7 Statistical properties of the galaxies in the Perseus cluster

7.1 Distribution of the galaxies in the field  

 

Figure 3:  Distribution of catalogued galaxies on a Tautenburg Schmidt plate centred on $\alpha=3^{\rm h} 21^{\rm m} 10^{\rm s}$ and $\delta=41^{\circ}\,33'$(J2000). The gap in the upper right corner is due the calibration wedge. The size of the symbols indicates the brightness of the galaxies. (S=$\bigstar$, S?=$\star$, Irr=$\blacktriangle$, Irr?=$\vartriangle$,E=$\blacklozenge$, E?=$\lozenge$, S0=$\Large\bullet$, S0?=$\Large\circ$, unknown=?)

 

Figure 4:  As Fig.3, but only for S0 and elliptical galaxies. (E=$\blacklozenge$, E?=$\lozenge$, S0=$\Large\bullet$, S0?=$\Large\circ$)

 

Figure 5:  As Fig.3, but only for spiral and irregular galaxies. (S=$\bigstar$, S?=$\star$, Irr=$\blacktriangle$, Irr?=$\vartriangle$)

The distribution of all 660 catalogued galaxies is shown in Fig.3. Note that the northwest corner of the field is reserved for the calibration wedge, hence no objects are recorded there. The lack of galaxies to the northeast of the cluster centre has been already reported by KS83 and was explained there as due to a sharp increase in the foreground extinction. A second lack is indicated toward the southwest of the cluster centre. Indeed, the IRAS 100$\mu$m map (see Ettori et al. 1998, their Fig.7) clearly shows enhanced absorption in both of these regions. Because of the low Galactic latitude of the field, the foreground extinction is expected to be rather irregular and may pretend substructures in the cluster. Therefore, we are not inclined to study details in the projected galaxy distribution.

However, we have to explain the prominent clump of galaxies at $\alpha ({J}2000.0) = 3^{\rm h}20\hbox{$.\!\!^{\rm m}$}4$, $\delta ({J}2000.0) = 43\hbox{$^\circ$}4'$,(about $1\hbox{$.\!\!^\circ$}5$ north of the Perseus cluster centre), clearly seen in Fig.3. This structure has not been reported before; it is not obvious from the Zwicky sample discussed by KS83 and Andreon ([1994]). The strong concentration and the faint magnitudes of the galaxies of the clump (typically B > 17) point towards a background cluster. The brightest member (no. 335) has B₂₅ = 16.1 and is classified as E/S0? with several faint nearby objects within a common halo. It is identified with the radio source B3 0317+428. From the spectra obtained for this galaxy and two other members of the clump (no. 329 and 353), a redshift of $z=0.050\pm0.001$ has been derived (Sect.4.3), confirming that it is indeed a background cluster. Nevertheless, we do not explicitly exclude this cluster from our sample in the further analysis, because background contamination will be corrected statistically.

As is well known, the bright galaxies in the centre of A426 are aligned along a prominent chain. Such a chain is not clearly seen in the distribution of all catalogued galaxies, and a flattening of the cluster is only marginally indicated. This has been noticed already by KS83.

7.2 Background galaxies  

Contamination by background galaxies is difficult to quantify. From the distribution of radial velocities for 187 galaxies in A426, KS83 estimated maximum radial velocities for cluster members in dependence on the distance r from the centre. We adopt this relation to discriminate between members and non-members. Unfortunately, radial velocities are available only for about 25% of the catalogued galaxies. Under the assumption that this subsample is not strongly biased towards cluster members we expect about 3, 10, and 27 background galaxies for limiting magnitudes $B_{\rm lim}=16, 17$, and 18, respectively. This, however, is presumably an underestimation of the true background contamination, since most galaxies have been measured in the inner region (r<30'), where both the fraction of cluster galaxies and the velocity dispersion are very large. KS83 argued that nearly all of the galaxies to a limiting magnitude V =17.5 in the central region belong to the cluster.

