What a hazy night looks like, frame by frame

A frame-by-frame movie is good for spotting things; numbers say how big they are. For every frame I measured three things: how bright the stars came out compared with the clear part of the night, how bright the empty sky was, and how much extra light sat on the middle of the field after an even veil was removed. ADU (analog-to-digital units) are the raw numbers the camera records for each pixel; for most of this night the empty sky sat at about 40 to 47 ADU above the camera's zero level. stated

Per sub: star dimming = ZP_ref − ZP_t, where ZP_t is the sub's photometric zero point against Gaia G and ZP_ref = 18.877 is the median over usable subs from 08:30 to 12:15 UTC (after the haze, before twilight; chosen for this page). Sky level is the model's additive level c_t (G channel, ADU above bias), which tracks the measured sky median at r = 0.9999. Center excess is the residual's median inside r < 700 native px minus its median in the 1000 to 1320 px annulus, sky view, single subs. stated

Before rendering a single frame I wrote down what I expected: most likely an even veil (I gave that 60 %), less likely visible patches or wisps drifting through (25 %), and least likely something stuck to the telescope, such as dew on the lens, which would stay put on the sensor while the sky turns (15 %). stated

The even veil won. In the hazy stretch the stars are fainter and the sky brighter, and that is all: once an even dimming and an even lift of the sky are taken out, nothing cloud-shaped is left, whether I looked at single frames or at averages of 5 to 50 frames. Nothing grew on the optics either: there was no dew-like smudge, and the focuser never moved all night. measured

How much did it cost? At its worst, in the first quarter hour (to about 07:18 UTC), stars lost about 12 % of their light (0.14 magnitudes over the first ten minutes; a magnitude is the astronomer's brightness scale, where bigger means fainter). For the rest of the hazy stretch they lost about 6 % (0.07 magnitudes), and by about 08:20 UTC they were back to normal. Stars were not blurrier while it was hazy: their sharpness, measured as FWHM (the width of a star's image at half its peak brightness), was 2.8 pixels, no worse than the 2.9 pixels later in the night. measured

The sky was also brighter while it was hazy: 46.3 ADU against 41.6 ADU for the rest of the night, about 11 % more. But not all of that is haze. The sky kept getting darker for three more hours after the haze had gone, from 43 ADU around 08:30 to 40 ADU around 11:30, as it often does after midnight when light pollution and the natural glow of the upper air fade. It also rose by about 5 ADU for 25 minutes around 08:35 to 09:00 while the stars were not dimmed at all, so the sky can change by that much without any haze. Over the whole night, sky brightness and star dimming hardly moved together. So the haze made the sky brighter by some part of that 4.8 ADU, probably not more, and I can't say exactly how much. measured inferred

One small extra: in the first nine minutes, 18 frames had a sky about 7.5 ADU brighter than the frames around them, flicking on and off from one frame to the next. That looks like thicker haze passing in the first minutes, but it never showed any shape in the frames. measured inferred

Expectations written before any frame was rendered: 60 % a uniform veil plus a smooth gradient with nothing center-weighted; 25 % structured patches drifting through the sky view; 15 % a sensor-fixed central feature (dew), which would sit still in the sensor view. I also set a test in advance: the residual center-minus-outer would correlate with ZP at |r| < 0.3 for a uniform veil and at |r| > 0.5 for a center-weighted one. stated The measured r = −0.49 (sky view, N = 1) meets neither threshold: it is outside the uniform band and just short of the center-weighted one, so by its own pre-set rule the test is undecided; the within-period correlations below show that most of it is a step between periods. measured

