HAL Id: hal-00017198
https://hal.archives-ouvertes.fr/hal-00017198
Submitted on 13 Dec 2020
HAL is a multi-disciplinary open access
archive for the deposit and dissemination of
sci-entific research documents, whether they are
pub-lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.
L’archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d’enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.
irregular galaxies - IV. 44 new velocity fields. Extension,
shape and asymmetry of Halpha rotation curves
P. Amram, C. Balkowski, J. Boulesteix, J.L. Gach, O. Garrido, M. Marcelin
To cite this version:
GHASP: an H
α kinematic survey of spiral and irregular galaxies – IV.
44 new velocity fields. Extension, shape and asymmetry of H
α rotation
curves
O. Garrido,
1,2M. Marcelin,
2P. Amram,
2C. Balkowski,
1J. L. Gach
2and J. Boulesteix
21Observatoire de Paris, section Meudon, GEPI, CNRS UMR 8111, Universite Paris 7, 5 Place Jules Janssen, 92195 Meudon, France
2Observatoire Astronomique de Marseille Provence, Laboratoire d’Astrophysique de Marseille, 2 Place Le Verrier, 13248 Marseille Cedex 04 France
Accepted 2005 June 3. Received 2005 May 26; in original form 2004 August 24
A B S T R A C T
We present Fabry–Perot observations obtained in the frame of the GHASP survey (Gassendi HAlpha survey of SPirals). We have derived the Hα map, the velocity field and the rotation curve for a new set of 44 galaxies. The data presented in this paper are combined with the data published in the three previous papers providing a total number of 85 of the 96 galaxies observed up to now. This sample of kinematical data has been divided into two groups: isolated (ISO) and softly interacting (SOFT) galaxies. In this paper, the extension of the Hα discs, the shape of the rotation curves, the kinematical asymmetry and the Tully–Fisher relation have been investigated for both ISO and SOFT galaxies. The Hα extension is roughly proportional to R25 for ISO as well as for SOFT galaxies. The smallest extensions of the ionized disc are
found for ISO galaxies. The inner slope of the rotation curves is found to be correlated with the central concentration of light more clearly than with the type or the kinematical asymmetry, for ISO as well as for SOFT galaxies. The outer slope of the rotation curves increases with the type and with the kinematical asymmetry for ISO galaxies but shows no special trend for SOFT galaxies. No decreasing rotation curve is found for SOFT galaxies. The asymmetry of the rotation curves is correlated with the morphological type, the luminosity, the (B − V ) colour and the maximal rotational velocity of galaxies. Our results show that the brightest, the most massive and the reddest galaxies, which are fast rotators, are the least asymmetric, meaning that they are the most efficient with which to average the mass distribution on the whole disc. Asymmetry in the rotation curves seems to be linked with local star formation, betraying disturbances of the gravitational potential. The Tully–Fisher relation has a smaller slope for ISO than for SOFT galaxies.
Key words: catalogues – galaxies: dwarf – galaxies: interactions – galaxies: irregular –
galax-ies: kinematics and dynamics – galaxgalax-ies: spiral.
1 I N T R O D U C T I O N
This paper is the fourth of a series presenting and analysing the observational data obtained in the frame of the GHASP survey (acronym for Gassendi Hα survey of SPirals). This survey consists in mapping the distribution of the ionized hydrogen of field galaxies using a scanning Fabry–Perot interferometer at the 1.93-m telescope of the Observatoire de Haute-Provence (OHP). High-resolution 2D velocity fields (with a sampling about 5 km s−1 in velocity and 3 arcsec in spatial resolution) in the Hα line of hydrogen are derived. Velocity fields enable us to deduce rotation curves in a more robust way than slit spectra, which most often assume that both
kinemati-E-mail: olivia.garrido@obspm.fr
cal and photometric axes are confused. GHASP galaxies were first chosen to cover the ‘galaxy mass–galaxy morphological type’ plane for a large range of luminosity (−15 Mb −22) and
morpholog-ical types (from Sa to irregular). We estimate that a total sample of about 200 galaxies is necessary (see Garrido et al. 2002) to cover the whole ‘MB–type’ plane. Furthermore, they were chosen in
low-density environments, excluding cluster, group or pair galaxies. This survey will provide a homogeneous reference sample at z = 0 of 2D Hα velocity fields (the largest by now after that of Schommer et al. 1993, which concerns cluster galaxies in the southern hemi-sphere) and will allow us to study the mass distribution all along the Hubble sequence for various luminosities, the evolution of galaxies when comparing 2D kinematics of distant galaxies (Flores et al. 2004) with nearby ones, the environmental effects and the inner kinematics with the help of simulations.
The search for links between the shape of rotation curves (RCs) and physical properties of galaxies has been the subject of many studies. Tully & Fisher (1977) have shown that both luminosity and maximal velocity are tightly linked. Rubin et al. (1985) then showed that in fact the maximal rotational velocity is linked both with the luminosity and the morphological type. Persic, Salucci & Stel (1991) noted that both the shape of the RCs and luminosity are linked, and derived a universal rotation curve (1996) which mainly depends on the luminosity. However, Verheijen (1997) and Sofue et al. (1999) showed that the URC is not able to reproduce systematically the inner and outer parts of their RCs.
Galaxies mainly belong to large-scale aggregations (Vettolani, de Souza & Chincarini 1986) providing environments of different den-sity. The environment is responsible for the morphological evolution of galaxies through dynamical modifications (Moore, Lake & Katz 1998; Dubinski 1999) resulting in a morphological–density relation (Dressler et al. 1997). But it is possible to find galaxies in low-density environments which have not suffered from recent interactions and which have therefore evolved in a secular way for the last billion years. A great number of studies based on large samples of RCs (e.g. Rubin, Waterman & Kenney 1999; Marquez et al. 2002; Dale & Uson 2003; Varela et al. 2004; Vogt et al. 2004a,b,c) concerns the gravitational effects on the shape of the RCs. But, in order to discrim-inate a secular from an external origin for any dynamical peculiar-ity, it is necessary to investigate deeply all the possible relationships between kinematical properties and fundamental quantities which characterize isolated and non-isolated galaxies. For this purpose, we have clearly defined in Section 2.1 the degree of interaction for each galaxy, differentiating the isolated galaxies from the galaxies subjected to faint interactions or strong interactions.
In this paper, we mainly discuss the 1D properties extracted from the 1D derived rotation curves. The 2D information is only used to derive kinematically determined position angles of the ma-jor axis and inclinations. Galaxies experiencing strong interactions have been excluded from this analysis since they are not numerous enough. In forthcoming papers, the impact of the environment (in a low-density environment) on the kinematical properties of nearby galaxies will be investigated together with a detailed analysis of the velocity fields.
The goal of this article is to evaluate the kinematical properties of a sample of 85 galaxies divided into two groups: undisturbed and softly interacting. Studying all the links between parameters reflecting the dynamical state of a galaxy will help us to have a better understanding of the evolution of galaxies. In this paper, we present a new set of 44 velocity fields providing 43 RCs. Including the previous papers, the GHASP survey now totals reduced Fabry– Perot data for 96 galaxies, uniformly covering the ‘magnitude–type’ plane (Fig. 1). In Section 2, the properties of the sample and the analysis of the isolation criterion are described. In Section 3, we describe the data reduction processing. In Section 4, we analyse the kinematical properties of the sample. More precisely, we study the variation of the Hα disc extension and the shape of the RCs (in terms of inner and outer slopes and degree of asymmetry of the RCs). In Section 5, a summary is given. Kinematical data are presented with comments for each object in the appendices.
