High Energy Neutrino Flashes from Far-Ultraviolet and X-Ray Flares in Gamma-Ray Bursts

The recent observations of bright optical and x-ray flares by the Swift satellite suggest these are produced by the late activities of the central engine. We study the neutrino emission from far-ultraviolet and x-ray flares under the late internal shock model. We show that the efficiency of pion production in the highest energy is comparable to or higher than the unity, and the contribution from such neutrino flashes to a diffuse very high energy neutrino background can be larger than that of prompt bursts if the total baryonic energy input into flares is comparable to the radiated energy of prompt bursts. These signals may be detected by IceCube and are very important because they have possibilities to probe the nature of flares (the baryon loading, the photon field, the magnetic field and so on).

Figure 1

Various cooling time scales and the acceleration time scale for FUV-ray flares with $L_{\max }={10}^{49}\mathrm{ergs}/\mathrm{s}$, ${\xi }_B=1$, and $r={10}^{14.9}\mathrm{cm}$ with $\Gamma =30$. Note that energy scale is measured in the shell comoving frame.

Figure 2

The observed muon-neutrino $({\nu }_{\mu }+{\overline{\nu }}_{\mu })$ spectra for one GRB event at $z=0.1$. X-ray flare (A): $L_{\max }={10}^{49}\mathrm{ergs}/\mathrm{s}$, ${\xi }_B=1$, ${\xi }_{\mathrm{acc}}=10$, and $r={10}^{14.9}\mathrm{cm}$ with $\Gamma =30$. X-ray flare (B): $L_{\max }={10}^{48}\mathrm{ergs}/\mathrm{s}$, ${\xi }_B=1$, ${\xi }_{\mathrm{acc}}=10$, and $r={10}^{15.3}\mathrm{cm}$ with $\Gamma =15$. FUV-ray flare (A): $L_{\max }={10}^{48}\mathrm{ergs}/\mathrm{s}$, ${\xi }_B=1$, ${\xi }_{\mathrm{acc}}=10$, and $r={10}^{15.3}\mathrm{cm}$ with $\Gamma =15$. FUV-ray flare (B): $L_{\max }={10}^{50}\mathrm{ergs}/\mathrm{s}$, ${\xi }_B=0.1$, ${\xi }_{\mathrm{acc}}=30$, and $r={10}^{14.9}\mathrm{cm}$ with $\Gamma =30$.

Figure 3

The neutrino background from flares. X-ray flare (the upper dashed line): $L_{\max }={10}^{49}\mathrm{ergs}/\mathrm{s}$, ${\xi }_B=1$, $f_{\mathrm{F}}{\xi }_{\mathrm{acc}}=1$, and $r={10}^{15.3}\mathrm{cm}$ with $\Gamma =15$; $N_{\mu }=3.7\mathrm{\text{events}}/\mathrm{yr}$. (The lower dashed line): $L_{\max }={10}^{49}\mathrm{ergs}/\mathrm{s}$, ${\xi }_B=1$, $f_{\mathrm{F}}{\xi }_{\mathrm{acc}}=0.5$, and $r={10}^{14.9}\mathrm{cm}$ with $\Gamma =30$; $N_{\mu }=0.8\mathrm{\text{events}}/\mathrm{yr}$. FUV-ray flare (the upper dotted line): $L_{\max }={10}^{49}\mathrm{ergs}/\mathrm{s}$, ${\xi }_B=0.1$, $f_{\mathrm{F}}{\xi }_{\mathrm{acc}}=5$, and $r={10}^{14.9}\mathrm{cm}$ with $\Gamma =30$; $N_{\mu }=8.8\mathrm{\text{events}}/\mathrm{yr}$. (The lower dotted line): $L_{\max }={10}^{48}\mathrm{ergs}/\mathrm{s}$, ${\xi }_B=1$, $f_{\mathrm{F}}{\xi }_{\mathrm{acc}}=1$, and $r={10}^{15.3}\mathrm{cm}$ with $\Gamma =15$; $N_{\mu }=1.4\mathrm{\text{events}}/\mathrm{yr}$. GRB: taken from [2] with $E_{\gamma ,\mathrm{sh}}^{\mathrm{iso}}=2\times {10}^{51}\mathrm{ergs}$, ${\xi }_B=1$, ${\xi }_{\mathrm{acc}}=10$, and $r=({10}^{13}–{10}^{14.5})\mathrm{cm}$; $N_{\mu }=21\mathrm{\text{events}}/\mathrm{yr}$. WB: Waxman-Bahcall bounds [1].