• No cloud-scale structure. Inspected by eye in contact sheets at N = 1, 5 and 25 and in the full player: no wisps, patches or drifting features in the hazy stretch; apart from the center, the residual is flat to within the noise. measured
• No sensor-fixed growth. No dew-like feature; the focuser position is 1205 on all 1,301 subs. measured
• Transmission. Median dimming 0.070 mag over the 336 usable hazy subs; 0.138 mag in the first 10 minutes, with the deeper dimming lasting to about 07:18 (2-minute medians 0.10 to 0.20 mag); 0.070 mag from 07:15 to 08:15. Back within 0.03 mag of the reference by 08:15 to 08:20 UTC. FWHM 2.82 px hazy against 2.90 px later outside the overhead pass (3.45 px during it). measured
• Sky level. c_t 46.35 against 41.59 ADU (medians, hazy against later usable subs; +4.8 ADU, +11 %), but c_t keeps falling until about 11:30 (43.2 ADU at 08:24–08:42, 40.1 at 11:18–11:48), apart from a rise to about 47 ADU from 08:33 to 08:55 with no star dimming at all, and r(c_t, ZP) = +0.16 over usable subs. The early-minus-late difference is therefore an upper limit on the haze's additive light, not a measurement of it, on the assumption that the haze-free sky early on was no darker than later (the after-midnight trend suggests so; it was not measured). measured inferred
• Brief brighter subs. 18 subs (17 usable) between 07:03 and 07:12 have c_t = 54.7 ADU (median) against 47.1 for their neighbors, alternating on a one-to-three-sub time scale. measured
• Gray transmission from the template fit. T_t is +93 mmag (dimmer) hazy against −40 mmag later, but it swings to −110 to −140 mmag during the overhead pass because smeared stars no longer match the template at 8×8 binning (r with FWHM = −0.63; r with ZP = −0.40). I use ZP, not T_t, for transparency. measured

I expected nothing special at the middle of the field, and that was wrong. After the even veil is removed, a faint, diffuse extra glow sits on the core of M 33, about the size of the galaxy's bright middle, but only while it's hazy. It is tiny: about 0.7 ADU, roughly 1.5 % of the sky's own brightness, far too faint to notice in a normal picture. But it is steady: every one of the 336 hazy frames shows it, against about one frame in five later in the night. measured

What causes it? Haze scatters a little of each light source's light a short way to the side, giving it a faint halo. Over the galaxy's core, where the galaxy's own glow and many stars crowd together, those halos could add up to a slightly brighter patch than an even veil predicts. That is my best guess, not a tested result. inferred

Two things keep it a guess. First, on this night the galaxy's core, the middle of the sensor and the point the field turned around were all in the same place, so I can't tell whether the glow belongs to the galaxy, to the telescope's optics, or to the way the frames were lined up. Second, the glow outlasted the haze by about half an hour, and faded just as the field started turning quickly as M 33 passed nearly overhead, so the haze is not the only thing that changed. measured inferred

I did rule out one simple camera explanation: a brighter sky does not by itself leave a brighter middle. At dawn the sky got more than ten times brighter, and the middle did not light up. measured

To separate the galaxy from the telescope I ran the same measurement on a second hazy night, on the Dumbbell Nebula (M 27), a small target with no big galaxy in the middle, taken from a different place through a light-pollution filter. There, hazier frames showed no extra glow in the middle. That points toward the galaxy, not the telescope. But that night was different in many ways (37 minutes long, patchy haze, little rotation), and I had already used it for other checks, so it's a second look, not proof. measured inferred

Residual center-minus-outer (median inside r < 700 native px minus median in 1000–1320 px; each frame's own median removed), medians over usable subs: measured

