# Far-ultraviolet Observations of the Taurus-Perseus-Auriga Complex

Tae-Ho Lim11affiliation: Korea Advanced Institute of Science and Technology
(KAIST), 373-1 Guseong-dong, Yuseong-gu, Daejeon, Korea 305-701, Republic of
Korea Korea Advanced Institute of Science and Technology (KAIST)
<EMAIL_ADDRESS>Kyoung-Wook Min11affiliation: Korea Advanced Institute of
Science and Technology (KAIST), 373-1 Guseong-dong, Yuseong-gu, Daejeon, Korea
305-701, Republic of Korea Korea Advanced Institute of Science and Technology
(KAIST)  Kwang-Il Seon22affiliation: Korea Astronomy and Space Science
Institute (KASI), 61-1 Hwaam-dong, Yuseong-gu, Daejeon, Korea 305-348,
Republic of Korea Korea Astronomy and Space Science Institute (KASI)

###### Abstract

We have constructed a far-ultraviolet (FUV) continuum map of the Taurus-
Auriga-Perseus complex, one of the largest local associations of dark clouds,
by merging the two data sets of GALEX and FIMS, which made observations at
similar wavelengths. The FUV intensity varies significantly across the whole
region, but the diffuse FUV continuum is dominated by dust scattering of
stellar photons. A diffuse FUV background of $\sim$1000 CU is observed, part
of which may be attributable to the scattered photons of foreground FUV light,
located in front of the thick clouds. The fluorescent emission of molecular
hydrogen constitutes $\sim$10 % of the total FUV intensity throughout the
region, generally proportional to the local continuum level. We have developed
a Monte Carlo radiative transfer code and applied it to the present clouds
complex to obtain the optical properties of dust grains and the geometrical
structures of the clouds. The albedo and the phase function asymmetry factor
were estimated to be $0.42^{+0.05}_{-0.05}$, and $0.47^{+0.11}_{-0.27}$,
respectively, in accordance with theoretical estimations as well as recent
observations. The distance and thickness of the four prominent clouds in this
complex were estimated using a single slab model applied individually to each
cloud. The results obtained were in good agreement with those from other
observations in the case of the Taurus cloud, as its geometrical structure is
rather simple. For other clouds, which were observed to have multiple
components, the results gave distances and thicknesses encompassing all
components of each cloud. The distance and thickness estimations were not
crucially sensitive to the exact values of the albedo and the phase function
asymmetry factor, while the locations of the bright field stars relative to
the clouds as initial photon sources seem to be the most important factor in
the process of fitting.

###### Subject headings:

ISM: clouds — ISM: dust, extinction — ISM: individual (Taurus, Auriga and
Perseus complex) — ISM: structure — ultraviolet: ISM

##  1\. Introduction

The immense complex of the Taurus, Perseus, and Auriga (TPA) clouds is known
to be one of the largest local associations of dark nebula. According to
Ungerechts et al. (1987), the total masses of the whole complex is $\sim
2\times 10^{5}$ solar mass. The TPA complex contains star-forming cloudlets
(TMC1, TMC2, NGC 1333, and IC 348, for example), a bright emission nebula (NGC
1499, also known as California Nebula), and stellar associations (Per OB2, for
example). Low-mass star formation processes are believed to be taking place in
the eastern section of the complex (Taurus and Auriga), where mostly low-mass
T Tauri type stars are observed, while both low- and high-mass stars are being
formed in the western section of the Perseus complex (the Per OB2 association,
the open cluster NGC 1333, and so on). The whole complex may be physically
associated with the Per OB2 stellar association, centered at (l, b)=(160.5,
-14.7) with a diameter of $\sim 20^{\circ}$, which is the second closest OB
association to the Sun with a distance of $\sim$300 pc on average (Belikov et
al., 2002). Recent supernova explosions in the Per OB2 association are
believed to have created an expanding HI supershell that is moving into the
surrounding interstellar medium (Sancisi et al., 1974; Hartmann & Burton,
1997).

The TPA complex may consist of multiple layers of molecular gas located at
various distances. The Taurus cloud is believed to spread between 100 pc and
200 pc (Ungerechts et al., 1987), with a large part of it blocked by the cloud
itself (Elias, 1978; Kenyon et al., 1994). The most distant part of the Taurus
molecular cloud complex may be interacting with a supershell blown by the Per
OB2 association (Olano et al., 1987). Cernis (1990) argued that the cloud in
the region of NGC 1333, one of the star forming regions located in and around
the Perseus cloud, consists of two layers, and estimated their distances to be
$\sim$170 pc and $\sim$230 pc based on an extinction analysis. The Auriga dark
cloud, located at a distance similar to that of the Taurus cloud, is usually
regarded as part of the Taurus-Auriga complex, and was suggested to overlap
with the California cloud at its farthest side (Ungerechts et al., 1987). The
California cloud seems to be the most distant cloud in this region: Lada et
al. (2009) argued that the cloud is located at $\sim$450 pc from the Sun.

