The geothermal gradient told us the mantle is hot, over $1,300^\circ\text{C}$ at 100 km. Yet the mantle is almost entirely solid: the S waves that cross it prove that. So magma must form only in special places, where something tips solid rock past its melting point. Plate boundaries are exactly those places.
Why it works
A rock melts when its temperature rises above its melting point (the solidus). There are three ways to get there, and only one involves adding heat. Pressure squeezes atoms together and makes melting harder, so the melting point of mantle rock rises steeply with depth. Water breaks bonds in the rock's minerals and lowers the melting point by hundreds of degrees.
- Decompression melting (mid-ocean ridges, hot spots, rifts): hot mantle rises and keeps nearly all its heat, but the pressure drops, so its melting point falls below its temperature.
- Flux melting (subduction zones): the sinking plate releases water into the hot mantle above it, lowering that rock's melting point.
- Heat transfer: hot basalt magma rising into the crust can melt the crust around it, which melts at lower temperatures than the mantle.
Key idea
Most magma forms without extra heat: rising rock melts because the pressure drops, and wet rock melts because water lowers the melting point. Hot magma can also melt the crust it rises into.
Worked examples
Worked example: Where rising mantle starts to melt
Under a ridge, rising rock at depth $z$ km is about $T = 1,350 + 0.4z$ °C, and its melting point is about $T_m = 1,120 + 4z$ °C. At what depth does it start to melt?
- Set them equal: $1,350 + 0.4z = 1,120 + 4z$.
- $230 = 3.6z$, so $z \approx 64\,\text{km}$.
- Above 64 km, the rock is hotter than its melting point and a few percent of it melts. That melt rises and builds new ocean crust.
Answer: About $64\,\text{km}$.
Worked example: Wet or dry?
At 100 km, mantle rock is at $1,100^\circ\text{C}$. Dry rock there melts at about $1,300^\circ\text{C}$; with water, about $850^\circ\text{C}$. What happens above a sinking slab?
- Dry: $1,100 < 1,300$, so the rock stays solid.
- With water from the slab: $1,100 > 850$, so it partly melts.
- That is how the Andes and the Cascades get their magma.
Answer: It melts only where the slab supplies water.
Common mistake
It is natural to think magma forms by heating rock up. Under ridges and hot spots, though, rock melts as it rises and the pressure drops; at subduction zones, it melts because water is added. Check yourself: under a mid-ocean ridge nothing is heating the mantle, yet it produces about 20 cubic kilometers of new crust every year.