Constraining the Nordtvedt parameter with the BepiColombo Radioscience experiment

BepiColombo is a joint ESA/JAXA mission to Mercury with challenging objectives regarding geophysics, geodesy and fundamental physics. The Mercury Orbiter Radioscience Experiment (MORE) is one of the on-board experiments, including three different but linked experiments: gravimetry, rotation and relativity. The aim of the relativity experiment is the measurement of the post-Newtonian parameters. Thanks to accurate tracking between Earth and spacecraft, the results are expected to be very precise. However, the outcomes of the experiment strictly depends on our "knowledge" about solar system: ephemerides, number of bodies (planets, satellites and asteroids) and their masses. In this paper we describe a semi-analytic model used to perform a covariance analysis to quantify the effects, on the relativity experiment, due to the uncertainties of solar system bodies parameters. In particular, our attention is focused on the Nordtvedt parameter $\eta$ used to parametrize the strong equivalence principle violation. After our analysis we estimated $\sigma[\eta]\lessapprox 4.5\times 10^{-5}$ which is about 1~order of magnitude larger than the "ideal" case where masses of planets and asteroids have no errors. The current value, obtained from ground based experiments and lunar laser ranging measurements, is $\sigma[\eta]\approx 4.4\times 10^{-4}$. Therefore, we conclude that, even in presence of uncertainties on solar system parameters, the measurement of $\eta$ by MORE can improve the current precision of about 1~order of magnitude

Photometric determination of the mass accretion rates of pre-main sequence stars. VI. The case of LH 95 in the Large Magellanic Cloud

We report on the accretion properties of low-mass stars in the LH95 association within the Large Magellanic Cloud (LMC). Using non-contemporaneous wide-band and narrow-band photometry obtained with the HST, we identify 245 low-mass pre-main sequence (PMS) candidates showing H$\alpha$ excess emission above the 4$\sigma$ level. We derive their physical parameters, i.e. effective temperatures, luminosities, masses ($M_\star$), ages, accretion luminosities, and mass accretion rates ($\dot M_{\rm acc}$). We identify two different stellar populations: younger than ~8Myr with median $\dot M_{\rm acc}$~5.4x10$^{-8}M_\odot$/yr (and $M_\star$~0.15-1.8$M_\odot$) and older than ~8Myr with median $\dot M_{\rm acc}$~4.8x10$^{-9}M_\odot$/yr (and $M_\star$~0.6-1.2$M_\odot$). We find that the younger PMS candidates are assembled in groups around Be stars, while older PMS candidates are uniformly distributed within the region without evidence of clustering. We find that $\dot M_{\rm acc}$ in LH95 decreases with time more slowly than what is observed in Galactic star-forming regions (SFRs). This agrees with the recent interpretation according to which higher metallicity limits the accretion process both in rate and duration due to higher radiation pressure. The $\dot M_{\rm acc}-M_\star$ relationship shows different behaviour at different ages, becoming progressively steeper at older ages, indicating that the effects of mass and age on $\dot M_{\rm acc}$ cannot be treated independently. With the aim to identify reliable correlations between mass, age, and $\dot M_{\rm acc}$, we used for our PMS candidates a multivariate linear regression fit between these parameters. The comparison between our results with those obtained in other SFRs of our Galaxy and the MCs confirms the importance of the metallicity for the study of the $\dot M_{\rm acc}$ evolution in clusters with different environmental conditions.Comment: Accepted for publication in ApJ; 26 pages, 12 pages, 3 tables; abstract shortened. Fixed a typo in the name of a co-autho

A new quasi-monte carlo technique based on nonnegative least squares and approximate Fekete points

The computation of integrals in higher dimensions and on general domains, when no explicit cubature rules are known, can be ”easily” addressed by means of the quasi- Monte Carlo method. The method, simple in its formulation, becomes computationally inefficient when the space dimension is growing and the integration domain is particularly complex. In this paper we present two new approaches to the quasi-Monte Carlo method for cubature based on nonnegative least squares and approximate Fekete points. The main idea is to use less points and especially good points for solving the system of the moments. Good points are here intended as points with good interpolation properties, due to the strict connection between interpolation and cubature. Numerical experiments show that, in average, just a tenth of the points should be used mantaining the same approximation order of the quasi-Monte Carlo method. The method has been satisfactory applied to 2 and 3-dimensional problems on quite complex domains

More properties of (β,γ)(\beta,\gamma)-Chebyshev functions and points

Recently, $(\beta,\gamma)$-Chebyshev functions, as well as the corresponding zeros, have been introduced as a generalization of classical Chebyshev polynomials of the first kind and related roots. They consist of a family of orthogonal functions on a subset of $[-1,1]$, which indeed satisfies a three-term recurrence formula. In this paper we present further properties, which are proven to comply with various results about classical orthogonal polynomials. In addition, we prove a conjecture concerning the Lebesgue constant's behavior related to the roots of $(\beta,\gamma)$-Chebyshev functions in the corresponding orthogonality interval

Polynomial mapped bases: theory and applications

In this paper, we collect the basic theory and the most important applications of a novel technique that has shown to be suitable for scattered data interpolation, quadrature, bio-imaging reconstruction. The method relies on polynomial mapped bases allowing, for instance, to incorporate data or function discontinuities in a suitable mapping function. The new technique substantially mitigates the Runge's and Gibbs effects