VALIDATION_CASE_STELLAR_HELIACAL_RISING - TheDaniel166/moira GitHub Wiki

Validation Case: Stellar Heliacal Rising — Sirius and the Four Royal Stars (Babylon 2025)

Subject: First morning visibility (heliacal rising) of five fixed stars
Stars: Sirius, Aldebaran, Regulus, Antares, Fomalhaut (classical Royal Stars + Sirius)
Substrate: Moira stars.heliacal_rising_event / DE441 (Sun) / ICRS J2000 + Hipparcos proper motion (star)
Oracle: astropy 7.2.0 / ERFA IAU 2006 — fully independent solar and stellar pipelines
Criterion layer: Schoch/Ptolemy arcus visionis stepped table
Status: VERIFIED — 20/20 exact across four years (2023–2026)
Verified: 2026-03-25 (baseline); 2026-04-10 (multi-year + elongation guard fix)

1. What is being tested

moira.stars.heliacal_rising_event(name, jd_start, lat, lon) predicts the first morning on which a fixed star becomes geometrically visible above the apparent horizon at the moment of morning twilight (Sun at −av° geometric altitude).

This is a completely separate code path from the planetary heliacal solver tested in the Mars and Venus cases. The stellar pipeline uses:

  1. ICRS J2000 catalog coordinates (Hipparcos) + proper motion propagation (_propagate_icrs_vector)
  2. Moira's own precession engine (icrf_to_true_ecliptic → ecliptic of date)
  3. ecliptic_to_equatorial using true_obliquity
  4. Local Apparent Sidereal Time via apparent_sidereal_time (GAST + longitude, IAU 2006)
  5. Geometric altitude formula (no atmospheric refraction in the body-check path)
  6. The solar twilight finder _find_sun_at_alt (DE441-based); morning-sky guard (se >= 0.0 skip)

The oracle exercises an entirely separate coordinate chain using only astropy/ERFA:

  1. Same Hipparcos ICRS J2000 catalog inputs
  2. astropy SkyCoord.apply_space_motion() for proper motion to epoch
  3. ERFA IAU 2006 precession/nutation via astropy's AltAz transform
  4. pressure=0 to suppress refraction (geometric altitude matching Moira's convention)
  5. get_body('sun', time, BABYLON) with ERFA full apparent solar position for twilight

The two pipelines share only the raw Hipparcos catalog coordinates.

2. Observer and epoch

  • Site: Babylon — 32.55°N, 44.42°E, height 0 m
  • Epoch: 2025 apparitions (modern scientific validation)
  • Horizon threshold: geometric altitude −0.5667° = apparent altitude 0° (standard refraction 34′)

3. Arcus visionis assignments

From Moira's _default_arcus_for_star() (Schoch/Ptolemy stepped table):

Star HIP V mag Mag branch av (°)
Sirius 32349 −1.46 ≤ −1.0 7.5
Aldebaran 21421 +0.86 ≤ +1.0 10.0
Regulus 49669 +1.40 ≤ +2.0 11.0
Antares 80763 +0.91 ≤ +1.0 10.0
Fomalhaut 113368 +1.16 ≤ +2.0 11.0

4. Star catalog provenance

All five stars use SIMBAD/Hipparcos ICRS J2000 coordinates, PM, and parallax from Moira's sovereign catalog. The astropy oracle uses identical catalog inputs (same HIP RA/Dec/pm_ra_cosdec/pm_dec/parallax values), so any coordinate agreement or residual reflects the comparison between Moira's precession/nutation/GAST engine and ERFA's IAU 2006 pipeline given the same catalog source.

5. Elongation guard

Moira's heliacal_rising_event applies a morning-sky guard:

se = _heliacal_signed_elongation(name, jd_midnight + 0.5)
if se >= 0.0:
    continue

se = star.longitude − sun.longitude (signed ecliptic elongation, degrees).
The se >= 0.0 check skips days when the star is in the evening sky (conjunction not yet past, or star west of Sun). No further elongation magnitude filter is applied — the arcus visionis altitude check (star_alt > −0.5667° at the −av° twilight) is the sole visibility criterion.

Prior behaviour (removed 2026-04-10): An earlier version also skipped days with abs(se) < 12.0°, a performance shortcut intended to avoid computing twilight near conjunction. Because Regulus's arcus visionis (11°) is smaller than this fixed threshold, the guard blocked the first valid rising day every year — a systematic +1-day offset fully explained by the threshold, not a coordinate error. The guard was redundant with the altitude check and has been removed from the rising solver. The setting solver retains its own elongation logic, which is semantically distinct.

6. Validation results

Each oracle step finds the morning JD when sun_geometric_altitude = −av° (astropy ERFA apparent Sun), then evaluates the star's geometric altitude at that JD. First day with star altitude > −0.5667° is the oracle's heliacal rising date.

