We have examined the trend between CO and HI linewidths by compiling the
linewidths of 219 nearby galaxies. The trend is that the CO linewidths of fast
rotating galaxies tend to be larger than the HI linewidths, and that the HI
linewidths of slow rotating galaxies tend to be larger than the CO linewidths,
whereas the intermediately rotating galaxies have almost equal values. We have
explained the trend using the synthetic rotation curve model, which provides
the linewidth - absolute magnitude relations at any radii, and concluded that
the trend has been occurred by the different distributions of CO and HI in a
galaxy and the gradient of the rotation curves. The exact linewidth should be
corrected for the effects of the gradient of the rotation curve and the gas
distribution.Comment: To appear in A&A, LaTeX manuscript(paper.tex, use A&A style file
  l-aa.sty) and five PS figures, 5 page

Sofue, Yoshiaki

Tutui, Yoshinori

English

arXiv

Abstract. We have found the trend between CO and Hi linewidths by compiling the CO and Hi linewidths of 219 nearby galaxies. The trend is that the CO linewidths of fast rotating galaxies tend to be larger than the Hi linewidths, and that the Hi linewidths of slow rotating galaxies tend to be larger than the CO linewidths, whereas the intermediately rotating galaxies have almost equal values. We have examined the trend using the synthetic rotation curve model given b

