Empirical Brightening Model for Distant Long-Period Comets
Abstract
Recent studies have shown the traditional comet brightening model, Hn, with a constant activity index n (i.e., single slope in log10(rh)), fails to accurately describe heliocentric lightcurves at large distances, where water-ice sublimation is inefficient. We present a new empirical model, Hab, for distant comet brightening in which the effective brightening slope varies with heliocentric distance, rh. Using a multi-year pre-perihelion dataset from uniform instrumentation for 23 comets, we found that Hab provides the best match to long inbound arcs spanning a wide range in rh. The best-fit coefficients a and b cluster tightly for our best-observed comets, suggesting a common brightening behavior; we therefore also tested one- and two-parameter Hab variants in which a and/or b are fixed to anchor values derived from these comets (A1 = 0.40 ± 0.09, B1 = −1.78 ± 0.68), either individually, jointly, or via a linear relation. The three-parameter Hab model is strongly favored by the Bayesian information criterion (BIC) for the full lightcurve, justifying its added complexity for characterization. We also tested predictive performance against Hn. For brightness forecasting from limited initial data (Δrh ≲ 2.5 au, the heliocentric distance range spanned by observations), Hab itself predicts poorly, whereas a one-parameter reduction, with both coefficients fixed, predicts more reliably, including outperforming Hn with a fixed n ∼ 2−4. Two-parameter reductions with only one coefficient fixed typically reach predictions within 1 mag of the observed brightness after only Δrh ∼ 1.0 au of inbound coverage.
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BibTeX
@misc{holt2026empirical,
title = {{Empirical Brightening Model for Distant Long-Period Comets}},
author = {Carrie E. Holt and Colin Snodgrass and Tim Lister and Michael S. P. Kelley and Matthew M. Knight and Quanzhi Ye and Abbie Donaldson and Cyrielle Opitom and Dennis Bodewits and Henry H. Hsieh and Edward Gomez and Joey Chatelain and Sarah Greenstreet},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.33167},
eprint = {2610.33167},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.33167},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Empirical Brightening Model for Distant Long-Period Comets
AU - Carrie E. Holt
AU - Colin Snodgrass
AU - Tim Lister
AU - Michael S. P. Kelley
AU - Matthew M. Knight
AU - Quanzhi Ye
AU - Abbie Donaldson
AU - Cyrielle Opitom
AU - Dennis Bodewits
AU - Henry H. Hsieh
AU - Edward Gomez
AU - Joey Chatelain
AU - Sarah Greenstreet
PY - 2026
DA - 2026/10/23
PB - arXiv
DO - 10.48550/arxiv.2610.33167
UR - https://arxiv.org/abs/2610.33167
AB - Recent studies have shown the traditional comet brightening model, Hn, with a constant activity index n (i.e., single slope in log_10(r_h)), fails to accurately describe heliocentric lightcurves at large distances, where water-ice sublimation is inefficient. We present a new empirical model, Hab, for distant comet brightening in which the effective brightening slope varies with heliocentric distance, r_h. Using a multi-year pre-perihelion dataset from uniform instrumentation for 23 comets, we found that Hab provides the best match to long inbound arcs spanning a wide range in r_h. The best-fit coefficients a and b cluster tightly for our best-observed comets, suggesting a common brightening behavior; we therefore also tested one- and two-parameter Hab variants in which a and/or b are fixed to anchor values derived from these comets (A_1 = 0.40 ± 0.09, B_1 = −1.78 ± 0.68), either individually, jointly, or via a linear relation. The three-parameter Hab model is strongly favored by the Bayesian information criterion (BIC) for the full lightcurve, justifying its added complexity for characterization. We also tested predictive performance against Hn. For brightness forecasting from limited initial data (Δr_h ≲ 2.5 au, the heliocentric distance range spanned by observations), Hab itself predicts poorly, whereas a one-parameter reduction, with both coefficients fixed, predicts more reliably, including outperforming Hn with a fixed n ∼ 2−4. Two-parameter reductions with only one coefficient fixed typically reach predictions within 1 mag of the observed brightness after only Δr_h ∼ 1.0 au of inbound coverage.
ER -