Neutron Star Mergers in Active Galactic Nucleus Accretion Disks: Cocoon and Ejecta Shock Breakouts

Jin-Ping Zhu; Bing Zhang; Yun-Wei Yu; He Gao

doi:10.3847/2041-8213/abd412

1. Introduction

Since the Laser Interferometer Gravitational wave (GW) Observatory (LIGO) detected the first GW signal GW150914 from a binary black hole (BBH) merger (Abbott et al. 2016), dozens of BBH GW events have been reported (Abbott et al. 2019, 2020a). The formation channels for BBH systems are still subject to debated. Two main channels include field isolated binary evolution (e.g., Belczynski et al. 2010; de Mink & Mandel 2016; Santoliquido et al. 2020) and dynamical interactions in dense environments including globular clusters (e.g., Sigurdsson & Hernquist 1993; Rodriguez et al. 2015), galactic nuclei (e.g., Antonini & Rasio 2016; Fragione et al. 2019), and active galactic nucleus (AGN) disks (e.g., McKernan et al. 2012, 2014; Bartos et al. 2017; Stone et al. 2017). BBH mergers can hardly generate electromagnetic (EM) counterparts in the absence of gas.⁵ In a dense environment, especially in an AGN accretion disk, BBH mergers are expected to produce EM emission. McKernan et al. (2019) suggested that the GW kick at the remnant BH after a BBH merger can cause ram pressure stripping of gas within the BH Hill sphere to power a UV/optical EM flare in an AGN disk. Recently, the LIGO/Virgo Collaboration announced a high-mass BBH merger system (Abbott et al. 2020b), GW190521, with two BH masses ${85}_{-14}^{+21}\,{M}_{\odot }$ and ${66}_{-18}^{+17}\,{M}_{\odot }$ , respectively. Intriguingly, Graham et al. (2020) reported a plausible optical EM counterpart ZTF19abanrhr detected by the Zwicky Transient Facility (ZTF; Graham et al. 2020) ∼34 days after the GW190521 trigger, which was consistent with a plausible association of the GW event with the AGN ${\rm{J}}124942.3+344929$ . Conversely, Ashton et al. (2020) and Nitz & Capano (2020) argued that the localization overlap between ZTF19abanrhr with GW190521 is insufficient to confidently associate the two events.

Besides BBH mergers, a large population of binary neutron star (BNS) and neutron star–black hole (NSBH) mergers are also expected to occur in AGN disks (Cheng & Wang 1999; McKernan et al. 2020). These neutron star mergers have long been proposed as the progenitors of short-duration gamma-ray bursts (sGRBs; Paczynski 1986, 1991; Eichler et al. 1989; Narayan et al. 1992) and kilonovae powered by the radioactive decay of r-process nuclei from the subrelativistic ejecta of these events (Li & Paczyński 1998; Metzger et al. 2010). The multimessenger observations of a BNS merger GW event (GW170817; Abbott et al. 2017a) and its associated EM signals, including a sGRB (GRB 170817A; Abbott et al. 2017b; Goldstein et al. 2017; Zhang et al. 2018), a broadband off-axis jet afterglow (e.g., Margutti et al. 2017; Troja et al. 2017; Lazzati et al. 2018; Lyman et al. 2018; Ghirlanda et al. 2019), and a kilonova (AT 2017gfo; Abbott et al. 2017c; Arcavi et al. 2017; Coulter et al. 2017; Drout et al. 2017; Evans et al. 2017; Kasliwal et al. 2017; Pian et al. 2017; Smartt et al. 2017), provided smoking-gun evidence for the long-hypothesized origin of sGRBs and kilonovae. The properties of sGRBs and kilonovae generated from BNS and NSBH mergers have been studied in detail. However, no study has focused on the properties of EM counterparts of BNS or NSBH merger systems that are in AGN disks.⁶ A smoking-gun signature of the EM counterparts from BNS or NSBH mergers in an AGN disk, if identified, would lend support to the formation channel of compact binary mergers in AGNs. The motivation of this paper is to study the observational signatures of neutron star mergers in an AGN disk.

2. Cocoon and Ejecta Shock Breakouts

Figure 1 illustrates the physical processes after a neutron star merger (BNS or NSBH merger) in an AGN disk. We consider a neutron star merger in an AGN disk, assume that merger can launch a relativistic jet, and study its propagation in the disk. For simplicity, we assume that the binary orbital plane is parallel to the disk plane so that the post-merger jet launched from the system is perpendicular to the disk.

A successful jet can penetrate through the surrounding environment (e.g., the stellar envelope of a massive star or the ejecta launched from a neutron star merger) and is surrounded by a hot cocoon with a lower speed (e.g., Mészáros & Rees 2001; Ramirez-Ruiz et al. 2002; Zhang et al. 2004; Nakauchi et al. 2013; Nakar & Piran 2017; Hamidani & Ioka 2021). In the case of a choked jet, the jet energy from a neutron star merger would be stored in a hot, shocked material, forming a broad cocoon without a spine jet (e.g., Gottlieb et al. 2018; Piran et al. 2019). As we show below, the GRB jet in an AGN disk cannot penetrate the disk so it produces a transrelativistic cocoon of this type. The breakout of this cocoon from the AGN disk would produce X-rays. The slower ejecta launched from the merger can also drive a nonrelativistic shock, which breaks out the disk at a later time and emits X-ray/UV photons.