For an independent estimate of the number of background galaxies we use the number-magnitude relation for field galaxies quoted by Binggeli et al. (1988) along with an adopted mean extinction of A_B=0.8 toward A426 (KS83):  

$$\log_{10} N_B(B)=0.6 B-9.79,$$ (2)

where N_B(B) designates the number of background galaxies brighter than B per square degree. For galaxies with a mean colour index $(B-V)_0\approx 0.7$ this relation is in agreement with the galaxy background densities adopted for A426 by KS83. As emphasised by KS83, these estimates have to be regarded as quite uncertain.

From the comparison of Eq. (2) with the luminosity function of all galaxies (Fig.12), we conclude that background contamination should be negligible for B₂₅<17, but becomes significant for B₂₅>18. This seems to be indicated also by the radial profile of the galaxy number density: if the number density of background galaxies was significantly underestimated by Eq. (2), the background-corrected profiles are expected to become shallower at large r. This is, however, not observed, at least for galaxies with B₂₅<17 (Fig. 7).

For the following statistical investigations we will, therefore, consider either the subsample of galaxies with B₂₅<17.5 or both the galaxies with B₂₅<17 and those with B₂₅<18 for comparison.

7.3 The optical centre of the Perseus cluster  

A426 belongs to the clusters presenting an offset between the optical centre and the X-ray centre. Such offsets may be the signature of a recent merger (Ulmer et al. 1992). Moreover, the choice of the cluster centre is crucial to the determination of the central density profile (Beers & Tonry 1986; see also next subsection). In the context of the present work, a complete discussion of the topic can not be presented, we refer the reader to Ulmer et al. (1992), Casertano & Hut (1985) and Beers & Tonry (1986).

Following Ulmer et al. (1992), we determine both the density centre and the luminosity centre. In both cases, increased weight is given to the (mainly brighter) galaxies in the core, and reduced weight to isolated (mainly fainter) outliers, especially randomly distributed background galaxies. The estimates are, however, to a certain degree sensitive to substructures in the projected galaxy distribution.

The density centre is derived from the density-weighted mean of all galaxy positions within a circular area of radius r centred on NGC1275. This reference point has been used since (a) it is obviously located near the centre of the dense central region (see Fig.3; cf. also KS83), and (b) its position almost exactly coincidences with the peak of the X-ray emission of the cluster (Ulmer et al. 1992). Each galaxy position is weighted by its inverse projected distance to its Nth nearest neighbour, which is a measure of the local density of galaxies. We set N=6 because the weights do not significantly change with N for $N\ge5$. To reduce the influence of background galaxies, all galaxies fainter than 18 have been excluded from the calculation. We have repeated the calculations considering only the galaxies brighter than 17. In addition, the weights have been corrected for an assumed constant background galaxy density $N(B_{25}\le18)=10.2$galdeg^-2, and $N(B_{25}\le17)=2.57$galdeg^-2, respectively (Eq.2). For the calculation of the luminosity centre the B-luminosities are used as weights. No corrections for background galaxies have been applied since they are negligible.

We calculate the centre positions for radii $r=1\ldots70'$ in steps of 1' and trace the resulting shifts of the centre. The wandering of the differently calculated centres is shown in Fig.6.

 

Figure 6:  Wandering of the deduced optical centre of the Perseus cluster. Shown is the traced position of the cluster centre as derived from the intensity- or density-weighted positions of the galaxies within a certain distance r from NGC1275 (marked by $\bigstar$). The distance r varies from 1' to 70' in steps of 1'. Solid line: trace of the luminosity centre of all galaxies, dashed lines: trace of the density centre of all galaxies with $B_{25}\le18$ (short dashes), and $B_{25}\le17$ (long dashes), respectively, both corrected for a constant background galaxy contamination. The positions of the centres at r=20',40', and 60' are marked by small open circles, filled circles, and triangles, respectively. Cluster centre positions given by Ulmer et al. (1992) are also marked ($\oplus$: median centre of optical galaxies, $\otimes$: density centre of optical galaxies, $\boxplus$: X-ray peak, $\boxtimes$: X-ray maximum)

The drifts of both the density and the luminosity centre are remarkably similar. This seems to indicate that the distributions of the brighter and fainter galaxies are similar, even though not obvious from the inspection of the projected distribution of the galaxies. The calculation of the centre position is only marginally influenced by background galaxies, as shown by the similarity between the density centre tracks for galaxies with B₂₅ < 17 and 18, respectively. The drifts do not significantly depend on the choice of the reference point. However, it can not be ruled out that they are affected by patchy foreground extinction.

