Line fluxes

Some useful formulas to remember are:

$$f = 1.986 \times 10^{-19} \, \frac{f'}{\lambda}$$ (6)

and (here, defined);

$${\rm AB}_{X\,{\rm km/s}} = - 2.5 \log f' + 2.5 \log X + 13.15$$ (7)

where

• f is the energy flux measured in ${\rm W}\: {\rm m}^{-2}$,
• f' is the photon flux measured in ${\rm s}^{-1}\,{\rm m}^{-2}$,
• $\lambda$ is the observed wavelength measured in $\mu{\rm m}$,
• ${\rm AB}_{X\,{\rm km/s}}$ is the magnitude assuming the flux is spread uniformly over a width of X kms^-1.

 

 

Table 3: Line flux conversions

wavelength	photon flux	energy flux	energy flux	${\rm AB}_{100\,{\rm km/s}}$	${\rm AB}_{300\,{\rm km/s}}$
( $\mu{\rm m}$)	( ${\rm s}^{-1}\,{\rm m}^{-2}$)	(W m-2)	(erg s-1 cm-2)
0.40	1.0	$5.0 \times 10^{-19}$	$5.0 \times 10^{-16}$	18.1	19.3
1.00	1.0	$2.0 \times 10^{-19}$	$2.0 \times 10^{-16}$	18.1	19.3
2.20	10.0	$9.0 \times 10^{-19}$	$9.0 \times 10^{-16}$	15.6	16.8