2 P R O P E RT I E S O F T H E S A M P L E 2.1 Isolation criterion
The GHASP galaxies have been chosen in low-density environ-ments since cluster galaxies have been excluded from this
pro-Figure 1. Histogram of the 96 GHASP galaxies according to the isolation criterion.
gramme and only a few pairs or groups of galaxies have been ob-served. The degree of isolation of the GHASP galaxies has been accurately estimated using the logarithmic ratio f between external and internal forces (equation 1) defined from numerical simulations (Athanassoula 1984): f = log Fexternal Finternal = 3 log R b + log MC MG (1) where R is the radius of the galaxy, b the impact parameter, MCthe
mass of the companion and MGthe mass of the galaxy.
The results of simulation works (Varela et al. 2004, and references therein) show that if, for a given galaxy, f −2 then the galaxy has not been affected by gravitational interaction for at least 2× 109yr. In this case, the galaxy can be considered as isolated.
Varela et al. (2004) have redefined this parameter replacing the estimation of the masses by the luminosity, and the impact parameter
b by the projected distance between a galaxy and its companion. The
expression for fthen becomes
f = 3 log R Dp + 0.4(mG− mC) (2)
where R is the radius measured along the major axis of the galaxy,
Dpthe projected distance in the plane of the sky between the galaxy
and the companion, and mGand mC, respectively, are the apparent
magnitudes of the galaxy and the companion.
We computed the f values, from equation (2), for the GHASP galaxies, using the ALADIN, NED and HyperLEDA data bases. The values of f are given in Table B1 (see Appendix B). For each galaxy, the investigation of the companions has been made within a radius of 20 times the diameter of the considered galaxy (which is the criterion used by Karachentseva 1973) and in the range of
±700 km s−1around the systemic velocity of the galaxy.
The interest in using such a parameter is to provide a degree of non-isolation for each galaxy since f ranges from−5 for isolated galaxies to∼1 for pair galaxies or compact group galaxies. Fig. 1 gives the number of GHASP galaxies according to bins of f values within the phase space explored (20 diameters and±700 km s−1). For the galaxies with no companion, we adopted f= −5. Studying the distribution of the f values for Coma cluster galaxies, Varela et al. (2004) adopted as a criterion for isolated galaxies that f should be less than−4.5. Nevertheless, Varela et al. (2004) were led to use this low value of the cut-off since they did not have additional kinematical information. Indeed, from a qualitative analysis of the
Hα (GHASP) and HI(WHISP) velocity fields, we found that 51 galaxies, with f less than−3.5 (classified as ISO below), present no kinematical disturbances, neither of the Hα disc nor of the HI
disc and furthermore can be considered as isolated or experiencing very faint perturbations without major consequences on their kine-matics. Some of the galaxies with−3.5 f −1.5 (classified as SOFT below) present perturbations in their morphology or/and in the HIkinematics, but their optical velocity field is not affected in these cases. Therefore, galaxies with−3.5 f −1.5 (34 galax-ies) can been considered as softly interacting galaxies. Most of the galaxies with−1.5 f suffered from strong interactions (e.g. the UGC 5931/35 pair) and present Hα (and also HI) disturbances.
Then, we excluded the 11 GHASP galaxies with−1.5 f from the analysis of this paper since the impact of the environment on the Hα kinematical properties will be investigated in a forthcoming paper.
2.2 Main properties
The GHASP sample aims at covering the ‘luminosity– morphological type’ plane in the ranges−16 MB −22 and
1 t 10. Bins of 2 in type and 1 in magnitude have been de-fined in this plane; each bin containing eight galaxies, a total of around 200 galaxies (4× 6 × 8) had to be observed to cover the whole plane. The selection procedure of the GHASP galaxies has been made in order to have the whole GHASP data set representa-tive of the LEDA sample (where only galaxies corresponding to the GHASP criteria have been kept:δ 0, Vsys 9000 km s−1, 1t
10) as much as possible. The Kolmogorov–Smirnov test in 2D
was applied to the total GHASP sample considered as a subsample of the LEDA sample. The results (Table 1) are given in terms of the probability that the GHASP sample could not be representative of the LEDA sample. This test shows that the total GHASP sample is well representative of the LEDA sample except for luminous and normal Sc/Scd galaxies.
The Kolmogorov–Smirnov test has also been applied to the sub-sample analysed here. The results given in Table 2 show that the GHASP subsample studied here is well representative of the total GHASP sample except for luminous Sc/Sd galaxies.
The data gathered with the first four observing runs have been published in Garrido et al. (2002, 2003); Garrido, Marcelin & Amram (2004) (Papers I, II and III). We present here the results of the fifth, sixth and seventh runs, representing a sample of 44 galaxies observed in October 2000 and May and November 2001. 86 of the 96 GHASP galaxies discussed here have been selected from the WHISP catalog (a survey carried out at the Westerbork interferometer which consists in mapping the distribution of the neutral gas for about 400 galaxies, Principal Investigator: T.S. van Table 1. Results of the Kolmogorov–Smirnov test comparing the total GHASP sample to the LEDA sample.
(0.5–2.5) (2.5–4.5) (4.5–7.5) (7.5–10) (−22,−21) 0.37 0.49 0.76 (−21,−20) 0.34 0.00 0.63 0.00 (−20,−19) 0.24 0.00 0.89 0.00 (−19,−18) 0.00 0.07 0.00 0.07 (−18,−17) 0.09 0.70 0.69 (−17,−16) 0.00
Column: bin of morphological type. Row: bin of total B magnitude. The numbers represent the probability that the total GHASP sample is not representative of the LEDA sample (values above 0.7 suggest that the corresponding class of galaxies is not sufficiently represented).
Table 2. Results of the Kolmogorov–Smirnov test comparing the subsample to the total GHASP sample.
(0.5–2.5) (2.5–4.5) (4.5–7.5) (7.5–10)
(−22,−20) 0.00 0.26 0.85
(−20,−18) 0.00 0.00 0.00 0.00
(−18,−16) 0.00 0.00
Column: bin of morphological type. Row: bin of total B magnitude.The numbers represent the probability that the subsample is not representative of the total GHASP sample (values above 0.7 suggest that the corresponding class of galaxies is not sufficiently represented).
Albada; http://www.astro.rug.nl/∼whisp). Unfortunately, it is not possible to compare the kinematics of neutral and ionized gas since most of the WHISP data are not yet published (except for a sample of dwarf galaxies studied by Swaters & Balcells 2002, and for which the comparison has been made).
Fig. 2 summarizes the actual state of the survey: all morphological types from Sa to irregular galaxies have been observed and isolated as softly interacting galaxies (first line). Comparing the distribution of ISO and SOFT galaxies, we note that only a few very luminous or very faint isolated galaxies have been observed (second line). Fig. 2 (line 3) shows that the 96 GHASP galaxies considered in this analysis are uniformly distributed in the ‘magnitude–type’ plane: a majority of barred galaxies has been observed since two-thirds of the galaxies are barred. There is, however, a bias in the two ISO and SOFT subsamples since the SOFT sample contains early-type galaxies more luminous than in the ISO sample. Note also that, more generally, the SOFT galaxies seem to be systematically brighter than the ISO galaxies, whatever the type.
In Fig. 3 the global properties of the sample are studied distin-guishing isolated and softly interacting galaxies; the colour or the central surface brightness show the same variations with the lumi-nosity or the type in both cases.
The journal of the observations for the 44 new galaxies (in fact 43 since UGC 11300 has already been observed with the old camera, see Paper II) is given in Table 3.
3 T H E D ATA 3.1 The data reduction
The principles and characteristics of the instrument are the same as for Papers I, II and III but the detector, a new image photon counting system (IPCS), is a more efficient one (see Gach et al. 2002) and can achieve a quantum efficiency of 23 per cent due to a GaAs photocathode (which is five times more efficient than the previous one). As a consequence, the pixel size and the field of view have been modified: the pixel size is now 0.68 arcsec (however the angular resolution of our data is limited by the seeing, about 3 arcsec), and the field of view is now 5.8 arcmin2. The data processing
and the measurements of the kinematical parameters remain the same (see Garrido et al. 2002). The acquisition of a new set of filters with a FWHM of 2 nm allowed us to observe galaxies with recession velocities up to 9000 km s−1. Note that when a galaxy has been observed twice, with different filters, the difference of exposure time through the two filters is mainly due to the difference of transmission of the filters or/and in transparency of the sky during the observations.
