---
abstract: |
    We analyze the velocity dispersions of individual [H[i]{}]{} and CO profiles in a number of nearby galaxies from the high-resolution HERACLES CO and THINGS [H[i]{}]{} surveys.  Focusing on regions with bright CO emission, we find a CO dispersion value [[$\sigma_{\rm{CO}}$]{}]{} $ = 7.3 \pm 1.7$ [kms$^{-1}$]{}.  The corresponding [H[i]{}]{} dispersion [$\sigma_{\rm{HI}}$]{}$ = 11.7 \pm 2.3$ [kms$^{-1}$]{}, yielding a mean dispersion ratio [[$\sigma_{\rm{HI}} / \sigma_{\rm{CO}}$]{}]{}$= 1.4 \pm 0.2$, independent of radius.  We find that the CO velocity dispersion increases towards lower peak fluxes.  This is consistent with previous work where we showed that when using spectra averaged (“stacked”) over large areas, larger values for the CO dispersion are found, and a lower ratio [[$\sigma_{\rm{HI}} / \sigma_{\rm{CO}}$]{}]{} $ =
    1.0 \pm 0.2$. The stacking method is more sensitive to low-level diffuse emission, whereas individual profiles trace narrow-line, GMC-dominated, bright emission.  These results provide further evidence that disk galaxies contain not only a thin, low velocity dispersion, high density CO disk that is dominated by GMCs, but also a fainter, higher dispersion, diffuse disk component. 
author:
- 'K.M. Mogotsi , W.J.G. de Blok , A. Cald[ú]{}-Primo , F. Walter , R. Ianjamasimanana , A.K. Leroy'
title: HI and CO Velocity Dispersions in Nearby Galaxies
---

Introduction
============

Gas velocity dispersions can be used to estimate the kinetic and thermal gas temperatures; to determine the mass distribution and structure of galaxies (e.g., [@petrup07]), and the stability, scale height and opacity of the gas disk.  Velocity dispersions are important in studies of star formation, turbulence, the interstellar medium (ISM), and dynamics of galaxies.  This is especially true of the vertical velocity dispersion $\sigma_{z}$. The rotation of the galactic disk has no effect on this component of the observed dispersion, and this makes it a useful parameter for studying the vertical structure of galactic disks.  Dispersions are used to determine the stability of galactic disks against gravitational collapse using the Toomre parameter [[@toomre64; @ken89]]{}.  Another link to star formation and turbulence studies is that dispersions can be used to determine the energy of the ISM (e.g., [[@agtz09; @tamb09]]{}).  They are also important in determining the midplane pressure of the gas disk [[@elm89; @ler08]]{} and in star formation laws that consider a variable disk free-fall time [[@elm89; @krumck05; @ler08]]{}. [ @lars81]{} used small-scale internal velocity dispersions to determine that molecular clouds are dominated by turbulent motions.  Studies at larger scales can be used to determine the level of turbulence found between giant molecular clouds and in large scale motions of gas in galaxies. 

Studies of velocity dispersions require high spatial and velocity resolution observations (for vertical velocity dispersion studies, galaxies of low inclination are required so as to minimize the contribution from the radial and azimuthal dispersion components).  The effective dispersion ($\sigma_{\rm eff}$) can be thought of as a combination of the thermal broadening ($v_{t}$) and turbulent dispersion ($\sigma_{t}$) : $$\sigma_{\rm eff}^{2} = v_{t}^{2} + \sigma_{t}^{2}$$ (e.g., [[@agtz09]]{}).  The turbulent component can be decomposed into a radial ($\sigma_{r}$), angular ($\sigma_{\phi}$), and vertical ($\sigma_{z}$) component, or a planar ($\sigma_{xy}$) and vertical component ($\sigma_{z}$).  Theory and simulations show that the velocity dispersion is expected to be anisotropic, with $\sigma_{r}
> \sigma_{\phi} > \sigma_{z}$ and $\sigma_{xy}
\sim 2\sigma_{z}$ [[@agtz09]]{}.  When the beam of a telescope is large compared to the rotational velocity gradient in the observed galaxy (e.g., in high-redshift galaxies and highly inclined galaxies), beam smearing can affect the measured dispersion.  For gas components with a clumpy structure (e.g., molecular gas), there are additional complications: the observed dispersion $\sigma_{\rm obs}$ is then a combination of the dispersion between clouds (cloud-cloud dispersions $\sigma_{\rm c-c}$) and the internal velocity dispersion within the clouds ($\sigma_{\rm internal}$):

$$\sigma_{obs}^{2} = \sigma_{c-c}^{2} + \sigma_{\rm internal}^{2}.$$

The structure of [[H[i]{}]{}]{} is more filamentary and less clumpy than that of molecular gas.  Its velocity dispersion is therefore generally not decomposed into internal and cloud-cloud components. 

