Question

A galaxy of absolute magnitude M= - 20 is at a distance of 700 kpc. Would it be visible to the unaided eye.

Answer 1

The apparent magnitude $m$ of an object is related to its absolute magnitude $M$ by the formula

$$m = M + 5 \log_{10} \frac{d}{10\,\text{pc}} \, ,$$

where $d$ is the distance to the object. Substituting the numbers $M = - 20$ and $d = 700\, \text{kpc} = 7 \times 10^5\, \text{pc}$ into this formula, we obtain $m \approx 4.2$. Since the dimmest objects visible to the unaided eye are assigned $m = 6$, our galaxy would be visible.

Answer: yes.