Magnetic field structure and evolution in NSs: Some open problems and questions

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Magnetic field structure and evolution in
NSsSome open problems and questions
José A. Pons University of Alicante, Spain

• Motivation. Why worrying about MF ?
• Observational issues. How do we see MFs ?
• A brief history of magnetized NSs.
• Structure of magnetized NSs
• Reminder about thermal evolution.
• Core vs. Crustal magnetic field evolution.
• Coupled magneto-thermal evolution. Feedback.
• Population synthesis studies vs. single NS
  fitting.

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Motivation

• Despite the observers tendency to name a new
  class every 1-2 newly discovered objects, or
  theorists to make use all sorts of exotic matter
  (kaons, quark matter, axions ) to explain some
  phenomena, the most basic question may be
• What is the NS model that includes the minimum
  reasonably well known physics and can explain or
  connect all (as many as possible) different
  classes ?
• And there is one thing we are sure NSs do have
  MFs.
• Despite MF-related issues are usually overlooked
  for simplicity, it is a
• Necessary ingredient in any NS model.
• Question Is magnetic field the missing link that
  explains the variety of NS and
• their connexions ?

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Observations The P-Pdot diagram
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B and age estimates magnetic dipole

• Rotating Magnetic dipole

• Emission

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B and age estimates magnetic dipole

• Rotational energy loss

• If born fast, P0lt P

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B and age estimates magnetic dipole

• Magnetic field estimate

• Typical values R ?106 cm, I?1045 g cm3

Uncertainty ? a factor of a few. But this simple
thing is what gives 99 of B field measures.
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Alternative Emission models
How does a magnetized hot body radiate ?
How are emitted photons processed through the
atmosphere and magnetosphere ? If you know it,
comparing your model spectra with obervation can
be used to estimate B fields

• Magnetic atmospheres ?
• Magnetospheric processes ?
• Solid/liquid surface. Gas undergoes a phase
  transition when TltTcrit
• Lai (2001) estimates
• Tcrit 27 B122/5 (Fe)
• Revisited by Medin Lai

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Cyclotron resonant absorption or condensed
surface ?
T106 K, B1013 G
a angle between magnetic field and normal to the
surface
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Example RX J0720 spectral fitting

• BBGaussian absorption line.
• But what is the absorption ?

A condensed surface model with a dipolar field
with B132.5 and polar temperature of 100 eV.
Several models can explain the same spectrum.
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Observational problems Summary

• Magnetic dipolar emission model provides most of
  B field estimates. Not too bad, but a factor of a
  few (angles ?) uncertainty. Measuring Pdot not
  always possible (easy in radio, harder in
  X-rays).
• Spectral fitting is strongly model dependent
  (emission model ?). Much to be improved in
  atmospheric/magnetospheric modelling.
• Luckily, both measures sometimes possible.

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Evolution A brief history of magnetars

• A neutron star is born hot and liquid (melting T
  approx 1e10 K).
• Hydrodynamics is appropriate, and if a strong
  magnetic field is present we can use MHD
• (large electrical conductivity).
• Stable MHD solutions are complex and require a
  toroidal component

MHD equilibrium must be established in few
dynamical timescales (seconds, minutes)
Braithwaite and Spruit 2004,2005
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Structure of (proto-)magnetars

• A perturbative approach fro equilibrium MHD
  reduces the equation describing the magnetic
  field structure to the Grad-Shafranov equation

Simplest case Decoupled multipoles
Toroidal field

• But is MHD valid ?
• Composition
• Stratified medium
• Ambipolar diffusion
• (Reiseneger 2009)

Lorentz force
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Structure of (proto-)magnetars

• Perturbative models can also explain this
  geometry (e.g. Lander and Jones, 2009, Ciolfi et
  al. 2009).

Toroidal field
In any case, very small ellipticities, 10-6, (not
promising for GWs). What is the most
energetically favoured configuration
? Conservation of helicity ?
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Evolution A brief history of magnetars

• But a NS cools fast, and in a few hours or days
  after birth two things happen
• The crust freezes
• Neutrons and protons become superfluid/superconduc
  tor
• If you were happy with MHD, I am sorry, but MHD
  is not valid in a superconductor or in a solid

SC
SOLID
Temperature profiles at different ages
from Aguilera et al. 2008
Not clear how much flux penetrates into the core,
and what is the evolution of a SC fluid (fluxoids
drift and interact with vortices ?)
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Magneto-thermal evolution of NSsIngredients

• Neutron star model (structure, EOS).
• Thermal evolution (energy balance equation)
  standard cooling of NSs. (Similar timescales,T-B
  coupling)
• Magnetic field evolution in the crust Hall
  induction equation. Field decay and Joule
  heating.
• Magnetic field evolution in the core
  superconducting fluid dynamics, interaction
  between fluxoids and vortices ??? (no formalism
  yet)
• Microphysics ingredients thermal conductivity,
  electrical resistivity, neutrino emission
  processes

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Thermal Diffusion (Energy balance
equation) Effects of magnetic field
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Cooling of weakly magnetized NSs
Intensively studied (Page et al., Yakovlev
Pethick)
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Thermal structure of magnetized NSs

• F - k . ÑT - k b (ÑT . b) - k b (ÑT b)
  - kL (b ÑT)
• Isothermal surfaces aligned with B Strong
  dependence on B field geometry !

