Quasi‐thermal noise (QTN) spectroscopy is an accurate technique for in situ measurements of electron density and temperature in space plasmas. A QTN spectrum is determined by plasma and antenna properties. On STEREO/WAVES, since the antennas are relatively short and thick, the QTN spectrum is dominated by electron shot noise, especially at low frequencies, which reduces the accuracy of the method. Here we use the STEREO low‐frequency receiver, proton density measured by Plasma and Suprathermal Ion Composition instrument, and a QTN and shot noise models to provide electron temperature data from both STEREO A and B spacecraft. This derivation is important since no reliable measurements of electron temperature exist on board these spacecraft. We compare the results of our analysis with the electron temperature provided by the Wind spacecraft during the period when Wind and STEREO B were close to each other. The comparison shows that our technique is reliable when results are integrated on a time scale of the order of 50 to 60 min.

Our main aim is to apply the theory of regularly varying functions to the asymptotical analysis at infinity of solutions of Friedmann cosmological equations. A new constant Γ is introduced related to the Friedmann cosmological equations. Determining the values of Γ we obtain the asymptotical behavior of the solutions, i.e. of the expansion scale factor a(t) of a universe. The instance Γ < 1 4 is appropriate for both cases, the spatially flat and open universe, and gives a sufficient and necessary condition for the solutions to be regularly varying. This property of Friedmann equations is formulated as the generalized power law principle. From the theory of regular variation it follows that the solutions under usual assumptions include a multiplicative term which is a slowly varying function.

We present an extended analysis of the relation between radio surface brightness and diameter -the so-called Σ − D relation for planetary nebulae (PNe). We revise our previous derivation of the theoretical Σ − D relation for the evolution of bremsstrahlung surface brightness in order to include the influence of the fast wind from the central star. Different theoretical forms are derived:for the first and second phases of evolution and Σ ∝ D −3 for the final stage of evolution. Also, we analyzed several different Galactic PN samples. All samples are influenced by severe selection effects, but the Malmquist bias seems to be less influential here than in the supernova remnant (SNR) samples. We derived empirical Σ − D relations for 27 sample sets using 6 updated PN papers from which an additional 21 new sets were extracted. Twenty four of these have a trivial form of β ≈ 2. However, we obtain one empirical Σ − D relation that may be useful for determining distances to PNe. This relation is obtained by extracting a recent nearby (<1 kpc) Galactic PN sample.

Quasi‐thermal noise (QTN) spectroscopy is a plasma diagnostic technique which enables precise measurements of local electron velocity distribution function moments. This technique is based on measurements and analysis of voltage fluctuations at the antenna terminals, induced by thermal motion of charged particles. In this work, we accommodate, for the first time, this technique to weakly ionized collisional plasmas. It turns out that the QTN spectrum is modified both at low frequencies, increasing the level of power spectrum, and around the plasma frequency, where collisions damp the plasma oscillations and therefore broaden and reduce the amplitude of so called “plasma peak,” while the spectrum at high frequencies is nearly unmodified compared to the collisionless case. Based on these results, we show that QTN spectroscopy enables independent measurements of the collision frequency, electron density, and temperature, provided the ratio of collision frequency to plasma frequency is ν/ωp∼0.1. The method presented here can be used for precise estimation of plasma parameters in laboratory devices and unmagnetized ionospheres, while application in the ionosphere of Earth is possible but limited to small, low‐frequency range due to magnetic field influence.

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