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We utilize the well-established properties of the solar gravitational lens (SGL) to consider more realistic observational scenarios. Actual exoplanets, which may be the target of an SGL observational campaign, are not stationary. Their appearance also changes in a variety of ways, including changes due to their diurnal rotation and varying illumination due to their orbital motion around their host star. The nature of the SGL is such that imaging with one telescope is accomplished with a cadence of one pixel at a time, with substantial per-pixel integration times. Therefore, capturing a single snapshot of the target planet with a realistically-sized telescope is not possible. Instead, the planetary surface must be reconstructed by inverting the combined effect of the SGL’s point-spread function and temporal changes induced by the planetary dynamics. Using the Earth as a stand-in, we demonstrate practical feasibility of this approach, by simulating a dynamical system and then recovering topographic images of acceptable quality. The dynamics-induced temporal variability of the exoplanet represents an added challenge, but even in the presence of such dynamics, use of the SGL for exoplanet imaging remains feasible.
We utilize the well-established properties of the solar gravitational lens (SGL) to consider more realistic observational scenarios. Actual exoplanets, which may be the target of an SGL observational campaign, are not stationary. Their appearance also changes in a variety of ways, including changes due to their diurnal rotation and varying illumination due to their orbital motion around their host star. The nature of the SGL is such that imaging with one telescope is accomplished with a cadence of one pixel at a time, with substantial per-pixel integration times. Therefore, capturing a single snapshot of the target planet with a realistically-sized telescope is not possible. Instead, the planetary surface must be reconstructed by inverting the combined effect of the SGL’s point-spread function and temporal changes induced by the planetary dynamics. Using the Earth as a stand-in, we demonstrate practical feasibility of this approach, by simulating a dynamical system and then recovering topographic images of acceptable quality. The dynamics-induced temporal variability of the exoplanet represents an added challenge, but even in the presence of such dynamics, use of the SGL for exoplanet imaging remains feasible.
We use galaxy–galaxy lensing data to test general relativity and f(T) gravity at galaxy scales. We consider an exact spherically symmetric solution of f(T) theory, which is obtained from an approximate quadratic correction, and thus it is expected to hold for every realistic deviation from general relativity. Quantifying the deviation by a single parameter Q, and following the post-Newtonian approximation, we obtain the corresponding deviation in the gravitational potential, shear component, and effective excess surface density profile. We used five stellar mass samples and divided them into blue and red galaxies to test the model dependence on galaxy color, and we modeled the excess surface density profiles using the Navarro–Frenk–White profiles. Based on the group catalog from the Sloan Digital Sky Survey Data Release 7 (SDSS DR7) we finally extract Q = − 2.138 − 0.516 + 0.952 × 10 − 5 Mpc−2 at 1σ confidence. This result indicates that f(T) corrections on top of general relativity are favored. Finally, we apply information criteria, such as the Akaike and Bayesian ones, and although the dependence of f(T) gravity on the off-center effect implies that its optimality needs to be carefully studied, our analysis shows that f(T) gravity is more efficient in fitting the data compared to general relativity and the ΛCDM paradigm, and thus it offers a challenge to the latter.
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