Apart from Aristotle, are there any other definitions of a tragic hero I should refer to when writing about Tragedy?

There are others, but I think you might find Arthur
Miller's "Tragedy and the Common Man" to be helpful if you're writing a comparison.  The
"older" view of tragedy holds that the person has to be of elevated nature (there's more
to it than that, but you can look at the last link below for more information on the
Poetics.

Miller lives in a democratic society that tends to
an egalitarian view of people and does not believe that an elevated character is
necessary for tragedy.  Here's a brief quote that suggests what he
thinks:

I
believe that the common man is as apt a subject for tragedy in its highest sense as
kings were. On the face of it this ought to be obvious in the light of modern
psychiatry, which bases its analysis upon classific formulations, such as the Oedipus
and Orestes complexes, for instance, which were enacted by royal beings, but which apply
to everyone in similar emotional situations.  (from Tragedy and the Common
Man)

If you are
familiar with any of Miller's work ("Death of a Salesman" or "All My Sons") you can see
how this works out. Since every person, regardless of his/her status in life, seeks
validation and meaning in life, everyone is a subject for tragedy when they are
frustrated in their efforts.

Here's how Miller ends his
essay:

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It is time, I think, that we who are without
kings took up this bright thread of our history and followed it to the only place it can
possibly lead in our time--the heart and spirit of the average
man.

Hope this
helps with your essay!