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

1. Magnetic field structure and evolution in NSs:Some 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.

2. 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 ?

3. Observations: The P-Pdot diagram

4. B and age estimates: magnetic dipole • Rotating Magnetic dipole • Emission

5. B and age estimates: magnetic dipole • Rotational energy loss • If born fast, P0< P

6. 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.

7. Alternative: Emission models How does a magnetized hot body radiate ? • Magnetic atmospheres ? • Magnetospheric processes ? • Solid/liquid surface. Gas undergoes a phase transition when T<Tcrit • Lai (2001) estimates Tcrit = 27 B122/5 (Fe) Revisited by Medin & Lai 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

8. Cyclotron resonant absorption or condensed surface ? T=106 K, B=1013 G a: angle between magnetic field and normal to the surface

9. Example: RX J0720: spectral fitting BB+Gaussian absorption line. But what is the absorption ? A condensed surface model with a dipolar field with B13=2.5 and polar temperature of 100 eV. Several models can explain the same spectrum.

10. 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.

11. 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

12. 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

13. 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 ?

14. 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/superconductor 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 ?)

15. Magneto-thermal evolution of NSs:Ingredients • 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 …

16. Thermal Diffusion (Energy balance equation): Effects of magnetic field

17. Cooling of weakly magnetized NSs Intensively studied (Page et al., Yakovlev & Pethick)

18. 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)

19. 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 A&A 2009

20. Joule heating ? Do the easy thing first: energy balance Prediction: slope=1/2 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.

21. Joule heating effective in many NSs ? Crust size = 1 km Bint = 10-15 x Bdip B decay time 1 Myr

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

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

24. 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

25. 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

26. B field evolution: weak field • B(pole)=1e13 G

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

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

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

30. Coupled B-T evolution • maximum B field for old NSs !! • higher fields = more heating = higher resistivity = faster decay

31. 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 ?

32. Population Synthesis studies: Motivation Question: we all agree we must compare models/theory with data/observations, buthow 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 won’t be biased by one particular data point or anomalous behaviour.

33. 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”.

34. Population synthesis I: nearby thermally emitting NS For Log-normal B field distributions, constraint on the number of high field NSs : 10% with B>1e14 G

35. 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) )

36. 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 ?

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

38. 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 ?