The l = 2 spherical harmonic expansion coefficients of the sky brightness distribution between 0.5 and 7 MHz

¹ Space Sciences Laboratory, University of California, Berkeley, CA 94720, USA
e-mail: brent_page@berkeley.edu
² Department of Physics, University of California, Berkeley, CA 94720, USA
³ Center for Astrophysics and Space Astronomy, University of Colorado, Boulder, CO 80309, USA
⁴ Department of Astrophysical and Planetary Sciences, University of Colorado, Boulder, CO 80309, USA
⁵ LESIA, Observatoire de Paris, PSL Université, CNRS, Sorbonne Université, Université de Paris, 92195 Meudon, France
⁶ NASA Ames Research Center, Moffett Field, CA 94035, USA
⁷ Research Institute for Advanced Computer Science, Universities Space Research Association, Washington, DC 20024, USA

Received: 28 July 2022
Accepted: 28 October 2022

Abstract

Context. The opacity of the ionosphere prevents comprehensive Earth-based surveys of low frequency ν ≲ 10 MHz astrophysical radio emissions. The limited available data in this frequency regime show a downturn in the mean sky brightness at ν ≲ 3 MHz in a divergence from the synchrotron emission power-law that is observed at higher frequencies. The turning over of the spectrum coincides with a shift in the region of maximum brightness from the Galactic plane to the poles. This implicates free-free absorption by interstellar ionized gas, whose concentration in the plane causes radiation that propagates in this region to suffer stronger absorption than radiation from the poles.

Aims. Using observations from Parker Solar Probe (PSP), we evaluate the l = 0 and l = 2 spherical harmonic expansion coefficients of the radio brightness distribution at 56 frequencies between 0.5 and 7 MHz. These data quantify free-free absorption’s global effects on the brightness distribution, which provides new constraints on the distribution of free electrons in the Galaxy.

Methods. The auto and cross spectra of the voltages induced on crossed short dipole antennas by radiation from a nonpolarized extended brightness distribution are linear combinations of the distribution’s l = 0 and l = 2 expansion coefficients. We extracted the least squares solution to these coefficients from PSP’s measurements of the radio background. Also, we generated hypothetical low frequency brightness maps that incorporated free-free absorption and tested their compatibility with the data. The maps primarily depended on models of the Galactic emissivity and distribution of free electrons. A comparison of the maps’ expansion coefficients with the empirical coefficients provided an indication of these input models’ accuracies.

Results. An average reduced x² ≈ 1.04 of the spherical harmonic analysis between 0.5 and 7 MHz indicates that PSP’s antennas act approximately as ideal short dipoles in this frequency band. The best-fit expansion coefficients show that, with decreasing frequency, the mean sky brightness decreases at ν < 3 MHz and the Galactic plane darkens relative to the poles. At ν > 0.6 MHz, these observations can be reproduced in synthetic brightness maps in which the Galactic emissivity maintains a power-law form and free-free absorption is modeled using free electron distributions derived from pulsar measurements. At lower frequencies, the empirical mean brightness falls below the mean in this model, possibly signifying a cutoff in the synchrotron power-law.