[[H[i]{}]{}]{} velocity dispersions
-----------------------------------

Since [[H[i]{}]{}]{} is the dominant gas component of galaxies and is easily observable through the $21$cm emission line, it has been extensively studied. [[ H[i]{}]{}]{} velocity dispersions of nearby galaxies have been well studied, most notably by [@petrup07]{} and [@tamb09]{}.  Early work showed that [[$\sigma_{\rm{HI}}$]{}]{} $\sim 6-13$[kms$^{-1}$]{} (e.g., [@shovnk84]{}, [@vnksho84]{}, [@kmpsanc93]{}), with the dispersions dropping with increasing radial distance from the center (e.g., [@kmpsanc93]{}). [ @hunter01]{} and [@hunter11]{} also studied [[$\sigma_{\rm{HI}}$]{}]{} in dwarf galaxies. [ @petrup07]{} performed high-resolution and high-sensitivity [[H[i]{}]{}]{} observations of the nearly face-on galaxy NGC 1058 to study its gas velocity dispersion.  They found a vertical velocity dispersion of $4-14$[kms$^{-1}$]{}, which decreased with radius.  These studies reached resolutions of $\sim
600$pc.  @tamb09 used high-resolution [[H[i]{}]{}]{} data from The [[H[i]{}]{}]{} Nearby Galaxies Survey (THINGS; [@walt08]{}) to study [[H[i]{}]{}]{} velocity dispersions.  They also found that the dispersions decreased with radius.  They found a mean [[$\sigma_{\rm{HI}}$]{}]{} of $\sim 10$[kms$^{-1}$]{} at $r_{25}$, dropping off to $\sim 5 \pm 2$[kms$^{-1}$]{} at larger radii.  Stacking analysis was used by [@ianja12]{} to study the velocity dispersions averaged over [H[i]{}]{} disks of the THINGS galaxies.  They found [[$\sigma_{\rm{HI}}$]{}]{} $= 12.5 \pm 3.5$[kms$^{-1}$]{} ([[$\sigma_{\rm{HI}}$]{}]{} $= 10.9 \pm
2.1$[kms$^{-1}$]{} for galaxies with inclinations less than 60$^{\circ}$).  This stacking analysis allowed them to study the [[H[i]{}]{}]{} velocity profiles at high signal-to-noise, enabling them to decompose the [[H[i]{}]{}]{} profiles into broad and narrow components.  Fitting these components with Gaussians, they found [[$\sigma_{\rm{HI}}$]{}]{} $= 6.5 \pm 1.5$[kms$^{-1}$]{} for the narrow (cold) [[H[i]{}]{}]{} component and [[$\sigma_{\rm{HI}}$]{}]{} $= 16.8 \pm 4.3$[kms$^{-1}$]{} for the broad (warm) [[H[i]{}]{}]{} component.  A similar analysis by @stilp13 of partially the same data found velocity dispersions of the bulk of the [[H[i]{}]{}]{} of $\sim 6-10$ [kms$^{-1}$]{}. 

CO velocity dispersions
-----------------------

CO velocity dispersions have been less studied than those of [H[i]{}]{}.  Mostly this has been due to technical limitations.  Early observations of the lowest three CO rotational transitions found dispersions in the range of $5 - 9$ [kms$^{-1}$]{} [@stark84; @wilsco90; @combec97; @walsh02; @wilson11].  Recent instrumental developments have enabled more extensive studies of the CO distribution in galaxies, such as the HERA CO Line Extragalactic Survey (HERACLES; [@ler09]{}); see also Section [\[sec:datamethod\]]{}.  HERACLES is a [CO $J = 2 \rightarrow 1$]{} survey of nearby galaxies, covering their entire star-forming disks.  It partially overlaps with the THINGS survey, meaning [H[i]{}]{} and CO data are available at comparable resolutions. 

@cal13 used data from HERACLES and THINGS to compare CO and [[H[i]{}]{}]{} velocity dispersions as averaged over large areas using the stacking technique.  They analyzed the dispersions of these stacked [[H[i]{}]{}]{} and CO velocity profiles, stacking by galactocentric radius, star formation, [[H[i]{}]{}]{}, CO and total gas density.  They found that [[$\sigma_{\rm{HI}}$]{}]{}$=11.9 \pm 3.1$[kms$^{-1}$]{}, [[$\sigma_{\rm{CO}}$]{}]{}$=12.0 \pm 3.9$[kms$^{-1}$]{} with [[$\sigma_{\rm{HI}} / \sigma_{\rm{CO}}$]{}]{}$= 1.0 \pm 0.2$. In other words, the CO dispersions they found are very similar to the [[H[i]{}]{}]{} dispersions.  @cal13 suggested that this indicates the presence of an additional, more diffuse, higher dispersion molecular disk component that is similar in thickness to the [[H[i]{}]{}]{} disk (see also [@shet14]{}).  This finding is in agreement with independent studies by, e.g., [@gar92]{} who find, in addition to a thin molecular disk, a 2–3 kpc thick molecular “halo” around the edge-on galaxy NGC 891.  A similar thick molecular disk is also found by @com12 in M33. [ @pet13]{} compared interferometric and single-dish observations of M51 (NGC 5194) and also found evidence of an extended molecular disk.  Similar results have been found by [@cal15]{}, again by comparing interferometric and single-dish imaging of the molecular gas disks in nearby galaxies. 

The results presented in @cal13 were based on stacked profiles, i.e., profiles averaged over large regions.  In this paper we use the same THINGS and HERACLES data [ as used by @cal13]{} to determine whether evidence for the diffuse molecular component can also be found in individual profiles.  In particular, we investigate whether the velocity dispersion of the CO profiles changes as a function of CO intensity, which is what one would expect if a diffuse, high-velocity dispersion component is indeed present. 