Compact binary mergers are expected to occur in the migration traps (Bellovary et al. 2016) plausibly located at $a\sim {10}^{3}\,{r}_{{\rm{g}}}$ , where a is the orbital semimajor axis of the system in units of supermassive BH gravitational radius ${r}_{{\rm{g}}}\equiv {{GM}}_{\mathrm{SMBH}}/{c}^{2}$ . The disk height at the location is

$\begin{eqnarray}&&H=1.5\times {10}^{14}\,{M}_{\mathrm{SMBH},8\odot }\left(\displaystyle \frac{H/a}{0.01}\right)\left(\displaystyle \frac{a}{{10}^{3}\,{r}_{{\rm{g}}}}\right)\,\mathrm{cm},\end{eqnarray} \tag{ 1 }$

where ${M}_{\mathrm{SMBH}}$ is distributed in $\sim [{10}^{7},{10}^{9}]\,{M}_{\odot }$ based on AGN observations (e.g., Woo & Urry 2002; Kollmeier et al. 2006), and $H/a\sim [{10}^{-3},0.1]$ is the disk aspect ratio (Sirko & Goodman 2003; Thompson et al. 2005). Therefore, the disk height at migration traps can be $O({10}^{14})\,\mathrm{cm}$ . Hereafter the convention ${Q}_{x}=Q/{10}^{x}$ is adopted in cgs units.

With the consideration of a gas-pressure-dominated disk, its vertical atmospheric density (Netzer 2013) is $\rho (z)\,={\rho }_{0}\exp (-z/H)$ , where ${\rho }_{0}$ is the midplane density at migration traps and z is the vertical distance. Near the migration traps, the midplane density is almost ${\rho }_{0}\sim O({10}^{-10})\,{\rm{g}}\,{\mathrm{cm}}^{-3}$ (Sirko & Goodman 2003; Thompson et al. 2005). The propagation direction and the shape of the shocks can be affected if there is an asymmetric density distribution for the AGN disk atmosphere. For an atmosphere with an exponentially decaying density profile, the density is $\rho \approx {\rho }_{0}$ for $z\leqslant H$ and decreases rapidly for $z\geqslant H$ . For simplicity, hereafter, we assume that the AGN disk has a uniform density profile at $z\leqslant H$ .

2.1. Cocoon Shock Breakout

After a neutron star merger (BNS or NSBH merger), a pair of relativistic jets would be launched along the axis of the binary merger, which could be observed as an sGRB if the merger is not in the AGN disk and if one of the jet points toward Earth. Observationally, sGRBs have durations shorter than ∼2 s with a distribution peaking at ${t}_{{\rm{j}}}\approx {T}_{90}\sim 0.8\,{\rm{s}}$ (Kouveliotou et al. 1993; Horváth 2002; Nakar 2007; Berger 2014). The statistic analysis of 103 sGRB broadband afterglow observations by Fong et al. (2015) revealed that the median beaming-corrected energy for sGRB jets is ${E}_{{\rm{j}}}\sim 1.6\,\times {10}^{50}\,\mathrm{erg}$ . Therefore, the jet luminosity ${L}_{{\rm{j}}}\approx {E}_{{\rm{j}}}/{t}_{{\rm{j}}}$ is usually a few ${10}^{50}\,\mathrm{erg}\,{{\rm{s}}}^{-1}$ .

The jet initially penetrates through the merger ejecta and gets collimated there. The jet breaks out from the ejecta in a ∼0.1 s, which is shorter than the duration of sGRB (e.g., Yu 2020). When it enters the AGN disk with a much lower density, it loses collimation but is reaccelerated by the waste heat in the ejecta cocoon. Energy from the central engine would be continually injected into the reborn fireball and reach a relativistic speed. Following Bromberg et al. (2011b), the critical parameter that determines the evolution of the jet is $\tilde{L}\simeq {L}_{{\rm{j}}}/{\rho }_{0}{c}^{3}{(\pi {r}_{{\rm{j}}}^{2})\approx ({10}^{14}\mathrm{cm}/{r}_{{\rm{j}}})}^{2}$ . Since the jet radius ${r}_{{\rm{j}}}\,\ll {10}^{14}\,\mathrm{cm}$ , one has $\tilde{L}\gg 1$ so that the jet head would travel with a relativistic speed. The jet would be uncollimated and then sweep AGN material to decelerate significantly. One may calculate the dynamical evolution of the jet to check whether the jet can successfully break out from the disk. For an order of magnitude estimation, hereafter we assume that the merger is located at the disk midplane and the propagation direction of the jet is perpendicular to the disk surface. The dynamical equation covering both ultrarelativistic and nonrelativistic shock dynamics may be written as (Huang et al. 1999)

$\begin{eqnarray}&&\displaystyle \frac{d{\rm{\Gamma }}}{{dt}}=-\displaystyle \frac{{{\rm{\Gamma }}}^{2}-1}{{M}_{{\rm{j}}}+2{\rm{\Gamma }}{m}_{\mathrm{sw}}},\end{eqnarray} \tag{ 2 }$

where Γ is the bulk Lorentz factor of the external shock, ${M}_{{\rm{j}}}$ is the jet mass, and ${m}_{\mathrm{sw}}$ is the swept-up disk medium mass. The total energy of the jet is ${E}_{{\rm{j}}}={{\rm{\Gamma }}}_{{\rm{j}}}{M}_{{\rm{j}}}{c}^{2}$ with ${{\rm{\Gamma }}}_{{\rm{j}}}$ is the jet Lorentz factor after breaking out the merger ejecta. The evolution of the swept-up disk mass ${m}_{\mathrm{sw}}$ and the distance r traveled by the jet can be calculated by

