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Surface photometry of low surface brightness galaxies 7
Table 1. Parameters of the sample
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12)
F 561­1 08 06 45 +22 42 25 14 47 16.43 21 16.16 29 15.63 15.42 0.11
F 563­1 08 52 10 +19 56 35 52 34 16.77 23 15.90 62 15.96 15.23 0.06
F 563­V1 08 43 48 +19 04 26 42 38 17.98 13 17.26 25 16.46 15.78 0.05
F 564­V3 09 00 03 +20 16 23 26 6 18.35 11 17.09 29 17.47 16.38 0.07
F 565­V2 09 34 47 +21 59 46 64 36 19.28 10 18.10 27 18.57 17.29 0.05
F 567­2 10 15 11 +21 18 47 37 56 18.61 9 17.07 31 17.69 16.41 0.06
F 568­1 10 22 57 +22 40 44 26 64 17.12 18 15.54 31 16.16 15.72 0.02
F 568­3 10 24 15 +22 28 51 39 58 16.45 21 16.15 31 15.54 15.30 0.02
F 568­V1 10 43 44 +22 23 50 35 60 17.20 16 16.69 29 16.28 15.85 0.00
F 571­5 11 27 49 +20 52 10 40 45 17.80 13 16.81 31 17.01 16.19 0.00
F 571­V1 11 23 42 +19 07 56 35 59 18.54 10 17.50 25 17.59 16.64 0.00
F 574­2 12 44 19 +22 04 34 29 66 18.77 9 17.17 27 17.80 16.47 0.14
F 577­V1 13 47 49 +18 30 53 33 80 17.57 17 16.95 29 16.90 16.43 0.01
U 0128 00 11 12 +35 43 00 57 48 15.98 31 15.07 78 15.07 14.36 0.18
U 0628 00 58 18 +19 13 00 56 56 15.84 31 15.56 51 14.91 14.64 0.09
U 1230 01 42 42 +25 16 00 20 40 16.16 21 15.06 62 15.31 14.46 0.40
U 5005 09 21 39 +22 29 20 40 37 -- 41R -- 49R 15.01 14.92 0.10
U 5209 09 45 04 +32 14 11 50 7 -- 33R -- 62R 15.54 15.21 0.00
U 5750 10 33 02 +21 15 00 61 71 -- 35R -- 70R 15.51 15.32 0.02
U 5999 10 50 13 +07 53 13 27 32 -- 45R -- 90R 15.11 14.65 0.05
U 6614 11 36 36 +17 25 00 54 66 -- 57R -- ?120R 13.08 !12.81 0.02
Note:
(1) Name of the galaxy. ``U'' means from the UGC; ``F'' means from the Schombert lists.
(2) Right Ascencion (1950.0) either from UGC or Schombert lists.
(3) Declination (1950.0) from UGC or Schombert lists.
(4) Inclination as derived from our data.
(5) Distance in Mpc (H 0 = 100 km s \Gamma1 Mpc \Gamma1 ).
(6) Total magnitude B 25 within 25 B­mag/ut 00 ellipse.
(7) Radius in arcsec of 25 B­mag/ut 00 ellipse.
(8) Total magnitude B 27 within 27 B­mag/ut 00 ellipse.
(9) Radius in arcsec of 27 B­mag/ut 00 ellipse.
(10) Total magnitude R 25 within 25 B­mag/ut 00 ellipse.
(11) Total magnitude R 27 within 27 B­mag/ut 00 ellipse.
(12) Applied extinction correction in B.
If the values in columns (7) and (9) are followed by an ``R'', then these are measured in the R­band.
17 exposures, and the I­filter stars also showed a deviation
of 0.02 mag, based on 5 exposures, all of these exposures
taken during 4 nights.
2.4 Sky subtraction
To determine the sky background and the errors caused by
its subtraction we used the following procedure.
If the sky background had a significant gradient across
the image an attempt was made to fit and remove this gradi­
ent, without changing the mean value of the sky background.
