© ESO, 2011

1. Introduction

The geometry and kinematics of gaseous disks in galaxies are mainly governed by the gravitational potential of stellar and non-baryonic components. Any perturbation of the equilibrium caused by either internal or external processes, may produce asymmetries in these disks. Atomic gas (H i) is the most extended cold component of the interstellar medium (ISM) and is a sensitive diagnostic of perturbations. The H i component in spiral galaxies has long been known to show both geometrical and kinematic asymmetries (e.g., Beale & Davies 1969; Huchtmeier 1972; Allen et al. 1973; Baldwin et al. 1980). Asymmetries in stellar disks are also common and are traced by optical and near-infrared light (the latter less affected by dust extinction). Observations show that 30% of galaxies are significantly lopsided at near-infrared wavelengths (Block et al. 1994; Rix & Zaritsky 1995; Zaritsky & Rix 1997; Bournaud et al. 2005). Asymmetries in the stellar component are not necessarily correlated with lopsidedness in the gaseous component (Kornreich et al. 2000; Wilcots & Prescott 2004). This lack of correlation is not surprising because the neutral hydrogen component in a galaxy is typically twice as extended as the stellar component (e.g., Broeils & van Woerden 1994), and might be perturbed in different ways with respect to the stellar component (e.g., stripping). The study of H i properties is thus a better probe of past and/or recent perturbations than the stellar counterpart, especially for weak interactions.

Study of global H i velocity profiles of galaxies has proven to be very useful for a quantification of the frequency and amplitude of disk asymmetries (e.g. Richter & Sancisi 1994). While only aperture synthesis can provide full 2D information about the H i distribution and kinematics, the 1D profiles provide a valuable measurement at a small fraction of the cost in observing time.

Past work suggests that the H i asymmetry properties of galaxies do not depend strongly on local environmental conditions. Studies of field and/or isolated galaxies suggest that at least 50 % show significant H i profile asymmetries (Richter & Sancisi 1994; Haynes et al. 1998), and even higher  ~75% in late-type spiral galaxies (Matthews et al. 1998). Although homogeneous studies of the asymmetry rate in richer environments are rare, it is usually believed that they show a comparable rate of asymmetric H i profiles.

The implications of a high asymmetry rate essentially independent of environment is currently the subject of debate (for a review see Jog & Combes 2009; Sancisi et al. 2008). It has been suggested that the mechanism responsible for producing asymmetric disks must be long-lived because high asymmetry rates are observed in samples of field and/or isolated galaxies. Because the signatures of tidal encounters are relatively short-lived, lasting only on the order of a dynamical time-scale for a wide range in mass ratios, orientations, inclinations, relative velocities and impact parameters (e.g., Bournaud et al. 2005), it cannot be the only agent responsible for the high asymmetry rate in different environments. A number of longer-lived mechanisms have been proposed, a) intermittent minor mergers (Walker et al. 1996; Zaritsky & Rix 1997); b) high-velocity cloud/gas accretion (Bournaud et al. 2005; Sancisi et al. 2008; Miller et al. 2009); c) halo-disk misalignment (Levine & Sparke 1998; Noordermeer et al. 2001); and/or d) internal perturbations including sustained long-lived lopsidedness owing to non-circular motions (Baldwin et al. 1980) or global m = 1 instabilities (Saha et al. 2007).

In order to address the relevance of the different proposed mechanisms (internal versus external, short versus long-lived) one must first study a sample of well isolated galaxies in the nearby Universe (≲150 Mpc). This approach should minimize any contribution from tidal interactions and facilitate the interpretation of results with respect to other samples of galaxies. Reference samples used to study the rate of H i asymmetries involve galaxies which, although assumed to be field/isolated, usually include a significant population of interacting galaxies (e.g., Richter & Sancisi 1994). Note that field galaxies are defined as galaxies not belonging to the cluster environment and a significant number of them are likely to be members of interacting pairs or multiplets (Sulentic et al. 2006). Richter & Sancisi (1994) find that about half of the nearby field galaxies show asymmetric profiles, estimated from a compilation of six H i surveys (1371 profiles were classified). It is important to remember that, 1) the overall environmental properties of the samples were not assessed meaning that a significant fraction of galaxies might be environmentally influenced; and 2) asymmetries were assessed using qualitative criteria (Richter & Sancisi 1994).

Statistical studies of H i asymmetries in large samples of galaxies selected according to a well defined isolation criterion and using an objective quantification are rare. The only existing systematic study of H i asymmetries in an isolated sample is that of Haynes et al. (1998), who studied the asymmetry rate for N = 104 (N = 78) galaxies that obey a 0.5° (1°) projected separation criterion with respect to any known companion in the Arecibo General Catalog (AGC, private database of Giovanelli and Haynes), where 0.5° corresponds to 175 kpc at a typical velocity of the core sample at V_r = 1500  km s^-1. About half of the galaxies appear to show significant H i asymmetries. However, only companions with a velocity difference ΔV < 400  km s^-1 relative to the primary are considered. The AGC is complete up to m ~ 15.4 mag and/or a diameter of 1′ (equivalent to a typical linear size of 6 kpc). The velocity criterion could make this sample biased against unbound plunging encounters, and owing to the size limit of the catalog, small galaxies would not have been taken into account – hierarchical systems of small galaxies may in principle produce significant asymmetries.

Other studied samples are composed of field galaxies. Matthews et al. (1998) studied a sample of N = 30 moderate to low surface brightness late-type spirals. Their galaxies lie between 2° and 6° from the center of the Fornax cluster or are field galaxies. They suggest that 77% of the H i profiles in their sample show a relevant asymmetry. Bournaud et al. (2005) studied N = 76 galaxies based on the OSUBS Galaxy Survey (Eskridge et al. 2002), a sample not selected according to any environmental criterion, which hence may have a relevant amount of interacting galaxies. However, it has been recently referred to as a field galaxy sample (e.g., Jog & Combes 2009). The asymmetry is larger than 10% for nearly 66% of the galaxies in this sample.

Fig. 1 Basic properties (normalized distributions) of the H i sample (N = 312 galaxies, blue dashed line), the H i refined subsample (N = 166 galaxies, blue solid line), as well as the optically complete sample (Verdes-Montenegro et al. 2005, red dash-dotted line): a) velocity (V[km s-1]); b) morphology (T(RC3), as in the RC3 catalog); c) optical luminosity (log(LB[L⊙])); and d) FIR luminosity (log(LFIR[L⊙])).

In this paper we use a large and complete sample of isolated galaxies (Verdes-Montenegro et al. 2005; Lisenfeld et al. 2007) to evaluate the intrinsic distribution of H i asymmetries. Comparisons show that our sample is more isolated than those used in previous studies and indeed is representative of the most isolated galaxies in the local Universe. The AMIGA project (Analysis of the interstellar Medium of Isolated GAlaxies¹, Verdes-Montenegro et al. 2005) involves vetting and analyzing the properties of galaxies in the Catalogue of Isolated Galaxies (N = 1050 galaxies, CIG, Karachentseva 1973), and provides a good starting point for this aim. This project includes a refinement of the sample through 1) revision of optical positions (Leon & Verdes-Montenegro 2003); 2) analysis of optical properties and completeness (Verdes-Montenegro et al. 2005); 3) revised optical morphologies (Sulentic et al. 2006); and 4) reevaluation of the isolation degree (Verley et al. 2007c,b). We use all these refinements in the present paper. The isolation criterion used for this compilation minimizes the probability of a major interaction within the last  ~3 Gyr (Verdes-Montenegro et al. 2005) while quantifying possible minor interactions. A multiwavelength characterization of different ISM components/phases and of the stellar component has been carried out including a) optical (Verdes-Montenegro et al. 2005); b) FIR (Lisenfeld et al. 2007); c) radio-continuum (Leon et al. 2008), and d) Hα emission (Verley et al. 2007a); as well as e) nuclear activity (Sabater et al. 2008, and in prep.).

