# Large–Scale Structure of the Molecular Gas in Taurus Revealed by High Linear
Dynamic Range Spectral Line Mapping

Paul F. Goldsmith11affiliation: Jet Propulsion Laboratory, California
Institute of Technology, 4800 Oak Grove Drive, Pasadena CA,
<EMAIL_ADDRESS>, Mark Heyer22affiliation: FCRAO, Department of
Astronomy, University of Massachusetts, Amherst MA , Gopal
Narayanan22affiliation: FCRAO, Department of Astronomy, University of
Massachusetts, Amherst MA , Ronald Snell22affiliation: FCRAO, Department of
Astronomy, University of Massachusetts, Amherst MA , Di Li33affiliation: Jet
Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove
Drive, Pasadena CA , and Chris Brunt44affiliation: University of Exeter

###### Abstract

We report the results of a 100 square degree survey of the Taurus Molecular
Cloud region in the J = 1 $\rightarrow$ 0 transition of 12CO and of 13CO. The
image of the cloud in each velocity channel includes $\simeq$ 3$\times$106
Nyquist- sampled pixels, sampled on a 20′′ grid. The high sensitivity and
large linear dynamic range of the maps in both isotopologues reveal a very
complex, highly structured cloud morphology. There are large scale correlated
structures evident in 13CO emission having very fine dimensions, including
filaments, cavities, and rings. The 12CO emission shows a quite different
structure, with particularly complex interfaces between regions of greater and
smaller column density defining the boundaries of the largest–scale cloud
structures. The axes of the striations seen in the 12CO emission from
relatively diffuse gas are aligned with the direction of the magnetic field.
We have developed a statistical method for analyzing the pixels in which 12CO
but not 13CO is detected, which allows us to determine the CO column in the
diffuse portion of the cloud as well as in the denser regions in which we
detect both isotopologues. Using a column density–dependent model for the CO
fractional abundance, we derive the mass of the region mapped to be
2.4$\times$104 $M_{\odot}$. This is more than a factor of two greater than
would be obtained using a canonical fixed fractional abundance of 13CO and a
factor three greater than would be obtained using this fractional abundance
restricted to the high column density regions. We determine that half the mass
of the cloud is in regions having column density below 2.1$\times$1021 cm-2.
The distribution of young stars in the region covered is highly nonuniform,
with the probability of finding a star in a pixel with a specified column
density rising sharply for $N(H_{2})$ = 6$\times$1021 cm-2. We determine a
relatively low star formation efficiency (mass of young stars/mass of
molecular gas), between 0.3 and 1.2 percent, and an average star formation
rate during the past 3 Myr of 8$\times$10-5 stars yr-1.

ISM: molecules – individual (carbon monoxide) ISM: structure; ISM:individual
(Taurus)

##  1 INTRODUCTION

The close association of young stars and concentrations within molecular
clouds indicates that stars form in cloud cores, which are regions of
increased density within the bulk of molecular clouds (cf. Beichman et al.,
1986). While the evolution from cloud core to protostar is dominated by
gravity, the physics controlling the process in which the cores themselves,
and the clouds in which they are embedded, are formed and evolve is still
quite controversial. While on the scale of pc to tens of pc molecular clouds
are close to satisfying virial equilibrium between gravitational and kinetic
energies, the significance of this equality is not entirely clear.
Furthermore, the role of magnetic field, while often postulated to be
significant, remains uncertain (Shu et al., 1987; Heiles & Crutcher, 2005).
Finally, the formation of molecular clouds themselves, and their lifetime,
remains very much a matter of discussion (e.g. Hartmann et al., 2001)

Molecular clouds may be formed by compression of atomic gas, with the
increased density and extinction enhancing the formation rate of molecules,
starting with H2, for which self–shielding enables the buildup of a
substantial fraction of the total hydrogen density even when the visual
extinction AV is only a fraction of a magnitude. It has also been suggested
that the large molecular cloud presence in galactic spiral arms is the result
of the agglomeration of molecular material existing in the interarm region, as
discussed by Pringle, Allen, & Lubow (2001). While one viewpoint has held that
molecular clouds have relatively long lifetimes, and are disrupted only by the
energy injected by massive star formation and evolution, another picture is
that molecular clouds are relatively transient objects, with the denser
regions representing only turbulent fluctuations of density rather than well-
defined gravitationally bound condensations (see e.g. review by
Vázquez–Semadeni, 2007).

These issues have been discussed on global scale, addressing the distribution
of clouds and the apportioning of molecular and atomic gas in the Galaxy. They
are also very relevant to studies of specific molecular cloud complexes, with
one of the best–studied of these being that in Taurus. The structure of the
interstellar gas in atomic and molecular form, the stellar population, the
issue of star formation rate, and the role of different physical processes
have all been the subject of numerous papers focused on the Taurus region,
primarily because its proximity (140 pc; Elias, 1978)111This value, from Elias
(1978), is so entrenched in the literature that we will use it despite the
plausible suggestion by Hartigan & Kenyon (2003) that the distance should be
reduced by about 10%, to $\sim$126 pc. allows very detailed studies of the
morphology of the gas and the relationship between gas and stars. The sheer
volume of the data that have been obtained and the number of analyses that
have been carried out preclude giving a complete listing of the references to
Taurus, so we will have to be selective rather than comprehensive, recognizing
that we may have omitted many valuable contributions.

The very closeness of Taurus means that available instrumentation,
particularly at radio frequencies, has faced a challenge to cover the entire
region with angular resolution sufficient to reveal the morphology of the gas.
The result has been that previous large–scale surveys of molecular line
emission at millimeter wavelengths have been limited to quite low angular
resolution (Ungerechts & Thaddeus, 1987). The survey of Ungerechts & Thaddeus
(1987) covers essentially all of Taurus and part of Perseus, but the 30′
angular resolution of the map (obtained by averaging multiple telescope
pointings to obtain a larger effective beam size) yields only 3000 pixels in
the 750 square degree region mapped. The pixel size corresponds to a linear
size of 1.2 pc at a distance of 140 pc, which is sufficiently large to blur
out structure at important astrophysical scales. In fact, the maps of
Ungerechts & Thaddeus (1987), while delineating the large–scale structure
quite well, show an almost complete absence of fine detail. This is in part
due to the use exclusively of 12CO, which is sufficiently optically thick that
significant variations in column densities can be entirely hidden, as well as
to the low angular resolution.

There have been a number of investigations of molecular gas in the Taurus
region with higher angular resolution, but these have typically been limited
to small subregions within the overall gas distribution. These studies, with
$\simeq$1′ to 2′ angular resolution include a few thousand to $\simeq$ 30,000
spatial pixels (Schloerb & Snell, 1984; Duvert, Cernicharo, & Baudry, 1986;
Heyer et al., 1987; Mizuno et al., 1995). These studies, with the combination
of higher angular resolution and use of the J = 1$\rightarrow$0 transition of
13CO do reveal considerable structure in the molecular gas, but have not
elucidated its relationship to larger–scale features in the molecular gas
distribution.

A number of other studies have utilized yet higher angular resolution and
different tracers to probe gas having different characteristic properties over
limited regions. Some examples include Langer et al. (1995) employing CCS,
Onishi et al. (1996) and Onishi et al. (1998) using C18O, Onishi et al. (2002)
using H13CO+, and Tatematsu et al. (2004) employing N2H+. Many individual
cores have been observed in ammonia, a tracer in which they appear relatively
well–defined, as indicated by compilation of Jijina, Myers, & Adams (1999).
Most of the regions covered by these studies have been pre-selected based on
the large–scale surveys discussed above. In these maps, we see indications of
finer–scale structure, but the emission is generally quite spatially
restricted compared to that seen in the more abundant isotopologues of carbon
monoxide.

In this paper we present the initial results from a large–scale high angular
resolution study of the Taurus molecular clouds using 12CO and 13CO. The data
cover approximately 100 square degrees on the sky (11.5° in R.A. by 8.5° in
decl.) corresponding to a region 28 pc by 21 pc. The reduced maps include
3.2$\times$106 Nyquist–sampled pixels in each isotopologue, with pixel size
20′′ corresponding to 0.014 pc. The linear dynamic range (LDR, defined as map
size divided by Nyquist–sampled interval) of the maps thus exceeds 1000, which
is the largest of any molecular cloud study carried out to date. The good
angular resolution and large LDR together allow us to examine in detail the
relationship between the relatively fine structures seen, especially in 13CO,
with the large–scale distribution of the molecular material, the young stars
in the region, and the magnetic field.

The region of Taurus studied here has been observed using a variety of other
tracers. The Leiden/Dwingeloo 21 cm study (Burton & Hartmann, 1994) traced the
atomic hydrogen in this direction, but with an angular resolution of 35′. One
investigation (Shuter et al., 1987) used the Arecibo radio telescope having an
angular resolution of 4′, but included only $\sim$ 1300 positions to probe the
self–absorption seen in the 21 cm HI line. This cold atomic hydrogen appears
to be associated with molecular gas (Li & Goldsmith, 2003; Goldsmith & Li,
2005), but the limited sampling of Shuter et al. does not reveal much about
its morphology. The far–infrared emission from Taurus has been studied by
Abergel et al. (1995), who also compared it to moderate resolution maps of
12CO J = 1$\rightarrow$0 emission. The dust column density distribution has
been examined by Padoan et al. (2002) and does bear a quite close resemblance
to the integrated intensity of 13CO and thus to the column density of gas in
relatively high extinction regions.

We discuss the observations and data reduction procedure in §2. Derivation of
the column density in the different portions of the maps is presented in §3,
in which we also discuss the distribution of column density and mass in the
region. We present a brief discussion of the large–scale gas kinematics in §4.
We address the relationship of the molecular material and the magnetic field
in §5, and discuss the relationship of the gas and the young stars in the
region in §6. We discuss some of the interesting features of the morphology of
the gas in §7. We summarize our results in §8.

##  2 OBSERVATIONS

The observations were taken between 2003 November and 2005 May using the 13.7m
radome–enclosed Quabbin millimeter wave telescope. The 32 pixel SEQUOIA focal
plane array222A 16 pixel single–polarization version of the array is described
in Erickson et al. (1999).  receiver observed the J = 1$\rightarrow$0
transition of 12CO and 13CO simultaneously. Since the receiver uses amplifiers
for the first stage, there is no issue of the sideband gain uncertainty and
its effect on calibration. Sixteen pixels are arranged in a 4 x 4 array in two
orthogonal linear polarizations. The main beam of the antenna pattern had a
full width to half maximum angular width of 45′′ for 12CO and 47′′ for 13CO.

The data were obtained using an on–the–fly (OTF) mapping technique. A standard
position was observed using position switching several times per observing
session to verify calibration consistency. Details of the data–taking, data
reduction, and calibration procedures are given by Narayanan et al. (2007).
The signals from a band of frequencies around each spectral line were sent to
an autocorrelation spectrometer with 1024 lags covering 25 MHz for each
spectral line. The lag spacing of the spectrometer system corresponds to 0.068
km s-1 for 13CO and 0.065 km s-1 for 12CO. The data cube of each isotopologue
employed in the subsequent analysis included 76 spectral channels for 13CO and
80 channels for 12CO covering approximately -5 km s-1 to +14.9 km s-1 and thus
included 2.4$\times$108 voxels.