Y Tutui

Y Sofue

CiteSeerX

Astron. Astrophys. 351, 467–471 (1999) ASTRONOMY
AND
ASTROPHYSICS
Compatibility of the CO and H I linewidths considering
the gas distribution and rotation curves
Y. Tutui and Y. Sofue
Institute of Astronomy, University of Tokyo, Mitaka Tokyo 181-8588, Japan
Received 23 June 1998 / Accepted 25 May 1999
Abstract. We have found the trend between CO and Hi
linewidths by compiling the CO and Hi linewidths of 219 nearby
galaxies. The trend is that the CO linewidths of fast rotating
galaxies tend to be larger than the Hi linewidths, and that the
Hi linewidths of slow rotating galaxies tend to be larger than
the CO linewidths, whereas the intermediately rotating galaxies
have almost equal values. We have examined the trend using
the synthetic rotation curve model given by Persic et al. (1996),
which provides the linewidth – absolute magnitude relations at
any radii. We conclude that the trend is produced by the differ-
ences in CO and HI distributions in a galaxy and the gradient of
a rotation curve that depends on the luminosity of the galaxy. We
should note that the distribution of the tracer of linewidths (e.g.
CO, Hi) and the gradient of rotation curves influence observed
linewidths, therefore the exact linewidths should be corrected
for them.
Key words: cosmology: distance scale – galaxies: distances
and redshifts – galaxies: general – galaxies: ISM – radio lines:
galaxies
1. Introduction
The Hi linewidth – luminosity relation (hereafter the Hi TF
relation) has been one of the most successful and widely
applied methods to determine distances to galaxies up to
cz ∼ 10,000 km s−1, or100h−1 Mpc (e.g. Tully & Fisher 1977,
Aaronson et al. 1986, Pierce & Tully 1988). Hi observations
with a single dish telescope for the Hi TF relation beyond
this redshift have been affected by the source confusion and
the signal dilution due to the larger beam size. For farther
galaxies beyond the Hi limit ‘the CO TF relation’ using CO
linewidths instead of Hi is available (Dickey & Kazes 1992,
Sofue 1992). It is advantageous for highercz galaxies, be-
cause the beam size in CO observations is sharper than HI,
also there are a lot of samples that have higher CO lu-
minosity. The compatibility of CO and Hi linewidths was
examined and showed good agreement for nearby spiral
galaxies (e.g. Dickey & Kazes 1992, Schöniger & Sofue 1994,
Send offprint requests to: Y. Tutui (tutui@mtk.ioa.s.u-tokyo.ac.jp)
Scḧoniger & Sofue 1997, Lavezzi & Dickey 1998). In the case
of interacting galaxies both linewidths are affected by the in-
teraction, the CO linewidth is stable enough to apply the TF
relation for weakly interacting galaxies (Tutui & Sofue 1997).
The distributions of CO and Hi in a galaxy are clearly
separated and the boundary is known as the molecular front
(Sofue et al. 1995, Honma et al. 1995). The rotation curves are
not completely flat and the shape and amplitude depend on the
size of a galaxy or luminosity (e.g. Sancisi & van Albada 1987,
Persic et al. 1996). Besides the CO and Hi linewidths are given
by the rotation velocity where the gas is distributed. This means
the relation between CO and Hi linewidths depends on the size
or luminosity of the galaxy. We discuss the CO and Hi distribu-
tions with a synthetic rotation curve model presented by Persic
t al. (1996).
In this paper we present the data and sample selection in
Sect. 2, the comparison between CO and Hi linewidths and the
analysis based on the rotation curve model given by Persic et
al. (1996) in Sect. 3, the discussion of the methods that we used
for the analysis and the summary in Sect. 4.
2. Data and sample selection
We have sampled the12CO(J = 1 − 0) linewidth data from
some catalogs of nearby galaxies. Although some of these CO
linewidths are measured by a single beam that is sufficient to
cover the extent of CO, most are synthesized from mapping
along the major axis. For the latter case we have estimated the
linewidths from the position – velocity diagram. This method
may diminish the correlation with the Hi linewidths that are
observed with the single beam. This effect is discussed in the
last section. The properties of the CO data are listed in Table 1.
We have compiled the Hi linewidths and the inclination us-
ing the LEDA (Lyon - Meudon Extragalactic Database). From
the original sample we have excluded (1) face-on galaxies of
i < 30◦ and (2) morphologically interacting galaxies. The num-
ber of galaxies after these selections is listed in Column 2 in
