Implications of the Conformal Constraint on Sound Speed on the Radius of PSR J0952–0607 within Rastall Gravity
W. El Hanafy, Adel Awad
Abstract
Abstract It has been shown that the nonminimal coupling between geometry and matter can provide models for massive compact stars that are consistent with the conformal bound on the sound speed, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mn>0</mml:mn> <mml:mo>≤</mml:mo> <mml:msubsup> <mml:mrow> <mml:mi>c</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>s</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msubsup> <mml:mo>≤</mml:mo> <mml:msup> <mml:mrow> <mml:mi>c</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> <mml:mrow> <mml:mo stretchy="true">/</mml:mo> </mml:mrow> <mml:mn>3</mml:mn> </mml:math> , where the core density approaches a few times the nuclear saturation density. We impose the conformal upper bound on the sound speed on Rastall’s field equations of gravity, with Krori–Barua potentials in the presence of an anisotropic fluid as a matter source, to estimate the radius of the most massive pulsar ever observed, PSR J0952–0607. For its measured mass M = 2.35 ± 0.17 M ⊙ , we obtain a radius R = 14.087 ± 1.0186 km as inferred by the model. We investigate a possible connection between Rastall gravity and the MIT bag model with an equation of state, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>p</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>r</mml:mi> </mml:mrow> </mml:msub> <mml:mo stretchy="false">(</mml:mo> <mml:mi>ρ</mml:mi> <mml:mo stretchy="false">)</mml:mo> <mml:mo>≈</mml:mo> <mml:msubsup> <mml:mrow> <mml:mi>c</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>s</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msubsup> <mml:mfenced close=")" open="("> <mml:mrow> <mml:mi>ρ</mml:mi> <mml:mo>−</mml:mo> <mml:msub> <mml:mrow> <mml:mi>ρ</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">s</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:mfenced> </mml:math> , in the radial direction, with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>c</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>s</mml:mi> </mml:mrow> </mml:msub> <mml:mo>=</mml:mo> <mml:mi>c</mml:mi> <mml:mrow> <mml:mo stretchy="true">/</mml:mo> </mml:mrow> <mml:msqrt> <mml:mrow> <mml:mn>3</mml:mn> </mml:mrow> </mml:msqrt> </mml:math> and a surface density ρ s slightly above the nuclear saturation density ρ nuc = 2.7 × 10 14 g cm –3 . The corresponding mass–radius diagram is in agreement with our estimated value of the radius and with astrophysical observations of other pulsars at 68% confidence level.