# Molecular Fraction in the Galactic Center: The Central Molecular and HI
Zones

Yoshiaki Sofue
Institute of Astronomy, The University of Tokyo, Mitaka, Tokyo 181-0015, Japan
E-mail<EMAIL_ADDRESS>
(Accepted; Received YYY; in original form)

###### Abstract

By mapping the molecular fraction of the Galactic Center (GC), we
quantitatively address the question of how much molecular and central the CMZ
(Central Molecular Zone) is. For this purpose we analyze the CO and HI-line
archival data, and determine the column- (surface-) and volume-molecular
fractions, $f_{\rm mol}^{\Sigma}$ and $f_{\rm mol}^{\rho}$, which are the
ratio of column-mass density of H2 projected on the sky to that of total gas
(H2 \+ HI) from the line intensities, and the ratio of volume-mass densities
of H2 to total gas from the brightness temperature, respectively. It is shown
that $f_{\rm mol}^{\Sigma}$ is as high as $\sim 0.9-0.95$ in the CMZ, and
$f_{\rm mol}^{\rho}$ is $0.93-0.98$ in the GC Arms I and II attaining the
highest value of $\sim 0.98$ toward Sgr B2. The expanding molecular ring (EMR,
or the parallelogram) has a slightly smaller $f_{\rm mol}^{\rho}$ as $\sim
0.9-0.93$. We define the CMZ as the region with $f_{\rm mol}^{\Sigma}\geq
0.8-0.9$ between the shoulders of plateau-like distribution of H2column
density from $l=-1^{\circ}.1$ to $+1^{\circ}.8$ having Gaussian vertical
distribution with a half thickness of $\pm 0^{\circ}.2$. The CMZ is embedded
in the Central HI Zone (CHZ), which is defined as an HI disc between
$l\sim-2^{\circ}$ and $+2^{\circ}.5$, $b=-0^{\circ}.5$ and $+0^{\circ}.5$.
Based on the analysis, we discuss the origin of CMZ and interstellar physics
such as the volume filling factors of molecular and HI gases inferred from the
difference between $f_{\rm mol}^{\Sigma}$ and $f_{\rm mol}^{\rho}$.

###### keywords:

galaxies: ISM — Galaxy: centre — ISM: atoms — ISM: molecules — radio lines:
ISM

††pubyear: 2022

##  1 INTRODUCTION

The Central Molecular Zone (CMZ) was introduced as the ”strong concentration
of gas of about 200-pc radius” around the Galactic Center (GC) [Morris &
Serabyn 1996]. Decades later today, the exact range of the CMZ is still not
well defined, referred to as ”a ring-like accumulation of molecular gas in the
innermost few hundred parsecs of the Milky Way” [Henshaw et al. 2022]. Some
authors think it even smaller area [Tsuboi et al. 1999, Tokuyama et al. 2019].

The purpose of this paper is to quantitatively address the question, how much
molecular and central the CMZ is, and to quantitatively define the CMZ. For
such a purpose, the molecular fraction, $f_{\rm mol}$, defined by the ratio of
the molecular hydrogen (H2 gas) density to the total gas density (HI and H2
gases) provides the most direct information along with various constraints on
the physical and chemical condition of the ISM (interstellar medium)
[Elmegreen 1993]. Since it is a hybrid measure of the gas pressure (density
and temperature), metallicity (dust abundance) and UV (ultra violet) radiation
pressure, the fraction may be used to determine one of these quantities, given
the other two are fixed. As a first approximation to the discussion of the
relative variation of molecular fraction in the GC region, we take the
conservative view that the conversion factors from the CO and HI lines to the
column densities of H2and H atoms are constant.

Analyses of large-scale distribution of the molecular fraction in nearby
spiral galaxies have been extensively obtained by comparing CO and HI line
mapping data, which generally indicate monotonic increase of $f_{\rm mol}$
toward the galactic centers [Sofue et al. 1995, Honma et al. 1995, Kuno et al.
1995, Hidaka & Sofue 2002, Tanaka et al. 2014]. More resolved behavior has
been obtained in the Milky Way, where the molecular fraction becomes as high
as $\sim 0.9$ to unity inside several hundred pc of the Galactic Center [Sofue
& Nakanishi 2016, Koda et al. 2016, Sofue 2022]. Three dimensional analysis of
the CO and HI discs of the Milky Way has also shown a steep vertical increase
and saturation of the molecular fraction toward the galactic plane [Imamura &
Sofue 1997, Sofue & Nakanishi 2016]. The high molecular fraction in the
central region seems ubiquitous in spiral galaxies, except for M33’s center
showing values as low as $f_{\rm mol}\sim 0.2-0.3$ [Tosaki et al. 2011].

In this paper, we investigate the three dimensional distribution of the
molecular fraction in the central several degrees of the Milky Way. We measure
the extent and size of the high-$f_{\rm mol}$ saturated region, and re-define
the CMZ using the quantified parameters. We assume that the GC distance of the
Sun is 8.18 kpc [Gravity Collaboration et al. 2019].

##  2 CO and HI maps

###  2.1 Data

We make use of the CO- and HI-line data from the archives as follows. The wide
field 12CO data were taken from the Columbia Galactic plane CO survey [Dame et
al. 2001], which had angular and spectral resolutions of $8^{\prime}.5$ and
1.3 km s-1. respectively. The all-sky HI data were taken from the survey using
the Bonn 100-m and Parkes 65-m telescopes [HI4PI Collaboration et al. 2016],
which had effective resolutions of $16^{\prime}$ and $1.5$ km s-1. The 12CO
data for the Galactic Center were taken from the survey of the central $\sim
4^{\circ}\times 1^{\circ}$ region using the 45 m telescope [Oka et al. 1998],
which had an effective angular resolution of $37^{\prime\prime}$
($={\rm(beam~{}width^{2}+grid~{}spacing^{2}})^{1/2}$, velocity resolution $2$
km s-1, rms noise of $\sim 1$ K, presented by a data cube with grid spacing of
$(34^{\prime\prime},34^{\prime\prime},2{\rm~{}km~{}s^{-1}~{}})$. The HI data
for the GC region were taken from the survey with the Australia Telescope
Compact Array (ATCA) of the central $10^{\circ}\times 10^{\circ}$ region
[McClure-Griffiths et al. 2012], which had an angular resolution of
$145^{\prime\prime}$, velocity resolution of $1{\rm~{}km~{}s^{-1}~{}}$, rms
noise of 0.1 K, and are presented in a cube of spacing
$(35^{\prime\prime},35^{\prime\prime},1{\rm~{}km~{}s^{-1}~{}})$.

