Evolution of OH and CO-dark Molecular Gas Fraction Across a Molecular Cloud Boundary In Taurus

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by  Duo Xu

PreprinttypesetusingLATEXstyleemulateapjv.05/12/14
EVOLUTION OF OH AND CO-DARK MOLECULAR GAS FRACTION ACROSS A MOLECULAR CLOUD
BOUNDARY IN TAURUS
Duo Xu1,2* , Di Li1,3* , Nannan Yue1,2 , Paul F. Goldsmith4
1 NationalAstronomicalObservatories,ChineseAcademyofSciences,A20DatunRoad,ChaoyangDistrict,Beijing100012,China
2 UniversityofChineseAcademyofSciences,Beijing100049,China
3 KeyLaboratoryforRadioAstronomy,ChineseAcademyofSciences
4 JetPropulsionLaboratory,CaliforniaInstituteofTechnology,Pasadena,CA91109,USA
ABSTRACT
6 We present observations of 12CO J=1-0, 13CO J=1-0, HI, and all four ground-state transitions of
1 the hydroxyl (OH) radical toward a sharp boundary region of the Taurus molecular cloud. Based on
0 a PDR model that reproduces CO and [CI] emission from the same region, we modeled the three OH
2 transitions, 1612, 1665, 1667 MHz successfully through escape probability non-LTE radiative transfer
n modelcalculations. We couldnot reproduce the 1720MHz observations, due to un-modeled pumping
a mechanisms, of which the most likely candidate is a C-shock. The abundance of OH and CO-dark
J molecular gas (DMG) are well constrained. The OH abundance [OH]/[H ] decreases from 8×10−7 to
2
3 1×10−7 as Av increases from 0.4 to 2.7 mag, following an empirical law
1
[OH]/[H2]=1.5×10−7+9.0×10−7×exp(−Av/0.81),

]
A which is higher than PDR model predictions for low extinction regions by a factor of 80. The over-
abundance of OH at extinctions at or below 1 mag is likely the result of a C-shock. The dark gas
G
fraction (DGF, defined as fraction of molecular gas without detectable CO emission) decreases from
. 80% to 20%, following a gaussian profile
h
p
- DGF=0.90×exp(−(Av0−.701.79)2).
o
r This trend of the DGF is consistent with our understanding that the DGF drops at low visual ex-
t tinction due to photodissociation of H and drops at high visual extinction due to CO formation.
s 2
a The DGF peaks in the extinction range where H has already formed and achieved self-shielding
2
[ but 12CO has not. Two narrow velocity components with a peak-to-peak spacing of ∼ 1 km s−1

were clearly identified. Their relative intensity and variation in space and frequency suggest colliding
1
streams or gas flows at the boundary region.
v
5 Subject headings: ISM: clouds – ISM: individual objects (Taurus) – ISM: molecules – ISM: evolution
6
1
3 1. INTRODUCTION (Medling et al. 2015) and “C-shocks” (Anderl et al.
0 The formation of molecular hydrogen is a critical step 2013). Shock waves play a major role in the ISM
1. in the transformation of interstellar gas into new stars. (Timmermann 1998). When shock waves propagate
through the molecular ISM the ambient gas is com-
0 Variouscomplexprocessesinthetransformationbetween
pressed, heated, andaccelerated. Furthermore, thecom-
6 atomic gas and molecular gas result in changes of the
position of the gas is significantly changed when chem-
1 physical state of gas. These changes affect the star for-
ical reactions occur especially in the warm shocked gas
: mation process in galaxies, and thus their evolution. It
v located in outermost parts of the transition region. The
isofgreatsignificancetostudythephysicalconditionsin
i abundance of OH can vary from 10−5 to 10−11 when a
X regions where the transformation between atomic gases
10 km s−1 C-type shock propagates into a diffuse cloud
and molecular gases occurs. The boundaries of molecu-
r with n =50 cm−3 (Draine & Katz 1986). Thus, search-
a lar clouds are locations where the chemical composition H
ingfortheevidenceofshocksattheboundaryregionvia
changes considerably and primarily atomic gas trans-
OH lines is of great significance.
forms into molecular gas.
