2 Photometry of $\alpha$ images, selection of candidates

We have used H$\alpha$ photographs (contact copies) obtained by Courtes et al. (1987) on the 6 m telescope with a focal reducer f/1. The H$\alpha$ band had a width FWHM=35 Å, the contribution of the nitrogen lines [NII] $\lambda$6548,6584 is estimated as less than 10%. The scale of the images is $34\hbox{$.\!\!^{\prime\prime}$ }5/$mm, the angular resolution is about $1{}^{\prime\prime}$. All the images were digitized with a square diaphragm of 20 $\mu$m and a step of 20 $\mu$m (one pixel $=\,0\hbox{$.\!\!^{\prime\prime}$ }68$).

We made a search for all blue stars on the H$\alpha$images, using their accurate coordinates. Even with the finding chart taken from B band images (IFM) being available, it is far from being always possible to identify H$\alpha$ objects, because of the dominant contribution of nebula and the strong and nonuniform H$\alpha$ background. We used the coordinate grid (Fabrika & Sholukhova 1995) whose accuracy is $0\hbox{$.\!\!^{\prime\prime}$ }3$. From stars and objects, which are positively identified for certain, the coordinate grid was transferred to the H$\alpha$ images. The accuracy achieved was about $1{}^{\prime\prime}$, which is better than that of the original catalogue (IFM) equal to $1\hbox{$.\!\!^{\prime\prime}$ }5$. All the catalogue star positions were plotted on the H$\alpha$ images with a three-fold error boxes ( $\pm 4\hbox{$.\!\!^{\prime\prime}$ }5$). The objects that fell against a very strong background were not considered. We could make the H$\alpha$ photometry for 1619 out of 2332 cataloque stars. From our estimates, the limiting stellar magnitude of a reliably measured OB star, which has no intrinsic H$\alpha$ emission and is located in the outlying parts of the galaxy, is V=18.5-19.0.

The photometry was performed with the program package developed by V.V. Vlasyuk (personal communication). The objects selected were measured with square diaphragms whose size was increased from 3 to 30 pixels with a step of 2 pixels ( $1\hbox{$.\!\!^{\prime\prime}$ }36$). The integral density in the diaphragm and background density along the diaphragm's perimeter were measured. For the following study we used density D, which is equal to the difference between total density inside chosen diaphragm and background density (average background per pixel multiplied by the diaphragm area). The object size (FWHM) was found in the following way. The level of half-intensity with subtracted background was found, and then the area at this level was put equal to an area of a circle with a diameter FWHM. Besides that, for the sake of inspection, the size was also determined through a fitting of an object profile with the Gaussian in two orthogonal sections. Hereafter we will call the density as a flux F, which is measured in our relative units. As a rule, with a diaphragm size increasing both the integral flux and the object size grow, then these values get a plateau. The ordinate of the plateau is just a measured quantity. The dependence of relative flux error $\sigma(F)/F$ on the flux shows that for faint objects the error does not exceed 10%, for the main body of the objects it does not exceed 5%. The size error is less than 30$\%$ at FWHM $\approx$ $2{}^{\prime\prime}$, less than 20$\%$ at $3{}^{\prime\prime}$ and below 5$\%$ at size greater than 5 ${}^{\prime\prime}$. We also tested a possible influence of an object position in the image (the edge effect) on the size measured accuracy. This could readily be done since the images were obtained (Courtes et al. 1987) with an overlap of 2'-3'. Analysis has shown that the change in the size of a star, as dependent on its position in the image, is well under the size measurement accuracy. To diminish the personal error, any procedure described in this paper has been performed by a single person. For more detail description of the photometry see Fabrika et al. (1997).

Quite an essential point of our work is that we measured not the intensities but the densities. The measured flux (density) may be related to the intensity in a complicated fashion through two characteristic curves, original and copy. This fact does not have any effect on the selection of the stars having H$\alpha$ line flux excess over the stars of the same V magnitude and in the same image, which is the principal result of the work. The relationship between the flux and intensity may be both linear, F$\propto$I and logarithmic, F $\propto \lg$I, depending on which part of the effective characteristic curve we work. The former is the most likely case since we measure very faint objects, therefore it is quite possible that we are working in the region of underexposures.

In Fig.1 a relationship between flux F and magnitude V is presented for 148 stars of the eastern part of M33 (image N6 from Courtes et al. 1987). In this plot one sees distinctly the basic sequence of the stars without emission (filled circles) having no H$\alpha$ excess. The sequence reflects the fact that the stars that are brighter in V band are brighter in the H$\alpha$ band. In our case the flux in the H$\alpha$ band will depend on magnitude V as ${F=a\,10^{-(0.4\,m_V)}}$, if the stars are on the lower ("nonlinear'') part of the effective characteristic curve, and as ${ F=b-c\,0.4\,m_V}$ or ${ F\propto \lg I}$, if the stars are on the logarithmic ("linear'') part of the curve. Approximations have shown that the first relation is valid. The exponential function satisfies the location of stars on the basic nonemission sequence much better than the linear. This means that we are working in the region of underexposures on the effective characteristic curve, where F$\propto$I. However, as we have already noted, the result of the selection of stars that have excess in H$\alpha$ (open circles) does not depend on this dilemma.

Figure 1: H$\alpha$ line flux F versus V magnitude for 148 measured stars of the image No.6 of the eastern part of M33. The stars selected by the criterion of flux excess are shown by open circles, the stars that comprise the basic sequence of nonemission stars -- by filled circles

The selection of candidates was performed in the following manner. In the intervals ${ \bigtriangleup m_V=0.5}$, the mean H$\alpha$ flux value and its standard deviation were found. The stars, whose flux was greater than the mean flux over 2$\sigma$, were rejected. The remaining objects have been fitted with the curve ${F=a\,10^{-(0.4\,m_V)}}$, and the stars with a deviation greater than 2$\sigma$ were rejected, then the fitting was repeated. The described procedure converged after 2-3 iterations. The "cleaned'' basic sequence of the nonemission stars ${ F_{\rm b}(m_V)}$and its rms deviation ${\sigma_{\rm b}(F)}$ were thus obtained. Then stars from the original data whose flux departed from it upwards by a value greater than 2 ${\sigma_{\rm b}(F)}$ were isolated. Application of this procedure distorts a little the basic sequence statistics. Nevertheless we used it because the procedure converges very well, and the final selection criterion is rather arbitrary. This criterion, S $\ge 2$, where ${ S=(F-F_{\rm b})/\sigma{\rm _b}}$, is a "soft'' enough, and it has been chosen in order to not miss possible interesting stars with a weak H$\alpha$ emission. The selected stars are the objects sought with a flux excess in the H$\alpha$ over OB stars without emission by a value higher than 2 $\sigma_{\rm b}$ of the basic sequence scatter. The same methods were applied for all the images from Courtes et al. (1987). All in all 549 objects were selected as a result of the ${\rm H}\alpha$ photometry of 1619 blue stars from IFM.