The interstellar radiation field (ISRF), composed of radiations originating
directly from stellar sources as well as the diffuse background, plays an
important role in the physical and chemical processes of the interstellar
medium (ISM). For example, far-ultraviolet (FUV) ISRF photons may ionize
atoms, dissociate molecules, or heat gases by ejecting electrons from dust
grains or by directly exciting atoms and molecules. The ISRF itself is also
affected by interactions with the ISM. In fact, most of the diffuse FUV
background radiation is believed to originate from the scattering of starlight
by interstellar dust (Bowyer, 1991; Seon, 2011). The effect of dust scattering
is well observed in reflection nebulae and dark clouds as well as in the
diffuse galactic light (DGL). Hence, the observations of these objects have
been used not only to trace interstellar dust, but also to obtain the optical
properties of dust itself, such as the albedo (a) and the phase function
asymmetry factor (g). In the case of the DGL, dust scattering was observed to
be moderately reflective in the forward direction (Lillie et al., 1976;
Joubert et al., 1983; Hurwitz et al., 1991; Murthy et al., 1991, 1994, 1995;
Witt et al., 1997), with the estimated values of a and g in general agreement
with those of the theoretical model for carbonaceous-silicate grains, i.e.,
0.40-0.60 and 0.55-0.65, respectively, at UV wavelengths (Weingartner &
Draine, 2001). For reflection nebulae (Murthy et al., 1993; Witt, 1992; Gordon
et al., 1994; Gibson et al., 2003) and individual clouds (Witt et al., 1990;
Mattila, 1970; Hurwitz, 1994), however, the results were varied and dependent
on the individual targets, probably due to uncertainties in the scattering
geometry of the target clouds as well as the star systems that were the
dominant sources of photons (Draine, 2003; Bowyer, 1991). Calzetti et al.
(1995) determined a and g to be 0.7-0.8 and $\sim$0.75 around 1600 Å,
respectively, for dust toward IC 43, while Gibson et al. (2003) estimated a
and g to be $\sim$0.22 and $\sim$0.74, respectively, for wavelengths below
2200 Å for the Pleiades nebula. For the Ophiuchus cloud, Sujatha et al. (2005)
found a and g to be $\sim$0.40 and $\sim$0.55, respectively, at $\sim$1100 Å,
while Lee et al. (2008) obtained $\sim$0.36 and $\sim$0.52 for a and g,
respectively, for 1370 Å–1670 Å.

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Figure 1.— The FIMS continuum image (a) and the GALEX FUV image (b).

The main goal in this line of research has been the estimation of the optical
properties of dust grains. The geometry of the clouds and the distribution of
stellar photon sources involved, however, were also assumed to influence the
intensity of light scattered by dust in the clouds, thereby providing
constraints on the geometrical structures of the clouds themselves. For
example, Sujatha et al. (2005) assumed two extended sheet-like structures for
their study on the Ophiuchus cloud. Shalima et al. (2006) also used the
morphology of a plane-parallel dust sheet in their scattering simulation of
the Orion nebula. Although these assumed clouds geometries were highly
idealistic, the estimated distances were more or less reasonable when compared
to results based on other observations. In this paper, we examine the results
of the FUV observations made for the TPA region and study the clouds
geometries, though the results might still be very simple. We perform Monte
Carlo simulations of dust scattering and compare the results with the observed
diffuse FUV emission map. In fact, it was revealed in the study of the Taurus
region that the continuum emission is closely related to dust extinction (Lee
et al., 2006). There have been several reports on the structures of the clouds
in this region, mostly based on star counting methods, extinction studies, and
comparisons with the distances of the associated stars and nebulae. We show
that the present method of dust scattering simulations gives consistent
estimates regarding the clouds’ geometries in this region. We also demonstrate
that the average albedo value obtained for this region is in good agreement
with a theoretical estimation.

##  2\. Data Reduction

We employed two data sets for the present study. The first is from
observations made by the FUV Imaging Spectrograph (FIMS) flown aboard the
Korean microsatellite STSAT-1, which was launched on September 27, 2003 and
operated for a year and a half. The second consists of FUV archival data of
the Galaxy Evolution Explorer (GALEX). FIMS is an imaging spectrograph
optimized for the observation of diffuse emissions with two wavelength
channels, a short wavelength channel covering $\lambda\lambda$ 900–1150 Å, and
a long wavelength channel covering $\lambda\lambda$ 1350–1700 Å. Both channels
have a resolving power of $\lambda/\Delta\lambda\sim$ 550\. We analyzed only
the long wavelength channel data in the present study since the short
wavelength channel was contaminated by many airglow lines. The field of view
of the long wavelength channel is $7.4^{\circ}\times 4.3^{\prime}$, with a
5–10′ imaging resolution along the slit, and the spectral half-energy line
width, averaged over the angular field, is 3.2 Å. The instrument, its in-orbit
performance, and the data analysis procedures are described in Edelstein et
al. (2006a, 2006b).

