How Reliable Are Our Assumptions? Sources of Scatter in Cluster HR Diagrams

In the Example 2, we noted that it is typically safe to assume that the stars in clusters are all at the same distance, they have the same metallicity, same extinction/reddening and they’re all the same age. But when do these assumptions not hold? And what impact do they have on our measurements when they do? These are questions we should address before moving on to have you image your own cluster and do your own isochrone modelling.

• Distance: if the cluster is so close to us that the distances between stars are significant fractions of the distance to the cluster, we can expect more scatter in the cluster’s main sequence than we’d see from the multiple star systems alone. However, the sizes of clusters are typically only a few parsecs (for reference, note that the Orion nebula is only about 7 pc across), so even a nearby cluster a few hundred parsecs away will have negligible scatter due to distance.
• Age: Similar to distance, if the period of star formation within a cluster is a significant fraction of the cluster’s average age, then we should expect to see scatter. Star formation can last a few tens of millions of years, so if a cluster’s age is less than 100 million years (i.e. log(Age (yr)<8), the formation period may yet be up to 10% of the cluster’s total age. In this case, it is still important to fit the isochrone to the bottom of the main sequence, but we can expect more scatter above the curve than normal due to the presence of cool, luminous protostars.
• Metallicity: the molecular clouds that form star clusters are typically well mixed, so metallicity can typically be considered constant throughout a cluster. It is worth noting that in particularly large clusters (e.g. some of the more massive globular clusters, with ~10⁶ stars), astronomers have found evidence of multiple star formation epochs. In this case, not only is there a broader range in ages, but due to the rapid life cycles of high mass stars we even see multiple populations with different metallicity. Such observations require spectroscopic analysis which is beyond the scope of this project, but it is worth noting that in such extreme cases the cluster’s ranges in both age and metallicity produce scatter about the average values you would expect to model with your own observations.
• Reddening/extinction: Interstellar reddening and extinction do often vary across a cluster, especially in active star forming regions where enough gas remains in the nebula to continue forming stars. The inhomogeneity of dust within our galaxy is typically enough to produce some scatter in a star cluster’s HR diagram, but the average value for a star cluster typically provides a good representation.

To summarize: we expect very little scatter in our data due to variability in distance and metallicity within a cluster, and we can expect somewhat more scatter due to variability in age and reddening/extinction. To give you a feel for how much scatter you could expect to see in practice, the next example takes you through the analysis of a young star-forming region where variable extinction and ongoing star formation make the effects immediately visible.