Using a menu outside of WordPress

I have some PHP pages that are outside of WordPress, but use WP authentication. I’d like to bring in the main nav menu to these pages, and if I insert the code:

<?php
wp_nav_menu( array( ‘menu’ => ‘mega-menu’ ) );
?>

the menu links get inserted as a hierarchical list, which is what menus are generally, but it’s not styled as a menu. What do I need to do to have it display as a menu like in the rest of the site? Thanks.