3.2 Description of the figures
For each galaxy (see Figs A1–A27, B1–B16 in appendices), we present two frames per figure: isovelocity lines superimposed on
Figure 2. First line: distribution of morphological types distinguishing ISO (left) and SOFT (right) galaxies. Second line: distribution of magnitudes distin-guishing ISO (left) and SOFT (right) galaxies. Third line: distribution of our sample in the ‘magnitude–type’ plane distindistin-guishing barred from unbarred galaxies (left) and ISO from SOFT galaxies (right).
the Hα image of the galaxy (left) and the rotation curve of the galaxy (right) with the model fit superimposed.
3.2.1 Velocity field
A colour-coded version of the original velocity field is available on the Web site of GHASP: http//www.oamp.fr/interferometrie/ GHASP/ghasp.html. Before deriving the velocity field, a Gaussian smoothing is first applied on the Hα profiles in order to increase the signal-to-noise ratio (S/N) in the faint regions. The smoothing applied on the data cubes has no incidence on the determination of
the internal motions since the size of the smoothing (3 pixels= 2 arcsec) is smaller than the seeing at the OHP (never below 2 arcsec, all the more since we have rather long exposure times). In order to get smooth contours, the isovelocities were drawn after a strong spatial Gaussian smoothing (7 arcsec) of the original velocity field, sometimes reiterated when the diffuse emission of the disc was too faint or when the coverage of the galaxy by HIIregions was too poor to get continuous lines. The data smoothing is made on the velocity data file itself (not on the complete data cube) with the same weight for each pixel, so that the final pattern of the isovelocity lines is not too biased by the bright HIIregions. In the areas lacking Hα
Figure 3. Top: distribution of the colour versus MBand morphological type distinguishing isolated and non-isolated galaxies. Bottom: distribution of the
central surface brightness versus MBand morphological type with the same distinction.
emission, the continuity of the lines has been artificially achieved by eye-estimate and a dashed line plotted to make the reading of the velocity field easier. In cases where only a few isolated HIIregions
were measured in a galaxy (e.g. UGC 3384, 9992), it was not possi-ble to draw any isovelocity line; then we directly wrote the average velocity value found for each HIIregion on the map.
The Fabry–Perot technique provides an Hα profile inside each pixel, so that a typical velocity field of a GHASP galaxy contains thousands of velocity points. For most of the galaxies observed with GHASP, the velocity field is not limited to the HIIregions but covers
most of the diffuse emission of the disc, as can be seen on the original colour-coded velocity fields on the GHASP Web site. The detection limit of our device is 10−9J m−2s−1sr−2(Amram et al. 1991), which is 2.4× 10−17erg cm−2s−1 arcsec−2, with a S/N ratio between 1 and 2 for a 15-min exposure time. As a result, our typical exposure times of 2 h ensure a good detection of the Hα diffuse emission of the disc of most galaxies since most of the Hα emission found below 1.6× 10−16 erg cm−2 s−1 arcsec−2 may be considered as filamentary and/or diffuse according to Ferguson et al. (1996). This is all the more true with our new IPCS detector (used since October 2000) because of its more sensitive GaAs photocathode (Gach et al. 2002) offering a five-fold gain in quantum efficiency.
3.2.2 Hα line
The Hα image is derived from the analysis of the Hα line pro-files, by measuring the flux found inside the line for each pixel. It gives a pure monochromatic image of the galaxy (continuum free).
To obtain the Hα flux inside each pixel, first, the continuum level was taken to be the mean of the channels which do not contain the line. The Hα integrated flux map was obtained by integrating the monochromatic profile in each pixel above the threshold defined by the continuum level. The scanning of the interferometer samples the point spread function (PSF) of the instrument sufficiently(the Airy function convolved by the surface and transmission defects) and covers the free spectral range through 24 scanning steps. When the profiles are structureless and the S/N high, the lines can be easily fitted by the convolution of the observed PSF (given by the narrow neon 6598.95-nm emission line) with a single Gaussian function. When the profile is more complex, multiple Gaussian components are needed. Nevertheless, since the number of scanning steps and the baseline of the continuum emission are relatively low, and the structure of the profile is often complex (asymmetries, multiple com-ponents, low S/N), we do not fit a function to the profile to extract the first-order momentum. Instead, the heliocentric radial velocity for a given pixel is directly given by the position of the barycentre of the line. Furthermore, we do not have to make assumptions on the fit used when the data are dominated by Poisson or receptor noise at low S/N levels. However, at high S/N, since we have a good knowledge of the PSF, the barycentre of the emission line profile may be measured with an accuracy much better than the sampling step, hence giving a precision of about 3 km s−1for a S/N= 5. For each pixel, the S/N level is given by the y-axis of the barycentre of the line normalized by the rms of the continuum level. Velocity maps were then obtained from the intensity weighted means of the Hα peaks for each pixel.
Table 3. Log of the observations.
N◦ N◦ α δ λc FWHM Date Exposure time Seeing
UGC NGC (2000) (2000) (Å) (Å) (s) (arcsec) (1) (2) (3) (4) (5) (6) (7) (8) (9) 508 266 00h49m47.8s 32◦0140 6665 23.1 Oct 26, 2000 7200 3.4 6662 21.4 Nov 20, 2001 3960 3 763 428 01h12m55.6s 00◦5854 6587 11.2 Oct 31, 2000 5760 4.1 1117 598 01h33m50.9s 30◦3937 6561 8.8 Oct 27, 2000 5760 4 1736 864 02h15m27.7s 06◦008.2 6597 10.3 Oct 23, 2000 7560 6.1 1886 02h26m00.5s 06◦008.2 6662 21.4 Nov 20, 2001 6480 4 1913 925 02h27m17s 33◦3443 6576 11.4 Oct 24, 2000 5400 3.4 2045 972 02h34m12.9s 29◦1847 6596 10.3 Nov 1, 2000 9360 4.8 2141 1012 02h39m14.9s 30◦0906 6585 11.2 Nov 17, 2001 5160 3 2183 1056 02h42m48.4s 28◦3427 6595 10.3 Oct 27, 2000 7920 4.8 2193 1058 02h43m30s 37◦2029 6574 11.4 Nov 19, 2001 9360 4 2503 1169 03h03m34.7s 46◦2311 6615 11.1 Nov 17, 2001 7200 4.4 3013 1530 04h23m27.1s 75◦1744 6615 11.1 Nov 16, 2001 3840 3.7 3273 05h17m44.4s 53◦3305 6575 11.4 Nov 9, 2001 5040 5.8 3384 05h59m47.7s 62◦0929 6634 21.7 Oct 26, 2000 9360 4 3429 2146 06h18m37.7s 78◦2125 6574 13.6 Nov 17, 2001 6480 3.5 3691 07h08m1.3s 15◦1042 6611 10.2 Oct 28, 2000 8640 4.4 3734 2344 07h12m28.6s 47◦1000 6585 11.2 Nov 9, 2001 5280 6.5 4273 2543 08h12m58s 36◦1516 6615 11.1 Nov 21, 2001 7200 4.4 6702 3840 11h43m59s 20◦0437 6725 50 May 26, 2001 5280 3.7 9366 5676 14h32m46.8s 49◦2728 6606 12 May 24, 2001 1680 2.4 6606 12 May 25, 2001 3600 3 9649 5832 14h57m45.7s 71◦4056 6576 11.4 May 27, 2001 6000 2.4 9753 5879 15h09m46.8s 57◦0001 6576 11.4 May 23, 2001 3120 3 6586 11.2 2160 2.4 9858 15h26m41.5s 40◦3352 6621 9.1 May 31, 2001 5280 2.7 9992 15h41m47.8s 67◦1515 6576 11.4 May 27, 2001 5760 3 10359 6140 16h20m58.1s 65◦2326 6587 11.2 May 28, 2001 4800 3 