Dana I. Casetti-Dinescu

As part of an effort to identify astrometric evidence of an intermediate-mass black hole in 47Tuc, we construct a new velocity-dispersion profile for the innermost 30″ of the cluster using WFPC2 and WFC3 images spanning an unprecedented 22 yr time baseline. The WFPC2 exposures were processed using a deep-learning centering procedure as well as an improved astrometric calibration of the camera. The resulting velocity-dispersion profile has a 1″ spatial resolution and error bars that compare very favorably to prior studies.

We measure the absolute proper motions of Andromeda V (And V) and Andromeda VI/Pegasus (And VI) dwarf galaxies, satellites of M31 located near its galactic plane. And VI is located the farthest from M31 among the six satellites with currently measured proper motions. A combination of Advanced Camera for Surveys/wide filed channel (WFC) and WFPC2 exposures is utilized, spanning a 20 yr time baseline. The WFPC2 exposures are processed using a recently developed deep-learning centering procedure as well as the most up-to-date astrometric calibration of the camera. We use on the order of 100 background galaxies per satellite to determine the correction to absolute proper motion. For And V, we obtain an absolute proper motion of ( μ α , μ δ ) And V = ( 26.1 ± 21.5 , − 74.2 ± 19.1 ) μ as yr⁻¹. For And VI, we obtain an absolute proper motion of ( μ α , μ δ ) And VI = ( − 1.6 ± 12.3 , − 52.6 ± 11.2 ) μ as yr⁻¹. Orbit integrations and analyses are made for these two Andromeda satellites using two estimates of both the mass and proper motion of M31. It is found that And V has an orbit consistent within errors with alignment with M31’s disk and counter orbiting it, although this alignment is not well constrained. And VI’s orbit is better determined and is very much consistent with coorbiting with M31’s disk. While currently at a distance of ∼280 kpc from M31, And VI will remain beyond a distance of ∼90 kpc from M31, thus experiencing low tidal influence compared to the other M31 satellites with known orbits. Both satellites are determined to be well-bound to M31.

We measure the absolute proper motion of Andromeda III (And III) using Advanced Camera for Surveys/Wide Field Channel and WFPC2 exposures spanning an unprecedented 22 yr time baseline. The WFPC2 exposures have been processed using a deep-learning centering procedure recently developed as well as an improved astrometric calibration of the camera. The absolute proper motion zero point is given by 98 galaxies and 16 Gaia EDR3 stars. The resulting proper motion is (μ _α , μ _δ ) = (−10.5 ± 12.5, 47.5 ± 12.5) μas yr⁻¹. We perform an orbit analysis of And III using two estimates of M31's mass and proper motion. We find that And III’s orbit is consistent with dynamical membership to the Great Plane of Andromeda system of satellites although with some looser alignment compared to the previous two satellites NGC 147 and NGC 185. And III is bound to M31 if M31's mass is M _vir ≥ 1.5 × 10¹² M _⊙.

We measure the absolute proper motion of Andromeda III (And III) using Advanced Camera for Surveys/Wide Field Channel and WFPC2 exposures spanning an unprecedented 22 yr time baseline. The WFPC2 exposures have been processed using a deep-learning centering procedure recently developed as well as an improved astrometric calibration of the camera. The absolute proper motion zero point is given by 98 galaxies and 16 Gaia EDR3 stars. The resulting proper motion is (μ _α , μ _δ ) = (−10.5 ± 12.5, 47.5 ± 12.5) μas yr⁻¹. We perform an orbit analysis of And III using two estimates of M31's mass and proper motion. We find that And III’s orbit is consistent with dynamical membership to the Great Plane of Andromeda system of satellites although with some looser alignment compared to the previous two satellites NGC 147 and NGC 185. And III is bound to M31 if M31's mass is M _vir ≥ 1.5 × 10¹² M _⊙.

We present an expanded and improved deep-learning (DL) methodology for determining centers of star images on Hubble Space Telescope/Wide-Field Planetary Camera 2 (WFPC2) exposures. Previously, we demonstrated that our DL model can eliminate the pixel-phase bias otherwise present in these undersampled images; however that analysis was limited to the central portion of each detector. In the current work we introduce the inclusion of global positions to account for the point-spread function (PSF) variation across the entire chip and instrumental magnitudes to account for nonlinear effects such as charge transfer efficiency. The DL model is trained using a unique series of WFPC2 observations of globular cluster 47 Tuc, data sets comprising over 600 dithered exposures taken in each of two filters—F555W and F814W. It is found that the PSF variations across each chip correspond to corrections of the order of ∼100 mpix, while magnitude effects are at a level of ∼10 mpix. Importantly, pixel-phase bias is eliminated with the DL model; whereas, with a classic centering algorithm, the amplitude of this bias can be up to ∼40 mpix. Our improved DL model yields star-image centers with uncertainties of 8–10 mpix across the full field of view of WFPC2.

We present an expanded and improved deep-learning (DL) methodology for determining centers of star images on HST/WFPC2 exposures. Previously, we demonstrated that our DL model can eliminate the pixel-phase bias otherwise present in these undersampled images; however that analysis was limited to the central portion of each detector. In the current work we introduce the inclusion of global positions to account for the PSF variation across the entire chip and instrumental magnitudes to account for nonlinear effects such as charge transfer efficiency. The DL model is trained using a unique series of WFPC2 observations of globular cluster 47 Tuc, data sets comprising over 600 dithered exposures taken in each of two filters, F555W and F814W. It is found that the PSF variations across each chip correspond to corrections of the order of 100 mpix, while magnitude effects are at a level of about 10 mpix. Importantly, pixel-phase bias is eliminated with the DL model; whereas, with a classic centering algorithm, the amplitude of this bias can be up to 40 mpix. Our improved DL model yields star-image centers with uncertainties of 8-10 mpix across the full field of view of WFPC2.

Symbolic regression, in general, and genetic models, in particular, are promising approaches to mathematical modeling in astrometry where it is not always clear which is the fittest analytic expression depending on the problem under consideration. Several attempts and increasing research efforts are being made in this direction mainly from the Genetic Programming (GP) viewpoint. Our proposal is, as far as we know, the first one to apply Grammatical Evolution (GE) in this domain. GE (and further GE extensions) aim to outperform GP limitations by incorporating formal languages tools to guarantee the correctness (both syntactic and semantic) of the generated expressions. The current contribution is a first proof to check the viability of GE on astrometric real datasets. Its success in finding adequate parameters for predefined families of functions in star centering (Gaussian and Moffat PSFs) with simple and naive GE experiments supports our hypothesis on taking advantage of the expressive power of GE to tackle astrometry scenarios of interest and hence greatly improve current astrometric software thanks to specific genetic approaches.

A deep learning (DL) algorithm is built and tested for its ability to determine centers of star images in HST/WFPC2 exposures, in filters F555W and F814W. These archival observations hold great potential for proper-motion studies, but the undersampling in the camera’s detectors presents challenges for conventional centering algorithms. Two exquisite data sets of over 600 exposures of the cluster NGC 104 in these filters are used as a testbed for training and evaluating the DL code. Results indicate a single-measurement standard error from 8.5 to 11 mpix, depending on the detector and filter. This compares favorably to the ∼20 mpix achieved with the customary “effective point spread function (PSF)” centering procedure for WFPC2 images. Importantly, the pixel-phase error is largely eliminated when using the DL method. The current tests are limited to the central portion of each detector; in future studies, the DL code will be modified to allow for the known variation of the PSF across the detectors.