Bring Gaia to HYG's epoch before merging, and keep a star's name when it matches

Gaia DR3 gives positions for J2016.0, HYG for 2000.0, and the merge matched
them on the sky to one arcsecond without propagating any proper motion.
Sixteen years of motion is 62" for Proxima and 166" for Barnard's Star, so
every star faster than ~62 mas/yr — most of the nearest ones — was kept twice,
some 23 000 in all. The slow ones were matched, and lost: the merge kept
Gaia's row whole, so 102 proper names, 1 336 Bayer/Flamsteed names and
32 000 spectral types became "Gaia DR3 <id>" and "Unknown", and 92 named
exoplanet hosts handed their planets to their anonymous twin.

Gaia is now asked for its proper motions and carried back to J2000 before it
leaves the fetcher. HYG is placed from its own x/y/z columns, which are right
where its `ra` is not: that column was carried from the Hipparcos epoch
without the cos δ its motion needs, 17.9" off for Proxima. A match combines
the two entries — Gaia's position, HYG's name, type, magnitude, colour and id
— instead of choosing one. The tolerance is 15" with a five-magnitude guard,
both set by measurement: 55 457 pairs sit under 1" once the epochs agree, the
Gliese-only entries up to 12" (Ross 248), shifting every entry a quarter of
a degree finds 16 chance neighbours at 15", and the guard keeps Sirius out
of Sirius B's entry. Entries of one source are never merged with each other:
the 1 411 Gaia doubles resolved under 1" are two stars, not one.

Regenerated: 425 071 stars (was 447 410), 56 082 of them Gaia positions
carrying HYG identities; no HYG id or name lost; the sixteen stars nearest
the Sun carry no survey designation; 196 residual doubles, all components
17" or more from their counterpart. Five planets of four bright giants
(7 CMa, HD 81688, omi UMa, xi Aql) lose their host link: their Gaia distance
sits 0.7–1.1 pc from the archive's Hipparcos-based one, past the 0.5 pc the
host match allows. Matching hosts on the sky rather than in space, as the
merge does, is the follow-up.

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01QL6F9Bgfh8SgAiAAcPB9Hw

src/app/shared/astro/star-merge.spec.ts

@@ -2,7 +2,7 @@ import { describe, expect, it } from 'vitest';
 
 import { raDegDecDistanceToXyz } from './coordinates';
 import { StarRecord } from '../models/star.model';
-import { directionCosine, isSameStar, mergeStarCatalogues } from './star-merge';
+import { directionCosine, isSameStar, MERGE_ANGULAR_TOLERANCE_DEG, mergeStarCatalogues } from './star-merge';
 
 /** A star at a given sky position and distance, which is how catalogues actually report them. */
 function at(id: number, raDeg: number, decDeg: number, distancePc: number, overrides: Partial<StarRecord> = {}): StarRecord {
@@ -13,17 +13,37 @@ function at(id: number, raDeg: number, decDeg: number, distancePc: number, overr
 const HIPPARCOS = { sourceId: 'hyg', parallaxPrecisionMas: 1 };
 const GAIA = { sourceId: 'gaia', parallaxPrecisionMas: 0.02 };
 
+/** Degrees of right ascension that span `arcsec` on the sky at declination `decDeg`. */
+function arcsecOfRa(arcsec: number, decDeg: number): number {
+  return arcsec / 3600 / Math.cos((decDeg * Math.PI) / 180);
+}
+
 describe('isSameStar', () => {
   it('matches two catalogues reporting the same star', () => {
     expect(isSameStar(at(1, 101.28, -16.71, 2.64), at(2, 101.28, -16.71, 2.63))).toBe(true);
   });
 
+  it('matches within the angular tolerance and not beyond it', () => {
+    const toleranceArcsec = MERGE_ANGULAR_TOLERANCE_DEG * 3600;
+    expect(isSameStar(at(1, 200, 10, 100), at(2, 200 + arcsecOfRa(0.9 * toleranceArcsec, 10), 10, 100))).toBe(true);
+    expect(isSameStar(at(1, 200, 10, 100), at(2, 200 + arcsecOfRa(1.1 * toleranceArcsec, 10), 10, 100))).toBe(false);
+  });
+
   it('tolerates the distance disagreement two parallaxes actually have', () => {
     // Hipparcos and Gaia routinely differ by tens of per cent at a few hundred parsecs. That
     // disagreement is the reason to prefer one of them, not evidence they are different stars.
     expect(isSameStar(at(1, 200, 10, 200), at(2, 200, 10, 260))).toBe(true);
   });
 
