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Application of Compressive Sensing for Gravitational Microlensing Events

Compressive sensing is a novel mathematical technique for simultaneous data acquisition and compression. This technique is particularly apt for time-series photometric measurements. In this work we apply compressive sensing to time-series photometric measurements specifically obtained due to gravitational microlensing events. We show through simulation modelling the error sensitivity for detecting microlensing event parameters. Particularly, we show the relation of the amount of error and its impact on the microlensing parameters of interest. We derive statistical error bounds to apply those as a baseline for analyzing the effectiveness of compressive sensing application. Our results conclude that for single and binary microlensing events we can obtain error less than 1% over a 3-pixel radius of the center of the microlensing star by using 25% Nyquist rate measurements.

Compressive Sensing↗

Probability of Detecting Planets with Microlensing

The proposed research to determine the probability of detecting extra solar planets from the ground with microlensing was completely accomplished during the grant period. A summary of the publications and their abstracts follow below. The publications include: 1) On microlensing rates and optical depth toward the Galactic center; 2) Newly discovered brown dwarfs not seen in microlensing timescale frequency distribution? 3) Probability of detecting a planetary companion during a microlensing event; 4) Comparison of a ground-based microlensing search for planets with a search from space; 5) Secular evolution of hierarchical planetary systems.

Peale, S. J.↗

New giant planet beyond the snow line for an extended MOA exoplanet microlens sample

Characterizing a planet detected by microlensing is hard if the planetary signal is weak or the lens-source relative trajectory is far from caustics. However, statistical analyses of planet demography must include those planets to accurately determine occurrence rates. As part of a systematic modelling effort in the context of a >10-yr retrospective analysis of MOA’s survey observations to build an extended MOA statistical sample, we analyse the light curve of the planetary microlensing event MOA-2014-BLG-472. This event provides weak constraints on the physical parameters of the lens, as a result of a planetary anomaly occurring at low magnification in the light curve. We use a Bayesian analysis to estimate the properties of the planet, based on a refined Galactic model and the assumption that all Milky Way’s stars have an equal planet-hosting probability. We find that a lens consisting of a 1.9(+2.2,−1.2)M(J) giant planet orbiting a 0.31(+0.36,−0.19)Mꙩ host at a projected separation of 0.75±0.24au is consistent with the observations and is most likely, based on the Galactic priors. The lens most probably lies in the Galactic bulge, at 7.2(+0.6,−1.7)kpc from Earth. The accurate measurement of the measured planet-to-host star mass ratio will be included in the next statistical analysis of cold planet demography detected by microlensing.

Clément Ranc↗

Search for Lensing Signatures in the Gravitational-Wave Observations from the First Half of LIGO–Virgo's Third Observing Run

We search for signatures of gravitational lensing in the gravitational-wave signals from compact binary coalescences detected by Advanced Laser Interferometer Gravitational-wave Observatory (LIGO) and Advanced Virgo during O3a, the first half of their third observing run. We study: (1) the expected rate of lensing at current detector sensitivity and the implications of a non-observation of strong lensing or a stochastic gravitational-wave background on the merger-rate density at high redshift; (2) how the interpretation of individual high-mass events would change if they were found to be lensed; (3) the possibility of multiple images due to strong lensing by galaxies or galaxy clusters; and (4) possible wave-optics effects due to point-mass microlenses. Several pairs of signals in the multiple-image analysis show similar parameters and, in this sense, are nominally consistent with the strong lensing hypothesis. However, taking into account population priors, selection effects, and the prior odds against lensing, these events do not provide sufficient evidence for lensing. Overall, we find no compelling evidence for lensing in the observed gravitational-wave signals from any of these analyses.

R. Abbott↗

Compressive Sensing Based Space Flight Instrument Constellation for Measuring Gravitational Microlensing Parallax

In this work, we provide a compressive sensing architecture for implementing on a space based observatory for detecting transient photometric parallax caused by gravitational microlensing events. Compressive sensing (CS) is a simultaneous data acquisition and compression technique, which can greatly reduce on-board resources required for space flight data storage and ground transmission. We simulate microlensing parallax observations using a space observatory constellation, based on CS detectors. Our results show that average CS error is less than 0.5% using 25% Nyquist rate samples. The error at peak magnification time is significantly lower than the error for distinguishing any two microlensing parallax curves at their peak magnification. Thus, CS is an enabling technology for detecting microlensing parallax, without causing any loss in detection accuracy.

