SUPERFLUID MAGNETARS AND QPO SPECTRUM

Transcription

1 SUPERFLUID MAGNETARS AND QPO SPECTRUM Andrea Passamonti Osservatorio Astronomico di Roma INAF. In collaboration with L. Stella, S. Lander SAIt Bologna 9/5/23

2 Magnetars Neutron stars with a strong magnetic field B> 4 G, rotation period P~2-2 s and age ~ 3-4 yr. The strong magnetic field powers: - persistent X-ray emission L ~ erg s - - outbursts L ~ 4 erg s - in ~. s - giant flares L ~ erg s - - intermediate flares L ~ 42 erg s - in ~ s Neutron stars are cosmic laboratories where matter is at extreme conditions (supernuclear densities in the core, high magnetic fields, superfluid/superconducting constituents, etc.) Main motivations Reproduce QPO spectrum. Extract Magnetar properties via Astereoseismology.

3 Magnetar Population about 2 Magnetars (AXP, SGR) 4-2 low B-field magnetars. - some showing pulsed radio emission. High B-field pulsars - in 28 one showed X-ray outbursts. Period Derivative ( 3 s s ).. 3 Are the magnetar properties shared by a wider neutron star population? (Pons & Rea, 2) 4. Period (s) What is the internal B-field configuration? Bt Bp?

4 QPOs (Israel et al., 25; Strohmayer & Watts, 25; Watts & Strohmayer, 26) Observed in three giant flares with Etail ~ 44 erg SGR (979): 44.5 Hz SGR 9+4 (998): P~5.2 s freq.: 28, 53, 84, 55 Hz SGR 86-2 (24): P~7.6 s freq.: 8, 26, 3, 93,5, 626, 837 Hz Possible seismic origin, but the strong B-field couples the crustal oscillations with the core leading to magneto-elastic waves.

5 QPOs (Israel et al., 25; Strohmayer & Watts, 25; Watts & Strohmayer, 26) Observed in three giant flares with Etail ~ 44 erg SGR (979): 44.5 Hz SGR 9+4 (998): P~5.2 s freq.: 28, 53, 84, 55 Hz SGR 86-2 (24): P~7.6 s freq.: 8, 26, 3, 93,5, 626, 837 Hz Possible seismic origin, but the strong B-field couples the crustal oscillations with the core leading to magneto-elastic waves.

6 Superfluidity Magnetar core becomes superfluid after few hundred years (Ho et al. 2) - Theory nuclear physics calculations determine energy gaps for neutrons and protons. - Observations a) Pulsar glitches: transfer of angular momentum between superfluid and crust. 9 T C/ K = b) NS cooling of Cas A: enhanced neutrino emission due to braking and formation of Cooper pairs (PBF process). Page et al (2), Shternin et al. (2). 2. Critical temperature: superconducting protons superfluid neutrons T pn K T cn K

7 Approach Two-fluid model: a zero temperature system may be reduced to twoconstituents: a component of superfluid neutrons in the core and the inner crust, and a neutral conglomerate of all the other particles. Method: Linear perturbation theory of a two-fluid equilibrium configuration. - Background model: two-fluid stars with strong magnetic field and elastic crust. - Entrainment: dynamical coupling between superfluid neutrons and protons due to the strong interaction. - Time evolutions of two-fluid dynamical equations: 2D-numerical simulations.

8 Oscillation modes Classification is based on the main restoring force acting on the displaced fluid element Alfvén speed v A = B 4πρp Typical Upper QPOs Eigenfunctions Shear wave speed v s = µ ρ p Superfluidity may affect the spectrum determined in normal matter neutron stars Alfvén modes Entrainment Crustal modes ν[hz]

9 Preliminary Results Passamonti A. & Lander S. (23) MNRAS 429, 767 We find the expected frequency scaling: Passamonti A. & Lander S. (23) in preparation σ = ε x p σ Entrainment The total effect leads to σ 6.3σ [ ( Np )] ( ε ) ( /2 xp () 2.3. ) /2 where σ B ρ

10 Astereoseismology From the identification of the oscillation modes in QPOs we can extract several properties of Magnetars. Magnetic field strength. Superfluid parameters (entrainment). Mass and Radius EOS? Crust properties?

11 Conclusions Superfluid constituents have a considerably impact on the oscillation spectrum of Magnetars. The shear and Alfvén mode frequencies may be 6 times larger. Open questions: Does the continuum spectrum still persist in superfluid stars? What is the effect of superconductivity on the QPO spectrum? What is the equilibrium B-field configuration of a Magnetar? Model the dynamics of neutron stars and its magnetosphere. LOFT will increase the resolution of QPO timing.