In Section [\[sec:datamethod\]]{} we describe the data used.  Section [\[sec:results\]]{} contains a description of the results of our analysis.  Section [\[sec:discussion\]]{} contains a discussion of our results and a comparison to other work.  In Section 5 we summarize our conclusions. 

Data and method {#sec:datamethod}
===============

We used Hanning-smoothed CO data cubes from HERACLES [@ler09], which is a molecular gas survey of nearby galaxies using the HERA receiver array on the IRAM 30-m telescope.  For the neutral hydrogen, we used residual-scaled natural-weighted [[H[i]{}]{}]{} data cubes from THINGS [@walt08], which is a 21-cm survey of 34 nearby spiral and dwarf galaxies.  The observations were done with the NRAO Jansky Very Large Array.  The work in this paper is based on the analysis done on 13 galaxies (see Table \[tab:props\]) that are common to both surveys and which have CO detections.  The properties of these galaxies can be found in Table 1 of @walt08.  For convenience, noise values and velocity resolutions of the [H[i]{}]{} and CO observations are listed in Table \[tab:props\]. [  Note that these are the same data as used in the analysis presented in @cal13.]{} 

[ccccc]{} Galaxy & [[H[i]{}]{}]{} Noise & CO Noise & [[H[i]{}]{}]{} $\Delta V$ & CO $\Delta V$\
& \[mJybeam$^{-1}$\] & \[mK\] & \[kms$^{-1}$\] & \[kms$^{-1}$\]\
(1) & (2) & (3) & (4) & (5)\
NGC 628 & $0.60$ & $21$ & $2.6$ & $5.2$\
NGC 925 & $0.57$ & $16$ & $2.6$ & $5.2$\
NGC 2403 & $0.38$ & $19$ & $5.2$ & $5.2$\
NGC 2841 & $0.35$ & $16$ & $5.2$ & $5.2$\
NGC 2903 & $0.41$ & $21$ & $5.2$ & $5.2$\
NGC 2976 & $0.36$ & $20$ & $5.2$ & $5.2$\
NGC 3184 & $0.36$ & $17$ & $2.6$ & $5.2$\
NGC 3198 & $0.33$ & $17$ & $5.2$ & $5.2$\
NGC 3351 & $0.35$ & $19$ & $5.2$ & $5.2$\
NGC 4214 & $0.69$ & $19$ & $1.3$ & $5.2$\
NGC 4736 & $0.33$ & $21$ & $5.2$ & $5.2$\
NGC 5055 & $0.36$ & $26$ & $5.2$ & $5.2$\
NGC 6946 & $0.55$ & $25$ & $2.6$ & $5.2$\

![ image](f1){width="80.00000%"}

\[fig:noisesim\]

The CO data generally have a spatial resolution of $13''$. The natural-weighted [[H[i]{}]{}]{} data cubes mostly have resolutions better than this, but were smoothed to $13''$ to match the resolution of the CO data. 

A number of recent studies of [[H[i]{}]{}]{} velocity profiles have used Gauss-Hermite profiles to take into account asymmetries in the profiles or used multiple Gaussian components to quantify the presence of different components of the ISM (e.g., @deB08, @ianja12).  We did explore these fitting functions for our profiles, but found that the CO profiles are better described by simple, single Gaussians.  In order to minimize the number of fit parameters, and as we are only interested in the general width of the profile, we therefore use single Gaussians to fit both the [[H[i]{}]{}]{} and CO profiles. 

In fitting the profiles we imposed a $4S$ noise cutoff on the fitted peak fluxes of the profiles, where $S$ is the rms noise of the profile.  Only positions where both [[H[i]{}]{}]{} and CO profiles had peak fluxes greater than $4S$ were retained.  For the [[H[i]{}]{}]{} data, determining the $4S$ values was done using non-residual-scaled cubes, as residual-scaling affects the relation between signal and noise (see @walt08 for a full description of the residual scaling procedure).  These results were then applied as a mask to the residual-scaled cubes.  The remaining velocity profiles of these masked residual-scaled cubes were then fitted and analyzed.  In addition to the peak-flux criterion, we also imposed a velocity resolution cutoff where all profiles with fitted dispersions smaller than the velocity resolution of their data cube were removed. 

We simulated how the uncertainties in the fitted dispersions behave by producing random Gaussian noise at velocity resolutions relevant to our data, adding pre-determined Gaussian velocity profiles to them and re-fitting the data.  Simulations were performed with input Gaussian profiles of different amplitudes and dispersions.  A thousand iterations of data simulation and fitting were performed for each input amplitude and dispersion value.  This was done for different velocity resolutions and the averages of the fit uncertainties are plotted in Fig.  \[fig:noisesim\] (top and middle panel).  Input dispersions ranged between $2.6$ [kms$^{-1}$]{} and $20$ [kms$^{-1}$]{}. 

For velocity profiles with peak fluxes greater than $4S$ and velocity resolutions of $2.6$ [kms$^{-1}$]{}, the mean uncertainties in the fitted dispersion were smaller than $\sim 2$ [kms$^{-1}$]{}.  For velocity profiles with peak flux equal to $4S$ and velocity resolutions of $5.2$ [kms$^{-1}$]{}, the mean errors in the fitted dispersion were between $1.4$ [kms$^{-1}$]{} and $\sim 3$ [kms$^{-1}$]{}. 