We now calculate the positions of the cluster centres for each galaxy type separately. For radii $r=10'\ldots50'$, the cluster centre of spirals is shifted as far as $\sim8'$ east of NGC1275, whereas E+S0 galaxies cluster rather west of NGC1275, reflecting the prominent chain which consists mainly of Es and S0s (cf. Figs.4 and 5). This result is opposite to the morphological centres derived by Andreon (1994).

Apparently, the asymmetric projected distribution of galaxies hampers the determination of a unique cluster centre. In the following sections, we will adopt the median centre proposed by Ulmer et al. (1992) as cluster centre, i.e. $\alpha_{\rm mc}=3^{\rm h} 19^{\rm m} 37\hbox{$.\!\!^{\rm s}$}0$, $\delta_{\rm mc}=41\hbox{$^\circ$}30'03''$ for J2000.

7.4 Surface density profile

 

Figure 7:  Surface density profile of the Perseus cluster. The number of galaxies per square degree $\mu$ in a circular bin of 10' size is shown as a function of the mean radius r of the bin: $r=\sqrt{r_{\rm min}^2+r_{\rm max}^2}$. From top to bottom: galaxies with $B_{25}\le18,\, \le17$ and $\le16$. All data are background-corrected (Eq.2)

The determination of the total extent of the Perseus cluster is hampered by patchy extinction and large-scale galaxy clustering. The projected surface density profile, derived from galaxy number counts in our field, traces the cluster to radii well beyond $1\hbox{$^\circ$}$ (Fig.7). We used circular bins with a bin size of 10', which are centred on the median centre of A426 proposed by Ulmer et al. (see Sect.7.3). In three different counts, galaxies with $B_{25}\le16$, $\le17$, and $\le18$, respectively, have been considered. The obtained galaxy surface densities have been corrected for background contamination according to Eq.(2). Despite some gaps, which might be caused by Galactic extinction and galaxy clustering, the profiles are similar and consistent with a simple power law. The surface density profiles indicate, that the Perseus cluster has a central cusp. This cusp persists if smaller bin sizes (e.g. 5') are applied. This result confirms the finding by Beers & Tonry (1986) that the presence of central cusps is a general property of rich clusters.

7.5 Morphological segregation  

 

Figure 8:  Radial segregation of morphological types: the number density ratio of early type (E+S0) to late type (S+Irr) galaxies, $f(r) = N_{\rm E+S0}(r)/N_{\rm S+Irr}(r)$,is computed within [r-15', r+15'] centred on $\alpha=3^{\rm h}\,19\hbox{$.\!\!^{\rm m}$}7,\, \delta=41^\circ\,30'$.The solid curve is for all 356 galaxies with $B\le 17.5$.This sample is complete to a distance r=65'. The distribution is compared with the sample of 157 galaxies which are expected to be cluster members according to their measured radial velocities (dashed curve)

 

Figure 9:  Density segregation of morphological types: the number density ratio f of early type (E+S0) to late type (S+Irr) galaxies as a function a) of the projected number density $\mu$(in number per $\square\hbox{$^\prime$}$; top) and b) of the B band luminosity density lB (in $L_{\odot,B}$ per $\square\hbox{$^\prime$}$; bottom). The densities are measured within circular areas of $10\hbox{$^\prime$}$ radius; $f(\mu)$ is computed in the intervals [log$\mu-0.2$, log$\mu+0.2$], f(lB) in [loglB-0.2, loglB+0.2]. Solid curves and dashed curves as in Fig.8

A radial morphological segregation in A426 was already noticed by Melnick & Sargent ([1977]), who found that spirals are less concentrated towards the cluster centre than E+S0 galaxies. However, their sample contains only 7% spirals, compared to 50% in our sample. Andreon ([1994]) conducted a thorough investigation of the galaxy distribution in the inner region of Perseus, based on a detailed morphological evaluation of the brightest BGP galaxies ($B\le 15.7$). He found a strong spatial segregation between the different morphological types and concluded, that the Perseus cluster is dynamically young and not virialized. In the present study, we extend the investigation towards fainter galaxies in a considerably larger field. Preliminary results have been presented by Brunzendorf & Meusinger ([1996]).