The FIMS data set that covers the TPA area of 154∘ – 180∘ in Galactic
longitude and -28∘ – -2∘ in Galactic latitude is composed of 38 observations
made during the sky survey toward this region. The total exposure time is
around 3.6 s per pixel, on average. Only the data from 1360 Å to 1680 Å,
excluding the intense O I airglow line at 1356 Å, was used for the present
analysis. The FIMS continuum image of the diffuse emission was constructed by
spatially binning the data with a square bin of 0.4∘ x 0.4∘ size, after
removing pixels that had more than 9,000 Continuum Unit (photons s-1 cm-1 sr-1
Å-1, hereafter CU) as these were suspected to be contaminated by bright stars.
The 9000 CU criterion was chosen as the data of GALEX, which intentionally
avoided the observation of bright stars, did not exceed 9000 CU in this
region. Figure 1(a) shows the resulting FIMS image, where the regions of
missing data are shown in black. While the map shows the expected general
features of the TPA region, including the dark Taurus cloud and the bright Per
OB2 association, we can also see that the bright regions of the Per OB2
association are very extended across the scanning direction. In fact, this
extended appearance is due to instrumental scattering along the slit.
Furthermore, some areas of the FIMS image were made with extremely short
exposures. Hence, we merged the GALEX FUV data with the FIMS data to remedy
these shortcomings, as the wavelength range of the GALEX data is similar to
that of the FIMS, i.e., 1350 – 1750 Å.

From the GALEX data release website, we extracted the All Sky Surveys imaging
data (AIS of GR4/GR5 Data Release) of the TPA region, and plotted the image
with 0.4∘ x 0.4∘ bins in Figure 1(b). We compared the intensities of the two
observations pixel by pixel to check for possible biases that might exist
between them. We limited our comparison to only the regions in which the FIMS
intensity was less than 6000 CU, to exclude the bright pixels affected by the
instrumental scattering and the pixels where FIMS exposure time was greater
than 2.5 s. In Figure 2, we show the resulting scatter plot, in which we can
see a remarkable correlation between the two data sets. The linear fitting
between the two intensities is given by $I_{GALEX}=1.01\times I_{FIMS}+185.50$
in CU. The standard deviation of the data about the linear fit is $\sim$ 550
CU. Since we believe GALEX data are more reliable than FIMS data in the region
where the GALEX data are available because of instrumental scattering and
short exposure times of FIMS, we used GALEX data as the basis of the merged
map and filled the regions where GALEX did not observe with the FIMS data
scaled according to the above linear fitting function. The resulting merged
map is shown in Figure 3(a).

Figure 2.— A pixel-to-pixel scatter plot for the intensities of the TPA region
observed by FIMS and GALEX showing a remarkable agreement. The red solid line
is a linear fit of the data points.

##  3\. Results

###  3.1. Examination of the FUV continuum map

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Figure 3.— (a) FUV intensity (in CU) overlaid by the dust extinction contours,
with thicker contours representing higher dust extinction levels, (b)
H$\alpha$ emission map shown in Rayleighs, (c) SFD dust extinction map,
E(B-V), and (d) CO emission map, shown in K km/s. The locations A, B, and C in
panel (a) are those with distinct physical characteristics and discussed in
the text.

Figure 3 shows images of the TPA region constructed at different wavelengths:
(a) the FUV map obtained by merging the FIMS and GALEX data, (b) H$\alpha$
emission map (Finkbeiner, 2003), (c) Schlegel, Finkbeiner & Davis (SFD) Dust
Survey map (Schlegel et al., 1998), and (d) the CO emission map (Dame et al.,
2001). The FUV continuum map of Figure 3(a) shows bright enhancement in the
regions of the Per OB2 association and the Pleiades cluster, as well as dark
regions coincident with the Taurus and Auriga clouds. Hence, the FUV flux is
bright on the low-longitude half where H$\alpha$ emission is also bright,
while FUV flux seems to be heavily absorbed by the dense cloud of the Taurus-
Auriga complex in the high-longitude half, where the dust extinction level is
high. The existence of a dense cloud, however, does not necessarily imply that
FUV intensity will be low there. For example, the California cloud near the
Per OB2 association is rich in dust but FUV intensity is still bright there, a
feature related to their respective distances, to be discussed later. In the
dust extinction and CO emission maps, shown in Figure 3(c) and Figure 3(d),
respectively, a common void or cavity is seen surrounded by the dark clouds of
the TPA complex. The void is coincident with the brightest region in the
H$\alpha$ emission map of Figure 3(b) in the vicinity of the center of the Per
OB2 association. Though not noticeable here, a dust emission ring is seen
around the cavity according to sub-millimeter and far-infrared maps (Watson et
al., 2005). In fact, the void region was identified to be an HI supershell
with a diameter of $\sim$100 pc, which is believed to have been formed by the
interaction of the Per OB2 association with the ambient interstellar medium
(Sancisi et al., 1974; Heiles, 1984). The bright spot south of the Taurus
cloud is the reflection nebula around the Pleiades cluster.

