Why was the Empire so obsessed with hunting down the Millennium Falcon in “The Empire Strikes Back?”

Question

I was thinking about one of the major plot points in “The Empire Strikes Back” (1980) which was tracking down the Rebels and capturing Luke Skywalker.

So when the Imperial fleet attacks the Rebels on Hoth, Rebel ships of all kind are flying all over the place with the intention of regrouping later once they are safe.

Knowing this, then what was the in universe rationale for Darth Vader’s fleet focusing on the Millennium Falcon? Why would he assume that the Millennium Falcon would contain Luke Skywalker or friends that could help lead them to Luke Skywalker?

Of course for out of universe reasons, the Millennium Falcon is iconic and the ship that typically has contained the heroes of the saga. And one can assume that Darth Vader members the Millennium Falcon from the actions on Death Star. But still… It seems a bit too OCD.

Looking for an answer with clear references; canon or “Legends” please. No armchair speculation please.

Answer 1

Vader thinks that Luke is on it.

“Asteroids don’t concern me, Admiral,” Vader said as he slowly clenched his fist. “I want that ship, not excuses. How long until you will have Skywalker and the others in the Millennium Falcon?”

_{^{Star Wars: The Empire Strikes Back - Official Novelisation}}

He assumes (erroneously) that Luke would be with his friends during the evacuation.

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There's also the fact that Solo and the Falcon were instrumental (along with Luke) in destroying the Emperor's shiny new toy, although it's made clear later in the film that Vader mostly cares about Solo and Leia as a route to Luke.

Without turning his head, Vader snarled through his mask, “The Millennium Falcon?”
Piett paused a moment before replying. He would have preferred to avoid that issue. “Our tracking scanners are on it now,” he responded a bit fearfully. Vader turned to face the admiral, his towering figure looming over the frightened officer. Piett felt a chill course through his veins, and when the Dark Lord spoke again his voice conveyed an image of the dreadful fate that would be inflicted if his commands were not executed.
“I want that ship,” he hissed.

_{^{Star Wars: The Empire Strikes Back - Official Novelisation}}

Answer 2

At no point in the movie does Vader tell the Imperial officers that he believes Luke is on board the Falcon. I've not read the novel, but I do think we must only be concerned with the actual movie.

In the movies, it is made very clear that Vader can sense Luke's presence when Luke is nearby. In Star Wars he can sense the presence of Luke during the attack on the Death Star ("The Force is strong with this one", he says, in the combat above the Death Star).

And in Return of the Jedi, Vader detects Luke's presence on board the stolen Imperial Shuttle Tyderium, during the approach to the Moon of Endor.

So it is simply not possible to include a scene in TESB in which Vader can express uncertainty as to whether Luke is aboard the Falcon. That would have undermined a key part of the powers Vader has from the Force, upon which the events of Return of the Jedi will depend.

In the movie TESB, Vader's motive is very clear: he wants to capture Han and the Princess, because by torturing them he can send a message to Luke, via the Force, which will draw Luke to him. He knows they are Luke's friends. He knows Luke will sense their pain through the Force.

There is actually a scene, in Cloud City, of Han being tortured. Han is baffled as to why this is happening, because they ask him no questions. But we, the audience, seen Luke's reaction, far away on Dagobah, when he feels the danger which Han and Leia are in.

Vader is solely interested in the occupants of the Falcon because they are Luke's friends, and can be used to draw Luke into a trap. And in one scene, we see Vader obtaining the Emperor's permission to try to turn Luke or to kill him, so we know that the Emperor considers Luke a significant threat, one that must be neutralised.

Later, we learn too that Vader had also a hidden motive for desiring to find Luke, as he has come to realise that Luke is his son.