$\begin{eqnarray}\begin{array}{rcl}\displaystyle \frac{{{dm}}_{\mathrm{sw}}}{{dr}} & = & 2\pi {r}^{2}(1-\cos {\theta }_{{\rm{j}}}){{nm}}_{p},\\ \displaystyle \frac{{dr}}{{dt}} & = & \displaystyle \frac{\beta c}{1-\beta },\end{array}\end{eqnarray} \tag{ 3 }$

where ${\theta }_{{\rm{j}}}$ is the half-opening angle of the jet, $n\approx {\rho }_{0}/{m}_{p}$ is the disk number density, m_p is the proton mass, and $\beta =\sqrt{1-{{\rm{\Gamma }}}^{-2}}$ . As shown in Figure 2, the jet in an AGN disk is quickly decelerated significantly before escaping the disk. The jet can be choked if the jet tail catches up to the jet head. This requires $({v}_{{\rm{t}}}-{v}_{{\rm{h}}}){t}_{{\rm{j}},\mathrm{bo}}\gt {z}_{{\rm{j}}}$ , where ${v}_{{\rm{t}}}\approx c$ is the velocity of the jet tail, ${v}_{{\rm{h}}}$ is the velocity of the jet head, ${t}_{{\rm{j}},\mathrm{bo}}$ is the time for the jet to break out from the AGN disk, and ${z}_{{\rm{j}}}\approx {{ct}}_{{\rm{j}}}$ is the jet length. So the condition for the jet to be choked is ${t}_{{\rm{j}},\mathrm{bo}}\gt 2{{\rm{\Gamma }}}_{{\rm{j}}}^{2}{t}_{{\rm{j}}}$ . Since the jet is decelerated to a transrelativistic speed in the AGN disk as shown in Figure 2, i.e., ${{\rm{\Gamma }}}_{{\rm{j}}}\approx 1\mbox{--}2$ , one would always have ${t}_{{\rm{j}},\mathrm{bo}}\gg {t}_{{\rm{j}}}\approx 1\,{\rm{s}}$ . Therefore, the jet would be stalled and deposit its energy to the cocoon with the cocoon energy being ${E}_{{\rm{c}}}\approx {E}_{{\rm{j}}}$ . The resulting profile of the cocoon is shaped like a cone with a half-opening angle ${\theta }_{{\rm{c}}}$ that is usually larger than ${\theta }_{0}\sim 10^\circ$ (Bromberg et al. 2011a, 2011b). The hot, transrelativistic cocoon expands, forms a radiation-mediated shock, sweeps the AGN disk material, and finally breaks out from the disk.

**Figure 2.** Evolution of distance and ${\rm{\Gamma }}\beta$ for a jet moving in an AGN disk. The following parameters are adopted: ${E}_{{\rm{j}}}={10}^{50}\,\mathrm{erg}$ , ${\theta }_{{\rm{j}}}=10^\circ$ , ${{\rm{\Gamma }}}_{{\rm{j}}}=200$ , and $n\approx {\rho }_{0,-10}/{m}_{p}=6\times {10}^{13}\,{\mathrm{cm}}^{-3}$ .
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${\rm{\Gamma }}\beta $ — **Figure 2.** Evolution of distance and ${\rm{\Gamma }}\beta$ for a jet moving in an AGN disk. The following parameters are adopted: ${E}_{{\rm{j}}}={10}^{50}\,\mathrm{erg}$ , ${\theta }_{{\rm{j}}}=10^\circ$ , ${{\rm{\Gamma }}}_{{\rm{j}}}=200$ , and $n\approx {\rho }_{0,-10}/{m}_{p}=6\times {10}^{13}\,{\mathrm{cm}}^{-3}$ .
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The shock would break out if the photons ahead of the shock diffuse faster than the shock propagation. The photons from the vertical location h would take ${t}_{\mathrm{diff}}\approx \kappa {\rho }_{0}{(H-h)}^{2}/c$ to diffuse to the disk surface at H , where κ is the opacity. The shock propagation time is ${t}_{\exp }\approx (H-h)/{v}_{{\rm{c}}}$ , where ${v}_{{\rm{c}}}$ is the velocity of the faster part of the cocoon shock. The shock breakout takes place when ${t}_{\mathrm{diff}}\approx {t}_{\exp }$ , so we can calculate the distance between the location of shock breakout and disk surface as

$\begin{eqnarray}&&d=H-h\approx 3\times {10}^{11}\,{\rho }_{0,-10}^{-1}{\left(\displaystyle \frac{{v}_{{\rm{c}}}}{0.1c}\right)}^{-1}\,\mathrm{cm},\end{eqnarray} \tag{ 4 }$

where $\kappa =0.34\,{\mathrm{cm}}^{2}\,{{\rm{g}}}^{-1}$ is adopted. Since $d\ll H$ , the shock breakout would take place near the AGN disk surface.

