Magnetar seismology. Lars Samuelsson, Nordita Nils Andersson, Southampton Kostas Glampedakis, Tübingen. NORDITA Hirschegg, January 2009

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1 Magnetar seismology Lars Samuelsson, Nordita Nils Andersson, Southampton Kostas Glampedakis, Tübingen

2 Outline Quasi-Periodic Oscillations in Soft Gamma-ray Repeaters. Can we do seismology? That is, can we invert the equation of state mode frequency relation? How well can we do seismology? How do we improve this? Conclusions

3 Application: Flares in Soft Gamma-Ray repeaters SGRs: persistent X-ray sources envisaged as magnetars B ~ G P ~ 1-10 s Key property: E mag >> E kin Three giant flares to date March 5, 1979: SGR August 27, 1998: SGR December : SGR T. Strohmayer & A. Watts, ApJ. 653 (2006) p.593 Flares are associated with large scale magnetic activity and crust fracturing Quasi-periodic oscillations discovered in the data

4 Observations SGR f QPO (Hz) f mode l n ? ? Newtonian limit, homogeneous stars, no dripped neutrons: Fundamental mode (n = 0): ? 1? 1840??? Overtones (n > 0): = crust thickness ~ 0.1 R Modes confined to the crust makes seismology doable.

5 Magnetic crust-core coupling The strong magnetic field threads both the crust and the fluid core (assuming non-type-i ancient superconductor...) The coupling timescale is the Alfvén crossing timescale Where is the Alfvén velocity and G Generic conclusion: If the crust is set to oscillate the magnetar s core gets involved in less than one oscillation period Pure crustal modes replaced by global MHD modes Puzzle: Why do we observe the seismic frequencies?

6 Toy model I [Glampedakis, LS, Andersson, MNRAS 371, L74 (2006)] Assume: uniform density, shear modulus and magnetic field, ideal MHD Correct MHD conditions at interface R c couple crust and core provided Key effect: crust-core resonance at the crustal frequencies:

7 Mode excitation Modes in the vicinity of a crustal mode frequency are preferable for excitation by a crustquake as they communicate minimum energy to the core: Consistent with QPO data Excitable modes below the fundamental crustal frequency Low frequency QPOs: Example: SGR Identify Hz Then: Hz Seismology may still work and may even tell us about the magnetic field.

8 The Alfvén continuum Consider the simplest fluid ball with a magnetic field (constant density, ideal MHD, constant B-field, clamped ) Look for global axial modes [~ exp(iωt)]. There are none! Are the QPO s of magnetodynamic origin? (Seismology will be difficult) Or, will the crust save the day? (Seismology possible) Note that v shear /v A ~ 1 B ~ (ρ I,14 ) 1/2 G

9 Magneto-elastics The problem is now global and is no longer spherically symmetric. Lee solved the problem by expanding the solutions in spherical harmonics Conclusion: at least some (most?) mode solutions appear to converge. The modes in which the kinetic energy dominates the magnetic have frequencies close to the shear modes. Large B-fields affect these modes. Status: Looking good. For now, assume that we can ignore the magnetic crust-core coupling.

10 Other couplings? GR couples also via matter currents. We have checked that the mode frequencies does not change importantly when gravity is properly taken into account. Rotation will also couple the core and crust. Vavoulidis et al. show that this does not affect the results appreciable for the slowly rotating magnetars. Caveat: Even with slow rotation we will have vortices connecting the crust and core.

11 Seismology exemplified by SGR frequency l n M=0.96M o R=11.4 km (720) 1837 (2387) ? 1 T. Strohmayer & A. Watts, astro-ph/

12 Model dependence: Superfluid neutrons Due to the static spherical background the neutron equation of motion become very simple. For non-static perturbations it amounts to The remaining equation is nearly identical to the purely elastic case. The only difference is that the frequency is multiplied by a factor

13 Modelling the QPOs: Input data 1.5! [g/cm 3 ] " #!"# x n m* (v A /v s ) 2 n /m n m * n /m n Eos by Haensel & Pichon, Douchin & Haensel Shear modulus (bcc) by Ogata & Ichimaru: n b [fm -3 ] Please improve this!

14 Seismology exemplified by SGR frequency l n M=1.05M o R=12.5 km (720) 1837 (2387) ? 1 T. Strohmayer & A. Watts, astro-ph/

15 Other model dependences: Shear moduli We have calculations for effective (angle averaged) bcc lattice, as functions of n b, composition and T. Monte Carlo by Ogata & Ichimaru Very recent Molecular Dynamics by Horowitz & Hughto gives reduction by ~ 10% What about the pasta? Anisotropic? Asymptotic behaviour near crust-core interface? This is critical for seismology!

16 Shear modulus & Neutron fraction

17 Other model dependences: Eos of the inner crust Examples: Douchin & Haensel vs Negele & Vautherin. M c = 1.4 Msun, R c = 10.5 km, Shear modulus by Horowitz & Hughto T=0 Factors of a few for both the Eos and m * Model n=0 [Hz] n=1 [Hz] DH, m * = DH, m * =fit DH, m * = NV, m * = NV, m * =fit NV, m * =

18 Other model dependences: Non-zero temperature Not so important unless near melting. But what about the superfluid?

19 Other model dependences: The local magnetic field Local effect: v 2 shear -> v2 shear + B2 /4π Toroidal field mainly affects the n = 0 modes. Poloidal field mainly affects the n > 0 modes. Big effects possible for B > G. Further global calculations necessary in order to pin down uncertainty.

20 Conclusions Seismic interpretation of the QPOs is in good shape The seismological analysis needs better input to be useful Many colleagues are working hard on this (please help them!) The potential return is a point in the mass radius diagram implying constraints for the high density equation of state (Prakash s talk)