The boundary of molecular clouds is the region where
Apart from traditional tracers such as CO and HI, the
all the physical and chemical processes mentioned above
hydroxylradical,OH,isthoughttobeanexcellenttracer
take place. As the dramatic changes of species at the
to determine the physical conditions of the early state
boundaries, the physical conditions at the boundaries
ISM, where CO is absent (Li et al. 2015). Such early
are distinct from those in other places. A clear example
state molecular ISM appears in boundary regions. A
of cloud boundaries can be found in Taurus (Goldsmith
three-waycomparisonofHI,OHandCOlinesisexpected
et al. 2008) north east of the TMC1 region. Orr et al.
to show molecular features in OH which are not traced
(2014) compared the observations of Taurus boundaries
by CO, but which highlight the transition from atomic
withlineintensitiesproducedbytheMeudonPDRcode.
gas (seen in the HI line) to molecular gas. They found a low ratio of 12C to 13C ∼ 43, and a highly
Additionally, OH can be the tracer of “J-shocks”
depleted sulfur abundance (by a factor ≥50) to explain
*Email: [email protected],[email protected] the very low [CI] emission. Moreover, Goldsmith et al.
2 Duo Xu. et al.
(2010)foundanunexpectedlyhighdegreeofexcitationof al. 2011). GALFA-HIusesALFA,aseven-beamarrayof
the H in the boundary layer of Taurus molecular cloud. receiversmountedatthefocalplaneofthe305mArecibo
2
Theybelievedthatanenhancedheatingratemaybethe telescope,tomapHIemissionintheGalaxy. GALFA-HI
result of turbulent dissipation. is a survey of the Galactic interstellar medium in the 21
As we are interested in the changes of chemical com- cm line hyperfine transition of neutral hydrogen which
position across the boundaries to study the transition covers a large-area (13,000 deg2) with ∼ 4(cid:48) resolution,
between atomic- and molecular-dominated gas,we need andhashighspectralresolution(0.18kms−1)withbroad
to find a boundary of molecular clouds without signifi- velocitycoverage(−700kms−1 <v <+700kms−1).
LSR
cantUVenhancement. H2 canbedestroyedbyUVpho- Typical RMS noise is 80 mK in a 1 km s−1 channel.
tons, making the statistical equilibrium function com-
plex. Moreover, it is easier to detect the emission of 2.3. 12CO and 13CO Data
molecular tracers such as OH without an enhanced UV The 12CO J=1-0 and 13CO J=1-0 observations were
field. We thus observed the Taurus boundary studied by
taken simultaneously between 2003 and 2005 using the
Goldsmith et al. (2010) and Orr et al. (2014), which has
13.7 m Five College Radio Astronomy Observatory
a relatively low UV field between χ=0.3 and 0.8 in units
(FCRAO) Telescope (Narayanan et al. 2008). The map
of the Draine’s field (Flagey et al. 2009; Pineda et al.
is centered at α(2000.0) = 04h32m44.6s, δ(2000.0) =
2010) and little foreground or background visual extinc-
24◦25(cid:48)13.08(cid:48)(cid:48),withanareaof∼98deg2. Themainbeam
tion (Padoan et al. 2002), making it favorable for the
oftheantennapatternhadafull-widthtohalf-maximum
comparison of observations with physical models.
(FWHM)beam-widthof45(cid:48)(cid:48)for12CO,and47(cid:48)(cid:48)for13CO.
WehavecarriedoutobservationsoftheTaurusbound-
The angular spacing (pixel size) of the resampled on the
ary in four OH transitions (1612, 1665, 1667, and 1720
fly(OTF)datais20”(Goldsmithetal. 2008),whichcor-
MHz) using the 305 m Arecibo Telescope. We made a
respondstoaphysicalscaleof≈0.014pcatadistanceof
total of five cuts across the boundary region each with
D =140pc. Thedatahaveameanrmsantennatemper-
17pointings3arcminuteapart(Fig.1). Wedescribethe
ature of 0.28 K and 0.125 K, in channels of 0.26 km s−1
observations of OH across the boundary region, and the
HI, 12CO J=1-0, and 13CO J=1-0 map of Taurus molec- and 0.27 km s−1 width for 12CO and13CO, respectively.
ular cloud in Section 2. We analyze the OH spectrum 3. ANALYSIS
and derive the physical parameters of 13CO across the
3.1. Spectral Analysis
boundary in Section 3. We use a cylindrical model and
RADEXtofitOHlinestodeterminethephysicalparam- The locations of the positions for the telescope point-
eters in Section 4. We discusse the conjugate emission ing used to study the TBR are shown in Fig. 1. To
of OH and pumping mechanisms in Section 5. In Sec- examine the transition zone with higher signal to noise
tion 6, we summarize our results and conclusions from ratio, we averaged all five cuts of spectra of OH 1612
this study. MHz, 1665 MHz, 1667 MHz, 1720 MHz, 12CO J=1-0,
13COJ=1-0,andHI,asshowninFig.2. The12COJ=1-
2. OBSERVATIONSANDDATA 0 and 13CO J=1-0 spectra were convolved to the OH
beam size of 3(cid:48) at each position. The emission lines of
We carried out observations of OH with the Arecibo
OH, 12CO J=1-0, 13CO J=1-0, and the absorption lines
Telescope in Project a2813. We extracted HI data from
the GALFA-HI survey, and extracted 12CO J=1-0 and of HI are well matched in velocity. Especially, the emis-
13CO J=1-0 data from the FCRAO Taurus survey. sion lines of OH 1665 MHz at positions 10 to 12 all have
twocomponents,andthespectralofHIatthesamepoint
have two corresponding narrow absorption components,
2.1. OH Observations
as shown in Fig. 3.
