According to Jerusalem Talmud Taanith Tract about fast and fast day, Rabbi Jose ben Halafta c. 150 AD (80 years after destruction of Jerusalem temple) said that course of Jehoiarib was in charge when destruction of the temple happened.
Whence do we know that the second Temple was also destroyed on the 9th of Abh? We have learned in a Boraitha: “A happy event is credited to the day on which another happy event happened, while a calamity is ascribed to the day when another calamity occurred; and it was said that when the first Temple was destroyed it was on the eve preceding the 9th of Abh, which was also the night at the close of the Sabbath and also the close of the Sabbatical year. The watch at the time was that of Jehoyoreb, and the Levites were chanting in their proper places, at that moment reciting the passage [Psalms, xciv. 23]: “And he will bring back upon them their own injustice, and in their own wickedness will he destroy them”; and they did not have time to end the passage, which concludes, “yea, he will destroy them–the Lord our God,” before the enemy entered and took possession of the Temple. This happened also at the destruction of the second Temple. (http://www.jewishvirtuallibrary.org/jsource/Talmud/taanit4.html)
First course of priests was Jehoiarib (1 Chronicles 24:7).
|First||Jehoiarib||1 Chronicles 24:7|
|Second||Jedaiah||1 Chronicles 24:7|
|Third||Harim||1 Chronicles 24:8|
|Fourth||Seorim||1 Chronicles 24:8|
|Fifth||Malchijah||1 Chronicles 24:9|
|Sixth||Mijamin||1 Chronicles 24:9|
|Seventh||Hakkoz||1 Chronicles 24:10|
|Eighth||Abia||1 Chronicles 24:10|
|Ninth||Jeshua||1 Chronicles 24:11|
|Tenth||Shecaniah||1 Chronicles 24:11|
|Eleventh||Eliashib||1 Chronicles 24:12|
|Twelfth||Jakim||1 Chronicles 24:12|
|Thirteenth||Huppah||1 Chronicles 24:13|
|Fourteenth||Jeshebeab||1 Chronicles 24:13|
|Fifteenth||Bilgah||1 Chronicles 24:14|
|Sixteenth||Immer||1 Chronicles 24:14|
|Seventeenth||Hezir||1 Chronicles 24:15|
|Eighteenth||Happizzez||1 Chronicles 24:15|
|Nineteenth||Pethahiah||1 Chronicles 24:16|
|Twentieth||Jehezkel||1 Chronicles 24:16|
|Twenty-first||Jachin||1 Chronicles 24:17|
|Twenty-second||Gamul||1 Chronicles 24:17|
|Twenty-third||Delaiah||1 Chronicles 24:18|
|Twenty-fourth||Maaziah||1 Chronicles 24:18|
Temple destruction happened in Sabbath, Ab 9, 3830 Hebrew Calendar, then course of Jehoiarib serve in a week of 9th-16th day of Ab.
Rosh Hashanah and Yom Kippur exists between first and eight courses of priests. In these fests, courses of priests served together. Hence, Abia was 8th course of priests which served on Tishri 15-21, 3831 by calculation:
8th week + 1 week = 9th week
9th week from Av 9-16 is Tishri 15-21, 3831.
This calculation is in line with Luke story of Gabriel visiting Zachariah.