When the shock breaks out, the total mass of the swept material by the cocoon is

$\begin{eqnarray}&&{M}_{{\rm{c}},\mathrm{sw}}\approx \displaystyle \frac{\pi {\rho }_{0}{\theta }_{{\rm{c}}}^{2}{H}^{3}}{3}=1.6\times {10}^{-3}\,{\rho }_{0,-10}{\theta }_{{\rm{c}},10^\circ }^{2}{H}_{14}^{3}\,{M}_{\odot }.\end{eqnarray} \tag{ 5 }$

The shock breakout velocity can be estimated as ${v}_{{\rm{c}}}\,\approx \sqrt{{E}_{{\rm{c}}}/{M}_{{\rm{c}},\mathrm{sw}}}$ , which is of the order

$\begin{eqnarray}&&{v}_{{\rm{c}}}/c\approx 0.19\,{E}_{{\rm{c}},50}^{1/2}{\rho }_{0,-10}^{-1/2}{\theta }_{{\rm{c}},10^\circ }^{-1}{H}_{14}^{-3/2}.\end{eqnarray} \tag{ 6 }$

Because ${v}_{{\rm{c}}}/c\gtrsim 0.1$ , there is not enough time to form a photon–electron thermal equilibrium and a blackbody spectrum (Weaver 1976; Katz et al. 2010; Nakar & Sari 2010). In such a case, electrons and photons are in Compton equilibrium at a much higher temperature ${T}_{{\rm{c}}}$ than the downstream temperature ${T}_{{\rm{c}}}^{\mathrm{BB}}$ . With an adiabatic index of $\gamma =4/3$ and by comparing the radiation energy density with the kinetic energy density, one can express the ejecta shock downstream temperature as ${T}_{{\rm{c}}}^{\mathrm{BB}}\approx {(7{\rho }_{0}{v}_{{\rm{c}}}^{2}/2a)}^{1/4}$ , where a is the radiation constant. Therefore, the downstream temperature is ${T}_{{\rm{c}}}^{\mathrm{BB}}\approx 1.1\times {10}^{6}\,{E}_{{\rm{c}},50}^{1/4}{\theta }_{{\rm{c}},10^\circ }^{-1/2}{H}_{14}^{-3/4}\,{\rm{K}}$ . Katz et al. (2010) suggested that ${T}_{{\rm{c}}}$ can be modified by Comptonization as ${T}_{{\rm{c}}}={T}_{{\rm{c}}}^{\mathrm{BB}}{\eta }^{2}/\xi {({T}_{{\rm{c}}})}^{2}$ , where $\eta \approx 16\,{\rho }_{0,-10}^{-1/8}{({v}_{{\rm{c}}}/0.1c)}^{15/4}$ is the thermal coupling coefficient of the breakout shell at the initial time in the expanding gas, and $\xi ({T}_{{\rm{c}}})\approx \max [1,0.5\mathrm{ln}({y}_{\max })(1.6\,+\mathrm{ln}({y}_{\max })]$ is the Comptonization correction factor. Here, ${y}_{\max }\,={k}_{{\rm{B}}}{T}_{{\rm{c}}}/h{\nu }_{\min }\approx 1.2\times {10}^{3}\,{\rho }_{0,-10}^{-1/2}{T}_{{\rm{c}},7}^{9/4}$ is the ratio between ${T}_{{\rm{c}}}$ and the lowest photon energy for Comptonization, where ${k}_{{\rm{B}}}$ is the Boltzmann constant. For ${v}_{{\rm{c}}}/c=0.19$ and ${\rho }_{0}={10}^{-10}\,{\rm{g}}\,{\mathrm{cm}}^{-3}$ , one can solve ${T}_{{\rm{c}}}\approx 1.8\times {10}^{7}\,{\rm{K}}$ while the observed temperature is ${T}_{{\rm{c}}}^{\mathrm{obs}}\approx {({v}_{{\rm{c}}}/c)}^{1/4}{T}_{{\rm{c}}}\approx 1.2\times {10}^{7}\,{\rm{K}}$ . Therefore, the main radiation of the cocoon shock breakout is in the soft X-ray band.

With the breakout velocity known, the distance from the AGN disk surface to the shell in which the breakout occurs can be estimated by Equation (4), i.e., ${d}_{{\rm{c}},\mathrm{bo}}\approx 1.6\,\times {10}^{11}\,{E}_{{\rm{c}},50}^{-1/2}{\rho }_{0,-10}^{1/2}{\theta }_{{\rm{c}},10^\circ }{H}_{14}^{3/2}\,\mathrm{cm}$ , while the diffusion time is

$\begin{eqnarray}&&{t}_{{\rm{c}},\mathrm{diff}}\approx \displaystyle \frac{\kappa {\rho }_{0}{d}_{{\rm{c}},\mathrm{bo}}^{2}}{c}\approx 28\,{E}_{{\rm{c}},50}^{-1}{\theta }_{{\rm{c}},10^\circ }^{2}{H}_{14}^{3}\,{\rm{s}}.\end{eqnarray} \tag{ 7 }$

The energy released during the shock breakout is approximately ${E}_{{\rm{c}},\mathrm{bo}}\approx {m}_{{\rm{c}}}{v}_{{\rm{c}}}^{2}$ , where ${m}_{{\rm{c}}}\approx {\rho }_{0}\pi {\theta }_{{\rm{c}}}^{2}{H}^{2}{d}_{{\rm{c}},\mathrm{bo}}$ is the mass of the breakout layer, i.e.,

$\begin{eqnarray}&&{E}_{{\rm{c}},\mathrm{bo}}\approx 4.7\times {10}^{47}\,{E}_{{\rm{c}},50}^{1/2}{\rho }_{0,-10}^{-1/2}{\theta }_{{\rm{c}},10^\circ }{H}_{14}^{1/2}\,\mathrm{erg}.\end{eqnarray} \tag{ 8 }$