TheOHobservationsweretakenusingtheL-bandwide
We did gaussian fitting of the OH 1612 MHz, 1665
receiver (with frequency range 1.55-1.82 GHz) on Octo-
MHz, 1667 MHz, 1720 MHz spectral with two gaussian
ber28-31,2013. WeobservedfourOHtransitionlinesat components, the fitting of 12CO and 13CO spectra with
the rest frequencies of 1612.231, 1665.402, 1667.359, and
asinglegaussiancomponent,andthefittingofHIspectra
1720.530 MHz with the total power ON mode. Spec-
with three gaussian components. We show the spectra
tra were obtained with the Arecibo WAPP correlator
and the fitted profiles in Fig. 2. The line ratio between
with nine-level sampling and 4096 spectral channels for
OH 1665 MHz and 1667 MHz is greater than 1 in the
each line in each polarization. The spectral bandwidth
outside TBR region (TBR-O) as shown in Fig. 2. Under
was 3.13 MHz for a channel spacing of about 763 Hz,
theassumptionofLTE,thelineratiobetween1665MHz
or 0.142 km s−1. The average system temperature was
and1667MHzrangesfrom0.6to1. Thelineratiogreater
about31K.Themainbeamoftheantennapatternhada
than 1 indicates a deviation from LTE for OH.
full-width at half-maximum (FWHM) beam-width of 3(cid:48).
We show the change of peak intensity of two compo-
Spectra were taken at 17×5 positions across the Taurus nents in OH 1665 MHz and a single component in 13CO
boundary region (TBR), as seen in Fig. 1. An integra-
across the TBR in Fig. 4. Component 1 of OH 1665
tion time of 300 seconds per position was used resulting MHz spectrum at 5.3 km s−1 appears after position 4,
in an RMS noise level of about 0.027 K.
and gets stronger across the TBR. Component 2 at 6.8
kms−1appearsintheTBR-Oandgetsfaintintheinside
2.2. HI Data TBR region (TBR-I), and disappears after position 13.
HI 21 cm observations of the Taurus boundary region The central velocities of 13CO shift from 6.3 km s−1 to
were extracted from the results of the Galactic Arecibo 5.7 km s−1. We assume that each component of the
L-Band Feed Array HI (GALFA-HI ) survey (Peek et OH emission indicates a gas stream. When the intensity
Evolution of OH and CO-dark Molecular Gas Fraction Across a Molecular Cloud Boundary in Taurus 3
12
T
T
B B
R
- R
O
8
T
B
R
-
I
T
L
B
4
0
Fig. 1.— The boundary region in 13CO J=1-0 peak intensity, with observed positions indicated. The size of circle indicates the OH
beamsize∼3(cid:48). Thenumbersofpositionsareshowninthefigure. ThewholeregionisTaurusboundaryregionandisdenotedTBR.The
Taurus linear boundary (TLB) located at position 9 is shown as red line. The outside and inside region of the TBR are abbreviated as
TBR-OandTBR-Irespectively. ThepeakintensityoftwolowestrotationaltransitionsofH2,S(0)andS(1),islocatedbetweenposition6
andposition7(Goldsmithetal. 2010). ThepeakcolumndensityofH2 islocatedbetweenposition12andposition13. Thepeakcolumn
densityof13COislocatedatposition13. Thearrowinthefigureindicatesthedirectionwepresentspectrallinemaps.
of OH component 2 is stronger than that of component entamountsof13COemissionatdifferentvelocities. Not
1 in TBR-O, the central velocity of 13CO is located at only OH 1665 MHz but also 13CO shows the central ve-
6.3 km s−1. When the intensity of OH component 1 is locity shifting after the streams collide from position 10
strongerthanthatofcomponent2inTBR-I,thecentral to position 13 in Fig. 3.
