Interstellar Absorption of the Galactic Polar Low-Frequency Radio Background Synchrotron Spectrum as an Indicator of Clumpiness in the Warm Ionized Medium

In the standard model of low-frequency synchrotron radiation propagation through the Galaxy, the absorbing warm ionized medium (WIM) is considered to be a thick slab of thermal electrons of uniform density. When the calculated polar radio spectrum is compared with the observed Galactic background radio spectrum, it is found that this model requires a much higher electron density n_e or much lower temperature T_e than permitted by current observations. A more realistic plane-parallel model, in which electron density, temperature, and cosmic-ray electron emissivity have smooth distributions with height z above the Galactic plane, is also found to suffer from the same setbacks as the standard model. However, a plane-parallel model in which the absorbing WIM has a clumpy distribution with clump densities of ~0.2 cm^-3 and filling factor of 0.08-0.15 agrees with both the low-frequency radio synchrotron spectrum and the observational parameters <n_e(z=0)>~0.025 cm^-3, T_e~7000 K, and DM~23 pc cm^-3. The clumpy WIM model also supports the idea of a local interstellar cloud (LIC), which is required to provide adequate absorption below ~0.5 MHz. This LIC appears to become optically thick only below ~0.1 MHz where future radio measurements may be used to determine the emissivity spectrum and, therefore, the local interstellar cosmic-ray electron spectrum at energies of ~40 MeV.