A very very good document regarding this topic is Troubleshooting Guide for Java from (originally) Sun. See the chapter "Troubleshooting System Crashes" for information about hs_err_pid* Files.
See Appendix C - Fatal Error Log
Per the guide, by default the file will be created in the working directory of the process if possible, or in the system temporary directory otherwise. A specific location can be chosen by passing in the -XX:ErrorFile product flag. It says:
If the -XX:ErrorFile= file flag is not specified, the system attempts to create the file in the working directory of the process. In the event that the file cannot be created in the working directory (insufficient space, permission problem, or other issue), the file is created in the temporary directory for the operating system.