velocity of 13CO is located at 5.7 km s−1. The central We show the change of line width along the cut direc-
velocityof13COshiftsinthesamewayasthecentralve- tion in Fig. 5. We can clearly see that the line width of
locity of stronger intensity OH component shifts. From 12CO and 13CO peak at the TLB. This mainly due to
Fig. 3 we see that component 2 of OH 1665 gradually the two gas streams which contribute to the line width
becomes fainter, and disappears at position 13. At the of 12CO and 13CO. The line width of OH 1667 MHz is
same time the central velocity of component 1 gradu- much wider than that of other lines in TBR-O. This is
ally shifts from 5.3 km s−1 at position 9 to 5.8 km s−1 mainly caused by the weak emission lines of OH 1667
at position 13, which indicates that the collision of two MHz in TBR-O. Since the height of OH 1667 MHz is
streamsresultsinthefinalcentralvelocitybeinglocated small in TBR-O, the fitted gaussian profile tends to be
between the velocities of the two components. The cen- flatter than that at other positions. So the line width of
tralvelocityofthefinalcombinedstreamislocatedcloser OH 1667 MHz is two times wider than that of the other
to component 1, which has a stronger emission line in three lines in TBR-O. Component 2 of OH 1667 MHz
TBR-I. This is consistent with the assumption of differ- whose central velocity is at 6.8 km s−1 is very weak in
4 Duo Xu. et al.
TBR-O
TLB
TBR-I
Fig. 2.—AveragespectraofallfivecutsofOH1612MHz,1665MHz,1667MHz,1720MHz,12COJ=1-0,13COJ=1-0,andHIoverlaid
with corresponding fitted gaussian profile(red curve). The 12CO J=1-0 and 13CO J=1-0 spectra were convolved to the OH beam size of
3(cid:48) at each position. We fitted the OH 1612 MHz, 1665 MHz, 1667 MHz, 1720 MHz spectra with two gaussian components, fitted the
12CO J=1-0 and 13CO J=1-0 spectra with single gaussian component, and fitted the HI spectra with three gaussian components. The
verticaldashedlinesindicatethecentralvelocitiesofthetwocomponentsofOH1665MHzatposition10.
Evolution of OH and CO-dark Molecular Gas Fraction Across a Molecular Cloud Boundary in Taurus 5
Fig. 3.— Average spectra of all five cuts of OH 1612 MHz, 1665 MHz, 1667 MHz, 1720 MHz, 12CO J=1-0, 13CO J=1-0, and HI at
positions 8 to 13. The 12CO J=1-0 and 13CO J=1-0 spectra were convolved to the OH beam size of 3(cid:48) at each position. The vertical
dashedlinesindicatethecentralvelocitiesofthetwocomponentsofOH1665MHzatposition10.
6 Duo Xu. et al.
0.5
T
B
R-I
0.4
T
L
B
T
BR- 0.2
O
0.0
Fig. 4.— Change of peak intensity of the two components of OH 1665 and the single component of 13CO across the TBR. The upper
stripeindicatestheintensityofcomponent2inOH1665MHzacrosstheTBR.Themiddleobliquestripeindicatestheintensityof13CO.
Thebottomstripeindicatestheintensityofcomponent1inOH1665MHzacrosstheTBR.Thecolorindicatesthevalueofpeakintensity
ofeachspectrumateachposition. Thepeakintensityof13CO shownintheobliquestripeisonefourthoftheobservedpeakintensity. A
moredetaileddiscussionisinSection3.1.
somepositionsinTBR-I,whichleadstoawiderlinewing
of the component 1, as shown in Fig. 2. The width of
component 2 in TBR-I is wider than that of other three
lines in TBR-I, which leads to the average line width of
OH 1667 behaving in an erratic way. The line width of
OH 1665 MHz is nearly constant across the TBR.
The line width of 12CO is significantly greater than
that of 13CO. Opacity may be one of the reasons. Ow-
ing to the different abundance of 12CO and 13CO, τ
12
is almost 70 times larger than τ . When τ is much
13 12
larger than unity, the term 1-exp[−τ φ(∆v)] in the line
12
profile of 12CO is much wider than that of 13CO, where
φ(∆v)isagaussianprofileofthevelocityoffsetfromline
center ∆v. We made an estimate of the line width ra-
tio between 12CO and 13CO only considering the opac-
ity. In TBR-O, the optical depth range from 0.05 to
0.4. We took position 8 having τ =0.2 as an exam-
13CO
ple. Thelinewidthratiobetween12COand13COis1.4,
Fig. 5.—ThechangeoflinewidthofOH1665MHz,1667MHz,
which is much less than the observed ratio 2.3. Other 12CO J=1-0 and 13CO J=1-0 along the cut direction shown in
broadening mechanisms must occur in the TBR. Park Fig.1.
& Hong (1995) took different broadening mechanisms
suchasmicro-turbulenceandmacro-turbulenceintocon- description of the OH spectra and components across
sideration and found that the line width ratio between TBR can be found in Table 1.
