Q = (U-B) - [ E(U-B) / E(B-V) ] (B-V)
= (U-B)0 - [ E(U-B) / E(B-V) ]
(B-V)0 == Q0
i.e., Q = = Q0.
The subscript0 denotes the true intrinsic value; otherwise
these are observed magnitudes.
Interstellar reddening moves objects in a color--color diagram with
the following slope:
E(U-B) / E(B-V) = 0.72 (approx).
[A more exact expression contains a correction term +0.05E(B-V), but it
can be ignored for most cases. ]
For O to A type stars, it is empirically known that (U-B)0 =
3.7 (B-V)0, i.e., the slope on a color-color diagram is 3.7.
So
Q = Q0 = (U-B)0 - [ E(U-B) / E(B-V) ]
(B-V)0
Q = (U-B)0 - [ 0.72 ] (B-V)0
Q = 3.7(B-V)0 - [ 0.72 ] (B-V)0
Q = 2.98(B-V)0
or
(B-V)0 = 0.33 Q
(B-V)0 = 0.33 [(U-B) - 0.72(B-V)]
The left hand side is the intrinsic color while the right hand side
contains the observed colors.
So one can get the true unreddened (B-V)0 colors
from the observed colors for early spectral type stars.
Likewise, one can get (U-B)0 as a fraction of Q.
For comparison, Q = 0.00 for an A star, and -0.93 for an O star.