10445 16h33m47.6s 28◦5906 6587 11.2 May 26, 2001 4320 3.4 10470 6217 16h32m39.2s 78◦1153 6597 10.3 May 25, 2001 7920 3.7 10502 16h37m37.7s 72◦2229 6650 21.7 May 31, 2001 3360 3.5 10546 6236 16h44m34.6s 70◦4649 6587 11.2 May 30, 2001 5280 3.4 10564 6248 16h46m22s 70◦2132 6587 11.2 May 28, 2001 4560 3.4 11124 18h07m26.9s 35◦3331 6597 10.3 May 28, 2001 3600 3 11300 6689/90 18h34m50.2s 70◦3126 6576 11.4 May 31, 2001 5040 3 11429 6792 19h20m57.4s 43◦0757 6663 21.4 May 29, 2001 1920 3 6663 21.4 May 30, 2001 3600 3.4 11557 20h23m58.3s 60◦1133 6597 10.3 May 29, 2001 4320 2.4 11707 21h14m31.7s 26◦4404 6582 11.2 Nov 20, 2001 5400 3.7 11852 21h55m59.3s 27◦5355 6687 23.1 Oct 31, 2000 7920 4.1 11861 21h56m24s 73◦1539 6595 10.3 Nov 9, 2001 5280 6.1 11909 22h06m16.2s 47◦1504 6585 11.2 Nov 10, 2001 4080 3 11914 7217 22h07m52.5s 31◦2133 6587 11.2 Oct 26, 2000 7200 4.8 12101 7320 22h36m3.5s 33◦5654.2 6587 11.2 Oct 29, 2000 2880 3.4 6576 11.4 2160 3.4 12276 7440 22h58m32.5s 35◦4809 6683 23.1 Oct 27, 2000 7200 4.8 12276c 22h58m41.3s 35◦4833.6 6683 23.1 Oct 27, 2000 7200 4.8 12343 7479 23h04m56.6s 12◦1922 6614 11.1 Nov 12, 2001 5760 5.5 12632 23h29m58.7s 40◦5925 6571 13.7 Nov 16, 2001 6120 3.7
(1) Name of the galaxy in the UGC catalog. (2) Name in the NGC catalog when available. (3) and (4) Coordinates of the galaxy in 2000. (5) Central wavelength of the interference filter used. (6) FWHM of the interference filter. (7) Date of the observations. (8) Total exposure time in s. (9) Seeing in arcsec (FWHM of a Gaussian fit of foreground stars).
The relative intensity of the Hα map is coded here through grey levels. The Hα images are sometimes markedly offset with respect to the centre of the image when we had to shift a bright star out of the field to prevent any damage to the microchannel plate of the IPCS as well as to prevent ghosts. Such ghosts are parasitic reflections of bright objects inside the instrument, between Fabry– Perot plates and the interference filter; those ghosts are out of focus and symmetrically located with respect to the optical axis, so that
they are easy to distinguish from normal field stars. It is important to get rid of them in the case of bright HIIregions since they will produce a symmetric diffuse patch with the same velocity, as shown by Georgelin (1970). Hence the interest of offsetting the galaxy in the field to prevent any parasitic ghost to be superposed on the galaxy itself. Ghost reflections may also be deflected to the edge of the field by tilting the etalon with respect to the optical axis, at the price of a degraded resolution limit at the detector edge (Bland & Tully
1989). In a few cases, when the velocity amplitude is comparable or higher than the width of the interference filter, the interference filter is not centred on the systemic velocity and one side of the galaxy may be better transmitted than the other side, leading to an artificial asymmetry in the intensity of the Hα emission. This is specified in the cases when it occurs.
3.2.3 Rotation curve
The rotation curve is drawn as explained in Paper I, using the ve-locity field obtained after a Gaussian smoothing of 3 arcsec. The set of kinematical parameters is adjusted through an iterative process minimizing the dispersion of the points along the rotation curve. The starting set of parameters is chosen as follows. The centre of rotation is supposed to be the nucleus identified on our continuum image (when no nucleus can be seen, neither on our images nor in other bands, it is chosen as the centre of symmetry of our veloc-ity field; four out of the 45 galaxies presented in this new set have a significant offset between the photometric and kinematic centre, and less than 10 out of the 96 GHASP galaxies studied up to now), the inclination is derived from the axis ratio found in the litera-ture, the position angle is defined by the outer parts of our velocity field, and the systemic velocity is adjusted in order to symmetrize at best both sides of the rotation curve. For well-behaved galaxies, the iterative process was quite easy and rapidly converged. However, for some irregular galaxies with asymmetric rotation curves it was hard to converge and we had a strong uncertainty on the kinemat-ical parameters, more especially the inclination which is the less constrained. The typical accuracy we reach is about 1 arcsec for the position of the rotation centre, 2–3 km s−1for the systemic velocity, 2◦for the position angle of the major axis, but only 5◦–10◦for the inclination. The curve is plotted with both sides superimposed in the same quadrant, using different symbols for the receding (crosses) and approaching (dots) sides (with respect to the centre). The rota-tion curves are sampled with bins of 3–6 pixels (∼2–4 arcsec). The choice of the width of the bin depends on the distance of the galaxy, the quality of the data, the inner gradient and the extension of the rotation curve. The error bars on our plot give the dispersion of the rotation velocities computed for all the pixels found inside each el-liptical ring defined by the successive bins. Rotation curves for the barred galaxies of our sample have been plotted without corrections for non-circular motions along the bar. For each rotation curve, a fit has been obtained using the analytical function defined by Kravtsov et al. (1998; see section 4). This model of the RCs is included in the plot as a full black line.
3.3 Kinematical parameters
2D velocity fields enables us to find accurately the position angle (PA) of the major axis of galaxies, providing they are regular rotative discs. They may be differences, however, with the photometrical values because of warps or strong spiral arms that could bias the outermost isophotal contours.
In Fig. 4 (top), the kinematical PAs obtained by GHASP are compared with the photometric PAs (found in HyperLEDA). On average, the difference between both position angles is abs(PA) = 15◦± 19◦and can be as large as 75◦. With long-slit spectrographs, the slit position is based on the photometry; the maximum velocity will hence be missed for many galaxies, leading to a systematic underestimating. We found no correlation between the largestPA and the morphological type, neither with the inclination nor with the degree of interaction.
Figure 4. Top: kinematical position angles obtained for the GHASP sam-ple versus photometric position angles found in the HyperLEDA data base. Middle: kinematical inclination versus photometric inclination found in the NED. Bottom: difference between GHASP and HyperLEDA systemic ve-locity versus the scanning wavelength.
In Fig. 4 (middle), kinematical and photometric inclinations (HyperLEDA) are also compared. The inclinations found in HyperLEDA take into account the thickness of the disc. On average, the difference between both inclinations is abs(i) = 9◦± 9◦, and
does not depend on the morphological type, nor on the degree of interaction. The low inclinations are apparently systematically un-derestimated by the photometry, whereas the high inclinations are overestimated. In the cases of edge-on galaxies, the determination of the type is hard and then the thickness correction (which depends on the type) can be false.
