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.ts

@@ -1,3 +1,4 @@
+import { isDesignation } from '../models/star-catalog';
 import { StarRecord } from '../models/star.model';
 
 /**
@@ -17,8 +18,32 @@ import { StarRecord } from '../models/star.model';
 
 const DEG_TO_RAD = Math.PI / 180;
 
-/** Angular separation, in degrees, below which two entries are taken to be the same star. */
-export const MERGE_ANGULAR_TOLERANCE_DEG = 1 / 3600;
+/**
+ * Angular separation, in degrees, below which two entries are taken to be the same star.
+ *
+ * Every source arrives here at epoch J2000.0 — HYG publishes it, Gaia is carried back to it with
+ * its own proper motions in `gaia.ts` — so what separates two entries of one star is measurement,
+ * not motion. Left at their own epochs, sixteen years of proper motion put Proxima's two entries
+ * 62″ apart and Barnard's 166″, and an arcsecond of tolerance kept every fast star twice while
+ * folding the slow ones.
+ *
+ * What measurement leaves is under an arcsecond for a Hipparcos position — 55 457 of the 56 000
+ * stars both catalogues hold — and up to tens of arcseconds for the Gliese-only entries HYG
+ * carries without Hipparcos astrometry: Wolf 359 sits 5″ from where Gaia has it, Ross 248 12″.
+ * Fifteen arcseconds takes those. The sky is sparse enough at this depth that shifting every
+ * entry a quarter of a degree finds only 16 chance neighbours within it, against 116 real ones
+ * between ten and fifteen; past twenty the two curves run together.
+ */
+export const MERGE_ANGULAR_TOLERANCE_DEG = 15 / 3600;
+
+/**
+ * How far two catalogues may disagree about a star's brightness and still describe the same
+ * star. Bands differ — HYG's V and Gaia's G are three magnitudes apart for the reddest dwarfs —
+ * but five is not a band, it is a companion: Sirius B sits 6″ from Sirius and ten magnitudes
+ * fainter, Polaris B 18″ and seven. Gaia saturates below G ≈ 3, so without this a bright primary
+ * it does not carry is folded into its companion's entry, and the companion is gone.
+ */
+export const MERGE_MAGNITUDE_TOLERANCE = 5;
 
 /**
  * How far two distances may disagree, as a ratio, and still describe the same star. Generous on
@@ -36,7 +61,7 @@ export interface MergeCandidate {
 
 export interface MergeSummary {
   readonly total: number;
-  /** Entries dropped because a better-measured catalogue already had that star. */
+  /** Entries folded into one a better-measured catalogue already had; see {@link combine}. */
   readonly duplicates: number;
   readonly bySource: Readonly<Record<string, number>>;
 }
@@ -86,8 +111,15 @@ export function directionCosine(a: StarRecord, b: StarRecord): number {
   return Math.max(-1, Math.min(1, ax * bx + ay * by + az * bz));
 }
 
-/** Whether two entries describe the same star: same direction, and distances not in conflict. */
+/**
+ * Whether two entries describe the same star: same direction, and neither distance nor
+ * brightness in conflict.
+ */
 export function isSameStar(a: StarRecord, b: StarRecord): boolean {
+  if (Math.abs(a.magnitude - b.magnitude) > MERGE_MAGNITUDE_TOLERANCE) {
+    return false;
+  }
+
   const [near, far] = [distanceOf(a), distanceOf(b)].sort((p, q) => p - q);
 
   // The Sun sits at the origin of this coordinate system and so has no direction at all, which
@@ -105,17 +137,37 @@ export function isSameStar(a: StarRecord, b: StarRecord): boolean {
   return (far - near) / near <= MERGE_DISTANCE_RATIO_TOLERANCE;
 }
 
