Battery Issue - Low level issue
The Apple logo lights up when the screen is on, so what's happening is that your screen isn't turning itself off. This usually happens when the power management extensions aren't loaded in the operating system, and issues with sleep are one of the biggest indicator of this. 

Have a look at this page : https://help.ubuntu.com/community/MacBookPro. It could be of help. The procedures should remain the same for Xubuntu as for Ubuntu, so don't worry about that.