When do you and when don't you use a comma after an adverb that

[Francis]

introduces a sentence? Here are some sentences from very reputable material:

"Formerly, science was taught by the textbook."
"Hopefully I'll leave on the noon plane."
"Evidently there used to be a shopkeeper in Bristol who deliberately stuck ungrammatical signs in his windows as a ruse to draw people into the shop."
"Honestly, what an annoying bunch of people."

 

[Gary]

I don't believe there is a standard convention for this. One journalistic convention is to not put a comma if it's just one word, but to put a comma if the phrase is several words, like, "Before the end of the day, ...." However, that's not an adverb, but a prepositional phrase.