As discussed in detail by Narayanan et al. (2007), the overall quality of the
data was excellent. After calibration and combination of the 30′ by 30′
submaps which were the units in which the data was taken, the data were
resampled onto a uniform grid of 20′′ spacing, which is very close to the
Nyquist sampling interval $\lambda/2D$ for the 13.7 m diameter telescope
operating at a wavelength of 2.6 mm. The images produced by the combination of
the submaps and regridding were 2069 pixels in RA by 1529 pixels in decl.,
thus comprising 3,163,501 spatial pixels resampled onto a uniform 20′′ grid.
The final data set has a well–behaved distribution of noise with a mean rms
antenna temperature equal to 0.125 K for 13CO and 0.28 K for 12CO in channel
widths of 0.27 km s-1 and 0.26 km s-1, respectively.

Figure 1:  Antenna temperature of the 13CO J = 1$\rightarrow$0 transition
integrated over the velocity range 2 km s-1 to 9 km s-1. The scale is shown in
the bar at the right; values have not been corrected for antenna efficiency.

We show the basic 13CO data in Figure 1, which gives the intensity of the 13CO
J = 1$\rightarrow$0 transition integrated over the velocity range 2 km s-1 to
9 km s-1. This interval encompasses almost all of the emission in the Taurus
region, with the exception of some isolated areas with gas at $\simeq$ 10 km
s-1, which may well not be associated with Taurus, and a limited amount of
emission in the velocity range 1 km s-1 to 2 km s-1. Figure 2 displays the
12CO J = 1$\rightarrow$0 peak emission within this same velocity interval.
Note that in both of these figures, the emission is not corrected for the
antenna efficiency. Narayanan et al. (2007) present images of the emission of
both isotopologues in 1 km s-1 bins covering the range 0 km s-1 to 13 km s-1.

It is evident that the 12CO is detectable over a significantly larger area
than is the 13CO. Particularly in the northeast portion of the map, we see
very extended 12CO emission, where there is relatively little 13CO. There are
also two interesting regions of quite strong 12CO emission, at 4h22m+28∘30′
and 4h48m+29∘40′, which are among the warmest regions observed, and yet which
do not show up as significant local maxima in the 13CO (and hence column
density). In general, the warmer gas as traced by 12CO is seen in regions of
high column density, but the amount of structure seen in the optically thick
12CO with our angular resolution, sampling, and sensitivity, is very
impressive.

Figure 2:  Maximum antenna temperature of the 12CO J = 1$\rightarrow$0
transition over the velocity range 2 km s-1 to 9 km s-1. The antenna
temperature has not been corrected for the antenna efficiency.

##  3 COLUMN DENSITY, COLUMN DENSITY DISTRIBUTIONS, AND CLOUD MASS

###  3.1 Mask Regions

In order to facilitate analysis of the data to determine column densities, we
have broken the Taurus data up into 4 regions, according to the detection or
nondetection of 12CO and 13CO. The detection thresholds are defined by the
requirement that the integrated intensity over the velocity range extending
from 0 km s-1 to 12 km s-1 be a minimum of 3.5 times larger than the rms noise
in an individual pixel over this 12 km s-1 velocity interval. The median
values are $\sigma_{T_{int}}$ = 0.18 K kms-1 for 13CO and $\sigma_{T_{int}}$ =
0.40 K kms-1 for 12CO. Since the peak values of the integrated intensity are 6
K kms-1 for 13CO and 18 K kms-1 for 12CO, the peak integrated intensities are
30 to 50 $\sigma_{T_{int}}$.

We define mask 0 to be the region in which neither 12CO nor 13CO is detected,
mask 1 to be the region in which 12CO is detected but 13CO is not, mask 2 to
be the region in which both isotopologues are detected, and mask 3 to be the
region in which 13CO is detected but 12CO is not. The different regions and
the number of pixels in each are given in Table 1.

Table 1:  Mask Regions in the Taurus Map Mask Region | Characteristics | Number of Pixels
---|---|---
0 | neither 12CO nor 13CO |  string944,802
1 |  12CO but not 13CO | 1,212,271
2 | both 12CO and 13CO | 1,002,955
3 |  13CO but not 12CO |  string3,473

The average spectra of mask 0, mask 1, and mask 2 regions are shown in Figure
3. These profiles are valuable for deducing general characteristics of the
regions, but it must be kept in mind that the characteristics of the average
profile are quite different from those of individual profiles. The difference
is primarily due to systematic velocity shifts across the cloud; these result
in the average spectra being much weaker and broader than individual spectra.
The line width of the averaged mask 1 spectra is close to a factor of 2
greater than the average line width of spectra in this region. For mask 2, the
ratio is $\simeq$1.5. Along with this, the peak intensities are much weaker
than those seen in individual spectra or even in spectra averaged over a
restricted region. Consequently, in determining characteristics of the
molecular gas, we have used individual spectra wherever possible to derive
physical quantities.

Figure 3:  Spectra averaged in each of the three significant mask regions of
the Taurus map, arranged from mask 0 (bottom) to mask 2 (top). In each panel,
the 12CO J= 1$\rightarrow$0 spectrum is the more intense (blue), while the
weaker 13CO spectrum is plotted in red. The antenna temperature scale for the
12CO is on the left hand side, while that for the 13CO is on the right hand
side, expanded by a factor of three relative to that of 13CO. The dashed
vertical lines delineate the velocity range used to define the material in the
Taurus region.

As expected, the lines are strongest in mask 2. The 12CO to 13CO ratio at the
line peak in mask 2 is just over 3, consistent with relatively high optical
depth in the more abundant isotopologue. We do see that when an average over
$\sim$ 106 pixels of mask 1 is formed, we readily see emission in 13CO as well
as 12CO. The ratio of peak intensities is significantly larger in mask 1 than
in mask 2. The value, about 10, is still much less than the presumed abundance
ratio [12CO]/13CO], suggesting that the 12CO in mask 1, while optically thick,
typically has lower opacity than in mask 2.

The mask 0 12CO and 13CO spectra show two or three peaks, including velocities
for which the emission in mask 2 is very weak compared to that in the range of
the peak emission, 5 km s-1 to 8 km s-1. In particular, the 10 km s-1 emission
feature comes from a fairly extended region in the northern portion of our
map, but is so weak that only when averaging over modest-sized ($\sim$1 square
degree) regions in mask 0 can it be detected. Emission in this velocity range
can be quite clearly seen in the mask 1 spectrum, but hardly can be detected
in mask 2. This is consistent with it being relatively low average column
density material, which is extended over quite large areas. Thus, even in what
we consider largely “empty” regions between the major, well–known subunits of
the Taurus molecular cloud complex, there is molecular gas. This is discussed
further in the following section. The overall composition of the mask 0
region, particularly the presence of atomic gas, is the subject of another
study.

The mask 0, mask 1, and mask 2 regions have close to equal numbers of pixels.
Their distribution, however, is very different. Figure 4 shows the four mask
regions. It is evident that the mask 1 predominantly surrounds mask 2, which
is consistent with the expectation that both isotopologues are detected in the
regions of highest column density (mask 2) while in the periphery of these
regions we detect in individual pixels the 12CO but not the 13CO emission.

Figure 4:  Image showing the mask regions (see text for definitions) in the
Taurus molecular cloud. Mask 0 is shown in black, mask 1 in blue, and mask 2
in red. The relatively few mask 3 pixels are not shown.

The pixels in mask 3 are unusual inasmuch as they exhibit detectable 13CO
emission but not 12CO. There are evidently very few such pixels ($\simeq$ 0.1%
of the total), although this number is considerably larger than would be
expected purely on the basis of Gaussian noise statistics. On close inspection
of these spectra, it appears that the problem is due to very low level
baseline imperfections partially canceling the 12CO integrated intensity,
resulting in a “non–detection” of this isotopologue. We thus ignore the mask 3
pixels in further analysis of the emission from Taurus.

###  3.2 Calculation of the Column Density

We wish to exploit the large linear dynamic range of our map to examine the
structure in the column density, and thus wish to determine the column density
for as many pixels as possible. This is also important for accurately
determining the total molecular mass of the region. In what follows we divide
the problem into two parts. The first is determination of the carbon monoxide
column density. While subject to its own uncertainties due to excitation,
optical depth, and limited signal to noise ratio, we can carry out this step
of the analysis based only on data in hand. The second step is conversion of
the carbon monoxide column densities to molecular hydrogen column densities,
and finally to total cloud mass. This is evidently dependent on the processes
which determine the fractional abundance of the various isotopologues
observed. Since the additional uncertainties in the second step are large, we
present results first in terms of the carbon monoxide distribution and
subsequently give results for the molecular hydrogen distribution and the
total molecular mass. This second step should benefit significantly from
combination of our data with dust column density determined from e.g. 2MASS
data. This effort is in progress and will be reported in a subsequent
publication.

####  3.2.1 Carbon Monoxide Column Density

The three different different regions of the cloud, defined by the
detectability of each isotopologue, require different schemes to determine the
carbon monoxide column density. We ignore mask 3 in determining the column
density and to the mass of the cloud as we cannot readily correct for the
artificial non–detections of 12CO (discussed above). Its extremely small area
and weak 13CO emission make its contribution negligible.

Mask 2 represents the portion of the cloud that is most conventional in terms
of column density determination. Since we have both 12CO and 13CO in each
pixel, we determine the kinetic temperature from the peak value of the 12CO
(with appropriate correction for antenna efficiency). Here (as well as for
other mask regions), we use the maximum antenna temperature of 12CO in the
velocity interval between 0 km s-1 and 12 km s-1. The kinetic temperature is
distributed from 3 K to 21 K, but with the vast majority of positions having
kinetic temperatures between 6 K and 12 K. Since mask 2 is the densest portion
of the cloud, we assume that the 13CO levels are populated in LTE at the
kinetic temperature, but we calculate a nominal value for the optical depth
from the ratio of the peak 13CO and 12CO intensities using the usual equation
of radiative transfer in a uniform medium. We assume a 12CO to 13CO abundance
ratio of 65, very close to the average value for local clouds found by Langer
& Penzias (1993). We use the value of optical depth obtained to make a
saturation correction to the 13CO column density derived assuming optically
thin emission, with the usual formula

$N(^{13}\rm{CO~{}corrected})=N(^{13}\rm{CO~{}assumed~{}optically~{}thin)}\frac{\tau}{1-exp(-\tau)}\>\>.$
(1)

Mask 1 presents the greatest challenge in terms of column density
determination since it encompasses approximately one third of the area mapped
and has reasonably strong 12CO emission. However, since the 13CO is not
detected in individual pixels, we need a different scheme to extract the
column density. We have developed a statistical approach, which should be
applicable to other large maps in which only the more abundant isotopologue is
detected in individual pixels. The procedure assumes that the 12CO is
optically thick at its peak, and that the value of the antenna temperature can
directly be converted to the excitation temperature of the 12CO. Since mask 1
points lie at the periphery of the regions of high extinction and greater
molecular column density (as witnessed by the detection of 13CO in each mask 2
pixel), they encompass lower column density gas which is presumably
characterized by lower volume density. Therefore we cannot assume that LTE
applies as it does in mask 2. Approximately half of the mask 1 positions have
an excitation temperature $\leq$ 7.5 K, and if in LTE the gas would have to be
unusually cold. It is thus reasonable to assume that this gas is subthermally
excited. To analyze positions in mask 1 we use a simple excitation/radiative
transfer analysis employing a spherical cloud large velocity gradient (LVG)
code to compute the line intensities (e.g. Snell, 1981; Goldsmith, Young, &
Langer, 1983). We are using an LVG model largely as a tool to characterize the
effect of trapping, which is important for excitation of CO at lower density.
We do not believe it necessarily represents any statement about the detailed
kinematics of the gas. The sensitivity of our results to the details of the
velocity field should be quite small.

