Constraining $$f({\mathcal {R}})$$ gravity by Pulsar SAX J1748.9-2021 observations

Abstract

Abstract We discuss spherically symmetric dynamical systems in the framework of a general model of $$f(\mathcal{R})$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>f</mml:mi> <mml:mo>(</mml:mo> <mml:mi>R</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> gravity, i.e. $$f(\mathcal{R})=\mathcal{R}e^{\zeta \mathcal{R}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>f</mml:mi> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>R</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>=</mml:mo> <mml:mi>R</mml:mi> <mml:msup> <mml:mi>e</mml:mi> <mml:mrow> <mml:mi>ζ</mml:mi> <mml:mi>R</mml:mi> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> , where $$\zeta $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ζ</mml:mi> </mml:math> is a dimensional quantity in squared length units [L $$^2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mrow/> <mml:mn>2</mml:mn> </mml:msup> </mml:math> ]. We initially assume that the internal structure of such systems is governed by the Krori–Barua ansatz, alongside the presence of fluid anisotropy. By employing astrophysical observations obtained from the pulsar S AX J1748.9-2021, derived from bursting X-ray binaries located within globular clusters, we determine that $$\zeta $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ζ</mml:mi> </mml:math> is approximately equal to $$\pm 5$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>±</mml:mo> <mml:mn>5</mml:mn> </mml:mrow> </mml:math> km $$^2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mrow/> <mml:mn>2</mml:mn> </mml:msup> </mml:math> . In particular, the model is capable of producing stable configurations for S AX J1748.9-2021, encompassing both its geometric and physical characteristics. We show that, within the framework of $$f(\mathcal{R})$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>f</mml:mi> <mml:mo>(</mml:mo> <mml:mi>R</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> gravity, the Krori–Barua ansatz establishes semi-analytical connections between the radial ( $$p_r$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>p</mml:mi> <mml:mi>r</mml:mi> </mml:msub> </mml:math> ) and tangential ( $$p_t$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>p</mml:mi> <mml:mi>t</mml:mi> </mml:msub> </mml:math> ) pressures, and the density ( $$\rho $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ρ</mml:mi> </mml:math> ). These relations are described as $$p_r\approx v_r^2 (\rho -\rho _{I})$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>p</mml:mi> <mml:mi>r</mml:mi> </mml:msub> <mml:mo>≈</mml:mo> <mml:msubsup> <mml:mi>v</mml:mi> <mml:mi>r</mml:mi> <mml:mn>2</mml:mn> </mml:msubsup> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>ρ</mml:mi> <mml:mo>-</mml:mo> <mml:msub> <mml:mi>ρ</mml:mi> <mml:mi>I</mml:mi> </mml:msub> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> and $$p_t\approx v_t^2 (\rho -\rho _{II})$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>p</mml:mi> <mml:mi>t</mml:mi> </mml:msub> <mml:mo>≈</mml:mo> <mml:msubsup> <mml:mi>v</mml:mi> <mml:mi>t</mml:mi> <mml:mn>2</mml:mn> </mml:msubsup> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>ρ</mml:mi> <mml:mo>-</mml:mo> <mml:msub> <mml:mi>ρ</mml:mi> <mml:mrow> <mml:mi>II</mml:mi> </mml:mrow> </mml:msub> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> . In this context, $$v_r$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>v</mml:mi> <mml:mi>r</mml:mi> </mml:msub> </mml:math> and $$v_t$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>v</mml:mi> <mml:mi>t</mml:mi> </mml:msub> </mml:math> denote the sound speeds in the radial and tangential directions, respectively. Meanwhile, $$\rho _I$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>ρ</mml:mi> <mml:mi>I</mml:mi> </mml:msub> </mml:math> pertains to the surface density, and $$\rho _{II}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>ρ</mml:mi> <mml:mrow> <mml:mi>II</mml:mi> </mml:mrow> </mml:msub> </mml:math> is derived from the model parameters. These connections are consistent with the equations of state derived from the best-fit solutions identified in the ongoing investigation. Notably, within the framework of $$f(\mathcal{R})$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>f</mml:mi> <mml:mo>(</mml:mo> <mml:mi>R</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> gravity where $$\zeta $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ζ</mml:mi> </mml:math> is negative, the maximum compactness, denoted as C , is inherently limited to values that do not exceed the Buchdahl limit. This contrasts with gen