We have selected three distinct subregions as shown in Figure 3(a) and made a
pixel-to-pixel plot of the FUV intensity against dust extinction, with
different colors according to the subregions. Subregion A includes the Taurus
cloud which is optically thick with low FUV intensity, and subregion B is
optically thin with a little higher FUV intensity. Subregion C is a region of
high FUV intensity that includes both optically thin and thick areas. The
result is shown in Figure 4. First, we note that region A, which includes the
thick Taurus cloud, indeed shows a general anti-correlation between the FUV
intensity and the dust extinction level, implying that FUV is heavily absorbed
by the dense Taurus cloud. On the other hand, the result for region B shows a
positive correlation, in agreement with the general notion that FUV intensity
increases with dust extinction level in the optically thin region (Hurwitz,
1994; Luhman et al., 1996). Indeed, most of the data points in region B
correspond to small values of color excess, below $\sim$0.5. On the other
hand, region C shows severe fluctuations, obviously due to the non-uniform
strong radiation fields of the Per OB2 association over a wide range of the
color excess values. Another interesting feature seen in Figure 4 is that FUV
intensity does not decrease below 1000 CU even at a very high extinction
level, part of which we may attribute to the scattered photons of the
foreground FUV light, located in front of the thick clouds (Lee et al., 2006).
Hurwitz et al. (1991) also observed a similar diffuse background for the
Galactic latitudes $10^{\circ}<|b|<20^{\circ}$.

Figure 4.— A scatter plot of the FUV intensity against dust extinction: the
blue, orange, and black colors correspond to the regions A, B, and C in Figure
3(a), respectively.

###  3.2. Monte Carlo simulation of dust scattering

As shown in Figure 4, the scatter plot of FUV intensity against the dust
extinction level shows complicated behaviors that depend on local extinction
levels, fluctuations of local radiation fields as well as mixing of the
foreground and background FUV photons. On the other hand, such complicated
behaviors might also make it possible to extract information regarding the
structure of the clouds, especially their relative locations, by comparing the
observed FUV intensities with those of dust-scattering simulations that
incorporate local photon sources and an assumed distribution of clouds. In
fact, similar methods have been previously applied to several cloud systems
(Gordon et al., 2001; Shalima et al., 2006; Lee et al., 2008; Sujatha et al.,
2005, 2007).

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Figure 5.— Spectra of the whole TPA region and subregions A, B, and C, in which the fluorescent emission lines of molecular hydrogen are indicated with vertical red bars. The dashed blue lines represent simple models for the continuum emissions.  |
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Figure 6.— (a) Dust scattered FUV map constructed from the observations and
(b) the Monte Carlo simulation results. The California nebula region is
excluded from our dust scattering simulations as its H$\alpha$ intensity is
extremely high and the associated two-photon effect is difficult to estimate.

