SharePoint: Share Search Service application across farms

Scenario: Publish SharePoint Search application from SP 2013 farm and consume it in SP 2010 farm. Both the farms are in the same domain. SP 2010 farm consists of a web application whose content will be crawled by SP 2013. However, the search results can be accessed from both the farms. 

There are already plenty of resources which show how service applications can be shared across farms. I won't repeat the steps. You can read about the steps involved by following this link by Issa Ayyash:  
Cross farm Service Applications Integration between two separate SharePoint farms.
Here, we will look into how to set up the Enterprise Search Center site and perform the search.
Suppose we have a web application in SP 2010. Enter some data into it. The example below shows some items in the task list.
Now create Enterprise Search center site ( a sub site )under the web application in SP 2010. Make sure that SharePoint Server Publishing Infrastructure feature is activated otherwise you may get error while creating an Enterprise Search Center site.
Go to SP 2013 farm and click on the Search service application in central admin site. Create a content Source and enter the address of the web application present in Sp 2010 farm.
At this time if you perform a full crawl you may get following error:
Access is denied. Verify that either the Default Content Access Account has access to this repository, or add a crawl rule to crawl this repository. If the repository being crawled is a SharePoint repository, verify that the account you are using has “Full Read” permissions on the SharePoint Web Application being crawled.
This is because we have not given "Read Access" to Default content access account.
Go to SP 2010 farm and open CA->Application Management->Manage Web Applications.
Select the web application and click on "User Policy" in the ribbon. Give Full Read permissions to the account.

Go to SP 2013 farm, select the search service and perform the full crawl. Once the crawl is completed, open the SP 2010 web application and browse to Enterprise search center site inside it. Perform the search and you should be able to see the results as shown:
In a similar way search results can be seen inside the web applications present in SP 2013.
profile for Nadeem Yousuf at SharePoint Stack Exchange, Q&A for SharePoint enthusiasts

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