To do this the brightest stars were first removed from the im­
age, after which the image was gaussian­smoothed, decreas­
ing its resolution by a factor of two. This removed small scale
noise fluctuations and showed more clearly which parts of
the image were affected by the glare of the remaining fainter
stars. A two­dimensional first order polynomial was then fit
to those parts of the smoothed sky background that were
judged to be free of any emission from stars or the galaxy
itself.
This gradient was then subtracted from the original im­
age, essentially flattening the image background, without
affecting the mean value of the sky or the values for the
galaxy. We then measured the mean value of the sky back­
ground and the standard deviation in small boxes that were
placed on parts of the image that were free of stellar or
galaxy emission.
The mean difference between the median sky levels in
these boxes was used as an estimate for the error introduced
by fitting and subtracting the sky. Typically these errors
were less than 0.5% of the subtracted sky evel.
2.5 Ellipse fitting and inclinations
We used the GIPSY image processing package to make el­
lipse fits to the isophotes of the galaxies, and to integrate
along these ellipses, thus obtaining azimuthally integrated
surface brightness profiles. The centers of the ellipses were
usually determined by taking the maximum of the light dis­
tribution as the center. In one or two cases the light distri­
bution was too irregular and the center position was taken
as a free parameter in the ellipse fit. For each set of UBVRI
images of an object only one set of ellipse orientation para­
meters was determined (usually from a slightly smoothed R
image), and applied to the other images to get radial sur­
face brightness profiles for each band. As the galaxies did
not contain any significant bulges or strong bars that might
twist the isophotes we fitted ellipses with constant axis ra­

8 W.J.G. de Blok, J.M. van der Hulst and G.D. Bothun
tios, centers and position angles where the axis ratios and
position angles were determined by the outer isophotes, as
these isophotes give the best idea of the overall shape of the
galaxy. Prior to the fitting, stars and cosmic ray defects were
first blanked out. The radial surface brightness profiles were
then used to determine colour profiles. As an extra check a
few images were also fit using a free parameter fitting rou­
tine, with no constraints on the axis ratio or orientation,
and resulted in virtually identical radial surface brightness
profiles.
Inclinations were derived from these ellipse fits, using
cos i = (b=a) and corrected for the intrinsic thickness of the
disk by using the following formula from Holmberg (1958):
cos 2 i = (b=a) 2 \Gamma q 2
0
1 \Gamma q 2
0
(1)
where q0 , the edge­on axis ratio of the disk is taken to be
0.15 (cf. Huizinga 1994; Giovanelli et al. 1994).
3 SURFACE BRIGHTNESS, SCALE LENGTH
AND HUBBLE TYPE
3.1 The data
It is well known that usually the surface brightness profile
of a disk galaxy can be decomposed into two components:
(i) an exponential disk component of the form
\Sigma(r) = \Sigma 0 exp
i
\Gamma
r
ff
j
; (2)
where \Sigma 0 is the surface brightness of the disk in linear units
(M fi pc \Gamma2 ), and ff is the exponential scale length of the disk
(de Vaucouleurs 1959), and
(ii) an r 1
4 law bulge of the form
\Sigma(r) = \Sigma e exp
i
\Gamma7:67 (r=re ) 1
4 \Gamma 1
j
; (3)
where \Sigma e is the surface brightness of the bulge at effective
radius re .
Figure 2 shows the surface brightness profiles of the
galaxies in our sample for the different bands. It is clear
from Fig. 1 and 2 that most of the galaxies in our sample
do not show significant bulges. We therefore did not try
a bulge­disk decomposition, but only fitted an exponential
disk. Equation (2) can be converted to logarithmic units and
gives
¯(r) = ¯0 + 1:086
i r
ff
j
; (4)
where ¯0 is the central surface brightness of the disk in log­
arithmic units (mag=ut 00 ). The central surface brightness ¯0
of the disk and the exponential scale length ff were found
by fitting a straight line to the exponential part of the pro­
file that is displayed in Figure 2, where the inner few points
were excluded from the fit.
Table 2 shows the fit parameters, along with some
other parameters derived from them. We have not corrected
the central disk surface brightness in Column (3) to face­
on value as the optical depth effects in LSB galaxies are
not known. [We do expect them to be small, however, as
LSB galaxies have a low dust content (McGaugh 1992)].