Our main purpose in the present study is to understand through simulations the
dust scattering properties and the morphological structures in this broad
region. More specifically, we seek to understand the distances and thicknesses
of the TPA clouds, which includes both thick clouds and strong radiation
fields of OB associations, based on the observed FUV emission features. Hence,
it is necessary to identify and remove contributions other than the dust-
scattered emission from the observed FUV image. In addition to dust-scattering
of stellar photons, diffuse interstellar FUV emissions can have three
different origins including: i) ion line emission coming from hot gas of
10${}^{4.5}-$ 105 K; ii) H2 fluorescent emission originating from the outer
regions of molecular clouds irradiated by interstellar UV photons; and iii)
two-photon effects which are mostly relevant to ionized regions. Of the other
FUV sources, ion line emissions should be negligible in the present region of
thick clouds. On the other hand, we expect significant H2 fluorescent
emissions in this region where both thick clouds and strong radiation fields
exist. Based on the spectral observations of FIMS, Figure 5 indeed shows that
H2 fluorescent emission is detectable throughout the whole TPA region. The
contribution from the H2 fluorescent emission lines is estimated to be
$\sim$10.8 %, $\sim$11.4 %, and $\sim$9.5 % of the total FUV intensity for the
regions A, B, and C, respectively, and $\sim$10% for the whole region. We have
accordingly subtracted 10 % of the total intensity from the map shown in
Figure 3(a) to account for the contribution from H2 fluorescent emission.
Estimation of the two-photon effect can be a little tricky since H$\alpha$
emission can also originate from regions other than ionized regions, and
H$\alpha$ photons may also be scattered in a manner similar to the FUV
continuum photons. Furthermore, Reynolds (1990) suggested a two-photon
continuum emission of $\sim$60 CU for 1 Rayleigh of H$\alpha$ line in the case
of a diffuse ionized gas, while Seon (2011) estimated it to be $\sim$26 CU for
1 Rayleigh of H$\alpha$ emission of a cooling ionized gas. Hence, we have
excluded the California nebula region, where H$\alpha$ intensity is especially
high, in our simulation and applied the formula of the FUV continuum intensity
of 60 CU for 1 Rayleigh intensity of H$\alpha$ throughout the region as a
simple approximation. We will discuss later the dependence of the optical
properties of dust on the models of the two-photon effects. Finally, we have
subtracted uniformly an isotropic FUV emission of $\sim$300 CU (Bowyer, 1991)
although this value was obtained for the high Galactic latitude region. The
resulting FUV map is shown in Figure 6(a).

We employed a Monte Carlo Radiative Transfer technique, in which photons were
allowed to have multiple scatterings (Witt, 1977; Wood et al., 1999; Seon,
2009, 2012). At each scattering, after moving a mean free path distance
determined by the optical depth, the photons were randomly scattered into an
angle with a probability given by the Henyey-Greenstein function (Henyey &
Greenstein, 1941). We adopted the peeling-off technique to achieve simulation
efficiency, i.e., regardless of the actual scattering angle determined
randomly, the probability that the photon would be scattered in the direction
toward the Sun was calculated for each scattering, and the corresponding
fraction of the intensity was added up for the final image (Yusef-Zadeh et
al., 1984). We did not consider any wavelength changes upon scattering. The
free parameters to be determined by the simulation were the albedo, the
asymmetry factor, and the distribution of dust, while the initial photon
sources were chosen to be the bright stars in the TPA region. There are,
however, infinite numbers of possible choices for the three-dimensional
spatial distribution of dust under the given information of integrated
extinction along the lines of sight, which we adopted from the SFD dust
extinction map (Schlegel et al., 1998). Therefore, we assumed, for convenience
that the dust was distributed uniformly inside a slab whose thickness and
distance from the Sun were to be determined. The E(B-V) values of the SFD map
were converted to optical depths at 1565Å, a representative FUV wavelength of
the present study, with an assumed RV value of 3.1.

Table 1Distance to the front face and the thickness of the four selected clouds, obtained by treating each cloud individually.  clouds | Taurus | Perseus | Auriga | California
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Distance to the front face (pc) | 120 ${}^{+20}_{-80}$ | 70 ${}^{+30}_{-20}$ | 140 ${}^{+20}_{-90}$ | 170 ${}^{+10}_{-10}$
Thickness (pc) | 110 ${}^{+20}_{-50}$ | 230 ${}^{+30}_{-40}$ aaThe large thicknesses of the Perseus, California, and Auriga clouds may be due to multiple layers. Refer to Section 4 for their discussions. | 190 ${}^{+70}_{-20}$ aaThe large thicknesses of the Perseus, California, and Auriga clouds may be due to multiple layers. Refer to Section 4 for their discussions. | 320 ${}^{+50}_{-30}$ aaThe large thicknesses of the Perseus, California, and Auriga clouds may be due to multiple layers. Refer to Section 4 for their discussions.
Distance to the center (pc) |  $\sim$175 |  $\sim$185 |  $\sim$235 |  $\sim$330

The simulation box consisted of a 400 $\times$ 400 $\times$ 400 pixel, with
each pixel equivalent to 1 pc. The Sun was located at the center of the front
face of the simulation box. A total of 88307 stars was employed as the
radiation sources, consisting of 18212 TD-1 stars and 70095 Hipparcos stars.
The luminosities of the stars were calculated using the observed FUV stellar
fluxes for the TD-1 stars and Castelli’s stellar models for the Hipparcos
stars, based on the listed spectral types, with extinction effects taken into
account (Thompson et al., 1978; Perryman et al., 1997; Castelli et al., 2003).
As a first step, we assumed a single dust slab model for the entire TPA
region, which was to be improved at the second step by considering individual
clouds separately, using the values of the albedo and the asymmetry factor
obtained in the first step. Simulations were carried out for the following
parameter ranges: the albedo values varied from 0.20 to 0.60 with 0.01 steps,
the asymmetry factor varied from 0.0 to 0.80 with 0.01 steps, the distance to
the front face varied from 10 pc to 390 pc with 10 pc steps, and the thickness
of the slab varied from 10 pc to 390 pc with 10 pc steps. The best-fit
parameters were determined by comparing the simulation results with the
observed FUV map using the chi-square minimization.

