Neutrino emission from Goldstone modes in dense quark matter

Abstract

We calculate neutrino emissivities from the decay and scattering of Goldstone bosons in the color-flavorlocked ͑CFL͒ phase of quarks at high baryon density. Interactions in the CFL phase are described by an effective low-energy theory. For temperatures in the tens of keV range, relevant to the long-term cooling of neutron stars, the emissivities involving Goldstone bosons dominate over those involving quarks, because gaps in the CFL phase are ϳ100 MeV while the masses of Goldstone modes are on the order of 10 MeV. For the same reason, the specific heat of the CFL phase is also dominated by the Goldstone modes. Notwithstanding this, both the emissivity and the specific heat from the massive modes remain rather small, because of their extremely small number densities. The values of the emissivity and the specific heat imply that the time scale for the cooling of the CFL core is ϳ10 26 yr, which makes the CFL phase invisible as the exterior layers of normal matter surrounding the core will continue to cool through significantly more rapid processes. If the CFL phase appears during the evolution of a protoneutron star, neutrino interactions with Goldstone bosons are expected to be significantly more important since temperatures are high enough (ϳ20-40 MeV) to admit large number densities of Goldstone modes.

Effective theory of the color-flavor-locked phase

“…(2) can also be used to compute many physical properties of the CFL phase. In recent work [19,20] we considered the specific heat, neutrino emission and neutrino scattering in the CFL phase. At energies E < ∆ these processes are dominated by Goldstone modes.…”

Photon emission from dense quark matter

“…This, in particular, implies that for an outgoing photon its (positive) energy E is always larger than E 1 and therefore E 2 > 0, that is, the Bremsstrahlungsprocess π(p 1 ) → π(p 2 ) γ(q) is not possible. 9 A similar discussion of the in-medium pion dispersion effects pertains to processes that contribute to the mean free path. As we have already pointed out in the previous Section, at a temperature corresponding to the pion mass the pion-induced mean free path exhibits a rather sharp decrease.…”

“…The (anomalous) neutral pion decay, π 0 → γ γ, has been considered in Ref. [9] for low temperatures of O (0.1 MeV), where the emissivity was found to be exponentially suppressed. For completeness, we have repeated the calculation for the larger temperatures we are interested in here.…”

“…It is therefore vital to address the question in how far the existence of CSC inside compact stars affects their properties, such as neutrino and photon emission as well as thermal evolution. Pertinent studies have recently been carried out for CSC phases in various scenarios [9,10,11]. Ref.…”

“…Ref. [9] mostly addressed neutrino emission for CFL matter at temperatures in the sub-MeV range (∼0.1 MeV or 10 9 Kelvin) relevant to the long-term evolution of a compact star. In Ref.…”