Origin of Pulsar Radio Emission

Since pulsars were discovered as emitters of bright coherent radio emission more than half a century ago, the cause of the emission has remained a mystery. In this Letter we demonstrate that coherent radiation can be directly generated in nonstationary pair plasma discharges which are responsible for filling the pulsar magnetosphere with plasma. By means of large-scale two-dimensional kinetic plasma simulations, we show that if pair creation is nonuniform across magnetic field lines, the screening of electric field by freshly produced pair plasma is accompanied by the emission of waves which are electromagnetic in nature. Using localized simulations of the screening process, we identify these waves as superluminal ordinary ($O$) modes, which should freely escape from the magnetosphere as the plasma density drops along the wave path. The spectrum of the waves is broadband and the frequency range is comparable to that of observed pulsar radio emission.

Figure 1

Formation of the electromagnetic wave during the process of dynamic screening of the electric field in the pair plasma discharge. Individual panels show two-dimensional distributions of (a) plasma density ($n$), normalized to the minimum density required to carry the current, $V_0{B}_0/4e\pi cR$. (b) Electric field component along the background magnetic field ($E_x$); electromagnetic field quantities computed by subtracting the $x$-averaged distributions to better visualize the wave pattern. (d) Transverse component of the electric field ${\tilde{E}}_y$. (c) Longitudinal component of the Poynting flux vector ${\tilde{S}}_x$. (e) Out-of-plane component of the magnetic field ${\tilde{B}}_z$. (f) Transverse component of the Poynting flux vector ${\tilde{S}}_y$. The electromagnetic field components are normalized to vacuum field, $(V_0/c)B_0$, and Poynting flux components are normalized to the bulk Poynting flux, $S_0=c(V_0/c{)}^2{B}_0^2/4\pi$, that a sheared conductor launches. In all panels distances are measured in units of the conductor’s half-length, $R$.

Figure 2

Formation of the superluminal electromagnetic wave during the process of dynamic screening of the electric field. First row shows two-dimensional distributions of (a) plasma density ($n$). (b) Electric field component along the background magnetic field ($E_x$). (c) Out-of-plane component of the magnetic field ($B_z$), at $0.47L_x/c$, where $L_x$ is the size of the computational box in the $x$ direction. Panels (d)–(f) show the snapshots of $n$ (blue line), $E_x$ (green line), and $B_z$ (red line) at three consecutive moments of time in the simulation, $0.47L_x/c$, $0.53L_x/c$, and $0.6L_x/c$. Blue vertical dashed lines move to the right at the speed of light. The wavefront clearly overruns the position of the lines, which proves the superluminal phase speed of the mode. Panels (a)–(c) show close-up onto the central part of our numerical domain which is larger in the $y$ direction. Simulation is performed for the angle between the normal to plasma injection front and the background magnetic field $\alpha =1/40$. In all panels distances are measured in units of the plasma skin depth $c/{\omega }_p$, where plasma frequency ${\omega }_p=\sqrt{4\pi e^2{n}_0/m_e}$ is calculated for the cold plasma of a fiducial density $n_0$.

Figure 3

One-dimensional pair discharge for realistic parameters ($P=33\mathrm{ms}$, $B={10}^{12}\mathrm{G}$, magnetic field line radius of curvature ${\rho }_c=1.67\times {10}^7\mathrm{cm}$). Shown are (a): charge densities $n_{\pm }$ of positrons (red line) and electrons (blue line), normalized to $n_{\mathrm{GJ}}$; (b) electric field $E$ normalized to the vacuum field $E_{\mathrm{vac}}=\mathrm{\Omega }B{r}_{pc}/2c=7.6\times {10}^{10}\mathrm{V}/\mathrm{cm}$; and (c) power spectrum of the electric field $E_k^2$ for spatial intervals shown by the gray bar in panel (b). The orange bar in panel (c) indicates the range of spatial frequencies $k$, measured in units of $1/L$, where $L=0.25r_{pc}$ is the size of the simulation box, corresponding to the range of plasma skin depths in the region shown by the gray bar in panel (b). Distance $x$ from the NS is normalized to the polar cap radius $r_{pc}=7.97\times {10}^4\mathrm{cm}$.