4 Discussion

4.1 The H$\alpha$ luminosity function

The H$\alpha$ luminosity functions were computed separately for the two clusters under study from the measured fluxes. H₀ = 50 km s^-1 Mpc^-1 is assumed to allow a direct comparison with Gallego et al. (1995).

H$\alpha$ fluxes were corrected for [N II] contamination and dust extinction. The first correction is the one proposed by Gavazzi et al. (2002, in prep.), based on the relationship found between the H band luminosities and the [N II]/H$\alpha$ ratio. After a empirical relationship between the H and r' magnitudes for the galaxies in common in both samples the correction was finally given by:

$$\log [\mbox{N{\sc ii}}]/\mbox{H}\alpha = 1.26 - 0.19 \times r' + 0.70 \times \log D$$ (3)

D being the distance of the galaxies in Mpc.

The morphological type dependent dust extinction correction was taken from Boselli et al. (2001). For galaxies with known morphological type (from NED or other sources), the correction was taken to be

$$\begin{array}{ll} A(\mbox{H}\alpha) = & \mbox{1.1 mag, for ty... ...r} \\ & \mbox{0.6 mag, for type Sd or later}. \\ \end{array}$$

For unclassified galaxies we adopted M_B = -18.25 as the statistical limiting magnitude for galaxy types intermediate between Scd and Sd, from Sandage et al. (1985).

Figure 5: Distributions of the radial velocities of the galaxies in Abell 1367 (upper plot) and Coma (lower plot). The velocity distributions of the clusters assumed Gaussians are plotted with dashed lines. The shaded regions correspond to the range of velocities not covered because of the low transmitance of the filter. Only galaxies with known redshift were included in the plots.

The contribution of active nuclei to the H$\alpha$ detections is negligible because no relevant point-like nuclear features were detected in the H$\alpha$ frames.

In order to normalize the luminosity function to a proper volume, angular radii of 3 and 4 degrees were assumed for Abell 1367 and Coma respectively (Gavazzi et al. 1995), corresponding to linear sizes of 4.6 and 6.5 Mpc. The clusters were assumed spherically symmetric, thus the surveyed volume corresponds to the intersection between the solid angle covered by our observations and the sphere containing the clusters.

A statistical correction was applied to account for the incomplete velocity coverage of the adopted [S II] filter. Figure 5 shows the flux distribution of galaxies with known redshift versus their radial velocities. The dashed line represents the Gaussian distributions of velocities described in Sect. 2. The shaded regions correspond to the velocity ranges excluded from the filter transmitance window for each cluster. We estimate that about 20% of the velocity distribution for Abell 1367 and 11% for Coma are not within the transmitance window of the narrow band filter. We also corrected in a consistent way the effects of the velocity distribution of the H$\alpha$ emitting galaxies with unknown redshift. The correction was performed as follows: first, we randomly distributed the velocities of these galaxies following the Gaussian probability density function with mean velocities and dispersions as described in Sect. 2. New H$\alpha$ fluxes were derived for these galaxies, according to the values of the transmitance of the [S II] filter, for the randomly chosen velocities. If the assigned velocity of any of these galaxies gave a transmitance <50%, the object was discarded. The final correction was performed by assuming that the relationship, if any, between the radial velocities of the galaxies and the H$\alpha$ fluxes should be symmetric with respect to the mean velocity of the cluster. We repeated this procedure ten times in order to estimate the statistical uncertainties induced by this effect on the luminosity function. Thus, H$\alpha$ luminosity functions were computed with ten different flux distributions for each cluster.

The functional form assumed for the LF is the Schechter (1976) function:

$$\phi(L){\rm d}L = \phi^{*}(L/L^{*})^{\alpha}\mbox{exp}(-L/L^{*}){\rm d}(L/L^{*}).$$ (4)

The size of the bins was taken to be $\delta\log L = 1.0$ in order to minimize the statistical errors. Table 2 shows the number counts per luminosity interval for both clusters, averaged over the different random distributions of velocities for the galaxies with unknown redshift.

Table 3 lists the obtained best fitting Schechter parameters of the upper and lower envelopes for each cluster, as well as the parameters for the average LFs finally adopted.

The upper and lower envelope H$\alpha$LFs of the two clusters are given in Fig. 6. Shaded regions between the envelopes show the range of uncertainty of the H$\alpha$ LF for each cluster. The points correspond to the mean values listed in Table 2, and the error bars show their typical poissonian uncertainties. As reference, we plot the H$\alpha$ LFs of field galaxies obtained by Gallego et al. (1995), Tresse & Maddox (1998) and Sullivan et al. (2000). The lines are truncated at the completeness limits of each sample.

