Radiation-pressure instability is an artifact of constant-$alpha$ closure. Implications for AGN disk tensions

Radiation-pressure instability is an artifact of constant-$alpha$ closure. Implications for AGN disk tensions
M. H. Naddaf, M. Ghasemnezhad, H. Ghanbarnejad, D. Hutsem’ekers, B. Czerny
arXiv:2606.31998v2 Announce Type: replace
Abstract: The standard $alpha$-disk formalism parametrizes turbulent angular momentum transport through a dimensionless coefficient $alpha$, assumed to be spatially and thermodynamically invariant. While analytically convenient, this assumption leads to the well-known thermal and viscous instabilities in radiation-pressure dominated (RPD) regions. We show that this instability is not the consequence of radiation pressure, but is due to enforcing a constant $alpha$ across distinct thermodynamic regimes. Requiring the steady thin-disk (TD) to remain thermally stable and single-valued in the $dot{M}$–$Sigma$ plane yields a necessary condition on the stress response, expressed as $eta_{rm x} equiv dlnalpha_{rm x},/,dln X > 4/7$, where $X equiv P_{rm gas}/P_{rm rad}$. The resulting viscosity law $alpha_{rm x} equiv alpha(X)$ emerges directly from the internal consistency of TD equations, without modifying the stress law or invoking any additional physics. $alpha_{rm x}$ removes the RPD unstable branch. The disk structure becomes smooth and globally single-valued, with higher $Sigma$ and $tau$ in the inner RPD disk, while preserving the standard effective-temperature profile. This increases thermal and inflow timescales, offering a natural route to accretion-state dependent variability without large-amplitude radiation-pressure limit cycles. It also motivates revisiting AGN disk tensions, including microlensing sizes and continuum reverberation lags with improved radiative-transfer modeling. The results show that the RPD instability, and possibly some associated AGN disk tensions, reflect an inconsistent viscosity closure.arXiv:2606.31998v2 Announce Type: replace
Abstract: The standard $alpha$-disk formalism parametrizes turbulent angular momentum transport through a dimensionless coefficient $alpha$, assumed to be spatially and thermodynamically invariant. While analytically convenient, this assumption leads to the well-known thermal and viscous instabilities in radiation-pressure dominated (RPD) regions. We show that this instability is not the consequence of radiation pressure, but is due to enforcing a constant $alpha$ across distinct thermodynamic regimes. Requiring the steady thin-disk (TD) to remain thermally stable and single-valued in the $dot{M}$–$Sigma$ plane yields a necessary condition on the stress response, expressed as $eta_{rm x} equiv dlnalpha_{rm x},/,dln X > 4/7$, where $X equiv P_{rm gas}/P_{rm rad}$. The resulting viscosity law $alpha_{rm x} equiv alpha(X)$ emerges directly from the internal consistency of TD equations, without modifying the stress law or invoking any additional physics. $alpha_{rm x}$ removes the RPD unstable branch. The disk structure becomes smooth and globally single-valued, with higher $Sigma$ and $tau$ in the inner RPD disk, while preserving the standard effective-temperature profile. This increases thermal and inflow timescales, offering a natural route to accretion-state dependent variability without large-amplitude radiation-pressure limit cycles. It also motivates revisiting AGN disk tensions, including microlensing sizes and continuum reverberation lags with improved radiative-transfer modeling. The results show that the RPD instability, and possibly some associated AGN disk tensions, reflect an inconsistent viscosity closure.