compressive sensing↗

Baryonic dark clusters in galactic halos and their observable consequences

We consider the possibility that approximately 10% of the mass of a typical galaxy halo is in the form of massive (approximately 10(exp 7) solar masses), compact (escape speeds approximately 100 km/s) baryonic clusters made of neutron stars (approximately 10% by mass), black holes (less than or approximately equal to 1%) and brown dwarfs, asteroids, and other low-mass debris (approximately 90%). These general properties are consistent with several different observational and phenomenological constraints on cluster properties subject to the condition that neutron stars comprise approximately 1% of the total halo mass. Such compact, dark clusters could be the sites of a variety of collisional phenomena involving neutron stars. We find that integrated out to the Hubble distance approximately one neutron star-neutron star or neutron star-black hole collision occurs daily. Of order 0.1-1 asteroid-neutron star collisions may also happen daily in the halo of the Milky Way if there is roughly equal cluster mass per logarithmic particle mass interval between asteroids and brown dwarfs. These event rates are comparable to the frequency of gamma-ray burst detections by the Burst and Transient Source Experiment (BATSE) on the Compton Observatory, implying that if dark halo clusters are the sites of most gamma-ray bursts, perhaps approximately 90% of all bursts are extragalactic, but approximately 10% are galactic. It is possible that dark clusters of the kind discussed here could be detected directly by the Infrared Space Observatory (ISO) or Space Infrared Telescope Facility (SIRTF). If the clusters considered in this paper exist, they should produce spatially correlated gravitational microlensing of stars in the Large Magellanic Cloud (LMC). If 10% of the halo is in the form of dark baryonic clusters, and the remaining 90% is in brown dwarfs and other dark objects which are either unclustered or collected into low-mass clusters, then we expect that two events within approximately 1 min of one another are likely to be seen after a total of order 20-30 microlenses have been detected.

Wasserman, Ira↗

Planetary System Physics

Contents include a summary of publications followed by their abstracts titeled: 1. On microlensing rates and optical depth toward the Galactic center. 2. Newly discovered brown dwarfs not seen in microlensing timescale frequency distribution? 3. Origin and evolution of the natural satellites. 4. Probing the structure of the galaxy with microlensing. 5. Tides, Encyclopedia of Astronomy and Astrophysics. 6. The Puzzle of the Titan-Hyperion 4:3 Orbital Resonance. 7. On the Validity of the Coagulation Equation and the Nature of Runaway Growth. 8. Making Hyperion. 9. The MESSENGER mission to Mercury: Scientific objectives and implementation. 10. A Survey of Numerical Solutions to the Coagulation. 11. Probability of detecting a planetary companion during a microlensing event. 12. Dynamics and origin of the 2:l orbital resonances of the GJ876 planets. 13. Planetary Interior Structure Revealed by Spin Dynamics. 14. A primordial origin of the Laplace relation among the Galilean Satellites. 15. A procedure for determining the nature of Mercury's core. 16. Secular evolution of hierarchical planetary systems. 17. Tidally induced volcanism. 18. Extrasolar planets and mean motion resonances. 19. Comparison of a ground-based microlensing search for planets with a search from space.

Peale, S. J.↗

Gravitational microlensing - The effect of random motion of individual stars in the lensing galaxy

We investigate the influence of random motion of individual stars in the lensing galaxy on the light curve of a gravitationally lensed background quasar. We compare this with the effects of the transverse motion of the galaxy. We find that three-dimensional random motion of stars with a velocity dispersion sigma in each dimension is more effective in producing 'peaks' in a microlensed light curve by a factor a about 1.3 than motion of the galaxy with a transverse velocity v(t) = sigma. This effectiveness parameter a seems to depend only weakly on the surface mass density. With an assumed transverse velocity of v(t) = 600 km/s of the galaxy lensing the QSO 2237+0305 and a measured velocity dispersion of sigma = 215 km/s, the expected rate of maxima in the light curves calculated for bulk motion alone has to be increased by about 10 percent due to the random motion of stars. As a consequence, the average time interval Delta t between two high-magnification events is smaller than the time interval Delta(t) bulk, calculated for bulk motion alone, Delta t about 0.9 Delta(t) bulk.

Kundic, Tomislav↗

Microlensing by the galactic bar

We compute the optical depth and duration distribution of microlensing events towrd Baade's window in a model composed of a Galactic disk and a bar. The bar model is a self-consistent dynamical model built out of individual orbits that has been populated to be consistent with the COBE maps of the Galaxy and kinematic observations of the Galactic bulge. We find that most of the lenses are in the bulge with a line-of-sight distance 6.25 kpc (adopting R(sub 0) = 8 kpc). The microlensing optical depth of a 2 x 10(exp 10) solar mass bar plus a truncated disk is (2.2 +/- 0.45) x 10(exp -6), consistent with the large optical depth (3.2 +/- 1.2) x 10(exp -6) found by Udalski et al. (1994). This model optical depth is enhanced over the predictions of axisymmetric models by Kiraga & Paczynski (1994) by slightly more than a factor of 2, since the bar is elongated along the line of sight. The large Einstein radius and small transverse velocity dispersion also predict a longer event duration in the self-consistent bar model than in the Kiraga-Paczynski model. The event rate and duration distribution also depend on the lower mass cutoff of the lens mass function. With a 0.1 solar mass cutoff, five to seven events (depending on the contribution of disk lenses) with a logarithmic mean duration of 20 days are expected for the Optical Gravitational Lensing Experiment (OGLE) according to our model, while Udalski et al. (1994) observed nine events with durations from 8 to 62 days. On the other hand, if most of the lenses are brown dwarfs, our model predicts too many short-duration events. A Kolmogorov-Smirnov test finds only 7% probability for the model with 0.01 solar mass cutoff to be consistent with current data.

