Planetary Radio Interferometry and Doppler Experiment (PRIDE) Technique: a Test Case of the Mars Express Phobos Fly-by. 2. Doppler tracking: Formulation of observed and computed values, and noise budget

Context. Closed-loop Doppler data obtained by deep space tracking networks (e.g., NASA's DSN and ESA's Estrack) are routinely used for navigation and science applications. By "shadow tracking" the spacecraft signal, Earth-based radio telescopes involved in Planetary Radio Interferometry and Doppler Experiment (PRIDE) can provide open-loop Doppler tracking data when the dedicated deep space tracking facilities are operating in closed-loop mode only. Aims. We explain in detail the data processing pipeline, discuss the capabilities of the technique and its potential applications in planetary science. Methods. We provide the formulation of the observed and computed values of the Doppler data in PRIDE tracking of spacecraft, and demonstrate the quality of the results using as a test case an experiment with ESA's Mars Express spacecraft. Results. We find that the Doppler residuals and the corresponding noise budget of the open-loop Doppler detections obtained with the PRIDE stations are comparable to the closed-loop Doppler detections obtained with the dedicated deep space tracking facilities

Radiative transfer effects in primordial hydrogen recombination

The calculation of a highly accurate cosmological recombination history has been the object of particular attention recently, as it constitutes the major theoretical uncertainty when predicting the angular power spectrum of Cosmic Microwave Background anisotropies. Lyman transitions, in particular the Lyman-alpha line, have long been recognized as one of the bottlenecks of recombination, due to their very low escape probabilities. The Sobolev approximation does not describe radiative transfer in the vicinity of Lyman lines to a sufficient degree of accuracy, and several corrections have already been computed in other works. In this paper, the impact of some previously ignored radiative transfer effects is calculated. First, the effect of Thomson scattering in the vicinity of the Lyman-alpha line is evaluated, using a full redistribution kernel incorporated into a radiative transfer code. The effect of feedback of distortions generated by the optically thick deuterium Lyman-alpha line blueward of the hydrogen line is investigated with an analytic approximation. It is shown that both effects are negligible during cosmological hydrogen recombination. Secondly, the importance of high-lying, non overlapping Lyman transitions is assessed. It is shown that escape from lines above Ly-gamma and frequency diffusion in Ly-beta and higher lines can be neglected without loss of accuracy. Thirdly, a formalism generalizing the Sobolev approximation is developed to account for the overlap of the high-lying Lyman lines, which is shown to lead to negligible changes to the recombination history. Finally, the possibility of a cosmological hydrogen recombination maser is investigated. It is shown that there is no such maser in the purely radiative treatment presented here.Comment: 23 pages, 4 figures, to be submitted to PR

The SFXC software correlator for Very Long Baseline Interferometry: Algorithms and Implementation

In this paper a description is given of the SFXC software correlator, developed and maintained at the Joint Institute for VLBI in Europe (JIVE). The software is designed to run on generic Linux-based computing clusters. The correlation algorithm is explained in detail, as are some of the novel modes that software correlation has enabled, such as wide-field VLBI imaging through the use of multiple phase centres and pulsar gating and binning. This is followed by an overview of the software architecture. Finally, the performance of the correlator as a function of number of CPU cores, telescopes and spectral channels is shown.Comment: Accepted by Experimental Astronom

Venus Express radio occultation observed by PRIDE

Context. Radio occultation is a technique used to study planetary atmospheres by means of the refraction and absorption of a spacecraft carrier signal through the atmosphere of the celestial body of interest, as detected from a ground station on Earth. This technique is usually employed by the deep space tracking and communication facilities (e.g., NASA's Deep Space Network (DSN), ESA's Estrack). Aims. We want to characterize the capabilities of the Planetary Radio Interferometry and Doppler Experiment (PRIDE) technique for radio occultation experiments, using radio telescopes equipped with Very Long Baseline Interferometry (VLBI) instrumentation. Methods. We conducted a test with ESA's Venus Express (VEX), to evaluate the performance of the PRIDE technique for this particular application. We explain in detail the data processing pipeline of radio occultation experiments with PRIDE, based on the collection of so-called open-loop Doppler data with VLBI stations, and perform an error propagation analysis of the technique. Results. With the VEX test case and the corresponding error analysis, we have demonstrated that the PRIDE setup and processing pipeline is suited for radio occultation experiments of planetary bodies. The noise budget of the open-loop Doppler data collected with PRIDE indicated that the uncertainties in the derived density and temperature profiles remain within the range of uncertainties reported in previous Venus' studies. Open-loop Doppler data can probe deeper layers of thick atmospheres, such as that of Venus, when compared to closed-loop Doppler data. Furthermore, PRIDE through the VLBI networks around the world, provides a wide coverage and range of large antenna dishes, that can be used for this type of experiments

Position and frequency shifts induced by massive modes of the gravitational wave background in alternative gravity

Alternative theories of gravity predict the presence of massive scalar, vector, and tensor gravitational wave modes in addition to the standard massless spin~2 graviton of general relativity. The deflection and frequency shift effects on light from distant sources propagating through a stochastic background of gravitational waves, containing such modes, differ from their counterparts in general relativity. Such effects are considered as a possible signature for alternative gravity in attempts to detect deviations from Einstein's gravity by astrophysical means.Comment: 9 pages, 1 figur

A monitoring campaign (2013-2020) of ESA's Mars Express to study interplanetary plasma scintillation

The radio signal transmitted by the Mars Express (MEX) spacecraft was observed regularly between the years 2013-2020 at X-band (8.42 GHz) using the European Very Long Baseline Interferometry (EVN) network and University of Tasmania's telescopes. We present a method to describe the solar wind parameters by quantifying the effects of plasma on our radio signal. In doing so, we identify all the uncompensated effects on the radio signal and see which coronal processes drive them. From a technical standpoint, quantifying the effect of the plasma on the radio signal helps phase referencing for precision spacecraft tracking. The phase fluctuation of the signal was determined for Mars' orbit for solar elongation angles from 0 - 180 deg. The calculated phase residuals allow determination of the phase power spectrum. The total electron content (TEC) of the solar plasma along the line of sight is calculated by removing effects from mechanical and ionospheric noises. The spectral index was determined as $-2.43 \pm 0.11$ which is in agreement with Kolomogorov's turbulence. The theoretical models are consistent with observations at lower solar elongations however at higher solar elongation ($>$160 deg) we see the observed values to be higher. This can be caused when the uplink and downlink signals are positively correlated as a result of passing through identical plasma sheets.Comment: The paper has 13 figures and one table. It has been accepted for publication in PASA and the article will receive its DOI in a week's tim

Very long baseline interferometry with the SKA

Adding VLBI capability to the SKA arrays will greatly broaden the science of the SKA, and is feasible within the current specifications. SKA-VLBI can be initially implemented by providing phased-array outputs for SKA1-MID and SKA1-SUR and using these extremely sensitive stations with other radio telescopes, and in SKA2 by realising a distributed configuration providing baselines up to thousands of km, merging it with existing VLBI networks. The motivation for and the possible realization of SKA-VLBI is described in this paper