Time scales in LISA

The LISA mission is a space interferometer aiming at the detection of gravitational waves in the [$10^{-4}$,$10^{-1}$] Hz frequency band. In order to reach the gravitational wave detection level, a Time Delay Interferometry (TDI) method must be applied to get rid of (most of) the laser frequency noise and optical bench noise. This TDI analysis is carried out in terms of the coordinate time corresponding to the Barycentric Coordinate Reference System (BCRS), TCB, whereas the data at each of the three LISA stations is recorded in terms of each station proper time. We provide here the required proper time versus BCRS time transformation. We show that the difference in rate of station proper time versus TCB is of the order of $5 10^{-8}$. The difference between station proper times and TCB exhibits an oscillatory trend with a maximum amplitude of about $10^{-3}$ s.Comment: 14 pages, 5 eps figures, 0 table, accepted in Classical and Quantum Gravit

Light deflection in Weyl gravity: constraints on the linear parameter

Light deflection offers an unbiased test of Weyl's gravity since no assumption on the conformal factor needs to be made. In this second paper of our series ``Light deflection in Weyl gravity'', we analyze the constraints imposed by light deflection experiments on the linear parameter of Weyl's theory. Regarding solar system experiments, the recent CASSINI Doppler measurements are used to infer an upper bound, $\sim 10^{-19}$m$^{-1}$, on the absolute value of the above Weyl parameter. In non-solar system experiments, a condition for unbound orbits together with gravitational mirage observations enable us to further constrain the allowed negative range of the Weyl parameter to $\sim -10^{-31}$m$^{-1}$. We show that the characteristics of the light curve in microlensing or gravitational mirages, deduced from the lens equation, cannot be recast into the General Relativistic predictions by a simple rescaling of the deflector mass or of the ring radius. However, the corrective factor, which depends on the Weyl parameter value and on the lensing configuration, is small, even perhaps negligible, owing to the upper bound inferred on the absolute value of a negative Weyl parameter. A statistical study on observed lensing systems is required to settle the question. Our Weyl parameter range is more reliable than the single value derived by Mannheim and Kazanas from fits to galactic rotation curves, $\sim +10^{-26}\ $m$^{-1}$. Indeed, the latter, although consistent with our bounds, is biased by the choice of a specific conformal factor.Comment: 20 pages, 2 figures (see published version for a better resolution, or online at stacks.iop/CQG/21/1). To be published in Classical and Quantum Gravit

Light deflection in Weyl gravity: critical distances for photon paths

The Weyl gravity appears to be a very peculiar theory. The contribution of the Weyl linear parameter to the effective geodesic potential is opposite for massive and nonmassive geodesics. However, photon geodesics do not depend on the unknown conformal factor, unlike massive geodesics. Hence light deflection offers an interesting test of the Weyl theory. In order to investigate light deflection in the setting of Weyl gravity, we first distinguish between a weak field and a strong field approximation. Indeed, the Weyl gravity does not turn off asymptotically and becomes even stronger at larger distances. We then take full advantage of the conformal invariance of the photon effective potential to provide the key radial distances in Weyl gravity. According to those, we analyze the weak and strong field regime for light deflection. We further show some amazing features of the Weyl theory in the strong regime.Comment: 20 pages, 9 figures (see published version for a better resolution, or online version at stacks.iop.org/CQG/21/1897

The observable light deflection angle

The physical deflection angle of a light ray propagating in a space-time supplied with an asymptotically flat metric has to be expressed in terms of the impact parameter.Comment: 11 pages, 1 figur

The Sun Asphericities: Astrophysical Relevance

Of all the fundamental parameters of the Sun (diameter, mass, temperature...), the gravitational multipole moments (of degree l and order m) that determine the solar moments of inertia, are still poorly known. However, at the first order (l=2), the quadrupole moment is relevant to many astrophysical applications. It indeed contributes to the relativistic perihelion advance of planets, together with the post-Newtonian (PN) parameters; or to the precession of the orbital plane about the Sun polar axis, the latter being unaffected by the purely relativistic PN contribution. Hence, a precise knowledge of the quadrupole moment is necessary for accurate orbit determination, and alternatively, to obtain constraints on the PN parameters. Moreover, the successive gravitational multipole moments have a physical meaning: they describe deviations from a purely spherical mass distribution. Thus, their precise determination gives indications on the solar internal structure. Here, we explain why it is difficult to compute these parameters, how to derive the best values, and how they will be determined in a near future by means of space experiments.Comment: 14 pages, 9 figures (see published version for a better resolution), submited to Proceedings of the Royal Society: Mathematical, Physical and Engineering Science

Solar gravitational energy and luminosity variations

Due to non-homogeneous mass distribution and non-uniform velocity rate inside the Sun, the solar outer shape is distorted in latitude. In this paper, we analyze the consequences of a temporal change in this figure on the luminosity. To do so, we use the Total Solar Irradiance (TSI) as an indicator of luminosity. Considering that most of the authors have explained the largest part of the TSI modulation with magnetic network (spots and faculae) but not the whole, we could set constraints on radius and effective temperature variations (dR, dT). However computations show that the amplitude of solar irradiance modulation is very sensitive to photospheric temperature variations. In order to understand discrepancies between our best fit and recent observations of Livingston et al. (2005), showing no effective surface temperature variation during the solar cycle, we investigated small effective temperature variation in irradiance modeling. We emphasized a phase-shift (correlated or anticorrelated radius and irradiance variations) in the (dR, dT)-parameter plane. We further obtained an upper limit on the amplitude of cyclic solar radius variations, deduced from the gravitational energy variations. Our estimate is consistent with both observations of the helioseismic radius through the analysis of f-mode frequencies and observations of the basal photospheric temperature at Kitt Peak. Finally, we suggest a mechanism to explain faint changes in the solar shape due to variation of magnetic pressure which modifies the granules size. This mechanism is supported by our estimate of the asphericity-luminosity parameter, which implies an effectiveness of convective heat transfer only in very outer layers of the Sun.Comment: 17 pages, 2 figure, 1 table, published in New Astronom