12 Superfluid Magnetars and QPO spectrum Andrea Passamonti INAF-Osservatorio Astronomico di Roma,Via Frascati 33, 44 Rome, Italy Abstract The analysis of Quasi Periodic Oscillations (QPOs) in Magnetars provides the first application of Asteroseismology in neutron stars. These oscillations are likely identified with magneto-elastic waves which originate from giant flares. As recent cooling calculations show the heat generated by magnetic field decay does not prevent the superfluid transition of the magnetar s core. Therefore realistic models of magnetars should include superfluid/superconducting constituents. This project aims at studying superfluid and magnetised neutron stars in GR showing the effect of superfluidity on the QPO spectrum. The results will be used to match the QPO observations and constrain the equations of state of dense nuclear matter and superfluid physics of neutron stars. Introduction QPO spectrum Magnetars are very active X-ray neutron stars (NSs) characterised by a persistent emission, sporadic bursts and flares which are powered by the strongest magnetic field observed in the Universe, B ~ 4 G []. According to the current model, the radiation is caused by the magnetic field evolution which strains the crust and produces fractures and starquakes. Several Quasi Periodical Oscillations (QPOs) have been revealed in the tail of three giant flares. They likely have seismic origin and provide a data set of extraordinary value for the application of Asteroseismology in neutron stars and therefore extract important information about the neutron star physics. - What are the effects of superfluidity on the magnetar QPOs? - How stellar oscillations propagate through the magnetosphere and influence the radiative processes? - What is the geometry of a stable magnetic field in NSs? - As Fig. 2 shows, each QPO appears at different times in the giant flare tail and has different duration. What is the mechanism under this behaviour? Is it due to non-linear coupling between various oscillation modes excited during the flare? Observations About 2 magnetars have been observed so far (Fig.) in which a strong magnetic field powers: - persistent X-ray emission L ~ erg s- - outbursts L ~ 4 erg s- in ~. s - giant flares L ~ erg s- - intermediate flares L ~ 42 erg s- in ~ s Magnetar s oscillations are studied by using linear perturbation theory. From the dynamical point of view a cold superfluid star can be considered as a two-fluid system [6]. In the NS core the constituents are superfluid neutrons and a neutral conglomerate of charged particles (protons and electrons), while in the inner crust a gas of superfluid neutrons permeates a lattice of heavy ions (Fig. 3). Fig. 3: Schematic structure of neutron stars The equilibrium configuration is a two-fluid non-rotating relativistic neutron star with a strong magnetic field and an elastic crust. εn= εp= Unstratified model Poloidal field: B = G polar-led modes - The linearised dynamical equations are evolved in time with a twodimensional (in space) numerical code. 5 Preliminary Results Superfluid physics affects considerably the QPO spectrum. Magnetoelastic mode frequencies may be up to 6 times larger than the values determined with no-superfluid models [3] (Fig.4). xp =. /2 The aim of this project is to study more realistic magnetar models in order to reproduce the QPO properties and answer to the following open questions: Approach ν / ( G ρ ) Scientific aims Fig. 2: Detectability periods of QPOs in the giant flare of SGR86-2 (Strohmayer T.E. & Watts A.L., (26) ApJ 653, 593). ν [Hz] After few hundreds years from the magnetar s birth the neutrons and protons of the core are in a superfluid/ superconducting state [2], as the heating generated by magnetic field decay does not prevent the star from cooling down below the superfluid transition temperature T 9 K. The dynamics of a superfluid/superconducting system is more complex and affect significantly the oscillation spectrum and therefore the QPO identification [3,4]. At the frequency band of QPOs, the spectrum is mainly characterised by a set of shear and Alfvén modes which are sustained, respectively, by crust elasticity and the star s magnetic field. For a strong magnetic field these two classes of modes are efficiently coupled and are commonly considered as a unique class of magneto-elastic modes (see [5] for a review). -fluid limit Due to the shift of magneto-elastic modes at higher frequencies the magnetic field requires to explain QPOs is weaker than previously determined /2 ε* Fig. 4: Effects of superfluid entrainment on Alfvén non-axisymmetric modes [3]. - A strong entrainment at the bottom of the inner crust mainly influences the crust s oscillation modes and can change the identification of the various QPOs [4]. Conclusions 4 In the near future new detectors will collect data in the electromagnetic and gravitational-wave spectrum, opening and era of multi-messenger astronomy. In the X-ray band, satellites like LOFT may provide excellent quality timing data on flaring magnetars and accreting neutron stars. This theoretical project will be necessary to interpret the new data from various observation channels and infer the stellar parameters from astrophysical observations. Period Derivative ( 3 s s ). Preliminary results show the superfluid physics has a relevant impact on NS dynamics and is therefore a key ingredient for the interpretation of magnetar QPOs.. 3 Fig. 5 typical eigenfunction of a magneto-elastic mode [4]. 4. Fig. : Magnetar population (red stars) in the P-dP/dt diagram. In the tail of three giant flares have been also revealed a series of Quasi-Periodic Oscillations modulated by the star s rotation (see Fig. 2). The QPO frequencies are:!sgr (979): ν = 44.5 Hz!SGR 9+4 (998): ν = 28, 53, 84, 55 Hz!SGR 86-2 (24): ν =8, 26, 3, 93,5, 626, 837 Hz Acknowledgements Period (s) References [] Mereghetti S., (28) A&A Rev., 5, 225 [2] Ho W. C. G., Glampedakis K., Andersson N., (22) MNRAS, 422, 2632 [3] Passamonti A. & Lander S. (23) MNRAS 429, 767 [4] Passamonti A. & Lander S. (23) in preparation [5] Watts A.L., 2, arxiv:.54 [6] Andersson N. & Comer G.L. 27, Living Rev. Relativity The research leading to these results has received funding from the European Union Seventh Framework Programme (FP7/27-23) under grant agreement n Astronomy Fellowships in Italy (AstroFIt).