This paper presents an analysis of global (1D) asymmetry measures for N = 312 H i AMIGA galaxies with high signal-to-noise (S/N) spectra (Sect. 2). We cleaned the sample of sources with uncertain asymmetry measures, yielding a total of N = 166 galaxies with high reliability data. For this subsample we studied the H i profile asymmetry rate (Sect. 3), the role of the environment for the rate of lopsided profiles (Sect. 4), as well as the correlations between H i asymmetry and stellar properties (optical luminosity, morphological type and signs of perturbation), and star formation rate (as traced by FIR luminostity, Sect. 5). Finally we identify the underlying distribution of intrinsic profile asymmetries and discuss the possible origin of asymmetries in gaseous disks (Sect. 6).

2. The sample

2.1. Sample selection

This paper presents descriptions of the shape of H i profiles with special emphasis on the degree of asymmetry. We identified the galaxies with the highest S/N H i profiles in the AMIGA project, obtained from observations at the Arecibo, Effelsberg, Nançay and GBT radio-telescopes, as well as from a compilation from archives/literature. The H i spectra are available at http://amiga.iaa.es. We initially consider for this study those H i spectra with a signal-to-noise S/N > 10 (S/N obtained as the peak flux to rms ratio), in total N = 383 galaxies. A S/N > 10 is appropriate to gain a good estimate of the asymmetry (Tifft & Huchtmeier 1990).

In addition we further restricted the sample to galaxies with profiles with high-velocity resolution to total width ratio, W₂₀/ΔV > 10, where W₂₀ is the width at a 20% level and ΔV is the resolution of the H i profile. This criterion is necessary to ensure that the profiles are well sampled. As a side-effect, it partially excludes face-on and low mass/luminosity galaxies. We excluded sources with evidence of problems related to bad baseline subtraction and/or interference contamination. Finally we chose galaxies with recession velocities V > 1500  km s^-1 to permit proper evaluation of the isolation. A prohibitively large region on the sky would be required to assess isolation for galaxies with V < 1500 (Verley et al. 2007c,b). In any case, they are all members of the Local Virgo Supercluster. Application of these restrictions yielded a sample of N = 312 isolated galaxies with high quality H i profiles. We will refer to this sample as the H i sample. We characterize profile asymmetry in two ways: 1) quality-based on visual inspection of the profiles; and 2) quantity-based on an areal asymmetry index A_{flux ratio} (Sect. 3). For a statistical analysis we performed a further refinement of the sample by considering only those galaxies with lowest uncertainty in their asymmetry parameter. This resulted in a final sample of N = 166 isolated galaxies, which we call the H i refined subsample (Sect. 3.4).

2.2. Basic properties of the samples

Figure 1 summarizes the basic optical/FIR properties of both the H i sample and the H i refined subsample. The different panels include recession velocity, morphological type as well as optical and FIR luminosity distributions. We compare these distributions with those corresponding to the optically complete sample, which was estimated to be 85–90 % complete to m_B = 15.0 mag, and is composed of N = 719 CIG galaxies (Verdes-Montenegro et al. 2005). The latter sample is appropriate to represent the entire population of isolated galaxies in the local Universe.

We summarize the dispersions of the basic properties for galaxies included in the different samples as well as the deviations between the H i samples and the optically complete sample:

• a) Radial velocity V (Verdes-Montenegro et al. 2005): velocities range over 1dex in the three samples, covering the range 1500  km s^-1  < V < 14   000  km s^-1. The H i refined subsample, and to a lower extent the H i sample, is slightly skewed toward lower velocities relative to the optically complete sample. The sample becomes seriously incomplete beyond 9000  km s^-1.

• b) Morphology T(RC3) (Sulentic et al. 2006): types are given in the RC3 numerical scale (de Vaucouleurs et al. 1991). The bulk of the CIG sample involves late-type galaxies in the range 3 < T < 7 (Sb to Sd) with 2/3 of the sample in a very narrow range T = 4 ± 1 (Sb–Sc). Only 14% of the sample involve early-type systems, which suggests that our sample represents the extreme (low) end of the morphology-density relation. The H i refined subsample contains a higher percentage of late-type galaxies (especially Sb–Sc) than the optically complete sample. This is not surprising because earlier type galaxies have a systematically lower H i content than later types and are especially excluded by selecting those H i profiles with S/N > 10.

• c) Optical luminosity L_B (Verdes-Montenegro et al. 2005): with few exceptions the sample spans a 1 dex luminosity range (9.5  <  log(L_B[L_⊙] ) < 10.5). Galaxies with log(L_B[L_⊙] ) < 10 are overrepresented in the H i sample (and H i refined subsample) likely because higher luminosity galaxies prefer the high-velocity tail of the sample (Malmquist effect) and often fall below m = 15.0.

• d) FIR luminosity L_FIR (Lisenfeld et al. 2007): the three distributions are relatively similar to each other. The shape of the FIR luminosity distribution is flatter than the optical and shows a peak near log L_FIR = 9.6. The full range covers 2 dex (8.5  <  log(L_FIR [L_⊙] ) < 10.5). The difference between the optical and FIR luminosity distributions likely reflects the extreme FIR “quietness” of our very isolated galaxy sample. Only detections are shown in Fig. 1.

3. H i profile shape and quantification of H i lopsidedness

In this section we present a general view of the H i profile shape and two ways of quantifying profile lopsidedness. First, we examine the profiles via visual inspection (see Sect. 3.1) using criteria similar to those employed in the largest H i profile shape study to date, Richter & Sancisi (1994). We then quantify the asymmetry level in a more objective manner using a numerical parameter (Sect. 3.2) and compare visual and numerical descriptions in Sect. 3.3.

3.1. H i profile shape and visual estimation of lopsidedness

Fig. 2 Example of a symmetric H i profile: CIG 266, Aflux ratio = 1.05 ± 0.05. The points where the horizontal (black) line intersects the profile correspond to the low (Vl) and high (Vh) velocity ends at a 20% level with respect to the peak. The derived mean velocity (Vm) at a 20% level is plotted as a (red) point.

Visual inspection of our H i sample shows that 88% show double horns with the rest showing single peaks that in most cases involve face-on spiral galaxies. We visually classified the profiles in the H i sample (N = 312 galaxies) as symmetric, slightly   asymmetric, and strongly   asymmetric, in a similar way as Richter & Sancisi (1994), who studied a sample of N = 1371 spectra (equivalent, respectively, to their notation as No, Weak and Strong). We find that N = 141 galaxies show symmetric H i profiles (45%), N = 126 sligthly asymmetric profiles (40%), and N = 45 strongly asymmetric profiles (15%). In order to illustrate this visual classification we show some examples of symmetric, slightly asymmetric, and strongly asymmetric H i profiles in Figs. 2–4, respectively. Based on the visual classification, our sample appears to show similar average rates as those obtained by Richter & Sancisi (1994): 47 ± 5%, 34 ± 6%, and 19 ± 6%.

Fig. 3 Example of a slightly asymmetric H i profile: CIG 421, Aflux ratio = 1.15 ± 0.03. See description in the caption of Fig. 2.

Fig. 4 Example of a strongly asymmetric H i profile: CIG 361, Aflux ratio = 1.51 ± 0.03. See description in the caption of Fig. 2.

