Radioactive Gamma-Ray Lines from Long-lived Neutron Star Merger Remnants

The rapid neutron-capture process ($r$-process) has long been considered responsible for the production of heavy elements beyond iron in the universe (Burbidge et al., 1957; Cowan et al., 2021). Neutron-rich materials ejected from the merger of binary neutron stars or neutron star–black hole are ideal sites for $r$-process nucleosynthesis (Lattimer & Schramm, 1974; Symbalisty & Schramm, 1982). Li & Paczyński (1998) first proposed that the radioactive decay of freshly synthesized heavy elements can thermalize the merger ejecta, leading to a rapidly evolving thermal transient known as a “kilonova”. Subsequent studies included the $r$-process nuclear reaction network and found that kilonova emission is centered in the optical/near-infrared band (Metzger et al., 2010; Korobkin et al., 2012; Barnes & Kasen, 2013; Kasen et al., 2013; Barnes et al., 2016; Metzger, 2019). In the first binary neutron star merger event detected by the LIGO/Virgo collaboration (GW170817, Abbott et al., 2017a), a thermal transient source was observed (AT2017gfo, Abbott et al., 2017b; Arcavi et al., 2017; Coulter et al., 2017; Cowperthwaite et al., 2017; Drout et al., 2017; Evans et al., 2017; Kasen et al., 2017; Kasliwal et al., 2017; Pian et al., 2017; Shappee et al., 2017; Smartt et al., 2017). The light curve and colour evolution of AT2017gfo are consistent with theoretical predictions of the kilonova model, providing the first strong evidence in support of neutron star mergers as the dominant contributor to the production of heavy $r$-process elements in the Universe (Kasen et al., 2017; Hotokezaka et al., 2018; Chen et al., 2024).

The radioactive decay of heavy elements in the merger ejecta during the optically thin phase may also produce a gamma-ray transient accompanying the kilonova (Hotokezaka et al., 2016; Li, 2019; Korobkin et al., 2020; Wang et al., 2020; Chen et al., 2021, 2022) and an MeV neutrino flash (Chen et al., 2023; An et al., 2023). Detecting radioactive gamma-ray photons from neutron star mergers can provide conclusive evidence for probing the nuclide composition and tracking its evolution. However, it is a great challenge to detect the radioactive gamma-ray emission during the kilonova phase. To convincingly observe radioactive gamma-ray lines generated by $r$-process elements, extremely nearby merger events and more sensitive MeV gamma-ray detectors are required (Chen et al., 2021, 2022). Wu et al. (2019) suggested that detecting gamma-ray lines produced by the radioactive decay of long-lived heavy nuclei during the remnant phase within the Milky Way is the most promising strategy in the near-term. In this work, we included the $r$-process nuclear reaction network and the astrophysical inputs derived from numerical relativity simulations to further investigate the gamma-ray line features generated by the radioactive decay of long-lived nuclei in the merger remnants.

According to the neutron star merger rate inferred from the LIGO/Virgo gravitational wave detectors, the occurrence rate of such mergers within the Milky Way ranges between $\sim 10$ and $\sim 100$ Myr^-1 (Chen et al., 2024). Therefore, the age of young neutron star merger remnants in our Galaxy typically falls between $\sim 10$ and $\sim 100$ kyr. To detect the radioactive gamma-ray line from merger remnants at this typical age, the heavy nucleus ${}^{126}_{50}$Sn with a half-life of $230$ kyr is the most promising heavy element. On one hand, ${}^{126}_{50}$Sn resides close to the second $r$-process peak, where its production typically occurs at a high yield level. On the other hand, the gamma-ray energy released by the decay chain of ${}^{126}_{50}$Sn is $\sim 2.8$ MeV per decay event, significantly higher than that of other heavy elements during the remnant phase. Moreover, a new MeV gamma-ray mission has recently been proposed, the MeV Astrophysical Spectroscopic Surveyor (MASS; Zhu et al., 2024). With its high line sensitivity in the MeV band, MASS is expected to a powerful instrument for gamma-ray line detection, providing an opportunity to detect radioactive gamma-ray line from merger remnants within the Milky way. In this work, we will focus on investigating the radioactive gamma-ray lines generated by ${}^{126}_{50}$Sn and explore their detectability by combining with the line sensitivity of MASS.