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Figure 7.— A scatter plot of the simulated FUV intensity against the observed FUV intensity for the regions of the Taurus, Perseus, Auriga, and California clouds. Panel a) shows the result obtained using a single dust slab model and panel b) shows the result obtained with the individual clouds treated separately. The navy, sky blue, yellow, and orange colors correspond to the regions of the Taurus, Perseus, Auriga, and California clouds, respectively.  |
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Figure 8.— 1-$\sigma$ confidence contours of the distance to the front face
and the thickness, plotted for the four clouds identified in Figure 3(d). The
cross symbol indicates the best-fit values. For this simulation, fixed values
of the albedo (a = 0.42) and the asymmetry factor (g = 0.47) were used.

Figure 6(b) shows the simulated map with the best-fit parameters: 0.42 for the
albedo, 0.47 for the asymmetry factor, 50 pc for the distance to the front
face, and 220 pc for the thickness. The error ranges of the parameter values
are mainly due to the statistical fluctuations of the FIMS data with low
exposure time: the 1-$\sigma$ ranges of the albedo and the asymmetry factor
are 0.37 to 0.47 and 0.20 to 0.58, respectively. Nevertheless, the estimated
albedo of 0.42 is close to the theoretical model value of $\sim$0.40, while
the asymmetry factor is rather small compared to the theoretical expectation
of $\sim$0.65 (Weingartner & Draine, 2001). Jo et al. (2012) obtained 0.43 and
0.45 for the albedo and the asymmetry factor, respectively, in their
simulation for the Orion-Eridanus Superbubble. The simulated map shown in
Figure 6(b) looks similar to the observed FUV map of Figure 6(a), but we note
that the region around the California nebula is less bright and the Taurus
region is less dark in the simulated map than in the observed map. Indeed, the
intensity varies less over the whole TPA region in the simulated map than in
the observed map. The reason for the reduced variability could be the
assumption of a single slab model for the entire region. For example, the
reduction of intensity in the region around the California nebula was
compensated by an increase in intensity in the Taurus region as the reduced
chi-square was to be minimized with a single dust slab model. Hence, it should
be meaningful for the individual clouds to be treated separately with their
own distances and thicknesses. With the values of the albedo (a = 0.42) and
the asymmetry factor (g = 0.47) determined from the single slab model, we
carried out simulations separately for the individual clouds of Taurus,
Perseus, Auriga, and California. For the California cloud, we enlarged the
simulation box to 400 pc $\times$ 400 pc $\times$ 800 pc as the cloud was
found to extend beyond 400 pc. Relative to the single slab model, the pixel-
to-pixel scatter plot of the simulated FUV intensity against the observed FUV
intensity shows significant improvement, as can be seen in Figure 7. Table 1
shows the improved distances and thicknesses of the TPA clouds, and Figure 8
shows contour plots for 1-$\sigma$ error ranges. These best-fit values are in
good agreement with the previous estimations based on other methods, as will
be discussed in the following section. In the cases of the Taurus and Auriga
clouds, the distances to the front faces seem to have rather large error
ranges in the lower limit. Unfortunately, very few bright stars exist in front
of these clouds that can constrain well the distances to their front faces.

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Figure 9.— A scatter plot of the simulated FUV intensity against the observed
FUV intensity for the two subregions A and B of the Perseus cloud, marked in
Figure 3(d): (a) when the whole system of the Perseus cloud is treated as a
single layer, and (b) when the two sub-regions are treated individually. The
green and purple data points correspond to the regions of A, where NGC 1333 is
located, and B, where IC 348 is located, respectively.

