Flux conservation hypothesis - Proto neutron stars - Dynamo - Post-dynamo relaxation - Progenitor field - Types of equilibrium - Summary
4 Flux conservation hypothesis Magnetic flux "inherited" from main sequence log B (G) log flux (G cm 2 ) main-seq. OBA <0 to 4 <23½ to 28½ white dwarf <4 to 9 <22 to 27½ young NS 10? to 15 22½? to 27½ But what about mass loss, convection, binary stuff?
5 Similar physics hypothesis log B (G) log flux (G cm 2 ) log Emag/Egrav main-seq. OBA <0 to 4 <23½ to 28½ -12 to -6 white dwarf <4 to 9 <22 to 27½ <-16 to -6 young NS 10? to 15 22½? to 27½ -16? to -6 Maximum energy in differential rotation Ed-r / Egrav ~ 1/30 Conversion into magnetic energy with certain efficiency?
6 Contents - Flux conservation hypothesis - Proto neutron stars - Dynamo - Post-dynamo relaxation - Progenitor field - Types of equilibrium - Summary
7 Proto neutron star Conditions: - Rotation: everything up to break-up (AIC fast?) - Strong differential rotation, i.e. ΔΩ/Ω 1/2? - Convection, turnover timescale tconv ~ 1 ms Questions: - Is a dynamo present? - What happens after convection and then diff. rot. die away? - Is progenitor field relevant?
8 Contents - Flux conservation hypothesis - Proto neutron stars - Dynamo - Post-dynamo relaxation - Progenitor field - Types of equilibrium - Summary
9 Dynamos in proto-nss small-scale dynamo α-ω dynamo Uses convection? Uses rot./diff.rot.? Conditions Prot > tconv Prot < tconv Growth timescale tconv? Geometry small-scale large-scale Strength G G Equipartion Emag ~ Econv Result of Duncan & Thompson 1992
10 Dynamos in proto-nss Rotation irrelevant: - Small-scale dynamo in "queiscent" regions Rotation important: (& dipole field created) - Solar cycle - Earth - Jupiter - M dwarfs - T Tauri stars Zeeman-Doppler imaging from SOHO
11 Dynamos in proto-nss small-scale dynamo α-ω dynamo MRI Tayler-Spruit Uses convection? Uses rot./diff.rot.? Conditions Prot > tconv Prot < tconv Ωcore > Ωenv Ωcore Ωenv Growth timescale tconv? 1/ΔΩ talfvén 2 Ω Geometry small-scale large-scale?? Strength G G??
12 Dynamos in proto-nss small-scale dynamo α-ω dynamo MRI Tayler-Spruit Uses convection? Uses rot./diff.rot.? Conditions Prot > tconv Prot < tconv Ωcore > Ωenv Ωcore Ωenv Growth timescale tconv? 1/ΔΩ talfvén 2 Ω Geometry small-scale large-scale?? Strength G G?? Both present? Mops up afterwards Too slow
13 Contents - Flux conservation hypothesis - Proto neutron stars - Dynamo - Post-dynamo relaxation - Progenitor field - Types of equilibrium - Summary
14 "Star-in-box" simulation Post-dynamo relaxation Simulation of nonconvective star (e.g. Braithwaite & Spruit 2004)
15 Post-dynamo relaxation Useful to consider the magnetic helicity H B.A dv where B = A H is approximately conserved in stellar interiors
16 R Post-dynamo relaxation l random: f 1/ N Dynamo: H ± Edyn f l Final state: H ± Eequil R coherent: f 1 so Eequil Edyn f l / R Bequil 2 Bdyn 2 f l / R
17 Timescales and crust formation Field reaches equilibrium on timescale (Braithwaite & Cantiello 2013) tequil ~ talfvén 2 / Prot ~ (Bequil / G) -2 (Prot / 1 ms) s Does this happen before crust forms? Bequil / G Prot / ms tequil Magnetar s Millisecond magnetar s Normal pulsar month CCO years If crust forms first, magnetic field held in place "against its will"
18 Contents - Flux conservation hypothesis - Proto neutron stars - Dynamo - Post-dynamo relaxation - Progenitor field - Types of equilibrium - Summary
19 Effect of convection on existing field Fully convective star: previous field lost, replaced by dynamo field -- but -- neighbouring nonconvective region(s) might retain some magnetic field Simulation of fully convective star (Mitchell, Braithwaite, Reisenegger, Spruit & Langer, submitted)
20 Contents - Flux conservation hypothesis - Proto neutron stars - Dynamo - Post-dynamo relaxation - Progenitor field - Types of equilibrium - Summary
21 Types of equilibrium "Star-in-box" simulations Effect of initial radial energy distribution more concentrated in centre flatter Blue shading = toroidal field Figures from Braithwaite 2008
22 Types of equilibrium "Star-in-box" simulations Effect of initial radial energy distribution more concentrated in centre flatter Surface dipole ~ average interior field Surface dipole < average interior field Surface dipole < average interior field Blue shading = toroidal field Figures from Braithwaite 2008
23 Types of equilibrium Radial component of field in three simulations at five rotational phases (figs. Kochukhov & Braithwaite)
24 Types of equilibrium Seen in OB stars Seen in OB stars Such complexity not seen in OB stars Radial component of field in three simulations at five rotational phases (figs. Kochukhov & Braithwaite)
25 Contents - Flux conservation hypothesis - Proto neutron stars - Dynamo - Post-dynamo relaxation - Progenitor field - Types of equilibrium - Summary
26 Field in young NS determined by - helicity: Eequil ~ H / R - radial energy distribution: determines geometry Summary Either: - convection erases progenitor field: rotation only degree of freedom problem with SNRs of magnetars (Vink & Kuiper 2006) - helicity from progenitor survives (requires some non-convective zone): rotation and progenitor magnetic field are two degrees of freedom Crust formation happens: - in magnetars after equilibrium is reached - in other NSs before equilibrium can be reached Interior field probably stronger than surface dipole (good for energy budget of magnetars) Same range of Emag/Egrav in OBA stars, WDs & NSs: similar physics, e.g. converting diff.rot. energy into magnetic energy with similar efficiency. Many situations have maximal rotation & strong diff.rot.
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