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

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.

• The paper presents a PSF–delta decomposition method with bicubic resampling to isolate nucleus signals from dominant coma emissions.
• The technique uses forward modeling and azimuthally averaged radial profiles to reliably constrain nucleus sizes consistent with HST limits.
• Application to interstellar comet 3I/ATLAS showcases robust error propagation and highlights potential for integration into future survey pipelines.

PSF–Delta Decomposition for Unresolved Cometary Nucleus Photometry: Methodology and Application to 3I/ATLAS (C/2025 N1)

Introduction

Precise photometric characterization of cometary nuclei remains a significant challenge due to the unresolved nature of most nuclei, even when observed with high-angular resolution platforms such as HST. The principal barrier is the dominant contribution of the unresolved inner coma, which impedes direct nucleus flux extractions critical for physical size inference. The work presents a robust data analysis framework—PSF–delta decomposition with bicubic resampling—that enables quantitative separation of the nucleus component from spherical coma emission, offering a methodology optimized for both survey-scale pipelines and targeted follow-up. The technique is applied to interstellar comet 3I/ATLAS (C/2025 N1), for which precise size constraints are of particular scientific interest.

Forward Modeling of the Central Profile

The forward model decomposes the intrinsic brightness profile into two fundamental components: a point-like nucleus represented by a Dirac delta term and a steady-state coma characterized by a $\rho^{-1}$ surface brightness law, mimicking isotropic, outflow-dominated coma conditions. These components are forward-convolved with the empirical or analytic PSF of the imaging system to construct the predicted observational profile. Fitting is then performed directly on azimuthally averaged radial profiles, focusing on two amplitudes: the unresolved nucleus and the normalized coma flux. This explicit separation yields both improved numerical stability and transparent residual diagnostics.

Figure 1: Schematic decomposition: a narrow PSF-like core and a $\rho^{-1}$ coma combine to produce the observed inner profile after convolution.

Bicubic Resampling and Core Stabilization

Pixel-phase systematics and undersampled PSFs typically degrade the fidelity of unresolved photometry. The implementation of $4\times4$ bicubic resampling on the core region produces a stable, central plateau in the radial profile, critically improving the separation and fitting quality of the narrow PSF kernel relative to the broad coma tail. This resampling is strictly flux-conserving and compatible with empirical PSF extraction from field stars in the same dataset.

Figure 2: Radial profile after $4\times4$ bicubic resampling. A central plateau stabilizes the PSF component fit against pixel-phase effects.

Profile Fitting and Error Diagnostics

Model fitting leverages weighted least squares across the azimuthally averaged, resampled profiles, with the PSF width either externally constrained or fit as a free parameter. Flat, structureless fit residuals signal an adequate model match; structured or systematic deviations reveal PSF mismatches or coma anisotropies (e.g., jets, fan-like outflows). The method offers direct visualization of degeneracies and informs on the model’s limitations in the presence of symmetry breakdown.

Figure 3: 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.

Application to Interstellar Comet 3I/ATLAS (C/2025 N1)

Applied to 3I/ATLAS, the method utilizes recent HST-based constraints on nucleus size and optical albedo ($p_V\simeq0.04$). Utilizing synthetic and observational datasets, the forward-fitted model yields nucleus radii in the range $0.16 \lesssim R_n \lesssim 2.8$ km—fully consistent with the current HST upper limits. The photometric chain, incorporating explicit error propagation through the magnitude, absolute magnitude, and size derivations, demonstrates that uncertainties are dominated by the albedo prior.

Figure 4: Schematic radius interval for the 3I/ATLAS nucleus based on recent HST analysis: $0.16$–$2.8$ km (assuming $p_V \simeq 0.04$).

A worked example employing 3I/ATLAS parameters and observed counts yields $R_n = 0.312 \pm 0.083$ km under Poisson-limited errors and $R_n = 0.312 \pm 0.089$ km with more conservative error assumptions, highlighting robust internal consistency and the dominant role of albedo uncertainty in the radius error budget.

Upper Limits and Nondetections

For nondetections, the methodology leverages the optimal properties of the matched-filter PSF fit, propagating noise estimates from residual fits directly into statistically rigorous upper limits on the nucleus flux. The translation to nucleus size limit proceeds identically to the detection chain, ensuring methodological consistency across variable detection regimes.

Implications and Future Prospects

The PSF–delta decomposition method represents a substantial advance in practical unresolved nucleus photometry, especially for cases where the coma core dominates and isotropy is approximately realized. Its compatibility with empirical PSF estimation and tractable computational cost positions it well for integration into future survey pipelines (e.g., LSST/Rubin). The explicit error propagation framework and internal diagnostics allow for straightforward extension to large samples. Its principal limitations—albedo uncertainty and sensitivity to unresolved coma anisotropy—are intrinsic to the data, not the methodology.

Given the critical dependence of physical parameter estimation (and thus population-scale inference) on reliable nucleus flux separation, this method provides a powerful means to extract quantifiable nucleus constraints from even heavily active or unresolved comets. The framework will be especially relevant for the statistical analysis of surveys in which most cometary nuclei will remain unresolved.

Conclusion

The PSF–delta decomposition approach, incorporating bicubic resampling and explicit convolutional modeling, offers a transparent, numerically robust methodology for resolving unresolved cometary nuclei photometry in the presence of a luminous central coma. The application to 3I/ATLAS not only reproduces independent HST-based constraints but also demonstrates the technique’s error diagnostics, reproducibility, and applicability to real survey data. The central limitations are governed by PSF characterization and the intrinsic uncertainty in nuclear albedo. Prospective advancements may arise from improved coma phase function modeling, high-SNR empirical PSF extraction, and multiwavelength extensions to further constrain nuclear albedo and composition.