QPO Spectrum in Superfluid Magnetars. Andrea Passamonti INAF-Osservatorio di Roma. 6 March 2014 Kyoto
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1 QPO Specrum in Superfluid Magnears Andrea Passamoni INAF-Osservaorio di Roma 6 March 214 Kyoo Thursday, 6 March 214
2 References A. Passamoni & S. Lander MNRAS 429, 767 (213) A. Passamoni & S. Lander MNRAS 438, 156 (214) Thursday, 6 March 214
3 Magnears Neuron sars wih a srong magneic field B> 14 G, roaion period P~2-12 s and age ~ 3-4 yr. 4 abou 2 Magnears (AXP, SGR) The srong magneic field powers: - persisen X-ray emission L ~ erg s -1 - ouburss L ~ 41 erg s -1 in ~.1 s - gian flares L ~ erg s -1 - inermediae flares L ~ 42 erg s -1 in ~ 1 s Period Derivaive ( 13 s s 1 ) Period (s) This aciviy is powered by he energy of a srong magneic field. Thursday, 6 March 214
4 QPOs (Israel e al., 25; Srohmayer & Was, 25; Was & Srohmayer, 26) Observed in hree gian flares wih Eail ~ 44 erg SGR (1979): 44.5 Hz SGR (1998): P~5.2 s freq.: 28, 53, 84, 155 Hz SGR (24): P~7.6 s freq.: 18, 26, 3, 93,15, 626, 1837 Hz Possible seismic origin: Magneic field reconfiguraion fracures he crus producing magneoelasic waves. Thursday, 6 March 214
5 QPOs (Israel e al., 25; Srohmayer & Was, 25; Was & Srohmayer, 26) Observed in hree gian flares wih Eail ~ 44 erg SGR (1979): 44.5 Hz SGR (1998): P~5.2 s freq.: 28, 53, 84, 155 Hz SGR (24): P~7.6 s freq.: 18, 26, 3, 93,15, 626, 1837 Hz Possible seismic origin: Magneic field reconfiguraion fracures he crus producing magneoelasic waves. Thursday, 6 March 214
6 Observed in hree gian flares. Inerpreaion of QPOs Axisymmeric orsional Alfvén modes form coninuum bands. Levin (27) Crusal modes are quickly damped when heir frequencies lay ino he coninuum. van Hoven & Levin (211), Gabler e al. (212) More general classes of modes as non-axisymmeric modes or poloidal axisymmeric modes do no show a coninuum. Soani e al. (28), Lander, Jones and AP (2), Colaiuda & Kokkoas (212) van Hoven & Levin MNRAS 4, 36 (211) Thursday, 6 March 214
7 Observed in hree gian flares. Purely crusal oscillaions R cr R l f l f n Axisymmeric orsional Alfvén modes form coninuum bands. Crusal modes are quickly damped when heir frequencies lay ino he coninuum. Inerpreaion of QPOs Levin (27) van Hoven & Levin (211), Gabler e al. (212) More general classes of modes as non-axisymmeric modes or poloidal axisymmeric modes do no show a coninuum. Soani e al. (28), Lander, Jones and AP (2), Colaiuda & Kokkoas (212) van Hoven & Levin MNRAS 4, 36 (211) Thursday, 6 March 214
8 Observed in hree gian flares. Inerpreaion of QPOs Axisymmeric orsional Alfvén modes form coninuum bands. Levin (27) Crusal modes are quickly damped when heir frequencies lay ino he coninuum. van Hoven & Levin (211), Gabler e al. (212) More general classes of modes as non-axisymmeric modes or poloidal axisymmeric modes do no show a coninuum. Soani e al. (28), Lander, Jones and AP (2), Colaiuda & Kokkoas (212) van Hoven & Levin MNRAS 4, 36 (211) Thursday, 6 March 214
9 Observed in hree gian flares. The srong B-field couples he crusal oscillaions wih he core leading o magneo-elasic waves Axisymmeric orsional Alfvén modes form coninuum bands. Inerpreaion of QPOs Levin (27) Crusal modes are quickly damped when heir frequencies lay ino he coninuum. van Hoven & Levin (211), Gabler e al. (212) More general classes of modes as non-axisymmeric modes or poloidal axisymmeric modes do no show a coninuum. Soani e al. (28), Lander, Jones and AP (2), Colaiuda & Kokkoas (212) van Hoven & Levin MNRAS 4, 36 (211) Thursday, 6 March 214