- Counting convention for morphological types
Since our morphological classification is ambiguous in many cases (especially for the fainter galaxies), we quantify the accuracy in all following calculations as follows: galaxies classified as type A are counted as 100% A; galaxies of type A/B are considered as 50% A and 50% B; galaxies of type A? as 50% A and 50% unknown, and finally type A/B? galaxies as 50% A, 25% B and 25% unknown. On the basis of this counting convention, we find that 52% of all 595 classified galaxies are spirals. If we consider only galaxies with $B_{25}\le17$ the spiral fraction is only slightly reduced to 47%.

- Radial segregation
Whitmore et al. ([1993]) have argued that the cluster-centric distance is the principal determinant of galaxy type within rich clusters. Figures4 and 5 already indicate that E+S0 galaxies dominate the cluster core, whereas S+Irr show only a weak concentration towards the centre. Galaxies of unknown type as well as irregular galaxies show a uniform radial distribution, they contribute 14% and 3%, respectively, to the sample.

Figure8 demonstrates the steep drop in the ratio f of early-type (E+S0) to late-type (S+Irr) galaxies by a factor of more than three. The fraction of identified spirals with B₂₅=18 drops from almost 60% in the outer region down to 30% in the inner 30' of the cluster. Thus, the conclusion of a general lack of spirals, reached in previous investigations of the Perseus cluster, turns out to be partly a consequence of the radial morphological segregation in combination with a bias in the galaxy sample. Those studies were based, at least partly, on the BGP sample which covers the central $\sim30'$ only.

- Density segregation
Dressler ([1980]) first suggested that morphological segregation is determined by the local galaxy density rather than by the distance from cluster centre. There is a well defined correlation between the fractions of S, S0, and E types and the local projected number density, independent of the cluster concentration. In Fig.9, we show the "morphological ratio'', f, for galaxies in A426 with $B\le 17.5$ as a function of the projected number density of galaxies and of the projected projected monochromatic B band luminosity density, respectively. A clear tendency is indicated for E+S0 galaxies to be relatively more abundant in regions of higher density.

The type-density relation has commonly been related to the active role of substructures in clusters. However, Sanromá & Salvador-Solé ([1990]) have shown by means of a very straightforward test that the observed morphological segregation can not be used as an argument in favour of the real existence of clumpiness or substructure.

- Direction segregation
Andreon ([1996], [1998a]) and Andreon et al. ([1997b]) presented arguments in favour of the interesting idea that morphological segregation is primarily based on a privileged cluster direction, perhaps related to the supercluster's main direction. In the clusters studied by Andreon, early-type galaxies show elongated distributions whereas the distribution of spirals is rather isotropic.

In order to study whether a privileged direction is the source of the morphological segregation we discuss the distribution of the galaxies as a function of their cluster-centric position angle, $\varphi$.To avoid edge effects, only galaxies with distances r<70' from the cluster centre are considered. Fig.10 shows the resulting distributions for S+Irr and E+S0 galaxies, respectively. Both type classes show a peak at $\varphi \approx 260\hbox{$^\circ$}$ (west), corresponding to the well-known chain of bright galaxies. This peak is stronger for E+S0, whereas S+Irr show their strongest maximum near $\varphi \approx 40\hbox{$^\circ$}$ (north-east).

For a quantitative analysis of the angular distributions, we apply the Wilcoxon test (U-test), because it is a robust statistical test which requires neither assumptions on the nature of the underlying distribution nor data binning. The U-test states whether the distributions of two independent data samples are different by direct comparison of the two sets; it is regarded as one of the most powerful nonparametric tests (e.g., Siegel & Castellan [1988]). To reduce the influence of a possible misclassification, we exclude all galaxies with ambiguous and/or uncertain morphological classification.

