Thermodynamic fluctuations and radiation properties around Schwarzschild black holes immersed in Hernquist dark matter halo

Abstract This study investigates the dynamics of circular motion and radiative properties of particles orbiting Schwarzschild black holes embedded in a Hernquist dark matter halo. By integrating the Hernquist potential with the Schwarzschild spacetime, we model the combined gravitational effects of the black hole and the surrounding dark matter distribution. We derive the conditions for stable circular orbits, analyzing the impact of dark matter parameters characteristic density $$\rho _s$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>ρ</mml:mi> <mml:mi>s</mml:mi> </mml:msub> </mml:math> and core radius $$r_s$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>r</mml:mi> <mml:mi>s</mml:mi> </mml:msub> </mml:math> on the effective potential, innermost stable circular orbit, and energy efficiency of accretion processes. Additionally, we explore the thermodynamic properties, including Hawking temperature, entropy, and corrected thermodynamic potentials under thermal fluctuations, highlighting the influence of the dark matter halo. Using the Novikov–Thorne model, we examine the electromagnetic flux, temperature profile, and differential luminosity of thin accretion disks, revealing enhanced energy output and spectral shifts due to the Hernquist profile. Our results demonstrate that the dark matter halo significantly modifies orbital dynamics, reduces the ISCO radius, and enhances radiative emissions compared to the Schwarzschild case. These findings provide critical insights into the interplay between dark matter and black hole environments, with implications for high-resolution observations of galactic centers and active galactic nuclei.