Candidate Explorer

1. A blind search for fast movers

The detector (Find movers) was not told what to look for. Afterwards its candidates were compared with SIMBAD. Each field has exactly one catalogued fast mover: Barnard's Star (10.4″ a year) and Epsilon Indi B (4.7″ a year). The chart shows how far the measured motion is from the catalogue motion.

Both objects were found in every run, and nothing else was reported (no candidate without a catalogue match). The differences are – pixel per year. Searching both detectors together gave the smallest difference for each star ( and ″/yr). Remade on 10 November, Barnard's Star gives the numbers of 7 November (D2 ″/yr); Epsilon Indi B's significance is higher than then because the error of the positions was corrected in the meantime (VALIDATION.md §2.1).

2. How many of the lines are chance?

A candidate is a line through dots in several images. In a crowded field some lines happen by chance, so the detector estimates how many lines this good the dots of that field would make by chance, and keeps a candidate only if that number is below 1. Epsilon Indi B in D6 shows why: with the first version of the rule it listed the real star and three false lines.

The real lines have at most chance lines expected; the three false ones on 7 November about each. The false ones were also supported by dots in only 2–3 of the images where the position could be measured, the real ones in all of them.

Not an independent test, and no longer something this page can remake. The rule was tightened after this failure was seen on these images. Run again today with the original rule, the same field in D6 lists candidate (the real one) and false lines: the dots found in each image are fewer now, so the failure belongs to the code of 7 November and its numbers above are kept as they were. A new field would be needed to test the rule.

3. A bright star and the bad-pixel mask

Barnard's Star is so bright that the core of its image is flagged as saturated in every exposure. The centre of a partly flagged core moves from date to date, which looks like a wrong proper motion. Fitting the star only to the unflagged pixels fixed it.

A fix, not a test. It was designed after seeing the large error on the same images. What argues against tuning: it does nothing for an unsaturated star, and synthetic tests cover it.

4. Are the brightnesses on the right scale?

For isolated, unsaturated stars the measured flux (a small aperture, in Jansky) was divided by the flux expected from the star's 2MASS or AllWISE magnitude at the wavelength of that image.

The scale is right to within about 10 %. A ratio a little below 1 is expected because the small aperture catches only part of a star's light. D6 sits lower than D2 in both fields ( against , and against ). This is not an absolute calibration, and the catalogue zero points were written from memory in the script.

5. An asteroid that moved between two images

The main-belt asteroid Arosa (V = 14.6) lies in two images of the same survey pass, hours apart. The ephemeris service SkyBoT says where it is at each time. The chart shows the flux at those two positions in each image.

The source is at the predicted position in each image and absent from the other: it moved ″ in hours (″ an hour; SkyBoT says ″). Its flux is the same at the two wavelengths, as expected of a sunlit rock, and its centre is ″ from the predicted position. It is not the brightest source of the field, which is why the proof of motion matters.

6. WISE 0855, the namesake object

WISE 0855 is the coldest known brown dwarf and far too faint to show as a dot in one exposure, so a blind search cannot find it. The weaker question: is there flux at the position its catalogue motion predicts, when all the images are added up? The same stack was made at 16 control places (the same path shifted 40 and 60 arcseconds), where nothing is expected.

Suggestive, not a detection. The stack is mJy, which is times the robust scatter of the controls, but it rests on images (two flagged ones were left out and would push in opposite directions), and one control sits on a field star (+4.81 mJy, off the chart), which makes the plain scatter of the controls so large that the target would be only 0.1 σ. The significance depends on how the controls are chosen.

D2 is not WISE 0855. At 1 µm this object is thought to be millions of times fainter than what was measured (a magnitude quoted from memory, to be checked). The flux belongs to . The app now warns when a second source sits within the measuring aperture.

7. Planet X mode on a real dwarf planet

Planet X mode looks for a body so far away that it swings across the sky as the Earth goes round the Sun, and reads its distance from that swing. Makemake (a dwarf planet at 52 AU) is in real images. Each cutout was centred on the position the ephemeris gives, and the ephemeris was otherwise used only for grading.

When told where to look, the fit works: AU against AU, with the residuals at most ″ (one pixel). It tests the Earth's position, the parallax formula and the geometry. But only degrees of freedom check the fit, and the dots were chosen with the ephemeris.

The blind search failed. Run with no ephemeris on all dots of the cutouts, it returned candidates at 52–54 AU, and of them is Makemake. The cutouts are centred on the body, so any dot near a centre follows its parallax track, and the body was detected in only of images, which lets chance combinations fit as well. That first test was biased; a fair one followed.