Firstly, we compare the cluster-centric galaxy position angles $\varphi$with those of an artificial sample of the same size but with an isotrope distribution around the cluster centre. The comparison shows that the galaxies are not uniformly distributed around the centre (error probability $\ll0.1\%$), no matter which magnitude range (B<16, B<17, B<18, all B) and which galaxy type (S, S0+E, all) is considered. These non-uniformities can be an artifact due to patchy foreground extinction. Therefore, we directly compare the angular distributions of the different morphological types with each other. The probabilities, that each pair of types has the same distribution, are derived from U-tests and are listed in Table2. To maximise the number of galaxies, on the one hand, and to reduce the influence of background galaxies, on the other, we determined the probabilities twice: (a) for galaxies with B<18 and (b) for B<17. The resulting probabilities are generally similar. We find significant differences (error probability $\sim0.3\%$) in the angular distribution of E, S0 and E+S0 types compared to S, whereas E and S0 are similarly distributed around the cluster centre. These segregations are detected in the inner part of the cluster (r<30'), which is dominated by E and S0 galaxies, as well as in the outer part (r>30'), where spirals dominate.

 

Table 2:  Probabilities (in %) for each pair of morphological types to have the same angular distribution around the cluster centre. The values refer to galaxies with B₂₅<18, values in brackets to galaxies with B₂₅<17

 

Figure 10:  Angular distribution of galaxies around the cluster centre. The number N of a) S+Irr galaxies and b) E+S0 galaxies with a distance r<70' from the cluster centre and a polar angle $\varphi$ is binned in intervals of width $\Delta\varphi=15\hbox{$^\circ$}$

Figure10 suggests a spatial segregation between S+Irr and E+S0 galaxies in east-western direction. Therefore, we compare the galaxy distributions of different morphological types in right ascension $\alpha$ and declination $\delta$, again by means of the U-test. We consider the inner region (r<30') and the outer region (30'<r<70') separately. We find statistically significant differences (error probability $\le 5\%$) in $\alpha$: the probability, that E+S0 galaxies and S+Irr galaxies with B<18 have the same distribution in $\alpha$ is only 0.3%. In contrast, we find no significantly different distributions in $\delta$,even when we choose less stringent significance levels up to error probabilities of 30% and more. This means that the distributions of E+S0 and S+Irr galaxies indeed differ significantly in right ascension, whereas a significant deviation in declination could not be found.

A recent analysis of the X-ray surface brightness profile of A426 from ROSAT PSPC data by Ettori et al. ([1998]) indicates strong deviations from an isothermal profile both east and west of the X-ray centre. This has been interpreted as evidence for groups merging with the main body of the cluster. While the western deviation has been related to the position of head-tail radio galaxy IC310, the galaxies in the field of the eastern excess have not been considered yet. In Fig.11, the "morphological ratio'' f is shown for the galaxies in an east-west strip of the width of $\Delta \delta = 1\hbox{$^\circ$}$, centred on NGC1275 (which is very close to the X-ray centre, see e.g. Table2 in Ettori et al.). Also shown is the distribution of the corresponding number density of galaxies along the strip. The distribution of the brightest galaxies ($B_{25}\le17$)shows a clear asymmetry, with more galaxies on the western side (the prominent chain). For fainter galaxies ($17 \le B_{25} \le 18$), the asymmetry is less pronounced with a local maximum at the position of the eastern X-ray excess (between 20 and 50 arcmin from the X-ray centre). Compared with the galaxies in the area of the prominent chain, the morphological mix in the area of the eastern X-ray excess is strongly weighted towards early types. Due to the strong eastward decrease in the number density of bright galaxies there are, unfortunately, only few radial velocities available in this field.

- Summary
To summarise, we find clear evidence for morphological segregation in the Perseus cluster. A strong radial segregation and a strong density segregation is clearly indicated. A segregation due to a privileged direction is confirmed in several independent tests: the cluster centre of spirals is displaced $\sim10'$ east of the cluster centre of E+S0 galaxies. Furthermore, the angular distribution of both types around the cluster centre and their distribution in right ascension are significantly different. Most pronounced is the privileged eastward direction in the distribution of E+S0 types. The analysis of ROSAT PSPC observations of the Perseus cluster yields a clear eastward excess of the distribution of the intracluster medium (Ettori et al. [1998]). This fact is in agreement with the conclusion by Andreon et al. ([1996]) that the privileged direction of morphological segregation in the Perseus cluster is aligned with the direction of the outer isophotes of the X-ray emission.

