What replaced the Temple as the center of Judaism following the destruction of the Second Temple?

Answer 1

Nothing. The center of Judaism is and always has been the Torah and our relationship to God, including our beliefs and all of the Torah's commands. The Temple was very important but was not THE most important thing.

We keep whichever of the Torah's commands that circumstances enable us to do. Without the Temple, we do not now offer sacrifices, but we learn their laws along with the rest of the Torah and we mourn the Temple's destruction. It is no less important than it was.

Note that the Question seems, at least partially, to be based upon a common misconception. Jews always worshiped in synagogues, even when the Holy Temple stood. Even within the Temple premises, there were several synagogues. During the Second Temple era, ancient Greek authors attest to the large synagogues that stood in all the countries where Jews lived. The Dioploston in Alexandria, for example, was famous for its size (Talmud, Tosefta Sukkah 4:6). In First Temple times also, synagogues served the same function (of daily prayer and study) that they do today (Talmud, Megillah 26b and Berakhot 31a).

The following changes took place after the Destruction:

1) After the Destruction, sacrifices would not be possible. Prayer (which had always existed) would now be the sole offering to God, alongside the Torah-study and performance of mitzvot (Torah-commands), which had also always existed.

2) In addition, there are a number of commands (relating to the sacrifices, the Temple, and the Kohanim) that we would be unable to perform.

3) Also, the Sages took several steps after the Destruction: they recorded the Temple-procedures in Talmud tractates such as Yoma, Midot, Shekalim and Tamid, and they enacted observances to remember the Temple (Talmud, Sukkah 41a) and mourn its destruction (Talmud, Sotah 49a).

4) The Jewish population was dispersing gradually more and more, so the sages soon permitted the writing of the entire Oral Tradition so it wouldn't be forgotten.

5) Certain changes were made in the daily prayers. Instead of praying that God accept the sacrifices, the prayers now asked for the rebuilding of the Temple.

Answer 2

Nothing. The center of Judaism is and always has been the Torah and our relationship to God, including our beliefs and all of the Torah's commands. The Temple was very important but was not THE most important thing. Public prayer had existed before the Temple was built and continued after its destruction.

See also the Related Links.

Link: Did Judaism change from priest-led to rabbi-led?

Link: Destruction and diaspora

Link: Jewish history timeline