12CO and 13CO can range from 1 to 3 depending on
thephysicalconditionofthegas, whichjustcorresponds 3.2. 13CO Column Density Calculation
to the line width ratio between 12CO and 13CO in our Fromthefittingresultof12COJ=1-0and13COJ=1-0
work. The wider line width of 12CO may be the result above,wecancalculatethecolumndensityof13CO.The
of larger turbulence due to the more extended distribu- column density of 13CO in the upper-level (J = 1) can
tion of 12CO. According to Larson’s law (Larson 1981),
be written as
alargerscaleofamolecularcloudleadstoalargerveloc-
ity dispersion. Consideringcurrent geometricalmodelof 8πkν2 (cid:90)
N = T (V)dV , (1)
photo-dissociation region (Tielens 2005), the larger self- u,13CO hc3A b
ul
shieldingthresholdof13COmakesitmoreconstrainedto
where k is Boltzmann’s constant, h is Planck’s constant,
theinnerregionoftheboundary,whichyieldsanarrower
line width than that of 12CO. c is the speed of light, Aul is the spontaneous decay rate
from the upper level to the lower level, and T is the
Wecanalsoseethecentralvelocitiesofcomponent1in b
OH1665MHzshiftingfrom5.3kms−1 to6.0kms−1 at brightness temperature. A convenient form of this equa-
tion is
positions 10-12 in Fig. 3. This velocity gradient may be
caused by colliding streams or gas flow at the TLB. The (cid:18)N (cid:19) (cid:90) (cid:18)T (cid:19) (cid:18) V (cid:19)
u,13CO =3.6×1014 b d . (2)
cm−2 K km s−1
Evolution of OH and CO-dark Molecular Gas Fraction Across a Molecular Cloud Boundary in Taurus 7
TABLE 1
The change of OH spectral lines across the boundary in Taurus
Position Offset OHspectrallines
ID ((cid:48) ) 1612MHz 1665MHz 1667MHz 1720MHz
C11 C22 C1 C2 C1 C2 C1 C2
1(outer) -24.0 we∗3 a6 n e n we n we
7(IH2peak) -6.0 we a n e we we n e
9(boundary) 0.0 e4 wa7 e e e we a e
11(NH2 peak) 6.0 e(→5) n8 e(→) e e(→) we a(→) we
12(NCO peak) 9.0 e(→) n e(→) we e(→) n a(→) n
17(inner) 24.0 e(→) n e(→) n e(→) n a(→) n
1 C1meansthecomponentat5.3kms−1. 5 →meanstheshiftingofcentralvelocityofcomponent1.
2 C2meansthecomponentat6.8kms−1. 6 ameansabsorption.
3 wemeansweakemission. 7 wameansweakabsorption.
4 emeansemission. 8 nmeansneitheremissionnorabsorption.
The total 13CO column density N is related to the by solving the following equation
tot
upper level column density N through (Li 2002)
u (cid:34) (cid:35)
hν 1 1
N =f f f N . (3) T = − , (9)
tot,13CO u τ b u,13CO max k ekhTνex −1 ekhTνbg −1
In the equation above, the level correction factor f can
u
be calculated analytically under the assumption of local where h, k and ν are Planck’s constant, Boltzmann’s
thermal equilibrium (LTE) as constant, and the central frequency of 12CO J = 1 → 0
line (115.27 GHz), respectively.
Q(T )
f = ex , (4) To examine the LTE assumption when calculating
u (cid:16) (cid:17)
g exp − hν the physical parameters of CO, we used a spherical 1-
u kTex d non-LTE spectral analysis radiative transfer model,
RADEX (van der Tak et al. 2007) to derive the exci-
where g is the statistical weight of the upper-level. T
is the euxcitation temperature and Q(T ) = kT /hBex tationtemperatureof12COand13CO.Wetookposition
ex ex 0
istheLTEpartitionfunction, whereB istherotational 10 as an example. We assumed the number density of
constant(Tennyson2005). Aconvenien0tformoftheLTE H2 to be 400 cm−3, which is given by Orr et al. (2014).
partitionfunctionisQ(T )≈T /2.76K. Thecorrection We also assumed the kinetic temperature to be 15 K,
ex ex
factor for opacity is defined as which is widely applied in the relatively diffuse region in
theTaurusmolecularcloud(e.g. Goldsmithetal. 2008).
(cid:82)
τ13dv The resulting excitation temperature of 12CO and 13CO
fτ = (cid:82)(1−e−τ13)dv , (5) are Tex,12co = 7.7 K and Tex,13co = 6.8 K, with a differ-
ence of about 10%. The assumption that the excitation
and the correction for the background temperaturesof12COand13COareequalseemsreason-
able. Owing to the difference of excitation temperature
(cid:34) ekhTνex −1(cid:35)−1 between 12CO and 13CO, the derived column density of
fb = 1− hν , (6) 13CO also has an error about 10%.
ekTbg −1 Weshowthechangeofexcitationtemperatureof13CO
where τ is the opacity of the 13CO transition and T and the change of column density of 13CO along the cut
13 bg direction in Table 2 and Fig. 6. The excitation temper-
is the background temperature, assumed to be 2.7K.