A small number of the CO spectra showed some minor baseline ripples resulting in a slightly non-Gaussian noise behaviour.  We therefore repeated the same procedure but added noise extracted from these CO cubes rather than random Gaussian noise.  This was done for profiles with peak values between $1S$ and $16S$. The results are plotted in Fig.  \[fig:noisesim\] (bottom panel).  The results for the CO noise simulation are consistent with the results from the Gaussian noise simulation down to $4S$ peak flux levels. 

Results {#sec:results}
=======

Comparing [[H[i]{}]{}]{} and CO velocity dispersions {#subsec:pixpixan}
----------------------------------------------------

Using the results from the Gaussian fits, [H[i]{}]{} and CO dispersion maps were made for each galaxy.  In addition, we made dispersion difference ([[$\sigma_{\rm{CO}} - \sigma_{\rm{HI}}$]{}]{}) and dispersion ratio ([[$\sigma_{\rm{HI}} / \sigma_{\rm{CO}}$]{}]{}) maps for each galaxy by taking the CO and [[H[i]{}]{}]{} dispersion maps and then doing a pixel-by-pixel subtraction or division. 

The dispersions were binned into $1$ [kms$^{-1}$]{} bins.  Histograms of the $\sigma_{\rm{HI}}$ and $\sigma_{\rm{CO}}$ distributions for those positions in each galaxy where [[H[i]{}]{}]{} and CO were both present are shown in Figs.  \[fig:HIDisp\] and \[fig:CODisp\].  The distribution of dispersion values from pixels outside the central 0.2$r_{25}$ and with small fit uncertainties ($\Delta \sigma \leq 1.5$ [kms$^{-1}$]{}) are shown as the shaded histograms in the figures.  The 0.2$r_{25}$ selection was used in order to minimize the effect of beam smearing, as discussed later in this section.  Dispersions are plotted against the number of resolution elements (defined as the ratio of the number of pixels and the number of pixels per beam), or, equivalently, the number of beams.  From the histograms it is clear that in regions where there is both [H[i]{}]{} and CO emission, $\sigma_{\rm{HI}}$ values range from $\sim 5 - 30$ [kms$^{-1}$]{} and $\sigma_{\rm{CO}}$ values range from $\sim 5 - 25$ [kms$^{-1}$]{}.  The $\sigma_{\rm{HI}}$ modes range from $9-
22$ [kms$^{-1}$]{} and $\sigma_{\rm{CO}}$ modes range from $6 - 15$ [kms$^{-1}$]{} (see Table \[tab:modes\]).  Most of the high dispersions have large fitting errors and/or are from pixels in the central regions of galaxies, as shown in Figs.  \[fig:HIDisp\] and \[fig:CODisp\].  Such large dispersions are usually due to multiple gas components in the line of sight and/or beam smearing.  These give non-Gaussian profiles resulting in bad fits. 

[rccccccc]{} Galaxy & [[$\sigma_{\rm{CO}}$]{}]{} & [[$\sigma_{\rm{HI}}$]{}]{} & & &\
& (kms$^{-1}$) & (kms$^{-1}$) & (kms$^{-1}$) & (kms$^{-1}$) & (kms$^{-1}$) & &\
(1) & (2) & (3) & (4) & (5) & (6) & (7) & (8)\
NGC 628 & 6 (7.5) & 9 (9.1) & 6 (6.5) & $-$1.70 ($\pm$0.04) & $-$2 ($-$1.6) & 1.2 ($\pm$0.01)& 1.2 (1.3)\
NGC 925 & 6 (8.5) & 11 (13.2) & 10 (10.9) & $-$3.5 ($\pm$0.3) & $-$3 ($-$4.7) & 1.4 ($\pm$0.04)& 1.3 (1.7)\
NGC 2403 & 6 (8.3) & 10 (12.3) & 7 (8.7) & $-$3.8 ($\pm$0.1) & $-$4 ($-$4.0) & 1.5 ($\pm$0.02)& 1.4 (1.6)\
NGC 2841 & 8 (10.9) & 10 (18.0) & 9 (15.5) & $-$3.5 ($\pm$0.9) & $-$3 ($-$7.1) & 1.3 ($\pm$0.06)& 1.3 (2.0)\
NGC 2903 & 15 (21.6) & 22 (25.3) & 8 (12.1) & $-$5.5 ($\pm$0.2) & $-$5 ($-$3.7) & 1.3 ($\pm$0.02)& 1.2 (1.4)\
NGC 2976 & 6 (9.3) & 11 (12.2) & 11 (13.2) & $-$3.1 ($\pm$0.2) & $-$5 ($-$2.9) & 1.3 ($\pm$0.05)& 1.1 (1.4)\
NGC 3184 & 8 (8.6) & 10 (11.1) & 7 (8.3) & $-$2.57 ($\pm$0.03) & $-$2 ($-$2.5) & 1.3 ($\pm$0.02)& 1.2 (1.4)\
NGC 3198 & 11 (15.0) & 17 (20.2) & 11 (12.5) & $-$6.6 ($\pm$0.4) & $-$5 ($-$5.2) & 1.4 ($\pm$0.06)& 1.2 (1.6)\
NGC 3351 & 7 (14.1) & 9 (18.9) & 7 (9.8) & $-$2.8 ($\pm$0.3) & $-$3 ($-$4.7) & 1.4 ($\pm$0.04)& 1.2 (1.5)\
NGC 4214 & 6 (8.0) & 16 (14.0) & 6 (7.4) & $-$6.0 ($\pm$0.2) & $-$6 ($-$5.8) & 1.4 ($\pm$0.04)& 1.6 (1.9)\
NGC 4736 & 10 (17.7) & 15 (23.5) & 7 (10.4) & $-$3.4 ($\pm$0.1) & $-$4 ($-$3.2) & 1.2 ($\pm$0.02)& 1.0 (1.2)\
NGC 5055 & 9 (14.9) & 11 (17.9) & 7 (9.9) & $-$2.9 ($\pm$0.1) & $-$3 ($-$3.0) & 1.2 ($\pm$0.01)& 1.3 (1.3)\
NGC 6946 & 9 (11.6) & 13.0 (13.5) & 7 (8.4) & $-$2.4 ($\pm$0.1) & $-$2 ($-$2.0) & 1.2 ($\pm$0.02)& 1.2 (1.3)\

