Synthetic Observations of 21cm HI Line Profiles from Inhomogeneous Turbulent Interstellar HI Gas with Magnetic Field

2.4 MB·

by  Yasuo Fukui

Draft version January 26, 2017
Typeset using LATEX preprint2 style in AASTeX61
SYNTHETIC OBSERVATIONS OF 21CM H I LINE PROFILES FROM INHOMOGENEOUS
TURBULENT INTERSTELLAR H I GAS WITH MAGNETIC FIELD
Yasuo Fukui,1 Takahiro Hayakawa,1 Tsuyoshi Inoue,1 Kazufumi Torii,2 Ryuji Okamoto,1
7
1 Kengo Tachihara,1 Toshikazu Onishi,3 and Katsuhiro Hayashi1
0
2

n 1Department of Physics, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8602, Japan
a
J 2Nobeyama Radio Observatory, National Astronomical Observatory of Japan, 462-2 Nobeyama, Minamimaki,
5 Minamisaku, Nagano 384-1305, Japan
2 3Department of Physical Science, Osaka Prefecture University, 1-1 Gakuen, Sakai, Osaka 599-8531, Japan

]
A (Received; Revised; Accepted)
G
Submitted to
.
h
p ABSTRACT
-
o We have carried out synthetic observations of interstellar atomic hydrogen at 21cm wavelength by
r
t utilizing the theoretical results of magnetohydrodynamical numerical simulations of the inhomoge-
s
a neous turbulent interstellar medium which includes both CNM and WNM (Inoue & Inutsuka 2012).
[
We used the ultraviolet absorption measurements of H in the local interstellar space in order to
2
1
constrain the model parameters. We find the following: (1) The W -N scatter plot shows a sys-
v Hi Hi
9 tematic change depending on T , (2) the contribution of H in the W -N plot is minor, indicating
s 2 Hi Hi
2
that “CO-free H ” is not important, (3) the H I optical depth measured by absorption toward a
1 2
7 radio continuum point source is significantly smaller than the optical depth derived from H I emis-
0
sion observed with large beams, because the covering factor of high H I optical-depth (τ > 0.5)
. Hi
1
regions is significantly small, ∼30%, as compared with that of low H I optical-depth regions, ∼70%.
0
7 It is also found that the W -τ (dust optical depth at 353GHz) plot is better explained if dust
Hi 353
1
1/1.3
: evolution expressed as NHi + 2NH2 ∝ τ353 is taken into account. H I column density derived by
v
emission-absorption (Heiles & Troland 2003a) is systematically smaller by a factor of ∼1.7 than that
i
X
corrected for the optically thick H I andfor the dust evolution as is consistent with Fukui et al. (2014,
r
a 2015). The total mass of H I in the local interstellar space is accurately estimated to be 1.7-times
the optically thin case by the latter method.
Keywords: ISM: atoms — ISM: clouds — radio lines: ISM
Corresponding author: Yasuo Fukui
[email protected]
2 Fukui et al.
1. INTRODUCTION difficult to test observationally the above H I
properties for the large volume where H I is
The main constituent of the interstellar
distributed.
medium is atomic hydrogen H I, and the sec-
The dust emission and extinction are also
ondary constituents, whose abundance is ten
used often as a proxy for N under an as-
times less than H I, include molecular hydro- Hi
sumption of constant gas to dust ratio. Previ-
gen H and atomic helium He over the global
2
ously, the scattering inthe datafor dust column
volume of the Galactic disk. It is of primary im-
density was large, making the method crude
portance to make precise measurement of H I
at best (see e.g., Chapter 21 of Draine 2011).
in our understanding of the structure, kinemat-
Planck Collaboration (2014) opened a new pos-
ics and physical conditions of the interstellar
sibility of precise measurement of dust optical
medium and the formation of interstellar clouds
depth by making extremely sensitive measure-
and stars.
ments of dust optical depth at sub-mm wave-
The 21cm spin flip transition of H I of-
lengths, 350, 550 and 850microns. These long
fers a direct method to measure interstellar
wavelengths are in the Rayleigh-Jeans regime
H I and has been used extensively over the
of the Planck function and, by combining the
last several decades since its discovery in 1951
IRAS data at 100 microns in the Wien regime,
(Ewen & Purcell 1951; Muller & Oort 1951).
