# How to calculate galaxy bolometric luminosity?

I am a bit confused by bolometric corrections. If I have an x-ray luminosity in the 2-10 keV band, how does one convert that to $$L_{bol}$$? From Netzer's book The Physics and Evolution of Active Galactic Nuclei I got these bolometric correction factors:

Optical: $$BC_{5100} = 53 - log(L_{5100})$$

and x-ray: $$log(L_{5100}) = 1.4\times log(L_X) - 16.8$$

where the bolometric correction for the x-ray luminosity ($$L_X$$) is obtained in two steps, using the equation for the optical BC again. The index $$5100$$ stands for the optical continuum measured at $$5100$$ angstrom. I can't figure out what I have to do with this $$BC_{5100}$$ once I've got it. Multiply by $$L_X$$? The book says "(...) BCs, that can be used to convert a single-band measurement of $$L$$ into an approximate $$L_{bol}$$."

I'm happy to use correction factors defined elsewhere instead of the ones I quoted. I just want to calculate an estimate for $$L_{bol}$$ for my galaxies.

## 1 Answer

The bolometric correction is the difference between a bolometric magnitude and the magnitude in some band.

$$BC = M_{\rm bol} - M_{5100} = -2.5\log\left(\frac{L_{\rm bol}}{L_{5100}}\right)$$ $$\log L_{\rm bol} = \log L_{5100} - 0.4BC \ ,$$ $$\log L_{\rm bol} = \log L_{5100} +0.4\log L_{5100} - 21.2 \ ,$$ $$\log L_{\rm bol} = 1.4(1.4 \log L_x -16.8) - 21.2\ ,$$ $$\log L_{\rm bol} = 1.96\log L_x -44.72\ .$$