6 The H$_\alpha$ emission of galaxies

6.1 Instrumental H$_\alpha$ fluxes

Following the data reduction steps described in Sect. 4, we have obtained 31 emission-line images, one for each HCG of our sample. We have computed both isophotal and adaptive-aperture H$_\alpha$ fluxes for the HCG galaxies in the 31 fields by using SExtractor (Bertin et al. 1996). The full analysis of each image is divided in six steps: sky background estimation, thresholding, deblending, filtering of the detections, photometry and star/galaxy separation. For each continuum-subtracted H$_\alpha$ image we have used a detection threshold of one sigma above the background. The H$_\alpha$ isophotal fluxes have been computed within the region defined by the detection threshold. In addition to the isophotal flux we have also considered the corrected isophotal flux estimated by SExtractor that should take into account the fraction of flux lost by the isophotal one (Bertin et al. 1996). In addition the adaptive-aperture photometry has also been calculated (Kron 1980; Bertin et al. 1996).

Out of the 127 accordant observed galaxies belonging to the 31 HCG of our sample, we have been able to compute isophotal and adaptive-aperture photometry for 73 and 69 galaxies respectively. The $1\sigma$ limiting flux, integrated within the mean seeing disk (2.3 arcsec), reached in our observations ranges between $1.43 \ 10^{-16}$ and $4.13 \ 10^{-17}$ erg cm^-2 s^-1.

For 22 galaxies, which have not been detected in our H$_\alpha$ images, we have computed the 3$\sigma$ upper limits above the background:

$$f_{\rm ul}= 3 \cdot {\rm rms} \cdot \left[\left(\frac{FWHM}{2} \right)^2 \cdot \pi \right]^{\frac{1}{2}}$$ (3)

being

$$\begin{array} {lp{0.6\linewidth}} {\rm rms} & the sky estima... ...}} & the squareroot of the seeing area in pixels.\\ \end{array}$$

For the remaining 32 galaxies we have not been able to estimate the H$_\alpha$ fluxes because of one of the following reasons:

1.

the night was not photometric ($\sigma_{Z_{\rm p}}\gg 0.05$ mag);

2.

the proper narrow band interference filter was not available;

3.

too much imperfections are present on the H$_\alpha$ image probably due to large variations in seeing conditions between the on and off band exposures, or due to changes in the telescope focus (e.g. because of substantially different thickness of the filters and/or temperature variations).

In Table 6 we list the galaxies for which it was not possible to measure their flux and the corresponding reason (1, 2, 3).

6.2 Zero point correction

In order to obtain calibrated fluxes and luminosities for our sample of galaxies, we have estimated the zero point flux correction, Z$_{\rm flux}$ such that  

$$f_{{\rm H}_\alpha}=(f_{\rm on}-f_{\rm off})=Z_{\rm flux} \cdot \left[C_{\rm on}-{C}_{{\rm off}} \right]$$ (4)

where:

$$\begin{array} {lp{0.7\linewidth}} f_{\rm on}, f_{\rm off} & ... ...laxy in the on and off band images respectively.\\ \end{array}$$

It can be proved that the $Z_{\rm flux}$ coefficient of each galaxy is proportional to $Z_{\rm flux_{\rm on}}$ i.e. the zero point flux correction of the on band image. Knowing the $Z_{\rm flux_{\rm on}}$ in magnitudes ($Z_{p_{\rm on}}$, see Sect. 5) and the extinction coefficient $k_{\rm on}$ of the site relative to each filter, we have derived the correction factor Z$_{\rm flux_{\rm on}}$ as follows:

$$Z_{\rm flux_{\rm on}}=\Delta\lambda \cdot 10^{-0.4(Z_{\rm p_{\rm on}}-(k_{\rm on} \cdot X_{\rm s})-b)}$$ (5)

where $X_{\rm s}$ is the airmass of the standard star and b is

$$b=2.5 \cdot \log_{10}f_{\lambda_{\rm eff}}(0).$$ (6)

Thus $Z_{\rm flux}$ is given by

$$Z_{\rm flux}=\frac{Z_{\rm flux_{\rm on}}} {10^{[-0.4(k_{\rm ... ...cdot X_{\rm s})]}} \cdot 10^{[0.4(k_{\rm on} \cdot X_{\rm g})]}$$ (7)

where $X_{\rm g}$ is the airmass of the target galaxy. This zero point correction was applied to the H$_\alpha$ instrumental fluxes and to the upper limits estimated for the undetected galaxies. Fluxes and upper limits have been also corrected so that the H$_\alpha$ emission-line of the galaxy passes exactly in the center of the corresponding on filter band, i.e. for the percentage of total flux lost if the H$_\alpha$ emission line of the galaxy does not pass exactly in the center of the corresponding on filter. The corrected fluxes are reported in Tables 7, 8 and 9.

