How to detect whether a browser supports window.close?

I'm building an app, where the auth flow goes as follows

• user clicks login button
• a login window opens, and the user logs in,
• the popup window uses postMessage to send the auth token to the main page, verifying the origin
• the main page closes th window after receiving the token.

This flow works great on desktop devices, but not in mobile browsers, where window.open opens a new tab that can't be programmatically closed.

On mobile devices, I can send the user to the login screen, and send them back with the auth token in the hash, but I only want to do that when I have to. How do I detect whether window.close works without browser sniffing?