Brown dwarfs in Eddington-inspired Born-Infeld and beyond Horndeski theories

Abstract

We studied herein the mass and the radius of brown dwarfs predicted by beyond Horndeski (BH) and Eddington-inspired Born-Infeld (EiBI) gravity theories by numerically solving the modified non-relativistic hydrostatic equations of both theories. We used a recent compilation of brown dwarf masses and radii obtained from Ref. Bayliss et al. (Astrophys J 153:1, 2016) to constrain the free parameter of both theories. We obtain the range of the corresponding parameters with 1σ and 5σ confidence by using chi-squared analysis. Furthermore, the minimum chi-squared values can be reached for the cases of κ = 0.17 × 10 2 m 5 kg −1 s −2 and γ = −0.1207 for EiBI and BH theories, respectively. The corresponding parameter values with the minimum chisquared values are relatively small; therefore, they cannot significantly change the brown dwarf mass limits determined from the equivalence of nuclear and photosphere luminosities for the pp (hydrogen burning) and pp+pd (deuterium burning) reactions.

Parameterized nonrelativistic limit of stellar structure equations in Ricci-based gravity theories

“…Many recent works in the field have shown the viability of the nonrelativistic stellar limit of modified theories of gravity to obtain specific predictions of these theories that can be accessible via astronomical observations. Prominent among them are the limiting masses between different kinds of dwarf and main-sequence stars [31][32][33][34][35][36][37][38][39][40][41][42]56]. These limits depend not only on the combination of astrophysical and nuclear physics modeling, but also on the underlying nonrelativistic equation employed, where modifications to the latter may slightly alter such limits and therefore yield new predictions and/or allow us to place constraints on the parameters of specific modified gravity theories.…”

“…are needed in order to achieve a realistic description of their structure, simple analytical models are capable to provide reasonable estimates to some global properties of such nonrelativistic stars. Examples of this are the limiting masses, such as the Chandrasekhar mass for white dwarfs [30][31][32][33][34][35] or the minimum required mass for a star to stably burn hydrogen [36][37][38] and deuterium [39], but it may also have a nonnegligible impact in the description of the early evolution of low-mass stars [40], in the cooling process of brown dwarfs [41], and in age-estimation techniques such as those based on the lithium depletion method [42].…”

“…Regarding the description of stellar structure, RBGs are capable to modify the mass-radius relations of neutron stars, which allows to raise their maximum mass with realistic equation of state to match observations of neutron stars above two solar masses [51]; and also alter the Chandrasekhar's limit of white dwarfs, which might allow to address the existence of super-Chandrasekhar white dwarfs, whose masses are suggested to be up to two times the standard Chandrasekhar limit [52][53][54][55] (see chapter 3 of [28] for details on these issues). Moreover, the nonrelativistic limits of some RBGs have been recently employed to work out the minimum main sequence mass of quadratic fðRÞ gravity [56] and or the minimum deuterium burning mass for Eddington-inspired Born-Infeld gravity (EiBI, [39]), where the current modeling of these scenarios and their compatibility with observations still leaves some room for modifications of GR, becoming a source of strong constraints on the parameters of RBGs. Furthermore, studies related to low-mass stars in Palatini fðRÞ gravity [40,42] demonstrated that RBGs could also provide an explanation of the discrepancy between predicted and dynamical masses of the M dwarfs and pre-main sequence stars with masses below 0.5 solar masses [57,58].…”

From fundamental physics to tests with compact objects in metric-affine theories of gravity

“…For instance, as shown in Ref. [86] in the case of EiBI gravity, the combination of both limiting masses M MMSM and M MMDB via statistical analysis allows to constraint EiBI parameter as −1.59 × 10 2 ≤ ǫ ≤ 1.16 × 10 2 m 5 kg −1 s −2 . Finally, the radius plateu (the constancy of the star's radius with the mass) of low-mass brown dwarfs could be also another test for the predictions of these theories [87].…”

Invariant quantities of scalar–tensor theories for stellar structure

“…The advantage of introducing such quantities is also of different type: they allow to classify mathematically equivalent theories, since a class of conformally-related frames will yield the same values of invariants. Stars in the scalar-tensor theories framework, relativistic [65][66][67][68][69][70][71][72][73][74][75][76][77] and non-relativistic ones [78][79][80][81][82][83][84][85][86][87][88], were widely studied in literature; however, the invariant theory has not been applied yet to stellar objects. In this paper, we aim at using the results of [61] in order to analyze stellar structure in ST theories in a way independent of the choice of conformal metric.…”