TESS WCS: endpoints, temperature and the remaining spatial field

1. Both starts and endings remain explicit

Archived whole-day withheld predictions. Gray is measured WCS displacement relative to a common reference; orange removes known aberration and measured attitude; blue is the remaining thermal-prediction error. Thin blue lines are individual cameras.

Three panels use the archived nested-selected thermal/lag policy and all-camera attitude. Orbit48 startup uses its separately archived instantaneous model and cameras2–4 attitude. Camera1 is flagged there. These are different policies/supports, not one homogeneous benchmark. All scores are 2D vector RMS; 1mpx=0.001 native detector pixel.

Window	Exposures	CCDs	After VA + measured attitude [mpx]	Thermal prediction error [mpx]
o47_first	49	16	9.203	3.625
o47_last	49	16	7.553	1.099
o48_first	38	12	10.294	3.624
o48_last	49	16	24.781	1.246

Actual signed probe fields at each interval’s largest thermal-error exposure. All after-thermal panels share one colour scale; the before-thermal scale differs. Gray orbit48 camera1 is missing, not zero.

Interpretation: coherent startup errors remain in both orbits. Small ending errors do not prove a complete physical or autonomous pointing model.

2. Does scale track temperature?

Each camera: measured scale and held-block prediction; partial temperature–scale relation with identical time/orbit terms removed from both axes; and held-block errors. Conditional slopes are full-sample descriptions, not heldout estimates.

Sensor2 supplies predictive information beyond orbit-specific linear time in all four cameras. Conditional slopes are −19.04 to −22.87ppm/°C in this sky-map convention.
These are effective mapping coefficients, not material expansion coefficients. Inverse plate-scale definitions reverse the sign.
Ten sequential blocks with a0.25day buffer reproduce the archived analysis on1100 clean exposures. It is a scalar scale test, distinct from full-field endpoint prediction.
Numeric sensor IDs avoid overstating component identity. The source descriptions and physical interpretation are below.

Underlying measured, calibrated and remaining spatial fields

Orbit47 window-mean fields: measured after aberration/attitude, full-data thermal calibration, and remaining field. Same arrow scale; these are descriptive calibration maps, not withheld prediction errors.

Orbit48 corresponding maps, with flagged camera1 at startup. All displayed maps use the same cameras2–4 attitude convention; the scalar scale plot above retains its original all-camera convention.

3. Do temperatures at different camera parts explain more?

We tested nine fixed feature families: time only; mean sensors2–5; extra sensor differences; all components; their contrasts; contrasts with rates; and contrasts with a12h causal history state.
Test days plus0.25day buffers are excluded; ridge selection uses six training-only inner folds. These previously examined endpoints are exploratory comparisons, not untouched final validation.
“Barrel” in these plots means mean PT1000 sensors2–5; “gradient” means sensor2−sensor5, a temperature difference without a physical distance normalization.

Three all-camera endpoint tests. Added component contrasts do not improve orbit47 startup beyond mean sensors2–5. Axes have different ranges; compare numerical values within each panel.

Prediction errors above, actual selected C3 temperature contrasts below. Startup sensor differences evolve strongly, but that alone does not establish additional predictive skill.

Actual signed errors and all-family image comparison

Signed errors for the fixed contrast family at its worst exposure in each day; all components use one symmetric scale.

Every family on identical selected exposures with common colour scaling. Statistics use every test exposure; these snapshots illustrate the underlying spatial pattern.

Separate orbit48 startup test using cameras2–4 only: extra component information helps modestly, unlike orbit47. Measured attitude is still supplied.

Orbit48 startup: actual spatial errors at one common exposure for all families, under one colour scale. Extra predictors leave visible residual structure.

Family	O47 first [mpx]	O47 last [mpx]	O48 first C2–4 [mpx]	O48 last [mpx]
time	7.001	2.298	16.259	2.081
barrel	2.757	1.105	4.127	1.217
barrel_gradient	2.765	1.109	4.026	1.223
barrel_sensor10	2.781	1.110	4.092	1.219
barrel_sensor67	3.023	1.092	3.589	1.267
contrasts	2.965	1.083	3.532	1.248
contrasts_history12h	5.283	1.102	4.127	1.250
contrasts_rate	2.984	1.053	3.386	1.234

Additional sensor6/7 contrasts and rates help orbit48 startup, but the same additions do not close orbit47 startup. The fixed12h model does not improve the aggregate startup results.
This is evidence against these predictors being universally sufficient, not against thermal physics. Correlated sensors cannot identify a unique mechanical cause.
Feature selection after inspecting this table requires new validation. No “best row” is promoted as an unbiased final score.

4. What shape remains?

The signed maps show broad offsets/gradients and localized edge structure. Per-CCD translation, isotropic scale, shear, rotation and non-affine terms describe that shape; they do not identify its mechanical cause. A per-CCD translation is not automatically spacecraft pointing. Camera-wide radial expansion can also contribute to those offsets; a local-mode budget alone cannot exclude it.

Actual withheld errors split into per-CCD modes. Left bars retain all exposure–probe squared errors; right bars square the time-averaged field. These are different denominators, not causal variance allocations.

Enlarged window-mean residual directions with a common5mpx key; nine actual probes displayed perCCD. Sky-map sign is opposite fixed-star displacement to first order; CCD orientations retained, camera placement schematic.