10 Observed in hree gian flares. The srong B-field couples he crusal oscillaions wih he core leading o magneo-elasic waves Axisymmeric orsional Alfvén modes form coninuum bands. Inerpreaion of QPOs Levin (27) Crusal modes are quickly damped when heir frequencies lay ino he coninuum. van Hoven & Levin (211), Gabler e al. (212) More general classes of modes as non-axisymmeric modes or poloidal axisymmeric modes do no show a coninuum. Soani e al. (28), Lander, Jones and AP (2), Colaiuda & Kokkoas (212) van Hoven & Levin MNRAS 4, 36 (211) Wha are he effecs of superfluidiy on he QPO specrum? Thursday, 6 March 214
11 Two-fluid model A zero emperaure superfluid sar may be described by a wo-consiuen sysem: 1) componen of superfluid neurons in he core and he inner crus 2) neural conglomerae of all he oher paricles Assumpions: Elecrons/muons in he core are coupled o he proons on very shor imescale. Vorices and fluxubes are sufficienly dense ha a smooh-averaging can be performed. Thursday, 6 March 214
12 Equaions of moion - Superfluid dynamics of magneised neuron sars (Glampedakis, Andersson, Samuelsson 211) Two-fluid mass and momenum conservaion equaions. Poisson and Inducion equaion. Two-fluids are coupled by he enrainmen which is a non-dissipaive process ha induces a relaive drag beween he superfluid consiuens. Srong enrainmen forces he fluid componens o co-move. Thursday, 6 March 214
13 Superfluidiy in Alfvén waves -Two-fluid decoupled sysem v s = µ v A = B ρ ρ p.5ρ p 4πρp Effec of enrainmen - In non-axisymmeric modes (models wihou crus) The oal effec wih composiion sraificaion and core s enrainmen. σ 6.3σ [ ( Np )] ( ε ) 1/2 ( xp () ) 1/2 where σ B ρ Thursday, 6 March 214
14 Axisymmeric oscillaions A.P. & Lander S. (214) MNRAS 438, 156 Sellar models wih magneic field and crus Consan proon fracion 2D-effecive FFT 5 r =.1 θ =.1 r =.94 θ =.1 r =.94 θ = Log ( PSD ) model A1 < 2.5 s C U U1 Log ( PSD ) U2 2.5 s < < 5 s U3-2 U4 U U Thursday, 6 March /2 ν / ( G ρ ).14
15 Axisymmeric oscillaions Role of enrainmen Bp~5 14 G 4 model A3 s < < 1.5 s 1.5 s < < 3 s Crus modes U 1 C U 4 U 2 U U 4 U 5 Log ( PSD ) 1-1 Alfvén modes ν ν / ( G ρ ) 1/2 Thursday, 6 March 214
16 Axisymmeric oscillaions Role of enrainmen Bp~5 14 G 4 model A3 s < < 1.5 s 1.5 s < < 3 s Crus modes U 1 C U 4 U 2 U U 4 U 5 Log ( PSD ) 1-1 Alfvén modes ν ν / ( G ρ ) 1/2 Thursday, 6 March 214
17 Axisymmeric oscillaions Role of enrainmen Bp~5 14 G 4 model A3 s < < 1.5 s 1.5 s < < 3 s Crus modes U 1 C U 4 U 2 U U 4 U 5 Log ( PSD ) 1-1 Alfvén modes ν ν / ( G ρ ) 1/2 Thursday, 6 March 214
18 Axisymmeric oscillaions Role of enrainmen Bp~5 14 G 4 model A3 s < < 1.5 s 1.5 s < < 3 s Crus modes U 1 C U 4 U 2 U U 4 U 5 Log ( PSD ) 1-1 Alfvén modes ν ν / ( G ρ ) 1/2 Thursday, 6 March 214
19 Axisymmeric oscillaions Bp~15G 4 3 Log ( PSD ) 2 U 4 s < < 1.5 s 1.5 s < < 3 s 6 U3 U2 U1 U model A3 2 Some hybrid modes? ν / ( G ρ ) Thursday, 6 March /2.4.5
20 Hybrid magneo-elasic waves In a model wih enrainmen and composiion gradiens we find hybrid magneo-elasic waves for 5 14 G Bp 2 15 G ν < Hz Thursday, 6 March Hz < ν < 2 Hz
21 Conclusions Superfluid consiuens have a considerably impac on he oscillaion specrum of Magnears. The shear and Alfvén mode frequencies may be up o several imes larger. In model wih srong enrainmen in he crus, we can idenify a se of hybrid magneo-elasic oscillaions in he QPO range. The QPOs can be explained in superfluid sar by 3 14 G < Bp 15 G. In superfluid NS he high frequency QPOs ν > 5 Hz migh be overone of hybrid magneo-elasic waves excied by a resonance wih crus oscillaions. Thursday, 6 March 214
22 Fuure work Nex quesions o answer: Does he coninuum specrum sill persis in superfluid sars? Wha is he effec of superconduciviy on he QPO specrum? Wha is he equilibrium B-field configuraion of a Magnear? How he various sellar vibraions modulae he emission of he fireball rapped in he magneosphere? An X-ray observaory like LOFT will increase he resoluion of QPO iming and help heir analysis. Are here QPOs in inermediae flares? Thursday, 6 March 214
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