Radioactive gamma-ray lines produced by the long-lived nucleus ${}^{126}_{50}$Sn from the Galactic supernova remnants have been investigated by Qian et al. (1998). They assumed that supernovae are the sites of $r$-process nucleosynthesis. However, subsequent studies have revealed that supernovae are only capable of producing some of the lightest $r$-process elements (Arcones & Thielemann, 2013; Wanajo, 2013). Conversely, neutron star mergers are considered more ideal astrophysical sites for $r$-process nucleosynthesis, as confirmed by the observation of the kilonova AT2017gfo. The light curve and color evolution of AT2017gfo suggest that approximately $0.05~{}M_{\odot}$ of heavy $r$-process elements were synthesized in the merger ejecta (Kasen et al., 2017; Chen & Liang, 2024). Subsequent analysis of the observed spectrum further identified the presence of the heavy element strontium (Watson et al., 2019). Furthermore, heavy element tellurium (which resides at the second $r$-process peak) has been discovered in the kilonova associated with gamma-ray burst 230307A observed by James Webb Space Telescope (Levan et al., 2024). These observational results confirm that neutron star mergers are the dominant contributors to the production of heavy $r$-process elements (Chen et al., 2024).

This paper is organized as follows. In Section 2, we provide the details of $r$-process nucleosynthesis and describe the procedure used to calculate gamma-ray emission powered by the radioactive decay of $r$-process elements. Section 3 presents the results of radioactive gamma-ray emission from neutron star merger remnants. Conclusions and discussions are presented in Section 4.

Figure 1 shows the time evolution of the abundance of the long-lived nucleus ${}^{126}_{50}$Sn. Due to its half-life of $230$ kyr, the abundance of ${}^{126}_{50}$Sn remains at the level of $10^{-4}$ for approximately $100$ kyr. After $\sim 100$ kyr, a significant amount of ${}^{126}_{50}$Sn decays via the $\beta$-decay chain ${}^{126}_{50}$Sn ($T_{1/2}=230$ kyr) $\to$ ${}^{126}_{51}$Sb ($T_{1/2}=12.35$ days) $\to$ ${}^{126}_{52}$Te (stable) to form stable element, leading to a dramatic decrease in the elemental abundance. Our calculations show that the variations in the abundance of the heavy nucleus ${}^{126}_{50}$Sn caused by different astrophysical inputs are within a factor of $\sim 2$. Note that the abundance of obtained through our detailed $r$-process simulations is broadly consistent with the initial abundance of ${}^{126}_{50}$Sn ($Y_{0}=1.7\times 10^{-4}$) used by Wu et al. (2019).

In Figure 2, we show the gamma-ray spectra generated by the radioactive decay of heavy nuclei from binary neutron star merger remnants at a time of $t=10$ kyr. The line sensitivities for MASS taken from Zhu et al. (2024) are also plotted for comparison. It is found that the energy of radioactive gamma-ray lines mainly ranges from $0.1$ to $3$ MeV, with specific energy fluxes between $10^{-8}$ and $10^{-5}$ MeV cm^-2 s^-1. The decay chain of ${}^{126}_{50}$Sn ($T_{1/2}=230$ kyr) $\to$ ${}^{126}_{51}$Sb ($T_{1/2}=12.35$ days) $\to$ ${}^{126}_{52}$Te (stable) produces more than 30 discrete gamma-ray lines, with a total gamma-ray energy release of approximately $2.8$ MeV. The bright gamma-ray lines with a high intensity (probability of emitting a gamma-ray per decay greater than 80%) are $415$ keV, $667$ keV, and $695$ keV. As seen in Figure 2, these bright radioactive gamma-ray lines can be detected by the MASS mission with an exposure time of $10^{7}$ s.

To further study the features of gamma-ray emission produced by long-lived nuclei, we use the astrophysical model BHBlp_M140140 as a representative case for our subsequent analysis. Figure 3 shows the radioactive gamma-ray spectra from neutron star merger remnants at times of $1$ kyr, $10$ kyr, and $100$ kyr. As time goes on, the total gamma-ray flux produced by the merger remnants gradually decreases. The specific energy flux of several bright gamma-ray lines generated by the radioactive decay of ${}^{126}_{51}$Sb decreases from $\sim 2\times 10^{-5}$ to $\sim 5\times 10^{-6}$ MeV cm^-2 s^-1 between $1$ kyr and $100$ kyr, decreasing by a factor of $\sim 4$. We further investigate the time evolution of photon fluxes of each bright gamma-ray line produced by heavy nucleus ${}^{126}_{51}$Sb, as shown in Figure 4. It is found that for neutron star merger remnants with ages less than $100$ kyr, the radioactive gamma-ray lines generated by heavy element ${}^{126}_{51}$Sb can be detected by the MASS if the source is at a distance of $3$ kpc. In other words, high energy resolution MeV gamma-ray detectors like MASS can identify young merger remnants ($\lesssim 100$ kyr) within the Milky Way.

