Enough to bring the iron atoms close enough to be tempted to contribute their electrons to the shared metallic bond. With no interference, this can be relatively little pressure, however, the more perfect the mating surfaces the closer we can get those atoms when asking them to shake hands. Two pieces of steel polished completely flat (much more than you typically do on your grinder or by hand) will act like magnets when you work them against each other at room temperature. This is called Vanderwaal force, and while it is not true welding, it gives you a basic idea of the concept of atomic attraction due to proximity. At test, done in a lab a long time ago, where a clean bar of gold was clamped to a clean bar of lead for about two years, showed that the lead contained gold atoms, just below the surface, when they were separated.
Two pieces of steel, ground as smooth as possible and kept in a totally inert atmosphere will weld at a much lower temperature than two that are rougher or have oxides on them. The pressure we need in performing the weld is, once again, a matter of getting as many surface atoms close to each other as possible. Heating makes the distance easier by exciting the electrons to a greater degree than at room temperature. On the inverse, the greater the pressure, the lower the temperature can go. Guys with really big hammers can fuse metal objects at relatively cold temperatures and explosion welding doesn’t involve any external heat, outside of what is generated by the extreme pressure of the bond.
There is a Catch-22 in forge welding- the higher the temperature, the less pressure required… but the higher the temperature, the more oxides that are formed that interfere with the weld, going too hot makes things harder for you. With no alloying this is not too much of a problem, since iron oxide does not interfere too badly. This is for the same reason that carbon steel rusts and will continue rusting after it starts to rust, it continues to be reactive. But things like Chrome and Nickel create an oxide that becomes non-reactive, that is how stain resistance works. But these more complicated oxides seriously interfere with the welding bond and must be defeated to get the weld to stick.
Years ago, there was a fad of makers using fluorspar in their welding flux to defeat nickel oxides. I gave it a try and hated it, the fluorspar would not go liquid at the temperatures that I welded at and made a pastey mess. When I asked one of the proponents of the fluorspar about it, he said you had to get it a lot hotter to use the fluorspar. When I told him the temperature range I welded in he said that it was too cool for fluorspar and that the nickel oxides would not be a problem in that range… I don’t think I need to tell you my next painfully obvious question. Sometimes bladesmiths create our own headaches. It has been years since I have heard of anybody using fluorspar, I think that is a good thing as it is indicative at how better we are with our temperatures these days.