the sub-mm dust optical depth and dust tem-
When the H I 21cm line is optically thin, the
perature for an appropriate dust emissivity β
following equation is used to calculate the H I
were calculated with unprecedented accuracy to
column density, N , from the 21cm line inten-
Hi
within .10%.
sity, W ,
Hi
Fukui et al. (2014, 2015) presented a method
N (cm−2) = 1.823×1018W (Kkms−1). (1) to use thePlanck dust optical depth at353GHz
Hi Hi
(τ ) as proxy of N by identifying the op-
353 Hi
As such, it has been commonly thought that tically thin regime of 21cm H I emission as
21cm H I emission is optically thin. Direct sup- a linear part of a scatter plot between W
Hi
port for the optically thin assumption for H I and τ , where dispersion of the data points
353
by emission-absorption measurements toward is smallest at the highest dust temperature.
radio continuum point sources, which shows Fukui et al. (2014) presented results for high-
that the H I peak optical depth is typically latitude clouds with the Galactic Arecibo L-
∼0.1 (e.g., Dickey et al. 2003; Heiles & Troland band Feed Array H I (GALFA-H I) survey data
2003a,b). High resolution H I observations with (Peek et al. 2011) taken with a 4′ beam of the
the Arecibo 305m telescope have been used Arecibo telescope and Fukui et al. (2015) for
to make high sensitivity emission-absorption the whole sky at |b| larger than 15◦ with a
measurements and revolutionized the knowl- 33′ beam in the Leiden/Argentine/Bonn (LAB)
edge on the H I gas physical conditions survey (Kalberla et al. 2005). The two papers
(Heiles & Troland 2003b). In the meantime the concluded that, in the local interstellar volume
question was raised that the 21cm H I emission within 200pc of the sun, interstellar H I is dom-
maybeopticallythickbasedonH Iprofileswith inated by cold and dense H I gas which is op-
self-absorption (Braun 2012). Because H I ob- tically thick with a typical H I optical depth of
servations provide physical quantities averaged ∼1, and that the average H I density is to be
along a line of sight, it is in principle impossible doubled approximately if the correction for the
to retrieve the original physical parameters of optical depth is applied. Fukui et al. (2015) ar-
the H I gas in the three dimensions, making it
Synthetic Observations of H I Line Profiles 3
gued that the opacity-corrected H I can explain deriving the WNM temperature in absorption,
the “dark gas”, which is detected in γ-rays and and only a lower limit for T was obtained to be
s
interstellar extinction A but not in the 2.6- around 300–1000K, leaving the mass of WNM
V
mm CO or optically-thin 21-cm H I transitions uncertain, which may occupy ∼ 60% of total
(Grenier et al. 2005; Grenier et al. 2015 for a H I (Heiles & Troland 2003b).
review), as an alternative to CO-free H gas FollowingFukui et al.(2014,2015),Stanimirovi´c et al.
2
(Wolfire et al. 2010). In order to understand (2014) made H I emission-absorption mea-
the behavior of H I, it is crucial to measure surements toward radio continuum sources in
the fraction of H in H I gas. Since H has Perseus with the Arecibo H I data and found
2 2
noradio transition, ultraviolet absorptionofthe that the absorption optical depth is not so large
electronic transition provides a unique tool to as suggested by Fukui et al. (2014, 2015), rais-
directly measure H . FUSE and Copernicus re- ing a question on the optically thick H I emis-
2
sultsaresuchdatasetsofH (e.g.,Gillmon et al. sion. Their results are consistent with those
2
2006). Since observations need background UV by Heiles & Troland (2003a,b). McKee et al.
source, the H observations measure H in the (2015)madeacomparisonofFukui et al.(2015)
2 2
local interstellar medium close to the sun. We with the H I model by Heiles et al. (1981) and
are able to use the H data in modeling the lo- discussed that the two results are consistent
2
cal interstellar medium. In some cases H I can within ∼10 % in spite of their different H I op-
be measure as well in UV. Also, H I measure- ticaldepth. Thereasonforthisagreementisnot
ments at 21cm in line absorption toward radio clarified. The method by Fukui et al. (2015) is
continuum sources provide H I column density based on a simple assumption of uniform in-
(e.g., Heiles & Troland 2003a,b). terstellar medium and may need modification
There remain two issues which were not ad- if realistic non-uniform physical properties of
dressed in Fukui et al. (2014, 2015). One is the interstellar medium are taken into account.
