I created a custom spatial reference at spatialreference.org ( http://spatialreference.org/ref/sr-org/8391/ ) and defined it in PostGIS using the INSERT statement generated by this site. I created my tables with geometry type using this custom SRID ( st_setsrid(geom,98391) ). These tables works fine when accessed through QGIS, but when I try to load at ArcMap with a Database Connection, I receive the message "Could not add the specified object to the map. The coordinate system identifier is invalid". Ok, I invented this identifier. But, how can I tell this to ArcGIS?
I tried this connection using different ArcGIS versions (10.2, 10.4) and database instances. The message is the same. So, it´s an old issue.
P.S.: I don´t have a geodatabase configured, and don´t want it.
You might be experiencing an issue similar as to what was described here: Add Data Query with Custom SRID. You might want to reach out to Melita who would likely be able to either answer your question or point you in the right direction to someone who can. I hope this is helpful!
We have no idea how to interpret 98391. The WKID gets used more on the DBMS side. For instance, if you had shapefiles, we would likely just ignore the WKID and use the well-known text.
There's a way to add a custom definition to ArcGIS with a WKID, but we use a certain range of numbers for that and 98391 wouldn't work. The range we use is 202000 - 202999. If you're interested in trying that, please send me an email at mkennedy at esri dot com.