###  2.2 Fore- and background disc elimination by velocity cut (DEV)

The integrated intensity of radio line emission from the GC region around
$l\sim 0^{\circ}$ is significantly contaminated by the emission by the fore-
and background Galactic disc rotating in the transverse direction to the line
sight, where the radial velocity is degenerated to ’local velocities’ at
$|V_{\rm LSR}|\leq\sim 50{\rm~{}km~{}s^{-1}~{}}$. The fore- and background
intensity of CO line amounts to the same order as that from the GC disc, and
HI emission is stronger than the GC emission by an order of magnitude.

This makes it difficult to measure such quantities properly arising from the
GC, particularly in the HI line. The difficulty can be eased by applying the
’disc-elimination by velocity cut’ (DEV) method as used in our previous paper
for a study of the three-dimensional structure of the central molecular zone
(CMZ) [Sofue 2022]. The method simply eliminates low-velocity emission from
the integration, or uses only the emission at radial velocities higher than a
threshold value, $||V_{\rm LSR}||>V_{\rm cut}{\rm~{}km~{}s^{-1}~{}}$. An
obtained map will be called ’DEV50’ map, if $V_{\rm
cut}=50{\rm~{}km~{}s^{-1}~{}}$.

In this paper, we adopt $V_{\rm cut}=50$ km s-1as read from observed
longitude-velocity diagrams (LVD) of the CO and HI line emissions, where the
fore- and background disc components are seen as numerous bright horizontal
belts in the $(l,V_{\rm LSR})$ plane (see the lVD in the later section).

By the DEV procedure, the emission from a fan-shaped area near the $Y$ axis
(Sun-GC line) between $V_{\rm LSR}=\pm 50{\rm~{}km~{}s^{-1}~{}}$ on the radial
velocity field are eliminated from the integration. The eliminated-fan angle
is $\theta\sim\pm 15^{\circ}$ for $|V_{\rm LSR}|=50$ and $V_{\rm rot}\sim
200{\rm~{}km~{}s^{-1}~{}}$, which means that about $\sim 15-20\%$ of the whole
galactic disc is not counted. As this also underestimates the emission from
the GC disc itself with the same proportion, the total mass of the GC disc may
be obtained by multiplying a factor of $\sim 1.2$ to the calculated mass from
the DEV map.

Fortunately, this correction is not needed to derive the molecular fraction,
because it contains only the ratio of HI and CO intensities, so that the over-
elimination (underestimation) of both components cancels out.

###  2.3 DEV50 in the inner Milky Way

In Fig. 1 we show the DEV50 ($V_{\rm cut}=50{\rm~{}km~{}s^{-1}~{}}$) maps of
the 12CO (top panel) and HI (2nd panel) line intensities using cube data from
the Columbia CO survey [Dame et al. 2001] and HI4PI HI survey [HI4PI
Collaboration et al. 2016]. In Fig. 9, we show the original, subtracted and
DEV50 maps, as reproduced from our previous paper [Sofue 2022]. The 3rd panel
shows an overlay of the HI (red) and CO (green) intensities. The bottom panel
shows the molecular fraction, as will be defined and discussed in detail in
the later section. It is stressed that the intensity maps are quite different
from those integrated over the whole velocity range as often used in the
literature.

From the maps we find that:
(i) Broadly extended fore- and background disc emissions are not seen.
(ii) The central concentration is evident not only in CO, but also in HI.
(iii) The GC is surrounded by a less bright or almost empty region at
$|l|=\sim 5^{\circ}$ to $20^{\circ}$.
(iv) The molecular fraction increases steeply in the central $\sim 5^{\circ}$
making a high-$f_{\rm mol}$ disc in the GC, confirming the results in the
literature [Koda et al. 2016, Sofue & Nakanishi 2016].

Figure 1: [Top] DEV50 map (fore- and background disc-eliminated intensity map
integrate d over $|V_{\rm LSR}|\geq 50{\rm~{}km~{}s^{-1}~{}}$) of 12CO line
intensity (moment 0) made from the Columbia CO line survey (Dame et al. 2001)
in K km s-1. [2nd] Same, but using the HI4PI HI survey (HI4PI et al. 2016) in
K km s-1. [3rd] Overlay of the HI (red) and CO (green) intensities. [Bottom]
Molecular fraction made from the DEV50 CO and HI intensity maps.

###  2.4 DEV50 in the GC

Figure 2 presents DEV50 intensity maps of 12CO (top panel), HI (2nd panel) and
their overlay (3rd panel) in the GC at higher angular resolutions obtained
using the cube data from the Nobeyama CO [Oka et al. 1998] and ATCA HI
[McClure-Griffiths et al. 2012] surveys. The bottom panel shows the molecular
fraction obtained from these maps. Strongly absorbed regions appearing in the
HI map near Sgr A and Sgr B against the continuum emission will be avoided in
the analysis of the molecular fraction.

The DEV50 CO and HI maps are different from those so far published by
integration over the entire velocity range in the sense that:
(i) Extended structures have been removed, which is about the same order as
the CO intensity and about ten times in HI, so that the structures properly
belonging to the GC are clearly distinguishable.
(ii) The CMZ ($l=-1^{\circ}.1$ to $1^{\circ}.8$) and CHZ (central HI zone,
$l=-2^{\circ}$ to $+2^{\circ}.5$) [Sofue 2022] are clearly visible.
(iii) The overlay demonstrates that the CMZ is embedded in CHZ as usual in
disc galaxies.
(iv) The highest $f_{\rm mol}^{\Sigma}$ region is coincident with the CMZ. The
fraction is as high as $\sim 0.9-0.95$ and attains the maximum of $\sim 0.98$
toward Sgr B2. Note that the locally high $f_{\rm mol}^{\Sigma}$ clumps near
Sgr A are due to HI-line absorption against the radio continuum.

Figure 2: [Top] DEV50 map of 12CO line intensity (moment 0, in K km s-1)
integrated over $|V_{\rm LSR}|\geq 50{\rm~{}km~{}s^{-1}~{}}$ made from
Nobeyama CO-line survey by Oka et al. (1998). [2nd panel] DEV50 HI map made
from ATCA HI survey by McClure-Griffiths et al. (2012). The dashed ellipse
encloses the region with significant absorption against the continuum, and is
not used in the analysis. [3rd panel] Superposition of HI and CO intensity
maps as above in red and green colors, respectively. [Bottom] Molecular
fraction made from the above maps. Contours are drawn from $f_{\rm
mol}^{\Sigma}=0.5$ at interval of 0.05.

###  2.5 Longitude and latitude profiles

In order to present the characteristic variation of the intensities and
molecular fraction more quantitatively, we show in Fig. 3 longitudinal
profiles of the column density $N$ of H atoms (2H per H2) as calculated from
the maps in Fig. 1 and 2 along the Galactic plane. The conversion factors are
taken constant, as described later.

