Appendix A: COBRA program

Due to the large number of star-forming regions in Mrk 86 and the intense and variable underlying emission we developed a program that allowed us to substract this underlying emission and the occasional contamination from neighbor star-forming regions. Then, on the underlying emission subtracted image, we determined the most reliable apertures, sizes, and integrated fluxes for all these regions. This program was written in FORTRAN77 programming language and it was called COBRA (see http://www.ucm.es/info/Astrof/cobra/).

COBRA uses different graphic output devices, including XWINDOWS and Postscript, and makes use of the AMOEBA (Press et al. 1986), PGPLOT, FITSIO and BUTTON (Cardiel et al. 1998; see also Cardiel 1999) subroutines.

In this Appendix we will describe the procedure followed to estimate the underlying emission and the criteria used to determine the sizes and fluxes of the star-forming regions and stellar clusters in Mrk 86 using the program COBRA.

   
A.1. Light profiles fitting

First, (1) an image section including the region of interest is selected interactively (see the original images in Fig. 10). The size of this section necessarily depends on the spatial scale of the change in the underlying emission and the proximity of neighbor regions. This section must be chosen in such a way that the background emission (underlying and neighbor regions emission) can be reproduced by a line in the x and y light profiles. Thus, when several relative maxima are placed too close to match this criterion they were studied as a single region.

After cropping the image section selected, (2) the position of the maximum of the region of interest is marked interactively. Then, the light profile along the x axis at this position is fitted.

In order to perform this fit three different components are used, a line that reproduced the underlying and neighbor regions contamination and two Gaussians that allowed to reproduce the light profile of the region of interest. In principle, any smooth, monotonic light profile can be approximated by a serie of Gaussians (somewhat analogous to the Fourier series), not only the PSF of an image, but also the light profiles of remote stellar clusters or galactic cores (see Bendinelli et al. 1990). Two Gaussians are employed in order to reproduce the light profile of these regions because the use of a larger number of components led in some cases to solutions with no physical meaning.

Then, the best fit for the initial light profile using the minimization subroutine AMOEBA is obtained. The AMOEBA subroutine needs an initial set of solutions which can be defined by the 8 parameters of the function to minimize (3 for each Gaussian and 2 for the line). These parameters were introduced interactively marking the approximate position of the center and FWHM for each Gaussian and two extreme values in the profile for the line. In Fig. 9 we show an example of the positions of the points used to define the set of initial parameters for the fit. Points 1, 2, 3 and 4, 5, 6 led to the initial parameters for the two Gaussians and points 7, 8 for the line. Using this set of parameters, (3) the best-fitting light profile is obtained (see Fig. 9).

Then, from the output of this fit and introducing the new positions of the two Gaussian maxima, (4) all the x axis profiles are fitted starting from those profiles adjacent to the initial one. The need of using previous results for the subsequent fits constitutes the main reason for starting this fitting procedure at the maximum of the emission region.

Next, (5) the same fitting procedure is applied to the y axis profiles. Finally, after the profiles have been fitted in both axis, the underlying emission images reconstructed are averaged and subtracted from the original input image (see several examples in Fig. 10). This background-free image is then used to determine the centers, apertures, sizes and integrated fluxes of the different regions.

   
A.2. Position, sizes and fluxes

The knot center is taken as the maximum of the sum of the two Gaussian components. Then, computing the knot surface, A_x, above different thresholds, I_x, we can estimate the equivalent knot e-folding radius, $R_{\rm {e-folding}}$, using,

$$R_{\mathrm{e-folding}}=\sqrt{\frac{A_{x}}{\pi \ln (\frac{I_{\mathrm{max}}}{I_{{x}}})}}$$ (1)

where I_max is the knot maximum intensity. In Fig. 11 we show the change in the area A_x for different thresholds as measured in the background subtracted image of the star-forming region #18 (with 1 e-folding radius of 0 $.\!\!^{\prime\prime}$93). The relatively small change deduced for the e-folding radius with the threshold guarantees the goodness of this size determination procedure.

The e² and e³-folding radii are then computed as $\sqrt{2}$and $\sqrt{3}$ times the e-folding radius. Then, the knot contours are derived at these three radii, i.e. at I_max/I_x = e, e², e³. The knot total flux is computed as the total flux in the background subtracted image. In order to ensure that most of the knot flux was included we derive the knot growing-curve, finding differences not larger than 20 per cent between total and growing-curve extrapolated flux.

Figure 8: Change in the area (Ax) of the region #18 with the threshold, Ix. The solid-line represents the result expected for a radius of 0 $.\!\!^{\prime\prime}$9 at 1 e-folding. The dashed-lines correspond to 0 $.\!\!^{\prime\prime}$8 and 1 $.\!\!^{\prime\prime}$0 e-folding radii

Acknowledgements

Based on observations at the Jacobus Kapteyn, Isaac Newton and Willian Herschel telescopes operated on the island of La Palma by the Royal Greenwich Observatory in the Spanish Observatorio del Roque de los Muchachos of the Instituto Astrofísico de Canarias and from International Ultraviolet Explorer archive at the ESA VILSPA observatory. Based also on observations collected at the German-Spanish Astronomical Center, Calar Alto, Spain, operated by the Max-Planck-Institut für Astronomie (MPIA), Heidelberg, jointly with the spanish "Comisión Nacional de Astronomía". We are grateful to Carme Jordi and D. Galadí for obtaining the V-band image. We would like to thank C. Sánchez Contreras and L.F. Miranda for obtaining the high resolution spectra, N. Cardiel for providing the REDUCEME package and C.E. García Dabó for the PLATEASTROM routine. We also thank A. Alonso-Herrero for her help in the acquisition and reduction of the nIR images. We also acknowledge Dr. Tosi for several helpful comments. Finally, we thank to C.E. García Dabó and J. Cenarro for stimulating conversations, and M. Sharina for providing a reprint copy of her article. This research has been supported in part by the grants PB93-456 and PB96-0610 from the Spanish "Programa Sectorial de Promoción del Conocimiento". A. Gil de Paz acknowledges the receipt of a "Formación del Profesorado Universitario" fellowship from the spanish "Ministerio de Educación y Cultura".