Gravitational perturbations on local experiments in a satellite : The dragging of inertial frame in the HYPER project

We consider a nearly free falling Earth satellite where atomic wave interferometers are tied to a telescope pointing towards a faraway star. They measure the acceleration and the rotation relatively to the local inertial frame. We calculate the rotation of the telescope due to the aberrations and the deflection of the light in the gravitational field of the Earth. We show that the deflection due to the quadrupolar momentum of the gravity is not negligible if one wants to observe the Lense-Thirring effect of the Earth. We consider some perturbation to the ideal device and we discuss the orders of magnitude of the phase shifts due to the residual tidal gravitational field in the satellite and we exhibit the terms which must be taken into account to calculate and interpret the full signal. Within the framework of a geometric model, we calculate the various periodic components of the signal which must be analyzed to detect the Lense-Tirring effect. We discuss the results which support a reasonable optimism. As a conclusion we put forward the necessity of a more complete, realistic and powerful model in order to obtain a final conclusion on the theoretical feasibility of the experiment as far as the observation of the Lense-Thirring effect is involved.Comment: Accepted in GRG (vol 36, Feb 2004

Tidal gravitational effects in a satellite

Atomic wave interferometers are tied to a telescope pointing towards a faraway star in a nearly free falling satellite. Such a device is sensitive to the acceleration and the rotation relatively to the local inertial frame and to the tidal gravitational effects too. We calculate the rotation of the telescope due to the aberration and the deflection of the light in the gravitational field of a central mass (the Earth and Jupiter). Within the framework of a general parametrized description of the problem, we discuss the contributions which must be taken into account in order to observe the Lense-Thirring effect. Using a geometrical model, we consider some perturbations to the idealized device and we calculate the corresponding effect on the periodic components of the signal. Some improvements in the knowledge of the gravitational field are still necessary as well as an increase of the experimental capabilities; however our conclusions support a reasonable optimism for the future. Finally we put forward the necessity of a more complete, realistic and powerful model in order to obtain a definitive conclusion on the feasibility of the experiment as far as the observation of the Lense-Thirring effect is involved.Comment: accepted to General Relativity and Gravitatio

Community mining with graph filters for correlation matrices

International audienceCommunities are an important type of structure in networks. Graph filters, such as wavelet filterbanks, have been used to detect such communities as groups of nodes more densely connected together than with the outsiders. When dealing with times series, it is possible to build a relational network based on the correlation matrix. However, in such a network, weights assigned to each edge have different properties than those of usual adjacency matrices. As a result, classical community detection methods based on modularity optimization are not consistent and the modularity needs to be redefined to take into account the structure of the correlation from random matrix theory. Here, we address how to detect communities from correlation matrices, by filtering global modes and random parts using properties that are specific to the distribution of correlation eigenval-ues. Based on a Louvain approach, an algorithm to detect multiscale communities is also developed, which yields a weighted hierarchy of communities. The implementation of the method using graph filters is also discussed

Probing Dark Matter Substructure in Lens Galaxies

We investigate the effects of numerous dark matter subhalos in a galaxy-sized halo on the events of strong lensing, to assess their presence as expected from the cold dark matter scenario. Lens galaxies are represented by a smooth ellipsoid in an external shear field and additional cold dark matter subhalos taken from Monte Carlo realizations which accord with recent N-body results. We also consider other possible perturbers, globular clusters and luminous dwarf satellites, for comparison. We then apply the models to the particular lens systems with four images, B1422+231 and PG1115+080, for which smooth lens models are unable to reproduce both the positions of the images and their radio flux ratios or dust-free optical flux ratios simultaneously. We show that the perturbations by both globular clusters and dwarf satellites are too small to change the flux ratios, whereas cold dark matter subhalos are most likely perturbers to reproduce the observed flux ratios in a statistically significant manner. This result suggests us the presence of numerous subhalos in lens galaxies, which is consistent with the results of cosmological N-body simulations.Comment: 19 pages, including 5 figures, ApJ in pres

The quasar Q0957+561: Lensed CO emission from a disk at z~1.4?

