Radiative acceleration and composition of self-consistently launched jets from advective accretion discs around Kerr black holes

Kumar & Chattopadhyay (2017) constructed self-consistent, fully general-relativistic accretion–ejection solutions around Kerr black holes: a low-angular-momentum advective disc, generically containing a standing centrifugal shock, launches a bipolar jet from the post-shock disc along von-Zeipel surfaces computed from the disc solution itself. Their jets are purely thermally driven and purely electron–proton, and reach only $v_{\rm j\infty}\sim 0.35c$ even for spin $a_s=0.99$ — far below observed jet speeds — because the authors explicitly neglected heating and cooling processes, omitted any radiation field acting on the jet, and fixed the composition at the pure electron–proton value $\xi=1$. They themselves posed the next step: radiative acceleration of such self-consistently launched Kerr disc–jets, in the footsteps of Kumar et al. (2014). The follow-up literature built every ingredient separately — radiation driving with pair composition in Schwarzschild spacetime with prescribed conical jets (Vyas & Chattopadhyay), time-dependent radiatively driven jets in pseudo-relativistic metrics with injected bases (Joshi et al.), and magnetized inflow–outflow solutions in a pseudo-Kerr potential (Jana & Das) — but no work combines full-GR Kerr geometry, self-consistent launching from the post-shock disc, computed radiation momentum/energy deposition, and pair-enriched composition. The open problem is to construct that model and determine whether jets self-consistently launched from shocked advective Kerr discs can reach the observed mildly-to-highly relativistic terminal Lorentz factors, and how the jet solution classes, mass-outflow rates, and disc/jet shock structure change relative to the thermal, electron–proton case.

Background

Accretion of plasma onto black holes powers the most energetic steady phenomena in the universe, from X-ray binaries to quasars. Many of these systems, called microquasars (stellar-mass black-hole binaries) and active galactic nuclei (AGN, harbouring supermassive black holes), also produce jets — collimated, often relativistic outflows whose speeds reach Lorentz factors (the factor $\gamma = 1/\sqrt{1-v^2}$ of the flow, in units where $c=1$, which grows without bound as the flow speed approaches the speed of light) of a few to tens. Since a black hole has no solid surface or atmosphere, jets must originate from the accreting matter, and observations tie jet strength to the accretion state of the inner disc.

The standard thin accretion disc is cold, Keplerian and wholly subsonic, but a second regime matters near the hole: hot, geometrically thick, low-angular-momentum flows that are transonic (the infalling gas passes through a sonic point) and advective, meaning a substantial fraction of the dissipated and gravitational energy is stored in the gas and carried inward rather than promptly radiated. In such flows the centrifugal barrier can halt the supersonic infall at a standing shock; the compressed, hot gas behind it forms the post-shock disc (PSD), which behaves as the Comptonizing corona — the hot electron region that up-scatters seed photons into the X-ray band by repeated inverse Compton scattering — seen in X-ray spectra and, as numerical simulations have long shown, can deflect part of the accreting matter along the rotation axis to seed a bipolar jet.

Kumar & Chattopadhyay (2017; hereafter KC17) built such an accretion–ejection model in full general relativity around a Kerr black hole — the unique metric of a rotating uncharged black hole, parametrized by the dimensionless spin $a_s\in[-1,1]$. They integrated the advective disc equations along the equatorial plane for a relativistic multi-species equation of state (EoS) with a variable adiabatic index $\Gamma$ (Chattopadhyay & Ryu 2009), and simultaneously integrated the jet equations along von-Zeipel surfaces — surfaces of constant angular momentum and entropy in the Kerr geometry above the equatorial plane — whose foot points sit on the PSD, so that the jet streamline and cross-section are determined by the disc solution instead of being prescribed (for example as a cone). The jet plasma composition is measured by the parameter $\xi$: $\xi=1$ for a pure electron–proton plasma and $\xi\to 0$ for a pure electron–positron (lepton-dominated) plasma; lighter, pair-rich jets are easier to accelerate because the same momentum deposition buys more speed per unit mass. KC17 mapped the jet solution classes (shocked jets with multiple critical points, smooth transonic jets, and bound or 'failed' jets) across the disc specific energy $\mathcal{E}$, specific angular momentum $\lambda$, and spin, finding jet shocks only for $a_s>0.6$ and, crucially, that purely thermally driven electron–proton jets top out at $v_{\rm j\infty}\sim 0.35c$ — about an order of magnitude faster than pseudo-Newtonian thermal jets, but far from relativistic.

