Can I delete the .migratedaplibrary file after migrated my photos to Photos to save disk space?

You can delete it but it may be a good idea to wait awhile just in case you find a need to go back to Aperture. It doesn't actually take up as much space as it appears to due to a bit of "magic" described in http://sixcolors.com/post/2015/02/the-hard-link-between-photos-and-iphoto/

I moved mine to an external drive as I wasn't sure my cloud backup service would correctly handle that and I didn't want both going to that service.

I have migrated my photos from Aperture to Photos and I noticed that I now have two photo library files (each over 250GB). One is xxxx.migratedaplibrary and the other one is xxxx.photoslibrary. The migratedaplibrary file has last modified date on April 9, which is the day I converted to Photos. So I guess it is a duplication and back up of my old Aperture file? Just want to double check with this community before I hit the no return delete key to claim back some space. Thank you!

Don't burn your bridges too soon. The xxxx.migratedaplibrary is your original Aperture library and will work with Aperture. The new " xxxx.photoslibrary" cannot be opened in Aperture. as Foxfifh pointed to, both libraries are sharing the media files, so the second library would not free much space, if you deleted it. Photos is very different from Aperture, and you may want to use Aperture again for things, that are not supported in Photos, for example:

For me, these features are missing:

• Batch changing titles, captions, dates.
• Batch copy of adjustments,
• Adjustment presets and Metadata presets.
• Support to add locations to photos.
• Metadata display below the thumbnails.
• More smart rules for the smart albums.
• Keyphotos for smart albums
• Merging Photos libraries and exporting partial photos libraries.
• More sort options for albums and moments.
• Maps for photos in albums and larger maps. Most of my travels I cannot show on a map, because the moment maps are limited to one state. I can neither show my drive along the Trans Canada Highway on one map, nor the trip to Antarctica with all stops on the way.
• For more versatile editing, brushed adjustments would be necessary - to be able to blur the background for example to add depth of field or touching up the colours of selected objects.
• Support for an external editor.

You may want to prepare new photos in Aperture before adding them to Photos, e.g.. add location data or batch change titles.

And on no account delete the xxxx.migratedaplibrary without making a backup. There may be hidden migration errors, that you only notice later, and you may need to repeat the migration. For example, with my Aperture library all dates and time have been migrated with an incorrect time zone and all photos are sorted incorrectly, so I'll have to wait for a bug fix, before I can try to migrate again.

I deleted the old aperture mediathek and I got 100GB space ... so I think its needs to delet it ...

I deleted the old aperture mediathek and I got 100GB space ... so I think its needs to delet it ...

It will depend on how you migrated the Aperture library and if you are syncing with iCloud afterwards or editing the photos. When you edit photos in Photos the previews will no longer be shared between the libraries, and when you use iCloud Photo Library and the originals are downloaded from iCloud again they will no longer bestirred with Aperture. As you keep using Photos, less and less files will be shared with Aperture and then deleting the Aperture library will free space.