As emphasized in Paper I, our systemic velocities suffer from a systematic bias, negligible when the recession velocity is close to 1650 km s−1(then the Hα emission line of the galaxy is coincident with the neon line at 659.895 nm used for the calibration) but in-creasing with departure from the calibration wavelength, reaching
−10 km s−1for recession velocities around 0 km s−1and,
symmetri-cally,+10 km s−1for velocities around 3300 km s−1. This is because the interferometer does not behave the same for calibration and ob-servation since the coating layers behave differently depending on the wavelength. This theoretical trend is clearly found when plotting the velocity difference between GHASP and LEDA as a function of the shifted Hα wavelength for each galaxy (Fig. 4, bottom). The resulting equation is (with a correlation coefficient of 0.7):
V = (−2077 ± 227) + (0.31 ± 0.03)λscan. (3)
The dispersion is quite large and the phase shift effect due to the interferometer is typically of the same order as the dispersion of the systemic velocities found in HyperLEDA. That is why we decided to give our values of systemic velocity without correcting from the phase shift, all the more since we do not use it in our analysis of the rotation curves for which knowledge of the absolute value of the velocities is not necessary. Indeed, the relative velocities we are looking for inside a given galaxy are almost not biased by the phase shift effect because the wavelength change is not significant between the receding side and approaching side.
Table 4 gives the values that we found for the main kinematical parameters, together with some fundamental parameters compiled from the literature.
4 A N A LY S I S : E X T E N S I O N O F T H E Hα D I S C S
A N D S H A P E O F O U R R OTAT I O N C U RV E S
In order to classify and analyse each rotation curve, we fitted our data (giving the rotational velocity averaged inside elliptical annuli) with the following analytical function containing five free parameters (Kravtsov et al. 1998) which presents the advantage of fitting every shape of curve: V (r )= Vt (r/rt)g 1+ (r/rt)a (g+b)/a. (4)
Different modellings of RCs are available in the literature: the arctan function, the universal rotation curve (URC) and multipa-rameter functions. The arctan function has the advantage of having the smallest number of free parameters but it cannot reproduce RCs with a bump at the turnover or RCs with a peculiar shape (Courteau 1997). The URC (Persic et al. 1991; Persic, Salucci & Stel 1996) takes into account the component of the disc and the halo. It is a physical model of RCs but several authors tried to use it without great success. One-third of the sample of Ursa Major cluster galax-ies of Verheijen (1997) cannot be correctly reproduced with the URC; Sofue et al. (1999) cannot fit correctly the inner parts of their RCs with the URC; Courteau (1997) has also applied the URC as a model for 131 RCs and found non-satisfying results for 40 RCs. Therefore, we decided not to use the URC for modelling our RCs.
The function of Kravstov et al. (1998) is similar to other multipa-rameter functions used by Rix et al. (1997) or Courteau (1997): rt
and Vtare the radius and the velocity of the turnover (rt = ∞ for
solid body rotation curve), g is linked to the inner slope (V (r rt)= rg) and b to the outer slope [V (r r
t)= 1/rtb], and a characterizes
the sharpness of the turnover. This analytical function derives from the family profiles of dark haloes and then has a physical origin. In fact, the term g is directly connected with the inner slope of the dark halo profile and the goal using this function is to check, at the end of this survey, whether our RCs (which are well constrained in the inner parts) are best fitted with cuspy or core haloes.
The fits were carried out by minimizing theχ2using the MINUIT
package, with the simplex search routine (Nelder & Mead 1965). For each fit, we measured theχ2and kept only rotation curves for which
the probability that the fit is representative of the data is greater than 50 per cent (comprised in the interval at 3σ ).
The global shape of a rotation curve is defined by an inner in-creasing slope, a turnover (at rt) and a plateau more or less constant
with a given slope (the outer slope). We have evaluated the inner and outer slopes of the rotation curves and correlated them with fun-damental parameters. We have also measured the extension of the ionized hydrogen disc and the asymmetry of our RCs. The galaxies larger than our field of view, those observed with a badly centred filter or affected by a warp on the optical part of the disc (see Table B1, below) are, of course, excluded from this analysis (five galax-ies: UGC 528, 1117, 2855, 4284, 6537) since, in these cases, the studied parameters are badly evaluated. Also, the 11 non-isolated galaxies (UGC 1249, 1256, 2045, 3851, 4499, 5931, 5935, 7278, 9969, 10310, 12276c), for which f values larger than−1.5 have been found (see Section 2.2), are excluded from this analysis.
4.1 Extension of the Hα discs
4.1.1 Results
For each galaxy, we measured the outermost point of our Hα rotation curves (Rlast) which corresponds to the maximal extension of the
ionized disc since we take into account velocity points in a large sector around the major axis. In Fig. 5, we plot Rlastas a function of
R25, the isophotal radius at a surface brightness of 25 mag arcsec−2
in the B band. These two quantities are linked by a linear relation which shows that, on average, the size of the Hα disc is proportional to R25. Fig. 5 also shows that isolated galaxies present Hα discs as
large as softly interacting galaxies.
In order not to induce a bias due to the distance, we studied the variation of the ratio Rlast/R25as a function of the morphological
type, t (Fig. 6). This ratio has already been studied in a previous paper (Garrido et al. 2004) and we have actualized it taking into account the new galaxies presented here but also distinguishing the points according to the nature of the emission (diffuse Hα emission or HIIregion). Globally, we note the following.
(i) ISO galaxies present the smallest Hα discs (around 0.6 R25),
and in these cases the Hα emission has a diffuse origin (by contrast, the largest discs are reached with HIIregions). From Sb to Sdm galaxies, the Rlast/R25ratio varies between 0.6 and 1.6. The presence
of HIIregions beyond R25means that massive star formation can
take place at the edge of the optical disc and beyond for isolated galaxies.
(ii) SOFT galaxies cover a smaller range of Rlastvalues, between
0.8 and 1.2 R25, except for Sc–Sd types where it reaches higher
values. In contrast to ISO galaxies, the last points of the detected emission are mainly produced by diffuse emission.
Table 4. Galaxy parameters.