The $\sigma_{\rm{HI}}$ distributions clearly peak at values much larger than the dispersion cutoffs imposed due to the velocity resolution of the data.  However, many of the $\sigma_{\rm{CO}}$ distributions have peaks near the dispersion cutoffs.  In a few cases clear $\sigma_{\rm{CO}}$ distribution peaks are not seen (e.g., NGC 2403), and therefore the true mean (and mode) $\sigma_{\rm{CO}}$ values for these galaxies are likely to be smaller than $5.2$ km s$^{-1}$.

The incomplete sampling and asymmetry of the velocity dispersion histograms means that, especially for the CO, the mean is not a good statistic to characterize the distribution (it will overestimate the typical dispersion value).  We therefore also use the mode to describe the dispersion distributions.  The modes were calculated after binning the dispersions using a $1$ [kms$^{-1}$]{} bin size.  The values are listed in Table \[tab:modes\]. 

Most of the [[$\sigma_{\rm{CO}}$]{}]{} modes range from $6$ to $11$ [kms$^{-1}$]{} (12/13 galaxies) while their means range from $7$ to $15$ [kms$^{-1}$]{} (11/13 galaxies); most of the [[$\sigma_{\rm{HI}}$]{}]{} modes range from $9$ to $17$ [kms$^{-1}$]{} (12/13 galaxies) and their means range from $9$ to $21$ [kms$^{-1}$]{} (11/13 galaxies).  NGC 2841, NGC 2903, NGC 3198 and NGC 3351 were not included in the determination of the average values due to their high inclinations and very asymmetric dispersion distributions.  The average [[$\sigma_{\rm{CO}}$]{}]{} mode is $7.3
\pm 1.7$ [kms$^{-1}$]{} (average of the [[$\sigma_{\rm{CO}}$]{}]{} means is $10.5 \pm 3.6$ [kms$^{-1}$]{}), and the average [[$\sigma_{\rm{HI}}$]{}]{} mode is $11.7 \pm 2.3$ [kms$^{-1}$]{} (average of the [[$\sigma_{\rm{HI}}$]{}]{} means is $14.1 \pm 4.3$[kms$^{-1}$]{}).  Characteristic values of [[$\sigma_{\rm{HI}}$]{}]{} and [[$\sigma_{\rm{CO}}$]{}]{} are listed in Table \[tab:dispval\].  We also list the median values there for comparison with results from @cal13 [ which were derived from stacking the same data we use]{} (see Section \[sec:discussion\]). 

![ image](f2){width="80.00000%"}

![ image](f3){width="80.00000%"}

\[fig:CODisp\]

We constructed histograms of the [[$\sigma_{\rm{CO}} - \sigma_{\rm{HI}}$]{}]{} values using bins of $1$ [kms$^{-1}$]{}.  For the [[$\sigma_{\rm{HI}} / \sigma_{\rm{CO}}$]{}]{} data we made histograms using bins of size $0.2$. Figure \[fig:DispDiff\] shows the [[$\sigma_{\rm{CO}} - \sigma_{\rm{HI}}$]{}]{} distributions for each of the galaxies.  Figure \[fig:DispRat\] shows the [[$\sigma_{\rm{HI}} / \sigma_{\rm{CO}}$]{}]{} distributions.  These all have Gaussian shapes and are symmetric and well-sampled.  We therefore fitted Gaussians to the distributions.  The fitted mean dispersion difference and ratios are shown in Table \[tab:means\].  The CO distribution in NGC 925 and NGC 4214 only encompasses a few resolution elements and care should be taken when interpreting their fits.  The mean [[$\sigma_{\rm{CO}} - \sigma_{\rm{HI}}$]{}]{} value is $-3.3 \pm 1.2$ [kms$^{-1}$]{}; the mean [[$\sigma_{\rm{HI}} / \sigma_{\rm{CO}}$]{}]{} is $1.4 \pm 0.2$ [kms$^{-1}$]{}.  A summary of the mean, modes, and medians of the dispersion values is shown in Table \[tab:dispval\]. 