the contribution of the warm neutral medium The real H I observations are, however, limited
(WNM). Because the dust grains are included because we are not able to assess the actual
in the both phases, the cold neutral medium three dimensional physical conditions of the H I
(CNM) and WNM, the H I emission analyzed gas emitting/absorbing 21cm line radiation.
with the Planck data should include the con- A possible solution to overcome the difficulty
tribution of WNM. The other is the possible ef- and to test the above discrepancy is to utilize
fect ofdust evolution foundbyRoy et al.(2013) the results of hydrodynamical numerical sim-
which may require some modification of the lin- ulations of the H I gas (Murray et al. 2015,
ear relationship between N and τ assumed 2016). Recently, three-dimensional hydrody-
Hi 353
by Fukui et al. (2014, 2015). Pioneering studies namical simulations modeled converging H I
by Field (1965) and Field et al. (1969) showed flows and achieved realistic density distribu-
that the interstellar medium consists of the two tions and kinematics with high inhomogene-
phases, CNM and WNM, which are in pres- ity and strong turbulence (Hennebelle et al.
sure equilibrium. H I emission-absorption mea- 2008; Heitsch et al. 2009; Banerjee et al. 2009;
surements were used to constrain H I param- V´azquez-Semadeni et al.2011;Inoue & Inutsuka
eters of CNM and WNM (Dickey et al. 2003; 2012; Kim et al. 2014). These simulations are
Heiles & Troland 2003a,b), where WNM mani- supported by observations of nearby galax-
fests itself as broad line wings of H I emission ies which show turbulent H I gas with den-
profiles. There remains yet an uncertainty in sity of 10–100cm−3 and molecular clouds
4 Fukui et al.
formed from H I gas (Blitz & Rosolowsky 2006; isparalleltothex-axis. TheH Igasflowisinho-
Fukui et al. 1999, 2008, 2009; Kawamura et al. mogeneous andcontinuously enters into thebox
2009; Fukui & Kawamura 2010). from the two opposite boundaries of a cube of
In order to test the method by Fukui et al. (20pc)3. Inthe interface of theconverging flows
(2015) and clarify the cause of the difference turbulence is excited and the magnetic field is
between the emission-absorption and emission amplified. Formation of molecules such as H
2
measurements of H I, in the present paper we formation on dust surfaces and CO formation
examine synthetic H I line profiles by using via CH+ with the effects of self/dust UV shield-
2
thedataofmagnetohydrodynamical(MHD)nu- ing are taken into account and radiative and
merical simulations where the density, temper- collisional heating and atomic and molecular
ature, and velocity of the H I gas are available cooling are incorporated. The simulation data
in three dimensions (Inoue & Inutsuka 2012). are provided as the three dimensional data cube
These simulations deal with converging H I with 5123 uniform pixels1 and each pixel having
flows as a function of time over 10Myrs. The a size of 0.04pc in each axis with the physical
gas is originally H I, while formation of H parameters as listed in Table 2. The simula-
2
molecules is incorporated by using the usual tions are made over a timescale of 10Myrs, ten
dust surface reaction. The results indicate two times the typical crossing timescale of the lo-
phases of H I, CNM and WNM, as well as time- cal H I gas in the solar neighborhood. The to-
dependent transient gaswhich behaves interme- tal gas mass in the numerical domain increases
diately. In the following we call for convenience withtime. Figure1comparesthedistributionof
thegaswithT below300KCNM andthatwith H I column density N and the fraction of H ,
s Hi 2
T above 300K WNM. f = 2N /(2N + N ), where the integra-
s H2 H2 H2 Hi
Thepresent paper isorganizedasfollows; Sec- tion was made for 10pc along the y-axis. Data
tion 2 gives the results of the simulations, Sec- at the four time steps, 0.3, 0.5, 1 and 3Myrs,
tion 3 presents results of synthetic observations are shown (see the physical parameters in Ta-
with discussion and Section 4 describes the spa- ble 3). UV observations of f toward extra-
H2
tial distribution of the H I optical depth with galactic sources (Gillmon et al. 2006) areshown
discussion. In Section 5 we present the conclu- by open circles in each panel and are summa-
sions. rized in Table 4, where the number of observed
sources for f is limited to 19. We did not in-
H2
clude Galactic OB stars which may be contam-
2. RESULTS OF SIMULATIONS
inated by localized gas (Rachford et al. 2002),
2.1. Simulation Data and Model Selection
possibly causing unreliable f values for the
H2
We summarize the relevant physical param- local ISM. The ranges of N and f are con-
Hi H2
eters and symbols in Table 1. We then give sistent with those of the synthetic data points,
a brief explanation of the physical parameters whereas the UV measurements are limited to
and settings of the MHD simulations. More de- N . 1021cm−2. The trend that f increases
H2 H2
tails are found in Inoue & Inutsuka (2012). The with N is consistent with the synthetic data.
