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The stellar mass distribution in early-type disk galaxies surface photometry and bulge-disk

The stellar mass distribution in early-type disk galaxies surface photometry and bulge-disk
The stellar mass distribution in early-type disk galaxies surface photometry and bulge-disk

a r X i v :a s t r o -p h /0701730v 1 25 J a n 2007

Mon.Not.R.Astron.Soc.000,000–000(0000)Printed 5February 2008

(MN L A T E X style ?le v2.2)

The stellar mass distribution in early-type disk galaxies:

surface photometry and bulge-disk decompositions

E.Noordermeer,1,2?and J.M.van der Hulst 1

1

Kapteyn Astronomical Institute,University of Groningen,PO Box 800,9700AV Groningen,The Netherlands

2University

of Nottingham,School of Physics and Astronomy,University Park,NG72RD Nottingham,UK

accepted for publication in MNRAS,19-12-2006

ABSTRACT

We present deep B-and R-band surface photometry for a sample of 21early-type disk galaxies with morphological types between S0and Sab and absolute B-band magnitudes between -17and -22.Six galaxies were also observed in I.We present radial pro?les of surface brightness,colour,ellipticity,position angle and deviations of axisymmetry for all galaxies,as well as isophotal and e?ective radii and total magni-tudes.We have decomposed the images into contributions from a spheroidal bulge with a general S′e rsic pro?le and a ?at disk with an arbitrary intensity distribution,using an interactive,2D decomposition technique.We caution against the use of simple 1D decomposition methods and show that they can lead to systematic biases,particularly in the derived bulge parameters.

We study in detail the relations between various bulge and disk parameters.In particular,we ?nd that the bulges of our galaxies have surface brightness pro?les ranging from exponential to De Vaucouleurs,with the average value of the S′e rsic shape parameter n being 2.5.In agreement with previous studies,we ?nd that the shape of the bulge intensity distribution depends on luminosity,with the more luminous bulges having more centrally peaked light pro?les (i.e.higher n ).By comparing the ellipticity of the isophotes in the bulges to those in the outer,disk dominated regions,we are able to derive the intrinsic axis ratio q b of the bulges.The average axis ratio is 0.55,with an rms spread of 0.12.None of the bulges in our sample is spherical,whereas in some cases,the bulges can be as ?at as q b =0.3?0.4.The bulge ?attening seems to be weakly coupled to luminosity,more luminous bulges being on average slightly more ?attened than their lower-luminosity counterparts.Our ?nding that most bulges are signi?cantly ?attened and have an intensity pro?le shallower than R 1/4suggests that ‘pseudobulges’,formed from disk material by secular processes,do not only occur in late-type spiral galaxies,but are a common feature in early-type disk galaxies as well.

Most galaxies in our sample have radial colour gradients,becoming bluer towards larger radii.Although this can partly be explained by the radially declining contribu-tion of the red bulges to the observed light,we show that disks must also have intrinsic colour gradients.

Key words:galaxies:photometry –galaxies:spiral –galaxies:structure –galaxies:stellar content –galaxies:fundamental parameters –galaxies:kinematics and dynam-ics.

1INTRODUCTION

One of the outstanding problems in our understanding of the structure and evolution of galaxies is the r?o le played by dark matter.Paradoxically,however,one of the main obstacles towards an exact measurement of the amount and distribu-tion of dark matter is,in many cases,formed by our limited

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email:edo.noordermeer@https://www.doczj.com/doc/2214083729.html,

knowledge of the contribution of the stars to the gravita-tional potential.The contribution of the stellar component is expected to be particularly important in early-type disk galaxies.Early-type disk galaxies are among the brightest galaxies in the universe,both in terms of total luminosity and of surface brightness (Roberts &Haynes 1994).It is to be expected that in these galaxies,the stellar mass is dynam-ically much more important than in low luminosity and low surface brightness galaxies,which are generally believed to

2 E.Noordermeer&J.M.van der Hulst

be dark matter dominated(e.g.Carignan&Freeman1988; de Blok&McGaugh1997;Swaters1999;C?o t′e et al.2000).

Historically,spiral galaxies were considered as a com-bination of a more or less spherical bulge and a?attened disk.Bulges were normally modelled as miniature elliptical galaxies,with surface brightness following an R1/4-law(fol-lowing de Vaucouleurs1948,1958),whereas the azimuthally averaged disk brightness was usually described with an ex-ponential pro?le(de Vaucouleurs1959;Freeman1970).

It was readily noted that not all galactic disks are well described by simple exponential pro?les at all radii (Freeman1970;van der Kruit1979),and recent develop-ments have shown that many bulges are not the sim-ple,structureless spherical bodies as previously thought ei-ther.HST observations by Carollo et al.(1997,1998)of the cores of75spiral galaxies revealed a wealth of nu-clear structure,including nuclear spirals,rings and dust lanes.Many of their galaxies showed signs of nuclear star formation.Erwin&Sparke(1999,2002)and Erwin et al. (2003)showed that many galaxies have nuclear bars and other disk-like structures in their centres.They noted that the central light concentrations in many spiral galax-ies seem to originate from highly?attened structures, rather than from spherical bodies.The photometric pro-?les of many spiral galaxy bulges are described better by exponential or R1/2-pro?les than by the classical R1/4-law(Andredakis&Sanders1994;Andredakis et al.1995; de Jong1996a;Courteau et al.1996;Carollo1999).Fi-nally,spectroscopic observations show that many bulges are much more rotationally supported than elliptical galax-ies(Illingworth&Schechter1982;Kormendy&Illingworth 1982;Kormendy1993;see also the recent results from the SAURON project for an overview of the complex dynamics, including disk-like rotation,in the centres of many spiral galaxies:Emsellem et al.2004;Fathi2004).

All these observations led Kormendy&Kennicutt (2004)to postulate that many central light concentrations are not classical,spheroidal bulges with a similar formation history as ellipticals,but rather disk-like structures,formed by secular processes;they call these disk-like bulges‘pseu-dobulges’.

For a study of the global dynamics of spiral galaxies, a proper understanding of the structure of bulges and disks is crucial.Irrespective of the exact formation mechanism of(pseudo)bulges,they will have experienced a di?erent evolutionary history than their surrounding disks.As a re-sult,their stellar populations,and corresponding mass-to-light ratios,are expected to be di?erent.Accurate bulge-disk decompositions are therefore needed to determine the contribution of each component to the gravitational poten-tial.Furthermore,the vertical structure of the bulge has a strong in?uence on the peak rotation velocity in a galaxy: a?at,disk-like structure will generally have a higher circu-lar rotation speed in the plane than a spherical system with the same projected surface density(see e.g.?gure2-12in Binney&Tremaine1987).

The current paper is part of a larger study of the re-lation between dark and luminous matter in nearby,early-type disk galaxies.In a previous paper(Noordermeer et al. 2005,hereafter paper I),we presented H i observations of a sample of68such galaxies.In an accompanying paper to the current one(Noordermeer et al.2006),we present rota-tion curves for a subset of the galaxies from Paper I,and in a future publication,we will compare them to the rotation velocities expected from the visible matter in order to in-fer the dark matter distribution.Here,we present another ingredient for our study,a study of the dynamical impact of the bulges and disks in our galaxies.We present B-,R-and I-band surface photometry for a subsample of21galax-ies from Paper I,with morphological type ranging from S0 to Sab and absolute B-band magnitudes?17>M B>?22. We have decomposed the images into contributions of a?at-tened disk(including rings,bars,etc.)and a spheroidal bulge with a genuine3D structure,using an interactive2D decom-position technique.The radial distribution of stars in each component is then carefully measured and luminosity pro-?les are constructed and?tted with a general S′e rsic pro?le (bulge)and exponential disk.

In addition to their use in the mass models described above,our data also provide interesting information about the internal structure of bulges and their relation with the surrounding disks.We present an analysis on the various cor-relations between di?erent bulge-and disk parameters and brie?y discuss the implications for di?erent bulge formation mechanisms.

The structure of this paper is as follows.We describe the sample selection in section2.The observations and data reduction steps are described in section3.In section4we dis-cuss the photometric analysis of the galaxies,including the derivation of radial surface brightness pro?les,total magni-tudes,diameters,etc.In section5,the consistency of our photometric results is checked by comparing di?erent ob-servations of the same galaxies.In section6we present the procedure that was developed to decompose our images into bulge and disk contributions.We discuss the implications of our results in section7.Finally,the individual galaxies in our sample are discussed in section8,and a brief summary of our study and the main conclusions are presented in sec-tion9.For clarity,all long tables have been placed at the end of the paper,in appendix A.In appendix B,we show the images and photometric pro?les for all galaxies and the results from the bulge-disk decompositions.

2SAMPLE SELECTION

The galaxies studied in this paper form a subset of the68 galaxies with H i observations from Paper I,which them-selves were selected from the WHISP survey(Westerbork Survey of H i in spiral and irregular galaxies;Kamphuis et al. 1996;van der Hulst et al.2001).The WHISP sample con-sists of galaxies on the northern hemisphere(δ>20?),with optical diameter and H i line?ux limits of D25>1′and f>20mJy respectively.The sample of Paper I consisted of all galaxies in the WHISP survey with morphological type between S0and Sab.A more detailed description of the par-ent sample and the properties of the selected galaxies is given in Paper I.

