Near-infrared and optical broadband surface photometry of 86 face-on disk dominated galaxies. III. The statistics of disk and bulge parameters

21 Pages·0.68 MB·English

by  Roelof S. de Jong

ASTRONOMY
AND
ASTROPHYSICS
1.2.2008
Near-infrared and optical broadband surface photometry
⋆
of 86 face-on disk dominated galaxies.
III. The statistics of the disk and bulge parameters.
6
9
9
1 Roelof S. de Jong

n Kapteyn Astronomical Institute,P.O.Box 800, NL-9700 AV Groningen, The Netherlands
a
J received May 19, accepted Nov 5 1995

2

1 Abstract. The statistics of thefundamentalbulgeanddisk parameters of galaxies andtheirrelation totheHubble
v sequencewereinvestigated byan analysis ofoptical andnear-infrared observations of86 face-on spiral galaxies. The
5 availability of near-infrared K passband data made it possible for the first time to trace fundamental parameters
0
relatedtotheluminousmasswhilehardlybeinghamperedbytheeffectsofdustandstellarpopulations.Theobserved
0
numberfrequencyofgalaxieswascorrectedforselectioneffectstocalculatevolumenumberdensitiesofgalaxieswith
1
respect totheir fundamental parameters. The main conclusions of this investigation are:
0
1) Freeman’s law has tobe redefined.There is no single preferred valuefor the central surface brightnesses of disks
6
9 in galaxies. There is only an upper limit to the central surface brightnesses of disks, while for lower central surface
/ brightnesses the number of galaxies per volume element decreases only slowly as function of the central surface
h
brightness.
p
2) TheHubblesequencetypeindexcorrelatesstronglywiththeeffectivesurfacebrightnessofthebulge,muchbetter
-
o than with thebulge-to-disk ratio.
r 3) The disk and bulgescalelengths are correlated.
t
s 4) These scalelengths are not correlated with Hubble type. Hubble type is a lengthscale-free parameter and each
a typetherefore comes in a range of magnitudes (and presumably a range of total masses).
:
v 5) Low surface brightness spiral galaxies are not a separate class of galaxies. In a number of aspects they are a
i continuationofatrenddefinedbythehighsurfacebrightnessgalaxies.Lowsurfacebrightnessgalaxiesareingeneral
X
of late Hubbletype.
r
a
Key words: Galaxies: fundamental parameters – Galaxies: luminosity function – Galaxies: photometry – Galaxies:
spiral – Galaxies: statistics – Galaxies: structure
1. Introduction these components lies in their support against gravita-
tionalcollapse.Thediskisalmostcompletelyrotationally
The light of a spiral galaxy is dominated by two compo- supported, while the bulge is for some fraction also pres-
nents,thediskandthebulge.Thebasicdifferencebetween suresupported.Atleasttwoparametersareneededtode-
scribe the light distribution of each of these components:
Send offprint requests to:R.S.deJong,UniversityofDurham, a surface brightness term and a spatial scaling factor.
Dept.of Physics, South Road, Durham, DH1 3LE, United The fundamental parameters of the disk are usually ex-
Kingdom, e-mail: [email protected] pressed in central surface brightness (µ ) and scalelength
0
⋆ BasedonobservationswiththeJacobusKapteynTelescope (h), while the bulge parameters are expressed in effective
andtheIsaacNewtonTelescopeoperatedbytheRoyalGreen- surface brightness (µ ) and effective radius (r ). These
e e
wichObservatoryattheObservatoriodelRoquedelosMucha-
fundamental parameters were determined for a large sta-
chos of the Instituto de Astrof´ısica de Canarias with financial
tistically complete sample of galaxies by de Jong (1995a,
support from thePPARC(UK)and NWO(NL) and with the
PaperII). The distributions of the fundamental parame-
UK Infrared Telescope at Mauna Kea operated by the Royal
ters are still poorly known andtheir statistics are investi-
ObservatoryEdinburghwith financialsupportofthePPARC.
gatedinthis paperwith someemphasisonthreerelation-
2 R.S.deJong: Near-IR and optical broadband observations of 86 spirals. III Statistics of bulge and disk
ships:1)“Freeman’slaw”,theempiricalrelationfoundby ofthemassiveoldstellarpopulationisrelativelythemost
Freeman (1970) indicating the constancy of disk central importantinthenear-infrared(near-IR)K passbandused
surface brightness among galaxies,2) the number density here. The K passband has the additional advantage that
of galaxies as a function of their fundamental parameters the extinction by dust is strongly reduced. The K pass-
and 3) the relation between the fundamental parameters bandisthereforebestsuitedtotracethe fundamentalpa-
and Hubble classification. rametersofthe luminousmass.However,otherpassbands
have been used as well in this study to investigate the
wavelength dependence of the bulge and disk parameters
1.1. Freeman’s law
due to dust and population effects.
