Converting surface brightness units

[Nekoteko]

Homework Statement

Simply want to know how to convert between mag arcsec^-2 to solar luminosities per square parsec.

Homework Equations

(from wiki)

The Attempt at a Solution

If the surface brightness S (B band) is 27 mag per square arcseconds, then to solve for the brightness in solar luminosities per sq. pc, it'd just be the absolute magnitude of the Sun in the B band + 21.572 - 2.5log(the value I want) = 27 mag arcsec^-2? Cause that doesn't work, haha. I'm terrible at conversions. Any suggestions? Thank you.

 

[anathema]

Hello,

To convert from mag arcsec-2 to solar luminosities per square parsec, you can use the following equation:

L = 10^(0.4*(M_sun - m))

Where L is the brightness in solar luminosities per square parsec, M_sun is the absolute magnitude of the Sun (4.83 in the B band), and m is the surface brightness in mag arcsec-2.

So, in your case, to solve for L, you would use the following steps:

1. Convert the surface brightness from mag arcsec-2 to mag per square arcsecond by dividing by 2.5. In this case, 27 mag arcsec-2 becomes 10.8 mag per square arcsecond.

2. Substitute the values into the equation: L = 10^(0.4*(4.83 - 10.8)) = 0.002 solar luminosities per square parsec.

I hope this helps! Let me know if you have any other questions.