The most common asymmetry found in our sample involves unequal peaks in the double horn profiles. The most extreme H i asymmetries occur for 43 galaxies (out of 312) where the peak flux difference is approximately larger than 25%. Only one of them has a peak flux difference larger than 50% (CIG 317). Some galaxies with double peaked profiles show peculiarities: CIG 144 shows a central peak stronger than the horns of the double peaked profile, CIG 858 shows a profile with a peculiar central trough, CIGs 238, 382, 928, and 1029 show apparent wings (significant excess flux – 3σ – within a 50–100  km s^-1 wide) beyond the outer walls of the double-horn profile. CIG 170 shows an uncommon flat H i profile. CIG 870 may also have wings that are 50–100  km s^-1 wide, although it seems to be a face-on galaxy. The observed wings may indicate a projected gas-rich companion or extra-planar motions owing to a nurture event.

3.2. Integrated density flux ratio parameter (A_flux ratio)

A variety of parameters have been used in the literature to quantify the asymmetry level in H i profiles. We employ an areal asymmetry index to quantify profile lopsidedness, namely the integrated flux density ratio A_{flux ratio} (e.g., Haynes et al. 1998; Kornreich et al. 2001), defined as A_{flux ratio} = A_l/h, if A_l/h > 1, and 1/A_l/h otherwise, where A_l/h is the ratio of the areas under the profile at velocities lower (S_l) and higher (S_h) than the central velocity (V_m): where V_l and V_h represent the low and high velocities measured at 20% intensity level with respect to the peak. V_m is calculated as the mean velocity at the same level, V_m = (V_h + V_l)/2. Note that A_{flux ratio} is invariant to the sense of rotation of the galaxy. We use this parameter since it is the most common asymmetry index that can be found in the literature and allows us to compare our results with other samples of galaxies (see Sect. 4.2). Equivalent definitions are found in the bibliography and can be easily converted to A_{flux ratio}, as e.g.: (Matthews et al. 1998) and E1 = 10 × (1−1/A_{flux ratio}) (Bournaud et al. 2005). We indicate the A_{flux ratio} values in Figs. 2–4 for the examples of H i profiles visually classified as symmetric, CIG 226, slightly asymmetric, CIG 421, and strongly asymmetric, CIG361, which are characterized by A_{flux ratio} = 1.05, 1.15, and 1.51, respectively.

3.2.1. Uncertainties of the A_flux ratio

We estimate the uncertainty of the asymmetry index, ΔA_{flux ratio}, by taking into account a) the rms noise per channel; b) the uncertainty in the calculation of the mean velocity; and c) the observational pointing offsets:

• a) Uncertainty owing to the rms of theH i profile (ΔA(rms)): owing to therms of the spectrum, σ, the uncertainty in S_l is , where N_l is the number ofchannels corresponding to S_l and R is the spectral resolution of theprofile. The uncertainty in S_h, ΔS_h can be obtained in the same way. Then ΔA_{flux ratio}can be calculated as .

• b) Uncertainty owing to the measurement of the mean velocity (ΔA(mean vel)): since the A_{flux ratio} is calculated as an areal ratio obtained from the mean velocity, an error in the determination of the latter can induce a wrong measure of A_{flux ratio}. An error ΔV_m in the estimate of the mean velocity V_m produced by limited velocity resolution and/or S/N ratio would artificially increase the asymmetry index of a symmetric profile (i.e. A_{flux ratio} = 1). Namely . A good estimate of the uncertainty can be obtained from the increase in A_{flux ratio} for a symmetric profile. If the profile were symmetric, then S_l = S_h = S/2, where S is the total area under the profile. ϵ can be estimated as ϵ ~ hΔV_m, where h is an intensity height scale. The uncertainty of ΔV_m can be estimated as (Fouque et al. 1990), where P = (W₂₀−W₅₀)/2, parameter that represents the steepness of the edges of the H i profile, and W₂₀ and W₅₀ are the widths at 20% and 50% with respect to the peak, respectively. Owing to the uncertainty in the determination of V_m, we can express ΔS_l (and ΔS_h) as: , where we estimated that h = h_max/2, being h_max the H i profile strongest peak.

• c) Uncertainty owing to pointing offsets (ΔA(pointing   offset)): a pointing offset of the antenna with respect to the kinematic center of the galaxy can induce an artificial lopsidedness in the H i profile when the telescope beam is comparable to the size of the galaxy (e.g., Tifft & Huchtmeier 1990; Springob et al. 2005). In some cases the observing coordinates were not coincident with the center of the galaxies owing to errors in the positions found in the CIG (e.g., Leon & Verdes-Montenegro 2003). The expected flux loss (f) owing to beam attenuation and known antenna pointing offsets can be calculated from the optical diameter of the galaxy, beam size, and pointing (Springob et al. 2005). We decomposed the expected flux loss (f) into two components, f = f_b.a.f_p.o., where f_b.a. is the flux loss factor arising from beam attenuation and f_p.o. is the factor where the contribution of the pointing offset is. The latter is intimately related to the flux loss that contributes to the asymmetry of the H i profile. Note that beam attenuation with no pointing offset causes no asymmetry in the H i profile. The difference in the A_{flux ratio} parameter if the flux loss that contributes to the asymmetry is on the receding or approaching side provides a measure of ΔA(pointingoffset). We find among the H i profiles only eight galaxies (out of the 312) that have differences larger than 0.01. The average is a factor 10 smaller than the contribution from the other two sources of uncertainty. The average is 0.001 and the standard deviation is 0.004. Thus, this source of error is negligible in most cases in our data. This is a result of the small known pointing offsets in the observations, where the average is equal to 3″ and the standard deviation is 3″.

We added these sources of uncertainty in quadrature to estimate the net uncertainty in A_{flux ratio}, ΔA_{flux ratio}.

3.2.2. Other possible sources of uncertainty

In addition to these sources of uncertainty, there are other effects that can induce an artificial asymmetry on the H i profiles. These include the effect of random pointing offsets and baseline fitting.

Flux loss due to this effect must be somewhere between  ≲1% (GBT, Haynes et al. 1998) and 5% (Arecibo circular feed, Haynes & Giovanelli 1984). If the profile were initially symmetric, then the induced asymmetry parameter by this effect would be in the range A_{flux ratio} < 1.02–1.11, if all flux loss is located either in the receding or approaching sides. Because we have data from different telescopes, our situation is probably intermediate between both cases. We assume that the resulting A_{flux ratio} distribution of a sample with symmetric H i profiles observed under similar conditions as our sample is likely well represented by a half-Gaussian with a σ = 0.04.

The baseline fitting process can also produce artificial asymmetries in the H i profiles (Haynes et al. 1998). Haynes et al. (1998) indicate that different order fits show flux differences of about 3%. As a result, the asymmetry parameter for symmetric H i profiles can be altered up to A_{flux ratio} = 1.06. A half-Gaussian curve with σ = 0.02 would mimic this effect well.

Given the random nature of these two effects, we cannot estimate their values individually, but their overall effect is taken into account in Sect. 3.4 to discuss the actual shape of the A_{flux ratio} distribution in isolated galaxies because they can broaden the resulting distribution.

3.2.3. Presentation of the asymmetry data

We list in Table 1 the following information:

• 1) CIG number;

• 2) Visual classification: 0 =  symmetric, 1 = slightly asymmetric, and 2 = strongly asymmetric (Sect. 3.1),

• 3) A_{flux ratio}, the asymmetry parameter (Sect. 3.2),

• 4) ΔA(rms), the uncertainty in A_{flux ratio} owing to the rms of the H i profile (Sect. 3.2.1),

• 5) ΔA(mean   vel), the uncertainty in A_{flux ratio} owing to the mean velocity (Sect. 3.2.1), and

• 6) ΔA_{flux ratio}, the global uncertainty in A_{flux ratio}, including the small contribution from ΔA(pointing   offset) (Sect. 3.2.1).

