Yep. AAU membership and/or Top 100 in the ARWU ranks is what the university presidents look at. For the Pac-12, I think that a school could get a yes vote on joining the conference if it is classified as an R1 (Carnegie classification for highest level of doctoral research).
In our footprint, AAU/Top 100 ARWU only includes Texas and Rice. Kansas is on the AAU list. With KU, UT or Rice, the conference could geographically bridge to AAU members Iowa State, Missouri and Tulane. That's it, guys.
So now we get to the 115 R1 options and which are within the footprint or close enough to it but don't make the other lists. (All 12 current members are R1.) Within the Carnegie classifications, also keep in mind that Pac-12 university presidents will consider how much of the research activity is in agriculture, which is devalued by them and is what keeps a lot of these R1 schools from being considered for AAU membership.
1. Colorado State
2. Kansas State
3. Texas Tech
4. Hawaii
5. Nebraska
6. New Mexico
7. Notre Dame
8. Oklahoma
Most of the schools we talk about within the footprint are R2 (107 nationally, high level of research). Good for doctoral research, but not up to the level of the rest of the Pac-12. Could be considered as a tag-along with others if the other school brought enough. But they would be expected to come up.
1. Baylor
2. BYU
3. Oklahoma State
4. San Diego State
5. SMU
6. TCU
7. UNLV
8. Nevada
9. Utah State
Then there are the R3 schools (moderate research activity). These are probably non-starters, no matter who they came with.
1. Air Force
2. Boise State
https://en.wikipedia.org/wiki/List_of_research_universities_in_the_United_States
From the standpoint of G5 programs within the footprint, the best fits are CSU, Hawaii and New Mexico.