##  4\. Discussion

We have estimated the locations of the four prominent clouds in the TPA region
by comparing the observed FUV images with the results of the Monte Carlo
simulations of dust scattering. For the Taurus cloud, we obtained a distance
to the front face and a thickness of the cloud of $120^{+20}_{-80}$ pc and
$110^{+20}_{-50}$ pc, respectively. There have been many reports on the
physical structure of the Taurus cloud. Elias (1978) estimated the mean
distance to the Taurus complex to be $\sim$135 pc, based on the distances to
the stars associated with the Taurus cloud. Ungerechts et al. (1987) suggested
that the cloud spreads between 100 pc and 200 pc, based on the results of star
counting, the distances of the reflection nebulae, and the color excess of the
field stars. Straizys (2001) also reported that extinction begins to increase
sharply at 130-180 pc. The present result agrees well with all these
observations. For the Perseus cloud, the present simulation estimates a
distance to the front face and a thickness of $70^{+30}_{-20}$ pc and
$230^{+30}_{-40}$ pc, respectively. The scatter plot of the simulated vs. the
observed FUV intensity in Figure 7(b) shows severely scattered data points for
the Perseus cloud, indicating that the model cloud does not adequately
describe its actual structure. In fact, the data points corresponding to the
observation are spread over a wide range of intensity, which we believe comes
from the assumption of a single layer for the cloud. Hence, we have divided
the Perseus cloud into two sub-regions and fit them separately. We name Per A
as the western part of the cloud and Per B as the eastern part, as shown in
Figure 3(d), and these include the two regions NGC 1333 and IC 348,
respectively. With the same fixed values of the albedo (a = 0.42) and the
asymmetry factor (g = 0.47) as used in the previous simulations, we find a
distance to the front face and a thickness of the Per A region of
$100^{+30}_{-30}$ pc and $180^{+30}_{-50}$ pc, respectively, and a distance to
the front face and a thickness of the Per B region of $\sim$320 pc and
$\sim$30 pc within ${}^{+10}_{-10}$ pc error range, respectively. The scatter
plot is now improved considerably, as shown in Figure 9. For the western
portion of the Perseus cloud, Cernis (1990) obtained $\sim$170 pc and
$\sim$230 pc for the distances of the two layers in this region, while Hirota
et al. (2008), using the parallax observation of the 22 GHz H2O maser,
directly measured the distance of NGC 1333 to be $\sim$240 pc. The rather
thick cloud obtained in the present simulation for Per A may reflect the
multi-layer nature of the cloud suggested by Cernis (1990). The distance to
the eastern portion of the Perseus cloud containing IC 348 was estimated to be
larger than 300 pc (Herbig & Jones, 1983). It is interesting that the
thickness was estimated to be rather small for Per B in the present
simulation. It was seen that the intensity of the scattered emission was very
high when the cloud was placed at a distance below 300 pc. We believe the
emission observed in the Per B region comes from backward scattering reflected
by the cloud itself.

Figure 10.— Distance estimations of the four clouds based on the present Monte
Carlo simulations of diffuse FUV emissions, compared with previous
observations.

For the Auriga cloud, the distance to its front face and its thickness are
estimated in the present study to be $140^{+20}_{-90}$ pc and
$190^{+70}_{-20}$ pc, respectively, and for the California cloud, they are
$170^{+10}_{-10}$ pc and $320^{+50}_{-30}$ pc, respectively. Eklof (1959)
suggested that the Auriga cloud has a two-layered structure near the eastern
end of the California cloud, with the layers located at $\sim$115-135 pc and
$\sim$270-380 pc, based on an extinction study. Ungerechts et al. (1987)
determined a distance to the California cloud of $\sim$350 pc while Lada et
al. (2009) suggested that the cloud is located at $\sim$450 pc from the Sun.
Straizys (2001) argued that the California cloud region is two-layered, with
the first layer at $\sim$160 pc and the second layer at $\sim$350 pc. With the
present single-slab model, it is impossible to reproduce such multi-layer
structures. Instead, we obtained single thick clouds, encompassing two layers
of the clouds. We note that the estimated value of $\sim$330 pc to the center
of the California cloud is larger than the distance to the Per OB2 association
($\sim$300 pc on average, Belikov et al. (2002)). Hence, the California cloud,
being located behind the Per OB2 association which is a candidate source for
the bright FUV emission seen in this region, does not block the emission from
the association. Figure 10 shows a summary of our distance estimations for the
four clouds, along with previous observations for the corresponding clouds.

We have plotted in Figure 11 the velocity-clipped CO emission maps for the
ranges given in the Local Standard of Rest (LSR) frame: (a) from -21.8 km/s to
+30.2 km/s, (b) from -10.7 km/s to -0.3 km/s, (c) from +0.3 km/s to +2.9 km/s,
and (d) from +4.2 km/s to +10.7 km/s. These maps are reproduced from the CO
sky survey data by Dame et al. (2001). While the differences in the LSR
velocities do not necessarily imply their relative distances, they may give
insightful clues to the physical associations of the corresponding clouds. For
example, the California cloud is seen in Figure 11(b) and no other clouds are
seen in that velocity range. In Figure 11(d), however, we can see indications
of the Taurus, Auriga, and Perseus clouds, but not of the California cloud.
Such a grouping may indicate that the California cloud is physically not
connected to other clouds, while the rest of the clouds system may be more or
less associated. Furthermore, parts of the Auriga and Perseus clouds are also
seen in Figure 11(c). Hence, the fact that these clouds are seen in a wide
range of the LSR velocities may be consistent with them having multi-layered
structures. Bally (2008) also noted that the large velocity gradient observed
in the Perseus cloud may be due to the nature of multi-components superimposed
along the line of sight.