Table 1. The linewidths are defined as the full width at 20% of
the maximum intensity and corrected for the inclination:Wi CO
(= WCO/ sin i) andWi HI (= WHI/ sin i) for CO and HI, re-
spectively.
468 Y. Tutui & Y. Sofue: Compatibility of the CO and Hi linewidths
0
200
400
600
800
1000
0 200 400 600 800 1000
W
iH
I (
km
/s
)
WiCO (km/s)
Young et al.
Sage et al.
Braine et al.
Lavezzi and Dickey
Kenney and Young
Nishiyama et al.
Tacconi et al.
Fig. 1. Plot of the linewidths of CO and HI. The face-on galaxies whose
inclination is less than 30deg have been excluded, and the linewidths
are corrected for the inclination. The references of each symbol are
listed in Table 1. The solid line is obtained by the least square fit of the
whole sample.
0
200
400
600
800
1000
0 200 400 600 800 1000
W
iH
I (
km
/s
)
WiCO (km/s)
Mean value
Fig. 2. Means and the standard deviations for each bin of the portion
of the CO linewidths. The properties of the bins are listed in Table 2.
The solid line is the same fitted line as Fig. 1.
3. Results
3.1. A trend between CO and Hi linewidths
We re-examined the CO and Hi linewidths relation as Dickey
& Kazes (1992) and Schöniger & Sofue (1992) did, with lager
samples. The samples that we used here were selected from slow
rotating galaxies to fast rotating galaxies listed in Table 1. Fig. 1
Table 1. References of the sample and the properties of the CO obser-
vations.
Reference No. Observatory HPBW(′′)
Young et al. 1995 42 FCRAO 14-m 45
Sage 1993 39 NRAO 12-m 55
Braine et al. 1993 51 IRAM 30-m 23
Lavezzi & Dickey 1998 39 NRAO 12-m 55
Kenney & Young 1988 16 FCRAO 14-m 45
Nishiyama 1995 21 NRO 45-m 15
Tacconi & Young 1987 11 FCRAO 14-m 45
Table 2. Properties of the portion of the CO linewidths in each bin.
Range No. Y95 S93 B93 L97 K88 N95 T87
0–100 12 0 3 1 0 0 1 7
100–200 12 3 5 0 1 0 0 3
200–300 28 3 8 7 4 3 2 1
300–400 52 7 7 14 16 5 3 0
400–500 66 16 8 17 10 6 9 0
500–600 34 11 6 8 4 0 5 0
600–700 12 2 2 4 1 2 1 0
700–900 3 0 0 0 3 0 0 0
total 219 42 39 51 39 16 21 11
Column 1:Range of the CO linewidth of each bin. The linewidth are
corrected for the inclination.Column 2:The number of galaxies in each
bin.Columns 3–9:Distribution of the number of galaxies for each ref-
erence: Young et al. 1995 (Y95), Sage 1993 (S93), Braine et al. 1993
(B93), Lavezzi & Dickey 1998 (L98), Kenney & Young 1988 (K88),
Nishiyama 1995 (N95) and Tacconi & Young 1987 (T87).
is the plot of CO linewidths against corresponding Hi linewidths
whose inclinations have been corrected. We see from Fig. 1 that
the values of both CO and HI linewidths are not entirely equiv-
alent, but Hi linewidths are broader than CO for slow rotating
galaxies (i.e. dwarf galaxies) and CO linewidths are broader
than Hi for fast rotating galaxies (i.e.massive galaxies). We fit-
ted the samples by the least square method, and obtained the
relation, that is shown as the solid line in Fig. 1:
Wi HI = 0.76Wi CO + 83.8. (1)
We divided the samples into eight bins of the portion of the
CO linewidths. The contents of the bins are listed in Table 2. We
evaluated the mean value and the standard deviation in each bin
and showed them in Fig. 2. Fig. 2 indicates the following: (1) The
subsamples of each bin obey the best fit relation (Eq. (1)) very
well through the whole linewidth. (2) For intermediately rotat-
ing galaxies whose linewidth is about between 300 km s−1and
600 km s−1, CO and Hi linewidths correspond very well within
the small dispersion. (3) The large dispersions of slow rotat-
ing galaxies are caused by not only the small samples but also
the difficulties in measuring the linewidths. As Giovanelli et al.
(1997) indicated, we see that the dispersion in linewidths for the
small rotating galaxies increases toward the smaller linewidths,
whereas the dispersion for the intermediately to fast rotating
galaxies is almost constant.
Y. Tutui & Y. Sofue: Compatibility of the CO and Hi linewidths 469
-1
-0.5
0
0.5
1
0 200 400 600 800 1000
(W
iC
O
 -
 W
iH
I)
 / 
W
iC
O
WiCO (km/s)
Fig. 3. Residual between CO and Hi linewidths that is normalized by
the CO linewidths noted as(Wi HI − Wi CO)/Wi CO, against the CO
linewidths for each bin. The normalization by the linewidth is useful
to evaluate the effect of the difference after applying the TF relation.
In the case of applying a linewidth into the TF relation,
the estimated absolute magnitude differs as a function of the
logarithm of the linewidth, therefore the comparison of both
