  The $\alpha$ person is the dominant person in a group. We define the
$\alpha$-author of a paper as the author of the paper with the highest
$h$-index among all the coauthors, and an $\alpha$-paper of a scientist as a
paper authored or coauthored by the scientist where he/she is the
$\alpha$-author. For most but not all papers in the literature there is only
one $\alpha$-author. We define the $h_\alpha$ index of a scientist as the
number of papers in the $h$-core of the scientist (i.e. the set of papers that
contribute to the $h$-index of the scientist) where this scientist is the
$\alpha$-author. We also define the $h'_\alpha$ index of a scientist as the
number of $\alpha$-papers of this scientist that have $\geq$ $h'_\alpha$
citations. $h_\alpha$ and $h'_\alpha$ contain similar information, while
$h'_\alpha$ is conceptually more appealing it is harder to obtain from existing
databases, hence of less current practical interest. We propose that the
$h_\alpha$ and/or $h'_\alpha$ indices, or other variants discussed in the
paper, are useful complements to the $h$-index of a scientist to quantify
his/her scientific achievement, that rectify an inherent drawback of the
$h$-index, its inability to distinguish between authors with different
coauthorships patterns. A high $h$ index in conjunction with a high
$h_\alpha/h$ ratio is a hallmark of scientific leadership.
