When reading many sources that address doing astrophotography, I often see the advice to take multiple exposures and stack them rather than one long exposure. Often the reason given is that the longer exposure results in more noise due to heat build up in the sensor that causes hot pixels. Yet it seems to me that taking one short exposure after another with virtually no cooling-off period between frames would do very little to reduce the overall buildup of heat in the sensor over the course of the series. While there is a benefit to be gained from using multiple frames regarding random noise often referred to as shot noise, is there any benefit from using many more shorter frames than there would be from using fewer longer frames over the same total amount of time? If so, is any of that benefit heat related?
If I, for example, want to take a 2 hour exposure of the night sky to create star trails would there be any appreciable difference in noise if I combined twenty-four five minute exposures than if I combined 240 thirty second exposures? If so, would any of that gain be related to heat? Or would it all be the result of more averaging of shot noise?
Answer
When it comes to night sky photography and stacking, there is no real substitute for actual SNR (Signal to Noise Ratio). You can virtually improve SNR by stacking hundreds of very short exposures (like stacking 720 10-second exposures), but the result will never quite be the same as if you stack say forty 3-minute exposures. Stacking a bunch of 30 second exposures is better, and might get you what you are looking for, however the longer you can get away with exposing, the better in the long run.
For star trails shots, you want to expose for longer. You could stack a gazillion shorter 30-second exposures, assuming a 30-second exposure actually produces trails. When stacking for star trails, exposing for a couple minutes at least is probably better, as you will actually get some decent trails in place. At wider angles (i.e. 16mm), you can expose for 45 seconds or even a little longer WITHOUT any noticeable trailing (you just get some slightly oblong stars). Longer focal lengths would reduce the minimum exposure necessary to start producing visible trailing.
Stacking and Signal Strength
When it comes to stacking, the stronger the actual image signal in each the better. There are a few reasons for this. First, read noise from the electronics of the camera becomes a higher ratio of a short exposure than a longer exposure. Expose for longer, and you increase the image signal to read noise ratio. The image signal itself still has noise, called photon shot noise, however again...a longer exposure will reduce that as well.
Next, you need to expose long enough such that the signal is strong enough to produce good color fidelity. Good color fidelity occurs in the midtonal range...from the highest shadows through just under the highlights. The best color fidelity occurs in the core midtones, a short range around 18% gray. (Technically speaking a digital sensor is linear, but even transistors have a response curve, and the broad range between the upper shadows and the lower highlights offers the best response.) Deeper nuances of color from nebula and the like will generally never appear at all unless the actual SNR of each of your frames that will be stacked is strong enough to render at least some of it. With shorter exposures, faint color will usually be lost to noise, and no amount of stacking will ever recover it.
Finally, to fully resolve finer, darker nuances of detail such as dust and those deep red filaments often present in nebula, or finer detail in galaxies, you need a complete enough signal to cover the whole area of the sky that you are imaging with at least some signal for each pixel in the lower midtones. Stacking lots of very short exposures can result in an image that encompasses the whole subject, but which lacks completeness as each frame is more sparsely sampled, and in which the entire signal is likely below that lower midtone cutoff. Longer exposures that produce a higher SNR produce more completely sampled frames, such that when stacked, all the darker nuances of detail become stronger.
Noise
Photon shot noise follows a Poisson distribution, which follows a standard deviation that is the square root of the signal strength. As a hypothetical example, if you expose for two minutes at ISO 800 on a 5D III to get a nearly saturated result, the maximum signal strength would be around 9000e-, while the photon shot noise would be ~95e-. If you take twelve 10-second exposures at ISO 6400, the signal strength is 900e-, and shot noise would be ~30e-. To put that in more obvious terms, noise with a two minute exposure is 1/95th the strength of the signal, where as noise with ten second exposures is 1/30th the strength of the signal. Assuming no other issues, stacking the ten second exposures should produce a result that is almost identical to the two minute exposure.
There are other issues, however. Read noise is also a greater percentage of the signal with ten second exposures. As such, color noise and other artifacts caused by the electronic readout of the image signal, will be higher with the ten second exposures. Assuming you take the necessary dark and bias frames to be used with stacking, a lot of that can be eliminated, but not entirely (stacking can only go so far to remove noise from sparse, noisy images). Heat, which is another contributor to shadow noise, will not be significantly different with a longer sequence of shorter exposures vs. shorter sequence of longer exposure, assuming continuous shooting.
Color fidelity with a ten second ISO 6400 shot will not be nearly as good as with a 120 second ISO 800 shot. A camera like the 5D III has a full well capacity of over 67,000e-. At ISO 800 the maximum signal strength is 9055e-, and at ISO 6400 it is 1079e-. Both are below that ideal midtone level, however 9055 is an order of magnitude better than 1079.
Star Trails
I know that you explicitly asked about star trails photography. Color fidelity is not going to be a primary concern here, and neither is capturing those deep, faint colors and dark detail elements like dust. However, to stack images to produce one of those star trails photos where the stars circle the sky, you need to expose long enough to actually produce trails...even if they are short.
At wider angles, such as 14mm and 16mm, you can expose for longer than 30 seconds and not actually get any trails at all. At 20mm and 24mm, you should start to see star trails around 30 seconds, assuming you are using an APS-C sensor with smaller pixels. You might start seeing star trails with a FF sensor at 24mm and only a 30 second exposure. By 35mm, you should get short trails with 30 second exposures...however 35mm is really starting to narrow the field, so you should make sure that is what you want.
To get decent trails, I recommend exposing for over a minute. You do not need to expose for the entire two hour duration in a single shot, but exposing for around two or three minutes should get you some nice trails that, when stacked, will produce a nice continuous arcing track. You can then stack as many shots as you need to get the trail length you want. The earth rotates about 15° an hour, so a two hour sequence of stacked trails shots will produce about a 30° arc in your trails.
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