A fair test. new cutouts of ′ (4 from each survey pass, chosen by date only), each cut a random 3–8′ off Makemake's position, so the body is somewhere in a field of about 300 dots. Makemake is a dot in of them. With the app's default options the search found nothing ( candidates). With loosened options it found Makemake: AU (1σ –) against – AU from the ephemeris, with all of its dots on the body — but as one of candidates. The same images scrambled (no body) give – chance candidates, so the list is mostly chance. What sets the body apart here is a tighter fit ( px, against 0.85–1.04 px for the 8-dot chance candidates of 8 controls): a hint, not a rule. One body, one field, V = 17: far brighter than a Planet-Nine-like body (section 10). The blind search has found a real body once; that is not yet a result.

8. How faint can it go? Fake movers in real images

Notice of 10 November. This section was measured on 7 November with three exposures of Barnard's Star in D2 counted twice (the backend held byte-identical copies; VALIDATION.md §2.1), so its Barnard D2 numbers rest on 15 images plus 3 copies and have not been re-run. The other fields are not affected.

To learn what the detector can and cannot see, fake moving stars of known brightness and speed were added to the real images (with the star shape given in the FITS headers) and the unchanged detector was run: fakes for every brightness and speed, 2400 per field. The chart shows the total flux at which one image finds the fake half of the time and nine times in ten.

In a clean field one image finds a star down to – mJy half of the time. Around a very bright, saturated star (Barnard's Star) the limit is 20–30 times worse ( mJy in D2): the detector's own noise estimate is about times the pixel noise there, because the star's halo thickens the upper tail. Above the limit a fake that moves more than about 0.8 pixel over the whole period (about 3.5″ a year over 1.4 years) is recovered 70–98 % of the time; below it almost never.

Limits of this test. Gaussian fakes, not the real star shape; six field and detector pairs of 5′ cutouts; about ±15 % on a share near 50 %. Two earlier versions of it used a star shape that was too broad and gave limits 2–3 times too high; Makemake, which the detector finds at fluxes well below those limits, exposed the mistake.

9. Is the “chance lines” number honest? Empty-sky test

Notice of 10 November. This section was measured on 7 November with three exposures of Barnard's Star in D2 counted twice (the backend held byte-identical copies; VALIDATION.md §2.1), so its Barnard D2 numbers rest on 15 images plus 3 copies and have not been re-run. The other fields are not affected.

Every real image was rotated or mirrored at random and moved by a random number of pixels, independently of the others, times per field. Real noise and real star counts stay, but nothing links one image to the next, so any candidate is false by construction. The chart shows how often the detector would still list one.

The number is conservative: the observed shares are never above what the number promises. But with only 3 survey passes and 6 images, about 1 empty field in 8 still shows a false candidate under the limit now used ( % and %); a stricter limit of 0.01 instead of 1 would hold every field here at 0.3 % or less and keep all six real candidates, but that change was not made. The original rule that failed on Epsilon Indi B gives a false candidate in 94–100 % of empty fields of 6 images with 3–4 passes: the test would have predicted that failure before it happened.

Not covered: real variable stars and real clusters of faint sources, which the scrambling removes.

10. Could SPHEREx see a “Planet X”?

A distant planet shines only by reflected sunlight. From the limit of section 8, one image shows stars down to about V = –. The chart compares that with what a planet of 2 to 4 Earth radii would be at 300, 500 and 1000 AU.

A body of that size is found in single images only out to about – AU. A hypothetical Planet Nine at 300–800 AU is 3–5 magnitudes too faint for that. Adding up 60 images along its track would gain about 2 magnitudes and still fall short at 500 AU. So Planet X mode is a method that works on bodies bright enough to be seen in single images (Makemake, a simulated body), not a claim that SPHEREx can find a Planet Nine.

From memory, not checked: the relation between brightness, size and albedo, the colour of the Sun, and the size and orbit of Planet Nine. Makemake itself, measured in the real images, comes out about one magnitude fainter than that formula says: the scale is right to the order of magnitude.

11. Every source Find everything lists on the six real fields

This is the list behind the real fields of the sections above (VALIDATION.md §14): every source the images show, each checked against SIMBAD, Gaia DR3, 2MASS and AllWISE at that catalogue's own date. Click a column to sort; filter, search and open a row. Derived numbers only (no pixels). A source nothing explains would be a lead, never a discovery.

How each field's list was made

Made by on , from the author's copy of the real images (not published). Each record above says what it was run with: input, settings, algorithm version and the time of the run. How faint a source must be to be missed is in VALIDATION.md §14.

12. What this does not show

Reproduce it

The commands are in docs/VALIDATION.md. They need the real cutouts, which are not published (they are fetched from IRSA by backend/scripts/fetch_real_sample.py), and a backend that serves only those files.