What do oscillations of magnetars tell us about their magnetic fields?

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1 What do oscillations of magnetars tell us about their magnetic fields? M. Gabler, E. Mu ller, P. Cerda -Dura n, T. Font, N. Stergioulas PRL, 111, 2013 MNRAS, 430, 2013 MNRAS, 421, 2012 MNRAS, 410, 2011

2 QPOs in giant flares of magnetars Giant flares SGR (1978), SGR (1998), SGR (2004) Strong modulation rotation period ( s) Additional quasi periodic oscillations (QPOs) (Israel et al. 2005, Strohmayer & Watts 2006, El-Mezeini & Ibrahim 2010, Hambaryan et al. 2011) QPO in intermediate flares: 93, 127 and 260Hz (Huppenkothen et al. 2014) Strohmayer & Watts 2006 Confirmed QPO frequencies SGR : 18, 26, 30, 92, , 1840 Hz SGR : 28, 53, 84, 155 Hz

3 Where do the QPOs come from? Are they Starquakes? Neutron Star Mass ~ 1.5 times the Sun diameter ~ 20 km Solid crust ~ km Magnetic field ~ G Heavy liquid core, mostly neutrons, with other particles Possible origin of the observed frequencies Discrete Shear modes (crust)? Alfvén oscillations at the turning points of a continuum (core+crust)? Magnetospheric oscillations? Coupled Crust-Core oscillations (Glampedakis et al. 06; Levin 07; Van Hoven & Levin 11 & 12; Colaiuda et al. 10 & 11 & 12; Gabler et al. 11 & 12)

4 Magneto-elastic QPOs inside the magnetar predominantly shear modes shear modes strongly damped magneto-elastic QPOs confined to core reach surface predominantly Alfvén QPOs

5 Identifying observed frequencies Frequency ratio of magneto-elastic QPOs (odd, even): 1 : 2 : 3 : 4 : 5 :... SGR : SGR : 18, 26, 30, 92, 150, 625, 1840 Hz 28, 53, 84, 155 Hz

6 Low and High frequency QPOs Low frequencies 150 Hz 18, 26, 30, 92, 150, 28, 53, 84, 155 High frequencies > 500 Hz 625, 1840 Without magnetic field n=0 Crustal shear modes n=1 Normal fluid, no crust, B > G Alfvén QPOs Normal fluid, with crust, B > G Global magneto-elastic QPOs Superfluid, no crust, B > G Alfvén QPOs

7 Superfluid neutron star core - one-fluid approximation Effective one fluid model (decoupling n from p): ρ ρ p 0.05ρ v 2 A = B2 ρ B2 ρ p Fundamental QPOs Exist as before but with: f sf 1 t A v A R To match observed QPOs: PṖ estimate: B R ρ p B G B R 0.05ρ 5 f n B G Andersson et al. 09, Glampedakis et al. 11, vanhoven & Levin 11 & 12, Michael Passamonti Gabler & Lander 13 Magnetar oscillations NS Workshop, Bonn, 27/10/2014

8 Superfluid neutron star core - High frequency QPOs High frequency QPOs Long-lived QPOs at f f n=1 crust Normal fluid n = 1 radial shear mode structure Localized close to equatorial plane ˆB ˆr predominantly shear mode only in crust Superfluid n = 1 radial shear mode structure Close to pole Resonance with Alfvén overtone of core Y [km] Superfluid Normal fluid X [km] X [km] 10

9 Identifying observed frequencies Frequency ratio of low frequency magneto-elastic QPOs (odd, even) is roughly 1 : 2 : 3 : 4 : 5 :... Different magnetic field configurations give more than one fundamental High frequency QPO as resonance of higher Alfven overtone in core with n > 0 crustal mode if core is superfluid SGR : (18), 26, 30, 92, 150, 625, 1840 Hz SGR : or 28, 53, 84, 155 Hz 28, 53, 84, 155 Hz

10 Magnetic fields confined to crust Frequency [Hz] µ s µ s /2 µ s /4 µ s /8 µ s /16 µ s /100 30Hz 26Hz 18Hz 1 10 Averaged surface magnetic field strength [10 14 G] No damping into core possible For low B shear-mode-like QPOs Frequencies increase with B cannot explain observed QPO frequencies

11 Mixed multipolar fields Minimal dipole-moment given by spin-down formula Additional higher moment possible Y [km] X [km] X [km] X [km] X [km] X [km] B dipole [10 15 G] (SGR ) B1 30Hz B2 30Hz B dipole (SGR ) Quadrupole / Dipole Different global configuration + local strength Different Spectrum Strong quadrupolar component decreases necessary dipolar component to match f 30 Hz

12 Conclusions n = 0 crustal shear modes are damped efficiently Fundamental magneto-elastic QPOs can explain low frequency QPOs Fields confined to crust: cannot reproduce all QPOs Quadrupole dominated fields: hard to reproduce all QPOs Inclusion of superfluid effects: Low and high frequency QPOs B estimates in agreement with spin down observations For the first time in a realistic magnetar model we can explain both groups of frequencies: QPOs of SGRs are probably superfluid magneto-elastic QPOs