One of the most remarkable results presented in the clas- De Vaucouleurs (1974) was one of the first to suggest
sicalpaperofFreeman(1970)wastheapparentconstancy that the constancy of µ might result from a selection ef-
0
oftheB passbandµ0ofspiralgalaxies.Forasubsampleof fect.ThiswaslaterquantifiedbyDisney(1976)andAllen
28 (out of 36) galaxieshe found µ0 =21.65 0.3 B-mag & Shu (1979). Catalogs of galaxies have usually been se-
arcsec−2. If the central M/L ishapiproximat±ely constant lected by eye from photographic plates using some kind
among galaxies, this translates directly into a constant of diameter limit. One might therefore selectagainstvery
central surface density of matter associated with the lu- compact galaxies with a high central surface brightness,
minous material. because these have small isophotal diameters. Likewise,
Several authors have tried to explain this result. It galaxies with a very low surface brightness might have
has been argued that ignoring the contribution of the beenmissedduetothelackofcontrastwiththeskyback-
bulge to the light profile could produce the effect (Kor- ground. Disney & Phillipps (1983; see also Davies1990)
mendy 1977;Phillipps&Disney 1983;Davies1990).Free- define a visibility for a galaxy, which enables one to cor-
man(1970)didnotdecomposetheluminosityprofilesina rect a sample for these selection effects if one has made a
bulgeanddisk,butfittedalinetothelinearpartofthelu- careful initial sample selection.
minosity profile plotted on a magnitude scale. This linear
part of the profile could be contaminated by bulge light.
With their models Kormendy(1977) and Davies(1990)
1.2. Bivariate distributions
show that the central surface brightness of low surface
brightness disks will be overestimated by this procedure
Correcting for selection effects is in fact trying to deter-
because of the extra bulge light near the center. The cen-
minefromtheobservedstatisticshowmanygalaxiesthere
tral surface brightnesses of high surface brightness disks
are per unit volume with a certain property. More than
with a short scalelength are underestimated; because of
one property can be used in determining such a distribu-
the small disk scalelength the bulge light dominates the
tion per volume. One needs at least two parameters to
luminosity profile again in the outer region, but with a
characterize the exponential light profile of a disk domi-
longerscalelengthandalowersurfacebrightnessthanthe
natedgalaxyandabivariatedistributionfunctionofboth
disk. Several arguments can be raised against this inter-
diskparametersisamoregeneralstatisticaldescriptionof
pretation(seealsoFreeman1978):1)evenwithbulgelight
galaxy properties than a one parameter function. The di-
included the result is still important, 2) many later type
ameter, the central surface brightness and the luminosity
galaxieshardly havea bulge, but the effect is still present
distribution functions of galaxies are integrations of this
(van der Kruit1987), 3) in samples where proper decom-
bivariatedistributioninacertaindirection.Inthisprocess
position techniques are used the effect is still found, al-
information is lost and the bivariate distribution function
though with a larger dispersion (Boroson1981), 4) a lim-
is therefore more useful in studies of deep galaxy counts
ited range in bulge parameter space was explored in the
andprovidesmoreconstraintsontheoriesofgalaxyforma-
models mentioned above, which might not be representa-
tion and evolutionthan its one dimensional counterparts.
tive of the bulges in spiral galaxies.
Bivariate distribution functions of galaxies have been
Dustextinctionhasalsobeenproposedasanexplana-
determined only a few times before (Choloniewski 1985;
tionfortheconstancyofµ (Jura1980;Valentijn 1990).If
0
Phillips & Disney 1986; van der Kruit 1987, 1989; Saun-
galaxiesareopticallythick in theB passband,one isonly
dersetal.1990;Sodr´e&Lahav1993).Eventhoughdiffer-
lookingoneopticaldepthintothegalaxiesandalwaysob-
ent fundamental parameters are used, almost all (except
serves the same outer layer. This removes the inclination
Saundersetal.)ofthese distributions describefundamen-
dependence fromthe Freemanrelation,butleavesthe un-
tally the same thing in different ways.These studies were
solved problem of why all galaxies should have the same
performed in the B or comparable passbands, which is,
surface brightness at optical depth equal to one.
as mentioned before, not the wavelength most suited to
Freeman established his relation in the B passband
study global fundamental properties of galaxies.
where the light of galaxies is dominated by a very young
population of stars, which make up only a few percent of
thestellarmass.Ofallcommonlyusedpassbandsthelight
R.S.deJong: Near-IR and optical broadband observations of 86 spirals. III Statistics of bulge and disk 3
1.3. Morphological classification the selection, observations and data extraction can be
found in de Jong & van der Kruit (1994, PaperI). The
ForclassificationofspiralgalaxiesontheHubblesequence
galaxies in this statistically complete sample of undis-
three principaldiscriminatorsareused: 1)the pitch-angle
turbed spirals were selected from the UGC (Nilson1973)
of the spiral arms, 2) the degree of resolution of the arms
to have red diameters of at least two arcmin and minor
(into Hii regions, dust lanes and resolved stars) and 3)
over major axis ratios larger than 0.625. The survey was
the bulge-to-disk (B/D) ratio. In his detailed description
limited to 12.5% of the sky globe. Standard reduction
oftheHubblesequence,Sandage(1961)indicatesthatthe
techniques were used to produce calibrated images.