Hi
simulations assume converging H I gas flows at Among the four time steps, we find the 0.5-Myr
20kms−1 which are initially in pressure equi-
librium with the standard interstellar H I hav- 1 Inoue & Inutsuka (2012) made the simulations with
ing pressure of pkB−1 = 5.2 × 103Kcm−3. The dividing thenumericaldomaininto10243 pixelsbutthe
x-, y- and z-axes are taken as in Figure 2 of data were provided at a factor-of-two lower resolution
Inoue & Inutsuka (2012) and the flow direction to reduce the data size.
Synthetic Observations of H I Line Profiles 5
Table 1. Summary of Symbols in the Text
Description
T Kinetic temperature of gas
k
τHi, Ts HI optical depth and spin temperature
τabs, Tabs HI optical depth and spin temperature obtained by
Hi s
emission-absorption measurements (Eqs. 10 and 11)
τF , TF HI optical depth and spin temperature derived by applying
Hi s
the method presented by Fukui et al. (2015) (Eqs. 14 and 15)
hT i Density-weighted harmonic mean of T along a line-of-sight (Eq. 16)
s s
Tb Brightness temperature of H I spectrum
WHi Velocity integrated-intensity of HI spectrum
WCNM W produced from CNM with T <300K
Hi Hi k
WWNM W produced from WNM with T > 300K
Hi Hi k
NHi HI column density
Nthin HI column density obtained under assumption of optically-thin H I line (Eq. 1)
Hi
NHT Heiles & Troland (2003a) HI column density
Hi
NHFi HI column density obtained from τ353 applying Equation (18)
with assuming N = 0
H2
MHi Mass of HI
Mthin Mass of HI obtained from Nthin
Hi Hi
Table 2. Summary of the Physical Parameters in the MHD model
Description
n Number densities of atomic/molecular species,
X
X =HI, H2 etc.
pk−1 Thermal pressure of gas, T = pk−1( n )−1
B k B X X
(Vx,Vy,Vz) Velocity vector P
model shows the best presentation of the ob- model. Figure 2 gives histograms of total col-
servations since the fraction of the data points umn density N +2N in the model and that
Hi H2
included within a 95% contour is the largest (14 of the observations by Fukui et al. (2015)2. Fig-
out of 19). We shall use the 0.5-Myr model for ure 3 shows histograms of n +2n and T in
Hi H2 k
the present analysis, whereas we do not exclude
the 1.0-Myr model whose physical parameters 2 Fukui et al. (2015) obtained H I column densities
are not significantly different from the 0.5-Myr assuming a linear relationship NHi ∝ τ353 but we ob-
6 Fukui et al.
Figure 1. (a) Plot of molecular fraction defined as f = 2N /(2N +N ) for total column density
H2 H2 H2 Hi
N +2N at a time step of 0.3Myr. The contours includes 45%, 70% and 95% of data points. The open
Hi H2
circles show the results of direct UV absorption measurements of H by FUSE toward AGNi (summarized
2
in Table 4, 3 out of 19 are not shown due to low f ∼ 10−6). (b)–(d) Same as (a) but at time steps of
H2
0.5Myr, 1Myr, and 3Myr, respectively.