+  it('keeps a bright primary out of the entry of its faint companion', () => {
+    // Gaia has no Sirius — it saturates — but has Sirius B, 6″ away at the same distance and ten
+    // magnitudes fainter. Direction and distance say "same star"; the brightness says otherwise.
+    const sirius = at(32263, 101.2875, -16.7161, 2.637, { name: 'Sirius', magnitude: -1.44 });
+    const siriusB = at(1, 101.2875 + arcsecOfRa(6.1, -16.7161), -16.7161, 2.67, { name: 'Gaia DR3 2947050466531873024', magnitude: 8.5, source: 'gaia' });
+    expect(isSameStar(sirius, siriusB)).toBe(false);
+    expect(isSameStar(sirius, { ...siriusB, magnitude: -1.3 })).toBe(true);
+  });
+
   it('does not match two different stars that happen to be at the same distance', () => {
     expect(isSameStar(at(1, 200, 10, 200), at(2, 200.5, 10, 200))).toBe(false);
   });
@@ -72,6 +92,44 @@ describe('mergeStarCatalogues', () => {
     expect(summary.duplicates).toBe(1);
   });
 
+  it('gives a matched star the better position and the name somebody gave it', () => {
+    // What a merge is for: Gaia knows where Proxima is to a fraction of a milliarcsecond and
+    // calls it by a nineteen-digit number; HYG knows its name, its spectral type and its V
+    // magnitude. Keeping one row whole loses half of that either way. The id follows the
+    // description, so a star HYG knows keeps its HYG id from one refresh to the next.
+    const hyg = at(70666, 217.4289, -62.6795, 1.2959, { name: 'Proxima Centauri', spectralType: 'M5Ve', magnitude: 11.01, colorIndex: 1.807 });
+    const gaia = at(1000064182, 217.4289, -62.6795, 1.302, { name: 'Gaia DR3 5853498713190525696', spectralType: 'Unknown', magnitude: 8.985, colorIndex: 3.805, source: 'gaia' });
+    const { stars, summary } = mergeStarCatalogues([{ ...HIPPARCOS, stars: [hyg] }, { ...GAIA, stars: [gaia] }]);
+
+    expect(stars).toEqual([{ ...hyg, x: gaia.x, y: gaia.y, z: gaia.z, source: 'gaia' }]);
+    expect(summary.duplicates).toBe(1);
+  });
+
+  it('keeps two entries of one source apart, however close they are', () => {
+    // Gaia resolves doubles Hipparcos saw as one star: two source ids 0.8″ apart are two stars,
+    // and only *another* catalogue can claim to have already listed either of them.
+    const { stars, summary } = mergeStarCatalogues([{ ...GAIA, stars: [at(1, 10, 10, 100), at(2, 10 + arcsecOfRa(0.8, 10), 10, 100)] }]);
+    expect(stars).toHaveLength(2);
+    expect(summary.duplicates).toBe(0);
+  });
+
+  it('folds an entry into the nearest match, and into each match once', () => {
+    // Gliese lists both components of a double; Gaia resolves them 0.8″ apart. Each HYG
+    // component must land on its own Gaia counterpart — not both on whichever the grid yields
+    // first, and not both on the same one.
+    const gaiaA = at(1, 10, 10, 2.68, { name: 'Gaia DR3 1', source: 'gaia' });
+    const gaiaB = at(2, 10 + arcsecOfRa(0.8, 10), 10, 2.68, { name: 'Gaia DR3 2', source: 'gaia' });
+    const a = at(118079, 10, 10, 2.63, { name: 'Gl 65A' });
+    const b = at(118080, 10 + arcsecOfRa(0.8, 10), 10, 2.63, { name: 'Gl 65B' });
+    const position = (star: StarRecord) => [star.x, star.y, star.z];
+
+    const nearest = mergeStarCatalogues([{ ...HIPPARCOS, stars: [b, a] }, { ...GAIA, stars: [gaiaA, gaiaB] }]);
+    expect(nearest.stars.map((star) => [star.name, ...position(star)])).toEqual([['Gl 65A', ...position(gaiaA)], ['Gl 65B', ...position(gaiaB)]]);
+
+    const onePlace = mergeStarCatalogues([{ ...HIPPARCOS, stars: [a, { ...b, x: a.x, y: a.y, z: a.z }] }, { ...GAIA, stars: [gaiaA, gaiaB] }]);
+    expect(onePlace.stars.map((star) => [star.name, ...position(star)])).toEqual([['Gl 65A', ...position(gaiaA)], ['Gl 65B', ...position(gaiaB)]]);
+  });
+
   it('keeps a star the better catalogue does not reach', () => {
     // The point of merging rather than replacing: Gaia is more precise but not a superset of
     // everything, and a bright star it omits should not vanish from the map.