Interpretation of the Structure Function of Rotation Measure in the Interstellar Medium

Abstract

The observed structure function (SF) of rotation measure (RM) varies as a broken power-law function of angular scales. The systematic shallowness of its spectral slope is inconsistent with the standard Kolmogorov scaling. This motivates us to examine the statistical analysis on RM fluctuations. The correlations of RM constructed by Lazarian & Pogosyan are demonstrated to be adequate in explaining the observed features of RM SFs through a direct comparison between the theoretically obtained and observationally measured SF results. By segregating the density and magnetic field fluctuations and adopting arbitrary indices for their respective power spectra, we find that when the SFs of RM and emission measure have a similar form over the same range of angular scales, the statistics of the RM fluctuations reflect the properties of density fluctuations. RM SFs can be used to evaluate the mean magnetic field along the line of sight, but cannot serve as an informative source on the properties of turbulent magnetic field in the interstellar medium. We identify the spectral break of RM SFs as the inner scale of a shallow spectrum of electron density fluctuations, which characterizes the typical size of discrete electron density structures in the observed region.

On the Origin of the Scatter Broadening of Fast Radio Burst Pulses and Astrophysical Implications

“…The warm ionized medium (WIM) has M s of order unity (Haffner et al 1999;Kim & Ryu 2005;Hill et al 2008) and hence Kolmogorov density distribution (Armstrong et al 1995;Chepurnov & Lazarian 2010), while in other colder and denser phases in the inner Galaxy with a higher compressibility (i.e., larger M s , Larson 1981;Heiles & Troland 2003), a shallower density spectrum is naturally expected (Kim & Ryu 2005;Burkhart et al 2015). Significant deviation from the Kolmogorov law and flattening of the density spectrum are indicated from e.g., spectroscopic observations (Lazarian 2006(Lazarian , 2009Hennebelle & Falgarone 2012), scattering measurements of the Galactic pulsars with high DMs (Löhmer et al 2001(Löhmer et al , 2004Bhat et al 2004;Lewandowski et al 2013Lewandowski et al , 2015Krishnakumar et al 2015;Xu & Zhang 2016, in preparation), and rotation measure fluctuations at low Galactic latitudes (Haverkorn et al 2004(Haverkorn et al , 2008Xu & Zhang 2016). Accompanying the shallowness of the spectral slope of density fluctuations, substantial discontinuous structures in density emerge at small scales due to supersonic compressions.…”

Scatter Broadening of Pulsars and Implications on the Interstellar Medium Turbulence

“…Such a large injection scale of turbulence was also reported in Haverkorn et al (2006Haverkorn et al ( , 2008 by measuring structure functions of Faraday rotation measure for Galactic interarm regions, suggesting the main sources of turbulence in the WIM as supernova and superbubble explosions (see review by Haverkorn & Spangler 2013). In other colder and denser phases in the inner Galactic plane, such as the cold neutral medium and molecular clouds, the turbulence is supersonic with M s > 1 (e.g., M s ≈ 5 − 20 in molecular clouds, see Zuckerman & Palmer 1974;Larson 1981), and consists of a network of shocks. Density fluctuations and velocity fluctuations exhibit distinct power spectra (Falceta-Gonçalves et al 2014).…”

“…The associated short-wave-dominated density spectrum results in the scatter broadening of the observed pulse width of e.g., a fast radio burst (Xu & Zhang 2016b). 5.…”

“…Regarding the latter case, despite the ample measurements of neutrals (see above), to our knowledge, such a shallow density spectrum of electron density fluctuations has only been extracted from the rotation measurements of polarized extragalactic sources (Xu & Zhang 2016a). Potentially, the scattering measurements of low-latitude pulsars enable us to carry out a more detailed investigation of the electron density distribution in the supersonic turbulence in the Galactic plane.…”

“…Motivated by both the numerical and observational evidence, we consider a spectral model for interstellar electron density fluctuations by incorporating not only a Kolmogorov density spectrum with β = 11/3 but also a shallower density spectrum with β < 3, to perform a comprehensive analysis of the interstellar scattering of pulsars. Moreover, the second-order density statistics in a turbulent flow, namely, the density spectrum in Fourier space and the structure function of density fluctuations in real space (Lazarian & Pogosyan 2004, can be used to recover statistical properties of the ISM turbulence, which imprint on observables such as velocity centroids (Lazarian & Esquivel 2003;Esquivel & Lazarian 2005;Burkhart et al 2014), Doppler-shifted emission and absorption spectral lines (Lazarian & Pogosyan 2000Lazarian 2006), rotation measure fluctuations (Minter & Spangler 1996;Xu & Zhang 2016a), as well as the scatter broadening time of pulsars that we focus on in the current study. The observationally measured DM and frequency scalings of the pulse broadening time impose constraints on the slope, amplitude, and cutoff scales of the density power spectrum.…”