Figure 3: Longitudinal variation of $N$ (left panels) along the Galactic plane
and $f_{\rm mol}^{\Sigma}$ (left). (a) Wide area Columbia CO and HI4PI HI
surveys (Fig. 1). Grey and pink thin lines indicate those without disc
elimination for comparison. (b) Same, but for the central region using
Columbia and ATCA HI (McClure-Griffithset al. 2012) surveys. (c) Same, but
using the Nobeyama CO survey (Oka et al. 1998) and ATCA after Fig. 2.

The top-left panel (a) shows the wide area variations, where thick blue and
magenta lines show $N$ from CO and HI intensities after DEV50, respectively.
The thin grey and pink lines are the same, but before DEV is applied, so that
they include emissions in the whole velocity range. Difference between DEV and
non-DEV profiles is evident. The non-DEV profiels both in CO and HI (thin
lines) are almost flat from $l\sim-30^{\circ}$ to $+30^{\circ}$, except for
the central few degrees near CMZ. On the other hand, the DEV profiles show
global minima near the GC an order of magnitude less than those by non-DEV.
The difference is therefore attributed to the ’contamination’ of the fore- and
background disc components of CO and HI gases in the non-DEV profiles.

The CMZ is visible both in DEV and non-DEV profiles as the sharp concentration
in the central $-1^{\circ}$ to $+2^{\circ}$ of H2gas. However, we must be
careful that the CMZ’s column density (intensity) is overestimated by about
$\sim 50\%$, if the DEV is not applied.

Although far outside of the GC, hence not a main subject here, the correction
is still two times at $l\sim\pm 30^{\circ}$. It is attributed to the still
large ratio of the line-of-sight depths inside to outside of the 50-km
s-1butterfly in Fig. 10. It is interesting to point out that two CO peaks
appear at $l\sim 23^{\circ}$ and $-23^{\circ}$ deg in the DEV profile (blue
line in Fig. 3(a)), but they not recognized in the non-DEV (grey). This may
indicate the usefulness of the method in deriving the Galactic structures from
the integrated intensities.

Panels (b) and (c) show close up of the central region after DEV50using the
Nobeyama CO survey and ATCA HI survey as well. The CMZ exhibits its plateaued
distribution both in the Columbia and Nobeyama CO data. The right-hand side
panels show the longitudinal distributions of column-molecular fraction
$f_{\rm mol}^{\Sigma}$, which will be described in detail in the later
section.

On the other hand, the HI distribution is milder both in the longitude and
latitude directions. The column-density increases gradually toward the GC,
although its peak is significantly disturbed by the absorption against Sgr A
and B. Thus, the CHZ is a concentration without clear cut shoulders, and the
$e$ folding radius is measured to be $\sim\pm 2^{\circ}-2^{\circ}.5$.

##  3 Molecular Fraction

###  3.1 Column molecular fraction $f_{\rm mol}^{\Sigma}$ from the integrated
intensity

Because the brightness temperature of HI emission at $|V_{\rm LSR}|\geq 50\
{\rm~{}km~{}s^{-1}~{}}$ is observed to be less than $\sim 30$ K in the
analyzed region (see the longitude-velocity diagrams in the later subsection),
while the excitation temperature is considered to be $T_{\rm ex}\sim 140$ K in
the disc and still higher in the GC [Sofue 2018, Pohl et al. 2022], we here
assume that the HI line is optically thin. This makes it simple to convert the
intensity to the column density of HI gas. As to the CO line, which is usually
optical thick, we make use of the empirical conversion relation as described
below.

The molecular fraction for the column mass density projected on the sky,
hereafter column molecular fraction, is defined by

$f_{\rm mol}^{\Sigma}{=\frac{\Sigma_{\rm H_{2}}}{\Sigma_{\rm HI}+\Sigma_{\rm
H_{2}}}}=\frac{1}{1+\eta_{\Sigma}}.$ (1)

Here, $\eta_{i}$ is the ratio of column density of HI gas, $\Sigma_{\rm HI}$
(or column number density $N_{\rm HI}$) to that of H2 gas, $\Sigma_{\rm
H_{2}}$ (or $2N_{\rm H_{2}}$), which is related to the ratio of HI to 12CO
line intensities using the conversion factors as

$\eta_{\Sigma}=\frac{\Sigma_{\rm HI}}{\Sigma_{\rm H_{2}}}=\frac{N_{\rm
HI}}{2N_{\rm H_{2}}}=\frac{X_{\rm HI}I_{\rm HI}}{2X_{\rm CO}I_{\rm CO}}.$ (2)

The conversion factor for the HI line is given by [Kraus 1966]

$X_{\rm HI}=1.823\times 10^{18}{\rm Hcm^{-2}[K~{}km~{}s^{-1}]^{-1}},$ (3)

assuming that the HI gas is optically thin, because the observed brightness
temperature ($<$ several tens K) is sufficiently lower than the excitation
temperature ($\sim 200$ K) measured in the GC [Pohl et al. 2022]. For the CO
to H2 conversion, we adopt the empirical relation including the galacto-
centric distance $R$, which considers the metallicity gradient (increasing
toward GC) [Arimoto et al. 1996],

${\rm log}\frac{X_{\rm CO}}{X_{\rm
CO,\odot}}=0.41\left(\frac{R-R_{0}}{r_{e}}\right).$ (4)

Assuming a local conversion factor of $X_{\rm CO,\odot}=2.0\times 10^{20}$ H2
cm-2 [K km s-1]-1[Bolatto et al. 2013, Sofue & Kohno 2020] and scale radius of
the Galactic disc $r_{e}=5.1$ kpc for $R_{0}=8.2$ kpc [Sofue 2022], we have

$X_{\rm CO}({\rm GC})=0.51\times 10^{20}\ {\rm H_{2}\ cm^{-2}[K\ km\
s^{-1}]^{-1}},$ (5)

so that

$\frac{X_{\rm HI}}{2X_{\rm CO}}=1.79\times 10^{-2},$ (6)

and

$\eta_{\Sigma}=1.79\times 10^{-2}\frac{I_{\rm HI}}{I_{\rm CO}}.$ (7)

###  3.2 $f_{\rm mol}^{\Sigma}$ distribution on the sky

In Fig. 1 and 2 we show the distribution of $f_{\rm mol}^{\Sigma}$ on the sky
calculated using the DEV50HI and 12CO intensity maps. The outline of highly
molecular region with high $f_{\rm mol}^{\Sigma}\geq 0.9$ nearly coincides
with the high 12CO intensity region. However, the $f_{\rm mol}^{\Sigma}$ value
is almost saturated above $\sim 0.9$ regardless the clumpy distribution of the
12CO intensity.

