Reference Documents

 R1)    ISO Reference wavelengths      SAI/96-240/Dc, 18/Dec/96

 R2)    Golay 1974 in ``Introduction to Astronomical Photometry'', Ch. 2

Postscript version

1 Introduction

This document summarises discussions held over the last three months or so, for the most part in the context of the monthly Cross-Calibration meetings, on how to present ISO photometric measurements. Specifically, it will specify the manner in which in-band fluxes will be converted to monochromatic flux densities, and the choice of wavelengths to which these flux densities will be referred.

2 Determining Flux Densities and Reference
Wavelengths

The subject of the conversion of a heterochromatic photometric measurement to a monochromatic one has been sumarised in R1, and full details can be found in R2. Following extensive discussion, the decision was made to adopt the IRAS convention, where the conversion is performed assuming a constant energy spectrum, i.e. This has the advantage of making the results immediately comparable to IRAS data (though the filters are not identical), and the drawback that significant correction factors will have to be applied to most data, as was the case with the IRAS data, since most of the sources observed do not have a constant energy spectrum. These correction factors can be as large as , and are largest for the broadest filters.

Alternative choices were:

1. to give only the in-band fluxes (in ): these have the advantage of directly proportional to the what is measured and to be expressed in physical units, but since the depend of the filter bandwidth they cannot easily be compared to one another or to other data.
2. to give the ratio of the in-band flux of the source to that of a reference source expressed in magnitudes: these are awkward at best, mostly because they are not expressed in physical units. Furthermore, there is no single reference source that could span the complete ISO wavelength range.
3. to assume a model Sirius spectrum: this would produce correct results for nearly all normal stars, but incorrect results for peculiar stars, galaxies, and other objects. This is the scheme adopted by MSX, whose output catalog will consist primarily of stars (M. Cohen, private communication).

Options (1) and (2) would leave the conversion to monochromatic flux density entirely up to the user.

From the definition of isophotal wavelength, ,

where E is the measured in-band flux, and is the spectral response of the system, and with , it follows that

where the denominator is a property of the photometric system alone. And finally, to convert from to we use the relation

Note that equations (2) and (3) define a linear relation between the in-band flux, E, and the flux density at the reference wavelength, .

From a formal point of view the choice of reference wavelengths is absolutely arbitrary. A reasonable choice of , however, will give an idea of the spectral energy distribution (SED) of the source, but in order to determine the true SED the user must convert and to and by using a known or assumed source spectral shape. For this purpose, ``color correction tables'' will be computed which will give correction factors and observed colours for many different types of energy distributions (namely power laws with different exponents, and Plank laws with a wide range of temperatures).

For the moment, and for the purpose of data presentation, a set of reference wavelengths has been chosen such that

1. they would clearly identify the filter, in particular where the filter is associated with a specific spectral band or line,
2. they are easy to remember numbers,
3. they are close to the for either an spectrum or for Sirius.

The reference wavelengths that deviate the most from either isophotal wavelength are the ones for the IRAS filters, for which the IRAS wavelengths have been adopted. The reference wavelengths are tabulated in Tables 1 and 2 for CAM and PHT filters, respectively.