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Mon. Not. R. Astron. Soc. 000, 000­000 (0000)

Printed 25 January 2007

A (MN L TEX style file v2.2)

The mass distribution in early-typ e disk galaxies: declining rotation curves and correlations with optical prop erties
E. Noordermeer,1,2 J. M. van der Hulst,1 R. Sancisi, T. S. van Albada1 1
2 3 4

1,3

R. S. Swaters4 and

arXiv:astro-ph/0701731v1 25 Jan 2007

Kapteyn Astronomical Institute, University of Groningen, PO Box 800, 9700 AV Groningen, The Netherlands University of Nottingham, School of Physics and Astronomy, University Park, NG7 2RD Nottingham, UK INAF-Osservatorio Astronomico di Bologna, Via Ranzani 1, 40127 Bologna, Italy Department of Astronomy, University of Maryland, Col lege Park, MD 20742-2421, USA

accepted for publication in MNRAS, 05-01-2007

ABSTRACT

We present rotation curves for 19 early-type disk galaxies (S0 ­ Sab). The galaxies span a B-band absolute magnitude range from -17.5 to -22, but the ma jority have a high luminosity with MB < -20. Rotation velocities are measured from a combination of Hi velocity fields and long-slit optical emission line spectra along the ma jor axis; the resulting rotation curves probe the gravitational potential on scales ranging from 100 pc to 100 kpc. We find that the rotation curves generally rise rapidly in the central regions and often reach rotation velocities of 200 ­ 300 km/s within a few hundred parsecs of the centre. The detailed shape of the central rotation curves shows a clear dependence on the concentration of the stellar light distribution and the bulge-to-disk luminosity ratio: galaxies with highly concentrated stellar light distributions reach the maximum in their rotation curves at relatively smaller radii than galaxies with small bulges and a relatively diffuse light distribution. We interpret this as a strong indication that the dynamics in the central regions are dominated by the stellar mass. At intermediate radii, many rotation curves decline, with the asymptotic rotation velocity typically 10 ­ 20% lower than the maximum. The strength of the decline is correlated with the total luminosity of the galaxies, more luminous galaxies having on average more strongly declining rotation curves. At large radii, however, all declining rotation curves flatten out, indicating that substantial amounts of dark matter must be present in these galaxies too. A comparison of our rotation curves with the Universal Rotation Curve from Persic et al. (1996) reveals large discrepancies between the observed and predicted rotation curves; we argue that rotation curves form a multi-parameter family which is too complex to describe with a simple formula depending on total luminosity only. In a number of galaxies from our sample, there is evidence for the presence of rapidly rotating gas in the inner few hundred parsecs from the centers. The inferred central masses and mass densities are too high to be explained by the observed stellar components and suggest the presence of supermassive black holes in these galaxies. Key words: galaxies: spiral ­ galaxies: lenticular ­ galaxies: structure ­ galaxies: fundamental parameters ­ galaxies: kinematics and dynamics ­ galaxies: haloes

1

INTRODUCTION

Rotation curves are the prime tool for studying the mass distribution in disk galaxies. In normal, unp erturb ed galaxies, gas moves on circular orbits around the centre, so measurements of the circular velocity can b e used to yield the en

email:edo.noordermeer@nottingham.ac.uk

closed mass at different radii. The study of the shap es of rotation curves therefore gives imp ortant insight into the overall distribution of mass in disk galaxies. Hi rotation curves in particular are useful, b ecause they prob e the mass distribution to much larger radii than can b e achieved with optical data and reach to the regions where dark matter dominates the gravitational p otential. In fact, it was the discovery, first made in the 1970's (Rogstad & Shostak 1972;