• Size against noise. The per-sub scatter of this statistic (1.4826 × MAD) is 0.17 ADU hazy and 0.38 ADU later; all 336 hazy subs are positive against 22 % of later ones. The per-pixel residual noise is 4.2 ADU per binned pixel at N = 1, but the statistic is a median over thousands of pixels. No significance test accounting for sub-to-sub correlation was run; the subs are strongly autocorrelated, so the 336 do not count as independent trials. measured
• It is mostly a step, not a tracking. r = −0.49 over all usable subs, but only −0.20 within the hazy stretch and −0.11 after it: the correlation comes mainly from the contrast between the two periods. measured (computed for this page)
• The later baseline is not flat. The later median, −0.32, includes the overhead pass (08:54–10:42 UTC, field rotation over 100°/h at its fastest, FWHM 3.45 px), where the statistic sits at −0.42; excluding that window gives −0.26. The excess holds at +0.45 to +0.66 for about 25 minutes after ZP recovers (08:15–08:40) and reaches zero near 09:00, as the rotation rate climbs from about 16°/h to over 100°/h. Haze and rotation state are confounded here. r(center excess, FWHM) = −0.36. measured inferred
• Not vignetting times sky level. If the vignetted sky were absorbed by an additive pattern, a brighter sky would leave a bowl-shaped residual. The fitted sensor pattern's own center-minus-outer is +0.07 ADU on a 43 ADU sky, so a 4.8 ADU sky change predicts under 0.01 ADU. Two direct checks agree: the brighter-sky subs of the first minutes (17 usable) have less excess than their neighbors (+0.55 against +0.71 ADU), and at dawn, with usable subs up to 650 ADU of sky, the statistic is −0.50. measured
• Second night. M 27, 22 August 2026: 154 subs (153 usable) over 37 minutes, light-pollution filter, a different location, about 12° of field rotation, patchy haze. Expectations written before any M 27 number was made: 55 % no haze-tied center excess (|r| ≤ 0.25 and a low-ZP-tercile minus high-ZP-tercile difference under 0.2 ADU), 30 % an M 33-like term (r < −0.3, tercile difference ≥ 0.3 ADU), 15 % inconclusive. Result: r = +0.07, tercile difference +0.09 ADU; slope of the excess on dimming −0.4 ± 1.2 ADU/mag against +4.4 ± 0.25 on M 33 (least squares, bootstrap errors over subs, which understate the error for autocorrelated subs). The first expectation held. Caveats: only the time-varying part is tested (with 12° of rotation the sensor and sky templates are nearly degenerate); the M 27 sky is 5.5× brighter and its residual noise twice M 33's; the night had been used in other analyses before, so it is not held-out data. measured stated
• Reading. The positive sign means the core region keeps more light than a gray veil allows, consistent with forward scattering moving light from compact sources (star cores) into a diffuse aureole over the crowded core, or with stars losing more light than the galaxy's extended light. A sensor- or optics-fixed glow that appears whenever haze lifts the sky is disfavored by the second night, but not excluded. inferred

A simple frame check would have kept almost every hazy frame: my own per-frame quality check, built to catch clouds, blur and trailing, passed 336 of the 337. I did not test the Seestar app's own frame selection, but a check aimed at clouds and blur has little reason to reject an even veil. That is fine for a pretty picture: the brighter background comes out with ordinary background removal, the dimming only costs some signal, and the 0.7 ADU glow on the core is far below what you would see. It matters only if you measure brightness precisely, for example of stars near a galaxy's core. measured inferred

• For sky-limited faint signal, SNR per sub scales as S/√B: 0.94/√1.10 ≈ 0.90, so about 1.25× the integration for the same depth if the full +11 % sky lift were haze (an upper limit, see above), and 1/0.94² ≈ 1.13× if the haze added no sky light. illustrative
• A per-sub quality screen built for gross failures (ZP, FWHM, elongation, star count, sky) passes moderate haze: 336 of 337 hazy subs were flagged usable. The Seestar app's own frame selection was not tested. A residual of this kind is a cheap way to see whether a night's haze is uniform before choosing a per-sub radial or gridded cloud correction. measured inferred
• For differential photometry near an extended source, a center-weighted additive term of order 1 % of the sky can appear under haze that a gray per-sub transmission term does not remove. One night; untested on a galaxy-free field with a long track. inferred
• On this alt-az mount, the overhead pass drives FWHM from 2.9 to 3.45 px (median) in 10 s subs and breaks template-based transparency estimates (T_t above). measured