Longitudinal variation of $f_{\rm mol}^{\Sigma}$ along the Galactic plane is
shown in the right panels of Fig. 3. The bottom-right panel from Nobeyama CO
and ATCA HI data shows a plateaued (saturated) distribution of molecular
fraction in the CMZ as high as $f_{\rm mol}^{\Sigma}\geq 0.9$ between
longitudes $l=-1^{\circ}.1$ and $+1^{\circ}.8$ and by the clear-cut shoulders
at these longitudes. This high $f_{\rm mol}^{\Sigma}$ region is isolated and
distinguished from the surrounding milder $f_{\rm mol}^{\Sigma}$ regions, as
is clearly seen in the wide area plots in the top panel.

Fig. 8 shows a vertical variation of $f_{\rm mol}^{\Sigma}$ at
$l=+0^{\circ}.6$ made from the Nobeyama CO and ATCA HI surveys. Molecular
fraction is as high as $f_{\rm mol}^{\Sigma}\sim 0.98$ near the Galactic
plane, while it rapidly decreases with latitude, dropping to $f_{\rm
mol}^{\Sigma}\simeq 0.9$ at $b\sim\pm 0^{\circ}.2\ (\pm 28{\rm~{}pc~{}})$, and
$\sim 0.8$ at $b\sim\pm 0^{\circ}.4\ (56{\rm~{}pc~{}})$. The peak position is
slightly displaced from the galactic plane toward the south by
$b\sim-0^{\circ}.05$.

Fig. 4 shows $f_{\rm mol}^{\Sigma}$ plotted against Galacto-centric distance
$R=8\rm{~{}sin~{}}\ l$ (kpc) as calculated using top-right panel of Fig. 3.
The plot is consistent with the radial plots of $f_{\rm mol}$ obtained from
the same data but using different methods [Koda et al. 2016, Sofue & Nakanishi
2016]. However, the present result shows lower values $\sim 0.5-0.6$ beyond
$R\sim 2$ kpc. This is because the present method measures the mean along the
line of sight on the sky including larger radii than the plotted radius. It is
also interesting to note the local maxim corresponding to the the 3-kpc
expanding arm/ring and the 4-kpc molecular ring

Figure 4: $f_{\rm mol}^{\Sigma}$ from the Columbia CO and HI4PI data as a
function of the galacto-centric distance $R$ as calculated from the longitude
plot in Fig. 1. Blue, pink and black lines represent curves at $l\geq
0^{\circ}$, $<0^{\circ}$, and their average respectively.

###  3.3 Volume molecular fraction $f_{\rm mol}^{\rho}$ from LVD

In order to examine the molecular fraction in the molecular Arms and clouds,
we make use of longitude-velocity diagrams (LVDs) of HI and CO brightness
temperatures $T_{\rm b}$, from which we calculate the volume-density molecular
fraction (hereafter, volume molecular fraction). LVDs were constructed using
the 12CO and HI cube data smoothed between $b=-0^{\circ}.1$ and $+0^{\circ}.1$
in order to cover the GC Arms I and II as well as the molecular complex around
Sgr B2. Fig. 5 shows the obtained LVDs in HI, CO, their overlay, and volume
molecular fraction.

The molecular Arms and clouds are now clearly visible and resolved, which were
not recognized in the integrated intensity maps on the sky. Prominent features
are the bright CO emitting region around Sgr B2 and B1 at $(l,V_{\rm
LSR})\sim(0^{\circ}.5,60{\rm~{}km~{}s^{-1}~{}})$, the tilted LV ridge
representing the molecular Arms running from $(l,V_{\rm
LSR})\sim(1^{\circ}.5,120{\rm~{}km~{}s^{-1}~{}})$ to
$(-1^{\circ},-200{\rm~{}km~{}s^{-1}~{}})$, and the oval or parallelogram
showing the expanding molecular ring or cylinder (EMR or EMC) with high non-
circular motion of $\pm 150{\rm~{}km~{}s^{-1}~{}}$.

The volume molecular fraction is written in terms of the brightness
temperature, $T_{\rm b}$, instead of the integrated intensity $I$ as follows:

$f_{\rm mol}^{\rho}{=\frac{\rho_{\rm H_{2}}}{\rho_{\rm HI}+\rho_{\rm
H_{2}}}}=\frac{1}{1+\eta_{\rho}}.$ (8)

and

$\eta_{\rho}=\frac{\rho_{\rm HI}}{\rho_{\rm H_{2}}}=\frac{n_{\rm HI}}{2n_{\rm
H_{2}}},$ (9)

where $\rho$ and $n$ denote the volume mass density and number density of the
gas, respectively. Let us recall that the gas density is related to the column
density and brightness temperature through

$n_{i}=\frac{dN_{i}}{dx}=\frac{dN_{i}}{dv}\frac{dv}{dx}{=\frac{d(X_{i}\int
T_{b,i}dv)}{dv}\frac{dv}{dx}}=X_{i}{T_{\rm b}}_{i}\frac{dv}{dx},$ (10)

where $X_{i}$ is constant with $i=$ CO or HI. Then, the HI to H2 mass ratio is
approximated by

$\eta_{\rho}=\frac{n_{\rm HI}}{2n_{\rm H_{2}}}\simeq 1.79\times
10^{-2}\frac{{T_{\rm b}}_{\rm HI}}{{T_{\rm b}}_{\rm CO}}\frac{[dv/dx]_{\rm
HI}}{[dv/dx]_{\rm CO}}.$ (11)

The radial velocity of HI and CO can be written as

$v_{i}(x)={V_{\rm rot}}_{i}\rm{~{}sin~{}}\theta_{i}+\delta v_{i},$ (12)

where $i=$ HI or CO, ${V_{\rm rot}}_{i}$ is the rotation velocity, $\delta
v_{i}$ is the velocity dispersion, and $\theta_{i}$ is the angle of the
gaseous motion and line of sight. We may safely assume that the rotation
velocities of HI and CO are equal and the velocity dispersion is much smaller
than $V_{\rm rot}$ and almost constant along the line of sight. Thus, we have

$\frac{dv}{dx}({\rm HI})\simeq\frac{dv}{dx}({\rm CO}),$ (13)

or

$\eta_{\rho}\simeq 1.79\times 10^{-2}\frac{{T_{\rm b}}_{\rm HI}}{{T_{\rm
b}}_{\rm CO}}.$ (14)

This formula is used to calculate the distribution of $f_{\rm mol}^{\rho}$ in
the LVD.