 

Figure 11:  Morphological segregation in right ascension for galaxies in the central strip of the width of $\Delta \delta = 1\hbox{$^\circ$}$, centred on NGC1275: a) the number density ratio f of early-type (E+S0) to late-type (S+Irr) galaxies and b) the number N of galaxies in the $\alpha$bins used to compute f; both f and N were calculated in bins of the width $\Delta \alpha = 15'$ for galaxies with $B_{25} \le 17.0$ (solid curve), $\le 17.5$ (dashed), and $\le 18.0$ (dotted), respectively

7.6 Orientation of galaxies

The investigation of galaxy alignments may provide clues to the formation and evolution of galaxies, and a large number of studies have searched for non-random effects in the orientation of galaxies relative to larger structures (e.g., Djorgovski [1987], and references therein). The results are still rather contradictory, but there are some indications for alignments of disk galaxies in both the Virgo (Hu et al. [1995]) and the Coma cluster (Wu et al. [1997]) of galaxies. Gregory et al. ([1981]) found a statistically significant (1.6% error probability) bimodal distribution for the position angles, PA, of both E and S galaxies in the Perseus supercluster, with one peak coinciding with the position angle of the supercluster filament. No correlation of PA with redshift or position in the supercluster was found.

In this subsection, we examine the distribution of PA for the 643 galaxies in the Perseus cluster with an ellipticity $\epsilon\ge0.3$.Our sample contains considerably more galaxies than the sample investigated by Gregory et al., yet it covers only a small fraction of the Perseus Supercluster. Two different statistical tests are applied to estimate the confidence of the hypothesis that the position angles in our sample are not uniformly distributed. We choose a rather low significance level of 90% (i.e. error probability 10%) at which the null hypothesis of a uniform PA distribution is considered to be disproved.

Firstly, we repeat the $\chi^2$ tests employed by Gregory et al. ([1981]) to detect non-uniformities in the PA distribution of (a) galaxies brighter B₂₅=17, (b) galaxies brighter B₂₅=18, and (c) known cluster members.

The resulting $\chi^2$ values either prove that the PA distribution is significantly different from a random distribution, or show that it is consistent with a random one, depending on the chosen starting angle of the first bin. Obviously, the way of binning strongly influences the results. We, therefore, reduce the original bin width of $15\hbox{$^\circ$}$ down to $10\hbox{$^\circ$}$,$5\hbox{$^\circ$}$, $3\hbox{$^\circ$}$, $2\hbox{$^\circ$}$, and $1\hbox{$^\circ$}$, respectively. Still, we can not unambiguously disprove the null hypothesis. The same results are obtained if only one morphological type is considered.

In a second test series, we employ the U-test to compare the galaxy position angles with artificial samples of the same size containing uniformly distributed angles. The U-test is more powerful than the $\chi^2$-test, because it avoids binning. The results are listed in Table3. For all morphological types, we find no significant difference between the observed distribution of galaxy position angles and a uniform distribution. The PA distribution of the known cluster members is also consistent with a uniform distribution. The PA distribution of E+S0 galaxies and S+Irr galaxies closely match as well.

Finally, we applied the Kolmogorov-Smirnov test to the samples (a) to (c). Again, the results show that the distribution of PA is consistent with a random one on a 90% significance level.

Our results suggest a uniform distribution of the galaxy position angles, i.e. the Perseus galaxies are not preferably orientated towards a particular direction.