Therefore, the luminosity of the cocoon shock breakout is approximately

$\begin{eqnarray}&&{L}_{{\rm{c}},\mathrm{bo}}\approx \displaystyle \frac{{E}_{{\rm{c}},\mathrm{bo}}}{{t}_{{\rm{c}},\mathrm{diff}}}\approx 1.7\times {10}^{46}\,{E}_{{\rm{c}},50}^{3/2}{\rho }_{0,-10}^{-1/2}{\theta }_{{\rm{c}},10^\circ }^{-1}{H}_{14}^{-5/2}\,\mathrm{erg}\,{{\rm{s}}}^{-1}.\end{eqnarray} \tag{ 9 }$

One can also estimate the cocoon breakout time after the merger as ${t}_{{\rm{c}},\mathrm{bo}}\approx H/\sqrt{2}{v}_{{\rm{c}}}$ , i.e.,

$\begin{eqnarray}&&{t}_{{\rm{c}},\mathrm{bo}}\approx 0.15\,{E}_{{\rm{c}},50}^{-1/2}{\rho }_{0,-10}^{1/2}{\theta }_{{\rm{c}},10^\circ }{H}_{14}^{5/2}\,\mathrm{days}.\end{eqnarray} \tag{ 10 }$

2.2. Ejecta Shock Breakout

The comprehensive observations (Cowperthwaite et al. 2017; Kasen et al. 2017; Kasliwal et al. 2017; Perego et al. 2017; Tanaka et al. 2017; Villar et al. 2017) for GW170817/AT 2017gfo indicated that the total mass of the ejecta lies in the range of $\sim 0.04\mbox{--}0.08\,{M}_{\odot }$ with a median velocity $\sim 0.1\mbox{--}0.2\,c$ . Therefore, the total kinetic energy of the ejecta ${E}_{{\rm{e}}}$ could only be a few ${10}^{51}\,\mathrm{erg}$ . Similar to the cocoon, the nonrelativistic ejecta can also sweep AGN disk materials, form an ejecta shock, and finally breakout from the disk.

We assume that the aforementioned cocoon shock would not change the disk environment significantly, and the ejecta profile formed after BNS and NSBH mergers is symmetric. The ejecta shock would also break out near the disk surface. The total mass of the swept material by the ejecta shock is

$\begin{eqnarray}&&{M}_{\mathrm{sw},{\rm{e}}}\approx \displaystyle \frac{4\pi {\rho }_{0}{H}^{3}}{3}=0.21\,{\rho }_{0,-10}{H}_{14}^{3}\,{M}_{\odot }.\end{eqnarray} \tag{ 11 }$

The ejecta shock velocity upon breakout can be estimated as ${v}_{{\rm{e}}}\approx \sqrt{{E}_{{\rm{e}}}/({M}_{{\rm{e}},\mathrm{sw}}+{M}_{\mathrm{ej}})}$ , where ${M}_{\mathrm{ej}}$ is the ejecta mass. Since ${M}_{{\rm{e}},\mathrm{sw}}\gg {M}_{\mathrm{ej}}$ , ${v}_{{\rm{e}}}$ is approximately

$\begin{eqnarray}&&{v}_{{\rm{e}}}/c\approx 0.05\,{E}_{{\rm{e}},51}^{1/2}{\rho }_{0,-10}^{-1/2}{H}_{14}^{-3/2}.\end{eqnarray} \tag{ 12 }$

Because ${v}_{{\rm{e}}}/c\lesssim 0.1$ , different from the cocoon shock, there is no significant departure from thermal equilibrium at ejecta shock breakout so that its emission spectrum can be roughly represented by a blackbody spectrum. The temperature is given by

$\begin{eqnarray}&&{T}_{{\rm{e}}}\approx 6.9\times {10}^{5}\,{E}_{{\rm{e}},51}^{1/4}{H}_{14}^{-3/4}\,{\rm{K}},\end{eqnarray} \tag{ 13 }$

which is mainly dependent on the ejecta kinetic energy and the disk height. The observed temperature is

$\begin{eqnarray}&&{T}_{{\rm{e}}}^{\mathrm{obs}}\approx {\left(\displaystyle \frac{{v}_{{\rm{e}}}}{c}\right)}^{1/4}{T}_{{\rm{e}}}\approx 2.7\times {10}^{5}\,{E}_{{\rm{e}},51}^{3/8}{\rho }_{0,-10}^{-1/8}{H}_{14}^{-9/8}\,{\rm{K}}.\end{eqnarray} \tag{ 14 }$

Therefore, the ejecta shock breakout signal would be a UV/X-ray flash.

Similar to the cocoon shock breakout, the energy released is ${E}_{{\rm{e}},\mathrm{bo}}\approx {m}_{{\rm{e}}}{v}_{{\rm{e}}}^{2}$ , where ${m}_{{\rm{e}}}\approx {\rho }_{0}\pi {H}^{2}{d}_{\mathrm{bo},{\rm{e}}}$ , i.e.,

$\begin{eqnarray}&&{E}_{{\rm{e}},\mathrm{bo}}\approx 4.3\times {10}^{48}\,{E}_{{\rm{e}},51}^{1/2}{\rho }_{0,-10}^{-1/2}{H}_{14}^{1/2}\,\mathrm{erg}.\end{eqnarray} \tag{ 15 }$

The diffusion time is

$\begin{eqnarray}&&{t}_{{\rm{e}},\mathrm{diff}}\approx 370\,{E}_{{\rm{e}},51}^{-1}{H}_{14}^{3}\,{\rm{s}}.\end{eqnarray} \tag{ 16 }$