+/**
+ * One entry from two of the same star: the position of the better-measured one — inserted first,
+ * so it is the one already `kept` — and the description of whichever knows the star as more than
+ * a catalogue number. HYG's "Proxima Centauri", "M5Ve" and V magnitude over Gaia's
+ * "Gaia DR3 5853498713190525696", "Unknown" and G; keeping either row whole loses half of that,
+ * and keeping Gaia's whole once cost the map 102 proper names and 32 000 spectral types. The id
+ * travels with the description, so a star HYG knows keeps its HYG id from one refresh to the next;
+ * `source` stays with the position, since that is what it records.
+ */
+function combine(kept: StarRecord, other: StarRecord): StarRecord {
+  const described = isDesignation(kept) && !isDesignation(other) ? other : kept;
+  return { ...described, x: kept.x, y: kept.y, z: kept.z, source: kept.source };
+}
+
 /**
  * Unions the given catalogues, keeping one entry per star.
  *
- * Sources are taken in order of how precisely they measure parallax, best first, and a star is
- * only added if no better-measured catalogue already has it. So where Gaia and Hipparcos
- * overlap, the position is Gaia's; where only Hipparcos reaches, the star is still there.
+ * Sources are taken in order of how precisely they measure parallax, best first. An entry that a
+ * better-measured catalogue already has is folded into that entry — the nearest one within the
+ * tolerance, see {@link combine} for what each side keeps. Only entries from *other* sources
+ * count as already there: a catalogue does not list a star twice, so two of its own entries
+ * within the tolerance are two stars, typically a double that Gaia resolves and Hipparcos did
+ * not. Where only one source reaches, the star is still there.
  */
 export function mergeStarCatalogues(candidates: readonly MergeCandidate[]): { stars: StarRecord[]; summary: MergeSummary } {
   const ordered = [...candidates].sort((a, b) => a.parallaxPrecisionMas - b.parallaxPrecisionMas);
   const merged: StarRecord[] = [];
-  const grid = new Map<string, StarRecord[]>();
+  const grid = new Map<string, number[]>();
+  // Entries that already absorbed one from a source, as `${index}/${source}`: a double that
+  // Gliese lists as two entries at one position has to land on two Gaia entries, not on one.
+  const taken = new Set<string>();
   const bySource: Record<string, number> = {};
   let duplicates = 0;
 
@@ -123,24 +175,41 @@ export function mergeStarCatalogues(candidates: readonly MergeCandidate[]): { st
     bySource[candidate.sourceId] = 0;
 
     for (const star of candidate.stars) {
-      const { raDeg, decDeg } = skyAngles(star);
-      const alreadyPresent = neighbouringCells(raDeg, decDeg).some((key) => (grid.get(key) ?? []).some((existing) => isSameStar(existing, star)));
+      const entry: StarRecord = { ...star, source: star.source ?? candidate.sourceId };
+      const { raDeg, decDeg } = skyAngles(entry);
 
-      if (alreadyPresent) {
+      let match: number | null = null;
+      let matchCosine = -1;
+      for (const key of neighbouringCells(raDeg, decDeg)) {
+        for (const index of grid.get(key) ?? []) {
+          const existing = merged[index];
+          if (existing.source === entry.source || taken.has(`${index}/${entry.source}`) || !isSameStar(existing, entry)) {
+            continue;
+          }
+          const cosine = directionCosine(existing, entry);
+          if (cosine > matchCosine) {
+            match = index;
+            matchCosine = cosine;
+          }
+        }
+      }
+
+      if (match !== null) {
+        merged[match] = combine(merged[match], entry);
+        taken.add(`${match}/${entry.source}`);
         duplicates++;
         continue;
       }
 
-      const withSource: StarRecord = { ...star, source: star.source ?? candidate.sourceId };
-      merged.push(withSource);
+      const index = merged.push(entry) - 1;
       bySource[candidate.sourceId]++;
 
       const key = cellKey(raDeg, decDeg);
       const cell = grid.get(key);
       if (cell) {
-        cell.push(withSource);
+        cell.push(index);
       } else {
-        grid.set(key, [withSource]);
+        grid.set(key, [index]);
       }
     }
   }