In recent years large efforts have been made to detect molecular gas towards high redshifted objects. Up to now the literature reports on only two cases of CO-detection in quasars at a redshift between 1 and 2 - Q0957+561, a gravitationally lensed system at z=1.41 (Planesas et al. 1999), and HR10 at z=1.44 (Andreani et al. 2000). According to Planesas et al. (1999), 12CO(2-1) emission was detected towards both the lensed images of Q0957+561 with the IRAM Plateau de Bure Interferometer (PdBI). In contrast to the optical spectra of the two images which support the idea that they are images of one and the same object, the CO-spectra were surprisingly different: the southern image (named CO-B) shows a single blueshifted line whereas a double-peaked line profile with a blue- and a redshifted part appears towards the northern image (CO-A). Based on the observations and on simulations with a gravitational lens program, we are tempted to argue that the line profile traces the presence of molecular gas of a disk in the host galaxy around the quasar. We have now new observations with the PdBI providing the necessary sensitivity to corroborate our disk model.Comment: 4 pages, 1 figure, to appear in "Proceedings of the 4th Cologne-Bonn-Zermatt-Symposium", ed. S. Pfalzner, C. Kramer, C. Straubmeier, and A. Heithausen (Springer Verlag

Chandra Observations of the Gravitationally Lensed System 2016+112

An observation of the gravitationally lensed system 2016+112 with the Chandra X-ray Observatory has resolved a mystery regarding the proposed presence of a dark matter object in the lens plane of this system. The Chandra ACIS observation has clearly detected the lensed images of 2016+112 with positions in good agreement with those reported in the optical and also detects 13 additional X-ray sources within a radius of 3.5 arcmin. Previous X-ray observations in the direction of 2016+112 with the ROSAT HRI and ASCA SIS have interpreted the X-ray data as arising from extended emission from a dark cluster. However, the present Chandra observation can account for all the X-ray emission as originating from the lensed images and additional point X-ray sources in the field. Thus cluster parameters based on previous X-ray observations are unreliable. We estimate an upper limit on the mass-to-light ratio within a radius of 800 h_(50)^(-1) kpc of M/L_(V) < 190 h_(50) (M/L_(V))_Sun. The lensed object is quite unusual, with reported narrow emission lines in the optical that suggest it may be a type-2 quasar (Yamada et. al. 1999). Our modeling of the X-ray spectrum of the lensed object implies that the column density of an intrinsic absorber must lie between 3 and 85 x 10^22 cm^-2 (3 sigma confidence level). The 2-10 keV luminosity of the lensed object, corrected for the lens magnification effect and using the above range of intrinsic absorption, is 3 x 10^43 - 1.4 x 10^44 erg/s.Comment: 9 pages, includes 2 figures, Accepted for publication in ApJ

A multipole-Taylor expansion for the potential of gravitational lens MG J0414+0534

We employ a multipole-Taylor expansion to investigate how tightly the gravitational potential of the quadruple-image lens MG J0414+0534 is constrained by recent VLBI observations. These observations revealed that each of the four images of the background radio source contains four distinct components, thereby providing more numerous and more precise constraints on the lens potential than were previously available. We expand the two-dimensional lens potential using multipoles for the angular coordinate and a modified Taylor series for the radial coordinate. After discussing the physical significance of each term, we compute models of MG J0414+0534 using only VLBI positions as constraints. The best-fit model has both interior and exterior quadrupole moments as well as exterior m=3 and m=4 multipole moments. The deflector centroid in the models matches the optical galaxy position, and the quadrupoles are aligned with the optical isophotes. The radial distribution of mass could not be well constrained. We discuss the implications of these models for the deflector mass distribution and for the predicted time delays between lensed components.Comment: 44 pages, 5 figures, 11 tables, accepted for publication in Ap

New Modeling of the Lensing Galaxy and Cluster of Q0957+561: Implications for the Global Value of the Hubble Constant

