Variable stars
Field size 94 deg²
STARS THAT WON'T SIT STILL.
Not everything the array finds is moving through the frame. Some of it is standing perfectly still and simply changing — brightening, fading, flickering on a clock a few hours long or a few hundred days long. This page is about that other kind of change: what a variable star actually is, the handful of physical mechanisms behind it, and how a wide-field, repeat-imaging survey turns a few hundred exposures of the same patch of sky into a confident classification. The instrument below is invented. The physics is not.
NOCTIS ARRAY does not exist. Variable stars do — and this page explains them the way a real time-domain difference-imaging pipeline actually has to think about them.
A star that changes brightness, on a clock or in a fit.
Astronomers sort variable stars first by cause, not by appearance: something happening inside the star (intrinsic), or something happening to our view of it (extrinsic). Three intrinsic pulsators and two extrinsic mechanisms cover most of what a survey like this one actually catalogues.
A star can vary because it is physically pulsating, because it just erupted, or because nothing about the star changed at all — only our view of it did.
Intrinsic · pulsatingThe star itself breathes.
A pulsating variable genuinely expands and contracts. In the classic case, a partly ionised layer of helium near the surface acts as a valve — trapping radiation as it ionises, releasing it as it recombines — turning the outer envelope into a heat engine that drives the whole star like a bellows. This single mechanism produces several instantly recognisable classes.
Cepheids are young, massive, evolved supergiants pulsating over days to a couple of months. Their defining trait is the period–luminosity relation — a longer pulsation period means a genuinely more luminous star, in a relation tight enough that Cepheids anchor much of the extragalactic distance ladder. RR Lyrae are older, lower-mass stars on the horizontal branch, pulsating faster — hours, not weeks — and fainter, and dense in globular clusters and the galactic halo, making them a direct tracer of an old stellar population. Long-period variables, including the Mira stars, are cool red giants near the end of their lives, swelling and shrinking over months to a couple of years, shedding the outer layers that will eventually become a planetary nebula.
Intrinsic · eruptiveSomething happened, once or repeatedly.
Eruptive and cataclysmic variables don't oscillate on a steady clock — they change because of an episodic physical event. A magnetically active red or M dwarf flares. A white dwarf pulling gas off a close binary companion periodically dumps that disc onto its own surface as a dwarf-nova outburst. At the more violent end, a nova is a thermonuclear runaway on an accreting white dwarf's surface, and a supernova is the star's actual death — the one "variability" event that never repeats. These light curves tend to be irregular, or semi-regular at best, rather than strictly periodic.
ExtrinsicThe star hasn't changed. Our view has.
Eclipsing binaries are two stars orbiting close enough, and edge-on enough to our line of sight, that each periodically blocks the other. The dimming is pure geometry — no physical change in either star — and the light curve's shape (how deep, how wide, whether the two dips match) encodes the pair's relative sizes and temperatures. Rotational variables are a single star with a lopsided surface — dark starspots, or a chemically mottled patch — whose brightness rises and falls simply because the star is spinning and a different side faces us. Again: the star itself never changes, only which face we're looking at.
You don't find a variable star in one exposure. You find it in hundreds.
A single image of a star only tells you its brightness at that instant. Everything above — periods, eclipse depths, pulsation shapes — only exists on the time axis, which means the whole method is about accumulating many honest brightness measurements of the same star and reading the pattern in them.
One exposure is a snapshot. Hundreds of exposures, of the same patch of sky, are a movie.
Repeat, don't stareTime-domain photometry.
The survey images the same field over and over on a fixed cadence, rather than staring at one target for a long integration. Every pass measures the brightness of every star in the field; stacking one star's measurements in time order produces its light curve. Cadence is a real design constraint — sample too slowly and a fast eclipse or a short pulsation falls between exposures entirely.
Subtraction, againThe same machinery, a different question.
The registration, PSF-matching and subtraction this array uses to hunt moving objects does double duty here. Subtract a deep, stable reference from each new frame and a star that genuinely brightened or faded shows up as residual flux at a fixed position, frame after frame — no motion, which is exactly what tells the pipeline "variable star," not "mover," on the very first pass.
Classify the shapeNot just the fact that it changed.
Once a light curve exists, classification is a shape-recognition problem: periodic or one-off? If periodic, what period, and is the rise and fall symmetric (a pulsator) or does it show two unequal dips (an eclipsing binary)? Real pipelines extract dozens of numeric features from a light curve — period, amplitude, colour, how lopsided the brightness distribution is — and hand them to a classifier trained to recognise each class's fingerprint.
What that subtraction step above actually produces, drawn instead of described:
Here is what our real pipeline actually does with variable stars — no NOCTIS involved.
Same general method as above, on real hardware: repeated ZTF exposures of the same sky, differenced against a deep reference, turned into a light curve, and handed to a classifier that judges its periodicity and shape. Two separate classifiers in this codebase do that judging, and both turn out to be strongest on variable stars.
The light-curve classifier runs a pretrained ALeRCE model — a Balanced Hierarchical Random Forest covering 15 fine classes under three top-level groups (Periodic, Stochastic, Transient) — on real ZTF light curves, and needs at least six detections in the g or r band before it will even attempt an object. On a 29-object evaluation set spanning six classes it scored 0.66 top-level accuracy and 0.38 fine-class accuracy overall — modest numbers, except for the two variable-star classes, which were its strongest by far: eclipsing binaries correct 5 of 5, RR Lyrae correct 3 of 5.