Given the context of the present paper as part of our larger study of rotation curves and dark matter in early-type disk galaxies,the selection of galaxies from the par-ent sample in Paper I was mainly based on the requirement that good rotation curves could be derived.In practice,the following,somewhat subjective criteria were used:1)the

The stellar mass distribution in early-type disk galaxies3 Table1.Sample galaxies:basic data.(1)UGC number;(2)alter-

native name;(3)morphological type(taken from NED1);(4)ab-

solute B-band magnitude;(5)distance(from Paper I).

89NGC23SB(s)a-21.4562.1

94NGC26SA(rs)ab-20.3262.6

624NGC338Sab-20.8365.1

1541NGC797SAB(s)a-21.1277.0

2487NGC1167SA0--21.8867.4

2916–Sab-21.0563.5

2953IC356SA(s)ab pec-21.2215.1

3205–Sab-20.8948.7

3546NGC2273SB(r)a-20.0227.3

3580–SA(s)a pec:-18.3119.2

3993–S0?-20.1961.9

4458NGC2599SAa-21.3864.2

5253NGC2985(R’)SA(rs)ab-20.9321.1

6786NGC3900SA(r)0+-19.93?25.9

6787NGC3898SA(s)ab-20.0018.9

8699NGC5289(R)SABab:-19.4836.7

9133NGC5533SA(rs)ab-21.2254.3

11670NGC7013SA(r)0/a-19.2012.7

11852–SBa?-20.4480.0

11914NGC7217(R)SA(r)ab-20.2714.9

12043NGC7286S0/a-17.5315.4

4 E.Noordermeer&J.M.van der Hulst sures for each galaxy were aligned using a number of bright stars.They were then combined,using a simple rejection criterion to remove cosmic ray events and cosmetic defects on the chip.

Special care was taken in the subtraction of the back-ground light.In the?rst three runs on the JKT,the camera su?ered from light-leaks which caused faint residual gradi-ents in the background after?at?elding,especially in the R-band images.In almost all cases,the residuals could be removed by?tting a?rst-or second-order2D polynomial to the background and subtracting it from the image.In a few cases we used polynomials up to order5.In all cases, extreme care was taken to exclude the image of the galaxy from the?tting region,so as not to subtract any light from the galaxy itself.

In all other observations,including the B-band obser-vations from the JKT runs with light-leaks,the?at?elding worked very well and residuals were small.For these images, the background was removed by?tting a?rst-order polyno-mial to the emission-free regions.

As an extra check that the light-leaks did not a?ect our results,we re-observed UGC2953and3546in the fourth observing run on the JKT,when the light-leaks were https://www.doczj.com/doc/2214083729.html,parison of the resulting photometric pro?les from the images with and without light-leaks shows that the gra-dients were adequately removed and that the resulting pro-?les are consistent within the errors(see section5).

Throughout the nights,standard star?elds from Landolt(1992)were observed at intervals of1–2hours. Using the instrumental?uxes of the stars and the magni-tudes given by Landolt,we?tted the magnitude zero-points and extinction coe?cients,such that

m Landolt=m obs+m0+e·A,(1) where m Landolt is the stellar magnitude given by Landolt, m obs is our instrumental magnitude,m0is the magnitude zero-point,e is the extinction coe?cient and A is the air-mass.The coe?cients were determined for each night and each colour separately.The errors?m0and?e on the?t-ted coe?cients were used to derive the photometric error for each observation:

σphot=

The stellar mass distribution in early-type disk galaxies5 in the?gures in appendix B.In the outer part of the galax-

ies,outside the region where bulges and bars complicate the

picture,they usually converge to more or less constant val-

ues(see UGC3205,3580and6787for nice examples).These

values were then assumed to represent the true position an-

gle and inclination of the galaxy.In some cases,however,the

position angle and/or ellipticity never converge,and either

keep varying till the last point(e.g.UGC89,1541or4458)

or show several plateaus(e.g.UGC9133).In these cases,we

visually compared the?tted isophotes to the shape of the

galactic disks and then estimated the position angle and el-

lipticity by eye.Note that large variations in the orientation

parameters in the very outer points(e.g.UGC3993,4458,

8699)can usually be attributed to asymmetries in the light

distribution of the galaxy or to imperfect?at?elding;these

variations were generally not considered real.The adopted

values for the position angle and ellipticity are indicated

with the dashed lines in the?gures in appendix B and listed

in columns(6)and(7)in table A2.

From the ellipticity we determined the inclination of the

galaxies using the standard formula

(1??)2?q20

cos2i=

(4)

?I m(r)2+σ2

bg

Finally,the intensities and corresponding errors were

calibrated and converted to surface magnitudes using the

transformations determined in section3.Only points with

intensities larger than2σbg were considered.The resulting

photometric pro?les are shown in the top middle panels on

the?rst row of the?gures in appendix B.In the bottom

middle panels on the?rst row of the?gures,the colour pro-

?les are shown.The errors on the points are given by the

quadratic sum of the errors on the individual bands.Points

are only shown when the total error is smaller than0.5mag.

4.3Deviations from axisymmetry

In addition to the average intensity on each ellipse,we also

measured the higher-order harmonic components to study

deviations from perfect axisymmetry.The intensity distribu-

tion along each ellipse was decomposed into a Fourier series

of the following form:

I(α)=I0+I1cos(α+φ1)+I2cos(2(α+φ2))+...,(5)

whereαis the azimuthal angle along the ellipse,I0is the

average intensity on the ellipse and I1and I2measure the

strength of the m=1and m=2Fourier components respec-

tively.Thus,a high value for I1/I0indicates a strongly lop-

6 E.Noordermeer&J.M.van der Hulst sided light distribution,whereas a high value for I2/I0re-veals the presence of a bar or oval distortion.

A statistically signi?cant measurement of these higher order terms in the light distribution requires a higher signal-to-noise ratio than is necessary for the zeroth order term. The m=1and m=2terms were therefore only measured on

√ellipses for which the average intensity was respectively2

The stellar mass distribution in early-type disk galaxies

7 Figure2.Internal comparison of the photometric pro?les.Data points show the di?erence between photometric pro?les from multiple observations of the same galaxy.The observations which are compared are indicated above each panel;see table A1for details.Errorbars give the combined errors on each point.Dashed lines give the weighted average of the points which are not a?ected by seeing di?erences. Solid lines give the combined1σphotometric errors.

?les disagree at a level of2times the combined1σerrors. Given the number of pro?les compared here,one case of2σdisagreement is to be expected.The only cases where we observe signi?cant di?erences between the pro?les that can-not be attributed to seeing e?ects or uncertainties in the sky-level are the pro?les which were observed with di?er-ent telescopes(R-band observations of UGC2953,6786and 7989);as above,these di?erences can probably be attributed to the di?erent?lters which were used for the observations under comparison here.

In conclusion,for galaxies that were observed under photometric conditions,the photometric errors listed in ta-ble A1seem to be reliable;for non-photometric observations the errors are lower limits.The errors on individual data points in our photometric pro?les are also realistic and ac-count well for the uncertainties in the determination of the sky level.Photometric pro?les which were derived from im-ages observed with the INT or MDM telescope show small deviations(~0.1?0.2mag arcsec?2)compared to the pro-?les derived from the JKT images.The deviations manifest both as systematic o?sets between the pro?les,as well as point-to-point variations within the pro?les.These di?er-ences are probably caused by di?erences in the?lters used for the observations.

6BULGE-DISK DECOMPOSITIONS

Many methods exist to decompose the light of spiral galax-ies into contributions from bulges and disks.Traditionally,

8 E.Noordermeer &J.M.van der

Hulst

Figure 3.The in?uence of projection e?ects on the central R-band photometric pro?le of UGC 6786.The pro?le shown with squares is derived using the standard method,i.e.the intensities are measured along ellipses with ellipticity ?xed at the value of the outer regions.The circles denote the pro?le when measured along ellipses with an ellipticity which better represents the isophotes of the bulge.

the decomposition is performed on the photometric pro?les directly,?tting them with the sum of an exponential disk and a certain pro?le for the bulge (usually either an r 1/4,exponential or general S′e rsic pro?le).As this is a 1D pro-cedure,it is quick and can therefore be used to study large samples of galaxies in short timespans (e.g.Baggett et al.1998;Graham 2001;MacArthur et al.2003).However,pho-tometric pro?les su?er from projection e?ects.The observed intensity at each point in a galaxy is a superposition of light from the bulge and disk.Because they have di?erent intrinsic shapes,the contributions from both components come from di?erent radii when the galaxy is observed un-der a non-zero inclination angle,and the average intensity along a given isophote is generally not directly related to the true mean brightness at that radius.Thus,deriving bulge and disk parameters from azimuthally averaged photometric pro?les will lead to systematic errors.A proper treatment of the projection e?ects requires a full 2D decomposition technique (e.g.Byun &Freeman 1995;de Jong et al.2004;Laurikainen et al.2005).

The projection e?ects described above are particularly severe in the type of galaxies studied here,which have of-ten large and luminous bulges.As an illustration,we show in ?gure 3two R-band photometric pro?les of the central part of the bulge-dominated galaxy UGC 6786.The pro?le shown with squares is derived following our standard proce-dures of section 4.2,that is,it shows the average intensities measured along ellipses with the ellipticity ?xed at the value of the outer regions.The circles show the intensities when measured along ellipses with a much lower ellipticity,which is more representative of the isophotes in the central,bulge-dominated region.Clearly,the bulge of UGC 6786is more centrally concentrated than is shown by our standard pho-tometric pro?le;any structural parameters of the bulges de-

rived directly from our photometric pro?les will be severely a?ected by systematic errors.