Figure 11.— Velocity-clipped CO emission maps for the ranges (a) from -21.8
km/s to +30.2 km/s, (b) from -10.7 km/s to -0.3 km/s, (c) from +0.3 km/s to
+2.9 km/s, and (d) from +4.2 km/s to +10.7 km/s.

The error ranges of the estimated optical properties are a little large,
especially in the value of the asymmetry factor, where the reason was
attributed earlier to the statistical fluctuations of the FIMS data with low
exposure time. Nevertheless, the best fit values of the distances to the
respective front face and the thicknesses of the clouds do not seem to change
much when even the upper or lower limits of these error ranges are used for
fitting. For example, the changes are mostly $\sim$10 pc for the distances to
the front faces and $\sim$30 pc for the thicknesses of the clouds. The most
sensitive parameters for fitting are instead the locations of the field stars
as the photon sources relative to the clouds, not the optical properties of
dust. We have also made a number of assumptions in the present study to obtain
the optical properties of dust and the geometrical structures of the clouds in
the TPA region. First, we used a conversion formula for the FUV continuum
intensity of 60 CU for 1 Rayleigh intensity of H$\alpha$ to estimate the two-
photon effects, which holds only for the case of a hot diffuse ionized gas
whose temperature is $\sim$8000 K (Seon, 2011). To see the effect of the
choice of the conversion factor, we ran the same Monte Carlo simulation by but
instead subtracting the two-photon effect with a conversion factor of 30 CU
for 1 Rayleigh of H$\alpha$ in one case and even with no subtraction in
another case. The results were a = 0.43, g = 0.49 for the former case, and a =
0.44, g = 0.52 for the latter case. All these values are within the 1-sigma
range of the nominal case, a = $0.42^{+0.05}_{-0.05}$ and g =
$0.47^{+0.11}_{-0.27}$, implying that the choice of the conversion factor does
not alter the conclusions made in the present study. Next, we subtracted 300
CU as an isotropic background of the FUV emission, which was obtained for high
Galactic regions. When we subtracted 500 CU instead, only the thicknesses of
the clouds changed while the distances to the respective front face remained
the same. The thickness decreased by $\sim$10 % for the Auriga and the
California clouds as well as Per A, and $\sim$30 % for the Taurus cloud
region, which is darkest of all and thus most affected. The reason for the
decrease in thickness is that reduction in FUV intensity was accomplished by
increasing the shielding effect in the case of these clouds. On the other
hand, the thickness of Per B increased by $\sim$20 pc, reflecting the nature
of backward scattering in the case of Per B. Nevertheless, these new values
are all within the 1-sigma range of the results obtained for the nominal case.

##  5\. Conclusions

We have constructed a FUV continuum map of the TPA complex using FIMS and
GALEX data. The morphological features seen in the complex are well understood
in terms of dust scattering, as demonstrated by Monte Carlo simulations. The
following are the main findings of the present study:

  1. 1.

The diffuse FUV emission seen in the complex originates mostly from scattering
of stellar photons by dust grains.

  2. 2.

The FUV intensity of 1000 CU is observed at a very high extinction level,
which we regard as diffuse background and attribute to scattered FUV photons
located in the foreground to the thick clouds.

  3. 3.

Molecular hydrogen fluorescent emission constitutes $\sim$10% of the total FUV
intensity throughout the region.

  4. 4.

We have derived the following scattering parameters for this region based on
the Monte Carlo Radiative Transfer (MCRT) simulations: albedo (a) =
$0.42^{+0.05}_{-0.05}$ and asymmetry factor (g) = $0.47^{+0.11}_{-0.27}$.
These values agree well with those obtained previously for the Orion-Eridanus
Superbubble region as well as theoretical estimations.

  5. 5.

We have estimated the distances to the four prominent clouds in this complex,
which are in good agreement with those estimated observationally using other
methods. The thickness of each cloud was also reasonably determined when it
has a simple structure such as the Taurus cloud. The present single slab
model, however, was not able to reproduce multi-layered clouds, but gives
rather thick clouds, instead.

  6. 6.

The geometrical structures of the clouds are less sensitive to the exact
values of the albedo and the asymmetry factor. Instead, the locations of the
field stars relative to the clouds are the main factors that constrain the
distance and thickness of the clouds.

FIMS/SPEAR is a joint project of KAIST and KASI (Korea) and UC Berkeley (USA),
funded by the Korea MOST and NASA grant NAG5-5355. This research was supported
by Basic Science Research Program (2010-0023909) and National Space Laboratory
Program (2008-2003226) through the National Research Foundation of Korea (NRF)
funded by the Ministry of Education, Science and Technology.

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