Unchanged predictions scored on all81, inner49 or outer32 probes perCCD. This diagnoses spatial concentration; it is not an improved correction. Outer probes remain inset from detector edges.

Window	CCD offsets [% squared error]	Scale [% squared error]	Non-affine [% squared error]
o47_first	57.080	3.638	33.594
o47_last	32.927	3.512	56.025
o48_first	75.249	1.542	18.697
o48_last	17.023	2.762	68.767

Startup residuals contain coherent CCD-level offsets and non-affine structure. The fitted per-CCD isotropic scale term accounts for only about1.5–3.6% of remaining squared error in these archived endpoint predictions.
At orbit48 startup, C3 retains an offset across all four CCD interiors; edge-localized failures alone do not explain it. Other CCDs show stronger outer-probe contributions.
The edge test changes only the scored support, not the predictions. Lower interior RMS is not an improved correction; it identifies where validation is needed.
Non-affine means the part not represented by a per-CCD linear transform. It could contain optical distortion, centroid bias or polynomial-WCS fitting artifacts. A coherent header residual is not proof of mechanical motion.

Gray: actual mean withheld residual. Blue: its fitted camera-centred radial component, using one free amplitude per camera and exposure in the matching attitude convention. This descriptive projection fits residuals; it is not a new heldout forecast.

A separate whole-camera radial-template test addresses the per-CCD-centering ambiguity. Even allowing a free amplitude for every camera and exposure, these templates capture only6.49%,5.32%,1.09% and2.00% of the remaining squared error for orbit47 first/last and orbit48 first/last, respectively.
Thus another simple camera-centred isotropic expansion cannot account for most of this remainder under the tested geometry. More general thermal deformation, tilt/alignment changes and estimator effects remain possible.

Supplement: full-data calibration mode inventory

Per-CCD spatial modes of window-mean fields after full-data calibration. This display can average away time-variable errors and is not a prediction-accuracy result. The heldout endpoint maps above determine the forecast limitations.

5. Sensor identities, possible causes and discriminating tests

Sensor identity

Channel	Sector20 FITS description	Instrument Handbook TableA.3
2	Lens Barrel	L1
3	Lens Barrel	L2
4	Lens Barrel	L3/4
5	Lens Barrel	L4/3
6	FPE Housing	Generic PT1000 sensor6
7	FPE Housing	Base Plate
9	FPA Housing	CCD Case
10	FPA Mosaic	Mosaic

Preserve exact channel numbers. The flight-file and design-document descriptions do not uniquely identify the mechanically responsible element.
Sensor differences are temperature contrasts, not gradients per metre: no calibrated sensor separation has been used.
The handbook describes multiple thermal paths, including the lens hood heat sink and isolation between focal-plane electronics and assembly. That motivates component-resolved tests without proving a particular residual's cause.
Primary source: TESS Instrument Handbook, §4.4 and AppendixA.

Shape of the withheld remainder

The archived endpoint errors contain coherent per-CCD offsets and non-affine structure. Per-CCD isotropic scale accounts for only about1.5–3.6% of their squared residual amplitude.
A spatial constant within each CCD is not an independent spacecraft-pointing measurement. Common attitude has already been removed.
Orbit48 camera3 retains residuals across CCD interiors. Some other CCDs show strong outer-probe concentrations; both physical distortion and WCS/centroid fitting artifacts remain plausible.
Window-mean maps show persistent patterns; exposure-averaged squared errors retain their time-variable part. The page plots both, without mixing their denominators.
A separate whole-camera radial-template projection (free camera amplitudes at every exposure) captures only1.09–6.49% of the remaining squared error across these endpoints. This descriptive fit addresses the CCD-centering ambiguity and limits simple isotropic expansion as the missing pattern; it does not rule out other thermal deformations.

What could cause the remainder?

Candidate	Signature to test	Present limit
Unequilibrated optics or unmeasured thermal gradients	History-dependent scale/distortion at matched sensor temperatures	Tested contrasts/history do not close both startups
Camera or detector alignment changes	Relative CCD translations, rotation/shear and smooth nonradial fields	Spatial decomposition identifies shape, not the moving component
Guide response or attitude convention	Common rotation with a distinct relative-camera pattern	Measured attitude is supplied; controller/commanded-attitude reconstruction remains open
PSF/centroid or WCS-fitting bias	Magnitude/colour/pixel-phase dependence or large edge-localized residuals	Header maps alone cannot distinguish physical motion from estimator errors

Tests that would make the paper's explanation stronger

Re-measure reserved startup/interior/ending images with the same profile-centre convention and held-source support; compare spatial modes with header maps.
Test a fixed model in another thermal/guiding regime; avoid repeatedly tuning against these two startups.
Resolve sensor locations/calibration and timing; add explicitly identified driver/interface and on-chip channels only after checking their data quality.
Test matched-temperature but different-history cases and predict a distinct spatial mode before attributing a component.
Report coherent residuals against an independently measured noise floor. An unexplained but bounded residual is a valid result; it must not be labelled fully explained.

Conclusion: temperature is a useful predictor, and the residual's spatial shape narrows the next tests. Complete physical attribution and an independently verified full-orbit WCS accuracy budget are not yet established.

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