The luminosity of the ejecta shock breakout can be then estimated as

$\begin{eqnarray}&&{L}_{{\rm{e}},\mathrm{bo}}\approx \displaystyle \frac{{E}_{{\rm{e}},\mathrm{bo}}}{{t}_{{\rm{e}},\mathrm{diff}}}\approx 1.2\times {10}^{46}\,{E}_{{\rm{e}},51}^{3/2}{\rho }_{0,-10}^{-1/2}{H}_{14}^{-5/2}\,\mathrm{erg}\,{{\rm{s}}}^{-1}.\end{eqnarray} \tag{ 17 }$

The breakout time after the merger is ${t}_{{\rm{e}},\mathrm{bo}}\approx H/\sqrt{2}{v}_{{\rm{e}}}$ , i.e.,

$\begin{eqnarray}&&{t}_{{\rm{e}},\mathrm{bo}}\approx 0.53\,{E}_{{\rm{e}},51}^{-1/2}{\rho }_{0,-10}^{1/2}{H}_{14}^{5/2}\,\mathrm{days}.\end{eqnarray} \tag{ 18 }$

In summary, if there is a neutron star merger in an AGN disk, two shock breakout events, i.e., a cocoon breakout and an ejecta breakout, would occur. Both shock breakouts have similar luminosities of the order of ${10}^{46}\,\mathrm{erg}\,{{\rm{s}}}^{-1}$ . The cocoon shock breaks out earlier at ∼0.15 days after the merger, while the ejecta shock breakout time is ∼0.5 days. We can also conclude the cocoon shock breakout should be an X-ray transient, while the ejecta shock breakout, having a low observed temperature, would be a UV/X-ray transient.

3. Implication for Future Searches

3.1. Comparison with the AGN Disk Spectra

We show the indicative spectra of cocoon shock breakout, ejecta shock breakout, AGN accretion disk, and its corona (Hubeny et al. 2001) in Figure 3. Various parameters are taken as their typical values (see Figure 3 caption). Since the X-ray emission from AGNs is less prominent, the cocoon shock breakout signal is less contaminated by the contribution of AGN emission and, therefore, easier to detect. The emission energy of the first (cocoon) breakout lies in the range of the nominal detection bandpass of the Einstein Probe (EP) mission (Yuan et al. 2016). After the peak time of ∼0.15 days, the temperature and luminosity of the cocoon shock breakout emission would drop rapidly. After ∼0.3 days, the second (ejecta) shock breakout emission, whose temperature is much lower, will emerge. As shown in Figure 3, the breakout of the second shock is likely greatly contaminated by the AGN disk emission and outshone by the bright emission from AGN disks in the optical ( $3.4\mbox{--}7.9\times {10}^{14}\,\mathrm{Hz}$ ) band. Nonetheless, this component would show up as a bright flare on top of the AGN disk emission in the NUV band, and could be detected by UV ( $\sim 1\mbox{--}2\times {10}^{15}\,\mathrm{Hz}$ ) transient searches, e.g., by Swift (Gehrels et al. 2004), Chinese Space Station Telescope (CSST; Zhan 2011), Ultraviolet Transient Astronomy Satellite (ULTRASAT; Sagiv et al. 2014), and others.

**Figure 3.** Spectra at the cocoon (blue solid line) and ejecta (green solid line) shock breakout. The dashed lines represent the calculated spectrum from SMBHs accreting at nearly the Eddington luminosity ( $L/{L}_{\mathrm{Edd}}\sim 0.3$ ) and central SMBH masses of ${M}_{\mathrm{SMBH}}={10}^{6}$ , 10⁷, and ${10}^{8}\,{M}_{\odot }$ (Hubeny et al. 2001). The disk viewing angle is set to 60° and viscosity parameter $\alpha =0.01$ . The blue shaded region represents the nominal detection bandpass for the Wide-field X-ray Telescope of the Einstein Probe mission (Yuan et al. 2016).
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Cooling of the shock heated AGN material can be described based on Appendix C of Piro & Kollmeier (2018). The diffusion timescale of cocoon cooling is ${t}_{\mathrm{cc},\mathrm{diff}}\approx {(\kappa {\rho }_{0}{H}^{3}/3{v}_{{\rm{c}}}c)}^{1/2}\,\approx 3\,{E}_{{\rm{c}},50}^{-1/4}{\rho }_{0,-10}^{3/4}{\theta }_{{\rm{c}},10^\circ }^{1/2}{H}_{14}^{9/4}\,\mathrm{days}$ , while the resulting peak luminosity is

$\begin{eqnarray}\begin{array}{rcl}{L}_{\mathrm{cc},{\rm{p}}} & \approx & {\left(\displaystyle \frac{{\theta }_{{\rm{c}}}^{2}}{2}\right)}^{4/3}\left(\displaystyle \frac{4\pi {\rho }_{0}{v}_{{\rm{c}}}{H}^{4}}{3{t}_{\mathrm{cc},\mathrm{diff}}^{2}}\right)\\ & \approx & 6.2\times {10}^{37}\,{E}_{{\rm{c}},50}{\rho }_{0,-10}^{-1}{\theta }_{{\rm{c}},10^\circ }^{2/3}{H}_{14}^{-2}\,\mathrm{erg}\,{{\rm{s}}}^{-1}.\end{array}\end{eqnarray} \tag{ 19 }$

The cocoon cooling emission would be outshone by the disk emission.