 

Table 3: Features of interferometric filters: central wavelength, FWHM and corresponding velocity interval

 

Table 4: Standard stars used for calibration

 

Table 5: Journal of observations

 

Table 6: Galaxies without estimated flux (see Sect. 6.1)

 

Table 7: Isophotal fluxes and luminosities

 

Table 7: continued

 

Table 8: Isophotal corrected and kron fluxes

 

Table 9: Upper limit to flux and luminosity

 

Table 10: SFR of galaxies in the sample

6.3 Galactic and internal extinction correction

The H$_\alpha$ fluxes have been then corrected for the galactic extinction due to the gas and the dust of our Galaxy. For each target galaxy we have computed the relative galactic hydrogen column density $N_{\rm h}$ (atoms cm^-2) as a function of the galaxy coordinates (R.A. and Dec.). $N_{\rm h}$ was obtained interpolating the data available from the Stark et al. (1992) data-base. We computed also an interpolation error defined as the mean of differences weighted on the distances. Using the relations:

$$\frac{N_{\rm h}}{A_{B}-A_{V}}= \frac{N_{\rm h}}{E(B-V)}=5.2 \ 10^{21} \ {\rm atoms}\ {\rm cm}^{-2}\ {\rm mag}^{-1}$$ (8)

and:

$$R=\frac{A_{V}}{E(B-V)}= 3.1.$$ (9)

(Ryder & Dopita 1994) we have derived the visual extinction coefficients A_V and A_B (mag) for each galaxy. Following Ryder & Dopita (1994), we have obtained the multiplicative correction $\alpha_{\rm G}$ to apply to the H$_\alpha$ flux:

$$\alpha_{\rm G}= 10^{(0.4 \cdot A_{{\rm H}_{\alpha}})}= 10^{(0.4 \cdot 0.64A_{B})}$$ (10)

where $A_{{\rm H}_{\alpha}}$ is the H$_\alpha$ extinction coefficient in magnitudes. The isophotal fluxes corrected for Galactic Extinction are reported in Table 7. The minimum and maximum values obtained for $\alpha_G$ are respectively 1.04 and 2.68.

The H$_\alpha$ fluxes of spirals have also been corrected for the Internal Extinction due to the interstellar medium inside the target galaxy itself. This correction in the blue band is usually obtained by summing to the galaxy magnitude the value

$$A_i=c_B \cdot {\rm log} (r_i).$$ (11)

(Haynes & Giovanelli 1984) where:

$$\begin{array} {lp{0.9\linewidth}} c_B & is a morphological ... ...i & is the intrinsic axial ratio of the galaxy.\\ \end{array}$$

On the basis of the interstellar extinction curve (e.g. Osterbrook 1974) we have derived the H$_\alpha$ extinction correction term $c_{{\rm H}_\alpha}$using the following transformation:

$$c_B \cdot \log(r_i) \!-\! c_{{\rm H}_\alpha} \cdot \log(r... ... -2.5 \cdot \log(e_B) \!+\! 2.5 \cdot \log(e_{{\rm H}_\alpha})$$ (12)

where e_B and $e_{{\rm H}_\alpha}$ are the extinction values at the effective wavelength respectively of the B and the H$_\alpha$ filters. Finally we have obtained the flux correction factor $\alpha_i=10^{[0.4 \cdot c_{{\rm H}_\alpha} \cdot \log(r_i)]}$, to apply to our spiral galaxies. The minimum and maximum values obtained for $\alpha_i$ are respectively 1.1 and 1.6.

On the basis of the fluxes thus obtained we have derived the H$_\alpha$ luminosity L$_{{\rm H}_{\alpha}}$ of galaxies:

$$L_{{\rm H}_{\alpha}}=4\pi \cdot f_{{\rm H}_{\alpha}} \cdot d_{\rm L}^2$$ (13)

where the luminosity distance $d_{\rm L}$ is defined as:

$$d_{\rm L}=\frac{c}{H_0 \cdot q_{0}^2} \cdot \left(q_0 \cdot z+(q_0-1) \cdot [-1+(2q_0 \cdot z+1)^{\frac{1}{2}} \right).$$ (14)

We adopted $H_0=100~{\rm km~s}^{-1}{\rm Mpc}^{-1}$ and q₀=0.5.

In Table 7 we report the isophotal luminosities of the galaxies ($L_{\rm iso}(1)$)uncorrected for Galactic and Internal Extinction.