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We present a new four‐parameter model of theD‐region (60–90 km) ionospheric electron density, useful in very low frequency (VLF, 3–30 kHz) remote sensing. VLF waves have a long history of use to indirectly inferD‐region conditions, as they reflect efficiently and thus are sensitive to small changes in the electron density. Most historical efforts use VLF observations along with a forward model of theD‐region and VLF propagation. The ionospheric assumptions in the forward model are altered until the output matches the observation. The most commonD‐region model, known as the Wait‐Spies ionosphere, takes the electron density as exponentially increasing with altitude and specifies a height and steepness. This model was designed to capture the VLF propagation variations evident at a single frequency. The realD‐region is likely more complex. The limited number ofD‐region rocket passes that have previously been compiled tend to show the existence of a “ledge” somewhere between 70 and 90 km. Broadband VLF signals emitted from lightning allows a more sophisticated parametrization. Using carefully averaged amplitudes and phases of VLF sferics, we formulate a more general four‐parameterD‐region model that includes a ledge discontinuity. Using lightning‐emitted VLF observations along with a theoretical model, we find that this model better describes the ionosphere during the daytime. During the ambient nighttime and during a solar flare the two‐parameter ionosphere may be sufficient, at least for the purposes of calculating broadband VLF propagation, since the ledge either weakens or moves outside the altitude range of VLF sensitivity.

 

Context. Brown dwarfs are transition objects between stars and planets that are still poorly understood, for which several competing mechanisms have been proposed to describe their formation. Mass measurements are generally difficult to carry out for isolated objects as well as for brown dwarfs orbiting low-mass stars, which are often too faint for a spectroscopic follow-up. Aims. Microlensing provides an alternative tool for the discovery and investigation of such faint systems. Here, we present an analysis of the microlensing event OGLE-2019-BLG-0033/MOA-2019-BLG-035, which is caused by a binary system composed of a brown dwarf orbiting a red dwarf. Methods. Thanks to extensive ground observations and the availability of space observations from Spitzer, it has been possible to obtain accurate estimates of all microlensing parameters, including the parallax, source radius, and orbital motion of the binary lens. Results. Following an accurate modeling process, we found that the lens is composed of a red dwarf with a mass of M 1 = 0.149 ± 0.010 M ⊙ and a brown dwarf with a mass of M 2 = 0.0463 ± 0.0031 M ⊙ at a projected separation of a ⊥ = 0.585 au. The system has a peculiar velocity that is typical of old metal-poor populations in the thick disk. A percent-level precision in the mass measurement of brown dwarfs has been achieved only in a few microlensing events up to now, but will likely become more common in the future thanks to the Roman space telescope.