the model. We find that these physical parame- 2.2. Calculations of H I Line Profiles
tershavelargerangescoveringCNMandWNM,
The basic equations in the synthetic obser-
whereas the two phases are not so clear due to
vations are line radiation transfer as given by
intermediate gas formed by the strong turbu-
equations
lent mixing in the model. The molecular gas is
peaked at the densest and coldest regime. Note ǫ (V)
j
I (V)=I (V)exp[−κ (V)∆y]+ {1−exp[−κ (V
that the typical ISM is affected by supernovae j+1 j j κ (V) j
j
with every a few million years and duration of 2ν2
I =B(T ) ∼ 0k T ,
compression(orlifetimeofasupernovashock) is 0 bg c2 B bg
about 1 million years. The ISM compressed by
the converging flows in the 0.5–1.0 Myr seems where I(V) the line intensity, κ(V) opacity,
to be the representative state of the dynamic ǫ(V) emissivity, B(T) the Planck function at
ISM. 21cm, ν = 1.420405751GHz, T = 2.7K the
0 bg
brightness temperature of the background radi-
ation field, c the light velocity and k Boltz-
tained total column densities by applying a nonlinear B
relationship NHi+2NH2 ∝τ315/31.3 (see Section 3.5). mann constant. The subscript j stands for the
j-th cell along a line of sight. The emissivity ǫ
Synthetic Observations of H I Line Profiles 7
Table 3. Physical parameters from the models at different
time steps
Time step M Mthin MHi M MH2
Hi Hi MHthiin H2 MH2+MHi
(Myr) (M⊙) (M⊙) (M⊙)
(1) (2) (3) (4) (5) (6)
0.3 581 508 1.1 4.7 8.1×10−3
0.5 742 634 1.2 20.8 2.7×10−2
(394)a (306)a (1.3)a (18.8)a (4.6×10−2)a
1.0 1052 848 1.2 86.9 7.6×10−2
3.0 1893 1257 1.5 690.8 2.7×10−1
a
The values in the masked region shown in Figure 6(a).
Note— Columns (2): mass of H I gas, (3): mass of HI given
from H I integrated-intensity under optically-thin assump-
tion , (4): ratio of (2) to (3), (5): mass of H gas, (6): mass
2
fraction of H gas.
2
and opacity κ of the 21cm transition at a radial satisfies φ(V)dV = 1,wherem = 1.67262178×
p
velocity V are calculated as follows; 10−24g is the mass of a proton and m =
e
R
hc 9.10938291×10−28g is that of an electron. The
ǫ (V)= n Aφ (V), (4)
j up,j j H I spin temperature T is derived by apply-
4π s
3c3h ing a method by Kim et al. (2014), which gives
κj(V)=8πν2k T nlow,jAφj(V), (5) Ts ∼ Tk in a Tk range from 20 to 3 × 103K.
0 B s,j
For T < 20K, we simply adopt T = T . The
where h and A = 2.8688754×10−15s−1 are the k s k
∼75% of the data pixels have T /T = 0.9–1.0
s k
Planck constant and the Einstein A coefficient,
and the others T /T = 0.8–0.9.
s k
respectively. The number density of H atom in
Figures 4(a)–(d) show H I profiles along a cer-
the lower state is given by
tain line of sight, density n, temperature T ,
k
n
n = Hi,j (6) line-of-sight velocity V and peak opacity κpeak.
low,j y
−hν
3exp 0 +1 An H I line profile is calculated by integrat-
k T
(cid:18) B s,j(cid:19) ing the line transfer Equations (2) and (3) from
and that in the upper state is the far side to the near side of the data cube
along the y-axis seen by the observer over a dis-
n = n −n (7)
up,j Hi,j low,j
tance of 10pc, a half of the full span of the data
for total H I density n . The line shape func-
Hi cube, and the observed brightness temperature
tion
is given by
m +m −(m +m )(V −V )2
p e p e y,j
φ (V) = exp
j
2k T π 2k T
s B s,j (cid:20) B s,j (cid:21) c2
(8) T (V) = I(V) −T . (9)
