Fast X-ray Transients produced by Off-axis Jet-Cocoons from Long Gamma-Ray Bursts

Abstract

Fast X-ray transients (FXTs) have been detected for over a decade, yet their origins are still enigmatic. The observed association between FXTs and broad-lined Type Ic supernovae (SNe Ic-BL) suggests that some may share the same progenitor with Long Gamma-Ray Bursts. In this work, we numerically simulate the long-term evolution of a relativistic jet propagating from inside the progenitor star up to the photon diffusion radius of the cocoon. Then we post-process the hydrodynamic results and calculate the cocoon cooling emission for various viewing angles from the jet axis. We find that, for viewing angles $θ_{\rm v}=10^{\circ}$--$20^{\circ}$, the off-axis cocoon emission can produce FXTs with luminosity $L_{\rm X}\simeq 10^{47-48} {\rm\, erg\,s^{-1}}$ and duration $t_{\rm X}\simeq 10$-$100\,$s. The observed spectra are quasi-thermal with the peak energy $E_{\rm peak}\simeq0.8$ keV. These properties naturally explain FXTs' observational features, including their high luminosity, soft spectra, and lack of gamma-ray counterparts. The Rayleigh-Jeans tail of the FXT spectra extends to the UV, producing an early UV flash simultaneously. As the cocoon expands and cools, the emission peak shifts to UV and optical bands, resulting in a bright optical plateau lasting for $\sim1$ day with color temperature $T_{\rm UV/opt} \simeq (1{-}3)\times10^{4}\,$K, before the emergence of supernova emission. Although our model underpredicts the UV/optical luminosity at $\sim1$ day, it still provides useful diagnostics for identifying the origins of FXTs.

Figures (15)

• Figure 1: Energy density maps, the sum of kinetic energy density $\Gamma(\Gamma-1)\rho'c^2$ and thermal energy density $\Gamma^2 e'$ of the canonical model (Lc). Different panels correspond to different lab frame times. The colorbar corresponds to the logarithmic energy density in unit of ${\rm erg\,{cm}^{-3}}$. The black solid lines and green dashed lines in the bottom panel are photospheric radius $r_{\rm ph}$ and diffusion radius $r_{\rm diff}$, respectively.
• Figure 2: X-ray lightcurves and spectra of the canonical (Lc) model. Left panel: The X-ray lightcurves in EP WXT band (0.5-4 keV). The blue, red, green, and purple lines correspond to the viewing angles of $10^{\circ}$, $20^{\circ}$, $45^{\circ}$, and $60^{\circ}$. The solid and dashed lines corresponds to the X-ray lightcurve produced at redshift $z=0$ and $z=0.7$. The black solid lines are sensitivity limits of EP WXT taken from Yuan2022hxga.book...86Y for sources at redshifts $z=0.1$ and $z=0.7$. Middle panel: The $T_{90}$-averaged spectra at different viewing angles. The EP WXT band is shown as the gray shaded region. The black dashed line indicates a power-law spectrum with a photon index of 2.5. Right panel: The evolution of peak energy in Lc model. The black dashed line indicates a power-law decay rate $E_{\rm peak}\propto t^{-0.6}_{\rm obs}$.
• Figure 3: EP WXT (0.5-4 keV) lightcurves in different models. The blue, red, green, and purple lines correspond to model $Lc$, $Lw$, $LI$, and $Llow$. The upper, middle, and lower panels show lightcurves at viewing angles of $\theta_{\rm v}=10^{\circ}$, $20^{\circ}$, and $45^{\circ}$, respectively.
• Figure 4: The $T_{90}$-averaged spectra in different models. Colors represent different models, as in Figure \ref{['fig:LXcom']}. The solid ($\theta_{\rm v}=10^{\circ}$), dashed ($\theta_{\rm v}=20^{\circ}$), and dash-dot ($\theta_{\rm v}=45^{\circ}$) lines represent different viewing angles. The black dashed line is a power-law spectrum with a photon index of 2.5.
• Figure 5: The time-resolved spectra in different models and for different viewing angles. The solid lines are spectra near the beginning of $T_{90}$ ($t_{\rm obs}=t_{5\%}$) and the dashed lines show the spectra near the end of $T_{90}$ ($t_{\rm obs}=t_{95\%}$). Colors represent different models, as in Figure \ref{['fig:LXcom']}. The black dashed line on the upper panel is the Planck function with $kT=0.8$keV. All spectra are quasi-thermal and only slightly broader than the Planck function.