B/Dratiois the weakestdiscriminatorunless galaxiesare
InPaperIItheextractionofthebulgeanddiskparam-
seen edge-on. He finds clear mismatches in type between
classificationsusingitems1)and2)andclassificationsus- etersfromthecalibratedimagesisdescribed.Anextensive
erroranalysiswasperformedusingdifferentfittechniques.
ing item 3). Another factor hampers the use of B/D ratio
The best results were obtained with a model galaxy with
forclassificationofearlyspirals.Onthephotographsused
anexponentialradiallightprofileforbothbulgeanddisk,
forclassificationthecentralregionofanearlyspiralgalaxy
that was two-dimensionally (2D) fitted to the full cali-
is normally overexposedin order to show clearly the faint
brated image. This 2D fit technique made it also possible
spiral structure.
to fit an additional Freeman bar (Freeman1966) compo-
Still,theB/Dratioisoftenassumedtobetheprinciple
nent, which improved the fit for 23 of the 86 galaxies.
parameterunderlyingtheHubblesequence,eventhougha
The error analysis revealed the two dominant sources of
tightcorrelationbetweenclassificationandmeasuredB/D
error in the derived component parameters to be: 1) the
ratioswasneverfound.Themeasurementsindicateatbest
assumed luminosity profile of the bulge and 2) the uncer-
a trend (e.g. Simien & de Vaucouleurs1986; Andredakis
tainty in the sky background subtraction. Other uncer-
& Sanders1994) and the discrepancies between B/D ra-
tainties, like errors in seeing correction, zero-point errors
tio and Hubble type have been attributed to two sources
andresolutionproblemswerefoundtobemuchsmallerin
of error. First there is the uncertainty in classification.
most cases.
Comparisonsof Hubble types givenby different classifiers
show an rms uncertainty in type index of order 2 T-units Assuming that the exponential profile is a reasonable
(Lahav et al.1995). The second source of error is the un- description of the bulge light distribution, the dominant
certainty in the bulge/disk decomposition,due to, among source of error in the parameters is caused by the uncer-
other things, the mathematicalpeculiarities of the widely tainty in the sky background level. This uncertainty was
used r1/4 bulge law (de Vaucouleurs1948). not taken into account using the 2D fit technique, but
the 1D errors can be used, because the 2D fit results are
1.4. Outline generally comparable to the double exponential 1D fit re-
sults (see PaperII, Fig.6). The 1D errors do include the
Themaingoalofthisinvestigationistodeterminethena-
uncertaintyofskybackgroundsubtractionandarealways
tureofthe Freemanlaw.Inordertoaddressthe problems
largerthantheformal2Dfiterrors.The1Derrorsareonly
concerningtheFreemanlaw,alargesampleofface-onspi-
showninthegraphspresentedhereiftheyaresignificantly
ralgalaxieswascarefullyselectedandsurfacephotometry
larger than the symbol size.
wasobtainedintheK passbandaswellasinseveralother
In this paper the RC3 (de Vaucouleurs et al.1991)
passbands. A large number of other globaland structural
morphologicaltypeindexTisused(seealsoPaperI).Be-
parameters of the galaxies were determined in this inves-
cause afew galaxieshadno RC3classification,I classified
tigation and their nature is also explored in this paper.
themasUGC1551–(8),UGC1577–(4),UGC9024–(8)and
The remainder of this article is organized as follows.
UGC10437–(7).Themeanerrorintype indexinthe RC3
The data set and the extraction of the observed bulge
is stated to be 0.89. This number seems to be very low.
and disk parameters are briefly described in Sect.2. The
Lahav et al.(1995) showed that the dispersion between
corrections to the observations in order to calculate num-
the RC3 T-indexand the T-values ofsix expertclassifiers
ber distributions are describedin Sect.3 and these distri-
was on average 2.2 T-units for a sample of 831 galaxies.
butions are presented for the B and the K passband in
Thedispersionbetweenanytwoclassifiersrangedbetween
Sect.4. The relations found are discussed within the con-
1.3 and 2.3 T-units, with 1.8 on average. It is safe to say
text of the three main points of interest (Freeman’s law,
thattheuncertaintyinclassificationintheRC3isatleast
bivariate distributions and Hubble sequence) in Sect.5.
1.5 T-units.
The conclusions are summarized in Sect.6.
Thedatasetcomprises86galaxiesinsixpassbands.To
keepaclearviewontheobtainedresultsIwillconcentrate
2. The data
onthetwomostextremecases,theB andtheK passband
In order to examine the parameters describing the global data. The results for the other passbands are available
structure of spiral galaxies, 86 systems were observed in in electronic form. The B and K passband results are
the B,V,R,I,H and K passbands. A full description of displayedinthegraphswiththesamedynamicrange(but
4 R.S.deJong: Near-IR and optical broadband observations of 86 spirals. III Statistics of bulge and disk
oftenwithdifferentzero-points)andthereforetheycanbe hypothesis. However, for a face-on selected sample such
compared directly. correctionsaresmall.The averagecorrectionfor the sam-
ple examined here is 0.26 mag arcsec−2 when C=1, with
a maximum of 0.60 mag arcsec−2 for the galaxy with the
3. Corrections
largest observed b/a of 0.58.