We have assumed that the kinetic temperature of the mask 1 region is uniformly
15 K, somewhat higher than well-shielded dense gas, which is plausible in view
of increased heating in the peripheral regions surrounding regions of high
extinction. (e.g. Li, Goldsmith, & Menten, 2003). We take advantage of the
large number of pixels in our map, and bin the data according to the
excitation temperature of the 12CO determined as described above. In each bin,
we have a sufficient number of pixels that the 13CO J = 1$\rightarrow$0 line
is detected with good signal to noise ratio. For each $T_{ex}$ bin, we then
have the 12CO excitation temperature and the observed 12CO/13CO integrated
intensity ratio. The data generally have the observed intensity ratio
decreasing with increasing $T_{ex}$, from $\simeq$ 22 for $T_{ex}$ = 4.5 K to
$\simeq$ 13 for $T_{ex}$ = 2.5 K. The free parameters are the 12CO column
density, the H2 density, and the 12CO/13CO abundance ratio. The latter cannot
be assumed to be a fixed value (e.g. 65), due to the complicating presence of
isotopic enhancement due to chemical and/or photo effects (e.g. Watson et al.,
1976; Bally & Langer, 1982; Chu & Watson, 1983; Van Dishoeck & Black, 1988).
We thus consider $R$ = 12CO/13CO between 25 and 65.

Table 2:  12CO Excitation Temperature Bins in Mask 1 and Best Estimates of Their Characteristics11The last three columns are model values. Tex |  12CO/13CO | Number of Pixels | n(H2) | N(12CO)/$\delta$v |  12CO/13CO
---|---|---|---|---|---
K | Observed |  | cm-3 | 1016 cm-2/kms-1 | Abundance Ratio
4.5 | 21.7 |  string32321 |  string125 | 0.7 | 30
5.5 | 21.7 | 113923 |  string200 | 1.0 | 35
6.5 | 19.6 | 202328 |  string250 | 1.4 | 38
7.5 | 16.7 | 245949 |  string280 | 2.0 | 40
8.5 | 14.9 | 211649 |  string325 | 2.7 | 42
9.5 | 13.9 | 175431 |  string425 | 3.1 | 45
10.5 | 13.4 | 122423 |  string550 | 3.6 | 50
11.5 | 13.0 |  string65428 |  string850 | 3.7 | 55
12.5 | 12.8 |  string27387 | 1200 | 4.3 | 65

With three free parameters and only two observables, we cannot uniquely
determine the properties of the gas in mask 1. Rather, we compute for each
$T_{ex}$ bin, a family of $R$, density and CO column density per unit line
width solutions. If we knew a priori the value of $R$, then we could compute a
unique density and CO column density per unit line width for each $T_{ex}$.
With no knowledge of $R$, then the values of density and CO column density per
unit line width span a range of approximately a factor of 4, with density and
CO column density per unit line width inversely correlated. The family of
solutions for the physical parameters of the gas show some significant general
characteristics. First, for higher values of $T_{ex}$, only solutions with
$R\geq 50$ fit the data. This is encouraging as the higher excitation gas has
on average the largest column density and we do not expect significant
fractionation in the more shielded regions. On the other hand, for lower
values of $T_{ex}$, values of $R$ as large as 65 are excluded, and the range
of acceptable solutions gradually shifts from $R$ $\leq$ 50 at $T_{ex}$ = 7.5
K to values of $R$ $\leq$ 30 at $T_{ex}$ = 4.5 K. Correspondingly, the
allowable solutions for the gas density and CO column density per unit line
width decrease with decreasing excitation temperature. This trend again is
consistent with increasing fractionation in the less well–shielded regions at
the periphery of the clouds (see Liszt 2007) for a discussion of this effect
in diffuse clouds). These regions dominate the positions found within our mask
1. This result agrees with the behavior found in previous observational
studies (e.g. Goldsmith et al., 1980; Langer et al., 1980; Young et al., 1982;
Langer et al., 1989; Goldsmith & Li, 2005; Kainulainen et al., 2006).

It is not possible to model the mask 1 observations with a fixed value of the
in situ carbon monoxide isotopic ratio but rather require that the value of
$R$ vary significantly with excitation temperature. We have chosen solutions
such that $R$ varies smoothly from a value of 65 at $T_{ex}$ $\geq$ 12.5 K to
a value of 30 for $T_{ex}$ = 4.5 K. With this choice of $R$, we find that the
gas density and CO column density per unit line width both increase
monotonically with increasing excitation temperature. The solutions we have
chosen are shown in Table 2 and in Figure 5. We emphasize that these solutions
are not unique, but depend on our choice of $R$. However, the general behavior
of the solutions are physically plausible, given that we expect the excitation
temperature to increase as one moves from the cloud interior to the cloud
periphery. This suggests that binning by $T_{ex}$ is a useful approach, and
gives us a reasonable handle on how the physical conditions vary as a function
of excitation temperature and position in the cloud.

Our assumption of 15 K for the kinetic temperature is a potential source of
error in determining the carbon monoxide column density. To assess this, we
have carried out some calculations using a kinetic temperature of 25 K which
seems an upper limit to what one might expect in a cloud edge in a region with
modest UV intensity. We find that for this value of the kinetic temperature,
the column density per unit velocity gradient is approximately a factor 1.5
larger than for a kinetic temperature of 15 K, and the derived H2 density is a
factor of 2.5 lower, for an assumed value of $R$. The same trends of carbon
monoxide column density and H2 density as a function of $R$ are seen for the
higher kinetic temperature as for the lower. The uncertainty resulting from
the assumption of a fixed kinetic temperature is thus of the same order as
resulting from our choosing a best value of $R$, and combining these could
yield a factor of 2 uncertainty in $N$(CO). Observations of multiple
transitions of carbon monoxide isotopologues would provide a more accurate
estimate of the molecular column density. However, observations of these
transitions over a region of comparable size would pose a formidable challenge
for currently available telescopes and receiver systems.

To obtain the column density for each line of sight, we utilize an analytic
fit to the relationship between the CO column density per unit line width and
the excitation temperature obtained for the set of $T_{ex}$ bins,
$N(^{12}CO)/\delta v=(-1.473\times 10^{16}+4.672\times 10^{15}T_{ex})$. We
multiply the results by the observed FWHM 12CO line width $\Delta v$ from the
data. The use of the LVG model introduces some uncertainty because the carbon
monoxide excitation is quite subthermal, and the excitation temperature does
depend on the optical depth, and is quite different for 12CO and 13CO.
Nevertheless, the likely error in the trapping predicted by the LVG and other
models is relatively modest compared to other uncertainties inherent in this
analysis.

Figure 5:  Parameters of mask 1 pixels binned by 12CO excitation temperature
$T_{ex}$. The bottom panel shows the observed 12CO/13CO intensity ratio (left
hand scale; triangles), and the number of pixels in each excitation
temperature bin (right hand scale; squares). The most common excitation
temperatures are between 6 K and 10 K. The middle panel shows the H2 density
(left hand scale; triangles) and 12CO column density assuming a line width of
1 km s-1 (right hand scale; squares). These are obtained from the 12CO and
13CO intensities. The top panel shows the derived 12CO/13CO abundance ratio.
The H2 density, 13CO column density, and the derived 12CO13CO ratio all
increase monotonically as a function of 12CO excitation temperature. Figure 6:
Histogram of 12CO column density distributions in mask 0, 1, and 2 regions
mapped in Taurus. The mask 0 data are indicated by the vertical dashed line,
which represents the approximately 106 pixels in this region. The distribution
for mask 1 is shown by the solid (blue) curve, that for mask 2 by dot–dashed
(red) curve, and the combination of the two regions by the long–dashed (black)
curve. The abscissa is the logarithm of the 12CO column density, defined in
bins of width 0.1 dex, except for mask 0 which is a single value. The ordinate
is the logarithm of the number of pixels in each column density bin. The total
number of pixels included is close to 3.1 million.

In mask 0, after averaging $\simeq$ 106 spatial pixels, we are able to detect
both isotopologues, and we thus analyze the emission for the region as if it
were a single spatial entity. The general analysis follows the procedure
described above for mask 1. The fact that the integrated 12CO/13CO ratio is
$\simeq$ 19 indicates that the 13CO is almost certainly optically thin. This
is also the case for mask 1, and here as well results in the 12CO and 13CO
having quite different excitation temperatures due to the radiative trapping
for the more abundant isotopologue.

Again, we fix the kinetic temperature to be 15 K, reflecting increased heating
in regions of low extinction, and assume that the average line width is 2 km
s-1, similar to that observed for the low excitation gas of mask 1. Note that
the average mask 0 spectrum (Figure 3) is much broader than 2 km s-1, but the
large value of the line width reflects changes in the line center velocity
over the entire region observed. Following the trend of $R$ from mask 1, we
assume this ratio to have a value of 20.

The mask 0 data cannot be fit satisfactorily by larger values of $R$ thus
confirming that relatively strong isotopic selective effects are at work in
the low density/low column density regions of Taurus. With these assumptions,
the parameters we derive, although again not unique as described above, are
$n(H_{2})$ = 75 cm-3, and $N$(12CO) = 7.5$\times$1015 cm-2. The carbon
monoxide excitation in this region is evidently highly subthermal, consistent
with the low derived H2 density and the modest 12CO optical depth. This very
low value for the density of the mask 0 region gives a reasonably low column
density for the extended component of the gas in Taurus. Taking a
representative dimension for mask 0 of 1.5$\times$1019 cm-2, we obtain
$N(H_{2})$ = 1.1$\times$1021 cm-2. This corresponds to Av $\simeq$ 1 for the
extended component of the cloud, consistent with that determined from stellar
reddening (Cernicharo & Guélin, 1987).

The spatial distribution of column densities from the three mask regions is
shown in Figure 6. The column density for mask 0 is a single value
$<N(^{12}CO)>$ = 7.5$\times$1015 cm-2 as given above. The column density
distribution in the mask 1 region is a relatively symmetric, fairly Gaussian
distribution with a mean value $<N(^{12}CO)>$ = 3.6$\times$1016 cm-2. The
column density distribution in the mask 2 region is flat–topped with a mean
value $<N(^{12}CO)>$ = 1.3$\times$1017 cm-2.

