Using X-rays to Determine Which Compact Groups are Illusory

If the large-scale galaxy distribution is filamentary, as suggested by some observations and recent hydrodynamical simulations, then lengthwise views of filaments will apparently produce compact groups (CGs) that are in reality stretched out along the line of sight. This possibility has been advocated recently by Hernquist, Katz \& Weinberg (1994). Here, we propose a test for this hypothesis using X--ray emission from CGs. The observable quantity $Q \equiv L_{x} a_{p}^{3}/L_{g}^2 T_{x}^{1/2}$ should be proportional to the axis ratio of the group, $a/c$, where $a$ and $c$ are the long and short axis of a prolate distribution, $a_p$ is the radius of the group projected onto the sky, $L_{x}$ is the bolometric X-ray luminosity, $L_{g}$ is the group blue luminosity, and $T_{x}$ is the gas temperature. We find that the distribution of $Q$ is consistent with the notion that many spiral-rich CGs with unusually small values of ($a/c)$ are frauds, i.e. that the values of $Q$ are anomalously small. An alternative possibility is that CGs are gas-poor relative to rich clusters; however, this can be tested using the Sunyaev-Zeldovich effect. If the groups have a normal ratio of gas-to-total mass, but are simply stretched out along the line of sight, a Sunyaev-Zeldovich signal should be detectable.