The observed bulge and disk parameters determined in
PaperIIhavetobecorrectedforallkindsofsystematicef-
3.3. Distances
fects.Thesecorrectionsareoftenuncertainbutnecessary.
One can only expect that they are at least in a statistical
sense correct.
3.1. Galactic foreground extinction
The measurements of brightness and surface brightness
werecorrected(unless statedotherwise)forGalacticfore-
groundextinctionaccordingtothepreceptsofBurstein&
Heiles(1984)andtheactualB passbandextinctionvalues
wereadoptedfromtheRC3.TheGalacticextinctioncurve
of Rieke & Lebofsky (1985) was used to convert these B
passband extinction values to other passbands. The sam-
plegalaxieswereselectedtohaveaGalacticlatitudelarger
◦
than25 ;the extinctioncorrectionis ingeneralsmalland
getssmallerforthelongerwavelengthpassbands.Theav-
erage correction is 0.14 B-mag and the largest correction
is 0.68 B-mag, which translates into 0.06 K-mag.
Fig. 1. The distance distribution of the sample galaxies. For
3.2. Inclination corrections
thedashedlinetheVGSRvelocitiesfromtheRC3wereused,the
full lineindicates thedistancedistributionwhenthevelocities
Since Valentijn (1990) reopened the debate of optically
are corrected for Virgo-centric infall.
thin versus optically thick spiral galaxies,inclination cor-
rections for surface brightness have become less trivial. A
simple equation for correcting surface brightnesses for in-
Thedistancestotheobservedgalaxieswerecalculatedus-
clination effects, taking internal extinction into account, ing a Hubble flow with an H of 100 km s−1 Mpc−1, cor-
has the form 0
rectedforinfallintotheVirgoclusterusingthe220model
µi =µ 2.5Clog(a/b), (1) of Kraan-Korteweg (1986). This model assumes that the
− Local Group has an infall velocity of 220 km/s towards
the Virgo cluster and describes the motions of the galax-
wherea/bisthe majoroverminoraxisratioofthe galaxy
ies around the cluster by a non-linear flow model. The
andC the internalextinctionparameter,whichtakesval-
V velocities needed for this model were calculated from
ues 0 C 1. Fully transparent galaxies are described by hel
≤ ≤ the V velocities listed in the RC3, which are also tab-
C=1, while the case C=0 describes the optically thick GSR
ulated in PaperI. The nearest galaxy is at 6.2 Mpc, the
ones.
most distant galaxy is at 82.5Mpc. The peculiar veloci-
It is unlikely that the inclination correction indeed
ties of galaxies were assumed to be on average 200 km/s
takessuchaformintheopticalpassbands,asextinctionin
in the line of sight, which introduces an uncertainty (σ )
the opticalpassbandsisforaconsiderablefractioncaused d
of 2 Mpc in the distance estimates. The distribution of
by scattering and not just by absorption alone.Light will
distances is displayed in Fig.1, which shows some excess
be scatteredpreferablyfromedge-ondirectionsto face-on
of galaxies at 45 Mpc because of an extension of the
directions, which means that extinctions will seem to be
∼
Pisces-Perseus supercluster. The relationships presented
higher for edge-on than for face-on galaxies. On top of
in this study are very little affected when other infall and
that, certain configurations of dust and stars can behave
flow models are used to calculate distances.
opticallythininaninclinationtest,whiletheymayinfact
be completely opaque. A clear example of this is a very
thin layer of optically thick dust between a thicker slab
3.4. Selection correction
of stars. It is not trivial to produce a better description
as there are too many unknowns and C itself may be a The physically relevant quantities are not the observed
function of galactic radius (see e.g. Giovanelli et al.1994; numbers of galaxies with a certain property, but the fre-
Byun et al.1994). Therefore Eq.(1) is used as a working quency of galaxies with a certain property in a volume.
R.S.deJong: Near-IR and optical broadband observations of 86 spirals. III Statistics of bulge and disk 5
Therefore, the fact that a galaxy is included in the sam- Othermethodstocorrectdistributionsforselectionef-
ple has to be linked to the statistical probability of find- fects havebeen advocated,because they takespatialden-
ing such a galaxy in a certain volume. The galaxies in sity fluctuations into account (for an overview see Efs-
the sample were selected to have UGC red major axis tathiou et al.1988). These methods assume that the in-
diameter (Dlim) of at least 2 arcmin. This creates a se- trinsicdistributionfunctionisindependentofposition(x)
maj
lection bias against galaxies with low surface brightness in space, so that we can write Φ(S)=φ(S)ρ(x), thereby
and/orsmallscalelengths,asthey appearsmalleronpho- losing the absolute calibration of the number density.
tographicplates.The distances (d)to the observedgalax- Thesemethodsallassumeaclearrelationbetweenthedis-
ies and their angular diameters (D ) are known and tribution parameter(s) and the limiting selection param-
maj
the maximum distance at which galaxy can be placed, eter(s). This is not the case for the current investigation.
whilestillobeyingthe selectioncriteria,canbecalculated A diameter limit is not trivially linked to the central sur-
(d =dD /Dlim). A galaxy can only enter the sam- facebrightnessdistribution,certainlynotwhenadifferent
max maj maj
ple if it lies in a spherical volume which has this max- passband is used for the selection and the distribution.
