Saswata Dasgupta, Boyuan Liu, Anastasia Fialkov, Furen Deng, Jiten Dhandha, Rennan Barkana

High-mass X-ray binaries are one of the primary drivers of the 21-cm signal from Cosmic Dawn and Reionization, playing a leading role in the thermal history of the intergalactic medium. In traditional semi-numerical simulations, a deterministic scaling relation between the total X-ray luminosity of high-mass X-ray binaries, $L_{\rm X}$, and star formation rate (SFR) is usually adopted. However, this assumption is inaccurate for high-redshift low-SFR regions hosting few sources. The spatial variation in the number and luminosity of these sources is expected to enhance fluctuations in the Cosmic Dawn 21-cm signal. Here we quantify this effect by introducing a stochastic $L_{\rm X}$ model sampled from a power-law X-ray luminosity function. Implementing this in 21cmSPACE, a large-scale simulation framework of Cosmic Dawn and Reionization, we find that the stochasticity leads to enhanced fluctuations in X-ray heating rate fields, and affects the 21-cm power spectrum on small scales ($k>0.3~ \mathrm{cMpc^{-1}}$). The impact of stochasticity on the global 21-cm signal and on the large-scale power spectrum is found to be negligible. Our results suggest these effects will remain undetected by the upcoming Square Kilometer Array. However, large-scale lunar-based experiments may be sensitive to the signatures of stochastic X-ray heating at $z\sim 25$. Quantifying these corrections is a vital step toward robust 21-cm modeling and ensuring that future precision data interpretation is free from astrophysical biases.