N◦ t Type D25/2 Mb Vsys D i PA Vmax Rlast 1/2 SA annuli
UGC (arcsec) (mag) (km s−1) (Mpc) (◦) (◦) (km s−1) (arcsec) (◦) (arcsec)
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) 508 1.5 SB(rs)ab 88.3 −22 4670±3 61.9 45±3 298±1 363 +185 60 3.4 763 8.7 SAB(s)m 108.9 −19.4 1145±2 15.1 50±5 295±2 109 +193.5 50 4.8 1117 6 S(s)cd 1982 −19.3 −191±2 0.9 50±3 23±3 61 +47.4 50 4.8 1736 5.1 SAB(rs)c 137.1 −20.5 1522±3 71.3 42±1 201±1 179 +116.9 60 3.4 1886 3.6 SAB(rs)bc 70.2 −19.8 4867±2 66.1 60±5 215±5 279 −134.8 50 3.4 1913 7 SAB(s)d 336.6 −20 552±3 20.8 58±5 100±2 −158.2 30 4.8 2045 2 Sab 97.8 −20.4 1529±2 9.1 55±1 145±2 141 −89.5 40 3.4 2141 0.3 SO/a 74.5 −18 961±2 12.9 68±10 18±5 136 −154.9 35 3.4 2183 1 Sa 69.8 −19.6 1542±2 21 62±1 338±2 122 +61.9 40 3.4 2193 5.3 S(rs)c 82.1 −18.2 510±1 10.6 21±1 138±3 57 −88.5 40 3.4 2503 2.6 SAB(r)b 125.6 −21.8 2403±1 31.4 53±5 216±1 284 −169.3 45 3.4 3013 3.1 SB(rs)b 124.2 −21.5 2465±1 33.4 50±1 8±5 209 −93.2 15 3.4 3273 8.8 Sm 75.4 −17.7 608±2 8.1 55±1 225±1 83 +96.4 50 2.7 3384 8.8 SB(rs)a 22.9 −14.8 3429 2.3 SB(s)abpec 164.9 −20.6 868 11.7 60±5 135±2 343.8 +167.6 40 3.4 3691 6 Scd 65.5 −20.3 2212 29.1 62±3 63±3 136.2 −62.9 50 2.7 3734 4 S(rs)c 57 −18.4 978 12.4 25±5 315±3 174.8 −101 45 2.7 4273 3.8 SB(s)b 75.7 −20.7 2475 32.7 56±5 33±2 193.6 +81.8 40 3.4 6702 1.3 Sa 30.1 −20.7 7420 98.6 43±10 68±6 178 +34.1 50 1.4 9366 4.7 S(rs)bc 114.8 −21.5 2110 28.8 62±10 43±3 238.2 +98.8 50 3.4 9649 3.1 SB(rs)b 95.3 452 5.2 54±6 45±3 110.8 −122.3 35 3.4 9753 3.6 S(rs)bc 118.6 −19.4 764 10.8 72±4 180±2 144.5 −116.4 30 3.4 9858 4 SABbc 128.6 −20.4 2626 35.8 79±5 252±2 178.7 −164.9 45 3.4 9992 9.8 Im 48.9 48.9 10359 5.6 SB(s)cdpec 146.6 −19.3 913 11.6 44±10 93±5 147.1 −201.9 40 3.4 10445 6 SBc 70.2 −17.5 957 12.5 60±5 280±1 72.4 −105.6 45 3.4 10470 4 SB(rs)bc 92.1 −20.2 1350 18.5 34±10 115±5 144 −96.2 40 3.4 10502 5.3 S(rs)c 66.1 −20.8 4315 57.5 35±5 275±5 313.8 +121.3 55 3.4 10546 6 SAB(s)cd 75.5 −18.3 1267 16.9 65±5 350±2 160 −110.3 45 3.4 10564 6.5 SBd 72.3 −17.4 1130 15.5 60±5 330±5 80.4 −103.3 50 3.4 11124 5.9 SB(s)cd 75.5 −18.6 1609 21.5 30±5 345±5 131 −71.4 45 3.4 11300 6.4 SBcd 118.3 480 6.3 65±3 348±3 103.9 +113.7 45 3.4 11429 3.1 SBc 65.2 −21.9 4718 61.8 60±3 24±4 187 +69.2 50 3.4 11557 7.8 SAB(s)dm 64.7 −18.5 1385 18.5 37±5 92±2 58.9 +66.5 50 3.4 11707 7.9 Sdm 75.4 −16.3 900 12 55±10 238±5 91.8 −160.7 30 3.4 11852 1 SBa 32 −20.2 5871 78 58±3 13±4 201.4 +25.2 40 2.1 11861 7.8 SABdm 79.8 −19.8 1484 19.8 50±7 33±3 81 −123 50 3.4 11909 4.5 Spec 74 −18.5 1100 14.7 77±10 0±1 164.2 +113.3 25 3.4 11914 2.5 S(r)ab 109.9 −20.5 947 12.9 35±5 88±7 262.4 +105.6 60 3.4 12101 6.6 S(s)d 57.3 −18.1 750 10.8 50±10 132±8 135.8 +50.2 40 2.7 12276 1.1 SB(r)a 39.4 −20.6 5688 75.5 38±10 140±3 120.1 −30.4 60 2.7 12276c 5707.5 76.1 35±10 150±5 +8.3 50 0.7 12343 4.4 SB(s)c 124.2 −21.6 2375 31.3 45±10 25±2 239.3 −139.9 60 3.4 12632 8.7 Sm 134 420 5.6 45∗ 210±5 58.1 −160.9 40 3.4
(1) Name in the UGC catalog. (2) Morphological type from the de Vaucouleurs classification (de Vaucouleurs 1979) in the HyperLEDA data base (Lyon-Meudon Extragalactic Data base). (3) Morphological type from the RC3 catalog. (4) Isophotal radius in arcseconds at the limiting surface brightness of 25 B mag arcsec−2, from HyperLEDA (Paturel et al. 1991). (5) Absolute B magnitude from HyperLEDA, corrected from galactic and internal extinction. (6) Systemic velocity deduced from our velocity field. (7) Distance D, deduced from the systemic velocity taken in the NED (and not corrected from the Virgo inflow), assuming H0 = 75 km s−1 Mpc−1, except for UGC 1117 and 1913 for which accurate measurements of the distance were
available (Paturel et al. 2002). (8) Inclination deduced from the analysis of our velocity field except for UGC 12632 (adopted values from the literature). (9) Position angle of the major axis deduced from our velocity field. (10) Maximum velocity, Vmax, derived from the fit of the rotation curve. NB: In Papers I
and II it was a rough estimate from our rotation curve and namedVmax/2. (11) Outermost point reached on the rotation curve. (12) Half sector around the
major axis taken into account for computing the rotation curve. (13) Size, in arcsec, adopted for the annuli to derive the rotations curves.
(iii) For irregular galaxies, we note a faint decrease of the max-imum values (around 1.2) reached by the ratio, but ionized gas re-mains present all over the optical disc. Hunter & Elmegreen (2003) did not find HIIcomplexes beyond R25in irregular galaxies. Our
data are consistent with their result since the GHASP galaxies hav-ing a Rlast/R25ratio larger than 1.0 exhibit diffuse emission in the
outer parts.
We excluded the following from this analysis.
(i) UGC 11951, which seems to be a badly classified galaxy. Indeed, it is classified as Sa; however, it exhibits a solid-body HI
rotation curve and its maximal velocity is around 180 km s−1(Paper III), typical of a later type (Sb/Sc galaxy); indeed, if we plot this point with t= 3, then it belongs to the main cloud.
Figure 5. Extension of the Hα disc, Rlastin kpc, versus R25in kpc (for
a total of 73 galaxies). The line represents a linear fit of all the points for which the equation is y= 0.99x + 0.16 (the correlation coefficient is 0.91). (ii) UGC 12060 and UGC 11707. They exhibit an abnormally high Rlast/R25ratio (4.0 and 2.2). We think that the determinations
of R25are erroneous since the values proposed by HyperLEDA are
clearly higher than those deduced from surface brightness profiles (Swaters & Balcells 2002) available in the literature. Even when taking into account these last values, the two galaxies are markedly out of the cloud of points. This should be due to the peculiar class of these two galaxies which have low surface brightness and then must be the object of a separate analysis.
4.1.2 Discussion
Why do late-type galaxies present larger Hα discs than early-type galaxies? Since star formation is directly linked with the reservoir of neutral gas, we checked if a similar trend existed for RHI/R25.
But when plotting the ratio RHI/R25as a function of the type for the
galaxies of our sample for which we could find values in the litera-ture, no clear trend can be seen. Also, Broeils & Rhee (1997) found no special trend with a sample of 108 galaxies, a result confirmed by Martin (1998) who studied a sample of 116 galaxies and found no relation between the HIextent and the morphological type.
Figure 6. Extension of the Hα disc, Rlastin units of R25versus the morphological type t (for a total of 73 galaxies) distinguishing isolated (left) and softly
interacting (right) galaxies. The points are coded differently according to the nature of Hα emission providing the outermost velocity point: triangles for diffuse emission, circles for HIIregions.
Studying the variation of the mean HI surface density, it ap-pears that it reaches its minimum value for early-type galaxies, then increases up to Sc galaxies and then remains constant (fig. 3d of Roberts & Haynes 1994, fig. 5a of Broeils & Rhee 1997 and fig. 6 of Martin 1998).
Finally, early-type galaxies barely have regions of massive star formation beyond R25. Thus, they have minimal sizes of the ionized
disc. They also have low values of mean HIsurface density sug-gesting that it is not sufficient at the edge of the discs of early-type galaxies for star formation to begin (Kennicutt 1989), whereas, for late-type galaxies, star formation can take place all over the optical disc, up to 1.5 R25. They exhibit the largest ionized discs together
with high HIsurface density, consistent with the maximum value of the star formation rate observed in these galaxies (James et al. 2004). The thickness of the discs (Ma 2002; Zhao, Peng & Wang 2004) decreases along the Hubble sequence (Sc galaxies are 40 per cent thinner than Sab galaxies), then Sbc to Sd galaxies have thin discs, hence low velocity dispersion and high density of neutral gas; they are certainly the most efficient for forming stars in the opti-cal disc and even beyond. Irregular and dwarf galaxies do not have significantly more extended ionized discs compared with early-type galaxies although their mean HIsurface density is higher. Irregu-lar and dwarf galaxies are 2–5 times thicker than spirals (Brinks, Walter & Ott 2002) and present a velocity dispersion of the same order as spirals, but their gravitational potential is not sufficient to form massive stars at high rate, particularly in the outer disc.