A second, separate classifier — a pretrained ALeRCE single-image "stamp" CNN, an older TensorFlow-1-era model run locally rather than through ALeRCE's own servers — sorts individual detections into four classes, one of which is "VS" for variable star. On a fair labelled evaluation it reached about 0.70 overall accuracy, with variable stars specifically around 0.60, confused mostly with AGN — genuinely similar-looking point sources without a light curve to tell them apart.
And in one full run over 114 real ZTF detections from a single field observed in 2020, variable stars — 36 of them — were the single largest astrophysical class the pipeline found, ahead of AGN (12) and everything else. That's consistent with what you'd expect of an ordinary equatorial star field: it's mostly stars, and a meaningful fraction of stars vary.
None of this is a discovery. Every object involved was already a known, catalogued ZTF source — the pipeline classified it, it did not find it for the first time. What's real is the method and the numbers above; the observatory drawing them onto this page is not.
Confusion happens exactly where you'd predict it.
None of the mechanisms above are hard to tell apart in principle. In practice, with real cadence gaps and real noise, several of them get hard to tell apart at exactly the same two places, over and over.
A light curve is only as good as its coverage. Thin coverage looks like the wrong class.
AliasingThe wrong period can look right.
A ground-based survey only observes at night, around the moon, and around the weather — so its sampling is never perfectly even. An uneven cadence can beat against a star's true period and produce a completely different, entirely plausible-looking false period; recovering the real one usually needs either much longer coverage or a second, differently-cadenced dataset to break the tie.
Class overlapSome light curves are genuinely ambiguous.
A grazing eclipsing binary, seen with sparse phase coverage, can look almost sinusoidal — indistinguishable from a pulsator until enough points happen to land inside the eclipse itself. A faint, noisy point source with only a handful of measurements can look "stochastic" whether it's a genuinely stochastic variable star or something else changing brightness for unrelated reasons — the light curve alone doesn't know which.
This isn't hypothetical. The two real classifiers described above hit exactly these walls: the stamp classifier's biggest single confusion is variable stars called AGN and back again — both are just unremarkable point sources without a light curve attached. The light-curve classifier's confidence is capped by how few brightness measurements a faint alert-stream object accumulates before nobody points a telescope at it again. Neither is a bug. It's the same aliasing-and-overlap problem above, showing up as real numbers.
A pulsing star and a feeding black hole can produce the same one photograph.
Both show up as a compact source at a fixed position that got brighter or fainter. Here's what actually breaks the tie — first the cues a person would reach for, then the numbers our own classifiers actually compute to reach for the same thing.
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01
What's underneath it — a bare point, or a smudge of galaxy?
A variable star is a naked point source: nothing extended around it, because it's just one star. An AGN sits at the centre of a whole galaxy — if that host is resolved in the image, a soft, diffuse glow surrounds the bright nucleus. This is the single most reliable tell when it's available, and the single most useless one when it isn't: a distant or faint AGN's host blurs into an unresolved point, indistinguishable from a star, at exactly the resolution most surveys actually deliver.
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02
The shape of its light curve — a clock, or a wander.
This is the one that actually decides most cases. A pulsating or eclipsing star repeats: fold enough visits on the right period and every point falls back onto the same curve. An AGN's accretion disk has no preferred rhythm — its brightness is a random walk, not a cycle, so no period ever makes the points line up. The catch is coverage: this tell only works once there are enough revisits to either find a period or confidently rule one out, and a sparse light curve looks the same — uninformative — either way.
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03
Colour and amplitude — a hint, not a verdict.
An AGN's accretion disk tends to run bluer than ordinary starlight, and its swings can be large and abrupt rather than the smooth, bounded rise-and-fall of a pulsator. Both are soft cues on their own — plenty of hot, blue stars exist, and plenty of AGN sit quiet for long stretches — which is exactly why no single signal above is treated as proof by itself, on this page or in the pipeline below.
How the ML actually looks for the same three things. Neither classifier "sees" a star or a galaxy the way a person does — each one turns the tells above into plain numbers.
The stamp classifierreads "point vs. extended" as a number.
Each detection is scored from a small image cutout plus a metadata vector of about two dozen real measurements — among them a Pan-STARRS point-source score for that position and its nearest neighbours. That score is the numeric stand-in for "is this a bare point, or does it sit on something extended" — the same host-structure cue from tell 01 above, just handed to the network as a number instead of a picture.
The light-curve classifiersplits on periodic-vs-stochastic first.
Roughly 180 numeric features get computed from each object's brightness history — period search results, amplitude, how lopsided the scatter is — and fed to a pretrained hierarchical random forest whose very first split is Periodic vs. Stochastic vs. Transient. That top-level branch is tell 02 above, made numerically: a real period pulls an object one way, a shapeless wander pulls it the other.
Both features exist and both are real. They just run out of information at the same place a person's eye would — a faint, sparsely-sampled point source with an unresolved host and too few visits to call a period either way. That's the ≈0.55 accuracy documented above, explained mechanically rather than just stated.
Go see what it actually classified.
The array, the cadence and the field notes above are invented. The browsers below are not — they open the same working ZTF difference-imaging pipeline whose light-curve and stamp classifiers are described in the panel above.
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