Suppose that a significant fraction of white dwarfs
    have absolute magnitudes down to M(G) = 23.  Would we see 
    them on this diagram?

         The difference between apparent magnitude m and 
         absolute magnitude M is the distance modulus, (m - M).
         It depends on distance d in pc as follows:

                  (m - M)  =   5 * log(d)   -   5


         So, at the maximum distance of this sample, d = 10 pc,
         we expect

                  (m - M)  =   5 * log(10)  -   5

                           =   0

             -->   m  =  M


         Since our sample is cut off at an apparent magnitude 
         m = 18, that means that at the maximum distance of d = 10 pc,
         we can only detect stars of absolute magnitude M = 18.

         Any stars with fainter absolute magnitudes, M > 18, 
         would have to be closer to the Sun for Gaia to measure it
         at m < 18.  In particular, a star of absolute magnitude
         M = 23 would need (m - M) = -5, which corresponds to 
         a distance of just d = 1 pc.
         
         

   Suppose that a significant fraction of stars have absolute 
   magnitudes as bright as M(G) = -3.  Would we see them on this diagram?


         Very luminous stars should be detected whether d = 1 pc 
         or d = 5 pc or d = 10 pc, or even much larger distances.
         For example, a star with M = -3 would have the critical
         apparent magnitude m = 18 at a distance given by
 

             (m - M)  =  (18 - (-3))  =  21   =  5 * log(d)  -  5

         Solving for the distance d at which this star would just
         barely make it into the Gaia sample,

                          0.2 * (21 + 6) 
                d  =   10                   =   160,000 pc


         So, yes, we ought to see it on this diagram.




   Would your answers to either question change if we included 
   stars out to a distance larger than 10 pc?

 
         If we look at larger distances, we should NOT find any
         more very low-luminosity stars, because they would be
         too faint to be detected; in other words, their 
         apparent magnitude would be larger than m = 18.

         On the other hand, even at distances much larger than
         d = 10 pc, very luminous stars should still appear 
         to have apparent magnitudes brighter than m = 18,
         and so they should be detected.