The A_{flux ratio} distribution is shown in Fig. 5. The best half-Gaussian fit² to the asymmetry parameter distribution is characterized by a σ = 0.15. However, this half-Gaussian fit is not able to reproduce the A_{flux ratio} distribution both at the high and low ends. First there is an excess of high values of A_{flux ratio} with respect to the Gaussian curve, and second, the peak of the distribution is too flat for A_{flux ratio} < 1.15.

Fig. 5 Upper panel: the Aflux ratio distribution (solid line histogram) of the H i sample (N = 312) and its best half-Gaussian fit (dashed line). Lower panel: the residual of the half-Gaussian fit to the observed Aflux ratio distribution.

We show in Fig. 6a,b the ΔA(rms) and ΔA(mean vel) distributions, respectively. The combined effect of all the previous uncertainties, ΔA_{flux ratio} (including the small contribution of ΔA (pointing offset)), is shown in Fig. 6c. We show the best Gaussian fits to the distributions.

Fig. 6 Upper right: uncertainty distribution owing to the rms of the H i profiles, ΔA(rms). Upper left: uncertainty distribution produced by errors in the mean velocity, ΔA(mean   vel). Bottom: uncertainty distribution of Aflux ratio for the H i sample (N = 312) combining the effect of ΔA(rms), ΔA(mean   vel) and the small contribution of ΔA (pointing offset) (See Sect. 3.2.1). The H i refined subsample (ΔAflux ratio < 0.05, indicated as a dotted line in the lower panel) is shown in the plots as blue filled histograms. Best Gaussian fits are presented for all distributions as dashed lines: for the H i sample: a) μ = 0.02, σ = 0.02; b) μ = 0.04, σ = 0.02; and c) μ = 0.04, σ = 0.03; and for the H i refined subsample: a) μ = 0.012, σ = 0.007; b) μ = 0.029, σ = 0.012; and c) μ = 0.033, σ = 0.012.

3.3. Comparison between the visual classification and A_flux ratio

We compare the asymmetry visual classification of the H i profiles (Sect. 3.1) with the A_flux ratio in Fig. 7. Three clearly distinct A_{flux ratio} distributions are seen for those galaxies visually classified as symmetric, slightly asymmetric, and strongly asymmetric (Sect. 3.1). The A_{flux ratio} distribution of H i profiles visually classified as symmetric has a mean value equal to 1.08, with a standard deviation of 0.065. The distribution for the slightly asymmetric H i profiles is characterized by a larger mean of 1.13 and a similar standard deviation, 0.09. The distribution of strongly asymmetric profiles is characterized by a mean of 1.37 and a considerably larger scatter, 0.17, with values as high as A_{flux ratio} = 1.8. The A_{flux ratio} distribution for the slightly asymmetric subsample partially overlaps with those of the symmetric and asymmetric distributions.

The large overlap that exhibits the A_{flux ratio} distribution for each visually classified subsample is not surprising, because this visual classification is of course subjective, and because the A_{flux ratio} parameter misses a few cases where the shape of a real asymmetric profile does not correspond to different areas in the approaching and receding sides. Future work would require to inspect other asymmetry parameters that are sensitive to flag these profiles as asymmetric.

3.4. H i refined subsample and characterization of the A_{flux ratio} distribution in a sample of isolated galaxies

The shape of the A_{flux ratio} distribution might be affected by artificially induced values from the effects explained in Sect. 3.2.1. By reducing the net uncertainty in the asymmetry measurement, we reduce errors that might bias our results. We show in Fig. 8 how the A_{flux ratio} distribution changes for different ΔA_{flux ratio} limits. The smaller the limit (i.e., only including accurate values of A_{flux ratio}), the better a half-Gaussian reproduces the distribution.

From now on we choose those H i profiles with ΔA_{flux ratio} < 0.05, namely the H i refined subsample, to remove from our statistical analysis those profiles with an uncertain determination of the asymmetry index. With this criterion we still have a large sample of N = 166 galaxies. The basic property distributions (velocity, morphological type, L_B and L_FIR) of the H i refined subsample are shown in Fig. 1 as (blue) solid lines, in comparison to those of the H i sample.

In order to characterize the intrinsic scatter of the asymmetry parameter distribution in a sample of isolated galaxies with minor contamination of artificially asymmetric H i profiles we fitted a half-Gaussian function to the H i refined subsample (Fig. 9). The fit yields a width of σ = 0.13 (Fig. 9). This time the fit successfully reproduces the asymmetry parameter distribution, including the low and high ends. Only 2% of the isolated galaxies are in excess of 3σ.

The width of the half-Gaussian distribution sets an upper limit to the intrinsic dispersion of the H i asymmetry in isolated galaxies. Errors in the calculation of the asymmetry index might be typically  ~0.03 (mean of the Gaussian fit) (Sect. 3.2.3). As discussed in Sect. 3.2.2, there might also be random errors in the pointing (~0.04) and baseline subtraction (σ ~ 0.02) that may increase errors in A_{flux ratio}. Hence it is reasonable to expect a lower value of the width, σ ~ 0.11, once these sources of errors are corrected.

Note that the quantification of the asymmetry distribution for the galaxies in the H i refined subsample is not affected by inclination effects (e.g. Jog & Combes 2009). Figure 10a shows that the inclination of the galaxies are distributed homogeneously above i = 30°. Only two galaxies have an inclination i < 15° (CIG 85 and 178). The lack of galaxies below i = 30 is caused by the width-to-channel ratio criterion explained in Sect. 2.1. This homogeneity in the inclination ensures that most of our galaxies do not show symmetric profiles because the galaxies are viewed face-on, where an asymmetry in the velocity field would remain unnoticed. To further inspect whether inclination can be introducing any bias in our results, we plotted the asymmetry index versus the inclination (Fig. 10b) and found that the two quantities are not correlated.

Fig. 7 Comparison between the visual classification and the Aflux ratio parameter for the N = 312 galaxies in the H i sample (symmetric: white histogram, slightly asymmetric: blue or dark gray histogram, and strongly asymmetric: green or light gray histogram). Mean and standard deviations (σ) for each distribution are also shown by vertical and horizontal lines, respectively.

Fig. 8 Aflux ratio distribution for the different cuts in ΔAflux ratio from 0.03 to 0.11 in bins of 0.02. Note that ΔAflux ratio < 0.05 (N = 166, purple filled histogram) corresponds to the H i refined sample (see Sect. 3.4), and the H i sample (N = 312) is the blue solid line histogram.

Fig. 9 Upper panel: Aflux ratio distribution of the H i refined subsample (ΔAflux ratio < 0.05) (N = 166, blue filled histogram), in comparison with that of the H i sample (N = 312, solid line histogram) (see Sect. 3.4). A half-Gaussian fit (red dashed line) to the H i refined subsample is presented. The half-Gaussian curve is characterized by a standard deviation σ = 0.13. Lower panel: the residual of the half-Gaussian fit to the observed Aflux ratio distribution for the H i refined subsample.

4. H i profile lopsidedness and environment

4.1. H i asymmetries and isolation parameters in CIG galaxies

A reevaluation and quantification of isolation degree for CIG galaxies was reported in Verley et al. (2007c,b). Verley et al. (2007c) derived two isolation parameters for each CIG galaxy: 1) a local surface density parameter η_K within the distance to the kth neighbor (a good tracer of average galaxy surface density); and 2) a tidal strength parameter Q (a parameter more sensitive to one-on-one interactions).