###  3.4 $f_{\rm mol}^{\rho}$ distribution in the LVD

As shown in the $T_{\rm b}$ LV diagrams in Fig. 5, the HI and CO temperatures
are comparable to each other except for the region with significant HI
absorption at low velocities and near Sgr A and B. This means that the CMZ is
composed mainly of molecular gas, because equal $T_{\rm b}$ between HI and CO
means $\eta\simeq 1.79\times 10^{-2}$, or $f_{\rm mol}^{\rho}\simeq
1/(1+0.0155)=0.989$, so that the molecular fraction is accordingly close to
unity.

In the bottom panel of Fig. 5 we show the $f_{\rm mol}^{\rho}$ distribution as
calculated using the top and middle panels for $T_{\rm b}$. The plot shows
that $f_{\rm mol}$ increases toward the density peak of the molecular arm,
where $f_{\rm mol}$ attains a maximum as high as $\simeq 0.95$, while it
decreases in the enveloping region to $f_{\rm mol}\sim 0.8$. The fraction
attains the maximum toward the molecular complex of Sgr B2, where it is as
high as $f_{\rm mol}^{\rho}\simeq 0.98-0.99$. Here, the data have been
smoothed in the longitude direction to the HI resolution of 145′′. Note that
CO $T_{\rm b}$ in the Sgr B2 region is higher than HI by twice, apparently
indicating $\eta\sim 0.005$ and $f_{\rm mol}\sim 0.995$. But such extreme
values are due to suppressed HI temperature by absorption against continuum
emission of Sgr B as well as to self absorption, and hence do not represent
true $f_{\rm mol}^{\rho}$.

Figure 5: [Top left] LVDs of HI $T_{\rm b}$ (in K). Horizontal lines enclose
the velocity range for DEV50, and vertical lines show longitude range with
significant absorption against continuum. [Top right] 12CO $T_{\rm b}$ (in K)
smoothed between $b=-0^{\circ}.1$ and $+0^{\circ}.1$ (width
$0^{\circ}.2=12^{\prime}=29$ pc). [Bottom left] Overlay of 12CO in green (0 to
15 K in Asinh scaling) on HI in red (0 to 50 K Asinh). [Bottom right] Volume
molecular fraction, $f_{\rm mol}^{\rho}$, smoothed to the same resolution as
that of HI map ($145^{\prime\prime}$).

Fig. 6 shows cross sections of LVD along the three lines A-A’, B-B’, and C-C’
in Fig. 5, which represent $f_{\rm mol}^{\rho}$ variation along the GC Arms,
across the molecular complex of Sgr B, and across the expanding molecular
ring, respectively. We stress that the molecular fraction along A-A’ and B-B’
are almost saturated at high level of $f_{\rm mol}^{\rho}\geq 0.96-0.98$. On
the other hand, EMR/EMC exhibits a slightly milder $f_{\rm mol}^{\rho}$ of
$\sim 0.9-0.95$ than the Arms, while it has an order of magnitude less density
[Sofue 2022].

Figure 6: [Top] $f_{\rm mol}^{\rho}$ variation from A to A’ of Fig. 5 along GC
Arms I and II from $(l,V_{\rm LSR})=(+1^{\circ}.8,+220{\rm~{}km~{}s^{-1}~{}})$
to $(-1^{\circ}.2,-220{\rm~{}km~{}s^{-1}~{}})$. [Middle] B to B’ across Sgr B2
at $V_{\rm LSR}=+62{\rm~{}km~{}s^{-1}~{}}$. [Bottom] C to C’ along the
expanding molecular ring (EMR) (or parallelogram) from $(l,V_{\rm
LSR})=(+2^{\circ},+220{\rm~{}km~{}s^{-1}~{}})$ to
$(-1^{\circ},+150{\rm~{}km~{}s^{-1}~{}})$.

###  3.5 Dependence on the conversion factor

The 12CO -to-H2conversion factor adopted here, $X_{\rm CO}=0.51\times 10^{20}$
H2 cm-2 [K km s-1]-1, is about a quarter of the local value of the Galactic
molecular clouds. This is consistent with the molecular mass estimations in
the GC obtained by various methods other than CO [Dahmen et al. 1998]. An even
smaller value of 0.24 H2 cm-2 [K km s-1]-1for the 12CO ($2-1$) line, which has
about the same intensity as 12CO ($1-0$), has been also obtained [Oka et al.
1998b]. Therefore, $X_{\rm CO}$ may have an uncertainty of a factor of two
that affects the molecular fraction. Figure 7 shows the dependence of $f_{\rm
mol}$ on $X_{\rm CO}$ for $I_{\rm HI}/I_{\rm CO}=1$ and 0.5 or ${T_{\rm
b}}_{\rm:HI}/{T_{\rm b}}_{\rm:CO}=1$ and 0.5, which represents typical cases
of CMZ. A range of $f_{\rm mol}$ between $X_{\rm CO}\sim 0.25$ and $\sim 1$,
as indicated by the thick line, will be still acceptable due to our current
uncertain knowledge of the conversion factor in the GC. However, even taking
into account such uncertainties, the definition of the CMZ based on the
relative variation of $f_{\rm mol}$ in the GC region will not change.

Figure 7: Dependence of the molecular fraction on the $X_{\rm CO}$ factor for
the case with $I_{\rm HI}/I_{\rm CO}=1$ (lower line) and 0.5 (more CO, upper
line) (or ${T_{\rm b}}_{\rm:HI}/{T_{\rm b}}_{\rm:CO}=1$ and 0.5), where
$X_{\rm CO}$ in H2 cm-2 [K km s-1]-1.

##  4 Discussion: How central and molecular is CMZ?

###  4.1 Comparison with interstellar clouds and disc gas

The presently detected high $f_{\rm mol}$ and low $\eta$ in the CMZ may be
compared with the values for interstellar clouds such as observed in $\rho$
Oph with $\eta_{\Sigma}=N_{\rm HI}/(2N_{\rm H_{2}})=1/112\ (f_{\rm
mol}^{\Sigma}=0.99)$ [Minn 1981], $\eta_{\Sigma}\sim 10^{-2}\ (f_{\rm
mol}^{\Sigma}\sim 0.99)$ of a GMC [sato+1992], or $\eta_{\Sigma}\sim 0.1-0.15\
(f_{\rm mol}^{\Sigma}\sim 0.85-0.9)$ of Sgr B2 [Lang et al. 2010]. However,
the highest value observed toward Sgr B, $f_{\rm mol}^{\rho}=0.99$, in this
study is still lower than that obtained in a local dark cloud having an
extremely high value of $\eta_{\Sigma}\sim 5-27\times 10^{-4}\ (f_{\rm
mol}^{\Sigma}\sim 0.997-0.999)$ [Goldsmith & Li 2005]. On the other hand, the
CMZ’s $f_{\rm mol}^{\Sigma}$ is far greater than the values observed in HI
clouds as $f_{\rm mol}^{\Sigma}\sim 0.2-0.5$ [Nakanishi et al. 2020], and
those along sight lines toward prominent radio sources through the arms
($f_{\rm mol}^{\Sigma}\sim 0.7-0.9$) and inter-arm regions ($\sim 0.1-0.3$)
[Winkel et al. 2017].

