Determination of absorption by Q-method for JHK photometry in embedded clusters

TL;DR

This work tackles the challenge of estimating star-by-star extinction in embedded clusters with spatially varying reddening by applying the infrared Q-method to 2MASS JHK_S photometry. It defines a zero-reddening sequence in two Q–color planes, revealing a two-segment structure whose boundaries depend on the color-excess ratio k_R, and fits the segments with parabolas. A luminosity-function–based segment selection method compares cluster data to a reference zero-reddening LF to assign stars to the appropriate segment and estimate absorption. Through extensive simulations of clusters with uniform and non-uniform absorption, the study shows typical misassignment rates around 10–20% (up to 30% near completeness limits), indicating practical viability for disentangling variable extinction in embedded clusters.

Abstract

In this paper we describe the absorption determination by the Q-method for 2MASS photometry ($J$, $H$ and $K_S$ bands). Using the Pleiades and Praesepe stars, we determine the zero-reddening sequence for different values of the color excess ratios $E(J-H)/E(H-K_S)$. In this paper we consider a sequence consisting of two segments, that leads to an uncertainty in the determining of absorption - one value of the Q parameter corresponds to two values of the non-reddened color index. We propose a method to select a segment of the zero-reddening sequence for the main sequence stars of the cluster. The method is based on the difference in the position of stars of different segments in the cluster luminosity function. To test the proposed method, we simulate the luminosity functions of clusters with the non-uniform absorption distribution in the cluster region. With the typical absorption values in embedded clusters, about 10 % of stars are erroneously assigned, but in some cases this fraction can reach 20 %. Thus, despite the fact that irregular absorption distorts the distribution of stars of different segments on the cluster luminosity function, our method allows to separate stars with an error of no more than 20 %.

Figures (4)

• Figure 1: Examples of "color index -- Q parameter" diagrams. Q is calculated using Eq. (\ref{['EqQ1']}) for different values of the color excess ratios $E(J-H)/E(H-K_S)$ (indicated at the top of the plot). The stars of the Pleiades and Praesepe are shown in black, the red lines are fittings for zero-reddening sequences, and the blue lines are boundaries of these sequences. For the diagrams plotted in the '$(J-K_S)$ -- Q' axes (right column), we did not fit the zero-reddening sequence, since in this case the scatter of stars is larger than for other color indices.
• Figure 2: Luminosity functions of the Pleiades (a) and Praesepe (b), plotted by the absolute stellar magnitudes in the $K_S$ band. The LF for stars of the left segment of the zero-reddening sequence are shown in orange, and for stars of the right segment in blue. The red vertical line shows the limiting magnitude value.
• Figure 3: Examples of model clusters. The left side: the absorption distribution in the model cluster projected onto the picture plane (the (x,y) plane, perpendicular to the z axis along which the absorption is calculated). The color shows the absorption of the star in the $K_S$ band. The right side: the luminosity functions of the corresponding model clusters. The stars of the left segment of the model cluster are shown in orange, the stars of the right segment are shown in blue. The stars of the left segment of the "reference" cluster are shown in gray, and the stars of the right segment are shown in black. The red vertical line is the limiting value of the stellar magnitude found by comparing the luminosity functions of the model cluster and the "reference" cluster.
• Figure 4: Dependence of the fraction of incorrectly identified stars in a model cluster on the difference between the maximum and minimum absorption of stars (in the $K_S$ band). a) the fraction of stars is calculated for all stars in the model cluster; b) the fraction is calculated only for stars with a magnitude less than the selected limit of the catalog completeness ($15.5^m$ in the $K_S$ band). Each point corresponds to one model. The color shows the width of the intersection region of the left and right segments of the luminosity function of the corresponding model. The black line is the boundary below which 90 % of all models are located.