We consider a search task as a set of queries that serve the same user information need. Analyzing search tasks from user query streams plays an important role in building a set of modern tools to improve search engine performance. In this paper, we propose a probabilistic method for identifying and labeling search tasks based on the following intuitive observations: queries that are issued temporally close by users in many sequences of queries are likely to belong to the same search task, meanwhile, different users having the same information needs tend to submit topically coherent search queries. To capture the above intuitions, we directly model query temporal patterns using a special class of point processes called Hawkes processes, and combine topic models with Hawkes processes for simultaneously identifying and labeling search tasks. Essentially, Hawkes processes utilize their self-exciting properties to identify search tasks if influence exists among a sequence of queries for individual users, while the topic model exploits query co-occurrence across different users to discover the latent information needed for labeling search tasks. More importantly, there is mutual reinforcement between Hawkes processes and the topic model in the unified model that enhances the performance of both. We evaluate our method based on both synthetic data and real-world query log data. In addition, we also apply our model to query clustering and search task identification. By comparing with state-of-the-art methods, the results demonstrate that the improvement in our proposed approach is consistent and promising.