4.2 Rotation curves shapes
Two parameters which characterize the global shape of a RC are the inner and outer slopes of the rotation curves. Both parameters, as well as the degree of asymmetry of the RC, are studied here for the ISO and SOFT groups.
4.2.1 The inner slope
In the case of solid-body rotation curves, the slope is defined unam-biguously by the ratio
Sin=
Vlast
Rlast
Figure 7. First line: inner slope versus the morphological type. Second line: inner slope versus the asymmetry of the RCs. Third line: inner slope versus the outer slope. The open square between parentheses corresponds to UGC 11914 which has an inner slope of 526 km s−1kpc−1, the highest of the sample.
where Rlast and Vlastrepresent, respectively, the radius and the
ve-locity of the outermost point of the rotation curve.
In the other cases, the radius of the turnover of the rotation curve,
rt, which corresponds to the transition zone between the inner
in-crease and the plateau, was deduced from our fit. In order not to contaminate the determination of the inner slope by the transition zone, we take into account only 70 per cent of the inner slope and define the inner slope as:
Sin=
V (0.7rt)
0.7rt .
We plotted it as a function of the morphological type, the asym-metry (see Section 4.2.3 for the definition) and the outer slope of the rotation curve (Fig. 7).
Barred galaxies exhibit, on average, smaller values of the inner slope than unbarred galaxies (also with a lower dispersion) for ISO as well as for the SOFT group:
Sin/barred/ISO= 39 ± 18
Sin/unbarred/ISO= 135 ± 157 Sin/barred/SOFT= 45 ± 37 Sin/unbarred/SOFT= 83 ± 99.
Studying the graphs of Fig. 7, we note the following for ISO galaxies.
(i) There is no large variation of the inner slope of the RCs for barred galaxies, and no correlation can be seen with none of the con-sidered parameters (type, kinematical asymmetry and outer slope). (ii) For unbarred galaxies, the range of variation of the inner slope (as well as the average inner slope itself) increases when we consider earlier types. We note an increase of Sinwhen considering
galaxies with bulges. Late-type galaxies never exhibit an inner slope above 60 km s−1kpc−1. Note that we obtain the same graphs when replacing t by MB.
(iii) For unbarred galaxies, the range of variation of the inner slope rises for symmetric RCs (see Section 4.2.3; log AD −0.75).
However, galaxies exhibiting a high value of ADhave faint values of
the inner slope (50 km s−1kpc−1) showing that only less massive galaxies are likely to exhibit asymmetric RCs.
(iv) No correlation appears between the inner and outer slope for the ISO group.
For the inner slope of the RCs of SOFT galaxies, we note the following.
(i) There is no clear correlation with the type for barred or for unbarred.
(ii) The tendency to decrease when the kinematical asymmetry increases, already observed for the unbarred galaxies of the ISO group, is observed here for both barred and unbarred.
(iii) The inner and outer slope seem to be correlated, with the outer slope increasing when the inner parts rotate faster.
Inner slopes of the RCs have been the object of few studies. In a review paper about RCs, Sofue & Rubin (2001) concluded that: ‘inner RCs have greater individuality’. Marquez et al. (2002) found the same trend as us for a sample of 111 isolated galaxies (adopting, as a definition of the inner slope, Sin= VG/rG where rGand VG
are, respectively, the radius and the velocity of the inner region of solid-body rotation). In fact, the inner velocity gradient seems to be better correlated with the bulge-to-disc luminosity ratio as shown by Marquez & Moles (1999) for 13 galaxies. In Fig. 8, we plot the central surface brightness in the R-band (available in the literature) versus the inner slope of the rotation curve and find a correlation between these two quantities. This result confirms the conclusions of Marquez & Moles (1999) that the inner gradient of rotational velocities is strongly correlated with the concentration of light in the central parts of the galaxies rather than with the total luminosity.
Figure 8. Central surface brightness in the R-band versus the inner slope of the RCs for 18 galaxies (the correlation coefficient of the fit is 0.65).
4.2.2 The outer slope
Optical RCs are not well suited for determining this parameter since we obtain a plateau for a low percentage of galaxies (exactly 27 galaxies). To measure the outer slope, we considered the formula:
Sout=
Vlast− V (1.3rt) Rlast− 1.3rt
.
If Soutis:
(i) less than−2, the RC is decreasing;
(ii) between−2 and +2, the RC marks a plateau; (iii) larger than+2, the RC is increasing.
We plot, in Fig. 9, Soutversus the type and the degree of asymmetry
(see Section 4.2.3 for the definition) of the RC (note that, for the luminosity, a graph similar to that with the type has been obtained). First of all, no decreasing RC has been found in the SOFT group; decreasing RCs concern only early-type ISO galaxies, but there are only two clearly decreasing RCs (one with a large error bar) and it is hard to tell whether this is significant or not. No correlation can be seen with the type or the kinematical asymmetry for the SOFT group. For the ISO group, however, the outer slope seems to increase with the type and, more clearly, with the kinematical asymmetry. Also, no significant difference can be seen between barred and unbarred galaxies. This is not surprising since bars are expected to have an effect only in the inner regions.
4.2.3 Kinematical asymmetries
Lopsidedness is a common feature of galaxies and affects both op-tical and HIdiscs of field galaxies. Asymmetry is mainly seen in
morphology (distribution of gas, distribution of light, extension of the disc) or dynamics (warps with U-shape, asymmetric velocity profiles) and reflects the degree of symmetry of the gravitational potential of a galaxy. There are different ways to measure the degree of asymmetry related to morphology or dynamics: 50 per cent of the HIprofiles are not symmetric (Richter & Sancisi 1994; Haynes et al. 1998) reflecting non-symmetry in the distribution of the neu-tral hydrogen; Conselice (1997) has measured the asymmetry of the light distribution and found that it is strongly correlated with both morphological type and colour. In this paper, we study lopsided kine-matics measuring the degree of asymmetry of our rotation curves. Nishiura et al. (2000) have developed the following formula:
A= 1 N N j=1 V (rj)− V (−rj) V (rj)+ V (−rj) 2 0.5
where N represents the number of annuli of the rotation curve, and
V (rj) and V (− rj) the velocity in the jth annulus of the
approach-ing (recedapproach-ing) side. Dale & Uson (2003) have refined this formula taking into account the dispersion of the velocity points within each annulus: A= N j=1 V (rj)− V (−rj) σ (rj)2− σ (−rj)2 0.5 × V (rj)+ V (−rj) σ (rj)2− σ(−rj)2
whereσ (rj) andσ(−rj) represent the velocity dispersion in the jth
annulus of the approaching (receding) side.
The parameter ADhas been calculated adopting the Dale–Uson
formula which is more representative of the asymmetry in the repar-tition of mass since it frees us from the dispersion of the motion. We consider the whole initial rotation curve to compute AD, then
Figure 9. Top: outer slope versus morphological type. Bottom: outer slope versus asymmetry of the RC defined by Dale & Uson (2003). The numbers between parentheses represent the number of galaxies for each case.
take into account kinematical asymmetry both in the inner and outer parts.
