The main noise sources in a camera element are:
- Quantum/shot noise (due to limited number of photons hitting the pixels), proportional to the square root of intensity
- Read-out noise (electrons lost or added during data readout), constant
- Dark signal current (thermal electron generation and/or leakage), proportional to the exposure time
Dark current can be compensated for to a certain extent (using dark frames), dark current shot noise (proportional to the square root of dark current) cannot. Dark current usually doubles every 5–6 °C, i.e. better keep it cool. This is what limits the longer exposure times.
To my eye the sample images look as if they were noisy due to image shot noise, but without really trying a couple of different exposures it is difficult to say.
Pixel size does not usually have much to do with dark current. Dark current is proportional to the surface area of a pixel, so the dark current proportional to the full capacity of a pixel is constant, and I would guess the constant is approximately the same for better smart phones and DSLRs.
The main problem here is that there is so little light falling on each pixel. That, in turn, is due to the small lens in front of the camera. Some examples of aperture diameters:
- good phone: 4 mm
- cheap DSLR lens: 15 mm
- small telescope: 150 mm
- large telescope: 5000 mm
The amount of light entering the optical system is proportional to the square of the aperture diameter. So, the main problem with a phone in low-light photography is its small size.