In Luke 23:44, the writer states that an eclipse of the sun took place at the time of Christ's crucifixion. Is there a basis of fact as to its occurrence? And, if so, was this solar eclipse coincidental and in accord with the laws of science?

I am not sure why you call it an “eclipse.” None of the Gospel writers use this term. Matthew, Mark and Luke use the Greek term σκότος (skotos), which means, simply, “darkness.”

As a general rule we should avoid applying certain meanings to texts that are more specific than the author intends. That there was darkness over the land from noon till three is certainly attested in the sacred text. But the cause of that darkness is unexplained. Perhaps God made use of natural causes, such as an eclipse or very heavy clouds to cause the darkness. But it is also possible that the darkness was of purely supernatural origin and was experienced only by some.

Hence, trying to explain the darkness simply in terms of “the laws of science” risks doing disservice to the text by missing its deeper meaning, namely, that the darkness of sin has reached its height. Whatever the mechanism of the darkness, its deepest cause is sin and evil.

Jesus had said elsewhere, “This is the judgment: Light has come into the world, but men loved darkness instead of light because their deeds were evil.” (Jn 3:19). He also said, referring to his passion; “Night is coming, when no one can work.” (Jn 9:4). And when Judas leaves the Last Supper to betray Jesus, John observes simply and profoundly, “And it was night.” (Jn 13:30). Yes, deep darkness had come upon the world.

You ask if there is a basis in fact that this darkness actually occurred. Though some modern scholars consider it a mere literary device, there seems little reason to doubt that it actually occurred. While some refer to a purported Letter of Pontius Pilate to Tiberius that verifies it, the historical value of the document is highly disputed. Yet, three of the gospels record it, and most of the Fathers of the Church treat the darkness as historical.

That said, how widely experienced, and how deep the dark, is not specified. We should balance accepting its historicity with an appreciation that the texts are restrained in terms of precise details.