Decided before I looked: where the hazy stretch ends (the first 1.35 hours, set from an earlier look at the stars' brightness on the same night); the size of the middle disk and the outer ring I compare; how many frames to average; one brightness setting for the whole night; and my written expectations, for this night and for the second night. stated

Changed after the first look: how the veil is removed (see What went wrong). Chosen while writing this page: the clear-sky reference for star dimming (08:30 to 12:15 UTC), the overhead-pass window, and the extra checks on the glow. Measured: everything else. stated

The Seestar's camera sees color through a pattern of tiny red, green and blue filters over its pixels, a Bayer matrix. I used only the green pixels, subtracted the camera's fixed zero level, and added up blocks of 8 by 8 pixels to make small, less noisy frames. Plate solving (matching each frame's stars to a star catalog, here ESA's Gaia) told me exactly where each frame pointed and how it was turned, so I could also redraw every frame north-up on one fixed map of the sky. stated

Then I split each frame into four parts: a pattern fixed to the telescope (such as the slight darkening toward the corners), a pattern fixed to the sky (the galaxy and the stars), an even lift of the background, and an even dimming of everything in the sky. Whatever those four can't explain is the “left over” view in the flip-book. Finally, I averaged runs of 1, 5, 10, 25 and 50 frames to see faint things through the noise, and played them back in order. stated

1. Frames. 1,301 raw 10 s subs, GRBG Bayer, 2160 × 3840 native, gain 200, IR-cut filter. G = mean of G1 and G2 minus the header bias (1112 ADU), binned 4 × 4 on the G plane (8 × 8 native) to 270 × 480. 1,225 subs passed the per-sub quality screen (ZP, FWHM, elongation, star count, sky). stated measured
2. Sky view. A TAN grid at the night's median pointing, north up, 792 × 792 at 29.4″/px (6.5°), sized to hold the rotating footprint. Each binned sub is resampled bilinearly through its own Gaia-matched WCS (pixel map computed on a coarse grid and interpolated). Bright Gaia stars land on binned peaks of 2,000–3,100 ADU; the vertically flipped placement gives about 0, which checks the orientation. stated measured
3. Model. F_t(x) = A(x) + c_t + T_t S(R_tx) + r_t(x): A sensor-fixed (vignetting, bias structure; median-zeroed), S sky-fixed (galaxy and stars), from two rounds of alternating medians over usable subs. Per sub, c_t and T_t by least squares against S minus its 20th percentile, with three passes of 5σ clipping (robust σ from the MAD). r_t is kept in both views. stated
4. Center statistic. On each rolling stack's residual, minus that frame's median: median inside r < 700 native px minus median in 1000–1320 px, about the frame center (sensor view) or the grid center (sky view). stated
5. Stacks and stretch. Rolling means of the last N = 1, 5, 10, 25, 50 subs (NaN-aware in the sky view). One asinh stretch per view and depth for the whole night; knee 2σ at that depth, so deeper stacks get a harder stretch. Residual noise per binned pixel: sky view 4.17 / 2.31 / 1.95 / 1.65 / 1.68 ADU and sensor view 6.20 / 3.21 / 2.52 / 2.02 / 1.81 ADU at N = 1 / 5 / 10 / 25 / 50; the sky view stops improving past N = 25 because stacks straddle rotation and pointing changes. stated measured
6. Star-based center term. An independent per-sub fit of star fluxes with a Gaussian radial term (σ = 700 native px about the frame center) over 300 subs with star-by-star photometry; it correlates with ZP at r = −0.85. Used here only as a comparison series. stated measured
7. Video. All frames encoded as H.264 at 10 frames per second, so the whole night plays as a movie; the flip-book tiles are taken from a smaller copy of the N = 25 video that keeps every fifth sub. stated