Zhao, Hongsheng↗

Compressive Sensing Based Data Acquisition Architecture for Transient Stellar Events in Crowded Star Fields

Compressive sensing is a mathematical technique for simultaneous data acquisition and compression. In this work, we show a CS based architecture for acquiring and reconstructing transient stellar events. This architecture reconstructs a differenced image itself, eliminating the need for any sparse domain transforms, otherwise required for traditional CS reconstruction. The resulting reconstructed differenced image is of critical importance as the information required for generating a time-series photometric light curve is obtained only from a differenced image. Hence, reconstructing a crowded star spatial image, followed by differencing is wasteful. This architecture eliminates the need to 1.) transform an image to a sparse domain, 2.) Reconstruct a dense field, and then apply differencing on the image to obtain the image of critical value. We study the case of microlensing to depict a star source experiencing magnification in time. Our results show that this architecture is able to reconstruct star source magnitudes with magnification factors greater than 1 for clean images with error less than 2% using only 10% of the Nyquist rate samples.

Asmita Korde-Patel↗

Compressive Sensing Based Data Acquisition Architecture for Transient Stellar Events in Crowded Star Fields

Compressive sensing is a mathematical technique for simultaneous data acquisition and compression. In this work, we show a CS based architecture for acquiring and reconstructing transient stellar events. This architecture recon-structs a differenced image itself, eliminating the need for any sparse domain transforms, otherwise required for traditional CS reconstruction. The resulting reconstructed differenced image is of critical importance as the information required for generating a time-series photometric light curve is obtained only from a differenced image. Hence, reconstructing a crowded star spatial image, followed by differencing is wasteful. This architecture eliminates the need to 1.) transform an image to a sparse domain, 2.) Reconstruct a dense field, and then apply differencing on the image to obtain the image of critical value. We study the case of microlensing to depict a star source experiencing magnification in time. Our results show that this architecture is able to reconstruct star source magnitudes with magnification factors greater than 1 for clean images with error less than 2% using only 10% of the Nyquist rate samples.

Compressive Sensing, Data acquisition, Image diffe↗

Compressive Sensing Based Data Acquisition Architecture for Transient Stellar Events in Crowded Star Fields

Compressive sensing is a mathematical technique for simultaneous data acquisition and compression. In this work, we show a CS based architecture for acquiring and reconstructing transient stellar events. This architecture recon-structs a differenced image itself, eliminating the need for any sparse domain transforms, otherwise required for traditional CS reconstruction. The resulting reconstructed differenced image is of critical importance as the information required for generating a time-series photometric light curve is obtained only from a differenced image. Hence, reconstructing a crowded star spatial image, followed by differencing is wasteful. This architecture eliminates the need to 1.) transform an image to a sparse domain, 2.) Reconstruct a dense field, and then apply differencing on the image to obtain the image of critical value. We study the case of microlensing to depict a star source experiencing magnification in time. Our results show that this architecture is able to reconstruct star source magnitudes with magnification factors greater than 1 for clean images with error less than 2% using only 10% of the Nyquist rate samples.

Asmita Korde-patel↗

OGLE-2015-BLG-1670Lb: A Cold Neptune beyond the Snow Line in the Provisional WFIRST Microlensing Survey Field

We present the analysis of the microlensing event OGLE-2015-BLG-1670, detected in a high-extinction field very close to the Galactic plane. Due to the dust extinction along the line of sight, this event was too faint to be detected before it reached the peak of magnification. The microlensing light-curve models indicate a high-magnification event with a maximum of A(max)≳ 200, very sensitive to planetary deviations. An anomaly in the light curve has been densely observed by the microlensing surveys MOA, KMTNet, and OGLE. From the light-curve modeling, we find a planetary anomaly characterized by a planet-to-host mass ratio, q=(1.00 (sup+0.18, sub -0.16) x 10(exp -4), at the peak recently identified in the mass-ratio function of microlensing planets. Thus, this event is interesting to include in future statistical studies about planet demography. We have explored the possible degeneracies and find two competing planetary models resulting from the s ↔ 1/s degeneracy. However, because the projected separation is very close to s = 1, the physical implications for the planet for the two solutions are quite similar, except for the value of s. By combining the light-curve parameters with a Galactic model, we have estimated the planet mass M(2)=17.9(sup +9.6,sub-8.8)M(ꚛ) and the lens distance D(L) = 6.7(sup +1.0, sub -1.3) kpc, corresponding to a Neptune-mass planet close to the Galactic bulge. Such events with a low absolute latitude (|b| ≈1ᵒ.1) are subject to both high extinction and more uncertain source distances, two factors that may affect the mass measurements in the provisional Wide Field Infrared Survey Telescope fields. More events are needed to investigate the potential trade-off between the higher lensing rate and the difficulty in measuring masses in these low-latitude fields.

Clément Ranc↗