As stated in the title, this Splunk search query will return a list of all successful logons by user name on linux hosts. The regex is provided in the event the field is not extracted:
sourcetype=linux_secure |rex "\w{3}\s\d{1,2}\s\d{2}:\d{2}:\d{2}\s\S+\s(?<session>gdm-\w+)\S:\s"| search session=gdm-password | rex "\w{3}\s\d{1,2}\s\d{2}:\d{2}:\d{2}\s(?<hostname>\S+)\s.+\Sgdm-password:auth\S:\s(?<authstatus>\w+\s\w+);\s.+user=(?<username>\S+)" | search authstatus="authentication success" | stats count by username