(Geppert, Küker, Page, 2004,2007,
Perez-Azorin et al. 2005, 2006a, 2006b, Henderson)
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Magnetized envelope models

• Meridional heat transfer important for large B
  fields
• Former 1D (plane-parallel) models revisited.
  Improved Tb-Ts relations.
• Significant differences when B tangential to the
  surface

Pons, Miralles, Geppert AA 2009
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Joule heating ? Do the easy thing first energy
balance

Prediction slope1/2 in a logT-logB plot We
have about 30 NSs (7 magnificents, 3 musketeers,
RRATs, 7 AXPs, 2 SGRs, some radio-pulsars ) with
reported thermal emission and B.
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Joule heating effective in many NSs ?
Crust size 1 km Bint 10-15 x Bdip B decay
time 1 Myr
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Joule heating masquerades fast cooling ?
High B
B0
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Joule heating masquerades fast cooling ?
Mass dependence vs. B field dependence
All NSs with fast cooling ? not ruled out !
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Crustal B field evolution

• In a real NS the crust is not a fluid, so the MHD
  approximation is not valid. It is more
  appropriate to describe it as a Hall plasma,
  where ions have very restricted mobility and only
  electrons can move freely through the lattice.
• The proper equations are Hall MHD. If ions are
  strictly fixed in the lattice, the limit is known
  as EMHD (electron MHD)
• There are two basic wave modes in the
  homogeneous limit (constant electron density),
  whistler or helicon waves, and also Hall drift
  waves in the inhomogeneous case.

Hall induction equation
Electrical resistivity depends strongly on T
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Crustal B field evolution
Problems

• Conductivity varies many orders of magnitude
• Magnetization parameter varies with time and can
  get very large (Hall term dominates)
• Back-of-the-envelope estimates vary in a range of
  5-6 orders of magnitude

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B field evolution weak field

• B(pole)1e13 G

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B field evolution intermediate field

• B(pole)1e14 G

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B field evolution strong field

• B(pole)1e15 G

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B field evolution asymmetric

• B(pole)1e14 G

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Coupled B-T evolution

• maximum B field for old NSs !!
• higher fields more heating higher
  resistivity faster decay

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Crustal B field evolution Summary

• The first Hall stage (few kyrs) is very active.
  Whistler and Hall waves stress the crust,
  resulting in frequent glitches and flares. The
  timing anomaly is always present, but only when
  the stresses break the crust or fast magnetic
  reconnexion releases enough energy there will be
  outbursts.
• After the Hall stage, the system reaches a
  quasi-equilibrium configuration (not simply
  dipolar) and the field has dissipated in about a
  factor of 10. Ohmic dissipation dominates during
  1 Myr. All NSs born as magnetars end up with
  similar fields. Look like isolated NSs or high
  field radio-PSRs. A chance of rare transient
  phenomena (less energetic).
• When Joule heating is not efficient any more, the
  star cools down and dissipation proceeds much
  slower. A second Hall stage may happen for NSs
  older than 1Myr and B fields of the order of 1e12
  (timing noise with large positive and negative
  braking index ?)
• Effect of B field on observed temperature large
  enough to masquerade fast cooling. Is rapid
  cooling going on in all NSs but we can only see
  it in some low field NSs ?

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Population Synthesis studies Motivation

• Question we all agree we must compare
  models/theory with data/observations, but how do
  we do that ?
• Given the large uncertainty in many of the
  physical ingredients of a magnetized NS model,
  and the limited quality of data (temperatures and
  B fields are not entirely reliable), can one
  really trust constraints based on fitting
  particular models on individual objects ?
• But we have something else physics (EOS,
  composition, processes on B fields) must be the
  SAME in all NSs. Whichever model that works for
  an INDIVIDUAL NS, must pass the test of being
  consistent with the WHOLE population.
• Population synthesis offers an interesting way
  simulate a large populations of NS in the whole
  galaxy (or an interesting region) and do an
  statistical analysis of general properties. It
  has lots of problems, but luckily you wont be
  biased by one particular data point or anomalous
  behaviour.

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Population synthesis I nearby thermally
emitting NS

• LogN-LogS study of known NSs at dlt3 kpc
• Same underlying physical model, same magnetic
  field geometry, only varying strength.
• Only ROSAT all sky survey with flux gt 0.1 counts
  per second is complete.

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Population synthesis I nearby thermally
emitting NS
For Log-normal B field distributions, constraint
on the number of high field NSs 10 with Bgt1e14
G
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Population synthesis II galactic magnetars
Same distributions are consistent with magnetar
population. Degenaracy in parameter space not
broken Maybe some extra luminosity needed for
young objects (lt1 kyr)
(magnetar data from McGill online catalogue, Muno
et al. estimates in shaded box) )
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Population synthesis III radio-pulsars
Evolution with field decay affects mainly to
highly magnetized objects and the first Myr of
evolution. Spin-down ages overestimated Can we
find statistically acceptable results for these
models ?
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Population synthesis III radio-pulsars
Faucher-Guiguere and Kaspi (2006), no field decay
Popov et al. (2009)
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Why population synthesis ? Summary

• After introducing magnetic fields in the game,
  even more parameters are needed to fit individual
  objects (and NS do have magnetic fields). Highly
  degenerate parameter space.
• Simultaneous population synthesis studies of
  different classes are a promising method to
  constrain the initial field distribution and its
  evolution, together with the internal physics of
  NSs.
• Both, explaining individuals and populations are
  needed. It is important to think also globally.
  If a model works (or seems to be requested) for a
  particular object, can I prove that it does not
  contradict properties of many others ?