[@cal13]{} quantified the effect of beam smearing in our galaxies by simulating spiral galaxies with $30^{\circ}$, $60^{\circ}$, and $80^{\circ}$ inclinations.  They found that beam smearing is greatest in the central regions of galaxies and in highly inclined galaxies.  The observed dispersion can be increased by at most a factor of 1.2 at $0.2$$r_{25}$ for galaxies with $30^{\circ}$ inclination, 1.5 for $60^{\circ}$, and 1.8 for $80^{\circ}$, with these factors decreasing quickly toward unity at larger radii.  They therefore used an $0.2$$r_{25}$ radial cutoff for their analysis.  Even though Figures [\[fig:HIDisp\]]{} and [\[fig:CODisp\]]{} and Table [\[tab:comp\]]{} show that including the inner pixels does not greatly affect our conclusions, in our radial analysis and distribution width analysis we only use pixels with radii greater than $0.2$$r_{25}$ which are therefore not affected by beam smearing. 

Our [[$\sigma_{\rm{HI}}$]{}]{} values are in agreement with [@ler08]{} ([[$\sigma_{\rm{HI}}$]{}]{}$ =
11 \pm 3$[kms$^{-1}$]{}), [@ianja12]{} ([[$\sigma_{\rm{HI}}$]{}]{}$ = 12.5 \pm
3.5$[kms$^{-1}$]{}) and [@cal13]{} ([[$\sigma_{\rm{HI}}$]{}]{}$ = 11.9 \pm 3.1$[kms$^{-1}$]{}) who all analyzed the THINGS galaxies. 

[lrrrrr]{} & & & &\
& & & &\
\
mode & 7.3 $\pm$ 1.7 & 11.7 $\pm$ 2.3 & $-$3.4 $\pm$ 1.4 & 1.3 $\pm$ 0.2\
mean & 10.5 $\pm$ 3.6 & 14.1 $\pm$ 4.3 & $-$3.3 $\pm$ 1.4 & 1.4 $\pm$ 0.2\
median & 9.5 $\pm$ 3.0 & 13.1 $\pm$ 3.0 & $-$3.3 $\pm$ 1.2 & 1.4 $\pm$ 0.2\
fitted mean & & & $-$3.3 $\pm$ 1.2 & 1.4 $\pm$ 0.2\

![ Distributions of the dispersion difference [[$\sigma_{\rm{CO}} - \sigma_{\rm{HI}}$]{}]{} values of the galaxies.  The lines are colour-coded by galaxy (see legend).  The y-axis is in resolution elements (resolution elements = \[number of pixels\]/\[number of pixels per single resolution element\]).  Values for NGC 925, NGC 2841, NGC 2903, NGC 3198, NGC 3351, NGC 4214 and NGC 4736 are multiplied by a factor of 5 for better comparison with the other galaxies.[]{data-label="fig:DispDiff"}](f4){width="45.00000%"}

![ Distributions of the dispersion ratios [[$\sigma_{\rm{HI}} / \sigma_{\rm{CO}}$]{}]{} of the galaxies for individual resolution elements.  The y-axis is in resolution elements (resolution elements = \[number of pixels\]/\[number of pixels per single resolution element\]).  Values for NGC 925, NGC 2841, NGC 2903, NGC 3198, NGC 3351, NGC 4214 and NGC 4736 are multiplied by a factor of 5 for better comparison with the other galaxies.[]{data-label="fig:DispRat"}](f5){width="45.00000%"}

We also studied radial trends of the dispersions.  The radial [[$\sigma_{\rm{HI}}$]{}]{}, [[$\sigma_{\rm{CO}}$]{}]{} and [[$\sigma_{\rm{HI}} / \sigma_{\rm{CO}}$]{}]{} distributions are shown in Figs.  \[fig:COHIrad\] and \[fig:DRrad\].  These plots were made using annuli where the filling factors were higher than $10$% and $25$%, respectively.  In our analysis we use the results from the 10% annuli.  Comparison with the 25% annuli shows that this choice of filling factor has little effect on our results.  The [[$\sigma_{\rm{HI}} / \sigma_{\rm{CO}}$]{}]{} values in this analysis were calculated by azimuthally averaging the [[$\sigma_{\rm{HI}} / \sigma_{\rm{CO}}$]{}]{} maps.\
Figure \[fig:COHIrad\] shows [[$\sigma_{\rm{CO}}$]{}]{} and [[$\sigma_{\rm{HI}}$]{}]{} decreasing with radius for most of the galaxies.  These also flatten off at larger radii.  This behaviour was already seen in [[H[i]{}]{}]{} by [@tamb09]{}.  The [[$\sigma_{\rm{HI}} / \sigma_{\rm{CO}}$]{}]{} values remain roughly constant for most of the radial range covered; this can be seen in Fig.  \[fig:DRrad\]. 