H i is known to be a sensitive diagnostic of interaction motivating us to compare these two parameters with our A_{flux ratio} asymmetry parameter. Figure 11 shows the lack of correlation between A_{flux ratio} and both η_K and Q. The Pearson’s correlation coefficient is ρ = −0.005 and 0.114, respectively, which indicates that the two quantities are essentially not correlated. A small trend in the Q parameter might be present in the sense that larger H i asymmetries seem to be found in less isolated systems. The calculated intercept and slope are −3.3 ± 0.7 and 0.8 ± 0.7, respectively.

The lack of correlation suggest that we are minimizing nurture effects that might affect the H i shape. The low values and small range in terms of galaxy density and tidal strength covered by CIG galaxies are not enough to see a correlation.

Bournaud et al. (2005) also suggest that there is no correlation between lopsidedness and tidal strength. However, they use the lopsidedness A₁ parameter on NIR surface density, and NIR emission is not as extended as the H i.

4.2. H i asymmetry distribution in field samples

We compare the asymmetry distribution of our H i refined subsample with that of different studies from the bibliography where a similar asymmetry index (Sect. 3.2) has been calculated and involve field/isolated galaxies (see also Sect. 1): Haynes et al. (1998), Matthews et al. (1998) and Bournaud et al. (2005).

Figure 12 shows the A_{flux ratio} normalized distribution for our refined subsample with 1) Bournaud et al. (2005); and 2) a combined sample (N = 186) including H i data in Matthews et al. (1998), Bournaud et al. (2005), and Haynes et al. (1998) excluding CIG galaxies (80 galaxies). The H i refined subsample shows the distribution best described by a half-Gaussian. It also shows the lowest absolute value of σ. The Bournaud et al. (2005) distribution shows the widest distribution (σ = 0.23) and noticeably deviates from a half-Gaussian curve. An intermediate case, σ = 0.17, is found for the combined sample without CIG galaxies. Table 3 gives σ values for each distribution as well as an asymmetry rate with ”asymmetric” profiles defined as A_{flux ratio} values exceeding the 2σ level of our H i refined subsample (A_{flux ratio} = 1.26).

Fig. 10 a) Distribution of inclinations for the N = 312 galaxies in the H i sample (solid line histogram) and the H i refined subsample (filled histogram); b) Aflux ratio versus inclination, from i = 10 to 90° in 10° bins for the H i refined subsample. Red points and their error-bars indicate the mean (connected by red solid line) and standard deviation, and green points the median and the median absolute deviation.

Figure 13 compares the A_{flux ratio} cumulative probability distribution for our H i refined sample and those of Haynes et al. (1998), Matthews et al. (1998), and Bournaud et al. (2005). In each plot the difference of the two curves indicates the asymmetry rate difference for a given A_{flux ratio} limit. Our sample lies below the field samples in almost every bin with differences typically between 10–20%. A result more similar to our sample is found for Haynes et al. (1998) likely in part because of the significant fraction of CIG galaxies (23%) included in their sample. Removing the CIG overlap increases both their σ and asymmetry rate.

We performed a χ² test to check whether the null hypothesis that any of the three A_{flux ratio} distributions is similar to our H i refined sample, could be rejected. Except for Haynes et al. (1998) (χ² = 9 and the associated p-value = 0.33) this hypothesis can be rejected. In the cases of Bournaud et al. (2005) and Matthews et al. (1998), χ² = 47 (p-value = 2 × 10^-7) and χ² = 14 (p-value  = 0.09) respectively. The sample differences we find are significant and cannot be ascribed to the refinement of the H i sample (Sect. 3.4). In principle we do not know how much Matthews et al. (1998) and Bournaud et al. (2005)’s observations are affected by systematic errors, but differences involving the same criterion as used in our study would yield an asymmetry rate difference  <5%. Haynes et al. (1998) included only high S/N profiles, avoided pointing problems and quantified baseline problems, suggesting it is reasonable to compare it directly with our H i refined sample. Overall, because of their degree of isolation, our H i refined subsample and Haynes et al.’s show a lower frequency (~10–20%) of galaxies with asymmetric profiles than in other samples such as Matthews et al. (1998) and Bournaud et al. (2005).

5. Relation between H i profile lopsidedness and optical/FIR properties

In this section we explore possible correlations between the asymmetry index A_{flux ratio} and optical properties of the H i refined subsample such as morphology, optical signs of perturbation, optical luminosity (L_B), and far-infrared luminosity (L_FIR).

5.1. Morphology and luminosity

Figure 14 shows the distribution of A_{flux ratio} values for each Hubble morphological class (median, mean, and standard deviation values are indicated). The bins representing the majority of our sample (T(RC3) = 3 to 6, i.e. Sb to Scd) show a fairly large scatter (standard deviation σ ~ 0.1). We see a slight decreasing trend in A_{flux ratio} toward later-type galaxies.

Studies of the relation between H i lopsidedness and morphological type are rare. Matthews et al. (1998) studied a sample of 30 moderate to low surface brightness (T = 6–9) galaxies and found a higher asymmetry rate than for more luminous (and higher surface brightness) late-type spirals. They found (for this type range) that later types were more likely to show larger asymmetries. In the Eridanus group the A₁ parameter as calculated from H i maps is larger for earlier type galaxies, suggesting that tidal interactions generate a higher lopsidedness rate in galaxies undergoing secular evolution toward earlier type (Angiras et al. 2006). This result (i.e., larger asymmetries for earlier types) agrees with the general trend seen in our sample.

We compared the A_{flux ratio} with luminosity. More luminous galaxies are slightly more asymmetric (Fig. 15, left panel). Figure 15 (right panel) presents the cumulative distribution of A_{flux ratio} for the high- and low-luminosity subsamples (Verdes-Montenegro et al. 2005). The two distributions are different at a level of α = 0.05 using a chi square test: χ² = 14 and p-value = 0.01.

5.2. Optical signs of interactions

Here we inspect a possible connection between optical signs of interaction and asymmetries in the H i profiles. Sulentic et al. (2006) revised the optical morphology classification for the CIG sample using POSS2/SDSS data. Although the CIG, the starting sample of AMIGA, has been selected to minimize close neighbors to the target galaxy and thus interactions, still Sulentic et al.’s revision revealed N = 193 objects with nearby companions or signs of distortion likely caused by an interaction. Sulentic et al. (2006) flagged these galaxies as interacting in the case of a morphologically distorted system and/or almost certain interacting system or flagged as possibly   interacting if there was any evidence of interaction/asymmetry with/without certain detection of a close companion.

There is no statistically significant difference in terms of H i profile asymmetry rate between galaxies that are optically classified as interacting and those without any sign of interaction. This result is consistent with the conclusion by Kornreich et al. (2000) and Wilcots & Prescott (2004) that optical asymmetries are not necessarily correlated with a lopsided H i component.