The distribution of carbon monoxide in the Taurus region is shown in Figure 7.
This figure dramatically illustrates the complexity of the molecular gas
distribution. The impression given is quite different from that of studies
with low angular resolution, in that instead of an ensemble of “relaxed”,
fairly smooth condensations one sees a great deal of highly filamentary
structure, a strong suggestion of cavities and surrounding regions with
enhanced column densities. The large size of the region covered also suggests
relationships between the different portions of the Taurus molecular region.
The most striking of these points will be addressed briefly later in this
paper.

Figure 7:  Distribution of carbon monoxide in Taurus region expressed as the
logarithm of the 12CO column density (cm-2) in mask 1 and mask 2 regions. The
scale is indicated by the bar on the right hand side. The 12CO column density
in the mask 0 region (indicated by light grey density) is 7.5$\times$1015
cm-2, as discussed in the text. The maximum 12CO column density is a factor of
$\simeq$ 100 larger.

####  3.2.2 Molecular Hydrogen Column Density and Mass

Most studies of molecular regions using carbon monoxide have emphasized
regions in which the column density is sufficiently large that dust shielding
plus self–shielding result in an “asymptotic” 12CO abundance between
0.9$\times$10-4 and 3.0$\times$10-4 relative to H2 (see e.g. Frerking, Langer,
& Wilson, 1982; Lacy et al., 1994). In our study of Taurus, only the mask 2
region is plausibly consistent with this assumption. The remainder of the
cloud is characterized by lower densities and column densities, and the
fractional abundance of carbon monoxide must be regarded as being
significantly uncertain and likely to be dependent on the extinction.

There is considerable value in trying to make a self–consistent model for the
carbon monoxide as a tracer of total molecular (H2) column density. To this
end, we have used the theoretical modeling by Van Dishoeck & Black (1988). We
have utilized the curve for $I_{UV}$ = 1.0 (in units of Habings), carbon
depletion $\delta_{C}$ = 0.1, and models T1–T6, which correspond to
temperature range 40 K to 15 K and nH = 500 cm-3 to 1000 cm-3 throughout the
model slab being considered. We have used a polynomial fit to the data from
the appropriate curve in Figure 8 of Van Dishoeck & Black (1988) for the
relationship between CO and H2 column densities. This value of carbon
depletion is recommended by Van Dishoeck & Black (1988) as agreeing with the
available Taurus data. We also note that the carbon monoxide fractional
abundance as given by these models of Van Dishoeck & Black (1988) agrees well
at low column densities with the UV measurements of Sonnentrucker et al.
(2007) and Burgh et al. (2007).

The lower CO lines in absorption from diffuse clouds lying in front of
millimeter continuum sources have been observed by Liszt & Lucas (1998). The
clouds, analyzed by Liszt (2007) have a range of H2 column density (determined
by UV absorption; Federman et al. 1994) which extends from 5$\times$1020 cm-2
to just above 1021 cm-2, and thus includes our mask 0 (and very low end of
mask 1) results. While there is considerable scatter among various clouds
having the same hydrogen column density, the best fit relationship gives
$X$(12CO) = 5$\times$10-6 for $N$(H2) = 1021 cm-2. This is quite close to our
results and again reinforces the general applicability of a reduced carbon
monoxide fractional abundance for low extinction cloud material. The specific
parameters we have adopted have been chosen, in addition to being consistent
with the measurements of low column density diffuse clouds, to give good
agreement at high column densities with the mm emission measurements of
Bachiller & Cernicharo (1986), Cernicharo & Guélin (1987), and Alves, Lada, &
Lada (1999).

The strong dependence of CO column density on H2 column density reflects the
onset of self–shielding when N(CO) reaches $\simeq$1015 cm-2. This produces a
rapidly increasing CO fractional abundance as a function of H2 column density
in the range covered by the mask 0 and mask 1 regions of our study, and a
gradual leveling out of N(CO)/N(H2) in mask 2. The most significant difference
is that using this approach we find that the low CO column densities
correspond to considerably larger H2 column densities than would be found if a
constant fractional abundance of CO were adopted. We convert our CO
distribution to a molecular hydrogen distribution using the nonlinear
relationship, and the result is given in histogram form in Figure 8.

Figure 8:  Histogram of H2 column density distribution in Taurus. The
distribution of column density in the mask 0 region is given by the vertical
(dashed) line, in the mask 1 region by the solid (blue) curve, in the mask 2
region by the dot–dashed (red) curve, and in the combination of the two
regions by the long–dashed (black) curve.

When compared to Figure 6, it is evident that the varying fractional abundance
has resulted in a significant compression in converting the carbon monoxide to
H2 column densities. The drop in X(CO) in regions of lower extinction and
lower density means that the relatively weak emission that we observe there
implies a greater H2 column density than would be derived assuming a constant
fractional abundance. Taking mask 0 as an example, the CO column density of
7.5$\times$1015 cm-2, with fractional abundance 7.0$\times$10-6 corresponds to
an H2 column density equal to 1.1$\times$1021 cm-2 using the variable
fractional abundance, more than an order of magnitude larger than would be
obtained using the canonical high–extinction fractional abundance of 10-4.

This suggests that the majority of the area within the Taurus molecular cloud
complex has a visual extinction from molecular hydrogen on the order of 1
magnitude. This is consistent with the hydrogen column density of mask 1
discussed in the previous section, as well as with the ”halo” component of the
HCL2 region discussed by Cernicharo & Guélin (1987). There is certainly a high
column density tail which reaches 1022 cm-2, but this includes only a very
small fraction of the cloud area and mass. While 13CO is not the ideal tracer
of the densest component of the cloud, this study makes it clear that only
about 10-3 of the pixels with 12CO detectable have $A_{v}$ $\geq$ 5.

Despite the relatively low density in mask 0 and mask 1 regions, the time
scale to arrive at the the low fractional abundance of carbon monoxide found
there is quite modest. Using the expression from Section 4.1 of Liszt (2007),
we find that if we start with $X(e)$ = 10-5 and $n$(H2) = 100 cm-3, the
characteristic time to reach $X$(CO) = 10-5 is only $\sim$ 105 yr. This is
consistent with results obtained using explicit time–dependent models with CO
formation and destruction by E. Bergin (private communication). Thus, whatever
the history of the diffuse surroundings of dense clouds, the low but
significant abundance of carbon monoxide found there appears entirely
plausible.

We show the spatial distribution of H2 column density in the Taurus region
mapped in Figure 9. The contributions of individual pixels in mask 1 and mask
2 are included. Approximately 50 percent of the total molecular mass of the
region is in directions in which 13CO cannot readily be detected in an
individual map pixel. From the masses in each mask region, we compute the
total mass of the region of Taurus mapped in the present study. The results
(including correction for He and heavy elements) are given in Table 3. For
mask 0, we have considered the entire area it comprises to be characterized by
the single set of conditions derived in the previous subsection, while the
contribution of mask 3 has been neglected.

Table 3 shows that assuming the physically plausible variable fractional
abundance of carbon monoxide gives a total mass of the region a factor
approximately 2.5 times larger than that obtained using a uniform high
abundance characteristic of well–shielded regions. We also see that the
contributions from the low column density mask 0 and mask 1‘ regions are
considerably enhanced and that their contribution to the total mass is no
longer negligible as would be the case if a constant fractional abundance
obtained.

Figure 9:  Image showing the molecular hydrogen column density distribution derived from mask 0, mask 1, and mask 2 regions in Taurus. The scale is indicated by the bar on the right, expressed as the logarithm of the derived H2 column density in cm-2.  Table 3:  Mass of Region in Taurus Mapped Mask Region | Mass (103 $M_{\odot}$) |
---|---|---
| a | b
0 | 0.1 |  string4.1
1 | 1.7 |  string7.7
2 | 7.8 | 11.8
Total | 9.6 | 23.6

###  3.3 Cloud Structure

Valuable insight into the structure of the cloud can be obtained by examining
the cumulative distribution of cloud mass and area as a function of column
density. This information in shown in Figure 10. Our survey focused on the
region of the Taurus molecular cloud known to have most prominent high density
regions with exceptional chemical diversity (TMC-1; Pratap et al., 1997) and
prominent star formation (e.g. L1495). Nevertheless, we see that half of the
cloud’s mass is in material with N(H2) less than 2.1$\times$1021 cm-2. Only
about 5% of the cloud’s mass occurs at H2 column densities above 5$\times$1021
cm-2, or visual extinction greater than 5. The column density we derive may be
modestly underestimated due to incomplete correction for saturation in our
13CO observations for large column densities, and as a consequence of
molecular depletion at high densities, but even together these effects are
unlikely to increase this fraction by a factor of 2 (see e.g. Alves, Lada, &
Lada, 1999). The fraction of the cloud area with N(H2) $\geq$ 5$\times$1021
cm-2 is only 0.02.

Figure 10:  Cumulative fraction of Taurus as a function of molecular hydrogen
column density. The solid (blue) curve gives the fraction of the area
characterized by column density less than specified value, and the dotted
(red) curve gives the fraction of the mass similarly characterized. Half the
area mapped has column density below 1.6$\times$1021 cm-2, and half the mass
of the cloud is included in regions having column density below
2.1$\times$1021 cm-2.

Another view of the mass distribution can be obtained by attempting to dissect
the cloud by extracting the well–recognized high column density regions from
the remainder of the gas. In Figure 11 we show the division into eight
regions, which together include approximately 25% of the area of the map. We
have generally followed the region limits and designations given in Fig. 3 of
Onishi et al. (1996).

Figure 11:  Image showing H2 column density overlaid with the eight well-known
regions of high column density as designated by Onishi et al. (1996). These
regions define the masses and areas given in Table 4.

We give the mass of each of these regions in Table 4. The total mass contained
in these regions, 9807 $M_{\odot}$, is 42% of the total mass included in the
region we have studied, and their combined area is 21% of that of the region
we have mapped. However, since we have made an unbiased map of 13CO rather
than a map restricted to regions of strong intensity (as Mizuno et al., 1995,
did in their 13CO survey), we include somewhat larger areas. The masses we
derive for L1495/B213 and for B18 are approximately a factor of 3 larger than
those obtained by Mizuno et al. (1995), and that for HCl2 is a factor of 2
larger. It is evident that a large fraction of the mass even within the
boundaries shown in Figure 11 is in relatively low–density gas.

Table 4:  Mass of High–Density Regions in TaurusaaRegions defined in Figure 11

Region | Mass bbUsing H2/CO ratio with I(UV) = 1.0 and $\delta_{C}$ = 0.1 from Van Dishoeck & Black (1988) | Area
---|---|---
| $M_{\odot}$ | pc2
L1495 | 2616 |  string31.7
B213 | 1095 |  string13.7
L1521 | 1584 |  string17.6
HCl2 | 1513 |  string15.8
L1498 |  string373 |  string5.7
L1506 |  string491 |  string7.7
B18 | 1157 |  string14.5
L1536 |  string978 |  string16.6
Total | 9807 | 123.3

bbfootnotetext: Includes correction for He

Having a well–sampled 12CO map of a large region and a mass determination
allows us to examine the application of a CO luminosity to mass conversion
factor (Dickman, Snell, & Schloerb, 1986) to Taurus. In Table 5 we show the
results for the different mask regions and the total. The entries in the third
column are obtained using a conversion factor M($M_{\odot}$) = 4.1LCO(K km s-1
pc2). This value is obtained using the Egret $\gamma$–ray data (Strong &
Mattox, 1996), and a factor 1.36 for the total mass per H2 molecule (including
He and metals) in the gas. For mask 0, the CO luminosity drastically
underestimates the mass, due to highly subthermal excitation of the CO and its
modest optical depth. For the denser regions, the agreement is much better.
The surprisingly close agreement for the complete Taurus region may, to a
certain extent, be fortuitous, but it suggests that use of the 12CO luminosity
to derive total mass of molecular regions does appear to work reasonably well
for regions with only low–mass young stars, as well as for regions with young
high–mass stars.

