Some aspects of magneto-thermal evolution of NSs

1. Some aspects of magneto-thermal evolution of NSs José A. Pons University of Alicante, Spain • Motivation. A brief history of magnetized NSs. • Thermal evolution. • Crustal magnetic field evolution. • Coupled magneto-thermal evolution. Feedback. • Population sysnthesis studies.

2. Motivation Despite the observers tendency to name a new class every 1-2 newly discovered objects, or some theorists to propose all sorts of exotic matter (kaons, quark matter, axions …) to explain some phenomena, the relevant question may be: What is the NS model that includes the minimum reasonably well known physics and can explain or connect different classes ? Goal:to follow the coupled evolution of temperature and B field, describing the different stages of a magnetized NS life.

3. 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

4. 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 • Glampedakis et al. 2010) Lorentz force

5. A brief history of magnetars Perturbative models can also explain this geometry (e.g. Lander and Jones, 2009, Ciolfi et al. 2009, Maxim Lyutikov). Toroidal field In any case, very small ellipticities (what is the most energetically favoured configuration ?)

6. 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/superconductor If you were happy with MHD, I am sorry, but MHD is not valid neither in a superconductor nor 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 ?)

7. Magneto-thermal evolution of NSs:Ingredients • Neutron star model (structure). Initial data. • Thermal evolution (energy balance equation): standard cooling of NSs • 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 ??? (no formalism yet, Nils Andersson’s or Bennet Link’s talk) • Microphysics ingredients: EOS, thermal conductivity, electrical resistivity, neutrino emission processes, composition, impurity content …

8. Thermal Diffusion (Energy balance equation)

10. Weakly magnetized NSs Intensively studied (Page et al., Yakovlev & Pethick)

11. 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)

12. Joule heating ? Do the easy thing first: energy balance Prediction: slope=1/2 in a logT-logB plot Data? We have about 30 NSs (7 magnificents, 3 musketeers, RRATs, 7 AXPs, 2 SGRs, some radio-pulsars …) with reported thermal emission and B.

13. Joule heating effective in many NSs ? Crust size = 1 km Bint = 10-15 x Bdip B decay time 1 Myr Pons et al., 2007, PRL, 98, 071101

14. Joule heating masquerades fast cooling ? High B B=0

15. Joule heating masquerades fast cooling ? Mass dependence vs. B field dependence All NSs with fast cooling ? not ruled out !

16. Effect of new physics: superfluid phonons Aguilera et al. 2009, Rishi Sharma’s talk

17. Effect of new physics: superfluid phonons Aguilera et al. 2009, Rishi Sharma’s talk, Jillian Henderson poster

19. Joule heating working in many NSs ? 2D heat transport, phenomenological B field evolution law Aguilera, Pons, Mirales, ApJ L673 (2008) 167, A&A 486 (2008) 255

20. 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

21. B field evolution • Decomposition into poloidal+toroidal components. • Diffusive (parabolic) terms. • C,D non-linear (Hall) terms (hyperbolic) • Toroidal field subject to an “advective” term proportional to the resistivity gradient. • For purely toroidal fields D=0 and (homogeneous charge density), C becomes Burgers Eq.

22. 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

23. B field evolution: weak field • B(pole)=1e13 G Pons & Geppert, A&A, 470 (2007) 303

24. B field evolution: intermediate field • B(pole)=1e14 G

25. B field evolution: strong field • B(pole)=1e15 G

26. B field evolution: asymmetric • B(pole)=1e14 G

27. The Hall Instability ? Linear analysis Rheinhardt & Geppert PRL 2002

28. The Hall Instability ? Rheinhardt & Geppert PRL 2002

29. Coupled B-T evolution • maximum B field for old NSs !! • higher fields = more heating = higher resistivity = faster decay Pons, Miralles, Geppert A&A 2009

30. Population synthesis I: nearby thermally emitting NS • LogN-LogS study of known NSs at d<3 kpc • Same underlying physical model, same magnetic field geometry, only varying strength. • Only ROSAT all sky survey with flux > 0.1 counts per second is ”complete”.

31. Population synthesis I: nearby thermally emitting NS Log-normal B field distributions

32. 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 (<1 kyr) (magnetar data from McGill online catalogue, Muno et al. estimates in shaded box) )

33. 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 ?

34. Population synthesis III: radio-pulsars Faucher-Guiguere and Kaspi (2006), no field decay Popov et al. (2009)

35. 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 ? • Simultaneous population synthesis studies of different classes are a promising method to constrain the initial field distribution and its evolution.