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I am currently conducting an experiment where a subject is shown a series of photographs of various objects. Each photo contains a single object. Before showing the photograph, a screen with a text indicating the name of the object is shown briefly. The objective is to analyze the eye-fixations that occur as subjects view the objects.

This is a free-viewing task, i.e. the subjects are asked to gaze at the pictures without explicitly searching for any attribute in particular. Typically, a bottom-up mechanism is thought to be active for such situations. Since I show the name of the object before showing its picture, most likely, I am priming the subject's visual system. Does this manner of priming make the task a top-down one even though there is no explicit "search" traditionally associated with top-down mechanisms ?

More generally, what is the relationship between top-down mechanisms and priming the visual system ?

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This is potentially an example of a top-down influence on the visual system.

That is, if the experiment demonstrates as expected, that priming the visual system with a word influences the pattern of eye movements (compared to not priming) when free-viewing the following object, then that would support the conclusion of a top-down mechanism at work.

In Biased Competition Theory:

Top-down processing is based on pre-existing knowledge when interpreting sensory information.

Top-down processes are contrasted with bottom-up processing that is based on sensory input alone - that is, it can be modelled using only features of the stimulus. When attention (eg, eye movement) is directed in ways that are not accounted for by sensory input, this provides evidence for a top-down (higher level cognitive) mechanism.

Although much research on top-down effects on eye movement in scene viewing is done using visual search tasks, search targets are not necessary for demonstrating top-down effects, and many experiments use free-viewing (non-directed) tasks to test such effects.

One of the earlier studies showing evidence of top-down influence in free-viewing conditions is Parkhurst et al (2002), who tracked eye movements in free-viewing of various scenes. Although bottom-up predictions correlated well with the data, some top-down influence was found as well. Since then, most theories of visual attention incorporate both bottom-up and top-down mechanisms in visual processing, whether task-directed or not.

In fact, even conscious awareness is not necessary for top-down influence: Kiefer et al (2012) review the significant literature on top-down influence of masked (unconscious) priming of the visual system. Per this review, priming the visual system in a variety of ways influences attention in a top-down manner.

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