Another problem with bulge-disk decompositions is the degeneracy that exists between the di?erent parameters (MacArthur et al.2003;de Jong et al.2004).The data can often be ?tted by di?erent combinations of parameters,so that it can be di?cult to reach unambiguous conclusions about the true values.

To overcome the di?culties mentioned above,we have developed a hands-on,interactive procedure that uses the full 2D information from the images to separate them into bulge and disk components.Our method bears some sim-ilarities with the one used by Palunas &Williams (2000)and can be summarised as follows.We model the bulges as ?attened axisymmetric spheroids,with intrinsic axis ratios q b and general S′e rsic photometric pro?les characterised by e?ective radius and magnitude r e and μe and shape param-eter n (S′e rsic 1968).The bulge parameters are determined from images where an initial estimate for the disks has been subtracted.Based on the ?tted parameters,model images of the bulges are created and subtracted from the original images.All light in these image is then assumed to originate from the disks,and their photometric pro?les are used to derive the disk light distributions.

A more detailed description of the separate steps is given in the following subsections.

6.1Bulge parameters

The ?rst step in our procedure consists of deriving initial estimates for the bulge and disk parameters from an ana-lytic ?t to the photometric pro?le.As discussed above,the central,bulge-dominated parts of the photometric pro?les su?er from projection e?ects.In the outer parts,however,the pro?le is usually dominated by the ?at disk,and projec-tion e?ects are not an issue.Thus,the initial estimates for the disk are generally su?ciently reliable for the next step.

Based on the initial estimates,an initial model image of the disk component is created by extrapolating the ?tted disk pro?le inwards.This model image is then subtracted from the original image to obtain an image with,to ?rst order,bulge-light only.

From the resulting image,the bulge-parameters can be obtained.We ?rst determine the ?attening of the bulge by ?tting ellipses to the R-band bulge image with ellipticity and position angle as free parameters.In most cases,the position angle of the bulge isophotes is close to the value derived for the outer disk,indicating that the bulge is a ?attened spheroid with the plane of symmetry coinciding with that of the disk.In a few cases,the position angle in the centre di?ers from the outer values,indicating the presence of a nuclear bar or other triaxial structure.The presence of these non-axisymmetric structures is ignored in the following;we model all bulges as oblate spheroids that are aligned with the outer disk and we simply average out any non-axisymmetric structures along the isophotes in the next step.Because the bulges are more vertically extended than the surrounding disks,their ellipticities are generally lower than those found for the outer disks.From the average ellipticity ?b of the bulge isophotes,the intrinsic ?attening of the bulge can be determined by rewriting equation 3as

The stellar mass distribution in early-type disk galaxies9 q2b=

(1??b)2?cos2i

r0 1/n .(7)

Here,I0,b is the central surface brightness and r0is the characteristic radius.n is a shape parameter,that describes the curvature of the pro?le in a radius-magnitude plot.For n=4,equation7reduces to the well-known De Vaucouleurs pro?le(de Vaucouleurs1948),whereas n=1describes a simple exponential pro?le.In the literature,equation7is usually written as

I b(r)=I e exp ?b n r

2Γ(2n),withγandΓthe incomplete and com-

plete gamma functions respectively.It can be approximated

by b n≈1.9992n?0.3271for1

in our?tting procedure,we determined b n more accurately

by numerically solving the equation above.

In magnitudes,equation8is written as

μb(r)=μe+1.0857b n r

h ,(10)

or in magnitudes:

μd(r)=μ0,d+1.0857

r

10 E.Noordermeer &J.M.van der

Hulst

Figure https://www.doczj.com/doc/2214083729.html,parison of the R-band bulge and disk parameters.Left:absolute magnitudes of bulge vs.disk;middle:bulge e?ective radius vs.disk scale length;right:bulge e?ective surface brightness vs.disk central surface brightness.The open squares indicate UGC 624,the circles indicate UGC 6786.

7DISCUSSION

The main purpose of the analysis described in this paper is to derive the contribution of the stellar component of our galaxies to their gravitational potential.In a forthcoming pa-per,we will calculate the contributions of the stellar disks and bulges to the rotation curves,and use the results to constrain the content and distribution of dark matter in our galaxies.Meanwhile,some interesting results concerning the structure and mutual dependence of the bulges and disks of our galaxies can be derived from our study as well.These re-sults are in some ways complementary to the larger studies of e.g.Graham (2001),MacArthur et al.(2003),de Jong et al.(2004),Hunt et al.(2004)and Laurikainen et al.(2005).Be-low,we discuss the most important points.

7.1A comparison of bulge and disk parameters

In ?gure 4,we compare the total luminosities,sizes and sur-face brightnesses of the bulges and disks of the galaxies in our sample with accurate bulge-disk decompositions.It is clear that there is only a weak coupling between the bulge and disk parameters.

There is a weak trend of more luminous disks harbour-ing more luminous bulges,but the scatter around the rela-tion is large.Moreover,several biases in our sample selec-tion could introduce an arti?cial correlation:galaxies with a highly luminous bulge and a faint disk might not be classi-?ed as disk galaxies,but rather be mis-identi?ed as ellipti-cals.Similarly,luminous disks with faint bulges might not be classi?ed as early-type disks,but rather as late-type spirals.This latter e?ect is,however,not expected to be as strong as the former,since the morphological type classi?cation is based on other parameters than bulge-disk luminosity ratios as well.Moreover,our sample contains a number of galaxies with high-luminosity disks and faint bulges (e.g.UGC 94,3205,3546),which are still clearly recognisable as early-type disk galaxies.UGC 12043even has no obvious bulge com-ponent at all,but is still classi?ed as an S0/a galaxy.

In any case,our results indicate a large range in bulge-to-disk (BD)luminosity ratio and show that the common belief that early-type disk galaxies have large and luminous bulges does not hold in all cases.This is also visible in the

left hand panel of ?gure 5,where we show the distribution of the BD luminosity ratio for all galaxies in our sample.The average value of log(L b /L d )is ?0.23±0.47in the R-band,where the error gives the standard deviation of the sample.

Apart from two galaxies,UGC 624and 6786,which have unusually large bulges (as measured from their e?ec-tive radii r e ),there is a weak correlation between disk scale length and bulge e?ective radius (middle panel in ?gure 4).In the following,we will show that UGC 6786di?ers from the rest of the sample in many aspects,and we will inter-pret this in section 8as an indication that this galaxy is not really a disk galaxy,but rather an elliptical galaxy with an additional disk of gas and stars.The o?set of UGC 624may be explained as a result of its high inclination with respect to the line of sight.There are indications that the image of this galaxy is signi?cantly a?ected by dust (note for exam-ple the strong asymmetry in the centre,visible in the I 1/I 0lopsidedness parameter,and by eye in the bulge-subtracted image).If there are indeed large amounts of dust present in this galaxy,it is conceivable that they introduce large errors in the shape of the photometric pro?les and in the resulting bulge-disk decomposition.

The other galaxies seem to follow the global trend that large bulges reside in large disks,although the scatter is,again,large.In the right hand panel of ?gure 5,we show the distribution of r e /h for all galaxies in the sample.The average value of this ratio is 0.51±0.72(the error indicates the standard deviation),but this value is heavily in?uenced by UGC 6786.The average value for the sample without UGC 6786is 0.35±0.19,whereas it is further reduced to 0.32±0.15if UGC 624is excluded as well.Even this last value is signi?cantly higher than the average r e /h for the late-type spiral galaxies studied by Courteau et al.(1996).It is also higher than the values found by Graham (2001)and MacArthur et al.(2003),who both noted a mild trend of the ratio r e /h increasing towards earlier type spiral galaxies,but only reaching an average of respectively 0.21and 0.24for the early types.

It is not immediately clear what causes the higher r e /h ratio for our sample,compared to the results of Graham (2001)and MacArthur et al.(2003),but it could well be related to the di?erent decomposition techniques used.We already argued in section 6.1that 1D decompositions suf-

The stellar mass distribution in early-type disk galaxies

11

Figure 5.The distribution of the R-band bulge-to-disk luminosity ratio (left )and size ratio (right )for the galaxies in our sample.Gray shading indicates UGC 624and 6786.

fer from systematic e?ects.Inspection of ?gure 3on page 8shows that,in an extreme case such as UGC 6786,a photo-metric pro?le measured along ellipses with ellipticity ?xed at the value of the outer disk is shallower than the true light distribution.A simple least-χ21D ?t to this pro?le yields an e?ective radius for this bulge of 24.0′′,almost a factor 2smaller than the value we derived using our 2D method described in section 6.1(43.5′′).Although UGC 6786is an extreme galaxy,it seems likely that the same e?ect plays a r?o le,perhaps to a lesser extent,in other galaxies as well.Thus,the discrepancy between the average r e /h ratios of our study and those of the 1D studies of Graham (2001)and MacArthur et al.(2003),strengthens the need for 2D decompositions to recover the bulge parameters accurately,especially in galaxies where the bulges contribute a substan-tial fraction to the total light (cf.Byun &Freeman 1995;de Jong et al.2004).Note that our average r e /h ratio is fully consistent with the study of Khosroshahi et al.(2000),who used a 2D decomposition method for a sample of predomi-nantly early-type disk galaxies.