b 2ν2k bg
0 B
8 Fukui et al.
Table 4. Parameters of the f Estimates
H2
Target l b N τ N +2N f
H2 353 Hi H2 H2
(cm−2) (cm−2)
(1) (2) (3) (4) (5) (6) (7)
3C 249.1 130◦.39 +38◦.55 9.5×1018 2.51×10−6 4.1×1020 4.7×10−2
ESO 141−G55 338◦.18 −26◦.71 2.1×1019 6.38×10−6 8.3×1020 5.0×10−2
H1821+643 94◦.00 +27◦.42 8.1×1017 3.37×10−6 5.1×1020 3.2×10−3
HE 1143−1810 281◦.85 +41◦.71 3.5×1016 2.63×10−6 4.2×1020 1.7×10−4
MRC 2251−178 46◦.20 −61◦.33 3.5×1014 1.23×10−6 2.3×1020 3.0×10−6
Mrk 9 158◦.36 +28◦.75 2.3×1019 3.73×10−6 5.5×1020 8.4×10−2
Mrk 335 108◦.76 −41◦.42 6.8×1018 2.62×10−6 4.2×1020 3.2×10−2
Mrk 509 35◦.97 −29◦.86 7.4×1017 2.33×10−6 3.8×1020 3.9×10−3
Mrk 1383 349◦.22 +55◦.12 2.2×1014 1.55×10−6 2.8×1020 1.6×10−6
Mrk 1513 63◦.67 −29◦.07 2.6×1016 2.57×10−6 4.1×1020 1.3×10−4
MS 0700.7+6338 152◦.47 +25◦.63 5.6×1018 3.21×10−6 4.9×1020 2.3×10−2
NGC 7469 83◦.10 −45◦.47 4.7×1019 5.44×10−6 7.4×1020 1.3×10−1
PG 0804+761 138◦.28 +31◦.03 4.6×1018 2.58×10−6 4.1×1020 2.2×10−2
PG 0844+349 188◦.56 +37◦.97 1.7×1018 2.58×10−6 4.1×1020 8.2×10−3
PG 1211+143 267◦.55 +74◦.32 2.4×1018 1.82×10−6 3.2×1020 1.5×10−2
PG 1302−102 308◦.59 +52◦.16 4.2×1015 2.33×10−6 3.8×1020 2.2×10−5
PKS 0558−504 257◦.96 −28◦.57 2.8×1015 3.00×10−6 4.7×1020 1.2×10−5
PKS 2155−304 17◦.73 −52◦.25 1.5×1014 7.92×10−7 1.7×1020 1.8×10−6
VII Zw 118 151◦.36 +25◦.99 6.9×1018 3.24×10−6 4.9×1020 2.8×10−2
Note— Columns (1): name of target, (2) and (3): position in the Galactic coordinates,
(4): H column density derived with the UV measurements (Gillmon et al. 2006), (5):
2
dust optical depth at 353GHz (Planck Collaboration 2014), (6): total column density
obtained from τ taking into account a nonlinear relationship (see Section 3.5), (7): H
353 2
fraction given by f = 2N /(2N +N ).
H2 H2 H2 Hi
Synthetic Observations of H I Line Profiles 9
Figure 5(c) shows the absorption spectra ob-
tained from the emission-absorption measure-
ment given as,
T (V)−T (V)
1−exp −τabs(V) = b,off b,on ,
Hi T −2.7K
cont
(cid:2) (cid:3) (10)
Figure 5(d) τabs, and Figure 5(e) the spin tem-
Hi
perature profile given as,
T (V)
Tabs(V) = b,off +2.7K, (11)
s 1−exp −τabs(V)
Hi
which are given by(cid:2)the off-so(cid:3)urce brightness
temperature T and on-source brightness
b,off
temperature T ;
b,on
T (V) = [T (V)−2.7K]{1−exp[−τ (V)]},
b,off s Hi
(12)
and
T (V) = [T (V)−T ]{1−exp[−τ (V)]}.
b,on s cont Hi
Figure 2. (a) Mass histograms of total column (13)
density, N + 2N in the 0.5-Myr model. The Here T is the temperature of an assumed
Hi H2 cont
red line represents the contribution of H2 (multi- background compact continuum source. The
plied by a factor of 5). (b) Same as (a) but for the actual observational sensitivity is, however,
observational dataset used in Fukui et al. (2015).
limited by the observational noise levels and
Here the total column densities are given from τ
353 there is an observational lower limit of Tabs
s
(Planck Collaboration2014)bytakingintoaccount
which is usually estimated to be 300–1000K
a nonlinear relationship (see Section 3.5).
