The extrapolated central surface brighness

In Fig. a plot is shown of the parameter relation ``central surface brightness versus absolute B magnitude'' for all galaxy types. The galaxies are also separated into two environmental density classes: a group&field sample, of globally low environmental density, and a cluster comparison sample of high environmental density. In Fig. the same relations are plotted for the early and late types separately¹¹. In the analysis, the group&field and cluster samples are compared irrespective of types, and subsequently divided into the two type categories.

Figure: Extrapolated central surface brightness 41#41 versus absolute 10#10 magnitude for all dwarf galaxy types. The group&field sample galaxies are coded with different symbols according to their environment, as indicated in the legend, and the cluster galaxies are represented by small dots. The lines are fits to the data as described in the text, i.e. the solid line is a fit to the entire cluster sample, the dashed line the same relation shifted to fit the group&field data within the analysis limits 47#47.

46#46

Figure: Extrapolated central surface brightness 41#41 versus absolute 10#10 magnitude for early type dwarfs (left) and late type dwarfs (right). Symbols and lines are as in Fig. . The solid line is a fit to the entire cluster sample, the dashed line is the same relation shifted to fit the group&field data within the analysis limits 47#47, and the dot-dashed line is a fit to the group&field data in the magnitude range 49#49, instead of 47#47 (see text).

48#48

There is a clear difference between the two classes, i.e. cluster and group&field, in the form of a systematic shift towards brighter central surface brightness 41#41 for the latter class, at a fixed absolute magnitude.A linear relation between magnitude and central surface brightness was fitted to the cluster data, for absolute magnitudes between 50#50 and 51#51, using a robust fit method. The fitted relation is plotted as a solid line in Fig. . An adjustment to the group&field data in the same magnitude range was also obtained, and is plotted as a dashed line.

Fig. shows the same data, but where the galaxies have been separated into late types and early types respectively. Fits to the data have been done in the same manner as described above. In addition, due to the very low number of early type galaxies in the group&field sample, within the magnitude range used for the fits, a second fit was made to all the group&field early type data points in the magnitude range 52#52 to 53#53. This second fit is shown as a dot-dashed line in Fig. .

The separation of the cluster and group&field samples remain when the dataset is divided into early and late type dwarfs, although it becomes slightly less clear in the case of late types, like in the case of the effective parameters shown in the previous sections.

Table gives the coefficients 54#54 and 55#55 of the fits to the data described above, in the range 50#50 to 51#51, where 56#56. The difference between early and late type dwarfs in the group&field sample is such that the early types are slightly brighter at a given absolute magnitude, whereas in the case of cluster galaxies the trend is slight in the other sense, the early types being of comparable central surface brightness, or slightly fainter. The offset between identical types in the group&field and clusters however are rather large, the group&field galaxies having brighter central surface brightnesses than the cluster galaxies, at a fixed absolute magnitude.

Table: Coefficients of robust fits to the data shown in Figs. and , i.e. central extrapolated surface brightness 41#41 versus absolute magnitude. The fits are of the form 56#56. The second line with field early type data refers to the magnitude range 49#49. All other data are for 47#47.

Sample	54#54	57#57	58#58	59#59	60#60
C All	61#61	62#62	63#63	64#64	-
C Early	65#65	66#66	67#67	68#68	-
C Late	69#69	70#70	71#71	72#72	-
G/F All	-	73#73	74#74	75#75	76#76
G/F Early	-	77#77	78#78	79#79	80#80
G/F Early	-	81#81	82#82	83#83	84#84
G/F Late	-	85#85	84#84	86#86	87#87

As one can see from Table , the offset between the two datasets is of the order of 88#88 for the late types to 89#89 for the early types and 90#90 if one considers the entire samples, irrespective of type.

To test the significance of these differences we apply a two sided KS test to the distributions in 41#41, where the data have been binned into one-magnitude-wide bins, in the range 47#47.

Figure: Distributions of 41#41 for all dwarfs (a), early types only (b), and late types only (c), binned in absolute magnitude. The bins are indicated in the plots. Hatched histograms represent the field sample. Open histograms represent the cluster sample.

91#91

The results of the KS test as well as the mean and standard deviation of the data in each bin for both galaxy classes are given in Table . Histograms of the distributions of 41#41 in each bin are shown in Fig. .

Table: Mean values of 41#41 for the cluster and group&field samples, in one magnitude bins, as well as results of a KS test applied to the distributions in the respective bins. The results for the whole sample are in the top part, the early types in the middle and late types in the bottom part. The KS probabilities for which a larger magnitude bin width was used are indicated.

Bin	cluster	field	ks prob
92#92	93#93	94#94	95#95
96#96	97#97	98#98	99#99
100#100	101#101	102#102	103#103
104#104	105#105	106#106	107#107
108#108	109#109	110#110	111#111
92#92	112#112	113#113	114#114
96#96	115#115	116#116	117#117
100#100	118#118	119#119	120#120
104#104	121#121	122#122	123#123
108#108	124#124	-	-
92#92	125#125	126#126	127#127
96#96	128#128	129#129	130#130
100#100	131#131	132#132	133#133
104#104	134#134	135#135	136#136
108#108	137#137	110#110	138#138

As one can see from Figs.  and and Table , the results of the KS tests show a consistently small probability that the two distributions (cluster and group&field) are drawn from the same parent population, except for the bright late type galaxy sample, as in the previous sections.