No obvious trend is visible between the surface bright-nesses of the bulges and disks in our sample (right hand panel in ?gure 4,cf.Hunt et al.2004).7.2

Correlations between di?erent bulge parameters

Previous studies such as the ones by Khosroshahi et al.(2000),Graham (2001)and de Jong et al.(2004)have re-vealed several correlations between the di?erent parameters which characterise the bulges.In ?gure 6,we study several of these correlations for our galaxies.

Panel (a)in this ?gure shows that the e?ective radius shows a clear correlation with the total luminosity of the bulge.This is not very surprising,and simply shows that larger bulges are more luminous.

A priori less expected is the relation between the S′e rsic index n and the total luminosity of the bulges (panel (d)):luminous bulges have predominantly higher n -values than their low-luminosity counterparts.This trend was noted before by e.g.Andredakis et al.(1995),Khosroshahi et al.(2000)and Graham (2001),and is also observed in ellip-tical galaxies (e.g.Caon et al.1993;Young &Currie 1994;

Jerjen et al.2000).It should,however,be approached with some caution,as there may be a selection e?ect at play.Low-luminosity bulges are generally small (panel (a))and in many cases,their e?ective radii are only a few arcsec-onds on the sky (see also table A4).In such cases,the seeing will smear out any sharp peaks in the light pro?les and,even though we deconvolve our bulge pro?les when ?t-ting the S′e rsic model,the n -value will e?ectively be low-ered (Trujillo et al.2001).Thus,the apparent correlation in panel (d)may be partly arti?cial,and sub-arcsecond images would be required to con?rm the trend at the low-luminosity end (cf.Balcells et al.2003).

The bulges in our sample span the full range from ex-ponential light pro?les (n ≈1)to De Vaucouleurs (n ≈4),with UGC 6786lying out at n =5.5.A histogram of the dis-tribution is shown in ?gure 7.The average value of n for the entire sample is 2.5±1.1,where the error gives the standard deviation of the sample;for the sample without UGC 6786,this becomes n =2.3±0.9.These values are fully consis-tent with previous results from e.g.Andredakis et al.(1995);de Jong (1996a);Graham (2001)and Hunt et al.(2004)and con?rm the view that the bulges of early-type disk galaxies form,at least as far as their n -values is concerned,an inter-mediate population between elliptical galaxies,which have n around 4but up to 15in extreme cases (Caon et al.1993;de Jong et al.2004),and late-type galaxy bulges,which usu-ally have exponential or even steeper pro?les (e.g.de Jong 1996a;MacArthur et al.2003).

The three fundamental bulge parameters from equa-tion 9,μe ,r e and n are all clearly correlated (panels (c),(e)and (f)in ?gure 6,cf.Khosroshahi et al.2000,de Jong et al.2004,Hunt et al.2004),but the selection e?ect described above may be important here as well:seeing e?ects may introduce a bias for small bulges towards lower n .Further-more,the correlations may partly be caused by the de?ni-tion of these parameters which intrinsically couples them.Bulges with higher n values have a shallower light pro?le at large radii,but with a suitable choice of the central surface brightness and e?ective radius,the pro?le can look relatively similar to that of low-n bulges in the inner parts.Such high-n bulges will have a larger e?ective radius r e than low-n bulges,and the surface brightness μe at that radius will be

12 E.Noordermeer &J.M.van der

Hulst

Figure 6.Correlations between di?erent bulge parameters:total magnitude M b ,e?ective radius r e ,e?ective surface brightness μc e (corrected for Galactic foreground extinction),S′e rsic parameter n and intrinsic axis ratio q b .All data refer to the R-band images.The open squares indicate UGC 624,the circles indicate UGC 6786.The crosses in the bottom panels indicate bulges where determination of the intrinsic ?attening of the bulge was di?cult (UGC 2916,3205and 3993;see table A4).

lower.These are exactly the trends which are visible in ?g-ure 6.

Parameter coupling alone cannot,however,explain the correlations between the bulge parameters.This can be ap-preciated,for example,by considering instead of the e?ec-tive surface brightness the central surface brightness μ0.In ?gure 8,we show that the ?tted central bulge surface bright-ness is highly variable,with a similar width in the distribu-tion as for the e?ective surface brightness μe .Moreover,it is strongly correlated with the S′e rsic shape parameter as well.Thus,for a given n ,bulges occupy a distinct region in surface brightness space.The correlations between the bulge

parameters are therefore real and must have a true physical basis (cf.Trujillo et al.2001).

There seems to be a weak trend between the ?at-tening of the bulges and their total luminosity,more lu-minous bulges being on average more ?attened than low-luminosity bulges (panel (g)in ?gure 6).This result is somewhat surprising,since previous studies had found that ?at ‘pseudobulges’are more common in late-type spiral galaxies than in early-type disk galaxies (Kormendy 1993;Kormendy &Kennicutt 2004,and references therein).One would thus expect the most spherical bulges in our sample to be the most luminous,but this is clearly not the case.

The stellar mass distribution in early-type disk galaxies

13 Figure7.The distribution of the S′e rsic n-parameter for the

bulges in our sample.The numbers were derived from the R-band

data.

Figure8.The correlation between S′e rsic n-parameter and?tted

central surface brightnessμ0(corrected for Galactic foreground

extinction)for the bulges in our sample.All data are derived from

the R-band images.

It is important to note that the uncertainties in individ-

ual measurements of the intrinsic axis ratio of the bulge are

large.In several cases,the ellipticity of the bulge isophotes

is not constant with radius,and it is problematic to assign a

unique value to the apparent axis-ratio of the bulge.In other

cases,where the bulges are small,seeing e?ects may lead to

biases as well.Finally,in galaxies that are close to face-on,

there is little leverage on the problem,as di?erent intrin-

sic axis ratios lead to very minor changes in the observed

image.The three galaxies where the determination of the

bulge?attening was particularly di?cult(UGC2916,3205

and

3993)are indicated with crosses in the bottom panels

in?gure6.In spite of all these problems,the correlation

Figure9.The distribution of the intrinsic axis ratios q b of the

bulges in our sample.All values were derived from the R-band

data.The white histogram shows the distribution for the entire

sample,the light gray shading indicates galaxies where the de-

termination of q b was particularly di?cult(UGC2916,3205and

3993,see table A4).Dark shading indicates UGC6786.

in panel(g)is suggestive,and the uncertain data points do

not appear to alter it.There seems to be a genuine trend of

more luminous bulges being?atter than less luminous ones.

Finally,the distribution of the intrinsic axis ratios q b

for our entire sample of bulges is shown in?gure9.The av-

erage value for the sample is q b =0.55±0.12,where the

error gives the standard deviation of the sample.Exclusion

of the three uncertain values does not lead to di?erent val-

ues.Note that none of the galaxies in our sample harbours a

truly spherical bulge.Furthermore,the least?attened bulge

is that of UGC6786,which di?ers from the rest of the sam-

ple in many respects(see discussion above)and seems to

be more resemblant of an elliptical galaxy with a small disk

of stars and gas(see also the note in section8).All other

bulges have an intrinsic axis ratio of0.7or less.

7.3Colour gradients

It has long been known that many spiral galaxies do not have

a uniform colour over their entire disk,but instead become

bluer towards larger radii(de Vaucouleurs1961;de Jong

1996b;Matthews et al.1999).Such colour gradients have

been interpreted in the past as a result of radial variations

in the dust content and star formation history(SFH)in the

disks of spiral galaxies.de Jong(1996b)concluded,based

on detailed radiative transfer and stellar synthesis models,

that dust reddening plays only a minor r?o le and that most of

the colour gradients are due to“a combined stellar age and

metallicity gradient across the disk,with the outer regions

being younger and of lower metallicity”.On the other hand,

M¨o llenho?et al.(2006)recently argued that“the tendency

for apparent scalelength to increase with decreasing wave-

length is primarily due to the e?ects of dust”.Clearly,the

14 E.Noordermeer &J.M.van der

Hulst

Figure 10.Bulge B-R colour vs.disk colour.In the left panel,the bulge colour is plotted vs.the integrated disk colour;in the right

panel,it is plotted against the ?tted central disk colour,μc 0,B ?μc 0,R .The dashed line gives the locations of equal colour.All colours are

corrected for Galactic foreground extinction.

underlying mechanisms causing the colour gradients are not fully understood yet.

Here we investigate whether colour di?erences between the bulges and the disks are responsible for (part of)the observed colour gradients in our galaxies.

Inspection of the ?gures in appendix B shows that many galaxies in our sample have colour gradients;most galax-ies become bluer towards larger radii.There are,however,also galaxies which show no evidence for colour variations,or which become redder towards large radii (e.g.UGC 89,2953).It is important to note that the errorbars on the colour pro?les become large in the outer regions of the galax-ies,predominantly as a result of the uncertainties in the de-termination of the background level of the images.Although we attempted to determine the background level in our im-ages as accurately as possible and we tried to include its uncertainty in the errorbars of our photometric pro?les (see section 4.2),it is possible that the large colour variations in the outer parts of e.g.UGC 6787are the result of incor-rect background levels in one of the colour bands.Colour variations in the bright inner regions of the galaxies cannot be explained by an improper background determination and must be real.

The results from our bulge-disk decompositions indicate that the bulges of our galaxies are on average signi?cantly redder than the disks surrounding them (see ?gure 10).The average B-R colour di?erence between the bulges and disks is (B ?R )bulge ?(B ?R )disk =0.43±0.30,where the error gives the standard deviation of the sample.This colour dif-ference between bulges and disks is,in most cases,at least partly responsible for the observed colour gradients:the rel-ative contribution of the red bulge light declines towards larger radii,at the cost of an increasing contribution of bluer disk light.Good examples of this e?ect are UGC 94,1541,5253and 11670.