imum observable distance as radius. Turning this argu- The correction of Eq.(3) is only valid if a particular
mentaround,onecanexpectonstatisticalgroundsthata galaxywouldhavebeenmeasuredatthesameintrinsic(as
selected galaxy samples a spherical volume with a radius opposed to angular) diameter, had it been at a different
equal to its maximum observable distance (a more for- distance.InPaperIitwasshownthatthisisprobablythe
mal discussion can be found in Felten 1976). The volume case forthe UGC galaxieswith type index T 6.For later
≤
sampledby agalaxyin adiameter limitedsample is thus typesthesituationislessclear,thereisatooshortarange
in diameters to check and it must be assumed that for
4π 4π
V = (d )3 = (dD /Dlim)3. (2) late-type systems the same type of galaxy is measured at
max 3 max 3 maj maj
the same intrinsic diameter at different distances. Under
Following the previous line of reasoning, an estimate for this assumption it is not important that the UGC eye
the average number of galaxies in a unit volume obeying estimated diameters of late-type galaxies correspond to
a certain specification (S) for a complete sample of N lower average surface brightness than that of early types
galaxies is (seePaperI,Fig.11).Thiseffectjustmeansthatthereare
morelate-typegalaxiesinthesamplethanexpectedbased
N on their isophotal diameter, but their average distance
Φ(S)=XSi/Vmiax, (3) will be larger so that the number of galaxies per sampled
i volume stays the same.
where i is summed over all N galaxies in the sample and The volume correction of Eq.(3) can be used to cal-
Si=1 if the specification is true for galaxy i and Si=0 culate number density distributions for all passbands, as
if false. The error in Φ(S), assuming Poison statistics in long as the red UGC diameters are used to calculate the
ahomogeneousuniverseandconsideringtheuncertainties Vmax.ThedistributionofanygalaxyparameterSi canbe
in the distances, can be calculated by determined in any passband; the use of the red UGC di-
ameters in Eq.(3) ensures the correction for the intrinsic
N N selection effects of the whole sample.
σΦ2(S) =X(Si/Vmiax)2+σd2X(3Si/dVmiax)2. (4) Next to the diameter limit, there are two more selec-
i i tioncriteriadefiningthesample.Theselectionwaslimited
There is always a chance that a member of a peculiar to12.5%oftheskyandonlygalaxieswithb/a>0.625were
classofgalaxyhappenstobenearbyandgetsalotweight used, which is only 37.5% of all possible random orienta-
in Eq.(3) and this volume correction can therefore only tions.Equation3wascorrectedfortheseselectioncriteria.
be appliedto largesamples.Onemustensure thatalarge A correction was also applied for the fraction of galaxies
enough volume of space is sampled so that galaxies are forwhichno(photometric)datawasavailableinacertain
randomly distributed in space. Figure1 shows that the passband. All these corrections were made under the as-
sample mainly traces the local density enhancement, as sumptionthattheincompletenesshadnocorrelationwith
large scale structures in the universe have scales of order the investigated parameters.
50 Mpc. Equation3 should therefore be used with care, Equation(3) can only be applied when the sample is
because the number of galaxieswith smallintrinsic diam- complete. The statistical completeness of the sample can
eters will be overestimatedrelative to the larger ones due be tested with the V/Vmax-test (PaperI). The V/Vmax of
to the local density enhancement. The averagenumber of a galaxy is the spherical volume associated with the dis-
galaxies per Mpc3 calculated with Eq.(3) might be more tance of a galaxy divided by Vmax as defined in Eq.(3),
representative of the local environment than of the mean thusforagalaxyinthisdiameterlimitedsampleV/Vmax=
cosmologicalvalues.Stillitisausefulequationto observe (Dmlimaj/Dmaj)3. For objects distributed randomly in space
general trends in bivariate distributions and to compare the average value of V/V should be 0.5 1/√12 N,
max
± ×
results obtained from different passbands. where N is the numberofobjects inthe test.For the cur-
6 R.S.deJong: Near-IR and optical broadband observations of 86 spirals. III Statistics of bulge and disk
rent sample V/V =0.57 0.03 and therefore there
max
h i ±
are slightly too many galaxies with a small angular di-
ameter in the sample. The original sample of 368 galax-
ies from which the current subsample was selected had a
V/V =0.496 0.015 (PaperI). Subsequent selection
max
h i ±
depended only on the position on the sky and therefore
the excess of small diameter galaxies is probably caused
by the density enhancement of the Pisces-Perseus super-
cluster, which gives some extra galaxies at the diameter
selection limit. This might give some extra high surface
brightnessand/orlargescalelengthgalaxiesinthesample
abovethe cosmologicalmean,because galaxieshaveto be
intrinsically large to be included in the sample being at
the distance of the Pisces-Perseussupercluster.