5.3. Bar and spiral strengths

We compared the H i asymmetry parameter with the relative spiral and bar strengths calculated as the maximal torque, or ratio of the maximum tangential force and the azimuthally averaged radial force. This has been obtained for a subsample of N = 96 CIG galaxies by Durbala et al. (2009) using Fourier analysis over spiral and bar components separately (Buta et al. 2003). Figure 16 shows the A_{flux ratio} parameter with respect to the relative spiral strength (Q_s). The overlapping sample between our H i refined subsample and the one used by Durbala et al. (2009) is composed of 40 galaxies. Q_s seems to anti-correlate with A_{flux ratio}: disks with weaker spiral arms show stronger asymmetries (Fig. 16). There are six galaxies (CIGs 11, 33, 689, 712, 912, and 931) that are outliers to this relation in the high end of the A_{flux ratio} parameter. These are likely galaxies whose H i asymmetry parameter is affected by instrumental effects. On the other hand we do not find any correlation of A_{flux ratio} and Q_b. The total strength Q_g is not correlated with A_{flux ratio} either, not surprisingly because Q_b and Q_g presents a good correlation (Durbala et al. 2009). The relation between Q_s and A_{flux ratio} may originate in the observed trends in Q_s versus T(RC3), because Q_s would be expected to correlate with the latter. However, we did not find a clear trend between Q_s and T(RC3).

The correlation found between A_{flux ratio} and Q_s suggests that other samples of galaxies characterized by lower spiral strengths will have higher H i asymmetry rates. This is consistent with the OSU sample (Eskridge et al. 2002), where spiral strength is lower than for the CIG (median equal to 0.132 versus 0.161, respectively) (Buta et al. 2005; Durbala et al. 2009), and have a higher H i asymmetry rate with respect to the H i refined subsample (see Sect. 4.2, and Bournaud et al. 2005).

5.4. FIR luminosities (L_FIR)

L_FIRis a good tracer of the star-formation rate and is related to the environment in the sense that IR luminous galaxies (L_FIR > 10¹¹   L_⊙) are usually interacting or merger systems (Sanders & Mirabel 1996). Unlike other samples of galaxies, our isolated population shows low FIR measures e.g. log(L_FIR) peaks from 9.0–10.5 with very few (<2%) galaxies above 10.5 (Lisenfeld et al. 2007). The low L_FIR values of the CIG sample support our claim that the revised CIG (AMIGA) is a sample with only isolated systems (Lisenfeld et al. 2007). Here we inspect whether the small fraction of IR-luminous systems in our sample corresponds to galaxies with larger H i asymmetries. We find N = 165 galaxies in our refined H i sample with IRAS measures, including upper limits. Figure 17 (left panel) presents a slight trend in the sense that more luminous FIR galaxies have more asymmetric H i profiles. Right panel of Fig. 17 shows the cumulative probability distribution for A_{flux ratio} in three bins: 8.0 < log (L_FIR [L_⊙] ) < 9.5, 9.5  <  log(L_FIR[L_⊙])  <  10.0 and 10.0  <  log(L_FIR[L_⊙])  <  11.0. We also show the distribution for those galaxies (N = 60) with FIR upper limits. The null-hypothesis that the first two bins are similar cannot be rejected (at a level of α = 0.05) using a χ² square test: χ² = 6 and p-value = 0.24. On the other hand we find that the A_{flux ratio} distributions for the latter two bins are different (χ² = 14, p-value = 0.008) from each other. We find a 10–20% excess of higher asymmetry values for the most FIR luminous galaxies (10.0  <  log(L_FIR[L_⊙])  <  11.0). If real, this excess might reflect asymmetries and FIR luminosities simultaneously enhanced by accretion events.

Fig. 11 Isolation parameters vs. Aflux ratio. The isolation parameters (Verley et al. 2007b) are the local number surface density parameter ηK to the Kth neighbor, where K = 5 (upper panel), and the tidal strength parameter Q (bottom   panel), which only takes into account similarly size neighbors (factor 4 in size, as defined in Karachentseva 1973).

Fig. 12 Comparison of the normalized Aflux ratio distribution between our H i refined sample (black solid histogram) and 1) Bournaud et al. (2005) (red dotted-dashed histogram); 2) a combined sample including H i data in Bournaud et al. (2005), Matthews et al. (1998) and Haynes et al. (1998) excluding CIG galaxies (green dotted line). Solid curves are the half-Gaussian curves fitted to each distribution. See Table 3 for a comparison of the σ’s of each half-Gaussian curve.

Fig. 13 Comparison of the cumulative Aflux ratio distribution between our sample (black solid line) and other samples (red dashed lines): a) Matthews et al. (1998, N = 30; b) Bournaud et al. (2005, N = 76; c) Haynes et al. (1998, N = 104 (N = 106); and d) Haynes et al. (1998) excluding CIG galaxies (N = 80). See Table 3 for an asymmetry rate comparison at a Aflux ratio = 1.26 level.

Fig. 14 Aflux ratio and T(RC3) (Sulentic et al. 2006) for the H i refined subsample. Red points and their error-bars indicate the mean (connected by red solid line) and standard deviation, and green points the median and the median absolute deviation, for each morphological type from T(RC3) = −5 to 10 (E to Im).

6. Discussion

The CIG sample represents the  ~3% most isolated galaxies in the Catalog of Galaxies and Clusters of Galaxies (CGCG, Zwicky et al. 1961). In these systems the effects of environmental perturbation such as tidal interactions and ram pressure stripping are minimized. The A_{flux ratio} distribution of our sample is well described by a half-Gaussian function with a 1σ width of 0.13 (possibly smaller σ ~ 0.11 if artificially induced effects are reduced). Only 9% of the galaxies show A_{flux ratio} > 1.26 (2σ) and only 5% A_{flux ratio} > 1.39 (3σ). If it is reasonable to assume that the distribution of intrinsic asymmetries should show a Gaussian distribution, then that of Fig. 9 is as close as we have ever come to isolating that intrinsic distribution. Comparison with field samples clearly shows that effects of nurture result in an excess population of high A_{flux ratio} values. This excess population measured as a deviation from the best Gauss fit is negligible in our sample. In isolation it is apparently very unlikely to find galaxies with H i disks showing A_{flux ratio} > 1.39. The small number of such extreme asymmetric profiles found in our sample show double-peaked profiles with unequal horns. This is in most cases not caused by contamination by gas-rich companions with systemic velocity suitable to create a false or amplified horn. We almost never observe such components in the middle or close to the edges (thus broadening one of the horns in) the H i profile. We are unlikely to find a narrower asymmetry distribution in any galaxy sample.

Unfortunately, using H i profiles does not allow us to distinguish between the roles of geometry and kinematics in producing an asymmetry. Aperture synthesis maps suggest that asymmetry is usually the signature of kinematic lopsidedness although galaxies with lopsided HI distributions are not unknown. The rotation curve on one side of the galaxy is usually steeper than the opposite one. Swaters et al. (1999) estimated from previous H i maps (Broeils & van Woerden 1994; Rhee & van Albada 1996; Verheijen 1997) that the fraction of kinematically lopsided galaxies may be as large as 15–50%. It is likely that the few asymmetric H i disks in our sample present this kinematically lopsidedness. However, to make a quantitative relation, it would be necessary to calibrate (statistically) how asymmetry parameters in 2D maps relate to those 1D parameters using single-dish data.

Fig. 15 Left: Aflux ratio versus log(LB[L⊙]). Symbols are as in Fig. 14. Right: cumulative probability distribution of Aflux ratio for log(LB[L⊙])  < 10 (solid line) and log(LB[L⊙])  >10 (dashed red line), using the H i refined subsample.

We searched for correlations between internal properties of galaxies and the measured A_{flux ratio} parameter. Although we maximized our sensitivity to internal correlations by removing all galaxies likely to have been affected by external perturbers, we did not find any strong correlations between stellar properties and H i asymmetry. We find a weak correlation between spiral arm strength and H i asymmetry parameter, in the sense that arms are stronger for galaxies with more symmetric H i profiles. The simplest interpretation for such a trend would be that gas asymmetries are more efficiently suppressed by the stronger spiral arm gravitational torques in more massive galaxies. A connection to spiral arm strength rather than to bar features should arise from the larger scale of the former. It has long been known that more developed spiral arms seem to exist in more luminous galaxies (van den Bergh 1960). Interestingly, the morphology of spiral arms is found to depend primarily on parent galaxy properties rather than on the environment (van den Bergh 2002). Therefore we would expect an anti-correlation between H i asymmetry and luminosity. However, Fig. 15 shows a hint of the opposite trend. This might be because unlike van den Bergh’s (1960) study, our study focuses on a sample with a small range in luminosity, as shown in Fig. 1c.

