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Determining cosmological growth parameter for stellar-mass black holes

Ema MlinarToma\v{z} Zwitter
Nov 2023
It has recently been suggested that black holes (BH) may exhibit growth of their mass with time, so that their mass is proportional to the cosmological scale factor to the power $n$, with suggested values $n \sim 3$ for supermassive BHs in elliptical galaxies. Here we test these predictions with stellar mass BHs in X-ray binaries using their masses and ages. We perform two sets of tests to assess the compatible values of $n$. First, we assume that no compact object grows over the Tolman-Oppenheimer-Volkof limit which marks the borderline between neutron stars and BHs. We show that half of the BHs would be born with a mass below this limit if $n=3$ applies. The possibility that all BHs were born above the limit is rejected at $4\,\sigma$ if $n=3$ applies. In the second test, we assume that masses of BHs at their formation stay the same over cosmic history. We compare the mass distribution of the youngest BHs, which could have not grown yet, to their older counterparts. Distributions are compatible for $n = -0.8^{+1.2}_{-4.5}$, with $n=3$ excluded with $87\,\%$ confidence. This result may be biased, as massive BHs tend to have a massive companion. Correcting for this bias yields $n\sim 0$. We conclude that mass and age estimates of stellar mass BHs are incompatible with cosmological growth with $n \sim 3$ and favor their mass not changing with time.
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