The gravitational wave models for binary compact objects

The gravitational wave detection GW150914 has been realized by LIGO. The theoretical model played an important role in the data analysis. The model not only extracts the signal enveloped in the detector noise, but also recognizes that the source is a binary-black-hole merger. Besides the ground-based detectors like LIGO, pulsar timing arrays and space-based detectors detect gravitational wave in different frequency band. Soon the FAST telescope will partly serve for pulsar timing arrays in the coming year. In the near future, SKA project will strongly enhance the gravitational wave detection with pulsar timing array. Regarding to the space-based detectors, eLISA project is going on in Europe. And the LISA pathfinder works quite well which implies that most instrument techniques for eLISA are ready. Besides eLISA, there are two more plans for space-based detectors in China including Taiji and Tianqin. Among all of these gravitational wave detection projects, theoretical models are very important for signal extraction and parameters inversion. Along the development of the gravitational wave astronomy, the theoretical model research becomes more and more important and urgent. Binary compact objects are among the most important and the most realistic gravitational wave sources for all the above mentioned gravitational wave detection projects. We briefly describe the research status of theoretical models for binary compact objects in this paper. Post Newtonian method, perturbation theory of black hole and numerical relativity are all introduced. Typically these three methods are applied to the inspiral, ringdown and merger stage respectively. And more we also introduced effective one body method which combines the results of all these three methods and constructs a full model for the whole inspiral-merger-ringdown (IMR) process. This model is called effective one body numerical relativity (EOBNR) model which is essential in the data analysis of GW150914.