Fig. 16 Aflux ratio versus spiral strength (Qs) for 40 CIG galaxies overlapping between the H i sample and the CIG galaxies in Durbala et al. (2009). The fit to the data points (slope and intercept are –0.34 and 1.16, Pearson’s correlation coefficient ρ = −0.45) is shown as a (red) solid line. The six outliers have been ignored in this fit.

The lack of a strong correlation between L_FIR and A_{flux ratio} indicates that the bulk of the star formation and the symmetry of the gaseous disk are not strongly linked, i.e., that induced SF caused by possible interactions in this sample is small compared to that from secular evolution. Still, there is an excess of about 10% of asymmetric profiles for the most IR luminous (10  <  log(L_FIR[L_⊙])  <  11) galaxies. This might be linked to recent accretion events in a small number of CIG galaxies.

In general the asymmetry distribution will likely deviate from a half-Gaussian curve for other samples containing galaxies that are perturbed by the environment. These samples are the rule while very isolated galaxies are the exception. The intrinsic asymmetry distribution found in our sample of isolated galaxies will be skewed toward higher values as a result of these interactions. This is confirmed by the wider distributions found in samples of field galaxies (Sect. 4.2) where a higher degree of interaction is expected, given the lack of a strict isolation criterion. The deviation from a half-Gaussian curve for the sample in Bournaud et al. (2005) is apparent as shown in Sect. 4.2, and the distribution is the widest (σ = 0.23) among those studied. Although it has been known for a long time that interacting galaxies usually show larger H i asymmetries (Sulentic & Arp 1983), a statistical analysis using a common H i profile asymmetry parameter in large and well-characterized samples in dense environments is still needed.

Mapelli et al. (2008) estimate from the density of (collisional) ring galaxies in the local Universe that major asymmetries for  ~10% of the galaxies may be produced as a result of a recent fly-by, resulting in a lopsidedness visible over a time scale of 1 Gyr. Within the uncertainties of this estimate, this may well match the 10–20% difference between our sample and field samples. As reviewed in Sect. 1, many mechanisms have been proposed other than tidal interactions or ram pressure from the intergalactic medium that may contribute to the asymmetry parameter distribution, such as minor interactions/mergers (e.g., Zaritsky & Rix 1997), gas accretion along cosmological filaments (Bournaud et al. 2005), halo-disk misalignment (Levine & Sparke 1998; Noordermeer et al. 2001), internal perturbations including sustained long-lived lopsidedness owing to non-circular motions (Baldwin et al. 1980) or global m = 1 instabilities (Saha et al. 2007). In principle the latter physical processes are likely to occur homogeneously for any sample independently of its environmental properties. Thus, the intrinsic asymmetry distribution found in our sample of isolated galaxies is likely due to a combination of these processes. Owing to the lack of spatial resolution in our data, at this moment we cannot distinguish their respective importance. High-resolution observations of isolated galaxies are a good probe to shed light into the origin of these more subtle asymmetries, though they are likely widespread in all kinds of environments.

Fig. 17 Left: Aflux ratio versus log(LFIR[L⊙]). Symbols are as in Fig. 14. Right: Aflux ratio cumulative probability distribution for three LFIR bins: 9 < log (LFIR[L⊙])  < 9.5 (solid line), 9.5 < log (LFIR [L⊙])  < 10.0 (blue dashed line) and 10.0  <  log(LFIR[L⊙])  <  11.0 (dash-dotted line). The (green) dotted line represents the Aflux ratio cumulative distribution for those galaxies with an upper limit.

We have started a follow-up study of the origin of H i asymmetries using Very Large Array (VLA), expanded VLA and Giant Meter Radio Telescope (GMRT) aperture synthesis H i observations of a subsample of  ~20 isolated galaxies, which will be presented in forthcoming papers (e.g. Portas et al. 2011). We selected galaxies covering the wide range of asymmetries found in our sample. One of the isolated galaxies presenting an asymmetric profile in this subsample is CIG 96 (NGC 864), whose H i synthesis imaging from the VLA has been studied in detail in Espada et al. (2005, 2011). The asymmetry in the H i profile is associated with a strong kinematical perturbation in the gaseous disk of the galaxy, where on one side the decay of the rotation curve is faster than Keplerian. Although a companion is detected, no tidal tail is found, and it is probably not massive enough to have caused this perturbation. Probably we are witnessing the recent merger of a small gaseous companion.

7. Summary and conclusions

We used H i global velocity profiles for a large sample of isolated galaxies to i) quantify the rate and amplitude of H i asymmetries in isolated spiral galaxies, where environmental processes such as tidal interactions and ram pressure are minimized; ii) study the role of the environment on the H i asymmetries; and iii) study possible correlations between H i lopsidedness and the properties of the stellar component, including their morphological types, signatures of optical perturbation, bar and spiral strengths, as well as optical and FIR luminosities.

To quantify the H i asymmetry, we calculated a flux ratio asymmetry parameter (A_{flux ratio}). We restricted our study to a sample of N = 166 galaxies (the H i refined subsample) for which we minimized undesired artificially induced lopsidedness by avoiding large uncertainties owing to the rms of the profile, determination of the mean velocity, and pointing offsets.

We found that a half-Gaussian curve properly fits the A_{flux ratio} distribution of this refined sample, with a σ = 0.13. We suggest that if we deconvolve other sources of errors such as baseline fitting and random pointing offsets, then the underlying σ is reduced to σ ~ 0.11. We confirm that by using this sample we effectively minimize nurture effects, because there is a lack of correlation between H i asymmetries and isolation parameters such as tidal force (one-on-one interactions) and number density.

We compared the distribution of H i asymmetries of previously studied field galaxies with that of our isolated galaxy sample. A half-Gaussian fit does not successfully reproduce in general the asymmetry distribution of field samples. Indeed, the intrinsic σ is larger in field samples than in isolated galaxies. This is likely a result of the lack of an isolation criterion in the selection of field galaxies, which are likely contaminated by interacting objects. This suggests that environmental mechanisms (producing short-lived effects  ~1 Gyr) are fundamental mechanisms to produce H i asymmetries in galaxies, and are indeed responsible for the  ~10–20% difference in the H i asymmetry rate we see in field galaxies with respect to isolated galaxies. The asymmetry distribution of galaxies in denser environments is likely even wider and more skewed.

Within the isolated galaxy sample, we did not find any strong correlation between the H i asymmetry and internal properties such as the morphological type, optical and FIR luminosities or signature of interaction. A signature of perturbed optical emission is not a necessary condition for the H i profile to be asymmetric, and vice versa. We found a trend for larger H i asymmetries to be located in more FIR luminous galaxies that are likely interacting objects. We also found evidence that galaxies with higher spiral arm strength have lower H i asymmetries.

The here presented H i refined subsample can be used to study the origin of intrinsic H i asymmetries in isolated galaxies, and it is also a baseline for samples of galaxies in denser environments with H i data that are properly evaluated for instrumental effects. This can help to shed light into the relative importance of different environmental and internally generated processes in shaping the H i disks of galaxies.