Table 5:  Comparison of Masses Determined from 12CO and 13CO With Those Derived from CO Luminosity Region | Mass from |  12CO Luminosity | Mass from
---|---|---|---
|  12CO and 13CO |  |  12CO Luminosity
| ($M_{\odot}$) | (K km s-1 pc2) | ($M_{\odot}$)
mask 0 |  string4081 |  string193 |  string791
mask 1 |  string7699 | 2052 |  string8413
mask 2 | 11752 | 3305 | 13550
Total | 23532 | 5550 | 22754

##  4 LARGE SCALE KINEMATICS OF THE MOLECULAR GAS

Previous studies have revealed a variety of motions on different scales within
the Taurus complex. These include velocity gradients along individual
filaments possibly indicative of rotation, along with a systematic East–West
velocity difference as one moves across the region. In Figure 12 we show a
color–coded image of the integrated intensities in three velocity intervals
for the two isotopologues. There is a great deal of structure seen even in
this relatively crude representation of the velocity field. Certain regions,
and particularly the edges of particular regions, show up as having
significantly shifted velocities relative to the surrounding gas.

This coarsely divided integrated intensity does not give the full measure of
the complexity of the 13CO and 12CO line profiles in Taurus. An indication of
this can be seen in Fig. 20 of Narayanan et al. (2007), in which it is evident
that in general the regions with multiply–peaked lines exhibit this
characteristic in both 12CO and 13CO. Since the visibility of the multiple
peaks is approximately equal in the two isotopologues, it is unlikely to be a
result of self–absorption, but rather an indication of multiple, kinematically
distinct components. These are most prominent in several regions of Taurus,
notably the western part of B18, north of L1521, in B213 and west thereof, and
in the southern part of Heiles’ Cloud 2. This indicates that some regions are
characterized by a considerably greater degree of velocity multiplicity along
lines of sight. There does not appear to be any correlation of this
characteristic with e.g. star formation.

Figure 12:  Color–coded image of the integrated intensities in three velocity
intervals of carbon monoxide in Taurus, with emission at velocities between 3
km s-1 and 5 km s-1 coded blue, between 5 km s-1 and 7 km s-1 coded green, and
between 7 km s-1 and 9 km s-1 coded red. Upper panel: 12CO with blue– and
red–coded intervals scaled to 7.5 K kms-1 and the green–coded interval scaled
to 15 K kms-1. Lower panel: 13CO with blue– and red–coded intervals scaled to
5.0 K kms-1 and the green–coded interval scaled to 2.5 K kms-1.

##  5 MOLECULAR GAS AND THE MAGNETIC FIELD

The Taurus Molecular Cloud has long been a target for investigations of the
interstellar magnetic field and its role within the dynamics of the molecular
gas component (Moneti et al., 1984; Heyer et al., 1987; Heyer, 1988; Goodman
et al., 1992; Troland et al., 1996; Crutcher & Troland, 2000). Many of these
studies have compared the distribution of gas and dust with respect to the
magnetic field geometry inferred from optical polarization measurements of
background stars. The relationship of the cloud geometry to the magnetic field
morphology is an essential aspect of models that have been developed for the
formation of Taurus (Gomez de Castro & Pudritz, 1992; Ballesteros-Paredes,
Hartmann, & Vázquez–Semadeni, 1999). These have hypothesized an initial
alignment of a more diffuse cloud with the Galactic magnetic field as part of
the initial conditions for formation of the dense cloud, with the gas
streaming along magnetic field lines.

Observationally, at intermediate scales ($\sim$1 pc), the situation has become
more complex. In particular, toward the western end of the Taurus cloud, the
long axis of the L1506 filament is oriented along the field in contrast to
alignments of Heiles’ Cloud 2 and the B216 and B217 filaments for which the
field is essentially perpendicular to the axis of the filaments (Goodman et
al., 1992). Note that the latter structure is denoted B213 in Figure 11. From
this departure from rigorous alignment, Goodman et al. (1992) conclude that
either the magnetic field does not dominate the cloud structure at these
scales and densities, or that the optical polarization measurements probe a
volume that is spatially distinct from the dense filaments. Goodman et al.
(1992) demonstrate that polarization by selective absorption at optical and
infrared wavelengths is produced by dust grains within the outer, low column
density envelopes of the molecular clouds and provides little or no
information on the magnetic field direction within the high density filaments.

The 12CO and 13CO data presented in this study afford an opportunity to extend
these comparisons to lower column densities than these previous
investigations. We have used the data assembled by Heiles (2000), taken from
other sources, and superimposed this on a figure showing the integrated
intensities of 12CO and 13CO. Figure 13 shows the results.

Figure 13:  Upper panel: magnetic field direction in Taurus superimposed on
the 12CO antenna temperature distribution integrated over the 5 km s-1 to 8 km
s-1 velocity range, chosen to emphasize striations and other fine structure.
The line segments indicate the direction of the magnetic field derived from
observations of absorption by polarized dust grains; their length is
proportional to the fractional polarization. The horizontal bar at lower left
in each panel indicates 5% fractional polarization. Lower panel: magnetic
field direction superimposed on the distribution of 13CO antenna temperature
integrated over the same velocity interval. The integrated intensities for
each panel in K kms-1 are indicated by the bar at the right.

This figure highlights the relationship between the field direction and the
morphology of the dense filaments of gas discussed in the references given
above.

We can use the 12CO emission to probe the relationship between the lower
column density portions of Taurus and the magnetic field. This comparison is
shown in the top half of Figure 13. Within the faint, low surface brightness
12CO emission, we see marked striations, which are discussed in more detail in
§7.2.6. Remarkably, these features within the Taurus Cloud follow the local
orientation of the magnetic field even as the polarization angles vary from a
mean of 53 degrees within the northeast corner of the surveyed area, to 81
degrees within the southwest corner. The alignment of these faint features
points toward a strong coupling of the gas with the interstellar magnetic
field. Such strong coupling may be expected in these low column density
regions that are more exposed to the ambient, UV radiation field, which
maintains a higher degree of ionization.

The origin of these threadlike features and the mechanism whereby they are
aligned with the magnetic field are not established, but we can speculate on
several processes that may be responsible. The channel maps of the molecular
line emission identify regions of systematic motions over scales from the
resolution limit up to 30′ to 60′. If the magnetic field is well coupled to
the neutral gas by frequent ion-neutral collisions but the magnetic energy is
small with respect to the kinetic energy of the gas, then the field can be
carried by these large scale flows within the cloud. Correspondingly, the
field lines would be stretched along the direction of the flow. Alternatively,
the narrow emission threads may arise from successive compressions and
rarefactions of the gas and magnetic field produced by magnetosonic waves that
propagate perpendicular to the field. Within the subthermally excited regime,
which likely prevails within these regions of low surface brightness, these
column density perturbations would produce corresponding variations in the
12CO intensity.

##  6 MOLECULAR GAS AND YOUNG STARS IN TAURUS

The distribution of young stellar objects with respect to the molecular gas
may offer valuable insights to the formation of stars within a dense
interstellar cloud. For comparison with our molecular images, we adopted the
set of pre-main sequence stars in the Taurus regions from S. Kenyon (2007
private communication, to be published in 2008). This list is comprised of
data from many surveys in optical and infrared wavebands 333We obtain
essentially the same results using the data compiled by F. Palla, which was
also provided to us as a private communication.. The pre–main sequence stars
are divided into three populations according to their colors. If the R-K
magnitude is larger than eight, the star is categorized as likely to be a
Class I or younger source. If R-K is smaller than eight, the source is likely
to be a T-Tauri star. If the source is not detected in either R or K, it is is
likely to be extended/nebulous, in which case it is probably still a
protostar, younger than a T-Tauri star. In the region covered by our map,
there are a total of 230 stars, 18 of which are Class I or younger, 44 are
extended, and 168 are likely to be T-Tauri stars. The stars are shown overlaid
on the distribution of the H2 column density in Figure 14. The distribution of
pre–main sequence stars generally follows that of the dense gas, although a
many of the stars in the older category are located in regions with only
diffuse gas emission. As noted by Hartmann (2002), the young stars are grouped
in three nearly parallel bands that are associated with Heiles’ Cloud
2/L1521/B213/L1495, B18/L1506 and L1536.

Figure 14:  Locations of young stars in Taurus superimposed on map of the H2
column density. The stellar positions are from Kenyon (2007). The diamonds
indicate diffuse or extended sources (of which there are 44 in the region
mapped), the squares indicate Class I or younger stars (18), and the asterisks
indicate T-Tauri stars (168). It is evident that the diffuse and younger
sources are almost without exception coincident with regions of relatively
large column density, while the older stars show a much larger probability of
being found in regions of lower column density.

The relationship between H2 column density and stellar population is examined
further in Fig. 15.

Figure 15:  Upper left: number of stars as a function of column density. The
same bins of column density are used in all panels. Upper right: fraction of
pixels in each column density bin. Lower left: surface density of stars
obtained by dividing the number of stars in each bin by the area of the map
corresponding to each bin. Lower right: surface density of stars in each bin
for likely class I and diffuse sources (solid line) and likely T-Tauri stars
(dashed line). The division of sources is discussed in the text.

Roughly equal number of stars can be found in each of the column density bins
spanning the range from 0 to $6.5\times 10^{21}$ cm-2 (upper-left panel).
Although the number of stars drops towards higher column density regions, such
direct examination of the distribution of stars is somewhat misleading
inasmuch as our map includes a substantial area with very weak or no carbon
monoxide emission, as shown in the upper right panel of Figure 15. The surface
density of stars versus column density is plotted in the lower left panel. A
significant jump in the surface density occurs at around $N(H_{2})=6\times
10^{21}$ cm-2, or roughly, Av = 6, suggestive of a threshold for star
formation. Note that the same trend is visible even in a sample of mostly
T-Tauri stars (lower right panel).

In Taurus, neither the dispersion of gas due to star formation nor the
dispersion of stars due to stellar motion is likely to have altered the
collocation of very dense gas and highly extincted young stars. The threshold
in column density for star formation is consistent with the conclusion of
Mizuno et al. (1995) with the difference being our finding a higher threshold
of $6\times 10^{21}$ cm-2 instead of $3\times 10^{21}$ cm-2. Given the larger
number of pre–main sequence stars available for the present work, the
significance of the change in the stellar surface density is also higher.

