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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. © 2024. The Astronomical Society of the Pacific. All rights reserved.
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We measure the absolute proper motion of Leo I using a WFPC2/HST data set that spans up to 10 yr to date the longest time baseline utilized for this satellite. The measurement relies on ∼2300 Leo I stars located near the center of light of the galaxy; the correction to absolute proper motion is based on 174 Gaia EDR3 stars and 10 galaxies. Having generated highly precise, relative proper motions for all Gaia EDR3 stars in our WFPC2 field of study, our correction to the absolute EDR3 system does not rely on these Gaia stars being Leo I members. This new determination also benefits from a recently improved astrometric calibration of WFPC2. The resulting proper-motion value, (μ α , μ δ ) = (-0.007 0.035, - 0.119 0.026) mas yr-1 is in agreement with recent, large-area, Gaia EDR3-based determinations. We discuss all the recent measurements of Leo I's proper motion and adopt a combined, multistudy average of (μ α 3 meas,μ δ 3 meas)=(-0.036±0.016,-0.130±0.010) mas yr-1. This value of absolute proper motion for Leo I indicates its orbital pole is well aligned with that of the vast polar structure, defined by the majority of the brightest dwarf spheroidal satellites of the Milky Way. © 2021. The Author(s). Published by the American Astronomical Society.
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Symbolic regression techniques are promising approaches to learning mathematical models that fit experimental data. One of the most powerful techniques for symbolic regression is Grammatical Evolution (GE). This evolutionary computation technique explores a space of candidate models that are ensured to be syntactically correct expressions built from a set of arbitrary building blocks and operators. In GE the syntax for these expressions is defined by a problem-specific formal grammar. Therefore, GE can produce an explainable solution (e.g. a formula), not a black-box model. The current contribution assesses the viability of GE for PSF characterization, using real datasets from HST/WFPC2. Our experiments show that our method is able to find the most likely candidate mathematical expression for the PSF shape, and can also model combinations of shapes taken from a predefined family of functions commonly used in astronomy (Gaussian and Moffat PSFs). These results support the hypothesis that the expressive power of GE can be used to tackle the problem of characterization of complex PSF functions, for example, as a necessary step in the prediction of intra-pixel position of stars. © 2024 SPIE.
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