The extinction law from photometric data : linear regression methods

Context. The properties of dust grains, in particular their size distribution, are expected to differ from the interstellar medium to the high-density regions within molecular clouds. Since the extinction at near-infrared wavelengths is caused by dust, the extinction law in cores should depart from that found in low-density environments if the dust grains have different properties. Aims. We explore methods to measure the near-infrared extinction law produced by dense material in molecular cloud cores from photometric data. Methods. Using controlled sets of synthetic and semi-synthetic data, we test several methods for linear regression applied to the specific problem of deriving the extinction law from photometric data. We cover the parameter space appropriate to this type of observations. Results. We find that many of the common linear-regression methods produce biased results when applied to the extinction law from photometric colors. We propose and validate a new method, LinES, as the most reliable for this effect. We explore the use of this method to detect whether or not the extinction law of a given reddened population has a break at some value of extinction.