6.1 Sirius — av = 7.5°

Date Twilight UT Astropy alt Moira alt
2025-Jul-26 1.622h −7.943° −7.949°
2025-Jul-27 1.635h −6.988° −6.994°
2025-Jul-28 1.647h −6.035° −6.041°
2025-Jul-29 1.660h −5.086° −5.091°
2025-Jul-30 1.672h −4.137° −4.143°
2025-Jul-31 1.685h −3.192° −3.197°
2025-Aug-01 1.698h −2.249° −2.255°
2025-Aug-02 1.710h −1.310° −1.316°
2025-Aug-03 1.723h −0.375° −0.381°
2025-Aug-04 1.736h +0.556° +0.551°

Oracle: 2025-Aug-03 = Moira: 2025-Aug-03 → EXACT
Altitude agreement at event JD: 0.006° (astropy vs Moira)

6.2 Aldebaran — av = 10.0°

Date Twilight UT Astropy alt Moira alt
2025-Jun-15 1.049h −3.671° −3.675°
2025-Jun-16 1.050h −2.887° −2.891°
2025-Jun-17 1.052h −2.097° −2.101°
2025-Jun-18 1.054h −1.298° −1.302°
2025-Jun-19 1.056h −0.490° −0.494°
2025-Jun-20 1.059h +0.327° +0.322°

Oracle: 2025-Jun-19 = Moira: 2025-Jun-19 → EXACT
Altitude agreement at event JD: 0.004°

6.3 Regulus — av = 11.0°

Date Twilight UT Astropy alt Moira alt
2025-Sep-01 1.792h −2.526° −2.531°
2025-Sep-02 1.804h −1.572° −1.577°
2025-Sep-03 1.816h −0.508° −0.513°
2025-Sep-04 1.828h +0.446° +0.440°
2025-Sep-05 1.840h +1.403° +1.397°

Oracle: 2025-Sep-03 = Moira: 2025-Sep-03 → EXACT
Altitude agreement at event JD: 0.005° (astropy vs Moira)

Regulus's altitude on Sep-03 (−0.508°) clears the −0.5667° apparent-horizon threshold. Prior to 2026-04-10 a 12° elongation magnitude guard in the rising solver blocked this day (Sep-03 elongation −11.06° < 12°), producing a systematic +1-day offset. That guard has been removed; see §5.

6.4 Antares — av = 10.0°

Date Twilight UT Astropy alt Moira alt
2025-Dec-12 3.116h −2.929° −2.934°
2025-Dec-13 3.127h −2.090° −2.096°
2025-Dec-14 3.138h −1.259° −1.264°
2025-Dec-15 3.149h −0.437° −0.442°
2025-Dec-16 3.159h +0.377° +0.372°

Oracle: 2025-Dec-15 = Moira: 2025-Dec-15 → EXACT
Altitude agreement at event JD: 0.005°

6.5 Fomalhaut — av = 11.0°

Date Twilight UT Astropy alt Moira alt
2025-Apr-15 1.715h −1.586° −1.589°
2025-Apr-16 1.693h −1.128° −1.132°
2025-Apr-17 1.671h −0.671° −0.674°
2025-Apr-18 1.650h −0.214° −0.217°
2025-Apr-19 1.629h +0.242° +0.239°

Oracle: 2025-Apr-18 = Moira: 2025-Apr-18 → EXACT
Altitude agreement at event JD: 0.003°

7. Summary table

Star HIP V mag av Moira Oracle Match
Sirius 32349 −1.46 7.5° 2025-Aug-03 2025-Aug-03 EXACT
Aldebaran 21421 +0.86 10.0° 2025-Jun-19 2025-Jun-19 EXACT
Regulus 49669 +1.40 11.0° 2025-Sep-03 2025-Sep-03 EXACT
Antares 80763 +0.91 10.0° 2025-Dec-15 2025-Dec-15 EXACT
Fomalhaut 113368 +1.16 11.0° 2025-Apr-18 2025-Apr-18 EXACT

8. Oracle pipeline architecture

Catalog input (Hipparcos ICRS J2000):
  ra_j2000, dec_j2000, pmra, pmdec, parallax
            │
            ▼
  astropy SkyCoord (frame='icrs', obstime=J2000.0)
  → apply_space_motion(new_obstime = twilight_JD)
  → SkyCoord at epoch of observation
            │
            ▼ (each star)
  AltAz(obstime=t, location=BABYLON, pressure=0)     ← geometric altitude
  → .alt.deg

Sun twilight:
  For each date, bisect Sun geometric altitude = −av°
  using get_body('sun', t, BABYLON) → AltAz(pressure=0)
  (ERFA/SOFA full apparent position: precession + nutation + aberration)
  Convergence: 1-second (30 bisection iterations)

9. Prior oracle error: J2000 astrometric vs epoch-of-date apparent Sun

An earlier version of this validation script used JPL Horizons QUANTITIES="1" (which returns J2000 ICRF astrometric RA/Dec — no precession, nutation, or annual aberration applied) combined with an IAU 1982 GMST formula. This produced a systematic solar altitude bias of approximately +0.33° at 2025 dates, caused by the ~26′ ecliptic-longitude precession offset between J2000 and 2025.6. The resulting ~1.75-minute twilight time shift was large enough to flip the date for rapidly-rising stars (Sirius, Aldebaran, Antares rise at ~11°/hr near Babylon's horizon) but not for slowly-rising ones (Regulus, Fomalhaut).