The 13CO opacity is estimated as follows. Assuming ature Tex of 13CO increases crossing the boundary. The
column density of 13CO shows a peakat position 13 and
equal excitation temperatures for the two isotopologues,
the ratio of the brightness temperature of 12CO to that 14 inside the boundary.
of 13CO can be written as
4. SIMULATIONOFOHEMISSIONLINEWITHRADEX
Tb,12 = 1−e−τ12 . (7) We assume a cylindrical geometry to model the linear
Tb,13 1−e−τ13 boundary region of the cloud. We adopted the results
of “cylindricalized” Meudon PDR model by Orr et al.
Assuming τ (cid:29) 1, the opacity of 13CO can be written
12 (2014)andappliedaspherical1-dnon-LTEspectraanal-
as
ysis radiative transfer model, RADEX (van der Tak et
(cid:18) (cid:19)
T
τ =−ln 1− b,13 . (8) al. 2007), to generate a sky-plane image of the TBR for
13 Tb,12 the transitions of OH.
The excitation temperature T is obtained from the
12CO intensity. First, the maxeximum intensity in the 4.1. Density Profile of Taurus Boundary Region
spectrum of each pixel is found. This quantity is de- We modeled the linear boundary as a cylinder with
notedbyT . Theexcitationtemperatureiscalculated a radius-dependent H volume density structure of the
max 2
8 Duo Xu. et al.
RADEX takes the following inputs: kinetic temper-
ature (T ), density of H (n ), H ortho-to-para ra-
k 2 H2 2
tio (OPR), background temperature (T ), column den-
bg
sity of OH (N ), and line width (∆v ). Rates for
OH OH
collisional excitation of OH are taken from Offer et al.
(1994).
The n is an input parameter estimated based on
H2
the cylindrical model in Orr et al. (2014). The Galac-
tic background emission is estimated to be about 0.8 K
by extrapolating the standard interstellar radiation field
(ISRF) to L band (Winnberg et al. 1980). T =3.5 K is
bg
thus used in the simulation.
WevarytheT ,H OPRandN tofindtheoptimum
k 2 OH
modelbyminimizingχ2 forthefourOHlines,definedas
χ2 = 1 (cid:88)N (Imodeli −Iobsi)2, (11)
N σ2
Fig. 6.— The change of column density of 13CO along the cut i=1 obsi
direction.
where I are the four observed OH lines’ instensities,
obs
I arethemodellinegeneratedbyRADEX,σ2 are
TABLE 2 thmeodRelMS of the four observed OH lines. obs
parameters along the boundary
We varied T , OPR and N to obtain the best fit
k OH
position Tex,13co N13co to the observation at position 1, shown in Fig. 7. The
(K) (1014cm−2) best fitting T , OPR and N are 31 K, 0.2 and 3.7×
k OH
1 6.5 2.5 1014 cm−2, respectively. We also calculated the column
2 6.3 2.3 densityofOHatposition1(assumingittobeopticalthin
3 5.9 2.8 and with no background emission) from the integrated
4 5.8 3.1 intensity (in K km s−1) of the 1667 MHz line through
5 5.6 3.2
(e.g. Knapp & Kerr 1973; Turner & Heiles 1971)
6 5.6 4.0
7 6.3 5.6 (cid:82)
N T (V)dV
8 6.3 5.6 OH =2.22×1014 b . (12)
9 6.9 13 cm−2 K km s−1
10 7.6 39 With these assumptions, N is 0.5×1014 cm−2. When
11 7.8 33 OH
theexcitationtemperatureofOHissolowthattheback-
12 7.7 42
ground cannot be neglected, we have a correction factor
13 7.6 59
14 8.5 58 fbg (e.g. Harju et al. 2000; Suutarinen et al. 2011)
15 8.5 34
1
16 8.0 20 f = . (13)
17 8.5 23 bg 1−Tbg/Tex
When T (cid:39) 3.5 K and T (cid:39) 4 K, f (cid:39) 8, which yields
following form (King 1962), bg ex bg
N (cid:39)4×1014 cm−2,almostthesameasthefittedN
OH OH
(cid:26)n a2/(r2+a2) :r ≤R from RADEX (denoted NRADEX). The problem with
n (r)= c . (10) OH
H2 0 :r >R using the “LTE method” is that we do not know the ex-
citation temperature of OH. Instead, we have to assume
ThisfunctionalformwasusedinanalysisoftheTaurus an excitation temperature for OH, which has a major
region by Pineda et al. (2010). effect on the correction factor f . Only with a statisti-
bg
This profile has a flat high-density center, which then cal equilibrium calculation (e.g. RADEX) can we know
transitions to a region of power-law decay, and finally, the excitation temperature of OH exactly. We should be
at a truncating radius, the density is set to zero. It as- cautious about the low excitation temperature of OH,
sumes only three parameters, the central core density otherwise we may underestimate the column density of
nc, a parameter characterizing the width of the central OH by a factor of 8 or more in many conditions where
core a, and the truncating radius R. Orr et al. (2014) the LTE method is used.
