On the Detectability and Use of Normal Modes for Determining Interior Structure of Mars

The InSight mission to Mars is well underway and will be the first mission to acquire seismic data from a planet other than Earth. In order to maximise the science return of the InSight data, a multifaceted approach will be needed that seeks to investigate the seismic data from a series of different frequency windows, including body waves, surface waves, and normal modes. Here, we present a methodology based on globally-averaged models that employs the long-period information encoded in the seismic data by looking for fundamental-mode spheroidal oscillations. From a preliminary analysis of the expected signal-to-noise ratio, we find that normal modes should be detectable during nighttime in the frequency range 5–15 mHz. For improved picking of (fundamental) normal modes, we show first that those are equally spaced between 5–15 mHz and then show how this spectral spacing, obtained through autocorrelation of the Fourier-transformed time series can be further employed to select normal mode peaks more consistently. Based on this set of normal-mode spectral frequencies, we proceed to show how this data set can be inverted for globally-averaged models of interior structure (to a depth of \(\sim 250~\mbox{km}\)), while simultaneously using the resultant synthetically-approximated normal mode peaks to verify the initial peak selection. This procedure can be applied iteratively to produce a “cleaned-up” set of spectral peaks that are ultimately inverted for a “final” interior-structure model. To investigate the effect of three-dimensional (3D) structure on normal mode spectra, we constructed a 3D model of Mars that includes variations in surface and Moho topography and lateral variations in mantle structure and employed this model to compute full 3D waveforms. The resultant time series are converted to spectra and the inter-station variation hereof is compared to the variation in spectra computed using different 1D models. The comparison shows that 3D effects are less significant than the variation incurred by the difference in radial models, which suggests that our 1D approach represents an adequate approximation of the global average structure of Mars.     

Is cygnus X-3 a low-mass X-ray binary?

We present examples of the quasi-periodic variations in the X-ray flux of Cyg X-3 which we have recently found during observations of this source with EXOSAT. Amplitudes and periods of the variations range from 5% to 20% of the total flux and from 50 to 1500 s, respectively. Our tentative interpretation of these quasi-periodicities, the occurrence of quasi-periodic phenomena in an accretion disk which partially occults the X-ray source, points towards an analogy of Cyg X-3 with certain ‘dipping’ low-mass X-ray binaries such as 4U 1822-37, as suggested /1/ previously. We point out, however, that there are also fundamental differences between Cyg X-3 and this type of low-mass X-ray binary.     

Perturbation solution of attitude motion under body-fixed torques

Approximate analytical solutions are established for the attitude rates and angles of a rigid body subjected to a constant body-fixed torque. The perturbation solutions obtained are valid for any arbitrary inertia parameters. The small parameter is defined as the ratio between representative transverse rotation rate and the spin or scan rate. The results should be useful for quickly evaluating the attitude response of a spin-stabilised or scanning spacecraft to a variety of torque inputs. The applicability of the theory is illustrated by means of practical examples such as the spin-down due to rate coupling of ESA's GEOS spacecraft and the prediction of the attitude drift of the HIPPARCOS satellite during payload initialisation. Furthermore, the compact first-order results should be suitable for implementation in on-board manoeuvre or attitude control software.     

The variable iron line in cygnus X-3

Cygnus X-3 was observed with the GSPC on board EXOSAT on several occasions, one observation lasting for 7 orbital cycles. The width W and centroid energy E of the iron emission feature near 6.7 keV show a smooth, correlated, sinusoidal-type modulation, the iron line being widest and E being lowest just before X-ray maximum. The line profile may show a low-energy wing, but apart from this does not deviate strongly from a symmetric, Gaussian-type shape. The continuum at higher energies than the line is not completely smooth, but shows bumps which remain stable in time. Two possible explanations are discussed for the correlated variation of E and W as a function of orbital phase.