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At a pressure of 1 bar, the temperature of liquid boiling oxygen stabilizes at 90 K. For sub-cooling of LOX, the temperature should be lower. It is possible to cool LOX by forced evaporation by a pressure lower than 1 bar. But the LOX tank in a rocket should be as light as possible. If the pressure inside the tank is substantially lower than outside, extra strength and weight is necessary. But according to these papers: (1) (2) and (3) there is another method.
Cold helium gas is injected at the bottom of the tank and the bubbles raise in the LOX. At the surface of the bubbles, LOX evaporates into the bubble and cools the remaining LOX. But extra space is needed for the bubbles in the LOX and for the gas mixture of helium and oxygen above the liquid level. For topping off, the injection of helium is stopped and the remaining space is filled with LOX. Figure 8 of the first paper shows the effect of different helium gas temperatures. The cooling works best with helium at 85 K, but even helium at 150 K cools the LOX.
A bubble injected into the LOX consists of 100 % helium and 0 % oxygen at first. The LOX around this bubble would boil just like in a vaccum because the partial pressure of oxygen in this bubble is zero. Even a bubble consisting of 50 % helium and 50 % oxygen is able to cool LOX at 90 K. Without sub cooling in a tank with boiling LOX at 90 K, the gas above the liquid is 100 % oxygen and the partial pressure of oxygen is 1 bar. If the partial pressure of oxygen is lower than 1 bar in the gas above the liquid or inside the bubbles, the LOX is cooled by evaporation.
At the launch pad the LOX may be precooled using a heat exchanger with ground suplied liquid nitrogen boiling at 77.355 K. To save weight of the rocket, this heat exchanger should be outside the rocket but close to it. Liquid nitrogen and oxygen should not be mixed to avoid solving of nitrogen within the LOX. Cooling with helium bubbles may be used within the rocket LOX tank.