linewidths for the effect of the TF relation should be taken as
the ratio. Fig. 3 shows the residuals of both linewidths as the
notation of(Wi HI − Wi CO)/Wi CO in each bin. This shows
that slow rotating galaxies are not a good sample when applying
the TF relation, we should also note that the observed rotation
velocity in CO and Hi provide different values.
3.2. Synthetic rotation curves and the TF relation
Fig. 4 shows the CO data distribution in each bin over the TF
(linewidth – absolute magnitude) diagram. Here the absolute
magnitude is calculated by theI-band TF relation given by
Pierce & Tully (1992):
MI = −8.72(logWi − 2.50) − 20.94. (2)
As we showed the difference in the CO and Hi linewidths in
the previous section, the most appropriate TF relation with the
CO linewidths is shifted from the HI TF relation for the slow
rotating galaxies and the fast rotating galaxies. This effect also
appears in Fig. 4. The TF relation connected by the CO data
points is different from the Hi TF relation. The connected CO
TF relation, except the slowest rotation portion, shows a linear
relation like the Hi TF relation. While it provides the different
values of the slope and offset from the Hi TF relation, the output
absolute magnitudes from both TF relations do not vary much
for the intermediately rotating galaxies. It suggests that the CO
and HI linewidths are compatible for the intermediately rotat-
ing galaxies, whereas the fast and slow rotating galaxies have
different values.
-24
-23
-22
-21
-20
-19
-18
-17
-16
-15
1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3
M
_I
 (
m
ag
)
log Wi (km/s)
0.3
2.50.7
R/Ropt
HI TFR
Fig. 4. Linewidth – absolute magnitude diagram: The crosses are the
CO data bin indicated in Table 2, and their absolute magnitudes are
estimated by theI-band TF relation of Eq. (2), which is drawn as the
solid line. If a CO linewidth is equal to a corresponding Hi linewidth,
the expected values of the absolute magnitude should be put on the
line of the Hi TF relation. The dotted lines show the specific radii of
the PSS model, forR/Ropt = 0.3, 0.4, 0.5, 0.7(thick dotted line), 1.0,
1.5(thick dotted broken line), 2.0 and 2.5, from top to bottom.
In order to discuss the difference between the two TF rela-
tions, we used the synthetic rotation curve model, that is based
the statistics of rotation curves, proposed by Persic et al.
(1996) (hereafter the PSS model). According to the PSS model
the rotation velocity is a function of not only the radius but also
the luminosity. The three variables in the PSS model are (1)
rotation velocity,Vrot, (2) absolute magnitude in theI-band,
MI and (3) the galacto-centric radius normalized by the optical
disk radius,R/Ropt. They make a surface in a three-dimensional
space1 (i.e. Vrot − MI − R/Ropt). Here,Ropt corresponds to
the de Vaucouleurs 25Bmag mag arcsec−2 photometric radius
for the Freeman disk, or corresponds to 3.2Rd for the exponen-
tial surface brightness distribution, whereRd is the disk scale
length. This surface is useful to discuss the rotation curves and
the TF relation, because they are obtained by the projection of
the surface. If the surface is projected onto theVrot vs.R/Ropt
plane, it shows the synthetic rotation curves, that is called ‘the
universal rotation curves’ by PSS96, with the parameter of the
absolute magnitudeMI (See dotted lines in Fig. 5.). On the other
hand, if the surface is projected onto theVrot vs.MI plane, it
shows a kind of TF relation (linewidth – luminosity relation)
with the parameter of the specific radiusR/Ropt. (See dotted
line in Fig. 4.) The values of the specific radius are shown as the
dotted lines ofR/Ropt = 0.3, 0.4, 0.5, 0.7(thick dotted line),
1.0, 1.5(dotted broken line), 2.0 and 2.5, top to bottom. Here we
1 See Fig. 10 in Persic et al. 1996
470 Y. Tutui & Y. Sofue: Compatibility of the CO and Hi linewidths
0
50
100
150
200
250
300
350
400
0 5 10 15 20 25 30 35 40
V
ro
t (
km
/s
)
R (kpc)
R/Ropt = 0.5 0.7 1.0
1.5
2.0
M_I
(mag)
-23.5
-23.0
-22.5
-22.0
-21.5
-21.0
-20.5
-20.0
-19.5
-19.0
-18.5
Fig. 5. Isoradius curves of the specific radius,R/Ropt, over the rotation
curves of the PSS model. The values ofR/Ropt = 0.5, 0.7(thick line),
1.0 and 1.5(thick line) are displayed.
have defined the linewidths as twice the rotation velocity used
in the PSS model.
In Fig. 4 the comparison between the PSS model and the Hi
TF relation shows the following: (1) The Hi TF relation does
