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Compact moment measurement

The moment measurement is a readable, deterministic measurement of every admitted parent island and its exact deblended regions. It produces owned-pixel photometry and a pixel-space Gaussian initializer, which compact Gaussian fitting consumes. Moment records themselves are not fitted sources or catalogue rows.

Inputs and ownership

measure_compact_moments runs inside the component-fit stage, on the same task that fits the parent. It receives bounded float64 physical residual and RMS windows, boolean scientific validity, and the exact int32 component labels that deblending published. A label-zero pixel is excluded even if it lies inside a region's rectangular bounds. The normalized detection plane is not used for flux or moments.

The kernel emits the parent island first and then its deblended regions in canonical label order. Only frozen dataclass records leave the task; pixel arrays stay inside it. Serial and Dask executors must return equal records.

The kernel creates only one-dimensional selected-value and coordinate workspaces for the target currently being reduced. Python iteration is over island and region records, never pixels or RMS windows.

Photometry

For positive, finite owned brightnesses (I_i) in Jy/beam, Hebog reports:

  • peak brightness and the first tied peak in canonical global pixel order;
  • mean background-subtracted brightness;
  • mean local RMS over the same owned pixels; and
  • owned-pixel integrated flux (\sum_i I_i\,\Omega_\mathrm{pixel}/\Omega_\mathrm{beam}) in Jy.

CompactMeasurementGeometry requires both solid angles explicitly. The pixel solid angle is the absolute local tangent-plane Jacobian determinant. The elliptical restoring-beam solid angle is (\pi b_\mathrm{major}b_\mathrm{minor}/(4\ln 2)), with FWHM axes in a consistent angular unit. Missing, non-finite, or non-positive geometry is rejected rather than inferred.

Owned-pixel integrated flux is deliberately named and modelled separately from fitted-Gaussian integrated flux. The latter integrates the fitted model over its infinite plane: (A\,2\pi\sigma_\mathrm{major}\sigma_\mathrm{minor} \Omega_\mathrm{pixel}/\Omega_\mathrm{beam}). Neither value is silently copied into the other.

Moment initializer

Centroids and covariance use positive physical brightness as the weight. The initializer contains global zero-based pixel-centre coordinates in (x, y) order, covariance entries in pixel squared, ordered major and minor Gaussian sigma axes in pixels, and a major-axis angle counterclockwise from positive pixel x modulo 180 degrees. A circular covariance receives the canonical pixel angle zero because its orientation is not physically determined.

This angle is not a celestial position angle. The astrometry boundary transforms the covariance with Astropy's local tangent-plane Jacobian and reports the east-of-north convention.

Explicit availability

The result union prevents invalid science values from masquerading as valid zeroes:

  • ValidMomentMeasurement contains photometry and a nonsingular initializer;
  • ShapeUnavailableMomentMeasurement preserves valid photometry but omits shape for an underdetermined or singular region; and
  • UnavailableMomentMeasurement contains neither flux nor shape when an owned measurement pixel is invalid/non-finite or non-positive.

CompactMomentConfig makes the minimum shape population and covariance relative tolerance explicit. These are numerical availability rules, not detection thresholds. Nonlinear fit convergence, fitted component semantics, beam deconvolution, and calibrated uncertainty belong to the later fitting and astrometry stages.