Magnetic fields in the Milky Way from pulsar observations: effect of the correlation between thermal electrons and magnetic fields

Pulsars can act as an excellent probe of the Milky Way magnetic field. The average strength Galactic field component parallel to line sight be estimated $\langle B_\parallel \rangle = 1.232 \, \text{RM}/\text{DM}$, where $\text{RM}$ and $\text{DM}$ are rotation dispersion measure pulsar. However, this assumes that thermal electron density interstellar medium uncorrelated. Using numerical simulations observations, we test validity assumption. Based on magnetohydrodynamical driven turbulence, show correlation between small-scale increases with increasing Mach number turbulence. We find assumption uncorrelated fields is valid only for subsonic transsonic flows, but supersonic severely overestimated by using $1.232 \text{RM}/\text{DM}$. then correlate existing pulsar observations from Australia Telescope National Facility regions enhanced probed ${^{12} \mathrm {CO}}$ data molecular clouds, Zeeman splitting 21 cm line, neutral hydrogen column density, H$\alpha$ observations. these observational data, largely over kpc scales. Thus, conclude relation \text{RM}/\text{DM}$ provides a good estimate scales might break down sub -