Big spoilers for this calc. So what is the final solution to the Three-Body Problem? Destroying one of the bodies. This is exactly what happens when the Gravity and Blue Space sends out the location of the Trisolaris (and the Solar System) to the Universe, and Trisolaris is destroyed by one of the hunters of the Dark Forest. The process of destroying Trisolaris; a photoid strikes on of the three suns it orbits, and the collision spews up part of the core, covering the 0.6 AU to the orbit Trisolaris in 4 hours.
One night, the telephone roused Cheng Xin from her slumber. She saw that the caller was Fraisse. It was 1:14 A.M. in China, and 3:14 in Australia. Fraisse knew that Cheng Xin suffered from severe insomnia, and without a sleep-aid machine, she could only manage two to three hours of rest a night. Unless it was an emergency, he would never be disturbing her at a time like this.
He sounded anxious. “Child, go out and look up in the sky.”
Cheng Xin could already tell something unusual was happening. In her uneasy sleep, she had been gripped by a nightmare. The dream was a familiar one: A gigantic tomb stood in the middle of a plain covered by the darkness of night. A bluish glow spilled from within the tomb and illuminated the ground nearby....
Just that kind of blue light could be seen outside.
She went onto the balcony and saw a blue star in the sky, brighter than all the other stars. Its fixed position distinguished it from the man-made structures orbiting in near-Earth orbit. It was a star outside the Solar System. Its brightness was still intensifying, and even overpowered the lights of the city around her, casting shadows against the ground. About two minutes later, the brightness reached a peak and was brighter even than a full moon. It was no longer possible to look at it directly, and the color of the light shifted to a harsh white, illuminating the city as though it were daytime.
Cheng Xin recognized the star. For almost three centuries, humans had looked at it more than at any other spot in the heavens.
Someone screamed in the leaf-building nearby, and there was the sound of something crashing to the floor.
The star now began to fade. From white it gradually dimmed to red, and about half an hour later, it went out.
Cheng Xin hadn’t brought the phone with her, but the floating communication window had followed her. She could still hear Fraisse’s voice, which had recovered its usual serenity and transcendence. “Child, don’t be afraid. What will happen, will happen.”
A lovely dream had ended: Dark forest theory had received its final confirmation with the annihilation of Trisolaris.
At the time of the catastrophe, Trisolaris was in a stable era, orbiting around one of the three stars in the system at a distance of about 0.6 AU. The photoid struck the star and tore a hole through the photosphere and the convection zone. The hole was about fifty thousand kilometers in diameter, wide enough for four Earths laid side by side. Whether as a result of a deliberate choice by the attacker or coincidence, the photoid struck the star at a point along the line where the star intersected Trisolaris’s ecliptic plane. Viewed from the surface of Trisolaris, an extremely bright spot appeared on the surface of the sun. Like a furnace with its door open, the powerful radiation generated by the core of the sun shot through the hole; passed through the convection zone, the photosphere, and the chromosphere; and struck the planet directly. All life outdoors on the hemisphere exposed to the radiation was burnt to a crisp within a few seconds.
Next, material from the core of the sun erupted from the hole, forming a fifty-thousand-kilometer-thick fiery plume. The spewed material was tens of millions of degrees in temperature, and while some of the material fell back onto the surface of the sun under the influence of gravity, the
remainder reached escape velocity and shot into space. Viewed from Trisolaris, a brilliant tree of fire grew from the surface of the sun. About four hours later, the ejected solar material reached 0.6 AU from the surface of the sun, and the tip of the flaming tree intersected the orbit of Trisolaris. After another two hours, the orbiting planet reached the tip of the fire tree and continued to pass through the ejected solar material for about thirty minutes. During this time, the planet might as well be moving through the interior of the sun—even after the journey through space, the spewed material was still at a blazing temperature of tens of thousands of degrees. By the time Trisolaris emerged from the fire tree, it glowed with a dim red light. The entire surface had liquefied, and an ocean of lava covered the planet. Behind the planet was a long white trail through space—steam from the boiled-off ocean. The solar wind stretched the trail out, making the planet appear as a long-tailed comet.
All signs of life on Trisolaris had been cleansed away, but only the fuse of the catastrophe had been lit.
Trisolaris falls into the sun, and shortly after that, due to there being less mass and slower fusion in the stars core, the star collapses and explodes.
The ejected solar material caused drag against the planet. After passing through the material, Trisolaris slowed down, and its orbit fell lower toward the star. The fire tree acted like a claw extended from the sun, pulling Trisolaris down with each revolution. After about ten more revolutions, Trisolaris would fall into the sun itself, and the cosmic football game played between three suns would come to its end. But this sun wouldn’t survive long enough to see itself emerge as the victor.
The solar eruption also lowered the pressure inside the sun, temporarily slowing down the fusion within the core. The sun dimmed rapidly until it was but a hazy outline. The giant fiery tree growing from the surface, in contrast, appeared even more striking, more brilliant, like a sharp scratch made against the inky black film of the universe. The diminished fusion meant that the core radiation no longer exerted sufficient pressure against the weight of the solar shell, and the sun began to collapse. The dim shell fell into the core, triggering a final explosion.
This was the sight witnessed by humankind three days ago on Earth.
Trisolaris is located in the Alpha Centauri star system, which is 4.367 lightyears away from the Earth (or 4.1315e+16m). Thus, using luminousity, we can determine just how much energy the collapse and ensuring explosion of the star is. Given it's described as lighting up the Earth like daytime and it's too bright to look at, I believe it's fair enough to use the luminousity of the Sun. The conversion factor from lux to apparent magnitude is -2.5 log I - 14.2.
L = -2.5 log I - 14.2
= -2.5 log 100,000 - 14.2
= -26.7
-26.7 = -26.73 - 2.5log((L/3.846*10^26)(146000000000/(4.1315e+16))^2)
Once again, going through this step by step...
(146000000000/(4.1315e+16))^2) = 1.24879226e-11
-26.7 - -26.73 = 1.24879226e-11/((L/3.846*10^26)
0.03 = -2.5Log(1.24879226e-11/((L/3.846*10^26))
0.03/-2.5 = (1.24879226e-11/((L/3.846*10^26))
10^(-0.012) = (1.24879226e-11/((L/3.846*10^26))
0.972747224 = (1.24879226e-11/((L/3.846*10^26))
0.972747224 X (3.864*10e26) = 1.24879226e-11
3.75869527e27/1.24879226e-11 = 3.00986432e38 joules
This isn't the end of it though; the energy is in watts (joules per second), so for our total yield, we'll multiply the above by the time frame. The brightness lasts around half an hour.
T = 60 X 30
= 1800s
E = 3.00986432e38 X 1800
= 5.41775578e41 joules
= 129.4874708413002044 tenatons
Very similar to the GBE of an Earth-sized star, which this star was.
Final Results
Trisolaris' sun explodes = 129.487 tenatons