However,the colour di?erences between bulges and disks are not su?cient to explain all radial colour gradi-ents.In some cases,the bulge-subtracted images (shown at the bottom right in the ?gures in appendix B)do not con-tain any remaining colour variations,showing that indeed the colour gradients in the original images were caused by the in?uence of the bulges (e.g.UGC 2916,9133,11670).But in most cases,the bulge-subtracted images still contain

colour gradients and become bluer towards larger radii (e.g.UGC 2487,3205,3993,6787).Thus,our results show that not only are bulges on average redder than their surrounding disks,the disks themselves are also bluer in the outer parts than at smaller radii.If De Jong’s conclusion was correct that dust reddening plays only a minor r?o le in the colour gradients (de Jong 1996b),then our results indicate that the stars in the bulges were on average formed earlier than those in the disk (or have higher metallicity),and that in the disks themselves,the star formation history and metallicity vary with radius (with the stars in the outer regions being younger and/or having lower metallicity).

8NOTES ON INDIVIDUAL GALAXIES

UGC 89(NGC 23)has a relatively small (r e /h =0.13)but bright bulge (central surface brightness μc,R =15.9mag arcsec ?2).The presence of the strong bar compli-cates the determination of the bulge parameters,as it dom-inates the light distribution to very small radii.In particu-lar,the ellipticity of the isophotes does not reach a constant value in the bulge region,so we were forced to estimate the bulge ellipticity ?b by eye.The bar is also responsible for the characteristic ‘dip’around r =35′′in the surface brightness pro?les.

UGC 94(NGC 26)has a very low bulge-to-disk luminosity ratio of L b /L d =0.09in R (0.04in B).The low luminosity of the bulge is caused by its low e?ective surface brightness

(μc e =21.4mag arcsec

?2

in the R-band),while its e?ective radius is normal (r e /h =0.31).Of all bulges in our sample,this one lies furthest to the bottom-left in panel (b)of ?g-ure 6(μc e vs.M b ).Although UGC 94is not classi?ed as a barred galaxy,it has a small but distinct bar in the centre,oriented approximately east–west.

UGC 624(NGC 338)has a relatively large and luminous bulge (r e /h =0.82,L b,R /L d,R =2.60,see ?gure 4).These extreme properties may,however,be a result of the poor bulge-disk decomposition for this galaxy.The combination of an exponential disk and S′e rsic bulge seems a rather in-adequate description of this galaxy and the extreme bulge properties may be simply an artefact caused by the ?tting of an inappropriate model to the data.Part of the problem

The stellar mass distribution in early-type disk galaxies15

with UGC624may be the high inclination and resulting dust extinction.There are strong indications for dust extinc-tion in the centre(note for example the strong asymmetry in the centre,visible in the I1/I0lopsidedness parameter, and by eye in the bulge-subtracted image).It is not incon-ceivable that the peculiar shape of the luminosity pro?le of this galaxy is at least partly caused by dust extinction. UGC1541(NGC797)has a distinct bar which causes the typical‘bump’in the luminosity pro?le around40′′.To the west,at the end of the spiral arm,a small companion ellip-tical galaxy is visible(cf.Zwicky&Zwicky1971).The light of this companion was masked out for the measurement of the luminosity pro?le and the subsequent bulge-disk decom-position.

The R-band image of this galaxy,which is shown in the ?gure in the appendix,was taken in windy conditions.As a result,the telescope su?ered from mild vibrations,causing the PSF to be elongated,roughly along the east-west di-rection.To avoid errors due to this e?ect,we measured the position angle and ellipticity of the bulge from the B-band image.Outside the region a?ected by the PSF elongation, the R-band image is consistent with the bulge orientation thus derived.

UGC2487(NGC1167)is the most luminous galaxy in our sample(M lim,R=?23.24).It is an almost perfect su-perposition of an exponential disk and a S′e rsic bulge;the residuals with respect to the?tted bulge and disk pro?les are less than0.05mag arcsec?2everywhere.Some very faint spiral structure is visible in the disk.

UGC2916has a nuclear bar;the ellipticity of the isophotes in the centre does not represent the shape of the bulge and we were forced to estimate the bulge ellipticity?b by eye. As as result,the derived intrinsic axis ratio of the bulge is uncertain.The colour gradient in this galaxy can be fully explained by the colour di?erence between the bulge and disk;the colour of the bulge-subtracted image does not vary with radius.

UGC2953(IC356)is a large and well-resolved galaxy on the sky,but it is relatively nearby(D=15.1Mpc)and the physical dimensions are rather average for our sample (h=4.1kpc).The decomposition into exponential disk and S′e rsic bulge is almost perfect,with residuals less than 0.1mag arcsec?2almost everywhere.It is also one of the most symmetric galaxies in our sample,without any strong lopsided or oval distortions.

UGC3205has the lowest R-band bulge-to-disk luminos-ity ratio of all galaxies in our sample(L b/L d=0.07).Its bulge is also very small compared to the surrounding disk (r e/h=0.15)and is only barely resolved in our images (r e=2.2′′,1.7times the seeing of the R-band observa-tions).As a result,the?tted S′e rsic parameter n and intrinsic axis ratio q b for this bulge have a limited accuracy;higher-resolution observations are necessary to study the structure of the bulge of this galaxy in detail.Although not classi?ed as a barred galaxy,UGC3205has a weak bar,roughly ori-ented east-west(see also the I2/I0Fourier term in the?gure in the appendix).Apart from the bar,the galaxy is highly symmetric.No spiral structure can be seen in our images;

a classi?cation as S0seems more appropriate than the Sa

b from the UGC.UGC3546(NGC2273)has the smallest bulge of all galax-ies in our sample,both in absolute terms(r e=0.29kpc) as relative to the surrounding disk(r e/h=0.10),but due to its high surface brightness,the bulge-to-disk luminos-ity ratio is larger than in UGC3205(L b/L d=0.12).The bulge is embedded in a distinct bar;two spiral arms emanate from the ends of it and form a ring in the outer parts(cf. van Driel&Buta1991).In the very inner parts,a secondary bar seems present,but high-resolution observations with HST by Erwin&Sparke(2003)showed that it is actually a nuclear ring with a star-forming spiral inside.UGC3546has a Seyfert2nucleus(Huchra et al.1982)and has been exten-sively studied at radio wavelengths(e.g.Ulvestad&Wilson 1984;Nagar et al.1999).This galaxy was observed during three di?erent runs in R and two runs in B,enabling a thor-ough check on the internal consistency of our observations and data reduction techniques(see section5);all observa-tions were found to be fully consistent.

UGC3580is a relatively small and low-luminosity galaxy, with an absolute R-band magnitude of-19.42and an R-band disk scale length of2.4kpc.It has an irregular appear-ance and seems strongly a?ected by dust.Although there is clearly excess light in the centre over the exponential outer disk,this‘bulge’has a patchy light distribution,bearing little resemblance to the smooth spheroids present in most other galaxies in our sample.It is also bluer than the other bulges in our sample((B?R)b=1.05,corrected for Galactic foreground extinction).Several‘knots’of bright emission are seen in the image as well,presumably regions of active star formation;James et al.(2004)report an equivalent width for Hα+[N ii]of2.9nm,unusually large for an early-type spiral galaxy,indicating that indeed,this galaxy is actively forming stars.In a forthcoming paper,we will show that the kinematical structure of this galaxy is also di?erent than that of the other galaxies in our sample.

All these facts lead us to assume that UGC3580is a(relatively luminous)member of a class of dwarf early-type spiral galaxies,which have distinctly di?erent morpho-logical and kinematical properties than the more common high-luminosity early-type disk galaxies.Other galaxies in our sample which probably belong this class are UGC12043 (see below),and UGC6742and12713(Paper I).

UGC3993is an example of a luminous bulge embedded in a low surface brightness(LSB)disk.The?tted central surface brightness of the disk is23.2mag arcsec?2(B-band, corrected for Galactic foreground extinction and inclination e?ects),but the description as an exponential disk is rather poor and this value may not represent the actual surface brightness of the disk in the centre.The bulge-subtracted image in the appendix shows that the disk is dominated by an inner ring with a radius of approximately10′′(~3kpc). The exact density contrast of this ring with the surrounding disk regions depends quite sensitively on the details of the bulge-disk decomposition;in particular,acceptable decom-positions can be performed where the central hole in the disk is not as deep as in our preferred solution.In all solutions, however,there is a clear overdensity at this radius,showing that the ring is a genuine physical feature.In addition to this inner ring,some very faint,?lamentary spiral arms are visible in the outer regions of the disk.

Due to the near face-on orientation of this galaxy

16 E.Noordermeer&J.M.van der Hulst

(i≈23?),the bulge and disk ellipticity could not be dis-tinguished,and the bulge?attening could only be guessed. UGC4458(NGC2599)has the second most luminous bulge of all galaxies in our sample(M b,R=?21.8),sur-passed only by that of UGC624(but see note for that galaxy above).The surrounding disk is highly extended,with an R-band exponential scale length of8.6kpc(second largest of all galaxies in our sample,after UGC9133).Some?lamen-tary structures can be recognised on the northwest of the disk,either faint spiral arms or shells caused by a merging event.

