Effective Radii Probabilities

• Objectives
• Techniques
• Results
  • Bootes 1
  • Palomar 13
  • Willman 1

Objectives

I hope to use the Collins et al. method to generate probabilities of star membership based on a star’s radius from the center of the object in relation to its effective radius.

Techniques

To calculate the distance of a star to the center of the object:

\[d = \sqrt{((\alpha - \alpha_0)*\cos{\delta})^2 + (\delta - \delta_0)^2}\]

Where $\alpha$ is the right ascension and $\delta$ is the declination of the object’s center, and $\alpha_0, \delta_0$ are the coordinates of the star.

The Collins et al. paper provides us with the equation for the probability:

\[P_{dist} = exp(\frac{-r^2}{2r_{h}^2}) \\ r_h = \frac{r_{eff}(1-\epsilon)}{1+\epsilon cos(\theta)}\]

Ignoring ellipticity and position angles of the major axis, we will set $\epsilon = 0, \theta = 0$.

Results

Applying this technique to Bootes 1, Palomar 13, and Willman 1:

Bootes 1

Palomar 13

Willman 1