With our rather complete coverage of gas and stars, we can examine the
relationship of the stellar mass to the gas mass, which defines the star
formation efficiency (or SFE). From a very simplified point of view of the
time evolution of the star formation process, we can define the star formation
efficiency in three ways. In the first, the SFE is defined as the mass of all
known young (pre–main sequence) stars divided by the total gas mass. Assuming
an average mass of 0.6 solar mass for each of the stars in our sample
(following Palla & Stahler, 2000) and the total molecular mass of 2.4$\times
10^{4}$ $M_{\odot}$ (Table 3), the star formation efficiency thus defined is
0.6 percent.

In the second, we define the SFE more strictly for the current epoch, i.e.,
counting only the mass of protostars and of dense gas (that in our mask 2
region). The SFE thus defined in this more restricted sense is about 0.3
percent. For the third method, we adopt a less physically motivated but
procedurally simple approach of defining the star formation efficiency to be
the mass of all pre–main sequence stars divided by the mass of dense gas, we
obtain an SFE equal to 1.2 percent. These low values confirm that Taurus is a
region of relatively low star formation efficiency.

Since star formation is an ongoing process in Taurus the SFE as defined will
evolve with time. A more meaningful quantity is the star formation rate per
unit molecular gas mass. The star formation history of Taurus is a topic of
some controversy (cf. Palla & Stahler, 2000; Hartmann et al., 2001; Palla &
Stahler, 2002), particularly the issue regarding whether the star formation
rate is presently accelerating or has already reached a peak and is declining.
Nevertheless, there does seem to be agreement that star formation has been
rapid. Star formation in Taurus began over 10 Myr ago, but most of the
identified pre-main sequence stars have formed in the past 3 Myr (Palla &
Stahler, 2002). The average star formation rate over the past 3 Myr within the
region of Taurus included in this study has been $\simeq$ 8$\times 10^{-5}$
stars yr-1.

Assuming as before an average mass of 0.6 solar masses, we derive a star
formation rate of 5$\times 10^{-5}$ $M_{\odot}$ yr-1. Thus, the star formation
rate per unit molecular gas mass is approximately 2$\times 10^{-9}$
$M_{\odot}$ per year per solar mass of molecular gas. If this rate were to
continue, the gas consumption timescale would be over 400 Myr. However, most
of the dense gas is likely to be dispersed by the winds from the newly forming
stars long before a significant fraction of the cloud mass is converted into
stars. It is intriguing that the star formation rate per unit molecular gas
mass in Taurus is very similar to that found globally in the Milky Way
(assuming a total molecular mass of 2$\times 10^{9}$ $M_{\odot}$ and a star
formation rate of 3 $M_{\odot}$ yr-1).

##  7 MORPHOLOGY OF THE MOLECULAR GAS

###  7.1 General Structure of the Gas

###  7.2 Regions of Interest

In this section we discuss several of the regions of particular interest that
stand out in the carbon monoxide emission from Taurus. These are to some
degree reflections of the complex structure seen on a large scale, but
highlight some of the varied structures that can easily be identified. The
present discussion is by no means complete but does illustrate the varied and
complex structures found in this region in which only low mass star formation
is taking place. These are grouped together by location within the cloud so
that they can be highlighted by detailed images, but this does not necessarily
reflect any physical relationship between different features.

####  7.2.1 Filamentary Structure Within the Dense Gas

A very striking feature of the molecular gas within the dense portion of
Taurus is the fact that the 13CO emission is highly structured even in
integrated intensity, as can be seen in Figure 1. An impressive example is
shown in Figure 16 which shows a several approximately parallel filaments at
4h27m+26∘45′, having a southeast to northwest orientation. The filaments are
$\simeq$ 20’ to 25’ (0.8 pc to 1.0 pc) long, with a $\simeq$ 6:1 length to
width ratio. These filaments are readily visible in individual velocity images
(Narayanan et al., 2007) as well as the 13CO integrated intensity image, but
are invisible in the 12CO data. The peak H2 column density of the filaments is
3$\times$1021 cm-2, about a factor of two greater than that of the region
between them.

Another very interesting feature visible in Figure 16 is the almost complete
ring–like structure centered at 4h31m +28∘01′. It is fairly circular, having
an angular diameter of 18′, corresponding to 0.73 pc. The molecular hydrogen
column density is typically 3$\times$1021 cm-2 around the periphery of the
ring and 1.8$\times$1021 cm-2 in the center. This ring shows up quite clearly
in the 12CO integrated intensity image in which $\int T_{A}dv$ increases from
7.5 K kms-1 in the center to $\simeq$ 11 K kms-1 on the periphery. This
features is not discernible in the 12CO maximum intensity image, indicating
that it is showing increased line width, although distinct kinematic structure
is not evident.

Figure 16:  Enlarged image of 13CO integrated intensity showing filamentary
structures located near 4h27m+26∘45′. A nearly circular ring–like structure
centered at 4h31m+28∘ is also visible. The young stars in this region are
indicated by the symbols defined in Fig. 14. The diamonds indicate diffuse or
extended young stellar sources, the square indicates a Class I or diffuse
source, and the asterisks indicate T-Tauri stars.

####  7.2.2 Cometary Globules and Ring in Large Cavity

A structure that appears to be a large cavity is visible at the eastern end of
B213, just to the north of B18, visible in the 12CO image, but more clearly in
the 13CO integrated intensity (Figure 1). An enlarged image is shown in Figure
17. The center of the cavity is approximately 4h29m+25∘30′. Although the
cavity is still clearly visible, it is considerably smaller, 40′ (1.6 pc) in
12CO compared to 70′ (2.9 pc) in 13CO. The minimum H2 column density of the
cavity is 1.4$\times$1021 cm-3 (it is included in mask 1), but the 13CO is
detected when averaged over a reasonable number of pixels.

Figure 17:  This enlarged 13CO integrated intensity image shows the cavity
between B213 and B18. At the northwest, three cometary globules are evident,
having properties presented in Table 6 and discussed in the text. A nearly
complete ring is also seen at the eastern edge of the cavity. The diamonds
indicate diffuse or extended young stellar sources, the squares indicate Class
I or younger stars, and the asterisks indicate T-Tauri stars.

The boundary of this cavity contains an impressive number of young stars,
which in fact nearly completely surround it. To the north, these seem to be
distributed around the periphery of the cavity, but at its western edge (the
eastern end of B213), there are three prominent condensations, looking
remarkably like cometary globules, projecting into the cavity. Some properties
of the condensations are shown in Table 6. The globules are undistinguished in
terms of maximum 12CO temperature. The maximum column density of each of the
globules is close to 4$\times$1021 cm-2. We have not been able to identify any
source that would be responsible for forming the cavity, but this may be a
result of its relatively great age.

Table 6:  Properties of Cometary Globules In B213–B18 Cavity Globule Number | RA(J2000) | Decl(J2000) | Mass | Embedded Star
---|---|---|---|---
|  |  | $M_{\odot}$ |
1 | 4h26m49s.8 | 25∘39′06′′ | 5.9 | DF Tau
2 | 4h27m06s.3 | 26∘06′07′′ | 8.3 | DG Tau
|  |  |  | FV Tau
3 | 4h29m25s.5 | 26∘14′42′′ | 4.1 | FW Tau

As indicated in Table 6 (see also Figure 14), each of the globules contains a
T Tauri star, with Globule 2 containing two stars. DF Tau is located slightly
inwards (toward the cavity center) relative to Globule 1, while the stars in
Globules 2 and 3 are located 3′ away from the cavity center compared to the
tip of the globule. There does not appear to be any readily discernible
kinematic signature giving clues to the origin of the globules, or revealing
an effect of the star formation. For example, although the star DG Tau B in
Globule 2 has an optical jet which is presumed to be driving the observed
red–shifted molecular outflow (Mitchell, Sargent, & Mannings, 1997), we do not
see an effect on the quiescent gas distribution.

The stars in question range from 0.2 $L_{\odot}$ to 2.2 $L_{\odot}$, and have
ages between 0.6 Myr (DG Tau) to 1.2 Myr (FW Tau). Stars of this age may well
have moved a significant distance since their formation, so that it is not
surprising that if they were formed in these globules by e.g. radiative
implosion (Bertoldi & McKee, 1990), they may now appear displaced from their
formation sites.

####  7.2.3 Irregular Filament or Boundary in L1536

Figure 18:  Filament running to northwest from L1536 seen in 13CO integrated
emission. The condensations have a maximum H2 column density of 5$\times$1021
cm-2. The diamonds indicate diffuse or extended young stellar sources and the
asterisk indicates a T-Tauri star.

A very long filament having one end in the south–central portion of L1536 and
extending to the northwest is visible in the 13CO emission, shown in an
enlarged view in Figure 18. The filament center is at 4h23m +23∘45′, and its
length is 2∘, corresponding to 4.9 pc. The morphology of the filament is
suggestive of its being a boundary between regions of lower (to the south) and
higher (to the north) column density. The form of the filament is somewhat
suggestive of a helix, but it could simply have an irregular shape. The H2
column density along the filament is typically 3$\times$1021 cm-2, but reaches
5$\times$1021 cm-2 in the regions of strongest emission. The region
surrounding the filament has a H2 column density of 1.3 to 1.5 $\times$1021
cm-2, only slightly greater than our minimum value defined by mask 0 of
1.1$\times$1021 cm-2. This filament, is roughly parallel to the structure
formed by B18 and L1506, to the filamentary part of B213, and also to the less
well–defined but still quite flattened structure formed by Heiles’ Cloud 2 and
L1521. This thin filament is the most southerly and furthest from the Galactic
plane of all of these structures. The position angle of all four of these
filamentary/elongated clouds is approximately 45∘ relative to the plane of the
Milky Way.

####  7.2.4 Molecular Ring and Planar Boundary

Figure 19 includes several different structures. The first is the “molecular
ring”, studied in detail by Schloerb & Snell (1984). This ring, 30′ (1.2 pc)
in diameter, centered at 4h40m30s +25∘45′, contains at least 6 dense
condensations visible in the 13CO integrated intensity image. The best–studied
of these is the chemically very interesting TMC-1 ridge, observed in detail by
Pratap et al. (1997) and many others. The ridge (the NH3 peak is at
4h41m21s+25∘48′) is not very prominent in the 13CO integrated intensity image,
which is presumably a result of the significant optical depth in the ring
material, which may not be corrected for entirely by the simple process
(described in §3.2.1) employed here. The peak H2 column density we derive is
7$\times$1021 cm-2 which is somewhat less than half of that which would be
derived from the C18O observations of Pratap et al. (1997). Given the
difficulties expected in deriving the column density in regions of optically
thick emission in which significant temperature gradients may be present, this
difference is not unreasonable. The ridge is more visible in our 12CO map than
in that of Schloerb & Snell (1984) due to the better sampling in the present
work.

Figure 19: 13CO integrated intensity image showing the molecular ring in
Heiles’ Cloud 2 centered at 4h40m30s +25∘45′. We also see the very
well–defined planar boundary centered at 4h38m30s +26∘50′. The 12CO boundary
in this region is not at all sharp, having a hair-like appearance as seen most
clearly in Figure 13. The diamonds indicate diffuse or extended young stellar
sources, the squares indicate Class I or younger stars, and the asterisks
indicate T-Tauri stars.