 

Table 3:  Probabilities (in %) for the position angles PA of spirals S, E+S0 galaxies, and all galaxies, respectively, to be uniformly distributed (Cols. 2 to 4). Last column: probability that S+Irr and E+S0 galaxies have the same distribution of PA Only galaxies with r<70' and ellipticities $\epsilon\ge0.3$ are considered. We find no evidence for a non-uniform distribution of the position angles

7.7 Luminosity function

 

Figure 12:  Luminosity function of all catalogued galaxies in the field, i.e. number of galaxies N vs. magnitude B25 in 0.5mag bins. Filled circles: original data without correction for background contamination, open circles: background-corrected data. Straight, dashed line: number of background galaxies per 0.5mag bin, derived from Eq.(2)

The luminosity function (LF) for all galaxies is shown in Fig.12, along with the number-magnitude relation for background galaxies (according to Eq.2) and the background-corrected LF. The uncertainties in the LF are dominated by the probably irregular Galactic foreground extinction and by background contamination at fainter magnitudes. For type-dependent LFs (Fig. 13), further uncertainties arise from the morphological classification. With regard to these uncertainties we have not tried to transform the measured B₂₅ magnitudes into $B_{\rm T}^0$ magnitudes.

Background contamination is expected to be unimportant for B₂₅<17. In the magnitude range 14.5<B₂₅<17.5, the LF is reasonably fitted by a power law with slope

$$\alpha = \frac{{\rm d}\,\log\,N(L)}{{\rm d}\,\log\,L} = -\Big(1+2.5\,\frac{{\rm d}\,\log\,N(B)}{{\rm d}\,B}\Big).$$ (3)

For the original data we have $\alpha_{\rm orig}=-1.58 \pm 0.03$,whereas the corrected LF is slightly shallower with $\alpha_{\rm corr}=-1.47 \pm 0.04$.For the most luminous galaxies the LF is much steeper. The change of the slope appears near $B_{25} = 14.7\pm0.5$ corresponding to $M_B = -21.3\pm0.5$ for a Hubble constant H₀ = 50kms^-1Mpc^-1. Within the uncertainties, this value agrees with the characteristic magnitude $M_{B_{\rm T}}^{\ast}$ given by Jerjen & Tammann ([1997]) for the Virgo cluster.

 

Figure 13:  Luminosity functions for different morphological types: S (solid, $\ast$), E (short dashes, $\bullet$), S0 (long dashes, $\circ$), Irr (solid, $\diamond$), non-classified (dotted, ?)

 

Table 4:  Type-dependent LFs for spirals (S), irregulars (Irr), ellipticals (E), S0 (S0), and non-classified (?) galaxies. (Decadic logarithm of the number of galaxies per 0.5mag interval)

 

Figure 14:  Simulation of the effect of enhanced foreground extinction on the LF of spirals. For successively stronger extinction the observed LF (solid curve) corresponds to true, extinction-corrected LFs (long dashes to dotted curves) with successively larger fractions of higher-luminosity spirals (see text)

 

Figure 15:  Comparison of the LF for all spirals (solid) with the LF for spirals with projected cluster-centric distances $r\le 50'$ (dashed). The LFs are normalised to 1

It is more reasonable to consider the LFs for different morphological types (Binggeli et al. [1988]; Jerjen et al. [1992]; Jerjen & Tammann [1997]; Andreon [1998b]). In Fig.13, we show the results for A426. The data are listed in Table4. The counting convention from Sect.7.5 has been used. We can compare Fig.13 with the type-dependent composite LFs constructed by Andreon ([1998b]) from 5 clusters (Virgo, Fornax, Centaurus, Coma, Cl0939+4713). Firstly, we agree with Andreon that the LFs of Es, S0s and spirals are different but overlap largely in luminosity. Furthermore, Es show a rather broad distribution. On the other hand, we find disagreement with regard to S0s: from Andreon's data (his Table1) we expect a strong peak in the S0 LF near B₂₅ = 16.5, where we indeed find the maximum, which is, however, much less pronounced than is expected from Andreon's LF. Nevertheless, S0s have the narrowest distribution both in Andreon's composite LF and in our A426 data.

The most obvious feature in Fig.13 is the strong increase in the spiral LF in the magnitude range where background contamination is not significant. For $15 < B_{25} \le 17.5$ we find $\alpha_S = -1.65\pm0.02$,i.e. steeper than the total LF. In the same magnitude range, the slope of the LF for all galaxies except spirals is only $\alpha_{\rm all-S}\le1.43\pm0.03$, even if we assume that there is no spiral among the unclassified galaxies. This result does not well agree with the assumption that different morphological types have the same LF.

