In "A New Hope", when the Falcon arrives at the ruins of Alderaan, they encounter a TIE fighter. Someone remarks that such a small ship wouldn't be out that far by itself. However, in "The Empire Strikes Back" we see that Luke's X-Wing, arguably a comparable craft as they served the same purpose, was able to travel to Dagobah on its own. What was it that the characters meant about the TIE fighter, and what made it too small to be out as far as it was?
Your comparison to an X-Wing is not actually a great comparison. That’s like comparing a Citroën Méhari to a Hummer H1. They’re both utility vehicles, and they have a handful of other similarities, but they are drastically different vehicles. Similarly, the Incom T-65B X-Wing and the Sienar Fleet Systems TIE/ln are both general-purpose star-fighters, but they are still drastically different.
The key differences that are relevant for this question¹ are that:
- The TIE/ln has no hyperdrive, while the T-65B X-Wing has a class 1 hyperdrive (which meant that even in hyperspace, it was actually faster than most capital ships).
- The TIE/ln only has sufficient room for two days of provisions, while the T-65B X-Wing has sufficient room for a full week of provisions.
Taken all together, this means that the absolute furthest that a TIE/ln fighter could be from it’s operational base unless it’s traveling to a different base that can resupply it is one day of sub-light travel. With a stated maximum acceleration of 4100G, no stated max speed outside of atmosphere, and ignoring relativistic effects, that translates to a distance of roughly 37.53 terameters (billion kilometers). This is roughly 1.5 times the distance from Earth to Voyager 1, still nowhere near far enough to get to another star system in a vast majority of cases (despite how obscenely fast it would be going).
That assumes though that all the TIE/ln pilot does is accelerate in a straight line for half a day, decelerate to a stop for half a day, turn around, and do the exact same thing again. Of course, that’s unrealistic for actual operations, with the likely combat effective range (how far it could be away from base and still be useful in a dogfight under the assumption it would have to return to base eventually) probably being at most around 1/3 of that, or maybe 1/2 at best (there is no canonical data I can find about this or any of the things I would need to infer this, it’s just a rough guess based on my limited knowledge of real-life fighter aircraft).
What that means is that from a practical perspective, if you see a TIE/ln fighter patrolling or scouting (which is what was seen in Episode IV), it’s a near certainty that there is either an Imperial military base or a large Imperial capital ship in the same star system as you.
1: For those who are interested, the other major differences are that the TIE/ln lacks shields, that it has only rudimentary life support (that’s why the pilots always wear those bulky full-body suits), and that it costs roughly 2/5 what a T-65B X-Wing does. The cost difference is why the Empire had them designed, the intent was to mass produce them and then rely on quantity of pilots instead of quality.
The film's official novelisation gives us a little more insight. Han sees the TIE and guesses (rightly) that this is the short-range version, one known to not have a hyperdrive. Kenobi then scans the ship and confirms this.
Chewbacca suddenly gave an angry bark. A huge flower of destruction blossomed outside the port, battering the freighter violently. A tiny, double-winged ball raced past the cockpit port.
“It followed us!” Luke shouted.
“From Tatooine? It couldn’t have,” objected a disbelieving Solo. “Not in hyperspace.”
Kenobi was studying the configuration the tracking screen displayed. “You’re quite right, Han. It’s the short-range TIE fighter.”
Star Wars: A New Hope by George Lucas