The second noticeable feature in Figure 19 is the very straight boundary of
the molecular emission seen in 13CO centered at 4h38m30s +26∘50′ and extending
for over 1 degree (2.4 pc). The questions of the formation of this interface
and how it is maintained are intriguing. In this region, the 12CO emission
extends significantly beyond that of the 13CO away from the high column
density portion of the cloud, typically by 0.5 pc. As can be seen in Figures 2
and 13, the 12CO emission is highly structured, particularly perpendicular to
the interface direction. This behavior is not restricted to this portion of
the cloud boundary, but in fact is a general characteristic of the 12CO
emission in the mask 1 region surrounding the high column density portion of
the cloud (mask 2) where 13CO is detected in individual spectra.

Finally, we note the intriguing feature to the west of the better–known ring
discussed above. With a center at 4h37m+26∘45′, this is again a slightly non
circular ring having a diameter of 30′ (1.2 pc). Given the complexity of the
structure observed in our study of the molecular gas in Taurus, this could
certainly be a superposition of filaments rather than a ring.

####  7.2.5 L1495 and B213

The L1495 region contains the greatest concentration of young stars within the
region of the Taurus molecular cloud that we have mapped. Figure 20 shows the
eastern part of L1495; the western part (seen in Figure 1) is more diffuse.
The enlarged image also shows the very narrow B213 filament which extends to
the southeast from L1495. The 13CO emission and the H2 column density we
derive from it, are relatively continuous over the high column density portion
of L1495 and the B213 filament. In C18O (Onishi et al., 1996) individual dense
cores are better resolved, and in HCO+ (Onishi et al., 2002) they stand out
yet more clearly.

The central part of of L1495 contains over 20 young stars in Palla’s
compilation (Palla, 2008), and has a maximum H2 column density of 1022 cm-2,
which is the highest we see in our map. The mass of the L1495 region is (Table
4) 2.6$\times$103 $M_{\odot}$, but a significant fraction of this is in the
spatially extended, lower density material.

The B213 filament is approximately 75′ or 3 pc in length, and only 4.5′ or 0.2
pc thick. One of the curious features about this structure is that while there
are dense cores seen along its entire length (Onishi et al., 1996, 2002),
young stars have apparently not yet formed in the northwestern 30′ (1.2 pc)
long portion closest to L1495. The magnetic field orientation at the
boundaries of this filament is strikingly oriented perpendicular to its long
axis, as seen dramatically in Figure 13, and discussed in §5.

Figure 20:  Enlarged 13CO integrated intensity image of the western portion of
L1495 (4h17m30s +28∘20′) and the filamentary region B213 (running to the
southeast from 4h17m30s +27∘40′. The diamonds indicate diffuse or extended
young stellar sources, the squares indicate Class I or younger stars, and the
asterisks indicate T-Tauri stars.

####  7.2.6 Striations in 12CO Emission

One of the surprising features in the map of 12CO is the prominent striations
(or threads, or strands) seen in the lower level emission seen away from the
main molecular condensations. These can be recognized in Figure 2, but this
effect is more visible in the enlarged image shown in Figure 21. Another
region in which this is very prominent is located at 4h15m +24∘30′. These are
similar to structures seen within some infrared cirrus clouds. The striations
are visible in images of maximum antenna temperature and also integrated
antenna temperature. The characteristic values are $T_{A}$ = 3 K on the
striations and 2 K between them, while $\int T_{A}dv$ drops from $\simeq$ 2.8
K kms-1 on the striations to between 1 and 1.5 K kms-1 between them. Given
that the density in these regions is low, the 12CO emission is almost
certainly subthermally excited so that it is difficult to determine the
kinetic temperature. Based on the procedure described in §3.2.1, which assumes
$T_{kin}$ equal to 15 K, the H2 column density of the striated features is
2$\times$1021 cm-2, approximately double that of the background emission. A
striking feature of the striations is their alignment parallel to the
direction of the magnetic field measured by optical starlight polarization, as
shown in Figure 13 and discussed in §5.

Figure 21:  One of the regions showing prominent striations in the 12CO
emission, displayed here in an image of the maximum 12CO antenna temperature.
The diamonds indicate diffuse or extended young stellar sources, the squares
indicate Class I or younger stars, and the asterisks indicate T-Tauri stars.

##  8 SUMMARY AND CONCLUSIONS

We have carried out a large–scale survey of the molecular gas in Taurus by
mapping a 100 square degree region with the 13.7 m Five College Radio
Astronomy Observatory millimeter telescope. The J = 1 $\rightarrow$ 0
transition of 12CO and of 13CO were observed simultaneously using the 32 pixel
Sequoia focal plane array receiver. The observing and data reduction
techniques are discussed by Narayanan et al. (2007). In this overview, we have
discussed some of the highlights of the data that we have obtained, deferring
detailed analyses to future papers.

The combination of an unbiased, high sensitivity survey with coverage of a
relatively large area allows us to study the structure and properties of the
molecular gas in new ways. With approximately 3 million independent spatial
pixels, we have a linear dynamic range which is unequaled in previous studies
of the Taurus region. While our angular resolution is inferior to that
obtained with larger/higher frequency telescopes or interferometers, the
strength of the present work is to show the relationship between structures on
scales ranging from $\simeq$ 1′ or 0.04 pc to 10 degrees (approximately 25
pc). Our observations are sensitive to a range of column densities equivalent
to a range in visual extinction between 1 and 10 magnitudes.

Cloud Morphology One of our key conclusions is that the morphology of this
region is very complex. In contrast to earlier large–scale surveys carried out
with low angular resolution in which clouds appeared largely smooth–edged and
having little structure, we find an astoundingly rich range of structures
including filaments, ridges, blobs, and holes. The internal structure is more
striking in 13CO than in 12CO which is not surprising given the large optical
depth of the former isotopologue. The filaments have lengths up to 3 pc, and
axial to transverse dimension ratios as large as 15:1. Holes in the molecular
emission appear on a large range of scales extending from 0.1 pc to 3 pc.

The edges of the dense molecular regions are generally very irregular, with
structures on the order of 0.1 pc in size visible especially in 12CO which
traces cloud boundaries which are more extended than seen in the 13CO. This
“hair–like” edge structure is found to be common in 12CO while the 13CO cloud
boundaries are relatively sharper but still quite irregular. There is one
notable exception in which we find a sharp, straight boundary in 13CO almost
2.5 pc in length.

Cloud Mass and Mass Distribution Having both the 12CO and 13CO detected in
regions of relatively large column density (mask 2, comprising about 1/3 of
the map pixels), we have used the standard method to derive the kinetic
temperature and molecular column density, including a correction for
saturation of the 13CO which becomes significant for the regions of greatest
column density. To analyze portions of the image (mask 1 comprising about 1/3
of total area of the cloud mapped) in which we detect 12CO but not 13CO in
individual pixels we use a different approach. With $\simeq$ 1 million such
pixels available, we have binned them by 12CO excitation temperature $T_{ex}$.
When spectra within a bin are averaged, the 13CO as well as the 12CO is
readily detectable, and we obtain the H2 density and the CO column density. We
thus have a relationship which gives us n(H2) and N(CO) as a function of
$T_{ex}$(12CO). Since the excitation temperature is available for each pixel,
we can derive the CO column density for each line of sight. Averaging together
all the pixels in mask 0 (in any one of which neither 12CO nor 13CO was
detectable), we detect both isotopologues, and use the two spectra to derive
the average density and column density for mask 0, the final third of the map.
This procedure allows us to determine the CO column density throughout the
region mapped, including even regions of relatively low column density.

To convert $N(CO)$ to total column density, we have used the results of Van
Dishoeck & Black (1988) which are appropriate for Taurus. The essential point
is that the fractional abundance of carbon monoxide drops as the total H2
column density is reduced, as a result of reduced dust shielding and
self–shielding. Inverting this argument, the column density of H2
corresponding to a low column density of carbon monoxide is larger than would
be obtained assuming a constant fractional abundance for CO. The result is
that the total mass for the region of Taurus mapped is close to 2.4$\times$104
$M_{\odot}$, compared to less than 1$\times$104 $M_{\odot}$ that would be
found using a standard, uniform fractional abundance. We find that half the
mass of the cloud is contained in regions having column density below
2.1$\times$1021 cm-2. This result reduces the fraction of mass found in dense
cores by a factor greater than 2, and also confirms the presence of
significant external pressure in the regions external to the dense regions.
The total mass for the region we have mapped thus obtained agrees well with
that predicted from the CO luminosity, 5.55$\times$103 K km s-1 pc2, and a
standard conversion M($M_{\odot}$) = 4.1 LCO (K km s-1 pc2). It seems likely
that our conclusion that a significant component of diffuse molecular gas
accompanies the more widely studied high density regions is not restricted to
Taurus. It reinforces the importance of observations which can study this
diffuse molecular material, which is not readily detected in individual
spectra with the sensitivity typically available in large–scale molecular
cloud surveys.

Cloud Structure and Star Formation The structural complexity over a wide range
of scale sizes hints at the richness of the physical processes which underly
the formation and evolution of molecular cloud complexes such as Taurus. The
present data set, both in terms of morphology and mass distribution,
constitutes a potentially valuable resource for comparison with outputs from
simulations of cloud formation. The large scale kinematic structure that we
see confirms that identified in earlier studies. Along with the complexity of
the line profiles observed along many lines of sight, this poses a real
challenge for any detailed theoretical model of this region.

We see a varied relationship between the magnetic field as measured by
polarization of background stars, and the distribution of the gas. In the more
diffuse regions traced by 12CO we see large–scale alignment between the field
direction and striated structure in the gas. Although we have not been able to
measure any kinematic signature, the appearance is strongly suggestive of
flows along the field lines. In several of the very elongated filaments seen
in the denser gas traced by 13CO, the magnetic field is oriented
perpendicular, or nearly perpendicular, to the major axes of the filaments.
Combined with the hair–like appearance of the boundaries of these filaments
seen in 13CO but more prominent in 12CO, this again suggests that motions of
material along the field lines have been responsible for building up the
regions of higher density within the overall molecular cloud.

The surface density of very young and moderately young stars shows a rapid
increase at a H2 column density of 6$\times$1021 cm-2, confirming the
existence of a threshold for star formation. We have used new compilations of
young stars in the Taurus region to calculate the star formation efficiency
(SFE). Our large value for the gas mass, especially in regions of lower column
density, results in the SFE, taken to be the mass of all young stars in the
region divided by the total molecular mass, to be 0.6 percent. Taking the SFE
for most recent star formation by comparing the mass of only the embedded
protostars with that of the dense gas, gives an SFE equal to 0.3 percent. If
we consider all of the young stars (whether embedded protostars or T-Tauri
stars) in the region of high column density, we obtain a SFE equal to 1.2
percent. The average star formation rate over the past 3 Myr within the region
of Taurus included in this study has been $\simeq$ 8$\times 10^{-5}$ stars
yr-1, corresponding to a mass going into new stars of 5$\times 10^{-5}$
$M_{\odot}$ yr-1.

