On the occurrence and detectability of Bose-Einstein condensation in helium white dwarfs

TL;DR

This paper investigates whether Bose-Einstein condensation occurs in helium white dwarfs and if it can be detected through their cooling behavior, finding it unlikely to produce observable signals in most cases.

Contribution

It introduces a simplified modeling approach to assess Bose-Einstein condensation effects on white dwarf cooling, focusing on stellar mass and luminosity conditions.

Findings

Condensation effects are noticeable only in massive, low-luminosity white dwarfs.

Most helium white dwarfs, including those in NGC 6397, are unlikely to show signs of condensation.

Detecting Bose-Einstein condensation in white dwarfs remains extremely challenging.

Abstract

It has been recently proposed that helium white dwarfs may provide promising conditions for the occurrence of the Bose-Einstein condensation. The argument supporting this expectation is that in some conditions attained in the core of these objects, the typical De Broglie wavelength associated with helium nuclei is of the order of the mean distance between neighboring nuclei. In these conditions the system should depart from classical behavior showing quantum effects. As helium nuclei are bosons, they are expected to condense. In order to explore the possibility of detecting the Bose-Einstein condensation in the evolution of helium white dwarfs we have computed a set of models for a variety of stellar masses and values of the condensation temperature. We do not perform a detailed treatment of the condensation process but mimic it by suppressing the nuclei contribution to the equation of state by applying an adequate function. As the cooling of white dwarfs depends on average properties of the whole stellar interior, this procedure should be suitable for exploring the departure of the cooling process from that predicted by the standard treatment. We find that the Bose-Einstein condensation has noticeable, but not dramatic effects on the cooling process only for the most massive white dwarfs compatible with a helium dominated interior (\approx 0.50 M_\odot) and very low luminosities (say, Log(L/L_\odot) < -4.0). These facts lead us to conclude that it seems extremely difficult to find observable signals of the Bose-Einstein condensation. Recently, it has been suggested that the population of helium white dwarfs detected in the globular cluster NGC 6397 is a good candidate for detecting signals of the Bose-Einstein condensation. We find that these stars have masses too low and are too bright to have an already condensed interior.