Assume Earth has been wrenched out of the Sun's orbit and has become a rogue planet (for the purposes of this question, assume that it happens near instantaneously, i.e. say the Sun just vanishes). The oceans will all be covered in ice in a matter of weeks, with the planet turning into Snowball Earth, and the atmosphere liquifying and falling as rain within a year or two before freezing solid.
According to this estimate, the equilibrium temperature will converge to around -240C and the oceans will freeze up entirely within 500,000 years.
Sunlight's absence forces Earth's surface temperature to become ~34 K – even during the postulated very harsh first-onset of a "Snowball Earth" period this planet's mean global temperature got to ~225 K – meaning the atmosphere will condense, forming an inconsistently thick draped stratum of solidified gases ~10 m-thick on the land and sea surface. Earth's atmosphere consists of 78% N2, 21% O2 and 1% other gases; the first substance to freeze would be H2O, followed by CO2, then N2 and finally O2. The pressure on the sub-aerial crust (1 atmosphere) will remain the same but the 10,329 kg/m2 will be in the form of solids, not gases. (Subsequently, Earth's world-ocean will commence to freeze, completing that phase transition in ~0.5 × 10^6 years. Without liquid water the tectonic plate motions would cease just as soon as all previously entrained water was lost, and without wet subducted tectonic plates, no active volcanism!)
Though there are also some projections which state that regions around hydrothermal vents will retain liquid water indefinitely, allowing extremophile life to subsist.
How long would it take for all or most of the oceans by volume to become ice? Is 500,000 years (as above) a plausible accurate estimate?
At what rate will the freeze progress - linearly, exponentially declining, or something else? What would be the depth of oceanic freeze after, say, 1 year, 10 years, 100 years, 1,000 years, and 10,000 years, respectively?
Thanks in advance!