One can argue that strong conclusions about the LFs are hampered by the possibility of irregular Galactic foreground extinction. This holds especially for the LF of spirals which are preferentially located in the external parts of the cluster, where extinction is largest (Sect.7.1). The effect of foreground extinction on the spiral LF is essentially twofold. Firstly, the observed LF will become steeper than the true, extinction-corrected LF since the luminosities of the galaxies are under-estimated. For illustration, we performed Monte-Carlo simulations of the spiral LF using about 10⁵ galaxies. Starting with the observed LF from Fig.13, we assume that a fraction g of the spirals is affected by additional foreground extinction $\Delta A_B$(in addition to the mean extinction A_B=0.8 adopted for the inner cluster region), where $\Delta A_B$ is randomly distributed in the interval $[0,\Delta A_{B, {\rm max}}]$.The corresponding extinction-corrected LFs are shown in Fig.14 for g=0.5 and $\Delta A_{B, {\rm max}}=0.3, 0.6, 0.9, 1.2$and 1.5mag, respectively. The interpretation of Fig.14 is that uncorrected foreground extinction yields an apparent steepening of the observed LF near its maximum, i.e. at $B_{25} \approx 17$.The effect becomes stronger for higher values of g and $\Delta A_{B, {\rm max}}$, of course. Thus, we can not definitely exclude the possibility that the observed slope of the spiral LF is influenced by extinction. At the bright end (), however, the slope is expected to be nearly unaffected. A quantitative correction of the LF can be made only on the basis of a detailed extinction map. Secondly, extinction may impair the visibility of the fainter outer part of spirals. Predominantly fainter objects will be either misclassified (for example as Es if only the brighter bulges are detected) or classified as unknown (? in Fig.13) and will drop out of the statistics. As a consequence of this misclassification effect, the observed spiral LF is expected to be shallower than the true one.

To summarise, these both extinction effects work in opposite directions with regard to the observed slope of the spiral LF, and it is difficult to estimate the net effect. According to the IRAS 100$\mu$m map (see Ettori et al. 1998), the region with projected clustercentric distances $r < 1\hbox{$^\circ$}$seems significantly less affected by Galactic extinction than the more distant regions, in particular north-eastward and south-westward, respectively. In Fig.15, we show the LF for spirals with r<50' along with the total spiral LF from Fig.13. The comparison yields no significant difference, though the trend shown in Fig.14 is slightly indicated. The net effect of the extinction on the slope of the spiral LF for seems to be negligible. Therefore, we guess that the stronger increase in the observed LF of spirals at brighter magnitudes, compared to other types, is probably real.

7.8 Total luminosity of the Perseus cluster

The combined apparent magnitudes B₂₅ of all galaxies in our survey yield a total magnitude $B_{\rm tot}=9.44$. When we correct for background galaxies according to Eq.(2), the total luminosity is reduced by at most 0.14mag. The contribution of non-cluster members to the total apparent luminosity is therefore $\le12$%. On the other hand, an unknown number of faint cluster galaxies is not included in our sample. A quick estimate shows that, under the assumption that the sample is essentially complete up to B₂₅=18, more than 10³ additional faint galaxies would be necessary to significantly alter the total luminosity. By applying galaxy luminosity functions from other studies of either field galaxies or cluster galaxies (Jerjen et al. [1992]; Driver et al. [1995]; De Propris & Pritchet [1998]), the contribution of missed faint galaxies to the total luminosity is estimated to be less than 0.1mag.

From the total apparent luminosity $B_{\rm tot}=9.44\pm0.14$ combined with a distance modulus of 36.0mag$~-~5\log_{10}\,h_{50}$ (assuming A_B=0.8mag, KS83), the total B-band luminosity of the Perseus cluster galaxies within the central 10 square-degree is

$$L_{B, {\rm tot}}=(6.5\pm0.9)\ 10^{12}\,L_{B, \odot} \times h_{50}^{-2}.$$ (4)

This value is more than twice as high as the Virgo Cluster luminosity (Sandage et al. [1985]).