Astron. Astrophys. 324, L5-L8 (1997)

3. Star count method

Usually, the extinction is evaluated by comparison of star counts in the absorbed region and a nearby area assumed to be free of obscuration (Wolf diagram method). Star counts are performed by adding up the stars up to a given magnitude (or in a given magnitude range, e.g., ) within a grid of fixed squares. The step of the grid is a compromise between the stellar density and the spatial resolution. In other words, the spatial resolution is underestimated wherever the extinction is low, while in highly obscured areas, the content of several cells must be merged, in order to pick up enough stars.

We have developed a new method to investigate the extinction across a cloud which consists in replacing usual star counts by an estimation of the local projected star density obtained by measuring the mean distance of the x nearest stars. The most important advantage of this method is to match the local extinction: it corresponds to a star count with adaptable square size. Another very interesting advantage of the method is to provide a map with white noise. Therefore, we can simply estimate the noise by computing the standard deviation of the mean distance on a part of our map with no signal.

We obtain a map where each point represents the square root of the local density. The extinction is then easily derived by the relation:

where a is defined by:

where is the magnitude, the mean distance of the x nearest stars in the cloud and the mean distance of the x nearest stars in a comparison field supposed unobscured. We found . We verified that the relation (2) is correct up to , i.e. our limit of completeness. Actually, we do not need a reference field to derive the extinction because the available data cover of latitude and, thus, widely exceed the cloud dimension. So, we plotted the density versus the galactic latitude to interpolate the density inside the cloud for no extinction. Then we convert into visual extinction using the extinction law of Cardelli et al. (1989) for . So .

A limitation to star counts behind molecular clouds, is the possible presence of young stars embedded inside the cloud itself. To draw out a reliable extinction estimate, the counts must be dominated by background stars. Therefore, we have attempted to remove these spurious, although interesting, objects using a colour excess criterion. A first iteration of the extinction estimation is carried out without taking into account these objects. Then, this map is used to deredden all stars, individually. Their colours are compared to the main sequence star at the cloud distance in a colour-magnitude diagram (K versus ). Then we flag each star which would have an extinction even greater than 5 and which are likely to be intrinsically very red objets. The colour-magnitude diagram is presented in Fig. 1. The spatial distribution of these flagged stars (Fig. 2) show essentially two clusters near the two stars HD 97300 (at the north) and HD 97048 (in the centre). This result is in agreement with several studies of T-Tauri associations in the Cham I with IRAS (Assendorp et al., 1990) and ROSAT (Lawson et al., 1996). We find also several red stars farther away from the dense cores of the cloud. They could be real objects (T-Tauri, red giant), or their position in the diagram might be unreliable because of the uncertainty on the colour. We emphasize the fact that our criterion identifies only the classical T-Tauri, but not the so called weak-line T-Tauri which have no or little infrared excess. Nevertheless, this type of T-Tauri does not concentrate in the dense cores as the classical one does, so they have probably little effect on star counts. Finally, this operation removes only of stars (). Counts are, thus, strongly dominated by background stars. Then, we have built an extinction map from the cleaned counts.

Fig. 1. Colour-magnitude diagram of dereddened stars in an area of 4.3 deg2. Diamonds represents young stellar object candidates (100 on 30 000 stars), the arrow corresponds to the extinction vector of

Fig. 2. Spatial distribution of young stellar object candidates. Extinction isocontours at 2, 4 and 7 are overplotted

We can consider our map as a digitized image which allows to use current technics of image processing such as the wavelet transform to restore the image and to filter the noise (Starck & Murtagh, 1994). We apply the à trous wavelet transform algorithm to split-off the image into 4 wavelet planes. The decomposition is made by convolving the image by a low-pass filtering matrix. The difference between the original image and the result of the first convolution gives the first plane of the wavelet transform which corresponds to the high frequency plane. Further iterations of this process provide the 4 wavelet planes and the final smooth plane.

Thus, we can use the high frequency plane to identify aberrant points and remove them in the final image in order to eliminate their contribution in all the planes, by replacing the bad pixels by the average of the surrounding 8 pixels. We are conscious that this process might result in a loss of information, but less than pixels are actually corrected in this way.

Lastly, we filter each wavelet plane using the following method. The noise on star counts is poissonian, but taking the logarithm, as defined in Eq. (1) changes the statistical properties which are no longer poissonian. A Poisson noise having the standard deviation estimated in a region of the map with no signal is simulated. Then we take its logarithm and we decompose this simulated noise into wavelet planes. The estimation of the standard deviations on each plane allows an adaptable thresholding. Then we filter each plane at .

© European Southern Observatory (ESO) 1997

Online publication: May 26, 1998

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