Non-axisymmetric disturbances, such as bars, oval distortions, spiral structures in the disc are observable in two-dimensional ve-locity fields but are usually ignored and azimuthally averaged in the rotation curves. These effects may introduce errors in the rotation curves and contribute, for instance, to shallower inner slopes or ro-tation curves. On the other hand, intrinsic asymmetries in the disc are observed. These asymmetries are lower values as long as they are minimized during the standard process of symmetrization of the rotation curve. In Fig. 10, we have plotted the variation of the loga-rithm of ADversus the morphological type, the luminosity, the (B−
V ) colour and the maximal velocity of the galaxies, distinguishing
barred and unbarred galaxies for both isolated and softly interact-ing groups. Correlations appear more or less clearly with the four quantities: the most asymmetric RCs are found for late-type galax-ies, fainter and bluer galaxies. Interestingly, Conselice, Bershady & Jangren (1997, 2000) find similar correlations between the asym-metry of light distribution (in R and J bands) and the morphological type as well as the colour. We conclude that the asymmetry in light distribution is well correlated with the asymmetry in mass distribu-tion deduced from the warm gas kinematics.
Fig. 10 also shows that the brightest and the most massive galaxies (fast rotators) are less asymmetric than the fainter ones. This result is consistent with the data extracted from Schoenmakers (1999), presented by Bosma (2004), showing that the scatter in the disc elongation and in the disc mass fraction is larger for slow rotators. This may mean that fast rotators have rounder discs than slower rotators. In other words, massive galaxies average more efficiently the mass distribution in the disc than slow rotators. Massive discs, which are dynamically more evolved, are close to an equilibrium state, which is not the case for fainter discs. This is consistent with
the fact that the less massive galaxies have a lower disc mass fraction. Indeed, intrinsic asymmetries in discs may exist as a consequence of torques induced by triaxial haloes. Such a torque is more efficient in a galaxy with a faint disc and a massive halo than in a galaxy with a massive disc and a faint halo.
No clear influence of the presence of a bar on the asymmetry of the RCs has been found.
(i) For isolated galaxies:
log( AD/BARRED)= −0.80 ± 0.27 (5)
log( AD/UNBARRED)= −0.72 ± 0.29. (6) (ii) For softly interacting galaxies:
log( AD/BARRED)= −0.90 ± 0.24 (7)
log( AD/UNBARRED)= −0.77 ± 0.19. (8) Note that kinematical asymmetry has been measured on the whole Hα disc and then inner and outer asymmetries are aver-aged. In a forthcoming paper, kinematical asymmetry should be measured for different aperture radii notably at the ends of the bars.
Fig. 10 shows no clear difference in the behaviour of the asym-metry between ISO and SOFT galaxies except with the type: the kinematical asymmetry increases almost linearly with the type for ISO galaxies whereas it remains constant for early SOFT galaxies and increases erratically for the late SOFT galaxies. What physi-cal process can explain such relations? In the case of optiphysi-cal discs, since the correlation with asymmetry and colour is clear, the origin is most probably massive star formation linked with local pertur-bations affecting both kinematics and light distribution. Mayya &
Figure 10. First line: kinematical asymmetry versus morphological type for the isolated (left) and the softly interacting galaxies (right). Second line: kinematical asymmetry versus absolute magnitude for the isolated (left) and the softly interacting galaxies (right). Third line: kinematical asymmetry versus colour for the isolated (left) and the softly interacting (right) galaxies. Fourth line: kinematical asymmetry versus maximal rotational velocity for the isolated (left) and the softly interacting (right) galaxies. UGC 11429 (point between parenthesis) does not belong to the main clouds. In this case, the origin of such a huge kinematical asymmetry seems to be due not to galaxy–galaxy interaction ( f = −3.5) but to galaxy–cluster potential interaction (see comments). The reference line at AD= −0.75 is the visual reference for asymmetry (galaxies above are the most asymmetric).
Romano (2001) found that the asymmetry in light distribution is correlated with the star formation. Haynes et al. (1998) found that 50 per cent of isolated galaxies present asymmetric HI profiles.
When studying spiral galaxies in clusters, Dale et al. (2001) found no relationship between the asymmetry of the RCs and the cluster-centric distance. In addition, no difference is seen in the asymmetry of the RCs between early and late types for cluster galaxies (Rubin et al. 1999; Dale et al. 2001) contrary to field galaxies (Conselice et al. 2000). Therefore, the asymmetry in mass distribution of field galaxies seems to be an intrinsic parameter and to have a secular origin. Of course, interactions are also likely to induce important asymmetries but in the cases where interactions dominate dynami-cal evolution, the galaxies do not follow the previous relations and present larger asymmetries (Conselice et al. 2000). In addition, the inverse correlation should be found (asymmetry decreasing along the Hubble sequence) if asymmetry in field galaxies were due to external perturbations (accretion, interaction, merger, harassment, ram-pressure stripping) since the morphology (and the brightness) depends on the environment in the sense that blue late-type galax-ies are more frequent in an isolated environment (Dressler 1980; Whitmore, Gilmore & Jones 1993; Tanaka et al. 2004; Varela et al. 2004).
In conclusion, since isolated and softly interacting galaxies follow the same correlations, Hα kinematical asymmetries are probably due to inhomogeneous mass distribution linked with massive star formation regions in both cases.
4.3 The Tully–Fisher relation
In Fig. 11, we plot MB as a function of log(Wmax) (where
Wmax= 2 Vmax) in order to check the consistency of our data with
the Tully–Fisher relation determined by Tully & Pierce (2000):
MB= −7.27[log(WMAX)− 2.5] − 20.11. (9)
This plot had been analysed in Paper III with 39 galaxies and is extended now to 66 objects. First of all, the impact of the low incli-nations on the deduction of maximal velocities has been evaluated. For this purpose, the equation of the Tully–Fisher relation has been first determined considering the 66 galaxies (equation 10), then
ex-Figure 11. Tully–Fisher relation for our isolated and softly interacting samples of galaxies. The solid line represents the Tully–Fisher relation determined by Tully & Pierce (2000) from nearby galaxies. Different symbols distinguish galaxies with different shapes of RCs. The ? symbol refers to RCs for which the turnover is just reached (then the shape of the RCs is unknown).
cluding seven galaxies with inclination less than 30◦(equation 11). The resulting equations show that the maximal velocity tends to be overestimated when we include low-inclination galaxies:
MB = −5.8[log(WMAX)− 2.5] − 19.8 (10)
MB = −6.1[log(WMAX)− 2.5] − 19.8. (11)
Then, in the final analysis, low-inclination galaxies have been excluded. We confirm that the agreement is good with the relation found by Tully & Pierce (2000), as well for the isolated and for the softly interacting galaxies, although we find a slightly differ-ent slope. On our plot, we used differdiffer-ent symbols to distinguish the different shapes of rotation curves: decreasing, flat (plateau), increasing, solid-body and undefined (for which we just reach the turnover). We also confirm that there is no significant difference in the behaviour of both types of rotation curves (solid body or not) thus confirming that our Hα observations enable us to reach the max-imum of the rotation curve in most cases. We found the following relations.
(i) For isolated galaxies (correlation coefficient= 0.80):
MB = (−5.6 ± 0.8)[log(WMAX)− 2.5] − (19.6 ± 0.2).
(ii) For softly interacting galaxies (correlation coefficient = 0.87):
MB = (−6.2 ± 0.7)[log(WMAX)− 2.5] − (19.8 ± 0.2).
The agreement with Tully & Pierce (2000) is not as good for ISO as for SOFT galaxies, probably because of the lack of both massive and small galaxies in the ISO sample. No difference can be noticed concerning the scatter of the Tully–Fisher relation between the ISO and SOFT galaxies.
Tully–Fisher relations for barred and unbarred galaxies are simi-lar; the presence of a bar does not significantly affect the maximum rotational velocity at a given luminosity. This result is in complete agreement with that of Courteau (2003).
Other authors working on optical kinematical data (e.g. Rubin et al. 1999; Marquez et al. 2002) also find a smaller slope for the Tully–Fisher relation than Tully and Pierce. It seems that optical studies systematically lead to smaller slopes than HI studies, as