 

 

Table 2: Counts per luminosity bin.

$\log L(\mbox{H}\alpha)$	Av. Number of gal.
erg s-1	Abell 1367	Coma
38.8	8	2
39.8	18	11
40.8	13	8
41.8	1	1

 

 

Table 3: Best fitting parameters for the upper and lower envelopes corresponding to Abell 1367 and Coma. Also, the average adopted parameters for the H$\alpha$ LF are listed.

	$\log \phi^{*}$	$\alpha$	$\log L^{*}$
	Mpc-3		erg s-1
Abell 1367
Upper envelope	-0.06	-0.94	41.37
Lower envelope	+0.20	-0.72	41.21
Average	+0.06	-0.82	41.30
Coma
Upper envelope	-0.09	-0.70	41.24
Lower envelope	-0.04	-0.53	41.21
Average	-0.07	-0.60	41.23

Disregarding non-completeness effects, which should only affect our lowest luminosity bins, the LFs of the two clusters are in fair agreement. The apparent difference with the field LFs is mainly in the normalization since the density of galaxies is several orders of magnitude larger in clusters than in the field. Beside the normalization, the shape of the cluster LFs appears steeper at the bright end and flatter at the faint end. The former derives from undersampling at high luminosity (due to small volume coverage in the two clusters we do not detect any object with $F(H\alpha) \geq 10^{42}$ erg s^-1 as opposed to Gallego et al. 1996).

The slope of the fitted LFs appear different among clusters and field at the faint end. However the data points, within the completeness limits of each survey, appear in full agreement among each other, as shown in Fig. 7.

Figure 6: H$\alpha$ luminosity functions for Abell 1367 (diamonds) and for Coma (asterisks). The best fittings to Schechter functions are shown together with those found for the local Universe (Gallego et al. 1995), for $z \approx 0.2$ (Tresse et al. 1998) and for a sample of UV selected galaxies (Sullivan et al. 2000). The shaded regions show the uncertainty region between the lower and upper envelopes.

 

 

Table 4: Some properties of the selected H$\alpha$ emitting galaxies in Abell 1367.