The corrected oracle uses astropy.coordinates.get_body('sun'), which applies the full apparent position pipeline (ERFA IAU 2006 precession/nutation/aberration), eliminating this bias and producing results consistent with Moira's sky_position_at() pipeline.

10. Coordinate agreement between Moira and astropy/ERFA

At each twilight JD, the table above shows both astropy and Moira stellar altitude. The consistent 0.003°–0.007° agreement reflects the comparison of:

  • Moira: ICRF J2000 → _propagate_icrs_vector proper motion → icrf_to_true_ecliptic (Moira precession) → ecliptic_to_equatorial (true obliquity) → IAU 2006 GAST altitude
  • Oracle: ICRF J2000 → apply_space_motion → ERFA IAU 2006 precession/nutation → AltAz

The residual (∼0.005°) is consistent with expected numerical differences between Moira's precession series and ERFA's full IAU 2006 model, and is well within any practical observational margin.

11. Validation script

tmp/stellar_heliacal_validation.py

Key parameters:

  • Observer: Babylon 32.55°N 44.42°E
  • Time scale: UTC (both Moira and astropy)
  • Morning window searched: UT 01:00 – 06:30 per day
  • Solar twilight bisection: 30 iterations, 1-second convergence
  • Star coordinate epoch: J2000.0 proper motion propagated to observation date
  • Atmospheric refraction: suppressed (pressure=0) in both pipelines

12. Multi-year coverage — 2023, 2024, 2026

Validation was extended to three additional apparition years (2023, 2024, 2026) using the same astropy/ERFA oracle, same observer (Babylon), and same five stars. This provides a 4-year sample (including the 2025 baseline) per star — 20 cases total.

Script: tmp/stellar_heliacal_multiyear.py

12.1 Results

Star Year av Moira Oracle Match
Sirius 2023 7.5° 2023-Aug-04 2023-Aug-04 EXACT
Sirius 2024 7.5° 2024-Aug-03 2024-Aug-03 EXACT
Sirius 2026 7.5° 2026-Aug-04 2026-Aug-04 EXACT
Aldebaran 2023 10.0° 2023-Jun-20 2023-Jun-20 EXACT
Aldebaran 2024 10.0° 2024-Jun-19 2024-Jun-19 EXACT
Aldebaran 2026 10.0° 2026-Jun-20 2026-Jun-20 EXACT
Regulus 2023 11.0° 2023-Sep-04 2023-Sep-04 EXACT
Regulus 2024 11.0° 2024-Sep-03 2024-Sep-03 EXACT
Regulus 2026 11.0° 2026-Sep-04 2026-Sep-04 EXACT
Antares 2023 10.0° 2023-Dec-16 2023-Dec-16 EXACT
Antares 2024 10.0° 2024-Dec-15 2024-Dec-15 EXACT
Antares 2026 10.0° 2026-Dec-16 2026-Dec-16 EXACT
Fomalhaut 2023 11.0° 2023-Apr-18 2023-Apr-18 EXACT
Fomalhaut 2024 11.0° 2024-Apr-17 2024-Apr-17 EXACT
Fomalhaut 2026 11.0° 2026-Apr-18 2026-Apr-18 EXACT

15 of 15 EXACT.

12.2 Regulus — elongation guard removal

Prior to 2026-04-10, heliacal_rising_event skipped days with abs(se) < 12.0°. Because Regulus's arcus visionis (11°) is below that threshold, the guard blocked the first altitude-valid day every year, producing a systematic +1-day offset. After removing the redundant guard (see §5), all four Regulus years are now exact:

Year Oracle Moira (fixed) Regulus elongation at event date
2023 Sep-04 Sep-04 ≈ −11.1°
2024 Sep-03 Sep-03 ≈ −11.0°
2025 Sep-03 Sep-03 −11.06° (measured; see §6.3)
2026 Sep-04 Sep-04 ≈ −11.1°

The altitude agreement between Moira and astropy at the event twilight JD is 0.005°–0.007° in all four years — identical to before the fix, confirming the change is isolated to the elongation guard logic only.

12.3 Four-year combined summary (2023–2026)

Including the 2025 baseline from §7:

Star 2023 2024 2025 2026 Exact / 4
Sirius Aug-04 ✓ Aug-03 ✓ Aug-03 ✓ Aug-04 ✓ 4 / 4
Aldebaran Jun-20 ✓ Jun-19 ✓ Jun-19 ✓ Jun-20 ✓ 4 / 4
Regulus Sep-04 ✓ Sep-03 ✓ Sep-03 ✓ Sep-04 ✓ 4 / 4
Antares Dec-16 ✓ Dec-15 ✓ Dec-15 ✓ Dec-16 ✓ 4 / 4
Fomalhaut Apr-18 ✓ Apr-17 ✓ Apr-18 ✓ Apr-18 ✓ 4 / 4

20 of 20 exact across four years.

All five stars match the astropy/ERFA oracle exactly across every tested year. The Regulus offset documented in earlier sessions was caused by a redundant elongation magnitude guard in heliacal_rising_event; that guard has been removed. See §5 and §12.2.