I’m trying to find the name of a book (or maybe a short story?) where some humans encounter a spaceship that is essentially half a Dyson sphere with a hole in the center. The craft concentrates lasers at the corresponding point on the star and the solar flares generated pass through the hole and propel the spaceship, dragging the half Dyson sphere along with it. Other details include that the aliens who command it are hyperintelligent birds/dinosaurs who are fully aware of their subconscious mind, referring to it as their “hindbrain”.
Since nebogipfel suggests someone else should write up the answer, and nobody else has, I'll do it... (Especially since I have this as an e-book and don't have to type up quotes.)
This is Bowl of Heaven (2012) by Gregory Benford and Larry Niven.
The Earth ramscoop spaceship Sunseeker is on route to another star system where a planet, named "Glory" with a potentially habitable biosphere has been detected. Shortly before Sunseeker leaves, a gravity wave detector, LIGO 22, detects a source of mysteriously regular gravity waves coming from the same system. Decades into the 550-year-long mission, unexplained underperformance by the ship's drive becomes a crisis just as a strange artifact is detected.
The artifact is half a Dyson sphere:
Abduss added helpfully, "Infrared study shows that it is not a disk. It's rounded. We witness it from behind, with the plasma plume coming through a hole at the exact rear center. The cap radiates at the temperature of lukewarm water."
"A...sphere?" He saw it then, the image snapping into perspective. He was looking at a ball with a hole in its bottom. Through that hole, the star glowed. His imagination scrambled after an old idea. "Maybe it's a, what was the name—?"
"A Dyson sphere," Mayra provided. "We thought so at first, too."
"So this is a shell?"
She nodded. "A hemisphere, perhaps—a sphere halfway under construction. Perhaps. Only—the old texts reveal quite clearly that Dyson did not dream of a rigid sphere at all. Rather, he imagined a spherical zone filled with orbiting habitats, enough of them to capture all of the radiant energy of a star."
Abduss thumbed up a reference to these ideas on a side screen. Good—they had done the homework before awakening him. But if not a Dyson sphere, what—?
Mayra said, "We have watched and run the Doppler programs carefully. The hemispherical cap is spinning about the same axis formed by the plume."
Abduss said helpfully, "Only by rotating such a shell could one support it against the star's gravity."
The plasma driving the artifact is excited off the star:
They zoomed the optics in on the disk’s flares, having to go through several settings that blanked out the blue white hot spot on the star’s surface. The glare of the hot spot was fierce, actinic, bristling with angry storms, a tiny white sun attached to the bigger pink star like an angry leech.
Above the white spot raged the filigree spikes of streaming plasma. They whirled around one another like fighting snakes, burning as they rushed up from the hot spot. It looked like they should bathe the hemispheric bowl in licking flames. But before they reached the curve of the bowl, they dovetailed into a slender jet. Among the streamers, Cliff could see little blobs and bright flecks moving out from the star, swarming up along the jet, toward the neatly circular hole in the bowl and out into the sky.
It's reflected starlight, not lasers, that excite the star, however:
They cheered and all eyes were on the screens. Now they could see the inside of the bowl...and it was a vast sheeted plain brimming with light. They rose swiftly, peeling off from the jet to the side, plasma falling behind, vistas clearing. Again there curved away over the misty distance great longitude and latitude grids in sleek, silvered sections the size of worlds. The sections had boundaries, thin dark lines, demarking different curvatures of a greater mirror—and from that their eyes told them that these were all focused far away.
Silence. In a whisper Abduss said, "Mirrors...reflecting the sunlight back, inward, onto the star. That's what causes the hot spot."
The Astronomers (their own name) resemble birds to the Sunseeker's crew, who call them "Bird Folk."
They all turned and saw a big colorful creature walking out of the trees. Swaths of blue, yellow, and magenta seemed splashed over it in elaborate designs. A big narrow head, with a long nose between two large eyes, swiveled and watched with stately elegance. The native looked to be at least three meters tall and strode forward on legs that articulated gracefully, taking great long strides. Mouth like a stubby beak. Spindly long arms ending in complicated hands. It came forward quickly, carrying something tubular, and then three more like it appeared from the trees. They seemed to stroll, taking their time but covering ground quickly.
Beth stood absolutely still, but part of her realized that this would be the first remark at the sighting of intelligent aliens. She said quickly, "They're...beautiful."
"Birds," Cliff said. "Those colors—they're feathers."
"Smart birds?" Fred asked.
"Hey, crows are smart," Irma said. Then shrugged. "Somewhat."
Howard Blaire just gaped at the Bird Folk, his gloved hands flat against the glassy surface.
Finding a map of ancient Earth leads to speculation that the Bird Folk are descended from dinosaurs:
He said, "A lot of stars come in pairs. Maybe most of them."
"I think that sphere was a map of Earth. Earth before the continents split up."
Lau Pin asked, "Why would they build a globe of Earth?"
Lau Pin laughed. "Yeah, right." The others were grinning.
"Some dinosaurs got smart. They developed space travel. They did some exploring. They visited Sol's companion star. Anyone ever wonder how the dinosaurs stayed warm enough? Sol used to be cooler, remember."
Lau Pin was still grinning. "Come on."
"Companion star," Tananareve said. "They stole it?"
"It was theirs. Earth was theirs, too. Left the solar system as it was, but maybe they took the planets around Wickramasingh's Star. Grist for the mill."
The Bird Folk/Astronomers don't have an unconscious mind like humans do, rather they have an autonomic portion of their mind that is fully examinable, that they call the "Undermind."
But some fundamental features of advanced minds were beyond these Late Invaders. Higher intelligence needed not mere utilitarian modes, but rather the creative ones. The source of cross-association, and thus ideas, had to be accessible. The Undermind was common to all sentient creatures—yet these primates could not see theirs! Only a mind unified at the upper levels, above the shop floor of bodily business, could have deep ideas, surely? Then a mind could manipulate them, force them on the twin forges of reason and intuition, into great leaps.
These aliens had no such ability. Their greatest drives, intuitions, associations—all lay concealed from their foreminds, the running agents and authorities of the immediate, thinking persona. They were primitives.
Yet they had built a starship.
Memor was shocked. In a while, she got control of herself and pondered. Interrogated her Undermind. Found no lurking answers. Perhaps the Undermind needed a rest. Often, sleep brought ideas.