Name	CGCG	Other	RA	Dec.	$v_{\rm r}$	r'	$F_{\alpha}$	$\Delta_{\rm f}$	$W_{\alpha}$	$\Delta_{\scriptsize {\mbox{W}}}$
114024+195747	--	--	11 40 24.90	+19 57 47.7	6749	15.48	-13.71	0.04	14	1
114038+195437	--	--	11 40 38.96	+19 54 37.4	6500 $\dagger\dagger$	17.35	-14.09	0.05	36	3
114107+200251	--	--	11 41 07.79	+20 02 51.3	6500$\dagger$	18.91	-14.60	0.05	43	4
114110+201117	--	--	11 41 10.47	+20 11 17.7	6500$\dagger$	17.57	-13.95	0.04	56	2
114112+200109	--	--	11 41 12.81	+20 01 09.9	6500$\dagger$	19.44	-14.80	0.07	38	5
114141+200230	--	--	11 41 41.20	+20 02 30.5	6500$\dagger$	17.37	-14.26	0.06	26	4
114142+200054	--	--	11 41 42.57	+20 00 54.9	6500$\dagger$	17.33	-14.36	0.07	19	3
114149+194605	--	--	11 41 49.79	+19 46 05.1	6500$\dagger$	17.52	-14.37	0.05	23	2
114156+194207	--	--	11 41 56.69	+19 42 07.8	6500$\dagger$	19.77	-15.10	0.07	36	5
114157+194329	--	--	11 41 57.90	+19 43 29.4	6500$\dagger$	20.21	-15.29	0.05	34	3
114158+194149	--	--	11 41 58.05	+19 41 49.6	6500$\dagger$	19.46	-15.02	0.06	38	4
114158+194205	--	--	11 41 58.10	+19 42 05.9	6500$\dagger$	20.30	-15.27	0.04	49	2
114158+194900	--	--	11 41 58.26	+19 49 00.9	6500$\dagger$	20.70	-15.53	0.07	32	4
114202+194348	--	--	11 42 02.30	+19 43 48.5	6500$\dagger$	20.83	-15.35	0.05	70	6
114202+192648	--	--	11 42 02.96	+19 26 48.2	6500$\dagger$	19.54	-14.66	0.06	32	4
114214+195833	097-062	PGC 036330	11 42 14.55	+19 58 33.6	7815	14.51	-13.19	0.04	28	1
114215+200255	097-063	PGC 036323	11 42 15.70	+20 02 55.2	6102	15.36	-13.69	0.04	13	1
114218+195016	--	--	11 42 18.08	+19 50 16.1	6476	15.79	-14.24	0.04	6	1
114239+195808	--	--	11 42 39.23	+19 58 08.0	7345	16.95	-13.89	0.04	40	1
114240+195716	--	--	11 42 40.36	+19 57 16.6	6500$\dagger$	17.68	-14.70	0.08	13	2
114256+195757	097-073	PGC 036382	11 42 56.67	+19 57 57.7	7275	15.50	-12.81	0.04	86	1
114313+193645	--	--	11 43 13.08	+19 36 45.8	6500 $\dagger\dagger$	17.27	-14.06	0.05	30	3
114313+200015	097-079	PGC 036406	11 43 13.93	+20 00 15.6	7000	16.50	-12.69	0.04	130	2
114341+200135	--	--	11 43 41.62	+20 01 35.3	6500$\dagger$	17.08	-14.15	0.06	25	3
114348+195812	097-087	UGC 06697	11 43 48.59	+19 58 12.8	6725	14.22	-12.19	0.04	81	2
114348+201456	--	--	11 43 48.92	+20 14 56.0	6146	15.86	-12.95	0.04	137	1
114349+195833	--	--	11 43 49.87	+19 58 33.2	7542	16.11	-13.99	0.04	19	2
114355+192743	--	--	11 43 55.71	+19 27 43.9	6500$\dagger$	18.72	-14.67	0.07	27	4
114358+201105	097-092	PGC 036478	11 43 58.17	+20 11 05.6	6373	14.71	-13.10	0.04	30	1
114358+200433	097-091	NGC 3840	11 43 58.81	+20 04 33.0	7368	13.92	-12.86	0.07	25	4
114400+200144	097-097	NGC3844	11 44 00.86	+20 01 44.5	6834	13.62	-13.41	0.04	5	1
114430+195718	--	--	11 44 30.41	+19 57 18.8	6500$\dagger$	20.23	-14.38	0.04	418	19
114447+194624	097-114	NGC 3860B	11 44 47.88	+19 46 24.6	8293	15.33	-13.24	0.05	40	4
114454+194733	--	--	11 44 54.22	+19 47 33.2	6500 $\dagger\dagger$	20.27	-13.99	0.06	103	17
114454+194635	097-125	PGC 036589	11 44 54.99	+19 46 35.8	8271	14.50	-13.00	0.05	24	2
114454+200101	--	--	11 44 54.71	+20 01 01.5	6500 $\dagger\dagger$	16.17	-14.41	0.04	6	1
114503+195002	--	--	11 45 03.38	+19 50 02.7	6500$\dagger$	17.90	-14.76	0.07	9	1
114506+195801	097-129E	NGC 3861B	11 45 06.91	+19 58 01.6	6009	14.64	-13.38	0.06	19	2
114513+194523	--	--	11 45 13.86	+19 45 23.0	6500 $\dagger\dagger$	15.60	-13.86	0.04	12	1
114518+200009	--	--	11 45 18.00	+20 00 09.5	6500$\dagger$	17.54	-14.28	0.06	22	3
114603+194712	097-143B	--	11 46 03.68	+19 47 12.9	7170	15.80	-14.93	0.05	1	1

$\dagger$

Objects with unknown redshift but detected in the net H$\alpha$frames

$\dagger\dagger$

Objects for which we have measured the redshift. It will appear in a subsequent paper.

   

Table 5: Some properties of the selected H$\alpha$ emitting galaxies in Coma.

