Open search results in new tab
You should install Custom Search module as it does provide an option to open results in new tab or lightbox. 

https://drupal.org/project/custom_search

Otherwise you can always look into using custom functions or js to achieve the same in your search template. 

Updated Answer

Since you are using solr and search-result.tpl.php you should have a line like: 

&lt;a href="&lt;?php print $url; ?&gt;"&gt;&lt;?php print $title; ?&gt;&lt;/a&gt;


change it by adding target value like: 

&lt;a href="&lt;?php print $url; ?&gt; target='_blank'&gt;&lt;?php print $title; ?&gt;&lt;/a&gt;