Will our Sun be blue for about a million years, if a solar mass black hole passed though the core of our Sun, at high speed and kept going.?

High speed ??

I think some stars in this galaxy orbit it with a velocity relative to our sun of up to 300 km / second.

These are stars from "small" galaxies that have been absorbed by the Milky Way galaxy.

If such a star turned into a black hole --- and then proceeded on a collision course with our sun, then there would be a finite time for the collision.

Diameter of sun = 1,400,000 km

Time for black hole to pass through

1,400,000 / 300 = 4,666 seconds ( 1 hour 20 minutes)

I suspect very little would be left of the sun -- and what there was would be scattered into some form of accretion disc that would be left behind.

Not exactly left behind -- I suspect it would have a net velocity relative to the planets. -- due to the gravitational interaction of the black hole. And some - at least - of the accretion disc would stay gravitationally bound to the black hole.

I'd be surprised if more than 20% of the sun stayed in the vicinity of where it is now. - But it would require time to coalesce back into a star.

Suffice to say that the planets would not survive the passage.

It would take more than a day to pass through the solar system - at least one planet would be absorbed into the black hole - depending on the trajectory. All of them will have their orbits changed to a huge degree, and possibly half ejected from what is left of the solar system.

Collision with a black hole is an "end of the world" scenario

Complete with fire and brimstone I'm afraid.

So a solar mass black hole would be what? About 3-5 miles across? If it was zipping through in seconds I don't know how bothered by that the sun itself would be as there's only a limited amount of material it can consume in that brief encounter... a few percent maybe. To be honest I don't know enough astrophysics to answer your question properly. My thinking here is that the sudden drop in core mass will lead to a fall in outward core pressure. The mass of the rest of the sun will then push down hard on the reduced core and ignite a much harder fusion burn in response. That would only be until the sun finds it's new slightly cooler burning equilibrium. Would that last a million years though? That I'll have to take your word on.

If it does burn blue for a time afterwards then that's not good news for us... but then I doubt that will be of much concern. If the lethal shower of x-ray and gamma radiation during the event didn't end life on Earth, then the massive orbital perturbation of the planets and the black hole's tidal influence causing terrible earthquakes probably would. A close encounter with a black hole, or indeed any high mass star is not high on the solar system's recommended list.

Edit: I'm going with Paula's answer. That sounds much more authoritative!

Through the core is the specification but a Black Hole of a mass to not drag the Sun apart on approach would be extremely small - very small = small absorption.

So you need to specify the size and relative speed.

I suspect our Sun was blue during compaction, before main sequence, for about one million years, and would cool to yellow for about a million years following the black hole induced blue stage, then settle to white (yellow or orange if it lost lots of mass: that would make Venus more hospitable) until a delayed red giant stage. Blue means more gamma, xray, and ultraviolet than visible and infra red light = hostile to life as we know it.

Black holes do not just dart around the solar system randomly.

High speed ?

I think it would just be *gone*.