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The influence of plasma lensing magnification to the luminosity function of fast radio bursts

Xinzhong Er, Weishan Zhu, Shude Mao, Dongzi Li

Abstract

Small scale clumps of ionized gas have been suggested by observations in interstellar medium and circumgalactic medium. The propagation of radio signals can be deflected by these plasma clumps, i.e. plasma lensing. One observable consequence is the magnification and demagnification of background sources. These effects distort the observed luminosity function and potentially introduce bias into population studies. In this work, we investigate these effects on fast radio bursts using Gaussian plasma clumps distributed across multiple lens planes within a small field of view. The central electron density for each clump is sampled from uniform, log-normal, and Gaussian distributions. Two analytical models are employed to mimic the intrinsic luminosity function. Our results show that plasma lensing can modify the observed luminosity functions. On one hand, our model shows that radio sources may be demagnified below the detection threshold, the strength varies between ~1-15% depending on the ionized gas model and the source redshift. On the other hand, magnification can produce anomalously bright sources at the high luminosity end. Both effects introduce potential biases in inferred source properties. The lensing strength correlates with the power spectrum of free electron density. However, scattering effect in the host galaxy or in the Milky Way can suppress the plasma lensing effects.

The influence of plasma lensing magnification to the luminosity function of fast radio bursts

Abstract

Small scale clumps of ionized gas have been suggested by observations in interstellar medium and circumgalactic medium. The propagation of radio signals can be deflected by these plasma clumps, i.e. plasma lensing. One observable consequence is the magnification and demagnification of background sources. These effects distort the observed luminosity function and potentially introduce bias into population studies. In this work, we investigate these effects on fast radio bursts using Gaussian plasma clumps distributed across multiple lens planes within a small field of view. The central electron density for each clump is sampled from uniform, log-normal, and Gaussian distributions. Two analytical models are employed to mimic the intrinsic luminosity function. Our results show that plasma lensing can modify the observed luminosity functions. On one hand, our model shows that radio sources may be demagnified below the detection threshold, the strength varies between ~1-15% depending on the ionized gas model and the source redshift. On the other hand, magnification can produce anomalously bright sources at the high luminosity end. Both effects introduce potential biases in inferred source properties. The lensing strength correlates with the power spectrum of free electron density. However, scattering effect in the host galaxy or in the Milky Way can suppress the plasma lensing effects.
Paper Structure (6 sections, 8 equations, 7 figures, 1 table)

This paper contains 6 sections, 8 equations, 7 figures, 1 table.

Table of Contents

  1. Introduction
  2. Basics of Plasma Lensing
  3. Magnification of plasma lensing
  4. A single Gaussian model
  5. Kolmogorov medium
  6. Discussion and Conclusions

Figures (7)

  • Figure 1: The ratio $\theta_0/\sigma$ of plasma lensing as a function of the lensing scale for different electron densities. The solid curves represent the case for a source at $z_s=3.0$ and a lens at $z_d=0.5$, while the dotted curves correspond to a source at $z_s=0.5$ and a lens at $z_d=0.1$. The black, blue and red curves indicate results for the density ($n_e$) of $0.001$cm$^{-3}$, $0.01$cm$^{-3}$ and $0.05$cm$^{-3}$ respectively.
  • Figure 2: The lensing probability for $\mu<\mu_t$ is shown as a function of lens redshift for a single Gaussian profile. The source redshift is $z_s=3.0$. The solid (dotted) curves represent the results for observational frequencies $\nu=1$ and $\nu=1.5$ GHz, respectively.
  • Figure 3: The luminosity function before and after a single Gaussian plasma lens. The gray shaded histograms represent the initial source distributions. The red histogram shows the distribution after lensing. The vertical lines mark the mock detection limits. From top to bottom, the initial luminosity functions correspond to the broken power-law and Schechter function, respectively.
  • Figure 4: The ratio of sources within the detection limit after lensing demagnification. The solid (dashed) lines show the result using a broken-power (Schechter) function. The black (blue) curves show the detection limit of 1 (5) mJy, which corresponding to $0.4$ (2)$\times10^{41}$erg s$^{-1}$ at redshift $3.0$.
  • Figure 5: The power spectrum of the 2D plasma density in one redshift bin is shown. The purple and cyan lines represent the theoretical power spectrum proportional to $\propto k^{-11/6}$ and $\propto k^{-11/3}$ respectively. $S1-$log-normal, $S2-$Gaussian, $S3-$log-normal with large clumps, $S1u-$log-normal with uniform clump size distribution.
  • ...and 2 more figures