$$\begin{aligned}
    a_0 &= 1.36(b-y)_0 + 0.36m_0 + 0.18c_0 - 0.2448 \\
        &= (b-y)_0 + 0.18[(u-b)_0 - 1.36], \\
    r^* &= 0.35c_1 - 0.07(b-y)-(\beta-2.565).
    \end{aligned}$$

Note that $r^*$ is a reddening free parameter, and thus indifferent to the use of reddened or unreddened photometric indices.

Extinction Correction {#subsec:reddening}
---------------------

Though the sample of nearby stars to which we applying the Strömgren methodology are assumed to be unextincted or only lightly extincted, interstellar reddening is significant for the more distant stars including those in the open clusters used in § \[subsec:openclustertests\] to test the accuracy of the ages derived using our $uvby\beta$ methodology. In the cases where extinction is thought to be significant, corrections are performed using the `UVBYBETA`[^1] and `DEREDD`[^2] programs for IDL.

These IDL routines take as input $(b-y), m_1, c_1, \beta$, and a class value (between 1-8) that is used to roughly identify what region of the H-R diagram an individual star resides in. For our sample, stars belong to only four of the eight possible classes. These classes are summarized as follows: (1) B0-A0, III-V, $2.59 < \beta < 2.88$, $-0.20 < c_0 < 1.00$, (5) A0-A3, III-V, $2.87 < \beta < 2.93$, $-0.01 < (b-y)_0 < 0.06$, 