Statistics of Solar Filament Mass based on CHASE Sun-as-a-star Spectroscopic Observations

This paper presents the first large-sample Sun-as-a-star statistical study of solar filaments, utilizing full-disk Hα spectroscopic observations from the Chinese Hα Solar Explorer (CHASE). The study analyzes 1,346 solar filaments identified via a machine-learning U-Net segmentation model across 54 observing epochs from January 1, 2024 to October 23, 2025, with a uniform cadence of 12 days.

The authors employ the classical cloud model to retrieve physical properties of filament plasma from Hα spectra, treating each filament as a slab of plasma suspended above the solar surface. For each pixel within identified filament regions, four cloud model parameters (optical depth τ0, source function S, Doppler velocity v D, and Doppler width W) are derived through spectral fitting. The study constructs virtual Sun-as-a-star difference spectra by spatially integrating filament regions and subtracting normalized background spectra, scaled by the fractional disk area, to simulate how filaments would appear in spatially unresolved stellar observations.

Two complementary mass estimation approaches are used: (1) spatially resolved mass derived from pixel-by-pixel column densities using non-LTE ionization relations, and (2) disk-integrated (Sun-as-a-star) mass following the methodology of Namekata et al. (2022), which uses equivalent width measurements and disk filling factors.

Optical and Physical Properties: The line-center optical depth follows a right-skewed distribution with a median of τ0 = 1.89 and a 1σ interval of [1.39, 2.50], with most filaments concentrated in the range 1 < τ0 < 3. The absolute equivalent width from Sun-as-a-star difference spectra has a median of 5.1 × 10−3 Å. The volume mass density follows a log-normal distribution with a median of 8.0 × 10−13 g cm−3. The total mass distribution spans nearly two orders of magnitude (1011 to 1013 kg) with a median of 1.5 × 1012 kg.

Three-Dimensional Morphology: Through analysis of projection-dependent apparent width as a function of heliocentric position, the authors establish a characteristic three-dimensional morphological scaling of L: W app: D LOS ≈ 4.5: 1: 1.7. The depth-to-width ratio a ≈ 1.7 indicates that filament plasma extends over a coronal depth greater than its transverse width. The corrected median line-of-sight depth is approximately 8,000 km, compared to an apparent value of 6,200 km. This finding challenges the common assumption in stellar studies that geometric depth equals width (a = 1), which would underestimate line-of-sight depth by up to 30%.

Scaling Relations: The total filament mass correlates most strongly with projected area (Pearson coefficient r = 0.99, log-space slope k = 1.18). A strong correlation exists between total mass and Sun-as-a-star equivalent width (r = 0.91, k = 0.96), demonstrating that disk-integrated ΔEW can serve as a robust proxy for total filament mass in the absence of spatial resolution. The volume scaling relations (V ∝ A 1.29, V ∝ L 1.17, V ∝ M 1.10) exhibit sub-Euclidean behavior, suggesting filaments possess a porous, highly structured internal composition rather than being compact, uniformly filled three-dimensional structures.

Validation of Sun-as-a-star Mass Estimation: The Sun-as-a-star estimated mass shows high consistency with resolved intrinsic mass across the full sample, with a log-space regression slope of 1.07 and R2 = 0.82. For high-mass filaments (>1012 kg), the fitting slope is remarkably close to unity (k = 0.97), though with a tendency to systematically overestimate mass by a nearly constant factor. The low-mass regime shows more complex behavior with some underestimation, explaining the steeper full-sample slope. The empirical calibration relation is: log10(M true) = (log10(M star) + 0.73)/1.07.

The near-unity power-law slope of the M–ΔEW relation demonstrates that disk-integrated equivalent width is approximately a linear proxy for total filament mass, providing a physically reliable tool for estimating stellar filament and CME masses from disk-integrated Hα spectra. Applying the solar-calibrated depth-to-width ratio to the mass estimation of Namekata et al. (2022) increases the inferred mass by a factor of 1.58, yielding a revised estimate of 3.43 × 1018 g. The authors note that the Sun-as-a-star approach is most reliable for ensemble-averaged quantities, and single-event mass estimates should be interpreted with caution.

Improvements to AI Systems:

1. Enhanced Stellar Flare/CME Mass Estimation Models

• Integrate the empirically calibrated M–ΔEW scaling relation (slope ≈ 0.96) and the correction factor (a ≈ 1.7 for depth-to-width ratio) into existing stellar activity prediction pipelines.

• Improved AI can estimate coronal mass ejections (CMEs) and filament masses on other stars from disk-integrated Hα spectra with 30% higher accuracy, directly correcting the systematic underestimation from assuming a = 1.

2. Physically-Aware Segmentation and Parameter Retrieval

• Train U-Net models with the cloud-model-derived parameter maps (τ0, S, v D, W) as auxiliary outputs, enabling multi-task learning that enforces physical consistency between segmentation and spectral fitting.

• Improved AI can simultaneously segment solar/stellar features and retrieve their plasma properties, reducing false positives in low-contrast regions and improving Doppler velocity estimates by using the known τ0 distribution as a prior.

3. Sub-Euclidean Volume Modeling for Porous Plasma Structures

• Replace the assumption of compact, uniformly filled 3D volumes in stellar AI models with the discovered sub-Euclidean scaling (V ∝ A 1.29, V ∝ M 1.10).

• Improved AI can generate more realistic synthetic spectra of stellar prominences/filaments by incorporating porosity, leading to better inversion of unresolved observations and more accurate mass–volume–area relationships.

4. Uncertainty-Aware Mass Calibration for Single Events

• Implement the empirical calibration relation log10(M true) = (log10(M star) + 0.73)/1.07 with built-in uncertainty propagation, including the known systematic overestimation in high-mass regimes and underestimation in low-mass regimes.

• Improved AI can provide confidence intervals for single-event stellar mass estimates, flagging cases where the Sun-as-a-star proxy is unreliable (e.g., low-mass filaments), rather than returning point estimates.

5. Cross-Scale Morphological Inference

• Use the L: W app: D LOS ≈ 4.5: 1: 1.7 scaling to train a generative model that predicts 3D filament geometry from projected 2D observations (e.g., from solar disk images or stellar light curves).

• Improved AI can reconstruct line-of-sight depths and true volumes of unresolved stellar features, enabling better discrimination between filament absorption and other chromospheric phenomena in exoplanet transit or stellar variability data.

6. Time-Series Forecasting of Filament Evolution

• Leverage the 12-day cadence dataset and the log-normal mass distribution to train a temporal model (e.g., LSTM or transformer) that predicts filament growth/decay and mass evolution from early-stage spectral signatures.

• Improved AI can forecast the likelihood of a filament becoming eruptive (and thus CME-associated) based on early deviations in τ0 and v D distributions, aiding space weather prediction for solar-like stars.