(Dickey et al. 2003; Heiles & Troland 2003a,b).
The calculated H I profiles are given in Fig- 3. RESULTS OF THE SYNTHETIC
ure 5(a) for three different directions. Figure
OBSERVATIONS
5(a)shows threeemission line profiles; theblack
3.1. H I emission profiles
solid line is the emission of the whole H I gas,
and the gray-solid and dashed lines give the In Figure 5(a) the H I emission profile consists
of two parts, the narrow component and the
emission fromthe warm gas with T higher than
s
broad wing-like component. The narrow com-
300K and 1000K, respectively. The profiles
ponent is in a velocity range from −5kms−1 to
only from the hot gas are calculated by setting
+5kms−1 and the wing component is extended
the emissivity ǫ of the cold gas equal to 0, while
in a range from −20kms−1 to +20kms−1. The
the opacity κ of the whole gasis held fixed. Fig-
total intensity integrated over velocity gives the
ure 5(b) shows a subtraction of the hot gas pro-
total intensity of the 21cm line emission W .
file higher than 300K from the whole emission Hi
ContributionofWNMisindicatedforT > 300–
profile. s
1000K, where self absorption by CNM is taken
into accounts.
10 Fukui et al.
Figure 3. Mass histograms of (a) total hydrogen density (n +2n ) and (b) kinetic temperature (T )
Hi H2 k
for each pixel in the 0.5-Myr model. The blue-long-dashed lines represents the contribution of H I and the
red-short-dashed lines represent that of H (multiplied by a factor of 5).
2
3.2. H I absorption profiles show that the fraction of WNM in W of the
Hi
narrow component varies from 30% to 70% (cf.,
Absorptionlineprofilesaredeterminedmainly
Figure 5(a) and Table 5).
by CNM whose H I optical depth is gener-
ally large (Figure 5(c)) and they consist of the
3.3. Application of the method by Fukui et al.
narrow component. It is notable that the ob-
(2015)
served solid angle where absorption has been
Once W and N are given, we are able
observed corresponds to a few tens of square Hi Hi
to apply the method presented by Fukui et al.
arc seconds which is much smaller than the
(2015) to the synthetic observations. In the
beam size of the H I emission measurement 4′
(the Arecibo beam), and 33′ (the LAB-survey method, a uniform single layer of H I gas is as-
sumed and the sub-mm dust optical depth is
beam). The spatial power spectrum of the
used as proxy for the total gas column density
H I emission fluctuations (Crovisier & Dickey
on the assumption that the sub-mm dust radi-
1983) affects the variation over one or two beam
ation properties are uniform per proton. The
widths in the emission T (Equation (12)),
b,off
method allows one to solve the two equations
which limits practically the precision of H I
optical depth in absorption in Equation (10). W = TF −T ∆V 1−exp(−τF )
Hi s bg Hi Hi
N of the broad component in emission is cal-
Hi (14)
(cid:0) (cid:1) (cid:2) (cid:3)
culated by the optically thin approximation,
and
though the narrow component is a mixture of
N (cm−2) 1
both CNM and WNM. It is impossible to dis- τF = Hi (15)
Hi 1.823×1018 TF(K)∆V (kms−1)
cern CNM and WNM from a single observed s Hi
intensity at V. This causes an uncertainty in toobtainTFandτF averagedoverthelinewidth
s Hi
the mass of the WNM, and only lower limits of
∆V . Here N and the linewidth ∆V are
Hi Hi Hi
T are given at 300–1000K (Dickey et al. 2003;
s calculated by N = (n ∆y), which is
Hi j Hi,j
Heiles & Troland 2003b). The WNM mass is
an exact value in the model, and ∆V =
Hi
guessed to be ∼60% of that of N , but it is P
Hi W /max[T (V)], respectively. Figures 6(a)–
Hi b
uncertain (Dickey et al. 2003; Heiles & Troland
(d) show two-dimensional distributions of N ,
Hi
2003b). The present synthetic observations W , TF, and τF in the sky.
Hi s Hi