Andy Resnick said:
That is not my experience (I shoot with a D810). I always shoot with as low an ISO as possible (ISO 64) to maximize the dynamic range, especially color information. Shooting with higher ISO values only increases the amount of noise in my stacked image.
A good rule of thumb for deep sky (not planetary) astrophotography is once you decide on an exposure time (usually determined by how long your equipment can maintain proper tracking, or how long, on average, you can go without a stray cloud messing things up), you should generally increase the gain (ISO) as high as you can go
without saturating stars. This generally minimizes the read noise, measured in electrons.
Check your camera's sensor's specs to be sure for that particular sensor, but its almost always the case that higher gain (i.e., higher ISO) reduces read noise.
As
@Devin-M mentions, increasing gain (ISO) sacrifices dynamic range, but it reduces read noise and increases resolution. So long as you're not saturating stars, you don't need the dynamic range anyway.
Keep in mind that whichever gain (ISO) you choose, you should take DARK and FLAT (and BIAS and/or DARKFLATs) frames with that same gain (ISO) setting.
Here's a spec sheet of a typical camera:
Note that when the gain (ISO) increases, the read noise in units of electrons, decreases. Also note that for this camera (above figure), there is a discontinuity in some of the curves right around a gain of 60, above and below different circuitry is switched in or out. This is why you should check the specs of your particular camera's sensor, so you know what to expect regarding different gain (ISO) settings.
Because higher gain means finer resolution (electrons per ADU), sub-frames with higher gain might show higher noise in units of ADU, but the signal is also greater in units of ADU. And actually, the signal to noise ratio is generally better at higher gain (higher ISO). That's why read noise is typically specified in units of electrons rather than ADU units, because units of electrons more closely tracks signal to noise ratio.
Just make sure you're not saturating stars. If you're saturating stars, lower the gain (i.e., lower the ISO).
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If you were like me, you might be saying, "Woah, now. That's crazy. I've done terrestrial photography, portraits, landscapes, etc., for years. And using higher ISO always makes noisier photos. Lower the ISO if you want less noise!"
The flaw in that argument is when doing terrestrial photography, the tradeoff is between ISO and exposure. If you increase the ISO you must correspondingly decrease the aperture or increase the shutter speed (i.e., decrease the exposure time). (Here, "exposure" is aperature \times shutter speed). Increasing the ISO means you'll have to decrease exposure to avoid blown highlights.
Most of the noise in that case is ultimately the result of reducing the exposure. Fewer photons hit the sensor, increasing shot noise. Less signal is allowed to reach the sensor, so that decreases signal the noise ratio. That, and as previously mentioned, the read noise in units of ADU can increase due to the finer electrons per ADU resolution.
However, in deep sky astrophotography, there is no such tradeoff (planetary astrophotography is a different matter -- let's leave planetary astrophotography out of this discussion). For deep sky astrophotography exposure times are kept as long as you can, given your equipment and cloud cover. And there's almost no sane reason why would ever reduce your aperture. Thus there is no tradeoff regarding ISO and exposure.
So for deep sky astrophotography, the rule of thumb is once you pick your exposure time, pick your gain setting (ISO) such that stars are not saturated. There's usually no need to reduce the gain (ISO) much lower than that.
(And don't forget that your DARKS, FLATs, DARKFLATs, and/or BIAS frames must use the same gain (ISO) setting as your LIGHTs.)