Integrate Radioactivity with Apache Solr (sort by popularity)
You should be able to do this without modifying schema.xml. At a minimum, you'll need to implement hook_apachesolr_update_index(), and you may also need to implement hook_apachesolr_modify_query() to add the Radioactivity data to each query.

Good examples for this can be found in the apachesolr_search.module file itself (and the apachesolr_date module that comes bundled with apachesolr), and also in the additional contrib modules apachesolr OG and apachesolr attachments.

The apachesolr_date module in particular has some code related to adding an available sort option.