2

E. Noordermeer et al.
sues, a systematic study of Hi rotation curves in spiral galaxies, covering a large range of luminosities, morphological typ es and surface brightnesses, is a crucial step. Although much work has b een done in this field in recent years (e.g. de Blok et al. 1996; Swaters 1999; C^t´ et al. oe 2000; Verheijen 2001; Gentile et al. 2004), most studies have focused on late-typ e and low-luminosity galaxies. Early-typ e disk galaxies, which generally contain less gas (Rob erts & Haynes 1994; Noordermeer et al. 2005), have received considerably less attention. One of the few studies so far aimed at a systematic investigation of Hi rotation curves over the full range of morphological typ es was that by Broeils (1992). However, in his sample of 23 galaxies, only one was of morphological typ e earlier than Sb and only four had Vmax > 250 km s-1 . The only large-scale Hi survey directed sp ecifically at S0 and Sa galaxies was carried out by van Driel (1987), but his study was severely hamp ered by the low signal-to-noise ratio of his data and his rotation curves were of rather p oor quality compared to modern standards. In the optical, little work has b een done on early-typ e spiral galaxies either, since the early studies by Rubin et al. (1985) and Kent (1988). S0 and Sa galaxies were thus also under-represented in the study by Persic et al. (1996); their Universal Rotation Curve is based on over 1000 rotation curves of which only 2 are of typ e Sab or earlier. This pap er is part of a larger study designed to fill this lack and to systematically investigate the relation b etween dark and luminous matter in early-typ e disk galaxies. These systems, lying at the high mass, high surface brightness end of the disk galaxy p opulation, are ideal test cases to investigate what determines the shap e of rotation curves. If the stars contribute significantly to the gravitational p otentials of galaxies, it is in these galaxies that their influence will b e most easily detected. In an earlier pap er (Noordermeer et al. 2005, hereafter pap er I), we have presented Hi observations for a sample of early-typ e (S0 ­ Sab) disk galaxies, and in an accompanying pap er to the present one (Noordermeer & van der Hulst 2006, pap er I I) we present optical photometry and bulge-disk decomp ositions. Here, we use the data for a subset of 19 galaxies from Pap er I to derive their rotation curves and to study the dep endence of their rotation curve shap es on the optical properties. In two future publications, we will use the results to study the location of massive, early-typ e disk galaxies on the Tully-Fisher relation and to create detailed mass-models. The Hi data from Pap er I can b e used to measure the rotation velocities of the gas out to large radii. In the central regions, however, the rotation curves can often not b e measured from the 21cm observations due to the presence of holes in the Hi disks (see Pap er I). Furthermore, the spatial resolution of our Hi observations is usually insufficient to obtain detailed information on the shap e of the rotation curves in the inner regions, where our velocity fields suffer from b eam smearing. To overcome these difficulties, we use long-slit optical sp ectroscopy to measure the central rotation curves. In most galaxies, optical emission lines can b e detected in the very inner regions, out to radii where reliable rotation velocities can b e determined from the Hi velocity fields. Moreover, due to the higher spatial resolution of the optical observations, the effects of b eam smearing are strongly reduced. The remainder of this pap er is structured as follows.

Rob erts & Whitehurst 1975; Bosma 1978; Bosma 1981), that Hi rotation curves stay flat till the last measured p oints, well outside the optical disk, which gave the final, irrefutable evidence of the presence of large amounts of unseen matter in galaxies (Bosma 1981; van Albada et al. 1985; van Albada & Sancisi 1986; Begeman 1987). A long standing question concerns the relation b etween the shap e of rotation curves and other prop erties of individual galaxies. It has b een known for a long time that the shap e of a rotation curve is strongly coupled to the optical luminosity of a galaxy: slowly rising and low amplitude for low-luminosity galaxies, high central gradient and high rotation velocities for high-luminosity systems (e.g. Rubin et al. 1985; Burstein & Rubin 1985). However, the question of whether or not other optical prop erties influence rotation curves as well has resulted in inconsistent answers. Rubin et al. (1985) and Burstein & Rubin (1985) found no dep endence on morphological typ e or on the shap e of the light distribution (notably the bulge-to-disk ratio) and presented synthetic rotation curves dep ending solely on a galaxy's luminosity. This idea was later elab orated by Persic & Salucci (1991) and Persic et al. (1996), who presented a `universal rotation curve', an analytic formula describing the shap e of a rotation curve which only dep ends on total luminosity. In contrast, several other studies suggested that rotation curve shap e is not correlated with luminosity only, but that other parameters need to b e taken into account as well. Corradi & Capaccioli (1990) found that the shap e of a rotation curve correlates with a galaxy's morphological typ e: early-typ e spirals with large bulges have rotation curves which rise more rapidly than galaxies of similar luminosity but with a less concentrated light distribution. Casertano & van Gorkom (1991) showed that the outer shap e of rotation curves is correlated with b oth the total luminosity and the shap e of the light distribution, exemplified by two luminous galaxies with highly concentrated light distributions which have declining rotation curves. Roscoe (1999) showed that the universal rotation curve formalism of Persic et al. (1996) can b e improved by including surface brightness as parameter influencing rotation curve shap e. The dep endence of rotation curve shap e on the optical characteristics was also confirmed in studies by e.g. Broeils (1992), Swaters (1999), Verheijen (2001), Matthews & Gallagher (2002) and Sancisi (2004). The systematics b ehind rotation curve shap es hold imp ortant clues on the structure and evolution of (disk) galaxies. Rubin et al. (1985) and Burstein & Rubin (1985) interpreted the lack of dep endence on the light distribution as evidence that luminous matter plays a minor r^le dynamio cally, and that large amounts of dark matter must b e present everywhere in disk galaxies. But if rotation curves are, instead, a multi-parameter family dep ending also on prop erties such as morphological typ e, surface brightness, etc., then the conclusion must b e that at least in some galaxies, the stars contribute significantly to the p otential. The rotation curve vs. optical prop erties relations also provide a p owerful b enchmark for simulations of galaxy formation: any viable theory of galaxy formation must b e able to reproduce realistic rotation curves which match the other characteristics of the simulated galaxy. In order to obtain a b etter understanding of these is-