Acknowledgments

We thank the anonymous referee for a careful reading and very detailed report, which helped to improve this paper significantly. D.E. thanks U. Lisenfeld, E. Battaner, P. Vilchez, R. Garrido, and E. Perez for useful comments. We appreciate the help of the staff members of the different telescopes that have made this work possible (Arecibo, Effelsberg, Nançay and GBT). We thank Francoise Combes for providing the H i asymmetry parameter list in Bournaud et al. (2005). D.E. has been supported by a Marie Curie International Fellowship (MOIF-CT-2006-40298) within the 6th European Community Framework Programme. D.E., J.S.M., L.V.M. and S.V. are supported by DGI Grant AYA 2008-06181-C02 and the Junta de Andalucía (Spain) P08-FQM-4205. This research has made use of the NASA/IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration. We acknowledge the usage of the HyperLeda database (http://leda.univ-lyon1.fr).

References

All Tables

All Figures

Fig. 1 Basic properties (normalized distributions) of the H i sample (N = 312 galaxies, blue dashed line), the H i refined subsample (N = 166 galaxies, blue solid line), as well as the optically complete sample (Verdes-Montenegro et al. 2005, red dash-dotted line): a) velocity (V[km s-1]); b) morphology (T(RC3), as in the RC3 catalog); c) optical luminosity (log(LB[L⊙])); and d) FIR luminosity (log(LFIR[L⊙])).

In the text

	Fig. 2 Example of a symmetric H i profile: CIG 266, Aflux ratio = 1.05 ± 0.05. The points where the horizontal (black) line intersects the profile correspond to the low (Vl) and high (Vh) velocity ends at a 20% level with respect to the peak. The derived mean velocity (Vm) at a 20% level is plotted as a (red) point.
In the text

	Fig. 3 Example of a slightly asymmetric H i profile: CIG 421, Aflux ratio = 1.15 ± 0.03. See description in the caption of Fig. 2.
In the text

	Fig. 4 Example of a strongly asymmetric H i profile: CIG 361, Aflux ratio = 1.51 ± 0.03. See description in the caption of Fig. 2.
In the text

	Fig. 5 Upper panel: the Aflux ratio distribution (solid line histogram) of the H i sample (N = 312) and its best half-Gaussian fit (dashed line). Lower panel: the residual of the half-Gaussian fit to the observed Aflux ratio distribution.
In the text

Fig. 6 Upper right: uncertainty distribution owing to the rms of the H i profiles, ΔA(rms). Upper left: uncertainty distribution produced by errors in the mean velocity, ΔA(mean   vel). Bottom: uncertainty distribution of Aflux ratio for the H i sample (N = 312) combining the effect of ΔA(rms), ΔA(mean   vel) and the small contribution of ΔA (pointing offset) (See Sect. 3.2.1). The H i refined subsample (ΔAflux ratio < 0.05, indicated as a dotted line in the lower panel) is shown in the plots as blue filled histograms. Best Gaussian fits are presented for all distributions as dashed lines: for the H i sample: a) μ = 0.02, σ = 0.02; b) μ = 0.04, σ = 0.02; and c) μ = 0.04, σ = 0.03; and for the H i refined subsample: a) μ = 0.012, σ = 0.007; b) μ = 0.029, σ = 0.012; and c) μ = 0.033, σ = 0.012.

In the text

	Fig. 7 Comparison between the visual classification and the Aflux ratio parameter for the N = 312 galaxies in the H i sample (symmetric: white histogram, slightly asymmetric: blue or dark gray histogram, and strongly asymmetric: green or light gray histogram). Mean and standard deviations (σ) for each distribution are also shown by vertical and horizontal lines, respectively.
In the text

	Fig. 8 Aflux ratio distribution for the different cuts in ΔAflux ratio from 0.03 to 0.11 in bins of 0.02. Note that ΔAflux ratio < 0.05 (N = 166, purple filled histogram) corresponds to the H i refined sample (see Sect. 3.4), and the H i sample (N = 312) is the blue solid line histogram.
In the text

Fig. 9 Upper panel: Aflux ratio distribution of the H i refined subsample (ΔAflux ratio < 0.05) (N = 166, blue filled histogram), in comparison with that of the H i sample (N = 312, solid line histogram) (see Sect. 3.4). A half-Gaussian fit (red dashed line) to the H i refined subsample is presented. The half-Gaussian curve is characterized by a standard deviation σ = 0.13. Lower panel: the residual of the half-Gaussian fit to the observed Aflux ratio distribution for the H i refined subsample.

In the text

Fig. 10 a) Distribution of inclinations for the N = 312 galaxies in the H i sample (solid line histogram) and the H i refined subsample (filled histogram); b) Aflux ratio versus inclination, from i = 10 to 90° in 10° bins for the H i refined subsample. Red points and their error-bars indicate the mean (connected by red solid line) and standard deviation, and green points the median and the median absolute deviation.

In the text

	Fig. 11 Isolation parameters vs. Aflux ratio. The isolation parameters (Verley et al. 2007b) are the local number surface density parameter ηK to the Kth neighbor, where K = 5 (upper panel), and the tidal strength parameter Q (bottom   panel), which only takes into account similarly size neighbors (factor 4 in size, as defined in Karachentseva 1973).
In the text

Fig. 12 Comparison of the normalized Aflux ratio distribution between our H i refined sample (black solid histogram) and 1) Bournaud et al. (2005) (red dotted-dashed histogram); 2) a combined sample including H i data in Bournaud et al. (2005), Matthews et al. (1998) and Haynes et al. (1998) excluding CIG galaxies (green dotted line). Solid curves are the half-Gaussian curves fitted to each distribution. See Table 3 for a comparison of the σ’s of each half-Gaussian curve.

In the text

	Fig. 13 Comparison of the cumulative Aflux ratio distribution between our sample (black solid line) and other samples (red dashed lines): a) Matthews et al. (1998, N = 30; b) Bournaud et al. (2005, N = 76; c) Haynes et al. (1998, N = 104 (N = 106); and d) Haynes et al. (1998) excluding CIG galaxies (N = 80). See Table 3 for an asymmetry rate comparison at a Aflux ratio = 1.26 level.
In the text

	Fig. 14 Aflux ratio and T(RC3) (Sulentic et al. 2006) for the H i refined subsample. Red points and their error-bars indicate the mean (connected by red solid line) and standard deviation, and green points the median and the median absolute deviation, for each morphological type from T(RC3) = −5 to 10 (E to Im).
In the text

	Fig. 15 Left: Aflux ratio versus log(LB[L⊙]). Symbols are as in Fig. 14. Right: cumulative probability distribution of Aflux ratio for log(LB[L⊙])  < 10 (solid line) and log(LB[L⊙])  >10 (dashed red line), using the H i refined subsample.
In the text

	Fig. 16 Aflux ratio versus spiral strength (Qs) for 40 CIG galaxies overlapping between the H i sample and the CIG galaxies in Durbala et al. (2009). The fit to the data points (slope and intercept are –0.34 and 1.16, Pearson’s correlation coefficient ρ = −0.45) is shown as a (red) solid line. The six outliers have been ignored in this fit.
In the text

Fig. 17 Left: Aflux ratio versus log(LFIR[L⊙]). Symbols are as in Fig. 14. Right: Aflux ratio cumulative probability distribution for three LFIR bins: 9 < log (LFIR[L⊙])  < 9.5 (solid line), 9.5 < log (LFIR [L⊙])  < 10.0 (blue dashed line) and 10.0  <  log(LFIR[L⊙])  <  11.0 (dash-dotted line). The (green) dotted line represents the Aflux ratio cumulative distribution for those galaxies with an upper limit.

In the text