This work was supported in part by the National Science Foundation through
grant AST-0407019 to Cornell University, and by the Jet Propulsion Laboratory,
California Institute of Technology. The Five College Radio Astronomy
Observatory is operated with support from the National Science Foundation
through NSF grant AST 05 40852 and with permission of the Metropolitan
District Commission. We thank Yvonne Tang for contributions to data taking and
analysis of dense condensations in Taurus, and Marko Krco for assistance with
observations. We thank Pierre Hily–Blant for the suggestion to compare the
magnetic field and integrated intensity maps in Taurus, and for many useful
conversations about this and other topics. We are indebted to Francesco Palla
and Scott Kenyon for providing compilations of young stars in the Taurus
region and their properties. We thank Ted Bergin for carrying out
time–dependent calculations of the CO abundance in diffuse regions. We thank
the anonymous reviewer for very carefully reading the lengthy manuscript,
noting some problems, and making some suggestions for further work which has
improved this study. This research has made use of NASA’s Astrophysics Data
System.

## References

  * Abergel et al. (1995) Abergel, A., Boulanger, F., Fukui, Y., & Mizuno, A. 1995, A&A, 111, 483
  * Alves, Lada, & Lada (1999) Alves, J., Lada, C.J., & Lada, E.A. 1999, ApJ, 515, 265
  * Bachiller & Cernicharo (1986) Bachiller, R. & Cernicharo, J. 1986, A&A, 168, 262
  * Ballesteros-Paredes, Hartmann, & Vázquez–Semadeni (1999) Ballesteros–Paredes, J., Hartmann, L., & Vázquez–Semadeni, E. 1999, ApJ, 527, 285
  * Bally & Langer (1982) Bally, J. & Langer, W.D. 1982, ApJ, 255, 143
  * Beichman et al. (1986) Beichman, C.A., Myers, P.C., Emerson, J.P., Harris, S., Mathieu, R., Benson, P.J., & Jennings, R.E. 1986, ApJ, 307, 377
  * Bertoldi & McKee (1990) Bertoldi, F. & McKee, C.F. 1990, ApJ, 354, 529
  * Burgh et al. (2007) Burgh, E.B., France, K., & McCandliss, S.R. 2007, ApJ, 658, 446
  * Burton & Hartmann (1994) Burton, W.B. & Hartmann, D. 1994, in Unveiling Large–Scale Structures Behind the Milky Way, ASP Conf. Series, Vol. 67, C. Balkowski & R.C. Kraan-Kortweg eds. (San Francisco: Astronomical Society of the Pacific), 31
  * Cernicharo & Guélin (1987) Cernicharo, J., & Guélin, M. 1987, A&A, 176, 299
  * Chu & Watson (1983) Chu, W.–H. & Watson, W.D. 1983, ApJ, 267, 151
  * Crutcher & Troland (2000) Crutcher, R. M., & Troland, T.H. 2000, ApJ, 537, L139
  * Dickman, Snell, & Schloerb (1986) Dickman, R.L., Snell, R.L., & Schloerb, F.P. 1986, ApJ, 309, 326
  * Duvert, Cernicharo, & Baudry (1986) Duvert, G., Cernicharo, J., & Baudry, A. 1986, A&A, 164, 349
  * Elias (1978) Elias, J.H. 1978, ApJ, 224, 857
  * Erickson et al. (1999) Erickson, N.R., Grosslein, R.M., Erickson, R.B., & Weinreb, S. 1999, IEEE Trans. Microwave Theory Tech., 47(12), 2212
  * Federman et al. (1994) Federman, S.R., Strom, C.J., Lambert, D.L., Cardelli, J.A., Smith, V.V., & Joseph, C.L. 1994, ApJ, 424, 772
  * Frerking, Langer, & Wilson (1982) Frerking, M.A., Langer, W.D., & Wilson, R.W. 1982, ApJ, 262, 590
  * Goldsmith et al. (1980) Goldsmith, P.F., Langer, W.D., Carlson, R.E., & Wilson, R.W. 1980, in Interstellar Molecules, IAU Symp. 87, B.H. Andrew ed. (Dordrecht: Reidel), 417
  * Goldsmith, Young, & Langer (1983) Goldsmith, P.F., Young, J.S., & Langer, W.D. 1983, ApJS, 51, 203
  * Goldsmith & Li (2005) Goldsmith, P.F. & Li, D. 2005, ApJ, 622, 938
  * Gomez de Castro & Pudritz (1992) Gomez de Castro, A.I. & Pudritz, R.E. 1992, ApJ, 395, 501
  * Goodman et al. (1992) Goodman, A.A., Jones, J.T., Lada, E.A., & Myers, P.C. 1992, ApJ, 399, 108
  * Hartigan & Kenyon (2003) Hartigan, P., & Kenyon, S.J. 2003, ApJ, 583, 334
  * Hartmann et al. (2001) Hartmann, L., Ballesteros–Paredes, J., & Bergin, E. A. 2001, ApJ,562, 852
  * Hartmann (2002) Hartmann, L. 2002, ApJ, 578, 914
  * Heiles (2000) Heiles, C. 2000, AJ, 119, 923
  * Heiles & Crutcher (2005) Heiles, C. & Crutcher, R. 2005, in Cosmic Magnetic Fields, R. Wielebinski & R. Beck ed. (Berlin: Springer), 137
  * Heyer et al. (1987) Heyer, M.H., Vrba, F.J., Snell, R.L., Schloerb, F.P., Strom, S.E., Goldsmith, P.F., & Strom, K.M. 1987, ApJ, 321, 855
  * Heyer (1988) Heyer, M.H. 1988, ApJ, 324, 311
  * Jijina, Myers, & Adams (1999) Jijina, J., Myers, P.C., & Adams, F.C. 1999, ApJS, 125, 161
  * Kainulainen et al. (2006) Kainulainen, J., Lehtinen, K., & Harju, J. 2006, A&A, 447, 597
  * Kenyon (2007) Kenyon, S. 2007, private communication; to appear in The Handbook of Star Forming Regions, ASP Conference Series, B. Reipurth, ed., 2008
  * Lacy et al. (1994) Lacy, J.H., Knacke, R., Geballe, T.R., & Tokunaga, A.T. 1994, ApJ, 428, L69
  * Langer et al. (1980) Langer, W.D., Goldsmith, P.F., Carlson, E.R., & Wilson, R.W. 1980, ApJ, 235, L39
  * Langer et al. (1989) Langer, W.D., Wilson, R.W., Goldsmith, P.F., & Beichman, C.A. 1989, ApJ, 337, 355
  * Langer & Penzias (1993) Langer, W.D. & Penzias, A.A. 1993, ApJ, 408, 539
  * Langer et al. (1995) Langer, W.D., Velusamy, T., Kuiper, T.B.H., Levin, S., Olsen, E., & Migenes, V. 1995, ApJ, 453, 293
  * Li & Goldsmith (2003) Li, D. & Goldsmith, P.F. 2003, ApJ, 585, 823
  * Li, Goldsmith, & Menten (2003) Li, D., Goldsmith, P.F., & Menten, K.M. 2003, ApJ, 587, 262
  * Liszt & Lucas (1998) Liszt, H.S. & Lucas, R. 1998, A&A, 339, 561
  * Liszt (2007) Liszt, H.S. 2007, A&A, 476, 291
  * Mitchell, Sargent, & Mannings (1997) Mitchell, G.F., Sargent, A.I., & Mannings, V. 1997, ApJ, 483, L127
  * Mizuno et al. (1995) Mizuno, A., Onishi, T., Yonekura, Y., Nagahama, T., Ogawa, H., & Fukui, Y. 1995, ApJ, 445, L161
  * Moneti et al. (1984) Moneti, A., Pipher, J.L., Helfer, H.L., McMillan, R.S., & Perry, M.L. 1984, ApJ, 282, 508
  * Narayanan et al. (2007) Narayanan, G., Heyer, M., Brunt, C., Snell, R.L., Goldsmith, P.F., & Li, D. 2007, submitted to ApJ
  * Onishi et al. (1996) Onishi, T., Mizuno, A., Kawamura, A., Ogawa, H., & Fukui, Y. 1996, ApJ, 465, 815
  * Onishi et al. (1998) Onishi, T., Mizuno, A., Kawamura, A., Ogawa, H., & Fukui, Y. 1998, ApJ, 502, 296
  * Onishi et al. (2002) Onishi, T., Mizuno, A., Kawamura, A., Tachihara, K., & Fukui, Y. 2002, ApJ, 575, 950
  * Padoan et al. (2002) Padoan, P., Cambrésy, L., & Langer, W.D. 1992, ApJ, 580, L57
  * Palla & Stahler (2000) Palla, F. & Stahler, S.W. 2000, ApJ, 540, 255
  * Palla & Stahler (2002) Palla, F. & Stahler, S.W. 2002, ApJ, 58, 1194
  * Palla (2008) Palla, F. 2008, private communication
  * Pratap et al. (1997) Pratap, P., Dickens, J.E., Snell, R. L., Miralles, M.P., Bergin, E.A., Irvine, W.M., & Schloerb, F.P. 1997, ApJ, 486, 862
  * Pringle, Allen, & Lubow (2001) Pringle, J.E., Allen, R.J., & Lubow, S.H. 2001, MNRAS, 327, 663
  * Schloerb & Snell (1984) Schloerb, F.P., & Snell, R.L. 1984, ApJ, 283, 129
  * Shu et al. (1987) Shu, F.H., Adams, F.C., & Lizano, S. 1987, ARA&A, 25, 23
  * Shuter et al. (1987) Shuter, W.L.H., Dickman, R.L., & Klatt, C. 1987, ApJ, 322, L103
  * Snell (1981) Snell, R.L. 1981, ApJS, 45, 121
  * Sonnentrucker et al. (2007) Sonnentrucker, P., Welty, D.E., Thorburn, J.A., & York, D.G. 2007, ApJS, 168, 58
  * Strong & Mattox (1996) Strong, A.W. & Mattox, J.R. 1996, A&A, 308, L21
  * Tamura et al. (1991) Tamura, M., Gatley, I., Wall, W., & Werner, M.W. 1991, ApJ, 374, L25
  * Tatematsu et al. (2004) Tatematsu, K., Umemoto, T., Kandori, R., & Sekimoto, Y. 2004, ApJ, 606, 333
  * Troland et al. (1996) Troland, T., Crutcher, R.M., Goodman, A.A., Heiles, C., Kazès, I., & Myers, P.C. 1996, ApJ, 471, 302
  * Ungerechts & Thaddeus (1987) Ungerechts, H. & Thaddeus, P. 1987, ApJS, 63, 645
  * Van Dishoeck & Black (1988) Van Dishoeck, E.F. & Black, J.H. 1988, ApJ, 334, 771
  * Vázquez–Semadeni (2007) Vázquez–Semadeni, E. 2007, in Triggered Star Formation in a Turbulent ISM, Proc. IAU Symp. 237, B.G. Elmegreen & J. Palous, eds. (Cambridge: Cambridge University Press), 292
  * Watson et al. (1976) Watson, W.D., Anicich, V.G., & Huntress, W.T. Jr. 1976, ApJ, 205, L165
  * Young et al. (1982) Young, J.S., Goldsmith, P.F., Langer, W.D., & Wilson, R.W. 1982, ApJ, 261, 513