Rotation curves of early-type disk galaxies
Table 1. Sample galaxies: basic data. (1) sample number; (2) UGC numb er; (3) alternative name; (4) morphological type; (5) distance; (6) and (7) absolute B- and R-band magnitudes (corrected for Galactic foreground extinction); (8) R-band central disk surface brightness (corrected for Galactic foreground extinction and inclination effects) and (9) R-band disk scale length. Column (4) was taken from NED, (5) from Paper I and (6) ­ (9) from Paper II. sample number (1) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 No data alternative Type D name Mp c (2) (3) (4) (5) 624 NGC 338 Sab 65.1 2487 NGC 1167 SA067.4 2916 ­ Sab 63.5 2953 IC 356 SA(s)ab pec 15.1 3205 ­ Sab 48.7 3546 NGC 2273 SB(r)a 27.3 3580 ­ SA(s)a pec: 19.2 3993 ­ S0? 61.9 4458 NGC 2599 SAa 64.2 4605 NGC 2654 SBab: sp 20.9 5253 NGC 2985 (R')SA(rs)ab 21.1 6786 NGC 3900 SA(r)0+ 25.9 6787 NGC 3898 SA(s)ab 18.9 8699 NGC 5289 (R)SABab: 36.7 9133 NGC 5533 SA(rs)ab 54.3 11670 NGC 7013 SA(r)0/a 12.7 11852 ­ SBa? 80.0 11914 NGC 7217 (R)SA(r)ab 14.9 12043 NGC 7286 S0/a 15.4 available in Paper II; MB taken from LEDA. UGC MB mag (6) 20.83 21.88 21.05 21.22 20.89 20.02 18.31 20.19 21.38 20.09 20.86 19.94 20.00 19.48 21.22 19.20 20.44 20.27 17.53 MR mag (7) 22.25 23.24 22.01 22.54 21.88 21.35 19.42 21.35 22.61 ­ 21.90 21.13 21.28 20.74 22.62 20.55 21.53 21.35 18.26
R mag arcsec2

3

µc , 0

-

-

(8) 21.92 20.12 20.99 19.25 19.59 19.49 21.58 22.37 21.26 ­ 21.32 19.30 20.49 22.24 21.27 19.58 20.74 19.91 19.90

hR kpc (9) 5.8 8.0 5.0 4.1 3.5 2.8 2.4 5.5 8.6 ­ 5.3 1.5 3.3 3.7 9.1 1.8 4.5 2.7 0.8

In section 2, the criteria which were used to select suitable galaxies from the parent sample of Pap er I are describ ed. Section 3 describ es the techniques that were used to derive the rotation curves from the Hi velocity fields and from the optical sp ectra. In section 4, the fitted orientation parameters and systemic velocities of our galaxies, as derived from different sources, are compared. In section 5, we briefly discuss the occurrence of warps in the galaxies in our sample. In section 6, several asp ects of the shap e of our rotation curves are discussed, including an analysis of the correlations with optical prop erties and the applicability of the concept of a `Universal Rotation Curve' to our data. Finally, we briefly discuss our results and summarize the main conclusions in section 7. In the app endices, we present some additional material. A detailed description of the individual rotation curves is presented in app endix A. In app endix B, we interpret the broad central velocity profiles which are present in some of our optical sp ectra. App endix C gives the graphical representation of the rotation curves and various other data for the galaxies in our sample.