fitted the profile with visual extinction data for this re- ComparedwithNRADEX,thecalculatedN through
OH OH
gion. Thefittedvaluesforthedensityprofileparameters Eq.12andEq.13(notedasNLTE representingthe“LTE
are n =626 cm−3, a=0.457 pc, and R=1.80 pc. The OH
c method”) is almost the same as NRADEX. The fitted
axisofthecylindricaldistributioniscentered11.5(cid:48) tothe OH
opacity(Table3)basedonthemodelisrelativelysmaller
southwest of the boundary position between position 12
(τ ∼ 0.04-0.3), which is consistent with the assumption
and position 13.
of optical thin in the “LTE method”.
TheH volumedensityof17observedpointsalongthe
2 Eq.12usedtocalculateN assumesLTE,buttheob-
boundary is obtained from Orr et al. (2014). OH
served line ratio between OH 1665 MHz and 1667 MHz
is obviously greater than 1, indicating that the OH at
4.2. RADEX Fitting Results
position 1 is far from LTE. The critical density of OH
Evolution of OH and CO-dark Molecular Gas Fraction Across a Molecular Cloud Boundary in Taurus 9
Fig. 7.—ObservedOHlines(blacklines)andthesimulatedOHprofiles(redlines)usingRADEXatposition1.
TABLE 3 TABLE 4
OH physical parameters at position 1 OH parameters along the boundary
nH2=62.6 cm−3 OPR=0.20 Tk=31.0K position Ratio(1665/1667) Intensity(1667)
NOH=3.7×1014cm−2 (Kkms−1)
line Tex τ TA 1 1.6±0.18 0.21±0.02
(K) (K) 2 1.2±0.14 0.20±0.02
1612 3.1 0.045 -0.025 3 1.3±0.13 0.22±0.02
1665 4.1 0.163 0.098 4 1.2± 0.12 0.24±0.02
1667 3.8 0.331 0.062 5 1.5±0.14 0.29±0.02
1720 5.4 0.024 0.055 6 1.6±0.13 0.26±0.02
7 1.3±0.10 0.35±0.02
HFS lines at 10-50 K is 1-20 cm−3, indicating that OH 8 1.2±0.08 0.31±0.02
9 1.1±0.05 0.42±0.02
excitation is dominated by collision in TBR with n=70-
10 0.51±0.02 0.49±0.01
600 cm−3. Compared with OH, low-J 12CO lines have a
11 0.54±0.02 0.53±0.02
larger critical density about 2000 cm−3. In most cases,
12 0.52±0.02 0.50±0.01
whencollisiondominatetheexcitation,theLTEassump- 13 0.61±0.02 0.49±0.01
tion is reasonable. Surprisingly, OH HFS lines are far 14 0.69±0.02 0.48±0.01
from LTE, which has a low critical density. 12CO is con- 15 0.72±0.02 0.42±0.01
sistentwithLTEasdiscussedinSection3.2withRADEX 16 0.77±0.03 0.40±0.01
analysis. ConsideringforthecomplexenergylevelofOH, 17 0.83±0.04 0.37±0.01
somepumpingmechanismmustbeoperativetoyieldthe
non-LTE of OH. We will have a detailed discussion in
4.4. Physical Parameter Analysis
Section 5. A most possible mechanism is C-shock. The
line ratio between 1665 MHz and 1667 MHz, and the in- We define the CO-dark molecular gas fraction or dark
tegrated intensity of 1667 MHz across the boundary are gas fraction (DGF) as
listedinTable4. InTBR-O,thelineratioisgreaterthan
N ×104
1. In TBR-I, the line ratio is between (cid:39) 0.5 and (cid:39) 0.8, DGF=1− CO , (14)
within the range allowed by LTE. N
H2
Thechangeofphysicalparametersacrosstheboundary
whichrepresentsthefractionofH thatcannotbetraced
is partially listed in Table 5. 2
by CO emission. N is obtained from the LTE calcu-
CO
lation in Section 3.2 with the assumption that the abun-
4.3. The Effect of the H Ortho-to-Para Ratio (OPR)
2 dance ratio of 12CO to 13CO is 65 (Langer & Penzias
on Fitting
1993; Liszt 2007). N is obtained from integration
Owing to the different cross sections between OH and of the density profile inH2Section 4.1 alone line of sight
two spin symmetries of H2, i.e. ortho-H2 and para-H2 and the visual extinction is obtained from the relation
(Offer et al. 1994), the OPR plays a significant role in N(H )/A =9.4×1020 cm−2 mag−1, by assuming that
2 V
the excitation of OH. The exact value of OPR is impor- the hydrogen is predominately in molecular form and
tant for producing the observed OH 1665/1667 intensity standard grain properties are appropriate for the diffuse
ratioincertainpositions,suchasforposition9,asshown ISM (Orr et al. 2014). We averaged the column density
in Fig. 8. Overall, the derived column density is insensi- of H within the OH beam size (∼ 3(cid:48)) at each position
2
tive to the numerical value of OPR, such as for position to make all the calculations refer to the same beam size.
