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This applies to any object, but I see the recent discovery of the oldest, most distant galaxy and it started me wondering what the limits are. Presumably you can do better with a bigger telescope and longer exposure, but I'm curious about literally how many photons you need to collect to decide whether or not something is actually there. And then presumably you need a bunch more to determine its red-shift and angular size and rotation etc.
I have absolutely no feel for these numbers. Is it tens of photons or a millions of photons?

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What matters is how many photons you collect versus how many you would expect to see if the object wasn't there.

Photons would be present, without a source, for a variety of astrophysical (e.g. diffuse background) or non-astrophysical (night sky brightness, dark current) reasons, so you need to be able to rule out the null hypothesis that what you have seen is consistent with no object at all. In principle, if you expect no background counts, then the detection of one photon is significant.

The lowest backgrounds tend to occur in space-based X-ray and gamma ray observations, where the detection of a few photons is often taken to be evidence of the presence of an X-ray source.

The backgrounds tend to be higher in optical observations. More photons from the source are needed to get a significant detection, because the variance in the background is proportional to the expected background.

Determining anything beyond detection typically needs an order of magnitude more photons because you are slicing your data into several positional or wavelength bins and you need significant detections in those individually. For rotation you need both position and wavelength, so I would say you need yet another order of magnitude increase to be able to say anything.

It is hard to write anything but a vague, general answer, because the details depend exactly on the telescope, the detector and the type of object being observed.

For example, one way of looking for very distant objects is to look for mere detections of high redshift Lyman alpha emitters. To minimise the background you use a set of narrow-band filters which would select the Lyman alpha line over a narrow range of redshifts. Detection of a source through one filter combined with non-detection in adjacent filters tells you it is an emission line object, and assuming it is Lyman alpha you then also know the redshift.

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  • $\begingroup$ +1 Since the question asks "How many...does it take?" it might be possible to ballpark a number of detected photons. For example, might 100 excess photons in each of a dozen pixels passing through a few different filters be enough to say "yup, that's probably a galaxy"? If so, 10,000 could be a ball-parked numerical answer. $\endgroup$
    – uhoh
    Commented Jan 31, 2021 at 13:22
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    $\begingroup$ @uhoh You can't ballpark it until you tell me how many background counts there are. That in turn depends on the size of the telescope, its angular resolution, the dark current, the read noise, the sky background, the exposure time... Determining whether something is a galaxy is a question of ruling out a point source, and depends on the angular resolution, the surface brightness profile of the galaxy... etc. Not trying to be awkward; that's just the way it is. $\endgroup$
    – ProfRob
    Commented Jan 31, 2021 at 16:16
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    $\begingroup$ @ProfRob A space telescope would have far less background radiation in most wavelengths than an Earth based telescope, though possibly more background radiation in some wavelengths. Thus for most frequencies the number of photons necessary to count as detection should be significantly smaller for space telescopes than for ground telescopes. $\endgroup$
    – M. A. Golding
    Commented Jan 31, 2021 at 21:42
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    $\begingroup$ @M.A.Golding Yes, that is correct. That is, if you are talking about something like HST. It wouldn't necessarily be tru for something like Kepler though, because of its poor PSF. $\endgroup$
    – ProfRob
    Commented Jan 31, 2021 at 22:13
  • $\begingroup$ @ProfRob that answer provides some good insights, thanks. A separate question: I'm curious about the photon efficiency of modern telescopes/detectors?. I assume with modern silicon detectors that it's a high number like 90% for visible light? FYI, separately I've tried to calculate how much illumination we get from that farthest galaxy GN-z11. If I've done it correctly, it's about 10 photons per square meter per second. It's quite remarkable to think about. $\endgroup$
    – Roger Wood
    Commented Feb 1, 2021 at 4:13

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