The reason for this shortfall is transparent: KC17 deliberately excluded radiative physics. The disc is treated adiabatically — in their words, 'we have not considered heating or cooling processes' — so no radiation field computed from the disc acts on the jet. Yet the adjacent literature shows each missing ingredient matters. In pseudo-Newtonian gravity, depositing the radiation momentum of a luminous advective disc onto a self-consistently launched thermal jet raises terminal speeds from a few hundredths of $c$ to $\sim 0.3c$ (Kumar, Chattopadhyay & Mandal 2014), and on lepton-dominated jets radiation can drive speeds in excess of $0.9c$ (Vyas et al. 2015). Radiation driving in full general relativity has been studied in Schwarzschild spacetime with prescribed conical jets and bases (Vyas & Chattopadhyay 2018, 2019), where Compton-scattering energy exchange even accelerates gravitationally bound jets. The dominant alternative jet-launching channel — magnetically driven outflows extracting disc orbital energy (the Blandford–Payne mechanism) or black-hole rotational energy (the Blandford–Znajek mechanism) — is a separate theoretical program requiring relativistic magnetohydrodynamics; KC17's solutions are stated to be valid for weakly magnetized or stochastic fields, and the authors posed the radiative extension, coupled to composition, as the natural next step for their framework.

Problem Statement

Construct steady, axisymmetric, self-consistent accretion–ejection solutions around Kerr black holes that extend Kumar & Chattopadhyay (2017) to include the radiative physics they omitted, and determine how radiation driving and jet composition change the jet outcome. Specifically: (i) treat the advective disc as dissipative, including the heating and cooling processes the source paper neglected, so that the emergent radiation field — the energy density, flux, and pressure, i.e. the moments of the radiation intensity in curved spacetime — is computed from the disc solution for disc luminosities $\ell$ from sub-Eddington to super-Eddington (in units of the Eddington luminosity, the luminosity at which radiation pressure on the accreting plasma balances gravity); (ii) launch the jet from the post-shock disc as in the source paper, with the jet streamline and cross-section given by the von-Zeipel surfaces determined by the disc solution rather than prescribed; (iii) include the momentum and energy deposition of the disc radiation field on the jet, in both the Thomson (elastic) and Compton-scattering regimes, including radiation drag; and (iv) retain the relativistic multi-species equation of state with variable adiabatic index while varying the jet composition from pure electron–proton ($\xi=1$) to lepton-dominated ($\xi\to 0$). For this model, map the accretion–ejection solution classes — shocked jets with multiple critical (sonic) points, smooth transonic jets, and bound or failed jets — across the disc specific energy $\mathcal{E}$, specific angular momentum $\lambda$, spin $a_s$, disc luminosity $\ell$, and composition, and quantify in each region: the jet terminal Lorentz factor, the relative mass-outflow rate (the ratio of the jet mass flux to the disc accretion rate), and the locations and stability of the accretion and jet shocks, each compared against the purely thermal $\xi=1$ solutions of Kumar & Chattopadhyay (2017). The central quantitative question: can bipolar jets self-consistently launched from shocked advective discs around Kerr black holes reach the observed mildly-to-highly relativistic terminal speeds (Lorentz factors of a few to tens) once radiative acceleration and pair-enriched composition are included, and in which regions of the parameter space?

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