Name	CGCG	Other	RA	Dec.	$v_{\rm r}$	r'	$F_{\alpha}$	$\Delta_{\rm f}$	$W_{\alpha}$	$\Delta_{\scriptsize {\mbox{W}}}$
125757+280343	--	FOCA610	12 57 57.73	+28 03 43.3	8299	15.23	-13.37	0.05	22	2
125805+281433	160-055	NGC4848	12 58 05.67	+28 14 33.2	7049	14.04	-12.54	0.05	34	2
125845+284133	--	FOCA353	12 58 45.64	+28 41 33.1	7001 $\dagger\dagger$	17.21	-14.02	0.06	35	5
125845+283235	--	FOCA399	12 58 45.80	+28 32 35.3	7001$\dagger$	17.76	-13.83	0.04	101	4
125856+275002	160-212	FOCA600	12 58 56.55	+27 50 2.7	7378	15.12	-13.84	0.05	3	1
125902+280656	160-213	FOCA498	12 59 02.14	+28 06 56.4	9436	15.15	-13.32	0.06	28	3
125907+275118	160-219	IC3960	12 59 07.97	+27 51 18.0	6650	14.50	-14.12	0.05	2	1
125923+282919	--	FOCA361	12 59 23.13	+28 29 19.0	7001 $\dagger\dagger$	15.75	-13.98	0.04	10	1
130006+281500	--	FOCA371	13 00 06.42	+28 15 0.9	7259	17.04	-14.48	0.07	6	1
130037+280327	160-252	FOCA388	13 00 37.99	+28 03 27.6	7840	14.68	-12.93	0.08	41	4
130037+283951	--	--	13 00 37.24	+28 39 51.6	7001 $\dagger\dagger$	16.86	-14.64	0.05	6	2
130040+283113	--	FOCA242	13 00 40.75	+28 31 13.4	8901	15.80	-13.11	0.05	68	6
130056+274727	160-260	FOCA445	13 00 56.03	+27 47 27.7	7985	13.11	-12.76	0.07	11	2
130114+283118	--	FOCA195	13 01 14.99	+28 31 18.5	8426	17.02	-14.04	0.05	29	3
130125+284036	160-098	FOCA137	13 01 25.04	+28 40 36.9	8762	14.41	-13.21	0.04	18	1
130127+275957	--	GMP2048	13 01 27.17	+27 59 57.0	7558	15.64	-14.35	0.04	4	1
130128+281515	--	--	13 01 28.63	+28 15 15.9	7001$\dagger$	20.41	-14.96	0.04	107	6
130130+283328	--	FOCA158	13 01 30.85	+28 33 28.0	7001 $\dagger\dagger$	16.76	-13.95	0.06	24	2
130140+281456	--	GMP1925	13 01 40.97	+28 14 56.6	7001$\dagger$	19.33	-14.43	0.07	132	36
130158+282114	--	--	13 01 58.43	+28 21 14.8	7001$\dagger$	19.81	-14.39	0.04	278	8
130212+281023	--	FOCA218	13 02 12.00	+28 10 23.0	8950	16.09	-13.41	0.05	30	2
130212+281253	160-108	FOCA204	13 02 12.55	+28 12 53.0	8177	14.93	-13.29	0.04	25	1

 

 

Table 6: Comparison of the H$\alpha$ fluxes and equivalent widths with data from the literature, for the objects in common.

CGCG	This work		M88 $^{{\rm a}}$		M98 $^{{\rm b}}$		K84 $^{{\rm c}}$		G91 $^{{\rm d}}$		G98 $^{{\rm e}}$
	$\log F$	EW	$\log F$	EW	$\log F$	EW	$\log F$	EW	$\log F$	EW	$\log F$	EW
097-062	-13.19	28	-	-	-12.93	58	-13.10	45	-	-	-	34
097-073	-12.81	86	-12.84	-	--	--	-12.84	80	-	-	-12.76	108
											-12.75	94
097-079	-12.69	130	-12.54	--	--	--	-12.64	145	-12.64	131	-12.66	137
097-087	-12.19	81	-12.22	64	-12.43	84	-12.19	61	-	-	-12.22	74
097-092	-13.10	30	-13.06	-	-12.95	30	-	-	-	-	-	27
097-091	-12.86	25	-12.92	17	-12.86	21	-12.74	23	-	-	-	-
097-114	-13.24	40	-12.82	79:	-12.82	60	-13.20	4	-	-	-	48
097-125	-13.00	24	-13.13	29	-13.04	26	-	-	-	-	-	21
097-129E	-13.38	19	-	-	-	-	-	-	-	-	-13.38	18
160-252	-12.93	41	-	-	-	-	-12.93	35	-	-	-	-
160-055	-12.54	34	-	-	-	-	-12.65	23	-	-	-12.51	34
160-260	-12.76	11	-	-	-	-	-	-	-	-	-13.03	8
160-098	-13.21	18	-	-	-	-	-	-	-	-	-13.15	20

$^{{\rm a}}$

Moss et al. (1988).

$^{{\rm b}}$

Moss et al. (1998).

$^{{\rm c}}$

Kennicutt et al. (1984).

$^{{\rm d}}$

Gavazzi et al. (1991).

$^{{\rm e}}$

Gavazzi et al. (1998).

