A.1 Infrared Units

The infrared wavelength range has borrowed units from the surrounding optical and radio (submm) regimes. Both magnitude and flux representations are widely used in the infrared.

Flux density $F_{\nu}$ of a source is defined as the flux per unit frequency. Flux density is the physical unit used for point sources. The unit of flux density is W m$^{-2}$ Hz$^{-1}$. For practical purposes in the infrared it is often convenient to scale this SI unit and use Janskys (Jy) instead.

$$1\,\,{\rm Jy} = 10^{-26}\,\,{\rm W\,m}^{-2}\,{\rm Hz}^{-1}$$ (A.1)

ISOCAM-CVF and SWS spectra are given in units of Jy/pixel and Jy, respectively in AAR data products.

ISOPHOT-S spectra are given in units of W m$^{-2} \mu$m$^{-1}$. The conversion to Jy can be done in the following way:

$$1 \frac{W}{m^2 \mu m} = 10^{13} \frac{\lambda^2}{29.98} Jy \qquad with \quad \lambda \quad in \quad [\mu m]$$ (A.2)

LWS spectra are given in units of $10^{-18}$ W cm$^{-2} \mu$m$^{-1}$. The conversion to Jansky can be done with the following equation:

$$10^{-18} \frac{W}{cm^2 \mu m} = \frac{\lambda^2}{299.8} Jy \qquad with \quad \lambda \quad in \quad [\mu m]$$ (A.3)

For extended objects, surface brightness $B_{\nu}$ is used instead of flux density. Also background emission, for point sources, is expressed in brightness units. Brightness is defined as the flux density per unit solid angle. The unit of brightness is W m$^{-2}$ Hz$^{-1}$ sr$^{-1}$, but in practice it is often scaled to MJy sr$^{-1}$.

$$1\,\,{\rm MJy\,sr}^{-1} = 10^{-20}\,\,{\rm W\,m}^{-2}\,{\rm Hz}^{-1}\,{\rm sr}^{-1}$$ (A.4)

The flux density of a point source, in particular for a stellar object, is often given in magnitudes $m$. In the ISO wavelength range these units are mostly used for ground based measurements below 20$\mu$m. The conversion to or from magnitudes is performed via the definition of the zero magnitude flux density $F_{0}$, which depends on the wavelength and on the photometric system used. In the case of ISO, the system zero point is defined by the model spectral energy distribution of Vega ($\alpha$ Lyr), available from http://www.iso.vilspa.esa.es/.

The magnitude $m$ of a ground based observation can then be converted into flux density through the formula

$$F_{\nu} = F_{0}\,10^{-\frac{m}{2.5}}.$$ (A.5)

For spectroscopic measurements, the total flux $F$ of a line is often the most interesting quantity. A flux calibrated spectrum may be presented in the form of flux density $F_{\lambda} = \frac{c}{\lambda^2} F_{\nu}$) as a function of wavelength $\lambda$. Flux $F$ of a line of interest can be obtained by subtracting an appropriate continuum flux density level of the spectrum before integrating over the entire line in wavelength $\lambda$. The unit of flux is Wm$^{-2}$.