b e moving in regular circular orbits around the centre of the galaxy. Strongly interacting galaxies, or galaxies with otherwise distorted kinematics cannot b e used. Strongly barred galaxies are excluded as well, b ecause non-circular motions in the bar p otential complicate the analysis of the data; 3) the inclination angle must b e well constrained and preferably lie b etween 40 and 80 . Few galaxies from Pap er I satisfy all these conditions and a strict application of these criteria (esp ecially the second one) would lead to a very small sample. We have therefore relaxed the latter two selection criteria and included a numb er of galaxies with e.g. weak bars, mild kinematical distortions or a more face- or edge-on orientation. The resulting sample consists of 19 galaxies; a few basic characteristics of the memb ers are given in table 1. The galaxies in our sample have morphological typ es ranging from S0- to Sab and span two decades in optical luminosity (-17.5 > MB > -22). The ma jority of galaxies in our sample have high optical luminosity, with MB < -20. See Pap er I for a more detailed description of the prop erties of the galaxies in our sample.

2

SAMPLE SELECTION

The galaxies for the rotation curve study presented here were selected from the 68 galaxies with Hi observations presented in Pap er I, which were in turn selected from the WHISP survey (Westerb ork survey of Hi in spiral and irregular galaxies; Kamphuis et al. 1996; van der Hulst et al. 2001). In order to b e able to derive high quality Hi rotation curves, galaxies were selected on the basis of the following criteria: 1) the velocity field must b e well resolved (> 5 ­ 10 b eams across) and defined over significant parts of the gas disks (i.e. not confined to small `patches'); 2) the gas must

3

OBSERVATIONS, DATA REDUCTION AND THE DERIVATION OF THE ROTATION CURVES

As mentioned in the introduction, the rotation curves in this pap er were derived from a combination of Hi synthesis observations and long-slit optical sp ectra. Below, we discuss the analysis of b oth comp onents separately.


4

E. Noordermeer et al.
Table 2. Dynamical properties: (1) UGC number; (2) and (3) position of the dynamical centre; (4) heliocentric systemic velocity; (5) position angle (north through east) of ma jor axis; (6) inclination angle; (7) maximum rotation velocity; (8) rotation velocity at 2.2 R-band disk scale lengths; (9) asymptotic rotation velocities at large radii; (10) total enclosed mass within last measured point and (11) rotation curve quality. dynamical centre Vsys PA i Vmax V2.2h Vasymp Menc quality RA (2000) Dec (2000) h m s km/s km/s km/s km/s M (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) 624 1 0 36.0 30 40 10 4789 288 64 300 300 270 5.2 · 1011 III 2487 3 1 42.7 35 12 21 4952 250­256 36 390 360 330 2.1 · 1012 I 2916 4 2 33.5 71 42 19 4537 242 42­50 220 210 180 2.8 · 1011 II 2953 4 7 46.8 69 48 46 892 98­104 50 315 315 260 1.1 · 1012 I 3205 4 56 14.9 30 3 8 3586 230­224 67 240 230 210 4.3 · 1011 I 3546 6 50 8.6 60 50 46 1837 56 55 260 185 190 2.4 · 1011 II 3580 6 55 31.2 69 33 54 1203 6­356 63 127 100 125 9.0 · 1010 II 3993 7 55 44 84 55 33 4364 220 20 300 290 250 8.6 · 1011 II 4458 8 32 11.2 22 33 36 4756 288­295 25 490 280 240 7.8 · 1011 II 4605 8 49 11.1 60 13 14 1347 240­247 84­74 225 220 185 2.8 · 1011 I 5253 9 50 22.2 II 72 16 44 1329 356­340 37 255 245 210 5.5 · 1011 6786 11 49 9.2 27 1 15 1795 181­186 68­64 230 ­$ 215 3.1 · 1011 I 6787 11 49 15.3 56 5 5 1172 107­118 69­66 270 250 250 5.0 · 1011 I 8699 13 45 7.7 41 30 19 2516 280 73 205 190 180 1.9 · 1011 I 9133 14 16 7.7 35 20 37 3858 24­45 53 300 265 225 1.3 · 1012 I 11670 21 3 33.5 29 53 50 774 336­330 70­68 190 155 160 1.6 · 1011 II 11852 21 55 59.6 27 53 55 5843 200­175 50­60 220 210 165 5.9 · 1011 II 11914 22 7 52.3 31 21 36 951 265­268 31 305 300 300# 1.9 · 1011 II 12043 22 27 50.4 29 5 45 1007 97­92 67 93 82 90 3.2 · 1010 I Kinematical inclination p o orly constrained by observations. Value copied from optical isophotal analysis. No accurate photometry available due to edge-on orientation of optical disk; optical scale length is estimate only. $ Galaxy do es not have regular exp onential disk; no optical scale length available. # Rotation curve extends out to 3.3 R disk scale lengths only and may converge to different velo city at larger radii. UGC

