How important are transport coefficients to learn about neutron stars?

Neutron stars are one of the most compact objects in the universe. They typically have one-two solar masses and radii of about ten kilometers. They are believed to have an onion-like configuration, with an atmosphere and two main layers, the crust and the core. The characterization of these layers is, however, still a matter of intense analysis.
One possible way to extract information on the structure of neutron stars is to study the dynamical processes that occur in their interior and the associated transport coefficients. A transport coefficient refers to the response of a system to some external perturbation. For example, the shear and bulk viscosities are associated to the resistance of the system to a deformation due to the shear and tensile stress, respectively. Other transport coefficients, such as the thermal or electrical conductivities, are related to the conduction of heat or electric current.
The determination of the transport mechanisms inside neutron stars depends crucially on their structure and it is fundamental for understanding, among others, the cooling, the damping of certain hydrodynamical modes (the r-modes) as well as the relaxation processes after accretion in binary systems or glitches.

Cooling of neutron stars
Neutron stars are formed at very high interior temperatures in the core of a supernova explosion. After an initial thermal relaxation stage, neutrino emission dominates the cooling of neutron stars until photon emission overtakes [1]. The thermal relaxation period, which lasts for the first hundred years, crucially depends on the thermal conductivity of the crust. As a consequence, the cooling of young neutron stars turns out to be very sensitive to the physics of the crust [2].

R-mode damping
R-mode oscillations are toroidal hydrodynamical modes that occur in rotating stars, the Coriolis force acting as their restoring force. These modes are generally unstable through their coupling to gravitational radiation emission. The r-modes, however, can be damped due to dissipative phenomena so that the star can rotate without losing angular momentum. The dissipative or viscous damping strongly depends on the interplay and characterization of the crust and the core of neutron stars [3].

Relaxation after accretion in binary systems or glitches
The physics of the crust determines its relaxation after the deposit of heat by accretion in a binary system [2]. Moreover, the structure of the core is fundamental for the analysis of the heat conduction mechanisms that take place in pulsars in their relaxation after a sudden increase of the rotation speed (glitch) [4].

Boundaries of the r-mode instability regions for different star compositions compared to pulsar data. It is depicted the standard static instability boundary compared to x-ray data with error estimates from different envelope models. The curves represent a 1.4 M¤ neutron star with standard viscous damping (long-dashed line) and with additional boundary layer rubbing at a rigid crust (dotted line), as well as 1.4 M¤ strange star (short-dashed line) and same with long-range NFL interactions causing enhanced damping (solid line). The thin curves show for the neutron star exemplarily the analytic approximation for the individual segments. The encircled points denote the only milisecond-radio pulsar J0437-4715 with a temperature estimate and the only LMXB IGR J00291+5934 that has been observed to spin down during quiescence.

Boundaries of the r-mode instability regions for different star compositions compared to pulsar data. It is depicted the standard static instability boundary compared to x-ray data with error estimates from different envelope models. The curves represent a 1.4 M¤ neutron star with standard viscous damping (long-dashed line) and with additional boundary layer rubbing at a rigid crust (dotted line), as well as 1.4 M¤ strange star (short-dashed line) and same with long-range NFL interactions causing enhanced damping (solid line). The thin curves show for the neutron star exemplarily the analytic approximation for the individual segments. The encircled points denote the only milisecond-radio pulsar J0437-4715 with a temperature estimate and the only LMXB IGR J00291+5934 that has been observed to spin down during quiescence. Reference: M.G. Alford and K. Schwenzer, What the Timing of Millisecond Pulsars Can Teach us about Their Interior, Phys. Rev. Lett. 113, no. 25, 251102 (2014); doi:10.1103/PhysRevLett.113.251102

 

Observational estimates of neutron star temperatures and ages together with theoretical cooling simulations for M=1.4M¤. The green error boxes indicate sources from which thermal optical emissions have been observed in addition to thermal x-rays. Simulations with Fe (H) envelopes are displayed by solid (dashed) curves; those including (excluding) the effects of superfluidity are in red (blue). The upper four curves include cooling from modified Urca processes only; the lower two curves allow cooling with direct Urca processes and neglect the effects of superfluidity. Models forbidding direct Urca processes are relatively independent of M and superfluid properties. The yellow region encompasses cooling curves for models with direct Urca cooling including superfluidity. Reference: J.M. Lattimer and M. Prakash, The physics of neutron stars, Science 304, 536 (2004); doi:10.1126/science.1090720

Observational estimates of neutron star temperatures and ages together with theoretical cooling simulations for M=1.4M¤. The green error boxes indicate sources from which thermal optical emissions have been observed in addition to thermal x-rays. Simulations with Fe (H) envelopes are displayed by solid (dashed) curves; those including (excluding) the effects of superfluidity are in red (blue). The upper four curves include cooling from modified Urca processes only; the lower two curves allow cooling with direct Urca processes and neglect the effects of superfluidity. Models forbidding direct Urca processes are relatively independent of M and superfluid properties. The yellow region encompasses cooling curves for models with direct Urca cooling including superfluidity.
Reference: J.M. Lattimer and M. Prakash, The physics of neutron stars,
Science 304, 536 (2004); doi:10.1126/science.1090720

 

References
[1] D.G. Yakovlev and C.J. Pethick, Neutron star cooling, Ann. Rev. Astron. Astrophys. 42, 169 (2004), doi:10.1146/annurev.astro.42.053102.134013
[2] N. Chamel and P. Haensel, Physics of Neutron Star Crusts, Living Rev. Rel. 11, 10 (2008), doi:10.12942/lrr-2008-10
[3] N. Andersson and K.D. Kokkotas, The R mode instability in rotating neutron stars, Int. J. Mod. Phys. D 10, 381 (2001), doi:10.1142/S0218271801001062
[4] M.B. Larson and B. Link, Simulations of glitches in isolated pulsars, Mon. Not. Roy. Astron. Soc. 333, 613 (2002), doi:10.1046/j.13658711.2002.05439.x;
P.S. Shternin and D.G.Yakovlev, Electron-muon heat conduction in neutron star cores via the exchange of transverse plasmons, Phys. Rev. D 75, 103004 (2007), doi:10.1103/PhysRevD.75.103004

 
Author: Laura Tolos
 

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