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Measuring Cometary Nuclei Behind Bright Comae: PSF Delta Decomposition with Bicubic Resampling and an Application to Interstellar Comet 3I/ATLAS C/2025 N1

Toni Scarmato

TL;DR

Measuring the sizes of unresolved cometary nuclei is hindered by bright inner comae. The paper introduces a PSF-delta decomposition approach that explicitly models the nucleus as a 2D Dirac delta plus a $K\rho^{-1}$ coma term and performs forward convolution with the PSF, enabling stable nucleus flux extraction after bicubic resampling. By fitting the azimuthally averaged profile with a two-amplitude model $I_{\rm obs}(\rho)=A P(\rho)+B (\rho^{-1} \ast P)(\rho)$ and converting the nucleus flux to a radius via $D=1329\times 10^{-H/5} p_V^{-1/2}$, the method provides nucleus size estimates with quantified uncertainties. Application to the interstellar comet 3I/ATLAS (C/2025 N1) yields a radius range of roughly $0.16$–$2.8$ km for $p_V\approx0.04$, consistent with HST upper limits, and demonstrates a robust, survey-ready workflow. The approach, being lightweight and compatible with Rubin LSST pipelines, offers a practical path to nucleus measurements across diverse datasets, with the dominant uncertainties arising from albedo and PSF/ coma systematics.

Abstract

Measuring cometary nuclei is notoriously difficult because they are usually unresolved and embedded within bright comae, which hampers direct size measurements even with space telescopes. We present a practical, instrumental method that, stabilises the inner core through bicubic resampling, performs forward point-spread function PSF+convolution, and separates the unresolved nucleus from the inner-coma profile via an explicit Dirac Delta function added to a Rho^-1 surface brightness law. The method yields the nucleus flux by fitting an azimuthal averaged profile with two amplitudes only PSF core and convolved coma, with transparent residual diagnostics. As a case study, we apply the workflow to the interstellar comet 3I/ATLAS alias C/2025 N1, incorporating Hubble Space Telescope constraints on the nucleus size. We find that radius solutions consistent with 0.16 <= Rn <= 2.8 km for Pv = 0.04 are naturally recovered, in line with the most recent HST upper limits. The approach is well-suited for survey pipelines Rubin LSST and targeted follow up.

Measuring Cometary Nuclei Behind Bright Comae: PSF Delta Decomposition with Bicubic Resampling and an Application to Interstellar Comet 3I/ATLAS C/2025 N1

TL;DR

Measuring the sizes of unresolved cometary nuclei is hindered by bright inner comae. The paper introduces a PSF-delta decomposition approach that explicitly models the nucleus as a 2D Dirac delta plus a coma term and performs forward convolution with the PSF, enabling stable nucleus flux extraction after bicubic resampling. By fitting the azimuthally averaged profile with a two-amplitude model and converting the nucleus flux to a radius via , the method provides nucleus size estimates with quantified uncertainties. Application to the interstellar comet 3I/ATLAS (C/2025 N1) yields a radius range of roughly – km for , consistent with HST upper limits, and demonstrates a robust, survey-ready workflow. The approach, being lightweight and compatible with Rubin LSST pipelines, offers a practical path to nucleus measurements across diverse datasets, with the dominant uncertainties arising from albedo and PSF/ coma systematics.

Abstract

Measuring cometary nuclei is notoriously difficult because they are usually unresolved and embedded within bright comae, which hampers direct size measurements even with space telescopes. We present a practical, instrumental method that, stabilises the inner core through bicubic resampling, performs forward point-spread function PSF+convolution, and separates the unresolved nucleus from the inner-coma profile via an explicit Dirac Delta function added to a Rho^-1 surface brightness law. The method yields the nucleus flux by fitting an azimuthal averaged profile with two amplitudes only PSF core and convolved coma, with transparent residual diagnostics. As a case study, we apply the workflow to the interstellar comet 3I/ATLAS alias C/2025 N1, incorporating Hubble Space Telescope constraints on the nucleus size. We find that radius solutions consistent with 0.16 <= Rn <= 2.8 km for Pv = 0.04 are naturally recovered, in line with the most recent HST upper limits. The approach is well-suited for survey pipelines Rubin LSST and targeted follow up.

Paper Structure

This paper contains 17 sections, 18 equations, 4 figures, 1 table.

Table of Contents

  1. Introduction
  2. Methodology
  3. Forward model in 2D
  4. Bicubic resampling and flux conservation
  5. Profile fitting
  6. Photometric calibration and radius inference
  7. Algorithmic workflow
  8. Application to 3I/ATLAS (C/2025 N1)
  9. Worked numerical example with 3I/ATLAS data
  10. Uncertainty propagation
  11. (ii) Poisson-limited lower bound.
  12. Upper-limit (non-detection) estimate
  13. Worked upper-limit for the 3I/ATLAS setup
  14. Numerical estimate for the 3I/ATLAS example
  15. (i) Conservative fit uncertainties.
  16. ...and 2 more sections

Figures (4)

  • Figure 1: Schematic decomposition: a narrow PSF-like core and a $\rho^{-1}$ coma combine to produce the observed inner profile after convolution.
  • Figure 2: Radial profile after $4\times4$ bicubic resampling. A central plateau stabilises the PSF component fit against pixel-phase effects; the outer tail follows $\sim \rho^{-1}$.
  • Figure 3: Schematic radius interval for the 3I/ATLAS nucleus based on recent HST analysis: $0.16$--$2.8$ km (assuming $p_V\simeq0.04$).
  • Figure 4: Residuals of the PSF--$\delta$ + convolved $1/\rho$ fit on a synthetic azimuthally averaged profile. Flat, structureless residuals indicate a good match; coherent patterns would suggest PSF mismatch or coma anisotropy.