not fit the PSS model in the slow rotation part (logWi . 2.3
km s−1). This is consistent with suggestion by Giovanelli et
al. (1997) that the Hi TF relation is not a good tracer for slow
rotating galaxies. (2) The Hi TF relation fits the PSS model
of aroundR/Ropt ∼ 1.5 well. This is consistent with the Hi
distribution in a galaxy, where it is extended over the optical
radius. (3) On the other hand, the CO data points trace the inner
radius of the PSS model than the optical radius through the
whole linewidth. This is also consistent the CO distribution in
a galaxy.
4. Discussion and summary
The results that we discussed in the previous section can be ex-
plained by how the distributions of CO and Hi differ and how
the rotation curves depend on the luminosity. Fig. 5 indicates
the specific isoradius curves ofR/Ropt over the synthetic ro-
tation curves using the PSS model. Rotation curves observed
by optical spectroscopy are within the radius ofR/Ropt ∼ 1.0.
We have found that the specific radius for the CO data is about
R/Ropt ∼ 0.7, where the rotation curves trace the maximum ve-
locity part of the disk component, whereas, for the Hi linewidths,
it is aboutR/Ropt ∼ 1.5 and it traces the outer rather flatter part
of the rotation curves. We should pay attention to the difference
between them when we discuss the rotation velocity or the TF
relation in CO and in HI. The PSS model is constructed from the
statistics of rotation curves and by fitting of two mass compo-
nents, a disk and a halo. We should note that the PSS model does
not follow the real rotation curves in the central region. Sofue et
al. (1999) have discussed the central rotation curves, and found
that most rotation curves, except for dwarf galaxies, are almost
flat towards the center or show a nucleus high velocity part for
some fast rotating galaxies. The bulge and nucleus components
are not considered in the PSS model, as the influence of these
components on the rotation curves is small for this analysis at
R/Ropt & 0.5.
The CO linewidths which we used in this analysis are esti-
mated by the position – velocity diagrams which are observed
along the major axis, except Lavezzi & Dickey’s (1998) sample
that has largercz enough to cover the CO extent in a single beam.
On the contrary, the Hi linewidths are measured by the single
beam. It may cause the bias for the relation between the CO and
Hi linewidths. Mapping along the major axis may not cover the
real linewidth. In order to avoid the bias we have excluded the
face-on galaxies.
In summary, we have found the trend between the CO and Hi
linewidths by compiling the CO and Hi datasets. Hi linewidths
are larger than CO for slow rotating galaxies, and CO linewidths
are larger than Hi for fast rotating galaxies. This trend is com-
mon through out all datasets, although the slow rotating portion
has a large dispersion. The linewidths for slow rotating galaxies
of Wi . 300 km s−1are not appropriate when applying the TF
relation. Although the trend gives a different slope and offset
values for the TF relation from those of Hi, the output abso-
lute magnitude of intermediately rotating galaxies of 300 km
s−1. Wi . 600 km s−1is approximately equivalent to that
provided by the Hi TF relation.
In order to explain the trend we have examined the syn-
thetic rotation curve model proposed by Persic et al. (1996).
The trend can thus be explained by both the different distribu-
tions of the CO and Hi in a galaxy and the entirely non-flatness
of the rotation curves. Combining the TF relation with the syn-
thetic rotation curves of the PSS model shows that the radius
within the optical radius where CO is distributed is reflected
in the CO linewidths, and the radius beyond the optical radius
where Hi is distributed is also reflected in the Hi linewidths.
It is worth noting that the distribution of CO, Hi or anything
else used in measuring the linewidths actually influences the
linewidths, therefore the exact linewidths should be corrected
for the effects of the rotation curves and the gas distribution.
Acknowledgements.The authorY T acknowledges the financial sup-
port by the Research Fellowships of the Japan Society for the Promo-
tion of Science for Young Scientists. This research made use of the
Lyon/Meudon Extragalactic Database (LEDA).
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Compatibility of the CO and HI Linewidths Considering the Gas Distribution and Rotation Curves

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