I'm creating a D&D campaign which takes place on a Mercury-sized planet, orbiting a Proxima-Centauri style red dwarf. It is tidally locked.
I would like it to make physical sense as much as possible, and only use magic or hand-waving if there is absolutely no alternative.
I would also like the sun to appear to be absolutely massive in the sky. At least 10 degrees in angular diameter, 20 if possible. This would correspond to the orbital radius of the planet to be between 5 and 11 solar radii, which is insanely small (earth's orbit is approximately 230 solar radii for comparison).
The problem is, it appears to me that it's absolutely impossible for a star to have a habitable zone this close to it. If the star is cold enough that liquid water can exist that close to it, it will be too cold to radiate in the visible. This can be fudged with a high albedo, but the trade-off there is that you won't be able to see the sun if the albedo is high enough to be in its habitable zone.
The thing is, we always model stars as blackbodies, but what would it look like if a star had a very low emissivity? This way, it could be hot enough to radiate in the visible, but its habitable zone could be extremely close. Would there be a conceivable reason/mechanism for such a thing, and would it be physically possible?
(The other concern I've glossed over here is the Roche limit, but I'm happy to say that I did the math and it's not a problem. For a star with the mass and radius of Proxima Centauri, and a very dense planet orbiting it -- sufficiently dense to be very small but have Earthlike surface gravity -- the Roche limit is only 4 solar radii)
EDIT: Oh boy, I just realized a big problem I hadn't considered, and that's that at these distances, at the surface of the planet, the gravitational force towards the planet would be LESS than the gravitational force towards the sun. I'm going to have to do some soul-searching here.
EDIT 2: Wow, thanks for all the feedback! This has metastasized to the spreadsheet stage, where I'm calculating whatever I can for red dwarfs, brown dwarfs, red giants, even white dwarfs and neutron stars (both complete nonstarters).
Yet another problem I hadn't considered until today was the actual luminance, i.e., how visibly bright the sun would appear, as opposed to the total energy the sun would be heating the planet up with. Putting all of these factors together - gravitation, heat, and luminance, makes it pretty tricky to find a solution to all of these, if I want the planet to be 5 solar radii from the sun.
Orbiting close enough for to a red dwarf, you'd be pulled towards the sun with 2.5 Gs. It would be about as bright as the Sun, but it would be receiving 340 times as much energy total.
With a brown dwarf, it would only be 0.4 Gs pulling you towards the sun, which you could deal with, and even jump twice as high as you could here, but it would be a significant game mechanic I don't want. Furthermore, it's only 5% as bright as the Sun, but it would still be 75 times as hot.
A red giant like Aldebaran would be MUCH better with respect to gravity - it has almost no effect there. And it's also visibly as bright as the sun. But it's still 350 times as hot.
So there's not really an existing star on which this would make sense. I'll take some time playing with numbers to see if I can find a temperature, mass, and radius that does let me do what I want and decide if that makes sense. Otherwise, I'll probably just fudge it with an atmosphere that's VERY reflective in all frequencies except for the visible. Or just magic, that's always cool.
EDIT 3: In response to @pluckedkiwi's comment, I'll use one specific example, in which my planet is orbiting around a red dwarf. The planet has a radius of 2500 km, and a mass m of about 10^24 kg. The red dwarf has a mass M of 10^30 kg, and the planet is in a circular orbit with a semimajor axis a of 700,000 km.
My conjecture: Orbital mechanics don't matter very much close to the surface of the planet, as you can predict what will happen to within a degree of error by using a rotating coordinate system. On the surface of this planet, you appear to be in a Cartesian coordinate system with the sun directly overhead. Plugging the numbers above into Newton's laws, your acceleration towards the planet's surface is 10.67 m/s/s. Your upwards acceleration, towards the sun, is 136/m/s/s. So you'll be falling upwards at a rate of 126 m/s/s.
Once you get more than a few hundred kilometers up, that very small and dense planet will be far enough away that that coordinate system doesn't hold up very well, and you'll model your movement as a keplerian orbit around the sun. From that perspective you'll be in a similar, but perturbed, orbit as that of the planet. You still have basically the same amount of tangential velocity/angular momentum as you did before, so you won't fall into the sun, but the planet's surface won't be pulling you downwards sufficiently to keep you on it. So the real way to look at it is you and the planet are in your own orbits around the sun. You're both falling into it at the same speed, but you won't feel much of an attraction to the planet at all. I think?
This is in contrast to where we are now, at 1 AU from the sun. The difference is much greater here, where the sun pulls us towards it with an acceleration of about 6 millimeters per second squared. If we were just two solar radii from it like in the scenario I describe here, that acceleration would be closer to 70 m/s/s. Our intuition breaks down because we're so much closer to the sun. It just looks like there isn't really a possible way to be this close to any sun relative to its radius, without your mechanics just completely breaking down on the planet's surface, unless the sun is very, very not dense, as in the case of a red giant.
Of course there's a lot of speculation in this and it's entirely possible I haven't thought it through enough.