The peak luminosity of a "kilonova" is thought to be a factor of $\sim {10}^{3}$ higher than a typical nova (e.g., Metzger et al. 2010; Zhu et al. 2020b). It is expected that the large amount of AGN disk material swept by the ejecta can make the kilonova darker. According to Arnett (1982), the characteristic timescale when the light curve peaks is approximately ${t}_{\mathrm{kn},{\rm{p}}}\approx {(\kappa {M}_{\mathrm{sw},{\rm{e}}}/{v}_{{\rm{e}}}c)}^{1/2}\,\approx 20\,{E}_{{\rm{e}},51}^{-1/4}{\rho }_{0,-10}^{3/4}{H}_{14}^{9/4}\,\mathrm{days}$ , while the peak luminosity is equal to the heating rate at the peak time, i.e., ${L}_{\mathrm{kn},{\rm{p}}}$ ≈ ${\eta }_{\mathrm{th}}{M}_{\mathrm{ej}}\epsilon ({t}_{\mathrm{kn},{\rm{p}}})$ ≈ ${10}^{40}\,{E}_{{\rm{e}},51}^{\alpha /4}{\rho }_{0,-10}^{-3\alpha /4}{H}_{14}^{-9\alpha /4}({M}_{\mathrm{ej}}/0.03\,{M}_{\odot })\,\mathrm{erg}\,{{\rm{s}}}^{-1}$ , where ${\eta }_{\mathrm{th}}\approx 0.5$ is the thermalization efficiency (Metzger et al. 2010), the heating rate is $\epsilon {(t)\approx 2\times {10}^{10}\mathrm{erg}{{\rm{g}}}^{-1}{{\rm{s}}}^{-1}(t/1\mathrm{days})}^{-\alpha }$ , and $\alpha \approx 1.3$ . Therefore, kilonova emission in the AGN accretion disks is also much dimmer than the disk emission.

3.2. Event Rate and Target-of-opportunity Follow-up of GW Triggers

For a cocoon shock breakout with luminosity ${L}_{{\rm{c}},\mathrm{bo}}\,\sim {10}^{46}\,\mathrm{erg}\,{{\rm{s}}}^{-1}$ , the detectable distance by EP (field of view ${\rm{\Omega }}\,\approx 1\,\mathrm{sr}$ and survey sensitivity threshold ${F}_{\mathrm{th}}\approx {10}^{-10}\,\mathrm{erg}\,{{\rm{s}}}^{-1}\,{\mathrm{cm}}^{-2}$ for a visit) is ${D}_{{\rm{L}},\max }\approx 3,000\,\mathrm{Mpc}$ , corresponding to a redshift ${z}_{\max }\approx 0.5$ . McKernan et al. (2020) showed that the event rate densities of BNS and NSBH mergers from the AGN channel are ${R}_{\mathrm{BNS}}\sim {f}_{\mathrm{AGN}}[0.2,400]\,{\mathrm{Gpc}}^{-3}\,{\mathrm{yr}}^{-1}$ and ${R}_{\mathrm{NSBH}}\,\sim {f}_{\mathrm{AGN}}[10,300]\,{\mathrm{Gpc}}^{-3}\,{\mathrm{yr}}^{-1}$ , respectively. They also suggested that only ∼10%–20% of NSBH mergers in AGN disks can result in tidal disruptions. Since the cocoon shock is transrelativistic (i.e., ${v}_{{\rm{c}}}\sim 0.19c$ ) when it breaks out, the breakout emission would be nearly isotropic and occupy nearly the 4π solid angle regardless of the opening angle of the breakout flow. On the other hand, the breakout signal may be suppressed if the jet axis has a very small inclination angle with respect to the AGN disk. By assuming that all BNS and 20% NSBH mergers in AGN disks can produce sGRBs and kilonovae, we expect a detection rate of

$\begin{eqnarray}\begin{array}{rcl}{R}_{\mathrm{bo}} & \approx & {f}_{\theta }\displaystyle \frac{{\rm{\Omega }}}{4\pi }({R}_{\mathrm{BNS}}+0.2{R}_{\mathrm{NSBH}}){V}_{\max }\\ & \approx & {f}_{\theta }{f}_{\mathrm{AGN}}[20,4200]\,{\mathrm{yr}}^{-1}\end{array}\end{eqnarray} \tag{ 20 }$

by EP for cocoon and ejecta shock breakouts of BNS and NSBH mergers in AGN disks, where ${V}_{\max }=4\pi {D}_{L,\max }^{3}/3$ , and the factor ${f}_{\theta }\lt 1$ accounts for the fraction of mergers that make a detectable X-ray shock breakout signal due to the distribution of the inclination angle between the binary merger orbital plane and the disk plane.

GW signals from the BNS and NSBH mergers that are embedded in AGN disks are expected to be detected by GW detectors. Abbott et al. (2018) showed that an advanced LIGO detector, after achieving their design sensitivity in O4, would have the detection range of a BNS (NSBH) merger at 160–190 Mpc (300–330 Mpc), while in O5 the BNS (NSBH) detection depth for one GW detector could be up to 330 Mpc (590 Mpc). The expected detection rate of GW triggers that are associated with AGN disk shock breakout signatures is ${R}_{\mathrm{bo}}\,\sim {f}_{\theta }{f}_{\mathrm{AGN}}[0.3,20]\,{\mathrm{yr}}^{-1}$ in O4 and ${R}_{\mathrm{bo}}\sim {f}_{\theta }{f}_{\mathrm{AGN}}[2,110]\,{\mathrm{yr}}^{-1}$ in O5.⁷

The cocoon shock breakout and ejecta shock breakout signals usually occur at ∼0.15 days and ∼0.5 days after the GW triggers. The delay times between GW triggers and breakout signals reserve enough preparation times for subsequent EM follow-up observations. Multimessenger observations of GW signals and the two breakout signals from AGN disks can lend strong support for the formation channel of compact binary coalesences in the AGN disks.

