Polarimetry of the eclipsing pulsar PSR J1748−2446A
Almog Yalinewich
19.10.18
Schematic
0.85 R_{\odot}
\approx 1 M_{\odot}
\approx 0.1 M_{\odot}
11 \rm ms
2 \rm h
Eclipse at different frequencies
Constraint from constant pulse width at different frequencies
\frac{d t}{d \omega} \approx -c r_e \frac{\int n dl}{\omega^3} \Rightarrow n < \Delta t/c r_e a \Delta \frac{1}{\omega^2}
\Delta t \approx 0.5 {\rm ms}
n < 10^6 \rm cm^{-3}
\omega^2 = \omega_p^2 + k^2 c^2, \omega_p^2 \approx \frac{q^2 n}{m_e }, q^2\approx r_e m_e c^2
\omega \approx 730 \rm MHz
Free Free Absorption
Emissivity
\varepsilon_{\omega} \approx \frac{m_e c^2}{r_e^3} \left(n r_e^3 \right)^2 \sqrt{\frac{m_e c^2}{k T}}
Blackbody
\mathcal{B}_{\omega} \approx \frac{k T}{c^2} \omega^2
Absorption
{\alpha}_{\omega} \approx \frac{\varepsilon}{\mathcal{B}_{\nu}} \approx \frac{c^2}{r_e^3 \omega^2} \left(n r_e^3\right)^2 \left(\frac{m_e c^2}{k T}\right)^{3/2}
Temperature constraint
Absorption
{\alpha}_{\nu} \approx \frac{\varepsilon}{\mathcal{B}_{\nu}} \approx \frac{c^2}{r_e^3 \omega^2} \left(n r_e^3\right)^2 \left(\frac{m_e c^2}{k T}\right)^{3/2}
\alpha_{\nu} a \approx 1 \Rightarrow k T < m_e c^2 \left( \frac{a c^2} {r_e^3 \omega^2}\right)^{2/3} \left(n r_e^3 \right)^{4/3}
Temperature less than 80K!
Gas will not be ionised
Apologetics
Arabian Nights
Large neutral density?
Ionisation fraction
Absorption will heat up plasma to
Cooling through charge exchange?
10^{-6}
10^{6} K
Polarisation outside Eclipse
Depolarisation during Eclipse
Minimum magnetic field from RM
\Delta \theta \approx \frac{q^3}{m_e^2 c^2 \omega^2} \int B_{\parallel} n \cdot ds
RM = \frac{\omega^2}{c^2} \Delta \theta \approx \frac{r_e^2}{q}\int B_{\parallel} n \cdot ds
RM \left[1 \frac{rad}{\rm m^2}\right] = 812 \int B_{\parallel}\left[\mu \rm G\right] n \left[\rm cm^{-3}\right] \cdot ds \left[\rm kpc\right]
B > 100 \mu \rm G
Magnetic field configuarations
B
l
\Delta \theta \propto a B
Random magnetic field, same path
B
l
\Delta \theta \propto \sqrt{l a} B
Multipath in random magnetic field
B
l
f \left(\Delta \theta\right) \propto \exp \left(- \frac{\Delta \theta^2 }{\frac{q^6}{m_e^4 c^4 \omega^4} n^2 B^2 l a} B\right)
Frequency dependence
Rotation angle decreases with wavelength
\Delta \theta \approx \frac{q^3}{m_e^2 c^2 \omega^2} \int B_{\parallel} n \cdot ds
Power law distribution of magnetic field domains?
Lower wavelengths sensitive to smaller, stronger domains