UGC5253(NGC2985)has a large featureless bulge which is well?tted with an R1/4-pro?le(we?nd n=3.9).How-ever,the ellipticity of the isophotes in the bulge-dominated regions is hardly lower than in the outer,disk-dominated re-gions,indicating that the bulge is highly?attened;we derive an intrinsic axis-ratio of q b=0.4.The disk is dominated by beautiful,grand design spiral arms;many‘knots’of bright blue emission can be discerned,presumably star forming re-gions(cf.Gonz′a lez Delgado et al.1997).

UGC6786(NGC3900)is in many ways di?erent from the other galaxies in our sample(cf.section7).It has the largest and most luminous bulge of all galaxies,compared to the disk(L b/L d=3.91,r e/h=3.54,all in R)and the S′e rsic parameter and intrinsic axis ratio of the bulge are larger than in any other bulge in our sample(n=5.5,q b=0.8).The bulge is so dominant that the isophotes of the original image do not probe the disk elongation at any radius,so the incli-nation derived using the standard method(section3)was not correct.Only after the subtraction of the bulge could the disk be distinguished properly and could we derive its orientation from the shape of the faint spiral structure.For the derivation of the disk pro?le and the intrinsic axis ratio of the bulge,we assumed an ellipticity of0.21,corresponding to an inclination of69?(close to the kinematical inclination angle of68?,derived from the H i velocity?eld).

The resulting disk pro?le shows a plateau of constant surface density in the centre(μR≈21.5mag arcsec?2)and an exponentially decaying pro?le outside35′′(~4.5kpc).A linear?t to the outer parts of the disk pro?le yields a scale length of12.3′′(1.6kpc)and a formal central surface bright-ness of19.3mag arcsec?2(R-band,corrected for Galactic foreground extinction and inclination).Note,however,that such high surface brightness is in reality not reached in the disk,due to the truncation of the pro?le around35′′.

All combined,UGC6786does not look like a normal early-type disk galaxy at all,but rather seems to resemble an elliptical galaxy which has acquired a disk of gas and stars. In the recent past,it was discovered that many galaxies which are classi?ed as ellipticals,harbour small stellar disks (e.g.Rix&White1990;Scorza&Bender1995);UGC6786 could well be an extreme example of such a class of galax-ies.There may also be a connection with galaxies such as NGC3108or NGC4278,elliptical galaxies with extended, regularly rotating gas disk around them(Oosterloo et al. 2002;Morganti et al.2006).It is conceivable that the gas in such galaxies will eventually form stars as well,and in fact,there is some evidence for a very faint stellar disk in the centre of NGC3108.UGC6786may be a similar,but more evolved,system to these galaxies.UGC6787(NGC3898)su?ers from the same problem as UGC6786:the luminous bulge distorts the isophotes of the disk out to large radii and the standard method to derive the inclination(section4.1)cannot be used.Only after the model image of the bulge was subtracted could the disk el-lipticity be determined.The?nal disk photometric pro?le and the intrinsic axis ratio of the bulge were derived using an inclination of61?.Note that this is still somewhat lower than the kinematic inclination which we derived from the H i velocity?eld(69?).

UGC8699(NGC5289)is highly inclined(i=77?),but we can still recognise the bright bulge,small bar and surround-ing ring.The disk component in this galaxy has a low surface brightness(μc0,d=23.4mag arcsec?2,B-band,corrected for inclination e?ects and Galactic foreground extinction).The strong asymmetry in the central light distribution is most likely the result of internal absorption by dust;at larger radii,the galaxy is highly symmetric.The sudden change in position angle and ellipticity around70′′is a result from imperfect?at?elding and is not real.

UGC9133(NGC5533)is a luminous galaxy(M R=?22.62)which can almost perfectly be decomposed in an exponential disk and S′e rsic bulge(the residuals being less than0.1mag arcsec?2almost everywhere).It has the largest disk scale length of all galaxies in our sample(h R=8.9kpc). The ellipticity of the bulge is barely lower than that of the disk,implying that the bulge is highly?attened;we derive an intrinsic axis-ratio of q b=0.3.Some faint,?lamentary spiral structure is visible in the outer disk.

UGC11670(NGC7013)is a small and relatively low-luminosity galaxy(h R=1.8kpc,M B=?19.20).It has a large,lens-shaped bar with conspicuous dust-lanes running parallel to it.In the outer parts,a di?use disk with very faint spiral structure can be seen.

UGC11852is the most distant galaxy in our sample (D=80Mpc).It consists of a relatively di?use bulge em-bedded in a highly elongated bar.The spiral arms are some-what irregular and develop into narrow?laments extend-ing to very large radii(barely visible in the?gure in ap-pendix B).

UGC11914(NGC7217)is a highly symmetric,nearly face-on galaxy,which can be well decomposed into a S′e rsic bulge and an exponential disk.The bulge is relatively large,compared to the disk(r e/h=0.71).The residu-als with respect to the model components are small,ex-cept for a distinct ring of blue stars which causes ex-cess light at a radius of approximately75′′(≈5.5kpc; cf.Buta et al.1995;Verdes-Montenegro et al.1995).This ring coincides with an enhanced surface density of neu-tral gas(Paper I)and contains many star-forming regions (Pogge1989;Battinelli et al.2000).However,as discussed in Paper I,the gas surface densities are below the star-formation threshold from Kennicutt(1989),so it is puzzling how this galaxy can sustain its large-scale star formation activity.

Note that our bulge-to-disk luminosity ratio for UGC11914is much lower than the value derived by Buta et al.(1995)(0.58vs.2.3,both B-band);this di?er-ence is presumably caused by the fact that they used an R1/4-pro?le for the bulge,whereas we left the S′e rsic index

The stellar mass distribution in early-type disk galaxies17

free in the?ts.Our?tted bulge pro?le has n=3.1,and thus contains much less light at large radii than an R1/4-bulge. This di?erence illustrates once more the importance of using a general S′e rsic pro?le for the bulge intensity distribution, rather than the less?exible de Vaucouleurs pro?le. Although UGC12043(NGC7286)has the characteristic smooth light distribution of early-type disk galaxies,it completely lacks a central bulge component.The light pro-?le shows only an exponential disk;the?tted exponential pro?les are overplotted with the bold lines in the?gure on page36.This galaxy is also smaller and less luminous than other galaxies in our sample(D c25,R=7.8kpc, M R=?18.26).This galaxy seems a member of a class of dwarf early-type spiral galaxies with distinctly di?erent properties from their high-luminosity early-type counter-parts(see also UGC3580).

9SUMMARY AND CONCLUSIONS

We have obtained deep R-and B-band surface photometry for a sample of21early-type disk galaxies with morpholog-ical types between S0and Sab and B-band absolute magni-tudes between-17and-22.For6galaxies,I-band photome-try is available as well.On average,our data reach surface brightness levels of26.95,26.07and24.26mag arcsec?2(3σ) in B,R and I respectively.

For all galaxies,we have presented the results of our isophotal analysis,including radial variations of surface brightness,colour,ellipticity,position angle and deviations from axisymmetry.We have also determined isophotal and e?ective diameters and total magnitudes.

We have developed a new,interactive,bulge-disk de-composition method which takes into account the full2D information from the images and decomposes them into spheroidal bulges with a general S′e rsic intensity pro?le and disks with an arbitrary intensity distribution.We made no prior assumptions about the intrinsic axis ratios of the bulges,but rather determined those directly from the images by comparing the ellipticity of the bulge isophotes to that of the outer disk.We have shown that1D bulge-disk decom-position methods,where analytic functions are?t directly to the radial photometric pro?les,su?er from systematic bi-ases,particularly in galaxies with large and luminous bulges. For example,they can lead to severe under-estimates of the e?ective radii of the bulges.2D techniques,which use the full information available in the image,are less a?ected by such biases and yield more accurate results on the structural parameters of the bulges.

From a comparison of di?erent bulge and disk param-eters,we?nd the following results concerning the structure of early-type disk galaxies:

–There is a wide range in bulge-to-disk luminosity and size ratios.The average value of log(L b/L d)is?0.23±

0.47and the average ratio r e/h is0.32±0.15(excluding

two galaxies,UGC624and6786,which have unusually large bulges,see section8).The errors give the stan-dard deviations of the samples.The common belief that early-type disk galaxies have large and luminous bulges does not hold in all cases;our sample contains several

galaxies with faint and/or small bulges compared to the surrounding disks(e.g.UGC94,3205,3546).

–Luminous bulges have on average larger values for the

S′e rsic shape parameter n,consistent with previous stud-

ies.The average value for all bulges in our sample is n =2.5±1.1.Bulges of early-type disk galaxies form, at least as far as their n-values is concerned,an interme-

diate population between elliptical galaxies and late-type galaxy bulges.

–The three fundamental bulge parameters,μe,r e and

n are all correlated,with the large bulges having a lower

e?ective surface brightness and a more strongly centrally peaked light distribution(higher n).

–None of the galaxies in our sample harbours a truly

spherical bulge;in contrast,several bulges are highly?at-

tened with intrinsic axis ratios as low as0.3–0.4(e.g.

UGC5253,9133).The average intrinsic axis ratio of the

bulges in our sample is q b =0.55±0.12.The?at-tening of the bulges is weakly coupled to their luminos-ity,more luminous bulges generally being more?attened than low-luminosity systems.The scatter in the relation is,however,large and more observations are needed to investigate this trend further.