###  4.2 Definition of CMZ: Isolated island

Using the spatial distribution of the surface-mass molecular fraction in Fig.
2 and 3, we define the CMZ as a region with a plateaued distribution of high
molecular fraction between the steeply increasing gradients in both sides of
the center at $f_{\rm mol}^{\Sigma}\sim 0.8-0.9$. The region is well defined
between the edges at $l=-1^{\circ}.1\ (-157{\rm~{}pc~{}})$ and $+1^{\circ}.8\
\ (+257{\rm~{}pc~{}})$ with eye-estimate errors $\pm 0^{\circ}.05$, or the
scale radii to be $r_{-}=-157$ and $r_{+}=257$ pc ($\pm 7$ pc). It is stressed
that the positions of the density shoulders exactly coincide with those of
$f_{\rm mol}^{\Sigma}$.

Namely, the CMZ is a region with plateaued distribution of H2 gas having
shoulders both in the column-density (intensity) and molecular fraction
profiles. So, this is the answer to the question of how much central and
molecular the CMZ is. The measured extent of CMZ is thus consistent with that
originally introduced [Morris & Serabyn 1996]. Also, the plateaued nature
indicates that the gas distribution inside CMZ is ring like [Henshaw et al.
2022]. A new point to be emphasized by this analysis is that the CMZ is an
isolated island in the shallow sea of low density HI that has not sufficient
mass to supply the CMZ.

The latitudinal profile of $f_{\rm mol}^{\Sigma}$ is shown in Fig. 8, which is
well represented by a Gaussian profile. The intensity distribution also has a
Gaussian profile in the latitudinal direction [Sofue 2022]. From Fig. 8, the
latitudinal extent at a threshold level of $f_{\rm mol}^{\Sigma}=0.9$ is
measured to be $z_{\rm 0.9}=0^{\circ}.2$ with eye estimate error of $\pm\sim
0^{\circ}.02$. This height is about equal to the column-density’s scale half
thickness . So, we define the latitudinal extent of the CMZ by this height,
$h_{z}=\pm 0^{\circ}.2$ ($\pm 29$ pc).

Figure 8: Latitudinal (vertical) variation of $f_{\rm mol}^{\Sigma}$ across
the Galactic plane at $l=0^{\circ}.6$.

Thus defined CMZ is significantly asymmetric, or lopsided, with respect to Sgr
A∗ (nucleus), being displaced to positive longitude by $\delta l\sim
0^{\circ}.35\ (50{\rm~{}pc~{}})$. It is also offset from the Galactic plane
toward the south by $\delta b\sim-0^{\circ}.05\ (7{\rm~{}pc~{}})$.

It is impressive that the CMZ is highly isolated from the surrounding less
molecular region, particularly in the wider area plot in Fig. 3 (b) and (d),
making an island of molecular gas in the central $\sim 430{\rm~{}pc~{}}$. The
CMZ composes a distinguished galactic structure (object) with the highest
molecular fraction in the Milky Way. Despite of the high $f_{\rm mol}$ inside,
it is surrounded by a low $f_{\rm mol}$ region or a gap with $f_{\rm
mol}^{\Sigma}\sim 0.5-0.7$ at $l>\sim 2^{\circ}$ and $<\sim-1^{\circ}.2$ (Fig.
3). However, the current studies of the Milky Way using the Columbia CO survey
[Dame et al. 2001] and HI survey using the Parkes 64-m telescope survey [HI4PI
Collaboration et al. 2016] at lower resolutions have shown a monotonic
increase of $f_{\rm mol}$ toward the GC inside $R\leq\sim 2$ kpc. Studies of
external spiral galaxies have also shown a monotonic increase of $f_{\rm mol}$
toward the centers [Sofue et al. 1995, Honma et al. 1995, Kuno et al. 1995,
Hidaka & Sofue 2002, Nakanishi et al. 2006, Tosaki et al. 2011, Tanaka et al.
2014, Sofue & Nakanishi 2016, Koda et al. 2016].

The variable $f_{\rm mol}$ outside CMZ has been detected here thanks to the
high resolution ($\sim 6$ pc), while the current works had effective
resolutions of $\sim 100$ pc or larger, so that the innermost large variation
of $f_{\rm mol}$ has not been detected. It is an interesting question whether
the $f_{\rm mol}$-gap around the CMZ is a general phenomenon, or it is
specific in the Milky Way’s center. This will be a subject for higher
resolution observations in the CO and HI lines of spiral galaxies in the
future.

###  4.3 Volume-filling factor and the difference of $f_{\rm mol}^{\rho}$ and
$f_{\rm mol}^{\Sigma}$

The volume-mass molecular fraction was observed to be generally higher than
the column-mass molecular fraction, or $f_{\rm mol}^{\rho}>f_{\rm
mol}^{\Sigma}$, in the CMZ. From Fig. 3 and 6 we approximate the mean values
to be $f_{\rm mol}^{\rho}\sim 0.96$ and $f_{\rm mol}^{\Sigma}\sim 0.93$. The
lower $f_{\rm mol}^{\Sigma}$ than $f_{\rm mol}^{\rho}$ is attributed to the
volume filling factor $\alpha_{\rm H_{2}}$ of H2 and $\alpha_{\rm HI}$ of HI
gas.

