FRB
scintillation in the
IGM
Almog Yalinewich
Clues from the Dispersion measure
\frac{d t}{d \omega} \approx - c r_e \frac{\int_0^d n_e ds}{\omega^3}
c^2 k^2 = \omega^2 -\omega_p^2
r_e
Classical Electron radius
\omega_p^2 \approx c^2 r_e n_e
Could it be the intergalactic medium?
Kolmogorov Turbulent Cascade
\left[\varepsilon\right] = \frac{\rm cm^2}{\rm s^3}
Dimensional analysis
\delta v \approx \left(\varepsilon l\right)^{1/3}
eddy size
Inner and Outer Scale
\frac{\delta v}{a} \approx \left(\frac{l}{L}\right)^{1/3}
L
Speed of Sound
Outer scale
l>l_{\min}
Inner scale
Scintillation
d
l
Phase Difference
\frac{\delta v}{a} \approx \frac{\delta T}{T} \approx \frac{\delta n}{n} \approx \left(\frac{l}{L}\right)^{1/3}
c^2 k^2 = \omega^2 -\omega_p^2 \Rightarrow \frac{\delta k}{k} \approx \frac{\omega_p^2}{c^2 k^2 } \frac{\delta n}{n}
\delta \phi \approx \delta k \cdot l
\Delta \phi \approx \sqrt{\frac{d}{l}} \delta \phi\approx \frac{\sqrt{d} \omega_p^2 l^{5/6}}{c^2 k L^{1/3}}
\Delta \phi \approx 1 \Rightarrow l_{\rm dif} \approx \frac{c^{12/5} k^{6/5} L^{2/5}}{\omega_p^{12/5} d^{3/5}}
Deflection Angle and Delay Time
\Delta \theta \approx \frac{\lambda}{l} \Delta \phi \propto l^{-1/6}
\Delta t \approx \frac{d}{c} \Delta \theta^2 \approx \frac{d}{c} \left(\frac{\lambda}{l_{\rm dif}}\right)^2 \propto \lambda^{4.4}
Dominated by small scales
Constraint from timescale on outer length
L \le 10^{13} \left(\frac{d}{\rm Gpc}\right)^{11/4} \left(\frac{n}{10^{-7} \rm cm^{-3}}\right)^3 \left(\frac{\Delta t}{\rm ms}\right)^{-5/4} \rm cm
Inequality if
l_{\rm min} > l_{\rm dif}
Heating the Intergalactic Medium
Bremsstrahlung cooling timescale
Viscous heating timescale
t_h \approx \frac{L}{a} \approx 12 \left(\frac{a}{100 \rm km/s}\right)^{-1} \left(\frac{L}{10^{13} \rm cm}\right) \rm days
t_c \approx \frac{r_e}{c} \frac{ \left(m_p a^2/ m_e c^2\right)^{3/2}}{\alpha \left(n r_e^3\right) } \approx 50 \left(\frac{a}{100 \rm km/s}\right)^{3} \left(\frac{n}{10^{-7} \rm cm^{-3}}\right)^{-1} \rm Gyr
Constraint on outer scale from heating
L > 10^{24} \rm cm
Large Scale Strucutre
\nabla \rho \neq 0
Dispersion and Scattering Meaure
\Delta t_d \approx \frac{c r_e}{\omega^2} n d \Rightarrow DM=\int_0^d n ds
\Delta \phi^2 \approx \frac{d \omega_p^4 l^{5/3}}{c^4 k^2 L^{2/3}} \Rightarrow SM\propto \int_0^d n^2 ds
Dispersion measure from Simulations
mean
standard deviation
contributions from different components
Scattering measure from Simulations
Comparisons to observations
Summary
L_0
Previous study
uniform density
1 \rm AU
Current study
Clumpy IGM
100 {\rm AU}
Prevent the universe from boiling
1 {\rm Mpc}
IGM cannot account for SM
frb scintillation in the igm
By almog yalinewich