3.1

Hi rotation curves

The Hi rotation curves were derived by fitting tilted ring models (Begeman 1987; Begeman 1989) to the observed velocity fields from Pap er I, using the ROTCUR algorithm implemented in GIPSY (Groningen Image Processing System; Vogelaar & Terlouw 2001)1 . In Pap er I, we showed velocity fields at either full ( 15 ), 30 or 60 resolution. Here, we fit tilted ring models to the velocity fields at all available resolutions. The higher-resolution velocity fields can b e used for the inner regions, whereas the velocity fields at lower resolution generally extend out to larger radii and can b e used to obtain information ab out the rotation curves in the outer parts. Tilted rings were fitted to the entire velocity fields, but p oints near the ma jor axis were given more weight than those near the minor axis by applying a | cos()| weighing scheme, with the azimuthal angle, measured from the major axis in the plane of the galaxy. In all cases, the rotation curves were determined in four steps. In the first step, all parameters (i.e. systemic velocity Vsys , dynamical centre p osition (xc , yc ), p osition angle P A, inclination angle i and rotation velocity Vrot ) were left free for each ring. In general, the fitted systemic velocities and dynamical centre p ositions show little variation with radius, esp ecially in the inner regions, and the average values were adopted as the global values for the galaxy. They are listed in table 2.

1

For two highly inclined galaxies, UGC 4605 and 8699, the standard tilted ring method is not suitable and a modified analysis was applied (see individual notes in appendix A).

In the second step, the systemic velocity and dynamical centre were fixed for each ring at the values derived in the first step. The values for the p osition angle derived from this step are shown with the data p oints in the figures in app endix C. The p osition angle is usually well-defined, but it often shows variations with radius as a result of warps in the gas disk. If a clear trend was visible, we fitted it by hand and used the fitted values for the next steps; otherwise we used the average of all rings. The adopted range of p osition angles, or the average value, for each galaxy is given in table 2, and plotted as b old line in the figures in app endix C. In the third step, only the inclination and rotation velocity were left as free parameters for each ring. From this fit, the inclination angle was determined. This parameter is the most difficult one to constrain, b ecause it is strongly coupled to the rotation velocity, esp ecially for inclinations lower than 45 (Begeman 1987; Begeman 1989). The fitted values are shown in the figures in app endix C. It is clear that for the more face-on galaxies, the uncertainties in the fitted inclinations are large. In practice, radial variations in inclination could only b e detected for galaxies that are sufficiently inclined; for galaxies with i < 45 only an average value could b e determined. When necessary, the fitted inclination angles were also compared to the values derived from the optical images (see Pap er I I) to make a more reliable estimate. The range of inclination angles, or the average value, used for the next step is given in table 2 and plotted as b old line in the figures in app endix C. The uncertainty in the inclination i(r ) was estimated by eye, based on the spread of the individual data p oints around the fitted values and the comparison b etween the


Rotation curves of early-type disk galaxies
Table 3. Observational parameters for optical spectroscopic observations: (1) UGC number; (2) telescope used: Isaac Newton Telescope (INT) or William Herschel Telescope (WHT) on La Palma or NOAO 2.1m telescope on Kitt Peak (KP 2.1m); (3) observing dates; (4) total exposure time; (5) and (6) effective slit width and length; (7) position angle (north through east) of the slit on the sky and (8) ­ (12) line weights used in the stacking procedure. UGC telescope dates texp slit orientation width length PA


5

[Nii]

6548

H

line weights wi [Nii]6583 [Sii]

6716

[Sii]

