Cook pasta in a 6- to 8-quart pot of boiling salted water until al dente. Reserve 1/4 cup cooking water, then drain pasta in a colander.

While pasta is cooking, pat scallops dry and season with salt and pepper. Heat 3 tablespoons butter in a 12-inch nonstick skillet over moderately high heat until foam subsides, then sauté half of scallops, stirring, until golden, about 3 minutes. Transfer with a slotted spoon to a bowl. Cook remaining scallops in remaining 3 tablespoons butter in same manner. Return first batch of scallops to skillet and stir in lime juice and tarragon.

Toss pasta in a bowl with half of scallops and 1/4 cup pasta cooking water. Top pasta with remaining scallops and sauce and season with salt and pepper.