Stable stellar magnetic

fields

Andreas ReiseneggerPontificia Universidad Católica

de Chile, Santiago

Current Challenges on the Physics of White Dwarf StarsSanta Fe, NM, USA, June 2017

«ANSWERS» groupAstrophysics of Neutron StarsWith Extra/Exotic/Energetic/Extreme Related Stuff

http://www2.astro.puc.cl/answers/

Funding:•FONDECYT Regular Grant 1150411 Rotational & magnetic effectsin neutron stars and beyond (2015-2019)•FONDECYT postdoctoral grants, CONICYT PhD Fellowships•PFB-06 (CATA) Center for Astronomy & Associated Technologies

Outline

• Ideal MHD: flux freezing, field lines as rubber bands• Magnetic flux & magnetic energy from gas to stars• 2 types of stellar magnetic fields• Neutron star magnetic fields• Hydromagnetic equilibria & stability• Possible effects of white dwarf magnetic fields• Origin of stable stellar magnetic fields?

MagnetoHydroDynamics: «hydro» part

• Fluid acceleration

• Mass conservation

• Equation of state = (P, …), complemented with entropy conservation or heat transport, particle diffusion, etc.

0)( v

t

cBjP

dtvd

MagnetoHydroDynamics: «magneto» part

Highly conducting fluid vanishing electric field in fluid frame:

Induction equation

Advection of field lines

Flux conservation

Magnetic force = “tension” + “pressure”

Magnetic field lines behave like rubber bands «frozen» into the fluid the crucial dynamical variable is B; can derive also not directly related to rotation

01 Bv

cE

)( BvEctB

http://www.pma.caltech.edu/Courses/ph136/yr2008/

8

)(41 2BBB

cBj

Bcj

4

Magnetic flux & energy

(AR 2009)

2 types of stellar magnetic fields

• Convective envelopes (solar-type & low-mass mainsequence) active dynamo– B strongly time-variable: solar cycle, flares– Small-scale structure: sunspots, magnetic loops– Present in all stars of this class

• Radiative envelopes (upper main sequence, WDs, NSs) stable field– No detectable B variability– B dominated by large scales– Detected only in ~10-20% of WDs & MS stars

NS spin-down & B

(magnetic dipole model)

422

2

2

332 B

dtd

cI

PPPPB

2||2||

3

Spin-down of the Crab pulsarPlot: C. Espinoza

P-Pdot diagram of NSs

www.atnf.csiro.au/research/pulsar/psrcatPlot: C. Espinoza

Most NSs are known because of their magnetic fields:• Pulsars: non-thermal emission• Magnetars: powered by B

But some are (probably) not: • «Central compact objects» in supernova remnants (CCOs)• X-ray dim isolated NSs (XDINS) Both types are detected throughtheir thermal X-ray emission, butthey are also magnetic!

No non-magnetic NSs?

Stratification & buoyancyNon-barotropic fluid: Stabilized by a gradient of

entropy (WD, stellar radiation zones) or composition (NS) blob displaced from equilibrium “remembers” where it came from

Brunt-Väisälä (buoyancy) frequency

> 0: stable oscillations (“g-modes”)< 0: unstable convection= 0: neutrally stable (“barotropic”)

“Ledoux criterion”

Hydromagnetic equilibria

Pc

Bj

0000 P

0 Pc

Bj

Axially symmetric equilibria

Poloidal + toroidal decomposition:

Both components independently satisfy

No fluid forces in - direction:

But cannot flow out of the star

2 types of toroidal “magnetic surfaces”:• closing outside the star: purely poloidal field

• closed inside the star: «twisted torus» field

Otherwise unconstrained, except for boundaryconditions (Akgün+ 2013; Mastrano+ 2011)

( No «Grad-Shafranov problem» to be solved)

BBB P

PPPP BBjBjBj

||~0

Braithwaite 2007

Pj

0 B

Stability??Purely toroidal (azimuthal) fields are unstable

Flux rings “repel” each other (Tayler 1973)

Figure from Spruit 1999

Purely poloidal (meridional) fields are also unstable

Braithwaite2008

Stable MHD equilibria?

Poloidal + toroidal: “twisted torus”

Arises naturally in simulations of stably stratified,magnetized balls of ideal plasma

Braithwaite & Spruit 2004, 2006; Braithwaite 2009

Effect of stable stratificationMitchell+ 2015: «ideal» MHD simulations

Random initial B                       Ordered initial B (twisted torus)

Warning: Ratio of diffusive/Alfvén time strongly reduced in the simulations!

In stably stratified stellar models, some configurations decay slowly (~diffusion time MHD‐stable) & others decay quickly (~Alfvén time unstable). 

In barotropicmodels, all configurations explored decay quickly unstable!

Diffusion only

StableStrat.

Barotropic

StableStrat.

Effects of B on WDs

Not likely to be important• Change in structure:

B is always «weak» (except for surface layers)AR 2009Peterson & Dexheimer poster 30

Likely to be important

• Quickly suppress differentialrotation (if there ever was)

• Suppress convectionTremblay+ 2015Gentile Fusillo & Tremblay poster 31

slower cooling?• Anisotropic thermal conduction

non-uniform surface temperature? modeled & observed in neutron starsShabaltas & Lai 2010; Guillot+ 2015

Origin of stable stellar B?• «Fossil» (flux freezing) hypothesis (MS, WD, NS)

– Woltjer 1964: prediction of magnetars!– AR 2001; Ferrario & Wickramasinghe 2006, 2008

• Dynamo in strong binary interaction/merger (MS, WD)– Regös & Tout 1995; Tout+ 2008; Ferrario+ 2009; Wickramasinghe+

2014; Langer 2014

• Core collapse dynamo (NS)– Duncan & Thompson 1992: another prediction of magnetars! (+ naming)– Spruit 2009

• Dynamo from phase separation above crystallizing core (WD)– Isern+ 2017

«Fossil» (flux freezing)

Pro:• Similar flux distribution

(maximum flux) in – Upper MS– WDs– Neutron starsAR 2001; Ferrario & Wickramasinghe 2006, 2008

• Unified explanation• Simple physics

Con:• Strong reduction of flux in star

formation• Different incidence of B in

single stars & different binaries• Convection & differential

rotation in red giant phase & in core collapse

• Unlikely to have largepopulation of weakly/non-magnetic NSs (not observed; birth rates [Woods 2008])

Dynamo from strong binary interaction/merger

Pro:• Lack of magnetic upper main

sequence stars with closebinary companions

Carrier+ 2002

• No high-B WDs with close, non-interacting, non-degenerate companion

Liebert+ 2005

• Accretion/differential rotationas plentiful energy source

Wickramasinghe+ 2014

Con:• Common-envelope field is

difficult to transfer to WDPotter & Tout 2010; Ohlmann+ 2016

• Accretion does not generallygenerate B– star formation– low-mass X-ray binaries– millisecond pulsars

• Only schematic physicalmodels

Wickramasinghe+ 2014

Dynamo from phase separation in WDs

Pro• Predictive physical model

Isern+ 2017

Con• Too late in WD evolution• Does not reach the strongest

observed fields• Difficult to get B to surface• Different incidence of B in

single stars & different binaries• Requires different mechanisms

for other star types– core convection in MS?– core collapse in NSs?

(Preliminary) conclusions

• B in upper MS, WD, NS is in a stable hydromagnetic equilibrium, involving– Stable stratification– Poloidal + toroidal B components

• «Least unlikely» origin for WD B proposed so far– Dynamo from strong binary interaction/merger

• Need to explore effects on WDs– Suppression of differential rotation & convection– Anisotropic conductivity