We here assume that each of molecular and HI clouds has a nearly constant
density and write the column densities as $N_{\rm HI}\sim\langle\rho_{\rm
HI}\langle$ and $2N_{\rm H_{2}}=\langle\rho_{\rm H_{z}}\rangle$, where the
angle-parentheses denote the average along the line of sight. We here
introduce filling factors $\alpha_{\rm HI}$ and $\alpha_{\rm H_{2}}$ for HI
and molecular clouds and rewrite the average in terms of the filling factors
as $\langle\rho_{\rm HI}\rangle=\alpha_{\rm HI}\rho_{\rm HI}$ and
$\langle\rho_{\rm H_{2}}\rangle=\alpha_{\rm H_{2}}\rho_{\rm H_{2}}$. Recalling
that $\eta_{i}\ll 1$, we obtain

$f_{\rm mol}^{\Sigma}=\frac{1}{1+\eta_{\Sigma}}\simeq 1-\frac{\langle\rho_{\rm
HI}\rangle}{\langle\rho_{\rm H_{2}}\rangle}\simeq 1-\frac{\alpha_{\rm
HI}\rho_{\rm HI}}{\alpha_{\rm H_{2}}\rho_{\rm H_{2}}}.$ (15)

On the other hand we have

$f_{\rm mol}^{\rho}\simeq 1-\frac{\rho_{\rm HI}}{\rho_{\rm H_{2}}}.$ (16)

So, we obtain

$\Delta f=f_{\rm mol}^{\rho}-f_{\rm mol}^{\Sigma}\sim\left(\frac{\alpha_{\rm
H_{2}}}{\alpha_{\rm HI}}-1\right)\frac{\rho_{\rm HI}}{\rho_{\rm H_{2}}}.$ (17)

The observed relation $f_{\rm mol}^{\rho}>f_{\rm mol}^{\Sigma}$ indicates
$\alpha_{\rm H_{2}}>\alpha_{\rm HI}$. If we assume $\rho_{\rm HI}/\rho_{\rm
H_{2}}\sim 0.01$ (e.g., $n_{\rm HI}\sim 20\ {\rm H\ cm^{-3}},$ $n_{\rm
H_{2}}\sim 10^{3}\ {\rm\ H_{2}\ cm^{-3}}$ ) for example, the observed $\Delta
f\sim 0.03$ yields $\alpha_{\rm H_{2}}/\alpha_{\rm HI}\sim 2$. The CMZ is thus
a molecular gas dominant region not only by mass and density, but also by the
volume filling factor.

###  4.4 Origin of high molecular fraction in CMZ

The molecular fraction is determined by the gas pressure $P$, metallicity $Z$,
and ultra-violet (UV) radiation field $U$ of the interstellar gas [Elmegreen
1993]. It can be expressed by a function of the galacto-centric distance $R$,
given a Galactic disc model for the radial variation of $P,Z$ and $U$. While
$U$ suppresses $f_{\rm mol}$, $P$ (density) and $Z$ act to increase $f_{\rm
mol}$, where $Z$ doubly affects to increase $f_{\rm mol}$ by UV shielding and
catalystic formation of H2 on dust grain surfaces. It has been shown that the
thus calculated $f_{\rm mol}$ monotonically increases toward the GC with a
scale radius comparable to that of the three quantities of about $R_{e}\sim
5-7$ kpc [Honma et al. 1995, Tanaka et al. 2014, Sofue & Nakanishi 2016, Koda
et al. 2016].

In so far as the exponential variations are assumed for $P$, $U$ and $Z$, as
in the current works, any model results in a monotonic increase of $f_{\rm
mol}$ toward the GC. So, the observed rapid $f_{\rm mol}$ variation at $R\sim
200$ pc must be due to more local variation of the three quantities. Among the
three parameters, the metallicity $Z$ cannot be variable at scale radius less
than $\sim 1$ kpc, because the time scale of variation is on the order of the
Galaxy’s evolution time including the Galactic bulge. The radiation field $U$
is expected to be highest inside CMZ according to the wealth of thermal radio
continuum sources indicating a number of HII regions [Sofue 1990, Sofue 2022,
Yusef-Zadeh et al. 2022]. This means that the UV field cannot be the cause for
depression of $f_{\rm mol}$ beyond $R\sim 200$ pc.

Therefore, only the parameter that can affect the sudden change in $f_{\rm
mol}$ at $R\sim 100-200$ pc is the pressure $P$ which is proportional to $\rho
T$ with $\rho$ and $T$ being the ISM density and temperature. Since the UV
field is weaker outside CMZ, the temperature may be lower outside CMZ, which
means that the pressure equilibrium between outside and inside CMZ does not
hold. So, only one possible mechanism for $P$ to be increased locally inside
CMZ is the dynamical confinement of ISM in the deep Galactic potential.

Such dynamical confinement can be obtained by accretion of the gas in the
surrounding disc, where $f_{\rm mol}^{\Sigma}\sim 0.5$ so that the gas is half
molecular and half in the shallow HI envelope (CHZ), onto the central region
by the loss of angular momentum by galactic shock waves in the bar potential
[Sorensen et al. 1976, Roberts et al. 1979, Wada & Habe 1995]. The gas between
the center and bar ends are swept away to make low gas density region
surrounding the accretion disc.

Once it is accumulated in the center, the gas is converted to molecules by the
phase transition due to the increase in the density ($\propto P$) and maybe
also due to locally high metallicity ($Z$) in the core of the Galactic bulge,
unless the radiation field ($U$) is too strong such as in a starburst phase.
The accumulating dense gas composes there a ring in circular rotation as shown
by the extensive numerical simulations [Li et al. 2015, Sormani et al. 2019,
Tress et al. 2020]. The ring will be sustained for a long time without
collapsing by their self-gravity because of the high differential rotation on
the order of $\sim 1000\ {\rm kms\ s^{-1}\ kpc^{-1}}$ in the deep
gravitational potential inside CMZ [Sofue 2013].

However, there remains a question whether the observed high $f_{\rm mol}$ can
be maintained still in such a high shear motion even though it is anticipated
by the current $f_{\rm mol}$ theories that consider $P,\ Z$ and $U$, but do
not take into account the dynamics. In fact, the numerical simulations as
above assuming a bar potential in the GC have shown rapid inflow of gas
yielding a turbulent gas ring, and accordingly indicate a very low molecular
fraction of $f_{\rm mol}\sim 0.55$ [Tress et al. 2020].

###  4.5 No HI-to-H2 transition in the CMZ

In such a high $f_{\rm mol}^{\rho}$ region as CMZ, the molecular Arms I and
II, including Sgr B complex, cannot be produced by the phase change of
surrounding HI gas by compression, because the HI reservoir inside CMZ
contains far less mass than the arms. Namely, the HI-to-H2phase transition is
not the major process to form the molecular gas structures in the GC. So, the
arms can be formed by coagulation of smaller molecular clouds and diffuse H2
by compression inside the CMZ [Koda et al. 2016].

###  4.6 Central HI Zone (CHZ)

We finally mention about the HI gas distribution from the DEV50 HI maps. The
horizontal HI intensity distribution in Fig. 3 shows enrichment of HI gas in
GC. In contrast to the CMZ with sharp edges, the HI concentration is milder,
continuous from the periphery, and shows a nearly linear increase towards the
center in the semi-log plot.

