Tau-squared Example 2

## Example 2 - Low-mass stars.

This example is the fit to the low-mass stars presented in Jeffries et al (2007). The output files are given in the download in a directory called Example2, but you should create a clean directory to try it in.

Once again we use monte to create the 2D isochrones. A range of 0.04 to 3 solar masses will cover the data. We will use the Baraffe et al (1998) mixing length 1.0 isochrones with the I vs R-I Jeffries Plieades tuned bolometric corrections. We require a binary fraction of 0.5, and an log10(age) range of 6.3 to 7.5 in 0.01 steps.

Monte will take some time to create the required 121 images, which are called things like I_R-I_07.200.fit.

Now you need to run grid. The input data catalogue is called hit.cat (which you can copy from ~/CMDfit/Example2). You should add an extra uncertainty of 0.03 mags in magnitude and 0.042 in colour. As before we use log10(age) 6.3 to 7.5 in steps of 0.01. You should search a distance modulus range of 8 to 11, with 200 points in the "grid". Finally, E(R-I)=0.14, and the range of allowed tau-squareds should be set to a negative number (i.e. do not allow any clipping).

You should find a tau-squared minimum of around 20 Myr, a distance modulus of 9.5 and a tau-squared of about 16. The precise numbers may be a little different, since the isochrones are made by a Monte-Carlo method. To discover whether this is a good fit you need to run tau2. You are first prompted for the best fitting model, which has been written out to best_model.fit. Then you need the original data, but with the adjusted uncertainties, which is called unclipped.cat, and the number of free parameters (2). The output should tell you that the probability of obtaining the best-fitting tau-squared is about 50 percent.

Finally you need to run uncer, which will tell you that the 68 percent confidence level is at a tau-squared of about 19. If you plot this on grid.fit (Starlink's gaia can do this for you) you should find the contour closes at about 5Myr and a distance modulus of 10.5. At the other end it may well close before it reaches 30Myr, but in fact this grid is not large enough to be sure, the experiment needs repeating to greater ages (but at lower resolution).

Home > Group > Tim Naylor > tau-squared > Example 2
Astrophysics