Survival of ultraheavy nuclei in astrophysical sources: applications to protomagnetar outflows

Abstract

Outflows of rapidly rotating protomagnetars have been considered as attractive sites for the synthesis of nuclei heavier than iron, but the question remains whether these nuclei are able to survive against photodisintegration as they make their way out of their formation environments. In this work, we present new analytic fitting formulae for the photodisintegration cross sections applicable to heavy nuclei beyond iron. We confirm that the results from the TALYS simulations are consistent with the theory of the giant dipole resonance, and apply the obtained new formulae to investigate whether ultraheavy nuclei entrained in protomagnetar outflows can be disintegrated by thermal and nonthermal photons before leaving the stellar envelope. We explore two outflow models: a spherical wind model and a jetted outflow model. For nuclei accelerated to the bulk speed of these outflows, their survival depends on the model and engine properties. For spherical winds, nuclei may survive for the first $\sim100\,{\rm s}$ post-core collapse, but as the wind Lorentz factor increases, the photodisintegration optical depth sharply rises and nuclei may no longer survive. For the jetted outflows arising from progenitors surrounded with stellar envelopes, nuclei can only survive before the jet breakout time in cases where the central engine has low spin-down energy, that is, with a low magnetic field strength and longer spin period. In progenitors with more extended envelopes, the jet break out time is much longer, allowing for nonthermal photons to readily photodisintegrate nuclei in high spin-down energy cases. These results also have implications for the capabilities of protomagnetars to source ultra-high energy cosmic ray nuclei.

Figures (5)

• Figure 1: The TALYS data (shown as blue dots in each panel) compared to old fits (orange lines, see KARAKULA1993229 (henceforth KT93)) and our new fits (green lines in each panel, except for the top right panel where our fit is the same as KT93). Top left: the TALYS peak cross-section data ($\sigma_{\rm GDR}$, see Eq. (\ref{['GDRxs']})) for GDR resonance. The best fit can be described by a power law $\sigma_{\rm GDR}\approx0.43A^{1.35}\times10^{-27}\,{\rm cm^2}$. Top right: the best fit to TALYS data for the central energy ($\overline{\varepsilon}_{\rm GDR}$) of the GDR resonance, in which case the prior fit describes the data well. The best fit is given by $\overline{\varepsilon}_{\rm GDR}\approx42.65A^{-0.21}\,{\rm MeV}$. Bottom left: the full-width at half-maximum ($\Delta\varepsilon_{\rm GDR}$) of the TALYS data versus $A$. The best fit is given by $\Delta\varepsilon_{\rm GDR}\approx21.05A^{-0.35}$, in contrast to a constant value of $8\,{\rm MeV}$ used in the previous studies. Bottom right: the product $\sigma_{\rm GDR}\Delta\varepsilon_{\rm GDR}\approx9A\times10^{-27}\,{\rm cm^2~MeV}\propto\sigma_{A\gamma}$, resulting in an approximately linear $A$-dependence.
• Figure 2: Schematic picture of the two models we consider. Left panel: a spherical wind originating from the protomagnetar central engine. In Region A, a neutrino-driven wind flows from the PNS central engine, which eventually catches up to the nonrelativistic pulsar wind nebula in Region B. Right panel: a jetted outflow which may also originate from protomagnetar central engines. In Region C, a pre-collimated jet expands into Region D, which is a collimated jet region. Region E is the jet head, which may break out of the surrounding stellar material.
• Figure 3: Thomson optical depth, $\tau_T$, for several cases is shown as a function of time. The dashed black line shows $\tau_T=1$. The shaded regions represent the minimum to maximum $\tau_T$ values that are calculated for our range of $B_{\rm dip}$ and $P_i$ configurations and the translucent lines between are the individual results for each configuration. The gray hatched region represents the time when the jets become collimated ($t_{\rm coll}$) and the gray shaded region is the breakout time for WRs ($t_{\rm bo,WR}$). For all cases, $t_{\rm coll}<t_{\rm bo}$. Left panel: $\tau_T$, for the spherical wind case for Regions A (blue shaded) and B (gray shaded). The vertical gray shaded region shows the range in $t_{\rm GJ}$ values for our range of $B_{\rm dip}$ and $P_i$ configurations. For all configurations of $B_{\rm dip}$ and $P_i$, $t_{\rm Th}<t_{\rm GJ}$, implying that nonthermal photons are expected by $t_{\rm GJ}$. Right panel: $\tau_T$ for the jetted outflow case of a WR progenitor in Regions C (green shaded) and D (red shaded). After $t_{\rm bo,WR}$, nuclei can freely escape the star. For WRs, $t_{\rm Th}>t_{\rm bo,WR}$ (except for one case), for BSGs, $t_{\rm Th}>t_{\rm bo,BSG}$ for rapidly rotating engines, and for all RSG cases, $t_{\rm Th}<t_{\rm bo,RSG}$.
• Figure 4: The photodisintegration optical depth, $f_{A\gamma}$, is shown as a function of time post core-collapse. In each panel, the value of $f_{A\gamma}=1$ is denoted by the horizontal dashed black line assuming a pure-iron composition ($A=56$). The nuclei energy is assumed to be $\Gamma_xm_Ac^2$, where $\Gamma_x$ is the bulk Lorentz factor in each Region. The shaded colored regions show the extent of values when varying the PNS magnetic field and spin period, whose boundaries are given by the maxima and minima values found. The lines within these regions correspond to the individual $B_{\rm dip}/P_i$ configurations. The hatched $t_{\rm coll}$ region shows the time when the jets become collimated, before which the calculations are unphysical. Finally, the shaded gray regions show the extent of breakout times for each case. Top left panel:$f_{A\gamma}$ for the spherical wind case. For the first $\sim100\,{\rm s}$ ($t_{\rm Th}$ for Region A), $f_{A\gamma}\ll1$ so nuclei can survive in both regions. Around this time, photons become nonthermal, but the energy density is not high enough in Region A to cause photodisintegration. However, very quickly, due to leaked photons in Region A and Region B, nuclei are efficiently destroyed. Top right panel:$f_{A\gamma}$ for the jetted outflow case from WR progenitors. In some high $P_i$ cases, $f_{A\gamma}\gg1$ in the regime where thermal photons can destroy nuclei before the breakout time. In all other cases, nuclei can survive photodisintegration before breaking out of the star. Bottom left panel:$f_{A\gamma}$ for the jetted outflow case from BSG progenitors. In this scenario, $f_{A\gamma}<1$ for all cases at $t_{\rm bo,BSG}$ (except the case of $B_{\rm dip}=10^{15}\,{\rm G}$, $P_i=10\,{\rm ms}$, where $f_{A\gamma}\sim1$). Bottom right panel:$f_{A\gamma}$ for the jetted outflow case from RSG progenitors. In this case, the breakout time is much longer. In this nonthermal photon regime, nuclei in high spin-down energy cases are readily photodisintegrated.
• Figure 5: Photodisintegration optical depths are shown as a function of time for our spherical wind model (left panel) and jetted outflow model (WR case, right panel), with varying nuclei composition. In black, we show the result for iron, which is the same result as the top row of Fig. \ref{['fig:efficiencyplot']}, to compare with other cases. In blue, orange, and purple, we also show the efficiencies for selenium, tellurium, and platinum. This shows there is a slightly positive correlation of $f_{A\gamma}$ with mass number, and heavier nuclei are somewhat less likely to survive in general.