Why does not regex_match throw a error when my regex is invalid?

I wrote a code like this regex_match("ab","a**b") and it returns true. As we know, "a**b" is a invalid regex, isn't it?--At least it is invalid in https://regex101.com/ . I try to catch a exception but nothing happened. It just performed as "a**b" is a valid regex expression. Nothing happened too when I try to use regex_search. I wonder if I misuse this function or there is a bug in the regex library.