In a recent paper Davies et al.(1994) argued that the
sample used by van der Kruit (1987) was incomplete in a Fig. 2. The apparent scalelength versus observed central sur-
magnitude V/V -test. They argued that a hidden mag- face brightness of the disks. The dashed line indicates the se-
max
nitude limit hadinfluenced the selection,so that anextra lection limit of Dmaj≥2′ at the 24.7R-mag arcsec−2 isophote
selection correction should be applied. I will follow up on forgalaxieswithperfectexponentialdisks.Theindicatederror
this argument as the sample used here has been selected estimates are theerrors from the1D profile fitting with expo-
nential bulge taking the uncertainty in the sky background
usingsimilarcriteriaasvanderKruitusedforhissample.
level into account. The errors are only plotted if they are sig-
1
nificantly larger than thesymbol size.
There is nothing hidden about a magnitude selection
effect for a diameter limited sample. On the contrary, it
is expected. For galaxies with a certain absolute magni- 4. The distribution of disk, bulge and bar param-
tude M there exists a range of possible (µ ,h) combi- eters
0
nations, satisfying M µ 5log(h), but only a limited
∝ 0− In this section I investigate the distributions of the struc-
range of them will satisfy the diameter selection criterion
tural parameters of the different galaxy components as a
D (µ µ )h>Dlim. Thus for galaxies of the same
maj∝ lim− 0 maj functionofmorphologicaltypeandofeachother.Firstthe
apparent magnitude we will miss some of the small scale-
structural parametersof the disk and bulge are examined
length, bright µ and some of the large scalelength, faint
0 independently. In the final subsection, the relationships
µ galaxies, while still having selected a complete sample
0 between disk and bulge parameters are investigated. The
indiameter.Thecomplicationarisesbecauseapparentdi-
distributions of bulge and disk parameters are corrected
ameters and magnitudes are not independent parameters
for selection effects to yield volume number densities.
for galaxies and their V/V -tests cannot be applied in-
max
dependently. Similar to Eq.(2), a V corresponding to
max
amagnitudelimitcanbeconstructed.Thesmallestofthe 4.1. The disk parameters
magnitude V and the diameter V values should be
max max
Figure 2 indicates some aspects of the completeness and
used for each galaxy in a combined V/V -test. These
max
selection effects of the sample. It shows the distribution
tests cannot be performed separately. The fundamental
of the observed central surface brightnesses versus scale-
premise of a diameter limited sample is that the diame-
length as obtained from the 2D fits of PaperII. The R
ter V is always smaller than the magnitude V , and
max max
passbandvaluesareplotted,becausethesevaluesaremost
therefore a “hidden” magnitude limit does not have to be
closely related to the (red UGC diameter) selection cri-
taken into account and Eq.(3) is sufficient.
teria. The dotted line indicates the selection limit for a
diameter cutoff at 2 arcmin at a surface brightness of
24.7 R-mag arcsec−2 for a perfect exponential disk. The
24.7R-mag arcsec−2 is the average surface brightness at
which the UGC red diameters were determined (see Pa-
1 Davies et al. (1994) also indicate that van der Kruit’s
per I).AsmentionedinPaperI,notallUGCgalaxieshad
sample becomes incomplete for low surface brightnesses at
theirdiametersestimatedatthesameisophotelevel.This
µ0 > 22.3 as hV/Vmaxi = 0.35 ± 0.08. I would like to note
explains why there are some galaxies to the left of the
that this might just be a statistical fluctuation of low num-
selectionline inFig.2.If allgalaxieshavethe samescale-
ber statistics, as hV/Vmaxi = 0.41 ±0.10 for µ0 > 22.5 and
hV/Vmaxi=0.46±0.13 for µ0>22.7, and thus for even lower length,thenumberofgalaxiesexpectedinthesamplewill
surface brightnessesthesampleisin thestatistically complete decreaseash3apandthereforeitisnotsurprisingthatthere
range of hV/Vmaxi=0.5. are hardly any galaxies in the sample below 22R-mag
R.S.deJong: Near-IR and optical broadband observations of 86 spirals. III Statistics of bulge and disk 7
hµ0i (B-mag arcsec−2) hµ0i (K-mag arcsec−2)
RC3 type nr. C =0 C =0.5 C =1 nr. C =0 C =0.5 C =1
0≤T < 6 61 21.32 ± 0.78 21.45 ± 0.76 21.58 ± 0.74 60 17.48 ± 0.71 17.61 ± 0.69 17.75 ± 0.67
6≤T < 8 12 22.01 ± 0.75 22.16 ± 0.73 22.30 ± 0.72 10 18.34 ± 0.90 18.50 ± 0.90 18.65 ± 0.90
8≤T ≤10 8 22.97 ± 0.60 23.12 ± 0.57 23.26 ± 0.55 7 20.05 ± 1.05 20.21 ± 1.03 20.37 ± 1.01
all 81 21.59 ± 0.92 21.72 ± 0.90 21.86 ± 0.89 77 17.82 ± 1.08 17.96 ± 1.08 18.10 ± 1.08
Table 1. The average Galactic extinction corrected central surface brightnesses for different inclination corrections (Eq.(1))
and type index bins. C = 0 corresponds to an optically thick disk, C = 0.5 to a semi transparent disk and C = 1 to a fully
transparent disk.The values are in mag arcsec−2 with their standard deviations.
Fig. 3. The Galactic extinction corrected central surface brightness of the disks as function of morphological RC3 type. The
crossesshowthevaluesaveragedoverthebinsindicatedbythehorizontalbars.Theverticalbarsindicatethestandarddeviations
of themean values.
