A universal critical accretion rate for black hole jet formation

Abstract

It has long been suspected that black hole accretion-outflow coupling is invariant from the stellar to supermassive scales. Stellar mass black hole accretion flows are known to launch jets and outflows as they transition through critical accretion rate thresholds, with values well constrained observationally owing to their short evolutionary timescales. In contrast, accretion flows in typical supermassive black hole (SMBH) systems (those in active galactic nuclei) evolve over thousands of years, making the critical transitions at which jets are launched impossible to constrain in individual systems. Tidal disruption events (TDEs) provide the unique opportunity to witness the birth and evolution of an accretion flow onto a SMBH which evolves on timescales of years. Here we show that TDEs launch outflows during a super-Eddington accretion phase and a second, physically distinct outflow, at a critical accretion rate of $L_{\rm crit} \approx0.02$ $L_{\rm Edd}$, the same as the critical accretion rate for state transitions observed in accreting stellar mass black holes. This work naturally explains the mechanism, observed properties, and detection rate for prompt and delayed outflows observed in TDEs, which until now have been open problems. More broadly, we demonstrate that SMBHs exhibit the same accretion-outflow coupling as stellar mass black holes and that the critical low accretion rate threshold for jet formation in black holes is scale invariant.

Figures (22)

• Figure 1: An example of the four steps in our analysis which constrain the accretion rate at outflow launch. Displayed is the TDE ASASSN-14li, all other sources are shown in the methods. Firstly, the radio spectra at multiple epochs are modelled to constrain the peak frequency, flux density, and optically-thin spectral slope (top left). Next, the constrained radio spectral properties are used to infer the outflow radius at each epoch - excluding epochs where the peak of the spectrum was unable to be constrained (black triangles) - which is then modelled to determine the outflow launch time (middle left). The optical, UV, and X-ray lightcurves of the TDE are modelled to constrain the disk properties over time (top right), from which the accretion rate evolution with time can be extracted (middle right). The accretion rate posterior is then sampled at the time of the outflow launch, and a posterior distribution for the accretion rate at the time of the outflow launch is obtained (bottom panel). The shaded regions on each plot indicate $1\sigma$ confidence intervals.
• Figure 2: The accretion rate of TDE accretion disks, normalised by the Eddington and presented on a log scale, at the time at which outflows were launched from the 10 TDE systems studied in this work. We split the outflows by prompt (pink) and delayed (purple). The total distribution is shown in blue, and is distinctly bi-modal. Every prompt flare is consistent with having been launched above $\dot m \sim 1$, while all delayed flares are consistent with being launched at $\dot m \sim 0.02$. Individual flares are shown by smoothed Gaussian profiles, while the full (numerical) distributions are shown by histograms.
• Figure 3: Population synthesis of TDEs, computed from a simulation of $N=10^6$ TDEs using the observationally constrained TDE black hole mass function. The upper panel shows the peak Eddington ratio reached in TDE disks, where $\simeq 42\%$ of TDE disks go super-Eddington (and can therefore produce prompt radio emission), comparable to the observed prevalence of $\sim 30-50\%$ (Alexander2020Anumarlapudi2024Somalwar2025Goodwin2025_eros) of prompt radio flares. The lower panel shows the time for TDE disks to reach $2\%$ Eddington (in blue), for which $\simeq 42\%$ to do within the first $7$ years (bounding the observational window of real TDEs). This is comparable with the observed prevalence of delayed flares $\sim 40\%$ (Cendes2024). In green we show the observed distribution of delayed flare launch times (computed in this work), which has near identical distribution median to that computed by population synthesis (vertical dotted lines).
• Figure 4: The 5-6 GHz observed radio lightcurves (black points) and the corresponding broken power-law model fits (pink) for each of the TDEs in which the rise indices were able to be constrained. The shaded regions indicate $1\sigma$ confidence intervals.
• Figure 5: The distribution of power-law rise indices for the "prompt" (pink) and "delayed" (purple) flare radio lightcurves modelled in Figure \ref{['fig:radio_lcs']}. On the left we show the two probability density functions, while on the right we show the cumulative distribution functions, highlighting the clearly distinct nature of the two distributions of rise index. This is strongly suggestive of two different physical mechanisms powering the two temporally distinct types of flares.