–The fact that most bulges in our sample are sig-ni?cantly?attened and have an intensity pro?le shal-lower than R1/4suggests that many of the bulges in our sample are not miniature elliptical galaxies,but rather‘pseudobulges’formed from disk material by sec-ular processes,in accordance with the ideas proposed by Kormendy&Kennicutt(2004).However,whereas they assumed that such pseudobulges occur mainly in later-type spiral galaxies,our results imply that they may be common in massive,early-type disk galaxies as well(cf.

Laurikainen et al.2006).

–The single exception to the last point is UGC6786.

This galaxy is fully dominated by its bulge(L b/L d=

3.91,r e/h=3.54,all in R),which has a S′e rsic n-

parameter of5.5and is almost spherical(q b=0.8).It

has a clear disk component,but its luminosity pro?le is

unusual,with a plateau of constant surface-density in the centre and a steep exponential fall-o?in the outer parts.It seems most logical to interpret this galaxy as an elliptical which has later acquired a disk of gas and stars(e.g.due to accretion or a merger event).

–Many galaxies become bluer towards larger radii.In some cases,this can be explained solely by the radially declining contribution of the red bulge to the total light.

In most cases,however,this e?ect is not su?cient and the disks themselves must contain colour gradients as well.

The results presented in this paper will be used in a

future paper to calculate the contributions of the stellar

components to the rotation curves of these early-type disk galaxies.

ACKNOWLEDGMENTS

EN is grateful to Alister W.Graham for helpful discussions about various issues related to bulge-disk decompositions,

18 E.Noordermeer&J.M.van der Hulst

and for kindly providing the FORTRAN code to perform the least-squares?ts to the bulge pro?les.We would also like to thank Jelte de Jong for carrying out the observations of UGC6786and7989on the2.4m MDM Hiltner Telescope. We thank the referee,Phil James,for pointing out a few unclarities in the original version of the manuscript and for several suggestions for improvement.

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APPENDIX A:TABLES

20 E.Noordermeer&J.M.van der Hulst

Table A1.List of observations:(1)galaxy name;(2)colour band;(3)telescope used;(4)observ-

ing dates;(5)total exposure time;(6)e?ective seeing;(7)photometric error and(8)magnitude

corresponding to3σbg above sky level.See text for detailed description of the columns.

89R JKT2/11/00?,4/11/002800 1.10.07626.12

B JKT4/11/002400 1.30.1226.63

94R INT5/11/00600 1.50.03825.77

B INT5/11/00600 1.70.02927.77

624R JKT31/10/0024000.80.04926.71

B INT5/11/00600 1.80.03028.64

I JKT27/1/011440 1.30.04924.19

1541R JKT2/11/00?,3/11/002880 1.60.09326.23

B JKT3/11/002400 2.20.1627.72

I JKT27/1/011500 1.40.04724.48

2487R JKT29/10/00,30/10/002400 1.80.02726.36

B JKT24/1/012400 1.30.07226.46

2916R JKT31/10/002400 1.00.05626.80

B JKT5/11/002400 1.80.01927.38

2953R?JKT18/11/01?2400 1.70.029$24.83

R?INT3/2/95?180 2.20.51$26.83

B?JKT4/11/00,5/11/003300 1.90.1425.47

B?JKT18/11/01?2400 2.10.055$25.43

I JKT29/1/011800 1.10.1523.05

3205R?JKT26/1/011800 1.30.1225.59

R?JKT29/10/002400 3.60.03225.22

B JKT1/11/002400 1.00.1726.68

I JKT30/1/012000 3.10.2023.92

3546R?JKT30/10/0024000.90.02826.27

R?JKT26/1/011800 1.20.1326.03

R?JKT18/11/01?2400 2.00.028$26.79

B?JKT30/10/00,5/11/002400 1.60.2227.77

B?JKT18/11/01?2400 2.00.052$27.09 3580R INT27/12/95300 1.00.05126.20

B INT27/12/95300 1.20.1228.05

3993R JKT26/1/012400 1.20.1626.86

B JKT2/4/02?500 1.70.1825.74

4458R JKT2/11/00?,3/11/003680 1.10.09526.56

B?JKT25/1/012400 2.00.1827.15

B?JKT3/11/002400 2.10.1526.32 5253R INT3/5/94300 1.60.2426.84

B JKT4/4/02??1800 1.60.14$26.19

6786R?JKT31/1/01720 1.10.05325.69

R?MDM1/1/03480 1.40.02225.63 6787R JKT29/5/001800 1.70.2626.41

B JKT31/1/011800 1.20.1127.82

8699R JKT24/5/002400 1.60.2425.33

B JKT24/5/002400 1.70.1125.76

9133R JKT26/5/00,27/5/002400 1.30.08625.61

B JKT1/6/00,19/4/02?3000 2.30.08527.23

11670R JKT26/5/003000 1.30.1125.98

B JKT30/5/00?2400 1.30.19$27.01

I JKT31/5/00?,1/6/002400 1.10.1425.12

11852R JKT27/5/0024000.90.08125.86

B JKT27/5/002400 1.10.08426.58

I JKT1/6/002400 1.10.07524.82

11914R JKT30/5/00?,31/5/00?,3/6/02?2900 1.10.2225.40

B JKT30/5/00?,3/6/02?2900 1.30.2426.65

12043R JKT29/5/002400 1.20.2626.04

B JKT31/5/00?,1/6/013300 1.40.1226.37

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(2)修改更新借阅者帐户信息 (3)添加书目 (4)修改和更新书目信息 (5)添加书籍 (6)删除书籍 1.3基本业务模块 基本业务模块包含的功能: (1)借书 (2)还书 (3)书籍预留 (4)取消书籍预定 1.4数据库模块 数据库模块的功能: (1)借阅信息管理 (2)书籍信息管理 (3)帐户信息管理 (4)书籍预留信息管理 1.5信息查询模块 信息查询模块主要是查询数据库中的相关信息: (1)查询书籍信息 (2)查询借阅者信息 2 系统的UML基本模型

外汇交易新手入门:认识最简单的外汇交易系统

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这四条原则是买入交易的基本原则,当市场没有出现这四中情况之一的时候,我根本不会考虑买的。巨汇外汇分析师这么写的意思,并非要你也这么做,而是想说,做为交易者,你同样需要类似的原则,在你的交易系统中。另外,你还需要相当的卖出的原则。 二、卖出 如果你有一些交易经验,很多时候对市场变化会有一些“感觉”,这些“感觉”应该建立在你的交易系统之上。我们相信,交易在更多的时候是要依靠感觉的。 当市场按照你的系统发展的时候,你不需要做什么,耐心看着就可以,你必须明白,就交易的行为而言,是一瞬间的事情,一年二百多个交易日,真正交易的时候,可能只有几个小时,其他都是漫长而寂寞的等待。 在市场有利的时候,你必须学会习惯于获利,这是区别交易者是否成熟的一个重要标志。假设你的成本是8元,市场价格现在是80元,但是趋势依然向上,你是否会坚定的持有?很多的交易者在获利的时候惴惴不安,而亏损的时候却心安理得,这样如何能够长期稳定的获利?

炒外汇入门详细教程全集

炒外汇入门详细全集 入门入籍,建议你看了后再加油看蜡烛图分析,货币战争等。 炒外汇教程 1、什么是个人外汇买卖? 答:个人外汇买卖一般有实盘和虚盘之分,目前只能进行实盘外汇买卖。 2、个人实盘外汇买卖和个人虚盘外汇买卖有什么区别? 答:个人实盘外汇买卖,俗称“外汇宝”,是指个人客户在银行通过柜面服务人员或其他电子金融服务方式进行的不可透支的可自由兑换外 汇(或外币)间的交易。 个人虚盘外汇买卖,是指个人在银行交纳一定的保证金后进行的交易金额可放大若干倍的外汇(或外币)间的交易。 3、个人实盘外汇买卖业务与传统的储蓄业务有什么不同? 答:传统的储蓄业务是一种存取性业务,以赚取利息为目的。个人实盘外汇买卖是一种买卖性业务,以赚取汇率差额为主要目的,同时客户还可以通过该业务把自己持有的外币转为更有升值潜力或利息较高的外币,以赚取汇率波动的差价或更高的利息收入。 4、哪些人可以进行个人实盘外汇买卖?

答:凡持有有效身份证件,拥有完全民事行为能力的境内居民个人,具有一定金额外汇(或外币)均可进行个人实盘外汇交易。 5、个人实盘外汇买卖可交易货币有哪些? 答:美元、欧元、日元、英镑、瑞士法郎、港元、澳大利亚元等主要货币,也包括加拿大元、荷兰盾、法国法郎、德国马克、比利时法郎、新加坡元等货币。 6、个人实盘外汇买卖可以进行那些货币之间的交易? 答:客户可以通过个人实盘外汇买卖进行以下两类的交易:一、美元兑欧元、美元兑日元、英镑兑美元、美元兑瑞士法郎、美元兑港元、澳大利亚元兑美元(还可以进行美元兑加拿大元、美元兑荷兰盾、美元兑法国法郎、美元兑德国马克、美元兑比利时法郎、美元兑新加坡元)。二、以上非美元货币之间的交易,如英镑兑日元、澳大利亚元兑日元等,在国际市场上,此类交易被称为交叉盘交易。 7、个人实盘外汇买卖中的基准货币指的是什么货币? 答:在个人实盘外汇买卖中,英镑、澳元、和欧元兑美元的报价,英镑、澳元和欧元是基准货币,其余的货币兑美元的报价中,美元是基准货币。 8、客户手上只有人民币没有外币,可以进行个人实盘外汇买卖吗?