Fig. 4. The scalelength of thedisk as function of morphological type.
arcsec−2.Obviouslynogalaxiescanenterthesamplewith might be classifiedaslate types just because they are low
µ fainter than 24.7 R-mag arcsec−2. surface brightness (LSB) systems. It can be readily seen
0
∼
that this difference between early and late-type galaxies
Let us now look at the central surface brightness as
increaseswhengoingfromtheB totheK passband.This
function of morphological type (Fig.3). Apparently the
indicatesthatdisksofthelatertypespiralsarebluerthan
galaxiesfromtypeT=1to6haveonaveragethesameµ ,
0 thedisksoftheearlyones,butthediscussiononthecolors
but with a large scatter. The later types have on average
of these galaxies is postponed to PaperIV in this series
a significantly lower centralsurface brightnesses and they
8 R.S.deJong: Near-IR and optical broadband observations of 86 spirals. III Statistics of bulge and disk
(deJong1995b).Theaverageµ valueswerecalculatedfor inthesamplethanthegalaxiesnearthe 10Mpc line!The
0
three morphologicaltype bins indicated by the horizontal fact that the number density of objects does not decrease
bars in Fig.3 as well as for the total sample. The values by 125 from one line to the other already indicates that
with their standard deviations are tabulated in Table 1. therearemanymore“small”galaxiespervolumeelement
Theaverageµ valueswerealsocalculatedwithanin- than “large” galaxies.
0
clination correction according to Eq.(1) with values for Thedistributionofthe absolutemagnitudeofthedisk
C = 0.5 and C = 1 (semi transparent and completely (M ) against type (Fig.6) can also be deduced from
disk
transparent behavior). The results can also be found in Figs 3 and 4 (M µ 2.5log(2πh2), no inclination
disk 0
∝ −
Table 1. The standard deviations on the average µ val- dependent extinction correction was applied). As scale-
0
ues are slightly smaller for C=1, and even though it is a lengths show little correlation with type, the distribution
smalleffect, it is persistent for allsubgroupsand allpass- of disk magnitudes reflects the distribution of the central
bands. The main result is of course a shift in the mean surface brightness against type. There was no apparent
central surface brightness of the disks. For all remaining segregation according to bar classification in Figs 3, 4, 5
plots an inclination correction with C=1 will be used. and 6.
Thedistributionoftheotherdiskparameter,thescale- Sofar,onlytheobserveddistributionswerepresented,
length(h),asfunctionoftype is showninFig.4.Thereis but the distributions per volume are of more importance.
notrendofhwithtypeandthereisalargerangeinscale- Therefore the volume correction as described in Sect. 3
lengths. There might be a lack of late-type galaxies with was applied. The correctiontransforms Fig.5 into the bi-
small scalelengths, but this can probably be attributed variatedistributioninthe(µ ,h)-planepresentedinFig.7.
0
to a selection effect: the selection criteria are heavily bi- This is a representation of the true number distribution
ased against LSB galaxies with small scalelengths. The of spiral galaxies per volume element of one Mpc3 with
scalelengths are smaller in the B passband than in the K respect to both disk parameters. The magnitude and µ
0
passband (discussion in PaperIV). upperlimitsnoticedinFig.5arealsopresenthere.Weare
TheinformationofFigs3and4arecombinedinFig.5. dealing with low number statistics now,whichis reflected
Thisfigureshowsthatthereisanupperlimitinthe(µ ,h)- intheerraticbehaviorofthedistribution.Theuncertainty
0
plane,asthereareno galaxieswithlargescalelengthsand increasesinthedirectionofsmallscalelengthandlowsur-
high central surface brightnesses. This cannot be caused face brightness.These galaxieshavesosmallisophotaldi-
by selection effects, large bright galaxies just cannot be ameters thatthey reallyhaveto be nearbyto be included
missed in a diameter selected sample. This upper limit in the sample and such a small volume is sampled that
hasbeennotedbeforebyGrosbøl(1985).Theupperlimit statistics are working against us. For example if the true
partlyfollowsthelineofconstanttotaldiskluminosity,as volume densities in the (17K-mag arcsec−2, 1kpc) and
indicatedbythedashedlineinFig.5.NotethattheTully- (21K-mag arcsec−2, 1kpc)-bins are equal, the chance of
Fisher relation (1977, hereafter TF-relation) implies that observing a galaxy in the last bin would be 0.5. If there
this is also a line of constant maximum rotation speed had been such a galaxy in the sample, a lot of weight
of the disk. There is also an upper limit to the central would have been given to it. In short, the distributions
surface brightness at about 20 B-mag arcsec−2 (16 K- are not well sampled in the low surface brightness, small
mag arcsec−2). Again galaxies brighter than these limits scalelengthregion.Nogalaxieswereselectedinthisregion,
are hard to miss because of selection effects. but the traced volume is also very small. The dominant
Late-type galaxies have lower central surface bright- type of spiral galaxyhas a scalelength of about 1kpc and
nessesinFig.5,buttheearlyandintermediatetypesshow a central surface brightness of 21B-mag arcsec−2 (17K-
no segregation.The scalelengths also givesno segregation mag arcsec−2).