6731

sec (1) (2) (3) (4) 624 INT 26/1/01 2400 2487 INT 28/1/01 7200 2916 INT 27/1/01 2400 2953 WHT 2/1/00 7200 3205 INT 26/1/01 6000 3546 INT 26/1/01 3600 3580 INT 28/1/01 3600 3993 INT 26/1/01 7200 4458 INT 27/1/01 3600 4605 INT 28/1/01 4800 5253 INT 27/1/01 2400 6786 INT 29/1/01 2400 6787 INT 31/1/01 6000 8699 INT 22/5/01 3600 9133 INT 22/5/01 7200 11670 INT 22/5/01 4200 11852 INT 23/5/01 4800 11914 INT 23/5/01 3150 12043 KP 2.1m 8/12/01 2400 Lines could not b e stacked b ecause of

(5) 1.5 1.0 1.0 1.0 1.5 1.5 1.0 1.5 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 stellar

(6) 3.3 3.3 3.0 4.0 3.3 3.3 3.3 3.0 3.0 3.3 3.2 3.3 3.3 3.6 3.6 3.6 3.6 3.6 5.2 absor

(7) 106 70 76 99 47 57 5 44 100 63 0 2 105 100 27 157 15 89 98 ption featur

(8) (9) (10) (11) 0.5 2.0 1.0 0.5 0.5 1.0 1.0 0.5 0.0 1.0 1.0 0.0 0.5 1.0 1.0 0.5 0.0 1.0 1.0 0.0 0.0 1.0 2.0 0.0 0.25 1.0 0.5 0.5 0.25 0.5 1.0 0.5 0.25 1.0 1.0 0.25 0.0 2.0 1.0 0.5 0.1 1.0 1.0 0.3 0.0 1.0 1.0 0.0 0.1 1.0 0.5 0.25 0.25 1.0 1.0 0.5 0.0 1.0 1.0 0.0 0.25 1.0 1.0 0.5 0.0 1.0 1.0 0.0 0.25 1.0 1.0 0.25 0.25 2.0 0.5 0.7 e in H (see note in appendix A

(12) 0.5 0.5 0.0 0.5 0.0 0.0 0.5 0.5 0.25 0.5 0.3 0.0 0.25 0.5 0.0 0.5 0.0 0.25 0.0 ).

tilted ring inclination angles and optical ellipticity. In general, we let the uncertainty i increase with radius, in order to account for the p ossibility of undetected or misfitted warps in the outer gas disks of the galaxies. The adopted uncertainties in the inclination angle are shown with the shaded regions in the b ottom middle panels in the figures in app endix C. In the final step, we derived the rotation curves by doing a fit with all parameters fixed except the rotation velocity. To prevent the inclusion of erroneous p oints in the final rotation curves, outer tilted rings were not accepted if they only covered a small numb er of pixels in the velocity field, or if the outer parts of the velocity fields showed clear signs of non-circular or otherwise p erturb ed motions. The final Hi rotation curves are shown as square data p oints in the b ottom right panels in the figures in app endix C.

3.2 3.2.1

Rotation curves from optical spectra observations

For most galaxies in the sample, long-slit sp ectra were taken with the IDS sp ectrograph on the Isaac Newton Telescop e (INT) on La Palma2 . For UGC 2953, a sp ectrum was obtained from the red arm of the ISIS sp ectrograph on the William Herschel Telescop e, also on La Palma2 . The sp ectrum of UGC 12043 was taken with the GoldCam sp ectro-

graph, mounted on the NOAO 2.1m telescop e on Kitt Peak, Arizona3 . A summary of the observations is given in table 3. The slits of the sp ectrographs were aligned with the ma jor axes of the galaxies. In some cases, the p osition angle of the slit on the sky was slightly different from the kinematical p osition angle of the galaxy as derived from the Hi velocity field. In these cases, the rotation curves were later corrected for the effect of the misalignment. The bulges of the galaxies were usually bright enough to enable the slit to b e p ositioned accurately over the centres using the TV camera in the focal plane. The sp ectral range of all observations was chosen such that each sp ectrum contains the redshifted lines of H (0 = ° 6562.80 °), [Ni i] (6548.04 and 6583.46 A) and [Si i] (6716.44 A A and 6730.81 °). The sp ectral resolution of the sp ectra taken A on the INT is 1.0 and 1.4 ° (FWHM) for slit widths of 1.0 and 1.5 resp ectively, corresp onding to a velocity resolution of approximately 45 and 65 km/s resp ectively. The sp ectrum for UGC 2953 has a sp ectral resolution of 0.9 ° ( 40 km/s), A whereas the resolution of the sp ectrum for UGC 12043 is slightly worse at 2.0 ° ( 90 km/s). A Total exp osure times were broken up into single exp osures of typically 20 minutes; the numb er of exp osures for each galaxy was determined at the telescop e, based on the strength of the emission lines in the first exp osure.

