Is a visual estimate of homoscedasticity rigorous enough? As part of my research in astronomy (quasar magnitudes at various wavelengths), I've been producing graphs such as the following:


The bottom plot on each graph shows the distribution of the residuals for the top plot on the graph. I can see that in the first graph, the residuals seem to have a concave upwards trend, while in the bottom graph, they're pretty randomly distributed around 0. I feel that I should point this out in my written report, since I'm using OLS to determine the trend in the magnitudes, but since my research isn't actually about statistics, would it be enough that I say something like "I assumed homoscedasticity since visual inspection showed the residuals to be randomly distributed", or is this frowned upon by statisticians? 
 A: I would say that (concentrating on the second plot) that heteroskedasticity is not clear, the spread (vertical) seems larger where the density of points is higher. So to evaluate that, maybe add a local smooth of the residual standard deviation. That could be very informative.
Also answered by comments:

I'm usually grateful that the paper's author actually even knows about
  the homoscedasticity assumption and gave it some thought: that puts
  you ahead of the vast majority of people who use OLS. Incidentally,
  for your data there's much more that could be said. There is a
  suggestion of positive skewness in the first set of residuals, making
  it likely that a simple nonlinear transformation of the response
  values might simultaneously make the residuals more symmetrically
  distributed and eliminate some (but not all of) that curved lack of
  fit you noticed.  

– whuber

@whuber is it positive skewness or do the residuals not seem to be
  distributed with zero mean as a function of redshift z? The issue here
  is not so much heteroscedasticity but much more an unequal
  distribution (weight) among the parameter z plus an wrong model. So
  the "erroneous" model is gonna follow the (locally linear) trend in
  that high density bulk with $0.2<\log(z)<0.6$ but should not be
  regarded as representative for other areas.

– Sextus Empiricus
