# How to obtain distance modulus and Total extinction from Isochrone fitting to CMD?

This is my first post here.

I am studying the following article: https://arxiv.org/abs/1901.03574.

On Page 5, Sec 3.1, the authors are presenting their results they obtained via Isochrone fitting to the CMD of the two GCs being discussed. My questions are:

1. How can I find out the distance modulus and the Total extinction $$A_{F606W}$$ from just the fitting? I know that Isochrone fitting is done when we need to estimate the age. In order to fit, we need to move the Isochrone both vertically (Distance modulus?) and horizontally (Color excess/Reddening/Extinction?). Is my understanding correct?

2. How do they convert the Reddening in filters to reddening in B-V? What is the technical details/physics of it?

3. What is the role of the Extinction law in getting these numbers?

4. In the end, they calculate the distance, which is simple once we get the distance modulus. Why is it the distance from the Sun? Did we assume a heliocentric coordinate system somewhere?

Thank You.

1. The isochrones are not straight lines in the CMD. Extinction moves the stars both redward (right) as well as fainter (down) in the CMD. The vertical shift (the extinction $$A$$) is calculated from the horizontal shift (the reddening) using an extinction law. (e.g. $$A_V = 3.1 E(B-V)$$). The effects of extinction and distance (which only moves the stars vertically) can therefore be separated. In the case of the paper referred to, the globular clusters have a horizontal branch and a giant branch. The horizontal branch is almost ...horizontal and the giant branch is almost vertical. This enables the authors to be independently sensitive to a vertical and horizontal shift of the model isochrones, as described above.

2. +3. There are simple conversion factors published in several papers. Extinction is wavelength dependent, so the spectrum of a star is attenuated in a wavelength dependent way The reddening in any colour (e.g. E(B-V)) is just the difference in extinction at the two wavelengths (well it needs to be integrated over the photometric bands) i.e. $$A_B - A_V$$. These differences in extinction coefficients can be calculated for any pair of bands. They depend on the wavelength dependence of extinction, aka the extinction law, but also on the intrinsic spectrum of the star (which is frequently ignored). Extinction laws can be empirically determined by observing stars with a known intrinsic spectrum.

'4. Does it matter? Have you compared a parsec with an astronomical unit?

• Re-1. If I understand you correctly, in fitting the isochrone, the redward shift due to extinction will be exactly the horizontal shift (average) of the fitted isochrone from the original one. But since both extinction and distance moves the stars vertically, how can I separate these two? Sorry if the questions are too basic, I am new to this. – Razor Feb 2 '19 at 0:51
• @Razor see edit. Because the vertical shift due to extinction is a fixed multiple of the horizontal reddening shift. They are not independent. So the amount of horizontal shift required tells you what proportion of the required vertical shift is due to extinction. – Rob Jeffries Feb 2 '19 at 7:44