3 2

The Isaac Newton are operated on the Group in the Spanish of the Instituto de As

Telescope and William Herschel Telescope island of La Palma by the Isaac Newton Observatorio del Roque de los Muchachos trofisica de Canarias.

The Kitt Peak 2.1m telescope is operated and IRAF is distributed by the National Optical Astronomy Observatories, which are operated by the Association of Universities for Research in Astronomy, Inc., under cooperative agreement with the National Science Foundation.


6

E. Noordermeer et al.

Figure 1. Example spectra to illustrate the spectral stacking procedure. The top panel at each column shows a section of the original spectrum, centered around the H- (middle) and the 6583 and 6548 ° [Nii]-lines (top and bottom respectively), after removal of the A stellar continuum and sky lines. The middle panels show the stacked spectra, where the emission from all lines (including the [Sii]-lines) is added, with weights wi as given in table 3. The bottom panels show the same spectra after binning along the spatial direction to 1 pixels. For each galaxy, the 3 spectra are shown on the same (logarithmic) intensity scale, to show the decrease in the noise levels between the subsequent steps. The arrows refer to specific features in the spectra and are discussed in the text.

3.2.2

data reduction

Standard data reduction steps were p erformed within the IRAF environment3 . Readout bias was subtracted using the overscan region of the chips; any remaining structure was removed using sp ecial bias frames. The sp ectra were then flatfielded using Tungsten flatfields. Wavelength calibrations were p erformed using arc sp ectra from Copp er, Neon and Argon lamps, taken b efore or after the galaxy sp ectra. The resulting wavelength solutions were used to map the sp ectra to a logarithmic wavelength grid, such that pixel shifts corresp ond to linear velocity shifts. The calibrations were also checked retrosp ectively by comparing the measured wavelengths of a few strong night-sky lines with the values given by Osterbrock et al. (1996); the systematic errors lie typically in the range 0.05 ­ 0.10 °, corresp onding to ab out 2.5 A ­ 5 km/s. Individual exp osures were then combined and cosmic rays were rejected using a simple sigma-clipping criterion. The continuum emission of the galaxy and the night-sky emission lines were removed by fitting low-order p olynomials along the sp ectral and spatial axes of the sp ectra resp ectively. In the final, cleaned sp ectra, the H line is usually the strongest line in the outer parts of the galaxies. In the central A parts however, the 6583.46 ° [Ni i] line and the [Si i] lines are often stronger, presumably due to underlying stellar absorption in H. Rather than first determining rotation curves for each line separately and then combining them into one single curve, we have chosen the reverse order. The parts of the sp ectrum around each of the 5 emission lines were shifted according to the difference in rest wavelength and stacked to create a single sp ectrum which contains emission from all lines. Each line was roughly weighted according to its relative strength; the weights wi are given in table 3. Before stacking, sp ecial care was taken to ensure that the different emission lines trace similar velocities, but we found no cases with significant differences. This procedure has the added advantage that the signal-to-noise ratio in the stacked sp ectrum is higher than in the original one; emission that was too weak to b e detected in each line individually could sometimes b e detected with sufficient significance in the stacked sp ectrum. In figure 1, we illustrate the stacking procedure for three

representative galaxies. In the sp ectrum of UGC 624 (left), the H line is the strongest line along the entire slit, but adding the other lines leads to a slightly higher signal-tonoise ratio (see for example the location indicated with arrows 1), and thus improves the accuracy of the fitted velocities. For UGC 4605 (midd le), the improvement is more significant. In the original sp ectrum, H is stronger in the outer parts, but the 6583.46 ° [Ni i]-line is stronger in the A centre. In the stacked sp ectrum, velocities can b e measured in b oth regions, as well as at locations where the signal in the individual lines was too weak to b e fitted (arrows 2). For UGC 6786 (right), the stacking procedure does not work due to a strong stellar H absorption feature in the centre (arrow 3). In this case, stacking the various lines causes the H absorption feature to dilute the little emission that is present in the 6583.46 ° [Ni i]-line, and thus degrades, rather than A improves, the quality of the data. In this case, we analysed b oth lines separately, and combined the resulting rotation curves afterwards (see also the note in app endix A). T