Gamma-ray Signatures of r-Process Radioactivity from the Collapse of Magnetized White Dwarfs

Abstract

We predict the gamma-ray line emission from $r$-process nuclei synthesized in the ejecta of the accretion-induced collapse (AIC) of a magnetized, rapidly rotating white dwarf. Using ejecta from a two-dimensional general-relativistic neutrino-magnetohydrodynamic simulation, further evolved with a radiation-hydrodynamics code coupled to an in-situ nuclear reaction network, we construct angle-dependent gamma-ray spectra in the $0.01$-$10\,\mathrm{MeV}$ band via composition-dependent ray-tracing through the ejecta. The emission between $\sim$1 and $10\,$d is dominated by $^{132}$I ($t_{1/2} = 2.3\,$h), continuously replenished by the decay of its parent $^{132}$Te ($t_{1/2} = 3.2\,$d), with additional contributions from $^{131}$I, $^{133}$Xe, and $^{132}$Te. At $t\gtrsim 20$ d, $^{56}$Co (from $^{56}$Ni decay) becomes the primary emitter. The simultaneous presence of $r$-process and iron-peak gamma-ray lines is distinctive of AIC ejecta and absent in binary neutron star mergers, where iron-peak nuclei are generally not synthesized. Comparing with the $3σ$ continuum sensitivities of planned MeV gamma-ray telescopes (COSI, AMEGO-X, e-ASTROGAM, GRAMS, GammaTPC), we find the brightest $r$-process lines detectable to $\sim 10\,\mathrm{Mpc}$ by GammaTPC and GRAMS, with the signal approaching their sensitivity threshold at $30\,\mathrm{Mpc}$. The $r$-process spectral features survive time integration over $\sim 30$ d exposures, demonstrating robustness against the long observation times required by gamma-ray detectors.

Figures (7)

• Figure 1: Geometry of the gamma-ray escape calculation. The ejecta (blue shading) occupy a 2D spherical $(r_{i}, \theta_{i})$ grid covering the full polar range $\theta = 0^\circ$ (pole) to $180^\circ$; only the $r > 0$ meridional half-plane is shown (the configuration is axisymmetric about the $z$-axis). An emitting cell at position $(r_{i}, \theta_{i})$ radiates gamma-rays toward the observer at polar angle $\theta_{\rm obs}$. The bold segment shows the path through the ejecta, along which the element column densities $\Sigma_Z$ (Eq. \ref{['eq:column']}) and optical depth $\tau(E)$ (Eq. \ref{['eq:tau_E']}) are accumulated; the thin arrow shows the free path outside. The angle $\alpha$ between the cell velocity $\mathbf{v}_{i} = \mathbf{r}_{i}/t$ and the observer direction $\hat{q}$ determines the Doppler shift (Eq. \ref{['eq:doppler']}).
• Figure 2: Fractional contribution of individual radioactive isotopes to the total escaping gamma-ray luminosity $L_{\gamma}^{\rm esc}$($0.01$--$10\,\mathrm{MeV}$) as a function of time for the polar viewing angle ($\theta_{\rm obs} = 0^\circ$). $^{132}$I dominates between $\sim$1 and $10\,$d, sustained by secular equilibrium with its parent $^{132}$Te ($t_{1/2} = 3.2\,$d). At late times, $^{56}$Co becomes the primary emitter.
• Figure 3: Gamma-ray energy flux (Eq. \ref{['eq:F_gamma']}) as a function of time for the polar ($\theta_{\rm obs} = 0^\circ$, left) and equatorial ($\theta_{\rm obs} = 90^\circ$, right) viewing angles, for a source at distance $d=1$ Mpc. Each curve corresponds to a different epoch (sampled every $2\,$d from $2$ to $30\,$d), with the color indicating time as shown by the colorbar. The dominant emitting isotopes are labeled at the spectral peaks; an isotope is labeled only when it contributes $\geq 50\,\%$ of the time-integrated fluence in that energy bin (see Fig. \ref{['fig:fluence']})
• Figure 4: Time-integrated gamma-ray fluence (Eq. \ref{['eq:F_gamma']} integrated from $0.5$ to $30\,$d) for the polar ($\theta_{\rm obs} = 0^\circ$, left) and equatorial ($\theta_{\rm obs} = 90^\circ$, right) viewing angles. In each energy bin the curve is coloured by the dominant emitting isotope, provided that isotope contributes $\geq 50\,\%$ of the bin fluence; bins without a clear dominant contributor retain the grey background curve. Each dominant isotope is identified by an arrow label at its spectral peak. Three source distances are shown with solid (1 Mpc), dashed (10 Mpc), and dotted (30 Mpc) lines. Superimposed are the minimum detectable fluence curves of proposed MeV gamma-ray telescopes, rescaled to a $30\,$d transient as described in Section \ref{['sec:spectra']}. The $r$-process spectral features, in particular the $^{132}$I lines, survive the time integration.
• Figure 5: Elemental mass fraction $X(Z)$ vs. fraction of time-integrated gamma-ray energy ($0.5$--$30\,$d) for each element, at $\theta_{\rm obs} = 0^\circ$. Points are coloured by atomic number $Z$. The dashed line marks equal fractions. Iodine ($Z = 53$) dominates the gamma-ray energy budget with $\sim$40% despite comprising only $\sim$5% of the ejecta mass.