Considering the absorption near Sgr A, the profile may be approximated by an
exponential function with gradient of $e$ folding radius of $r_{\rm
HI}\sim+3^{\circ}\ (\sim 430{\rm~{}pc~{}})$ on the positive longitude side,
and $\sim-2^{\circ}(\sim 285{\rm~{}pc~{}})$ on the negative longitude side.
This ”central HI zone (CHZ)” may constitute an extended outskirt of the CMZ.
The CMZ stands as an isolated island in the extended shallow sea of
HI.However, the CHZ does not work as a reservoir to supply the gas to CMZ
because the density and total mass is too small [Sofue 2022].

More global HI concentration in the GC is visible in the DEV50 HI map as the
peak in the central few degrees over the global minimum (Fig. 3(a), Fig. 11).
Such HI enhancement in integrated intensity maps has been not clearly seen in
the current presentations, being buried by the fore- and background disc. In
the appendix, we demonstrate how efficient the DEV method is to eliminate the
HI disc contamination and to quantify the density distribution of HI gas in
the CHZ.

We point out that the longitudinal HI distribution is asymmetric with respect
to the center in the sense that CHZ is shifted to the west (negative longitude
side) by $\sim 1-2^{\circ}$. Interestingly, the HI asymmetry is in the
opposite sense to that of the CMZ that is shifted to the east (positive
longitudes).

##  5 Summary

We have obtained a detailed comparison of the CO and HI maps and LV diagrams
in the GC region, and showed that the molecular fraction is as high as $f_{\rm
mol}^{\rho}\sim 0.9-0.95$ in the CMZ. The highest fraction was observed toward
Sgr B2 molecular complex at $f_{\rm mol}^{\rho}\sim 0.98$, and it remains at
high values $0.93-0.98$ in the GC Arms I and II. The expanding molecular ring
or the parallelogram shows a slightly milder fraction of $f_{\rm
mol}^{\rho}\sim 0.9-0.93$, but with an order of magnitude lower gas density
than CMZ. We quantitatively re-defined the CMZ’s location and extent as the
region on the sky with the column (projected) molecular fraction at $f_{\rm
mol}^{\Sigma}\geq 0.8-0.9$ spanning from $l=-1^{\circ}.1$ to $+1^{\circ}.8$
and $b=-0^{\circ}.2$ to $+0^{\circ}.2$, and answered the question how much
central and molecular the CMZ is. We also defined the Central HI zone (CHZ) as
an HI enhanced disc from $-2^{\circ}$ to $+2^{\circ}.5$ and $|b|\leq
0^{\circ}.5$, which envelopes the CMZ.

ACKNOWLEDGEMENTS

The author express his sincere thanks to the authors and collaborators of the
archival data as follows. Data analysis was performed at the Astronomy Data
Center of the National Astronomical Observatory of Japan.

DATA AVAILABILITY

The CO- and HI-line data were downloaded from
https://www.nro.nao.ac.jp/ nro45mrt/html/results/data.html
https://www.atnf.csiro.au/research/HI/sgps/GalacticCenter/ Home.html.

NO CONFLICTS OF INTEREST

I have no conflicts of interest.

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##  Appendix A CO and HI maps

We reproduce the 12CO and HI intensity maps used to derive the DEV50 maps from
[Sofue 2022].

Figure 9:  Integrated intensity maps using the Nobeyama 12CO (Oka et al.
1998a) and ATC HI (McClure-Griffiths et al. 2012) surveys, as reproduced from
our previous paper (Sofue 2022). Squares in the top and bottom panels mark the
CMZ and CHZ, respectively

##  Appendix B DEV50 HI longitudinal profile

We check how well the DEV50 profile for a HI gas distribution model can
reproduce the observed profile. We assume a model density distribution as
follows, composed of a disc mimicking the observed HI disc [Nakanishi & Sofue
2016] and an HI central disc representing the CHZ, respectively,

$\rho=\rho_{1}+\rho_{2},$ (18)

where

$\rho_{1}=0.2(r/r_{\rm d})^{4}\exp(-(r/r_{\rm d}))$ (19)

represents the disc component and

$\rho_{\rm c}=10\exp(-(r/r_{\rm c})^{2})$ (20)

is the CHZ. The scale radii are taken to be $r_{\rm d}=3$ kpc and $r_{\rm
c}=0.3$ kpc. We also assume a simple rotation cuve with constant velocity
$V_{\rm rot}=200{\rm~{}km~{}s^{-1}~{}}$. Fig. 10 shows the model density
distribution and radial-velocity field.

Calculated longitudinal profile of the HI column density is shown in Fig. 11.
The thick line shows the result for DEV50, and the upper thin line shows the
profile without DEV. The bottom panel shows the observed column density
profiles for DEV50 by thick line and non-DEV integration (thin line) for the
HI4PI survey along the Galactic plane. The red line is the DEV50 profile using
the ATCA survey, which shows about 50% larger densities. The higher density in
ATCA profile may be due to the higher resolution more effectively picking up
high-density structures near the Galactic plane as well as to smaller
absorption effect against the continuum sources compared to single-dish
observations by HI4PI.

Figure 10: (a) Model radial distribution of HI density in the Galactic plane.
(b) Velocity field for flat rotation curve with $V_{\rm
rot}=200{\rm~{}km~{}s^{-1}~{}}$. The Sun is at the white circle. DEV50
integration is obtained outside the fan-shaped area with $|V_{\rm
LSR}|>50{\rm~{}km~{}s^{-1}~{}}$ as indicated by the thick contours. Contours
are drawn at interval of 25 km s-1, with the Solar circle at $V_{\rm LSR}=0$
km s-1and the thick contours are $\pm 50$ km s-1. Figure 11:  (a) Longitudinal
profile of column density $N$ of HI by DEV50 (thick line) for a flat rotation
curve with $V_{\rm rot}=200{\rm~{}km~{}s^{-1}~{}}$, and non-DEV (thin line).
(b) Observed HI column density by DEV50 (thick line) and non-DEV using HI4PI
HI data. Red line shows DEV50 profile for ATCA HI data.

The DEV50 longitudinal profile can be used to abstract the central HI zone. In
Fig. 12 we show a profile (thick line) after subtracting the extended HI
component by fitting to the outer profile (thin line) at $|l|\geq 15^{\circ}$
by a Gaussian function with scale radius $16^{\circ}$ and amplitude $1.0\times
10^{22}$ H cm-2 (dashed line). The CHZ is clearly visible as the central
concentration inside $-4^{\circ}\leq l\leq+2^{\circ}.5$, and is further
surrounded by a broader enhancement from $l\sim-13^{\circ}$ to
$\sim+10^{\circ}$.

Figure 12: $N$ of HI gas (thick line) in linear scaling after subtracting the
residual disc component, as fitted by a Gaussian profile (dashed line) to the
observed DEV50 $N$ map (grey line) from HI4PI HI data. Red line shows the
same, but for ATCA HI data.