Astronomy · Finding change in the sky

Candidate alerts and follow-up observations

Trace an alert to its measurement and reference inputs, choose follow-up to distinguish hypotheses, and calculate covariance caused by a reused reference.

Continue in the approved chapter order. Necessary vocabulary, quantities and assumptions are explained in the lesson.

Back to the chapter

After reading, you can

Distinguish alert messages, detections and associated astronomical sources.
Identify context and provenance needed to interpret a candidate.
Calculate shared-reference covariance without assuming independent repeated differences.

A message announces evidence to investigate

An astronomical alert packages a selected candidate measurement and contextual information. The candidate may correspond to changing flux, motion, an ordinary variable source or an instrumental or processing artifact. Packaging the alert does not establish a physical cause.

Useful context can include time and band, position and uncertainty, a science image, a reference image, a difference image, quality information and earlier measurements or limits. The meaning of each field depends on the system’s schema and measurement definitions.

Patterson and collaborators’ ZTF alert-system paper describes a concrete historical design, while Masci and collaborators describe its measurement and processing context. These examples support the distinction between candidate, history and image inputs; they are not a universal schema or a statement of current stream availability.

A source association is also an inference. Two detections close on the sky may be associated with one object under a matching rule, while a moving object can change position. A catalogue crossmatch alone does not prove identity without its timing, positional uncertainty and resolution conditions.

Do not count a replay as another observation

A message identifier can distinguish delivery records. A detection identifier can refer to a particular extraction from particular input data. A source identifier can group detections associated with a proposed astronomical object. These are different levels of provenance.

If the same packet is delivered again, there is another message arrival but no new photons or exposure. Reprocessing one image can also change the extracted candidate without supplying an independent observation. Processing and reference versions are therefore part of the evidence.

A history may contain measured non-detections with defined limits, prior detections or gaps in coverage. Those records should retain their original time, band and selection meaning. A missing earlier detection is not automatically a newly appeared source.

These distinctions help preserve a reproducible interpretation as calibration, matching or classification changes. They also prevent the apparent number of messages from being mistaken for the amount of independent corroboration.

Two science exposures can reuse one uncertain input

For an original uncertainty model, let D₁ = S₁ − R and D₂ = S₂ − R be differences on the same compatible signal scale. Assume the primitive errors in S₁, S₂ and R are independent and zero mean, with variances 9Q0², 16Q0² and 4Q0² respectively. Q0 is an arbitrary positive calibrated signal unit.

The difference variances are Var(D₁) = 9Q0² + 4Q0² = 13Q0² and Var(D₂) = 16Q0² + 4Q0² = 20Q0². Both differences contain the same negative reference error, so Cov(D₁, D₂) = Var(R) = 4Q0².

The arithmetic mean has variance Var[(D₁ + D₂)/2] = [13 + 20 + 2(4)]Q0²/4 = 41Q0²/4 = 10.25Q0². Incorrectly declaring the differences independent would omit the covariance and give 33Q0²/4 = 8.25Q0².

The two science measurements can be distinct while their differences remain correlated. No stationary time-series model or actual noise distribution is asserted; this result follows directly from the supplied linear model and finite second moments.

Original shared-reference uncertainty model. Primitive S₁, S₂ and R errors are independent with variances 9, 16 and 4 in Q0²; each difference subtracts the same R. Entries below are the difference covariance matrix, with variances on the diagonal.
Covariance / Q0²	D₁	D₂
D₁	13	4
D₂	4	20

More information is useful when it distinguishes alternatives

A repeat exposure can test whether a candidate persists and can reveal motion or an unstable image artifact. Its usefulness depends on the expected timescale, sensitivity and whether it repeats the same problematic reference or calibration.

A different band can constrain colour and the spectrum of a change, while a spectrum can reveal lines and velocities. Better spatial resolution can separate a blend. Each observation should be chosen for the distinction it can make, rather than because one follow-up type always confirms every class.

Timing matters: the candidate may evolve while an observation is arranged, and coverage or weather may limit what can be learned. An operational delay between a packet and follow-up is not automatically an intrinsic physical lag at the source.

A non-detection in follow-up is conditional on its time, band, sensitivity and detection definition. It can constrain an alternative without uniquely establishing an artifact, especially when a short-lived signal or changing spectrum remains possible.

A candidate can remain useful while uncertain

Record which observations support each interpretation and which questions remain unresolved. A candidate can be worth following while its physical class is uncertain. A reliability assessment of the detection and a classification of the source are separate judgements.

Repeated measurements can strengthen evidence when their dependencies are understood. The shared-reference example shows why simply counting them is insufficient. Independent instruments or response models can probe some shared failure modes, while still needing compatible calibration and time conventions.

Preserving input identifiers, processing versions, selection criteria and classification changes allows later evidence to refine the conclusion. Replacing an earlier uncertain label without retaining its basis can hide why the interpretation changed.

The next lesson examines artifacts and classification explicitly. A finite probability ledger will distinguish the chance of flagging a desired event from the chance that a flagged item belongs to the desired class.

Worked examples

Keep the covariance when averaging

Why does the supplied mean difference have variance 10.25Q0² rather than 8.25Q0²?

The two difference variances are 13Q0² and 20Q0².
Their common reference adds covariance 4Q0², entering twice in the variance of the sum.
Divide 13 + 20 + 2 × 4 = 41 by 4 for the arithmetic mean.

The mean variance is 41Q0²/4 because the reference uncertainty is reused in both differences.

Count measurements at the correct level

A packet describing one extraction arrives twice. What additional observational evidence does the second delivery provide?

Check whether the detection and input-image identifiers are the same.
If this is a replay of the same extraction, it contains the same underlying exposure and processing result.
Two deliveries are distinct message events, but they do not supply a second independent astronomical measurement.

A replay adds no new exposure by itself; its message identity must be distinguished from detection and source identity.

Try the reasoning

Does producing an alert confirm a specific physical source class?
Show the answer and reasoning
No.
An alert packages selected candidate evidence and context for further interpretation.
Do independent science-image errors make differences independent when both reuse one uncertain reference?
Show the answer and reasoning
No.
The shared reference contributes cross-measurement covariance.
Is one follow-up observation type guaranteed to settle every candidate’s cause?
Show the answer and reasoning
No.
The best additional evidence depends on the competing hypotheses and available observing window.
Is the delay between an alert and a scheduled observation necessarily a physical response delay at the source?
Show the answer and reasoning
No.
Acquisition, processing, delivery and observing constraints are distinct from source physics.

What to carry forward

Messages, detections and source associations have different identities and evidential roles.
Shared inputs can correlate apparently separate measurements.
Follow-up should target an unresolved distinction while preserving calibration, timing and provenance.

References

Teaching resources and research supporting this lesson’s explanations and examples.