![ image](f6){width="80.00000%"}

![ image](f7){width="80.00000%"}

[l r r r r]{} & & &\
& & &\

[[$\sigma_{\rm{CO}}$]{}]{} mean & 9.3 $\pm$ 2.1 & 8.9 $\pm$ 2.1 & 12.8 $\pm$ 3.9\
[[$\sigma_{\rm{CO}}$]{}]{} median & 8.6 $\pm$ 1.8 & 8.4 $\pm$ 2.0 & 12.0 $\pm$ 3.9\
[[$\sigma_{\rm{HI}}$]{}]{} mean & 12.7 $\pm$ 2.1 & 12.3 $\pm$ 2.3 & 12.7 $\pm$ 3.1\
[[$\sigma_{\rm{HI}}$]{}]{} median & 12.2 $\pm$ 1.9 & 11.9 $\pm$ 2.1 & 11.9 $\pm$ 3.1\
[[$\sigma_{\rm{HI}} / \sigma_{\rm{CO}}$]{}]{} mean & 1.5 $\pm$ 0.2 & 1.5 $\pm$ 0.3 & 1.0 $\pm$ 0.2\

Comparison with Stacking Results {#sec:discussion}
================================

We now compare our results with the stacking analysis by @cal13.  In that study, [ which used the same data sets as the ones used here,]{} the stacking procedure included all possible CO profiles, i.e., there was no rejection based on CO peak-flux and all positions where an H[[i]{}]{} velocity was available for use in stacking the CO profile were used.  The only profiles excluded from their analysis were those at radii less than $0.2 r_{25}$. The mean and median dispersion values they found are shown in Table \[tab:comp\].  These [[$\sigma_{\rm{CO}}$]{}]{} values are higher than our mean and median values. 

To check whether this difference is not caused by the higher uncertainties associated with low peak-flux profiles, we rederived our values for a number of different noise cutoffs between $4S$ and $8S$. Our mean and median dispersion values for data with the central $0.2 r_{25}$ pixels removed and using $4S$ and $8S$ noise cutoffs are shown in Table \[tab:comp\].  Our pixel-by-pixel [[$\sigma_{\rm{CO}}$]{}]{} values are lower irrespective of which noise cutoff we use.  Our [[$\sigma_{\rm{HI}}$]{}]{} values remain similar to the @cal13 values. 

Due to the noise cutoff used here, our analysis does not probe the low peak-flux regime that the stacking analysis in @cal13 is sensitive to.  It is therefore possible that the difference found in dispersion values could be caused by profiles with a peak flux lower than $4S$ having systematically higher velocity dispersions.  It is, however, difficult to directly and accurately measure the individual velocity dispersions of these low peak-flux profiles. 

We therefore evaluated the impact of the low peak-flux spectra by creating histograms of the velocity dispersion values for different noise cutoff values.  If lower peak-flux profiles do indeed have higher velocity dispersions, then we would expect the fraction of high-dispersion profiles to decrease with increasing noise cutoff.  In other words, the prominence of any high-dispersion tail in the histogram should decrease.  For this analysis we used data from pixels with radii greater than $0.2$$r_{25}$. An example is shown in the top left panel of Fig.  \[fig:width\].  Here we show the normalized $\sigma_{\rm CO}$ distributions for NGC 2403 derived using various noise cutoffs between $4S$ and $10S$. It is clear that the distribution becomes more narrow with increasing cutoff value.  We quantify this with the histogram half-width at 20 percent of the maximum, where the half-width is measured in the direction of higher dispersions, with respect to the value of the histogram maximum (or the mode), as indicated in the left panel of Fig.  \[fig:width\].  We have repeated this analysis for all our sample galaxies, except for NGC 925, NGC 4214 and NGC 3198, where CO emission is faint and limited in extent, and NGC 2903, where the dispersion values are dominated by streaming motions along the bar.  We also excluded the central part of NGC 3351 which is dominated by a compact bar. 

![ image](f8){width="80.00000%"}

![ Differences between the stacked mean [[$\sigma_{\rm{CO}}$]{}]{} dispersion calculated for profiles with peak flux $> 8S$ (${\sigma}_{8}$) and $>5S$ (${\sigma}_{5}$) plotted against radius.[]{data-label="fig:stack2"}](f9){width="45.00000%"}

The top-right panel of Fig.  \[fig:width\] shows the values of the measured widths as a function of noise cutoff.  For the majority of the galaxies shown there, the width becomes narrower toward higher cutoff values and the high-dispersion tail less prominent.  We thus find that the fraction of high-dispersion spectra does indeed decrease with increasing peak flux and it is therefore likely that the low peak-flux profiles included in the stacking analysis (but excluded in ours) have systematically higher velocity dispersions. 

This implies that repeating the stacking analysis of @cal13 with a *higher* noise cutoff should give *lower* dispersion values than their original analysis.  We therefore performed a stacking analysis on our data using various cutoffs.  As an example, in Figure \[fig:stack2\] we show, as a function of radius, the difference between the $5S$ and the $8S$ stacked dispersions.  The average difference between the dispersions is $\sim 1.5$ [kms$^{-1}$]{}, independent of radius, with the $5S$ values systematically higher than the $8S$ ones. 

To test whether the trend in velocity dispersion we found is not caused by the increasing importance of the noise toward lower peak fluxes (which might be expected to broaden profiles), we repeat our analysis using simulated profiles.  We created Gaussian profiles with peak values between $4S$ and $10S$, and with dispersions chosen with a probability distribution equal to the observed [[$\sigma_{\rm{CO}}$]{}]{} distribution of NGC 2403, as shown in Fig.  \[fig:CODisp\] (for pixels with radii greater than $0.2$$r_{25}$).  We explicitly assume that the velocity dispersion is independent of the peak flux.  We compare the dispersion distributions found at various peak-flux levels in Figure [\[fig:width\]]{} (bottom left).  The change in these distributions is very different from that as observed for NGC 2403, as shown in the bottom right panel in Figure [\[fig:width\]]{}.  The higher velocity dispersions measured at low peak flux are therefore not due to noise affecting the profiles, but due to an increase of the velocity dispersion toward lower peak fluxes. 

