Home People Tim Naylor tau-squared Example 2

Example 2 - Low-mass stars.

This example is an update to the fit to the low-mass stars presented in Jeffries et al (2007). We've had to update it because we no longer distribute the Jeffries tuned isochrones, as the Bell et al (2014) ones supercede them. 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 1.9 isochrones with the I vs R-I Bell et al (2014) bolometric corrections for the Bessell filter set (BT-Settl+Bell Bessell). We require a binary fraction of 0.5, and an log10(age) range of 6.3 to 7.5 in 0.01 steps. You also need to include an extinction of 0.20 in E(B-V).

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, since we have already reddened the models we created, you should not add any further extinction, and the fraction of stars which are likely to be members can be set to one.

You should find a tau-squared minimum of around 13 Myr, a distance modulus of 9.8 and a tau-squared of about 27. The precise numbers may be a little different, since the isochrones are made by a Monte-Carlo method. The first thing you should do is overlay the model on the data and check it looks reasonable (see the manual on how to do this). Next you should check that the best fit does not lie outside the rage of the parameter search, by plotting grid.fit. Finally you should check that all the data points lay within the model areas created by monte by looking at grid_npts.fit. In this case you can see that at young ages and small distance modulii there is a decrease in the number of points fitted, but as this is far away from the best-fit parameters, it does not matter.

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 fitted.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 32 percent.

Finally you need to run uncer, which will tell you that the 68 percent confidence level is at a tau-squared of about 30. If you plot this on grid.fit (Starlink's gaia can do this for you) you should find the contour closes at about 10Myr and a distance modulus of 10.05. 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). It also suffers (if you look at the models) from a lack of extreme mass ratio low-mass binaries (the "binary wedge") because the models do not go down to cool enough temperatures.


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