The gravitational lens 0957+561 is modeled utilizing recent observations of the galaxy and the cluster as well as previous VLBI radio data which have been re-analyzed recently. The galaxy is modeled by a power-law elliptical mass density with a small core while the cluster is modeled by a non-singular power-law sphere as indicated by recent observations. Using all of the current available data, the best-fit model has a reduced chi-squared of approximately 6 where the chi-squared value is dominated by a small portion of the observational constraints used; this value of the reduced chi-squared is similar to that of the recent FGSE best-fit model by Barkana et al. However, the derived value of the Hubble constant is significantly different from the value derived from the FGSE model. We find that the value of the Hubble constant is given by H_0 = 69 +18/-12 (1-K) and 74 +18/-17 (1-K) km/s/Mpc with and without a constraint on the cluster's mass, respectively, where K is the convergence of the cluster at the position of the galaxy and the range for each value is defined by Delta chi-squared = reduced chi-squared. Presently, the best achievable fit for this system is not as good as for PG 1115+080, which also has recently been used to constrain the Hubble constant, and the degeneracy is large. Possibilities for improving the fit and reducing the degeneracy are discussed.Comment: 22 pages in aaspp style including 6 tables and 5 figures, ApJ in press (Nov. 1st issue

Values of H_0 from Models of the Gravitational Lens 0957+561

The lensed double QSO 0957+561 has a well-measured time delay and hence is useful for a global determination of H0. Uncertainty in the mass distribution of the lens is the largest source of uncertainty in the derived H0. We investigate the range of \hn produced by a set of lens models intended to mimic the full range of astrophysically plausible mass distributions, using as constraints the numerous multiply-imaged sources which have been detected. We obtain the first adequate fit to all the observations, but only if we include effects from the galaxy cluster beyond a constant local magnification and shear. Both the lens galaxy and the surrounding cluster must depart from circular symmetry as well. Lens models which are consistent with observations to 95% CL indicate H0=104^{+31}_{-23}(1-\kthirty) km/s/Mpc. Previous weak lensing measurements constrain the mean mass density within 30" of G1 to be kthirty=0.26+/-0.16 (95% CL), implying H0=77^{+29}_{-24}km/s/Mpc (95% CL). The best-fitting models span the range 65--80 km/s/Mpc. Further observations will shrink the confidence interval for both the mass model and \kthirty. The range of H0 allowed by the full gamut of our lens models is substantially larger than that implied by limiting consideration to simple power law density profiles. We therefore caution against use of simple isothermal or power-law mass models in the derivation of H0 from other time-delay systems. High-S/N imaging of multiple or extended lensed features will greatly reduce the H0 uncertainties when fitting complex models to time-delay lenses.Comment: AASTEX, 48 pages 4 figures, 2 tables. Also available at: http://www.astro.lsa.umich.edu:80/users/philf/www/papers/list.htm

Constraining H0 from Chandra Observations of Q0957+561

We report the detection of the lens cluster of the gravitational lens (GL) system Q0957+561 from a deep observation with the Advanced CCD Imaging Spectrometer on-board the Chandra X-ray Observatory. Intracluster X-ray emission is found to be centered 4.3 +/- 1.3 arcsec east and 3.5(-0.6,+1.3) arcsec north of image B, nearer than previous estimates. Its spectrum can be modeled well with a thermal plasma model consistent with the emission originating from a cluster at a redshift of 0.36. Our best-fit estimates of the cluster temperature of T_e = 2.09(-0.54,+0.83) keV (90 percent confidence) and mass distribution of the cluster are used to derive the convergence parameter kappa, the ratio of the cluster surface mass density to the critical density required for lensing. We estimate the convergence parameter at the location of the lensed images A and B to be kappa_A = 0.22(+0.14,-0.07) and kappa_B = 0.21(+0.12,-0.07), respectively (90 percent confidence levels). The observed cluster center, mass distribution and convergence parameter kappa provide additional constraints to lens models of this system. Our new results break a mass-sheet degeneracy in GL models of this system and provide better constraints of ~ 29 percent (90 percent confidence levels) on the Hubble constant. We also present results from the detection of the most distant X-ray jet (z = 1.41) detected to date. The jet extends approximately 8 arcsec NE of image A and three knots are resolved along the X-ray jet with flux densities decreasing with distance from the core. The observed radio and optical flux densities of the knots are fitted well with a synchrotron model and the X-ray emission is modeled well with inverse Compton scattering of Cosmic Microwave Background photons by synchrotron-emitting electrons in the jet.Comment: 18 pages, includes 7 figures, Accepted for publication in Ap