This is the prequel to "You're Very Lucky, Leia" and "No Manner of Luck at All", both of which can be found here or on AO3. It explains how Vader became Emperor, how Leia was captured, and everything else! Happy New Year, Everyone!
Darth Vader entered the Throne Room as quietly as he could. He was the last of Emperor Palpatine's closest advisors to arrive, since he'd been halfway across the galaxy when the summons had come. As always, he knelt before the throne and his master. "Rise, Lord Vader," Palpatine rasped.
"Yes, my master," he replied.
"Now that Lord Vader is here, we can proceed," Palpatine said. "Come, my advisors. The time draws short."
Vader could feel how much power the Sith Master was expending to project the appearance of strength. The other advisors, both civilian and military, were not Force strong, but they had to know that Palpatine was putting up something of a front. Everyone in the room knew what this meeting was about. Palpatine had been diagnosed with Cardonian Dementia. It was fatal 95% of the time, and even the Jedi had never found a cure. The best anyone had managed to do was delay the mental degradation.
Palpatine took a deep breath. "I am counting on all of you in this room to ensure a smooth transition of power, my friends," he said. "I know that past Empires have crumbled after their founder was gone, and I do not wish for that to happen to our Empire. My will is clear, but I will tell all of you now- Lord Vader is my heir, and will be the next Emperor. I am sure he will continue the traditions that make the Empire the greatest in history. Lord Vader?"
"Thank you, my master," Vader said. "I am honored." He wasn't at all surprised, of course. Who else could rule a Sith Empire but a Sith?
"Excellency, what shall be done for…"
"Most of what I wish done is in my will," Palpatine interrupted Isard. "Lord Vader knows the rest." He took a deep breath, and Vader watched has he loosened his grip on the Dark Side, enough so that the other beings in the room could see how weak he was. "I am dying, my friends. I do not wish to send the Empire into a period of weakness as I waste away. That is why I called you all here today. You will bear witness that I asked this of Lord Vader. I want none of you to insinuate that anything other than my will led to today's events."
Everyone either agreed verbally, or bowed in acknowledgement. Vader could feel their confusion. He, of course, knew exactly what was happening. He just had a faint wish that this was happening in the traditional way, and that he had already secured his son to be his apprentice.
"And now, my friends, you will witness something few beings will ever see. Lord Vader and I have a history, and our Order has certain traditions that must be kept. Are you prepared, Lord Vader?"
Vader would have taken a deep breath if he could. "I am ready, my Master," he said as he drew his lightsaber.
Sidious smiled thinly. "One to hold power, and one to crave it, My Apprentice."
"One to hold power, and one to take it, My Master," Vader replied, almost ritually.
Sidious, the Sith Master, spread his arms. "I do not want to die wasting away as I am, Lord Vader. Spare me that."
Vader, the Sith Apprentice, bowed his head and lit his saber. "As you wish, my Master."
He lit his blade, saluted his Master one last time, and drove the red blade forward, piercing Palpatine's heart in one smooth movement. It was an almost instantaneous death.
He shut down his saber quickly and caught his Master's body. He bowed his head over it, carefully making sure that the Dark Side energies did not explode. After a moment, he looked up.
"The Emperor is dead," Sate Pestage said solemnly. "Long Live the Emperor."
The rest of the group went to their knees as Vader stood. "Our founder will be shown all due honors. His funeral will be held after a standard week of mourning. I will take up my position as Emperor after a month of mourning."
He turned to the Red Guards. "Call for a funeral detail," he ordered. "Full honors. Have all banners and flags at half staff for the next month." He turned to Grand Admiral Pitta. "Grand Admiral, have a press release prepared and released within an hour. State that Emperor Palpatine died after a long battle with Cardonian Dementia."
"Yes, your highness," he said. "He only had a few months before he started declining regardless, am I correct?"
Vader nodded. "He did," he said. "He contacted me last week and told me of his intentions. He knew that one of the symptoms of the disease was insanity, and he didn't want to bring that on his Empire."
Pitta bowed his head. "He was a great man, my l… your highness."
Vader stepped back as the funeral guard arrived. He didn't say anything as they worked. One, the medic, called time of death before folding the sheet over the Emperor's face. The military men stood at attention as Palpatine's body was taken away. The civilians bowed their heads or stood at attention as well.
Finally, Vader closed his eyes, though no one could see it. "We must prepare. Some would try to take advantage of Emperor Palaptine's death and cause chaos."
The Imperial council gathered around. There was much to do.
I am aware of the EU of how Palpatine planned to destroy the galaxy when he died, but in this universe, his dementia never got to progress, so he never came up with the idea. In fact, the difference in this universe is he was actually diagnosed. (you can't tell me that the idea that Luke would just join him wasn't the product of insanity...)