This week is a follow-on, on last week’s post about the selection of members in a young cluster. It briefly discusses what we can learn about the cluster once we have identified its members based on their distances and proper motion values.
The best way to investigate the cluster is a Hertzsprung-Russel diagram. This is a plot of the surface temperature against the luminosity of all stars. As both of these properties are difficult to measure, astronomers usually plot related properties. The colour of a star is equivalent to the surface temperature. Similarly, the absolute magnitude, which is the magnitude the star would have if it was at a fixed distance of 10pc from us, is equivalent to the luminosity. Gaia measures the colour of the stars, which is simply the difference in the magnitudes between two filters – in this case Blue and Red. We can also determine the absolute magnitude, because we know the distance for each star and its apparent magnitude.
In the plot above, we show for the IC348 field, how the colour vs absolute magnitude plot looks. All stars that are not cluster members are shown as small gray dots. The cluster members are the larger dots. Stars identified in Gaia as a cluster member are shown in blue. If the star has also a light curve in HOYS, it is shown in green. And finally, if the star is considered variable in HOYS, it is shown in red.
In such a diagram, stars in a cluster usually line up along a track. The reason for this is that the stars in a cluster have almost the same age, but different masses. And the mass mostly determines the position in such a diagram. More massive stars are hotter (smaller colours) and more luminous (lower magnitudes) – i.e. they are more to the upper-left in the diagram. Lower mass stars are in the opposite (lower-right) corner, as the are cooler/redder and less luminous.
This allows us to draw theoretical tracks in the diagram that connect all stars at a fixed age and varying masses. These are hence called isochrones and we over-plotted a number of them into the figure. By comparing which isochrone fits the data best, we can estimate the age of the cluster. In this case (see figure) the the accepted literature age for the cluster is 2Myr, which seems to fit the data quite well. However, there is quite a scatter, which can be caused by a number of things.
1) There is a real age spread. Usually star clusters form over a period of about 1Myr. Thus, especially when the cluster is very young, the age spread matters. 2) Young stars vary. This is due to many aspects discussed at length in our posts. Thus, their colour and apparent luminosity changes over time, causing scatter around the actual isochrone. Hence, note the isochrones are average positions for the young stars in the plots. 3) Some stars are binaries or higher order multiples. Thus, e.g. if both stars have the same mass, they can appear up to 0.75mag (a factor of two in flux) brighter at the same colour. 4) There is varying extinction along the line of sight to each cluster member, again causing changes in colour and observed brightness.
Finally, one can see that the young (a few million years) isochrones are all above (at brighter luminosity) the older (one billion year) isochrone. The reason is that the young stars are larger and still shrink due to gravity. This shrinking stops when the fusion in the star ignites, and the resulting radiation pressure balances gravity – the main sequence phase of the star. For stars that have about the same mass as the Sun, this shrinking ‘towards’ the main sequence takes about 30Myr. This process is faster for more massive stars and can take up to 100Myr for the lowest mass stars.