The nuclear physics inputs may affect the radioactive gamma-ray emission from neutron star merger remnants. To explore its sensitivity to the nuclear physics inputs, we estimate the radioactive gamma-ray spectrum using the Weizs$\ddot{\rm a}$cker-Skyrme model provided by Wang et al. (2014), as shown in Figure 5. The merger remnant’s age is $1$ kyr and its distance is $10$ kpc, consistent with the possible kilonova remnant associated with the guest star recorded in AD 1163 (Liu et al., 2019). One can observe that the radioactive gamma-ray spectrum calculated using the nuclear physics input derived from the Weizs$\ddot{\rm a}$cker-Skyrme model has a similar total flux and global shape compared to that calculated using the Finite-Range Droplet model (Figure 2). Bright MeV gamma-ray lines generated by the radioactive decay of the heavy nucleus ${}^{126}_{51}$Sb can be identified in the gamma-ray spectrum. Our analysis further indicates that it is promising to use high energy resolution MeV gamma-ray detectors to observe these gamma-ray lines from Galactic kilonova remnants.

Detection of radioactive gamma-ray photons emitted from neutron star mergers can provide direct evidence for probing the nuclide composition and tracking its evolution. In this study, we used the $r$-process nuclear reaction network and the astrophysical inputs derived from numerical relativity simulations to investigate the gamma-ray line features arising from the radioactive decay of long-lived nuclei in the merger remnants. Among these nuclei, ${}^{126}_{50}$Sn, with a half-life of $230$ kyr, emerges as the most promising candidate. The abundance of heavy element ${}^{126}_{50}$Sn typically reaches a high level of $\sim 10^{-4}$ within $\sim 100$ kyr (Figure 1). Given such high yield, the decay chain of ${}^{126}_{50}$Sn ($T_{1/2}=230$ kyr) $\to$ ${}^{126}_{51}$Sb ($T_{1/2}=12.35$ days) $\to$ ${}^{126}_{52}$Te (stable) produces several bright gamma-ray lines with energies of $415$, $667$, and $695$ keV (Figure 2 and Figure 3). The photon fluxes of these bright gamma-ray lines reach $\sim 10^{-5}$ $\gamma$ cm^-2 s^-1 for neutron star merger remnants with ages less than $100$ kyr, which can be detected if the source is at a distance of $3$ kpc (Figure 4). This suggests that it is promising to use high energy resolution MeV gamma-ray detectors to observe gamma-ray lines generated by the radioactive decay of heavy $r$-process elements and to identify young neutron star merger remnants ($\lesssim 100$ kyr) within the Milky Way. Our results are consistent with the analysis given by Wu et al. (2019). They suggested that ${}^{126}_{50}$Sn is the most promising nucleus for gamma-ray searches in neutron star merger remnants by investigating individual long-lived nuclei and assuming that each merger event contains a distribution of $r$-process nuclei following the Solar $r$-process abundances.

The event rate of binary neutron star merger inferred from the LIGO/Virgo gravitational wave detectors is $\sim 1000$ Gpc^-3 yr^-1 (Abbott et al., 2017a). Assuming a local density of Milky Way-equivalent galaxies of $\sim 0.01$ Mpc^-3, the occurrence rate within our Galaxy is then $\sim 100$ Myr^-1. Thus, the age of the most recent Galactic merger remnant is estimated to be $\sim 10$ kyr. However, it’s worth noting that the youngest Galactic merger remnant could be substantially younger, with approximately a $10\%$ probability of having an age less than $1$ kyr. Liu et al. (2019) proposed that G4.8+6.2 is a possible kilonova remnant associated with the Korean guest star of AD 1163 in the Milky Way, with an age of $\sim 1$ kyr. If G4.8+6.2 and AD 1163 are indeed associated, the radioactive gamma-ray emission lines produced by this kilonova remnant can be identified by MeV gamma-ray detectors (Figure 5).

The line sensitivity for the current gamma-ray mission INTEGRAL (Winkler et al., 2003) at 1 MeV is $3\times 10^{-5}$ $\gamma$ cm^-2 s^-1, which is not sufficient to detect radioactive gamma-ray lines from long-lived neutron star merger remnants. Recently, Zhu et al. (2024) proposed a new MeV gamma-ray mission, the MeV Astrophysical Spectroscopic Surveyor (MASS). The MASS mission is a large area Compton telescope using 3D position sensitive CdZnTe detectors optimized for MeV gamma-ray line detection. The line sensitivities for the MASS mission could achieve $1\times 10^{-5}$ and $4\times 10^{-6}$ $\gamma$ cm^-2 s^-1 with exposure times of $10^{6}$ and $10^{7}$ seconds, respectively. With an energy resolution of $0.6\%$ in the MeV band, MASS is sufficient to detect gamma-ray lines produced by the decay chain of ${}^{126}_{50}$Sn and to identify young Galactic kilonova remnants.