according to type. Very few late-type galaxies with very By summing all bins in one direction, the bivariate
shortscalelengthswereselected,butasshownbefore,late- distributions of Fig.7 can be used to calculate the dis-
type galaxies have lower surface brightnesses and the se- tributions of µ and h separately. This figure indicates
0
lection biasesagainstgalaxieswith low surface brightness therefore where one can expect problems in the determi-
andshortscalelengthsarelarge.Thesebiasesareindicated nations of the µ and h distributions due to the under-
0
bythedottedlinesinFig.5.Totherightoftheselinesthe sampling in the low surface brightness, small scalelength
sample shouldbe complete to the indicated distance.The region. The µ distributions will get incomplete for cen-
0
linesarecalculatedundertheassumptionthatallgalaxies tralsurfacebrightnessesfainterthan21.5B-magarcsec−2
have perfect exponential disks with the same color at the (19 K-mag arcsec−2) and the h distributions should not
selection radius (B–R=1.3, R–K=2.5) and that the se- betrustedforscalelengthssmallerthan1kpc.Theunder-
lection limit is at 2′ diameter at the 24.7 R-mag arcsec−2 sampling in the µ distribution is considerably reduced
0
isophote (as in Fig.2). Although these assumptions are when only the galaxieswith scalelengthlargerthan 1 kpc
notvalidforanindividualgalaxy,the dottedlineshelpto areused.Theundersamplingproblemofthissamplecould
estimatetheselectioneffects;thegalaxiesnearthe50Mpc also be circumvented by imposing absolute magnitude or
line had about 125 times more chance of being included intrinsicdiameterlimits.Tospeakoftheµ distributionis
0
R.S.deJong: Near-IR and optical broadband observations of 86 spirals. III Statistics of bulge and disk 9
Fig. 5. The scalelength of the disks versus the central surface brightness. Different symbols are used to denote the indicated
morphological type ranges. Exponential disks with equal absolute luminosity of indicated magnitude are found on the dashed
line. Equality lines of other magnitudes lie parallel to the dashed line. The dotted lines indicate the selection limits for all
exponential disk galaxies closer than 10 and 50Mpc respectively, undertheassumptions made in thetext.
Fig. 6. The distribution of absolute disk magnitudes as function of typeindex.
incorrectandoneshouldindicatetowhattypeofgalaxies sampleisbiasedagainstgalaxieswithaµi fainterthan23
0
the sample is restricted. B-mag arcsec−2 even for galaxies with scalelength larger
than1kpc.Obviouslygalaxieswithcentralsurfacebright-
The distributions of central surface brightnesses of nessfainterthan26B-magarcsec−2 couldneverenterthe
galaxieswithscalelengthlargerthan1kpcaredisplayedin
sample. The distributions ofµ in Fig.8 could be slightly
Fig.8. The distributions are remarkably flat for the total 0
higher at the faint end and should probably be extended
sample.Thenumber densitydensity decreasesby abouta
factor of 4 from µ i 21 to 24 B-mag arcsec−2 and by a to much lower surface brightnesses.
0
factor 10from17.5≃to22K-magarcsec−2.Thedistribu- The volume corrected distributions of the logarithm
∼ of the scalelengths (Fig.9) show first a small increase of
tions are narrower when only types earlier than T=6 are
galaxies to scalelengths of about 1kpc. This is probably
used. Disks of late-type galaxies are bluer, which makes
caused by the undersampling effect at low surface bright-
theoveralldistributionnarrowerinB thaninK.Thedis-
nessesandsmallscalelengths.Forscalelengthslargerthan
tributionsarenotlimitedbyselectioneffectsatthebright
1kpc we notice a steady decline of about a factor 100 in
end, even if one assumes there is an upper limit to the
onedex.Thereisnosegregationwithmorphologicaltype.
totalluminosityofagalaxy(seeFig.5).Thenumberden-
sityofgalaxiesdecreasessharplywithµi brighterthan20 Themostimportantresultsobtainedinthissubsection
0
B-mag arcsec−2 ( 16 K-mag arcsec−2). At the faint end are as follows. There is a large range in disk central sur-
∼
alimited volumeissampled,andFig.5indicates thatthe face brightnessesamonggalaxies,mainly due to the lower
10 R.S.deJong: Near-IR and optical broadband observations of 86 spirals. III Statistics of bulge and disk
Fig. 7.Thevolumecorrectedbivariatedistributionofgalaxiesinthe(µ0,h)-plane.ThenumberdensityΦ(µi0,h)isperbinsize,
which is in steps of 0.3 in log(h) and 1 mag arcsec−2 in µi.
0
Fig. 8.Thevolumecorrecteddistributionofthecentralsurfacebrightness.Thedashedlineindicatesthedistributionfortypes
earlier than typeT=6. The numberdensity is per bin size, which is in steps of 0.75 mag arcsec−2 in µ0.
Fig. 9. The volume corrected distribution of the disk scalelengths. The dashed line indicates the distribution for type earlier
than T=6. The numberdensity is perbin size, which is in steps of 0.2 in log(h).