10, as shown in Fig. 8. We will discuss this issue in a The variation of T , N , N /N and DGF across
separate paper and focus on the dark gas and OH abun- the boundary as a fkunctOioHn ofOeHxtincHt2ion A is shown in
v
dance content in the present work. Fig. 9. When the extinction A increases from 0.4 to 2.6
v
10 Duo Xu. et al.
TABLE 5
The change of physical parameters across the boundary in Taurus
Position Offset PhysicalParameters
ID ((cid:48) ) Tk (K) NOH (1014 cm−2) Av (mag) NOH/NH2 (10−7) DGF1
C1 C2 C1 C2
1(outer) -24.0 – 37 – 2.9 0.4 7.2+3 0.75+0.1
−2 −0.1
7(IH2peak) -6.0 25 35 2.9 1.3 1.3 3.5+−00..73 0.70+−00..11
9(boundary) 0.0 26 32 1.5 4.9 1.8 3.7+0.4 0.13+0.2
−0.2 −0.3
11(NH2 peak) 6.0 10 27 1.5 4.5 2.4 2.6+−00..53 0.03+−00..24
12(NCO peak) 9.0 23 26 2.1 2.5 2.6 1.9+−00..42 0.07+−00..24
17(inner) 24.0 24 – 3.3 – 1.5 2.3+0.5 0.12+0.2
−0.3 −0.3
1 DGFmeansdarkgasfraction.
known caveats. In other words, we may seriously under-
estimatetheamountofmoleculargasthrough“X-factor”
in low extinction clouds or regions of galaxies.
Fig. 9.— The change of Tk, NOH, NOH/NH2 and DGF across
theboundaryasafunctionoftheextinctionAv.
We parametrize the trend of N /N and DGF in
OH H2
an exponential law and a gaussian profile, respectively,
asshowninFig.10. ThetrendofN /N canbefitted
OH H2
as
N A
OH =1.5×10−7+0.9×10−7×exp(− v ). (15)
N 0.81
H2
Whenthevisualextinctionismuchlargerthan0.48mag,
N /N remains roughly a constant 1.5×10−7. This
Fig. 8.—Theprobabilityspaceofeachparameteratposition9 coOnHstanHt2indicates the abundance of OH at large visual
(top panel) and position 12 (bottom panel). In the contour map
extinctions within molecular clouds. A calculation using
of probability space of two different parameters, different shades
representdifferentconfidencelevels. Thedotrepresentstheχ2 the Meudon PDR Code (Le Petit et al. 2006) with con-
min
fittedparameter,andthetrianglerepresentsthemeanvalueofthe ditions appropriate for the TBR yields reasonably good
parameterbyintegratingtheparameterinprobabilityspace. agreement with OH abundance [OH]/[H ] for moderate
2
extinction (A ∼ 2). The prediction of [OH]/[H ] at ex-
v 2
magnitudes, the kinetic temperature, the abundance of tinctions at or below 1 mag is far lower (by a factor of
OH and the dark gas fraction all decrease. Especially, 80)thatwederive,suggestingthattheremaybeanaddi-
the DGF decreases from 80% to 20%, which means the tional channel of OH production active, possibly due to
amount of molecular gas that cannot be traced by CO is theshock(e.g. Draine&Katz1986)producedbythecol-
three times larger than that of molecular gas traced by lidingstreams. Whenshockwavespropagatethroughthe
CO when the extinction is below 1.4 magnitude. Empir- molecular ISM the ambient gas is compressed, heated,
ically, CO intensities have been used as an indicator of and accelerated. When temperature is above 300 K, the
the total molecular mass in the Milky way and in galax- neutral-neutral reactions become important, which yield
iesthroughtheso-called“X-factor”withnumerouswell- the overabundance of OH (Neufeld et al. 2002).