Delta-resonances and hyperons in proto-neutron stars and merger remnants

Abstract

Abstract The equation of state (EoS) and composition of dense and hot $$\varDelta $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Δ</mml:mi> </mml:math> -resonance admixed hypernuclear matter is studied under conditions that are characteristic of neutron star binary merger remnants and supernovas. The cold, neutrino free regime is also considered as a reference for the astrophysical constraints on the EoS of dense matter. Our formalism uses the covariant density functional (CDF) theory successfully adapted to include the full $$J^P=1/2^+$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mi>J</mml:mi> <mml:mi>P</mml:mi> </mml:msup> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> <mml:mo>/</mml:mo> <mml:msup> <mml:mn>2</mml:mn> <mml:mo>+</mml:mo> </mml:msup> </mml:mrow> </mml:math> baryon octet and non-strange members of $$J^P=3/2^+$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mi>J</mml:mi> <mml:mi>P</mml:mi> </mml:msup> <mml:mo>=</mml:mo> <mml:mn>3</mml:mn> <mml:mo>/</mml:mo> <mml:msup> <mml:mn>2</mml:mn> <mml:mo>+</mml:mo> </mml:msup> </mml:mrow> </mml:math> decouplet with density-dependent couplings that have been suitably adjusted to the existing laboratory and astrophysical data. The effect of $$\varDelta $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Δ</mml:mi> </mml:math> -resonances at finite temperatures is to soften the EoS of hypernuclear matter at intermediate densities and stiffen it at high densities. At low temperatures, the heavy baryons $$\varLambda $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Λ</mml:mi> </mml:math> , $$\varDelta ^-$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>Δ</mml:mi> <mml:mo>-</mml:mo> </mml:msup> </mml:math> , $$\varXi ^-$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>Ξ</mml:mi> <mml:mo>-</mml:mo> </mml:msup> </mml:math> , $$\varXi ^0$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>Ξ</mml:mi> <mml:mn>0</mml:mn> </mml:msup> </mml:math> and $$\varDelta ^0$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>Δ</mml:mi> <mml:mn>0</mml:mn> </mml:msup> </mml:math> appear in the given order if the $$\varDelta $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Δ</mml:mi> </mml:math> -meson couplings are close to those for the nucleon-meson couplings. As is the case for hyperons, the thresholds of $$\varDelta $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Δ</mml:mi> </mml:math> -resonances move to lower densities with the increase of temperature indicating a significant fraction of $$\varDelta $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Δ</mml:mi> </mml:math> ’s in the low-density subnuclear regime. We find that the $$\varDelta $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Δ</mml:mi> </mml:math> -resonances comprise a significant fraction of baryonic matter, of the order of $$10\%$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>10</mml:mn> <mml:mo>%</mml:mo> </mml:mrow> </mml:math> at temperatures of the order of several tens of MeV in the neutrino-trapped regime and, thus, may affect the supernova and binary neutron star dynamics by providing, for example, a new source for neutrino opacity or a new channel for bulk viscosity via the direct Urca processes. The mass-radius relation of isentropic static, spherically symmetric hot compact stars is discussed.