In this figure we scaled the cluster LFs in such a way that they match the field LF at $\log L(\mbox{H}\alpha) \approx 41$ erg s^-1. Above $\log L(\mbox{H}\alpha)\approx 40$ erg s^-1, where all the samples are complete, there is consistency between the field and the cluster datasets. Nothing can be said for fainter luminosities because the field samples are incomplete or present rather poor statistics, opposite to the present cluster survey which is complete to $\log L(\mbox{H}\alpha) \approx 39$ erg s^-1. Deeper H$\alpha$surveys of the field are necessary to assess if the differences at the faint luminosity end are significant.

4.2 The Virgo cluster

It is instructive to compare the H$\alpha$ LF of A1367 and Coma with that of the Virgo cluster. Given its large angular size, performing a complete H$\alpha$ survey of this cluster would be prohibitive. However H$\alpha$ observations of most of the brightest galaxies (230 objects brighter than B=16 mag) are available (Boselli & Gavazzi 2002; Gavazzi et al. 2002). Using these data we construct a "pseudo'' H$\alpha$ LF by transforming the B band LF into an H$\alpha$ one after having shown that H$\alpha$ luminosity and M_B are found proportional one-another.

Figure 8 shows the H$\alpha$ luminosity vs. the absolute M_Bmagnitude relationship. Distances are estimated according to the Virgo cluster group membership, as defined in Gavazzi & Boselli (1999). The best fit to the data gives a slope of 0.37, consistent with 0.40 (i.e. a slope of 1 in a luminosity-luminosity plot). For simplicity we adopted this last value, because it allows to transform the observed B band Schechter function into an H$\alpha$ LF of the same functional form. Therefore we adopt:

$$\log L(\mbox{H}\alpha) = -0.40 \times M_{B} + 33.12.$$ (5)

Combining this relationship with the B band luminosity function for spirals and irregulars in the Virgo core obtained by Sandage et al. (1985) we obtain an H$\alpha$ LF:

$$\phi'(L) = 1.07 \times (L/10^{41.2})^{-0.8}~\mbox{exp}[-(L/10^{41.2})].$$ (6)

Figure 9 shows the Virgo H$\alpha$ LF together with the ones obtained for Abell 1367 and Coma. The shaded region reflects the scatter in the relationship between H$\alpha$ luminosities and M_B found in Virgo. The shape of the Virgo LF appears consistent with that of Abell 1367 and Coma, despite the different nature of the three clusters, Virgo being unrelaxed and spiral rich, Abell 1367 relaxed and spiral rich, and Coma relaxed and spiral poor.

4.3 Star formation rates in clusters

The total star formation rate per unit volume for clusters is derived by integrating the best fitting Schechter functions over the whole range of luminosities. To be consistent with Gallego et al. (1995), we convert the H$\alpha$luminosities to star formation per unit time using:

$$L(\mbox{H}\alpha) = 9.40 \times 10^{40} \frac{SFR}{M_{\odot}~\mbox{yr}^{-1}}\mbox{erg~s}^{-1}.$$ (7)

Total integrated SFRs of 2.20 and 1.36 $M_{\odot}$ yr^-1 Mpc^-3 are obtained for Abell 1367 and Coma respectively, i.e. more than two orders of magnitude higher than the value of 0.013 $M_{\odot}$ yr^-1 Mpc^-3 reported for the local Universe by Gallego et al. (1995).

Figure 7: Galaxy number density per unit volume vs. the H$\alpha$ luminosity for the clusters and for the different field samples. The cluster counts have been normalized to properly match the field counts.

The estimate of the contribution of the clusters to the total SFR per unit volume of the local Universe, is obtained by taking into account the local spatial density of clusters. For Abell type 2 clusters, like Abell 1367 and Coma, this value was reported to be $1.84 \times 10^{-5}$ Mpc^-3 (Bramel et al. 2000), although this number is affected by large uncertainties. We conclude that the typical contribution of Abell type 2 clusters to the SFR per unit volume is about $3.3 \times 10^{-5}$ $M_{\odot}$ yr^-1, that is 0.25% of the total SFR in the local Universe.

Similarly, by integrating the Virgo H$\alpha$ luminosity function, we obtain a total H$\alpha$ luminosity density of $1.56 \times 10^{41}$ erg s^-1 Mpc^-3, which gives a SFR of 1.65 $M_{\odot}$ yr^-1 Mpc^-3. Taking into account that the Virgo cluster is classified as Abell type 1 (Struble & Rood 1982), and assuming the spatial density for clusters of this type (Bramel et al. 2000) of $8.46 \times 10^{-4}$ Mpc^-3, we obtain that the contribution of type 1 clusters is $1.40 \times 10^{-3}$ $M_{\odot}$ yr^-1 Mpc^-3, corresponding to 10.8% of the total SFRdensity in the local Universe.