$νp$-process in Core-Collapse Supernovae: Imprints of General Relativistic Effects

TL;DR

The paper investigates how general relativistic (GR) corrections alter the νp-process in neutrino-driven outflows from core-collapse supernovae. By solving GR steady-state hydrodynamics in spherical symmetry and stitching tracer trajectories to the subsequent homologous ejecta, the authors post-process with SkyNet to quantify changes in p-nuclide production. They find that GR tends to suppress seed formation but enhances overall p-nuclide yields, enabling solar-system abundances up to $A\lesssim102$ for an $18\,M_\odot$ progenitor, and markedly boosting late-time isotopes like $^{92}$Nb by factors up to $\sim$25 compared to Newtonian calculations. The outcomes depend on progenitor mass, shock velocity, and the dynamical regime (subsonic vs transonic), with heavier progenitors more conducive to robust νp-processing under GR. The work highlights the critical role of GR corrections, blueshifted neutrino heating, and the evolving proto-neutron star radius in shaping nucleosynthetic yields relevant to solar abundances and meteoritic isotopes.

Abstract

The origin of a number of proton-rich isotopes in the solar system has been a long-standing puzzle. A promising explanation is the $νp$-process, which is posited to operate in the neutrino-driven outflows that form inside core-collapse supernovae after shock revival. While recent studies have analyzed several relevant physical effects that influence the efficiency of this process, the impact of General Relativity (GR) on it remains unexplored. We perform a comparative analysis of the time-integrated $νp$-process yields in Newtonian and fully GR calculations, using detailed models of time-evolving outflow profiles. The GR effects are seen to suppress the production of seed nuclei, significantly boosting the resulting $p$-nuclide abundances. Our reference GR model, with an 18~$M_\odot$ progenitor, reproduces both the relative and absolute solar system abundances of the entire set of the $p$ nuclides in the mass range $74\leq A\leq102$. The yields are suboptimal in our 12.75~$M_\odot$ GR model, where the outflow transitions to the supersonic regime several seconds into the explosion, suppressing further $p$-nuclide production. In both models, most of the production of the crucial $^{92,94}{\rm Mo}$ and $^{96,98}{\rm Ru}$ $p$ isotopes occurs relatively early, 1--3 seconds after shock revival. In contrast, a large fraction of the shielded isotope $^{92}{\rm Nb}$ is produced in the subsequent ejecta. The impact of GR on this isotope is especially large, with its final abundance boosted by a factor of 25 compared to a Newtonian calculation. In summary, with the GR effects taken into account, the $νp$-process in a sufficiently massive progenitor can provide a unifying explanation for the origin of all $p$ nuclei in the solar system up to $^{102}$Pd.

Figures (19)

• Figure 1: Radius of the PNS from the 1D CCSN code GR1DOConnor:2014sgn (black) and our fit defined in Eq. \ref{['eq:pns-fit']} (red) as functions of the time after bounce. The simulation is for an artificially exploding CCSN of a $15~M_{\odot}$ progenitor leaving a $1.8~M_\odot$ PNS. The crucial input to determining the PNS mass is the EoS which in this case is the modern SFHo Steiner:2012rkHempel:2009mc.
• Figure 2: Steady-state outflows with various degrees of relativistic corrections, plotted over radius at $t=2.5$ s for our benchmark $18~M_\odot$ progenitor model. For the temperature and density profiles we also show the relative difference (with the fully Newtonian as reference) in the inset. Newtonian profiles are in black and GR in red. Two classes of GR corrections are shown: those for the hydrodynamic equations and those for neutrino heating (redshift and geodesic bending together). All GR outflows, if not labeled otherwise, use the correct heating terms (with an initial blueshift from 500 km to the neutrinosphere radius), while Newtonian outflows using fully GR heating terms are labeled with 'blue'. Also shown is the homologous expansion behind the front shock, $v_h(r)=v_{\mathrm{FS}}~r/R_{\mathrm{FS}}$ (thin black line), used to determine the location where $P_f$ is imposed.
• Figure 3: Transonic GR outflow and other selected Newtonian and relativistic outflows for comparison at $t=4$ s for the 12.75 $M_\odot$ progenitor. Outflows with GR hydrodynamic equations are shown in red, NW outflows are in black and the modifier 'blue' denotes whether GR heating terms are used. For outflows with termination shocks, the corresponding vacuum solutions are also shown in faded tone and the dots represent the sonic points at 422 km for GR (red) and 594 km for NW with blueshift (black). The thin black line in the upper left panel represents the homologous expansion velocity $v_h$ defined in Eq. \ref{['eq:FS:homologous']}. As shown in the figure, the supersonic solutions arise by the boosted heating from neutrino blueshift to the PNS radius.
• Figure 4: Velocity (left panels) and temperature (right panels) profiles of outflows with constant $g_*=5.5$ (red) versus variable RDF $g_*(T)$ (blue), assuming radiation domination, for the $18$$M_\odot$ model at $t=2.5$ s (upper panels) and the 12.75 $M_\odot$ model at $t=4$ s (lower panels). In the upper right panel, the temperature profiles overlap. In the lower panels, the outflows with far temperature $T_f$ imposed at $r=10^4$ km are shown in solid lines. For reference, the vacuum solutions (dashed lines) and the critical subsonic solutions (dotted lines) are also shown.
• Figure 5: Instantaneous yields at $t_{\rm launch}=2.5$ s for different test cases based on Newtonian (black) and GR (red) equations and different corrections, in our $18~M_{\odot}$ progenitor model. See the caption of Fig. \ref{['fig:outflows:gr']} and the main text for more details.