Small hollow circle in math, smaller than \circ

Question

I am writing a markdown document and I want to reproduce the following formula:

I'm trying to do it with the following:

$$
\underbrace{X_t}_\text{Population at time $t$} =
\underbrace{\alpha \circ X_{t-1}}_\text{Survivors from time $t-1$} +
\underbrace{\epsilon_t}_\text{Immigration} 
$$

But I get this:

In which the circle operator between $\alpha$ and $X_{t-1}$ is quite bigger (and thinner?) than what it needs to be. How can I solve it?

(I am going to ask another question about underbrace sizes.)

---

Edit: Related question: Making a thicker \cdot for dot product (that is thinner than \bullet)

Answer 1

One solution would be to insert a tikz circle, with width and line width that you chose.

\documentclass{article}
\usepackage{amsmath}
\usepackage{tikz}
\newcommand{\circo}{~\raisebox{1pt}{\tikz \draw[line width=0.6pt] circle(1.1pt);}~}
\begin{document}
$$
\underbrace{X_t}\text{Population at time $t$} =
\underbrace{\alpha \circo X{t-1}}\text{Survivors from time $t-1$} +
\underbrace{\epsilon_t}\text{Immigration} 
$$
\end{document}