4. Conclusions and Discussion

A neutron star (BNS or NSBH) merger in the migration traps of an AGN disk can generate two bright EM signatures, i.e., a cocoon shock breakout transient and an ejecta shock breakout transient. We show that the jet launched from such a system would be choked and its energy is deposited to the cocoon, which can be energetic enough to break out. Such systems likely would not produce detectable GRBs. The cocoon shock breakout produces soft X-ray emission, which can be easily discovered by EP in the future. The second, ejecta breakout would produce a UV/soft X-ray flash. Due to the contamination of the AGN disk emission, such a signal is most prominent in the NUV band and could be detected by UV transient searches. The two breakout signals peak at ∼0.15 days and ∼0.5 days after the BNS or NSBH merger. The cocoon cooling and kilonova emission signals are typically too faint and would be outshone by the disk emission. Since BNS and NSBH mergers are the search targets for GW detectors, taking advantage of GW triggers for subsequent follow-up observations would be essential to detect these breakout signals, which in turn, will offer support to the formation channel of compact binary mergers in the AGN disks. This is also helpful to test the hypothesis of the BBH population in AGN disks and constrain their fraction.

We have assumed that the jet is launched perpendicular to the disk. In general, the jet orientation in the AGN disks could be random. A cocoon shock driven by an inclined jet would take a longer time to break out from the disk with the emission having a lower temperature and luminosity. We also assumed that the first cocoon shock does not significantly affect the disk environment for the later ejecta shock breakout. This needs to be verified by detailed numerical simulations. If the merger leaves behind a long-lived engine, e.g., a magnetar (Gao et al. 2013; Yu et al. 2013) or a BH with continued accretion (Ma et al. 2018), the ejecta would receive additional energy up to $\sim O({10}^{52})\,\mathrm{erg}$ , which would significantly enhance the ejecta shock breakout signature. If this happens, similar to the cocoon breakout case, the ejecta shock breakout event would also make X-rays.⁸

In the AGN disks, besides compact binary mergers, other destructive explosions, such as supernovae and tidal disruptions (e.g., Assef et al. 2018), could also occur. Shocks would form if these events are embedded in the AGN accretion disk and release a large amount of energy to accelerate AGN disk materials. These events would produce shock breakout events similar to (but probably more energetic than) the transients discussed in this paper.

After the completion of this work, we learned that Perna et al. (2020) have independently investigated the general properties of GRBs in an AGN disk. Different from our approach to focus on the characteristics of EM signals of BNS/NSBH mergers located at migration traps in AGN disks, they discussed the various possible outcomes of a GRB originating from different distances from the supermassive BH and different BH masses. For a GRB occurring near the migration trap of an accretion disk, if ${M}_{\mathrm{SMBH}}\gtrsim {10}^{7}\,{M}_{\odot }$ , their results showed that the prompt radiation and afterglow emission would occur inside the disk photosphere and get thermalized by Thomson scattering. The outcome would be a thermal transient emerging on a diffusion timescale of days to years. For the case with a smaller ${M}_{\mathrm{SMBH}}$ , they indicated the diffusion for prompt and afterglow emissions could be rapid while the late normal afterglow could be observed. This is in general consistent with our conclusions drawn in this paper.

We thank Rosalba Perna for exchanging their paper with us before submission and a referee for constructive suggestions. We thank Yuan-Pei Yang, Liang-Duan Liu, Zhuo Li, Hui Sun, Shao-Ze Li, Yuan-Qi Liu, Rong-Feng Shen, and Er-Lin Qiao for valuable comments. The work of J.P.Z is partially supported by the National Science Foundation of China under Grant No. 11721303 and the National Basic Research Program of China under grant No. 2014CB845800. Y.W.Y is supported by the National Natural Science Foundation of China under Grant Nos. 11822302, 1183303. H.G. is supported by the National Natural Science Foundation of China under Grant Nos. 11722324, 11690024, 11633001, the Strategic Priority Research Program of the Chinese Academy of Sciences, Grant No. XDB23040100 and the Fundamental Research Funds for the Central Universities.

Neutron Star Mergers in Active Galactic Nucleus Accretion Disks: Cocoon and Ejecta Shock Breakouts

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Abstract

1. Introduction

2. Cocoon and Ejecta Shock Breakouts

2.1. Cocoon Shock Breakout

2.2. Ejecta Shock Breakout

3. Implication for Future Searches

3.1. Comparison with the AGN Disk Spectra

3.2. Event Rate and Target-of-opportunity Follow-up of GW Triggers

4. Conclusions and Discussion

Footnotes

Neutron Star Mergers in Active Galactic Nucleus Accretion Disks: Cocoon and Ejecta Shock Breakouts

Article metrics

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Share this article

Author e-mails

Author affiliations

ORCID iDs

Dates

Abstract

1. Introduction

2. Cocoon and Ejecta Shock Breakouts

2.1. Cocoon Shock Breakout

2.2. Ejecta Shock Breakout

3. Implication for Future Searches

3.1. Comparison with the AGN Disk Spectra

3.2. Event Rate and Target-of-opportunity Follow-up of GW Triggers

4. Conclusions and Discussion

Footnotes