UML系统建模基础教程课后习题答案

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1?填空题 (1)依赖泛化关联实现 (2)视图图模型元素 (3)实现视图部署视图 (4)构造型标记值约束 (5)规格说明修饰通用划分 2.选择题 (1)D (2)C (3)A (4) A B (5)D 3?简答题 (1 )在UML中面向对象的事物有哪几种? 在UML中,定义了四种基本的面向对象的事物,分别是结构事物、行为事物、分组事物和注释事物等。 (2 )请说出构件的种类。 构件种类有:源代码构件、二进制构件和可执行构件。 (3)请说出试图有哪些种类。 在UML中主要包括的视图为静态视图、用例视图、交互视图、实现视图、状态机视图、活动视图、部署视图和模型管理视图。 (4 )请说出视图和图的关系。

视图和图是包含和被包含的关系。在每一种视图中都包含一种或多种图 (5)请简述UML的通用机制。 UML提供了一些通用的公共机制,使用这些通用的公共机制(通用机制)能够使UML在各种图中添加适当的描述信息,从而完善UML的语义表达。通常,使用模型元素的基本功能不能够完善的表达所要描述的实际信息,这些通用机制可以有效地帮助表达,帮助我们进行有效的UML建模。UML提供的这些通用机制,贯穿于整个建模过程的方方面面。前面我们提到,UML的通用机制包括规格说明、修饰和通用划分三个方面。 第三章Rational统一过程 1?填空题 (1)角色活动产物工作流 (2)逻辑视图过程视图物理视图开发视图用例视图 (3)设计开发验证 (4)二维 (5)周期迭代过程里程碑 2?选择题 (1) A B C D (2) A C D (3) A C D (4)ABC (5) A B C D

操盘手教程外汇交易

操盘手教程外汇交易 Prepared on 22 November 2020

谭建飞先生外汇交易培训材料精选 一. RST RST是一种相当有效的价格逆转图形,全称叫做Reverse Symmetrecal Triangle,翻成中文叫做“反向对称三角形”。这 是一种当价格振动性扩大时出现的图表形态。 我们先看一下常见的对称三角形Symmetrical Triangle 对称三角形是一般技术分析资料中经常提到的图形。 对称三角形一般来说有5 个价格转折点,其中第五点往往不接触三角形的一边,提早显示价格有可能向另一面突破。见图-9 下降趋势中的对称三角形则和上面讲的正好相反。价格在突破三角形的下边之后,往往会形成新的下滑趋势。见图-10 对称三角形这一类的图形都应用了价格的震动性在逐步由大变小之后,又会从小变大,带来价格的突破。 反向对称三角形则和上面的对称三角形正好相反。见图-11(买入图形)和图-12(卖出图形) 反向对称三角形(RST)这样的图表形态一直是存在的,但是很少有操盘手会按照RST图形进行操作,因为这类图形往往使观察者得出和我们要操作的方向正好相反的结论,特别是在即日操盘或超短线的时间阶段内。 我们做的恰恰是和大多数人得到的结论相反,当振动性达到极端时,我们就要考虑应用RST图形来选择高概率的入场时机。 在实际操作中,RST并不一定每次都是具备完美规则的对称图形,但经过一定的练习,你就不会有什么困难来找出这样的图表形态。 具体寻找RST图形的方法是从图表的右边向左看起,确认五个明显的价格转折点。最靠右边的高点或是低点就是第五点。如果这些价格转折点不全是上升高点和下降低点的话,则该图形就不能算是有效的RST图形。 从RST图形的定义来看,一个有效的RST图形必须至少包括7 条价格线,见图-13 当然,绝大多数时候一个有效的RST图形包含远远多于7 条的价格线。见图-14,这是一个RST买入图形。 图中从右向做看起,最新的一个价格转折低点为第五点。 然后我们向左确认其余的四个价格转折点。 图中价格转折高点都是上升趋势(2、4),而转折低点都是下降趋势(1、3、5)。 RST卖出图形,见图-15。 此图形和上面买入图形正好相反。 应用RST图形进行操作,我们是希望在价格出现逆转时尽早的入场,在应用RST图形时,也要尽量结合其他的分析手段,包括轴线,支撑/阻力线,振动带,费伯纳奇,移动平均线等等。 我们会结合实例对这种图表分析方法做更多讲解。

外汇新手入门教程

外汇新手入门教程 一、认识外汇市场 (一)外汇汇率定义 外汇汇率是一国货币对外国货币的兑换率,取决于两国相互间的国际收支状况,或两国货币的购买力,在实际经验上,外汇汇率决定于两国间的长期经济因素,也是投资人预期的表现。 (二)外汇市场 外汇市场从广义上讲泛指外汇交易场所,包括个人外汇买卖场所,外币期货交易所等;从狭义上讲是指以外汇专业银行,外汇经纪商,中央银行等为交易主体,通过电话、电传、交易机等现代化通讯手段实现交易的交易市场;外汇市场既是一个有形的市场也是一个无形的市场,有形是指外汇交易市场有自己的地理位置,比如东京外汇市场、纽约外汇市场等;而无形则是表明市场并没有一个具体的范围,个人、机构、银行之间发生货币转化也可以无形中形成外汇市场。 国际上主要的外汇市场有:悉尼、东京、新加坡、香港、法兰克福、苏黎世、伦敦、纽约,由于以上各个城市地跨多个时区,工作时间基本上为当地时间的早9点到下午4点,因此基本上可以将一天24小时覆盖。 以下按北京时间计算的各个主要外汇市场开休市时间表: 悉尼开市时间早7:00 东京开市时间早8:00 欧洲开市时间下午14:30 伦敦开市时间下午15:30 纽约开市时间晚21:00 伦敦休市时间晚24:30 纽约休市时间早4:00

了解各个外汇市场的开市时间的现实意义在于:及时掌握市场信息,通过阅读经济数据对汇率预测有很大帮助,理解汇率的真实性。 一般汇率会在市场开市的时间内较为活跃,许多重要的经济数据也会在这些时候公布。像日本央行干预日元一般都发生在北京时间的白天,也就是在东京市场开市的时候,德国、英国公布央行利率决定一般会在我们北京时间的下午5点到7点,而美国公布一些重要的数据在晚上8点半,9点半这样的时间,美联储的重要决议一般在北京时间的凌晨公布。 通常我们所说的收盘价格是指纽约市场的收市价格。 (三)外汇汇率的表达方式 工商银行的汇率表示方式一般采取的是国际常用报价方式,按照直接报价法、间接报价法进行报价。 直接报价法:以本国货币表示每一单位外国货币的价格。(本国货币是价格,外国货币是商品)例如在日本,一件衣服=5000日元,一辆汽车=15万日元,在日本,货币的报价方式也采用了此种方法,如1美元=118.35日元。还有几个常见的币种也是采取此报价方式:瑞士法郎(CHF)、加拿大元(CAD)、新加坡元(SGD)、日元(JPY)、港币(HKD)、瑞典克朗(SEK)。 间接报价法:每一单位的本国货币折合若干的外国货币。(本国货币是商品,外国货币是价格)如:在英国,1英镑=1.5980美元。在国际市场上:英镑(GBP)、澳大利亚元(AUD)、新西兰币(NZD)、欧元(EUR)采用此报价法。 (四)基础货币与非基础货币 基础货币是指一个货币对中写在前面的货币;非基础货币是指一个货币对中写在后面的货币。 例如:美元/日元中美元是基础货币,日元是非基础货币;欧元/英镑中欧元是基础货币,英镑是非基础货币。工商银行基础与非基础货币的表现方式按照国际常用方式。 (五)买入价(BID)与卖出价(OFFER或ASK) 在国际市场上,买入价与卖出价表示的含义是指银行准备从对手(通常指客户)那里的买入(BID)价、卖出(OFFER)价,买入价(BID)在左,卖出价(OFFER)价在右。 对于买入价与卖出价实际应用中的说明:银行所标示的买入价均是对基础货币而言的买入价格,银行所标示的卖出价均是对基础货币而言的卖出价格。例如:工商银行的美元兑日元买入、卖出价分别为109.30/109.60;即表明工商银行从客户处买入美元卖出日元使用的牌价为109.30,则客户卖出美元买入日元就要使用109.30的牌价,反之亦然。 银行的卖出价均要高于银行的买入价,也就是客户在与银行进行交易的时候,客户的买入价高于客户的卖出价;原因有二:(1)客户不论何时均可与银行进行交易,银行要无条件的买入或卖出,这样就要求银行必须要用这样的价差来保证自己的利益。(2)对于投资者而言,只有市场发生变化时,才有可能获利,如果市场没有任何变动,投资者在汇率静止的情况下,进行一买一卖是要赔钱的。而投资者的投资的目的是为了获利,获利的要素就是要求我们看准汇率走势方向,待汇市变化的时候,才有获利的可能,汇市汇率静止,客户将不可能获利。 (六)国际外汇市场主要币种及其符号 美元:USD、英镑:GBP、欧元:EUR、日元:JPY 澳元:AUD、港币:HKD、加元:CAD、瑞郎:CHF、瑞典克朗:SEK 新加坡元:SGD、挪威克朗:NOK、丹麦克朗:DKK

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