Objection 1. It would seem that children born out of true marriage are legitimate. For he that is born according to law is called a legitimate son. Now everyone is born according to law, at least the law of nature, which has more force than any other. Therefore every child is to be called legitimate.
Objection 2. Further, it is the common saying that a legitimate child is one born of a legitimate marriage, or of a marriage that is deemed legitimate in the eyes of the Church. Now it happens sometimes that a marriage is deemed legitimate in the eyes of the Church, whereas there is some impediment affecting its validity; which impediment may be known to the parties who marry in the presence of the Church: or they may marry in secret and be ignorant of the impediment, in which case their marriage would seem legitimate in the eyes of the Church, for the very reason that it is not prevented by the Church. Therefore children born out of true marriage are not illegitimate.
On the contrary, Illegitimate is that which is against the law. Now those who are born out of wedlock are born contrary to the law. Therefore they are illegitimate.
I answer that, Children are of four conditions. Some are natural and legitimate, for instance those who are born of a true and lawful marriage; some are natural and illegitimate, as those who are born of fornication; some are legitimate and not natural, as adopted children; some are neither legitimate nor natural; such are those born of adultery or incest, for these are born not only against the positive law, but against the express natural law. Hence we must grant that some children are illegitimate.
Reply to Objection 1. Although those who are born of an unlawful intercourse are born according to the nature common to man and all animals, they are born contrary to the law of nature which is proper to man: since fornication, adultery, and the like are contrary to the law of nature. Hence the like are not legitimate by any law.
Reply to Objection 2. Ignorance, unless it be affected, excuses unlawful intercourse from sin. Wherefore those who contract together in good faith in the presence of the Church, although there be an impediment, of which however they are ignorant, sin not, nor are their children illegitimate. If, however, they know of the impediment, although the Church upholds their marriage because she knows not of the impediment, they are not excused from sin, nor do their children avoid being illegitimate. Neither are they excused if they know not of the impediment and marry secretly, because such ignorance would appear to be affected.
Source: Summa Theologica (New Advent)