A similar anti-correlation, but for [[H[i]{}]{}]{} rather than CO, was found for a number of dwarf galaxies by @hunter01 [@hunter11].  @hunter11 suggest that this anti-correlation is roughly consistent with a uniform pressure throughout these galaxies, as also found in simulations of magneto-rotational instabilities by @piontek05. 

Returning to the observed CO velocity dispersions, @cal13 note that the higher dispersion values that are found in the stacked profiles can be explained with a diffuse, extended molecular gas component that pervades our galaxies in addition to the molecular gas in GMCs in the thin, “cold” CO disk.  Our pixel-by-pixel analysis is limited to pixels with bright CO emission, which is dominated by the GMCs.  These velocity profiles are narrower than those dominated by emission from the diffuse CO disk. 

These differences therefore are further evidence that a diffuse, high-dispersion component of molecular gas is present in our galaxies in addition to a thin molecular disk.  The diffuse component of molecular disks may thus be a common feature in disk galaxies. 

Summary
=======

We have measured the velocity dispersions in individual [H[i]{}]{} and CO profiles of a number of THINGS disk galaxies.  We find an [H[i]{}]{} velocity dispersion of [[$\sigma_{\rm{HI}}$]{}]{}$ = 11.7 \pm 2.3$ [kms$^{-1}$]{}.  The corresponding CO value is [[$\sigma_{\rm{CO}}$]{}]{}$ = 7.3 \pm 1.7$ [kms$^{-1}$]{}.  The ratio between these two dispersions is [[$\sigma_{\rm{HI}} / \sigma_{\rm{CO}}$]{}]{}$ = 1.4 \pm 0.2$ and is not correlated with radius. 

In a previous study using the same data, @cal13, by stacking individual velocity profiles, found a systematically higher CO velocity dispersion and a ratio [[$\sigma_{\rm{HI}} / \sigma_{\rm{CO}}$]{}]{}$ = 1.0 \pm 0.2$. This difference can be explained if low peak-flux CO profiles have a systematically higher velocity dispersion than high-peak flux profiles.  Our pixel-by-pixel analysis preferrentially selects the bright, high peak-flux CO profiles, in contrast with the stacking analysis which also includes large numbers of low peak-flux CO profiles. 

The relation of [$\sigma_{\rm{CO}}$]{} decreasing with increasing profile amplitude is consistent with a picture where the bright CO regions (preferentially selected in studies of individual profiles) are dominated by narrow-line GMCs, with a more diffuse, higher dispersion component (more efficiently detected in stacking analyses) becoming more prominent toward lower intensities.  A pixel-by-pixel analysis is therefore a good way to study the thin molecular disk component where GMCs dominate the emission.  In turn, stacking analyses are more sensitive to the diffuse, high-dispersion extended molecular disk component. 

Our results thus provide further evidence for the suggestion presented in [@cal13]{} that many disk galaxies have an extended, diffuse molecular disk component in addition to a thin, GMC-dominated, molecular disk. 

We gratefully thank the anonymous referee for all the comments and suggestions that improved the content of the paper.  K.M.M. gratefully acknowledges support from the Square Kilometre Array South Africa (SKA-SA) and the National Astrophysics and Space Science Program (NASSP).  K.M.M. would like to thank S. Schutte for the useful discussions during the preparation of the manuscript.  The work of W.J.G.d. B. was supported by the European Commission (grant FP7-PEOPLE-2012-CIG \#333939).  R.I. acknowledges funding from the National Research Foundation (NRF grant number MWA1203150687) and the University of South Africa (UNISA) postdoctoral grant. 

Facilities: , . 

Comparing [[H[i]{}]{}]{} velocity dispersions and second moments
================================================================

In a previous study, @tamb09 determined the second moments of the [[H[i]{}]{}]{} profiles of the THINGS galaxies as an estimate for the velocity dispersions.  These second moments were measured as a function of radius over the full extent of the [H[i]{}]{} disk. 

To gauge how well the second-moment values match the Gaussian dispersion values [$\sigma_{\rm{HI}}$]{}, we derive both parameters for our [H[i]{}]{} profiles, as also measured over the entire radial range and full area of the [H[i]{}]{} disk, i.e., also including regions without CO emission. 

![ image](f10){width="80.00000%"}

Figure \[fig:HIallrad\] shows that there are some slight differences in the second-moment values and Gaussian fitted dispersions.  For most galaxies the largest differences between second-moment values and Gaussian fitted dispersions are found in the inner regions of galaxies, with second-moment values being larger than the Gaussian fitted dispersions.  The inner regions of the galaxies have more non-Gaussian profiles than the outer regions.  This shows that the second moment is more sensitive to non-Gaussianities than profile fits and in these cases should be interpreted with care. 

We note that the [[H[i]{}]{}]{} dispersions associated with the CO disk (the inner star-forming disk) are higher than the dispersion as measured over the entire [[H[i]{}]{}]{} disk (which includes the outer parts of the galaxy where there is no detectable CO).  This is can be explained by the higher star formation rate in the inner disk compared to the outer disk.  A further discussion of this is, however, beyond the scope of this paper. 

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