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Centroids in every sector

On 12 October 2026 we measured the difference-image centroid of every counted candidate in every sector with transits, and tested whether the offsets point consistently away from the target star, and toward which star. Until then the pixel checks used the offset in one sector (followup.py: the best-quality difference image among a few cheap sectors). The TOI-913 case on issue #2 showed the problem: one sector can look on target while the others point to a neighbour.

Method

  • pipeline/centroid_sectors.py fits transit-diffImage's PRF model to the difference image of each sector with transits (up to 12 per candidate, highest per-sector SNR first), through LEO-Vetter as followup.py does, with cutouts from the TESS cubes on the STScI open-data bucket. Each fit is kept as an offset east and north of the target (arcsec), measured in the sector's pixel frame from transit-diffImage's position of the target. The TIC stars within 2′ are kept with their offsets.
  • pipeline/centroid_test.py treats the per-sector offsets as scattered about the true source with a common, unknown spread. With n sectors and RSS the scatter of the offsets about their mean (floored at 1″ per axis, since the PRF fits have systematic errors of about that size), F = (n |mean − s|² / 2) / (RSS / (2(n − 1))) follows F(2, 2(n − 1)) if the source is at s. It needs at least two sectors. The test is made for the target and for every star within 2′ bright enough to cause the dip: a total eclipse of that star, diluted by the target, must reach the observed depth. Offsets beyond 60″ are treated as failed fits.

The same code ran on two calibration sets:

Calibration

Signals With ≥ 2 sectors Target rejected at p < 0.001 at p < 0.01 True source fits (p ≥ 0.01)
Known planets 565 0 3 (0.5%) –
… with MES < 30 160 0 2 (1.3%) –
Signals from neighbouring stars 175 127 (73%) 141 (81%) 164 (94%)
… source within 15″ 50 38% 90%
… source 15–30″ away 39 77% 100%
… source 30–60″ away 82 91% 95%

Results

517 of the 546 candidates counted on 11 October have difference images in at least two sectors; 29 have one and are not tested.

18 reject their target at p < 0.001 (14 in tier N, 4 in tier B). No known planet does, so we expect fewer than one of the 18 to be on target by chance. They leave the counted tiers: the 16 that a star bright enough to cause the dip fits (p ≥ 0.01) become likely nearby false positives, and the 2 that no catalogued star fits go to tier C. Several have mean offsets of 14–60″; their best single sector had passed the 15″ check.

TIC P (d) Tier before → now Sectors Mean offset p, target Best-fitting star: TIC (separation, T) p, that star
61411095 0.6139 N → likely nearby FP 5 10.8″ 0.0009 940451958 (11.6″, 18.5) 0.86
247464683 0.6594 N → C 6 8.7″ < 0.0001 247483851 (7.4″, 18.4) 0.0016
160983090 0.7985 B → likely nearby FP 5 21.4″ < 0.0001 2004563149 (24.0″, 18.5) 0.46
308058319 0.9492 N → likely nearby FP 5 12.4″ 0.0001 308058320 (12.4″, 17.2) 0.54
92329533 0.9738 N → likely nearby FP 7 5.4″ 0.0002 1964952499 (4.3″, 18.4) 0.41
207141752 1.1134 N → likely nearby FP 3 59.8″ < 0.0001 207141748 (60.0″, 17.0) 0.74
235711821 1.1277 B → likely nearby FP 9 14.3″ < 0.0001 1271379812 (19.2″, 18.5) 0.011
207398162 1.3856 N → likely nearby FP 6 12.9″ < 0.0001 1201126191 (12.7″, 18.7) 0.85
261461983 1.4434 N → likely nearby FP 5 17.3″ 0.0001 261461979 (17.6″, 17.6) 0.28
393339333 1.9213 N → likely nearby FP 7 21.5″ 0.0001 815720478 (18.9″, 18.8) 0.18
167171288 2.8751 N → likely nearby FP 3 11.8″ 0.0001 167171280 (12.1″, 16.7) 0.52
231829497 3.2786 B → likely nearby FP 6 23.2″ 0.0003 231829496 (30.9″, 14.3) 0.13
399426297 3.7869 N → likely nearby FP 6 41.6″ < 0.0001 399426324 (41.4″, 14.7) 0.87
399202562 4.5723 N → likely nearby FP 3 29.2″ 0.0001 399202578 (27.8″, 13.1) 0.63
38943164 4.7793 B → likely nearby FP 10 22.5″ 0.0001 38943169 (29.0″, 14.4) 0.2
45996905 6.2806 N → C 5 12.9″ 0.0002 45996903 (6.0″, 16.8) 0.0071
451538987 10.5492 N → likely nearby FP 8 9.2″ 0.0001 451538984 (5.5″, 17.8) 0.064
463343440 19.9477 N → likely nearby FP 5 11.6″ < 0.0001 861750026 (9.4″, 17.9) 0.21

13 reject their target at 0.001 ≤ p < 0.01 (10 in tier N, 3 in tier B, one of them from the earlier searches). Known planets with MES < 30 reach this level 1.3% of the time, so about half of the 13 could be on target. They stay counted, with centroid_flag set: TIC 18441994, 137609439, 166574088, 177021616, 184506615, 185840936, 258827696, 267824267, 293616610, 310097407, 352414078, 407232246 and 409700778.

The counted candidates are now 470 from the full sky (11 A, 250 B, 159 N, 50 L1) and 58 from the earlier searches: 528 in all. The catalog columns cs_sectors, cs_offset_arcsec, cs_pa_deg (east of north), cs_p_target, cs_neighbour, cs_neighbour_sep_arcsec, cs_p_neighbour and centroid_flag hold the results.

Limits

  • The test is weak for sources within 15″ (38% caught at p < 0.001), which is where tier N candidates have their neighbour, so it removes only the clearest cases there.
  • It assumes the same spread in every sector, although the per-sector SNR differs; the calibration measures how often it flags real planets.
  • Two signals outside the catalog were tested as well. TOI-913's 5.45 d signal (issue #2) has a mean offset of 5.3″ east across 8 sectors, with a large scatter: p = 0.49 for TOI-913 and 0.62 for the giant 9.5″ away, so the test cannot tell them apart. WASP-166's 27.0 d signal sits 10″ northeast in 4 sectors (p = 0.007 for WASP-166, 0.02 for the star 6.7″ east), while WASP-166 b's transits, measured the same way, fall within 1–4″ of the star.

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