The mean error in the central surface brightness is about
0:1 mag=ut 00 and the mean error in the scale length is ¸ 20%.
These errors are derived from the error in the fit and the
errorbars in the outer points, which are in turn mainly de­
termined by the error due to sky subtraction. The total in­
tegrated magnitude of the disk, integrated out to infinity, as
given in Column 6 is calculated using
mT = ¯0 \Gamma 2:5 log(2úff 2 ) \Gamma 2:5 log(cos i); (5)
where the last term corrects the area of a face­on disk to
the apparent area of an inclined disk. The method used to
determine the simulated aperture photometry magnitudes
in Column 7 is described in Section 3.2. All magnitudes in
this and other tables are corrected for Galactic foreground
extinction, as described in Section 2.1.
3.2 Total magnitudes
The total magnitude out to infinity mT , as defined by Equa­
tion (5), is a better estimate for the total luminosity of a
LSB galaxy than the conventional m25 magnitude, which
gives the amount of light within the 25 mag=ut 00 isophote.
While in HSB galaxies most of the light is concentrated
within this isophote, this is not the case for LSB galax­
ies. F565­V2 for example has a central B­surface bright­
ness of ¸ 24:5 mag=ut 00 , meaning that only a small part of
the light will come from inside the 25 B­mag=ut 00 isophote.
One step fainter we have objects with central surface bright­
nesses fainter than 25 mag=ut 00 , so m25 would not even be
defined for these objects. However, it is not easy to get pre­
cise values for mT as it depends on an extrapolation using
the scale length, which by itself already has an ncertainty
of some 20%. Isophotal magnitudes are determined directly
from the data and do not depend on extrapolations. To get
an estimate for the total magnitude of the galaxies without
introducing any fits or assumptions we have determined the
magnitudes mapt using curves of growth to simulate aper­
ture photometry. We plotted the total intensity within an
ellipse as a function of the radius of the major axis of that
ellipse. This results in a curve of growth, which starts to flat­
ten off at the radius where the galaxy disappears in the noise
of the sky. We thus find no more extra light if we increase
the radius even more. For each galaxy we have measured the
amount of light within this maximum radius. This gives a
better estimate for the total magnitude than an extrapolated
disk magnitude, as any central surplus non­disk light is also
taken into account, and no extra light is introduced at very
large radii. Evidently this method only works if the data are
good and deep enough, as the errors in the magnitudes are
still mainly determined by the errors in the sky subtraction.
In our case the maximum visible optical radius in B usually
occurs around ¸ 28 mag=ut 00 , and we can trace the galaxy
out to 3.5 to 4 scale lengths on average and sometimes even
further. If our galaxies were perfect exponential disks then
the above limits would mean we had etected more than 90%
of the total light.
It is instructive to compare m25 with mapt , the amount
of light within the maximum aperture radius. This is done
in Fig. 3. It is clear that m25 underestimates the amount of
light present: most points fall well below the line of equality.
Therefore, one should be careful in using m25 to calculate for

Surface photometry of low surface brightness galaxies 9
1 2
Figure 1. Radial surface brightness and colour profiles. Top panels contain B (lower profile) and R (upper profile) surface brightness
profiles, bottom panels contain radial colour profiles (where measured). In all cases V \Gamma I has been offset by +0.5 magnitude
example mass­to­light ratios, since using m25 will artificially
raise this ratio, and more so in LSB galaxies.
3.3 Surface brightnesses and scale lengths
Figure 4 shows the distributions of central disk surface
brightnesses and scale lengths. The median values for our
sample are ¯B (0) = 23:6 mag=ut 00 and ff = 3:2 kpc.
Combining our data with those of McGaugh y (1992, his
Fig. 2.3), yields median values of respectively 23:4 mag=ut 00
and 3:2 kpc. The median of the surface brightness is thus
shifted more than 6oe from the Freeman (1970) value
¯B (0) = 21:65 \Sigma 0:30 mag=ut 00 or approximately 2oe from the
van der Kruit (1987) value of (21:6) \Sigma 0:8. The distribution
y The selection of the sample of McGaugh's study is similar to
ours, and a direct comparison is valid