# Dust Scattering from the Taurus Molecular Cloud

Sathyanarayan1, Jayant Murthy2 and K. Narayanankutty1
1Amrita Vishwa Vidyapeetham, Kollam 690525, India
2Indian Institute of Astrophysics, Bengaluru 560034, India
sathyanarayank<EMAIL_ADDRESS>
(Accepted . Received ; in original form )

###### Abstract

We present an analysis of the diffuse ultraviolet (UV) emission near the
Taurus Molecular Cloud based on observations made by the Galaxy Evolution
Explorer (GALEX). We used a Monte Carlo dust scattering model to show that
about half of the scattered flux originates in the molecular cloud with 25%
arising in the foreground and 25% behind the cloud. The best-fit albedo of the
dust grains is 0.3 but the geometry is such that we could not constrain the
phase function asymmetry factor ($g$).

###### keywords:

Taurus Molecular Cloud, ultraviolet: ISM

††pagerange: Dust Scattering from the Taurus Molecular
Cloud–References††pubyear: 2015

##  1 Introduction

The Taurus Molecular Cloud (TMC) is part of the larger Taurus-Auriga complex
of molecular clouds which extends over more than 100 square degrees in the
sky. It is one of the nearest star forming regions at a distance of only 140
pc from the Sun with a thickness of around 20 pc (Kenyon et al., 1994; Loinard
et al., 2005; Lombardi et al., 2010). Although it is near the Galactic Plane
(b $\sim$ -14), there is little dust either in front of or behind the
molecular cloud (Padoan et al., 2002; Lombardi et al., 2010). The TMC has been
studied intensively at many different wavelengths and has provided a
laboratory for the study of molecular cloud evolution and star formation in
fine spatial and spectral detail.

High resolution optical maps show that the TMC is comprised of loosely
associated diffuse filaments mixed with highly clumpy molecular cores
(Panopoulou et al., 2014). The clumpy molecular gas cores in TMC have a
density of about few hundred $cm^{-3}$ (Pineda et al., 2010) and produce very
few low mass stars (Whittet et al., 2004; Palmeirim et al., 2013) with a
stellar density of about 1 - 10 stars pc-3 (Luhman, 2000). In contrast to
other star-forming regions such as Orion or Ophiuchus, the TMC is quiet with a
low rate of star formation (Kenyon & Hartmann, 1995) and no massive stars and
hence no ionizing radiation (Walter & Boyd, 1991).

The first diffuse UV studies of the TMC were made by Hurwitz (1994) using the
BEST (Berkeley Extreme Ultraviolet Shuttle Telescope) instrument, which flew
on the Space Shuttle (STS-61C) in 1986 as part of the UVX payload. He observed
both continuum emission due to starlight scattered by interstellar dust and
emission lines from H2 fluorescence. The continuum emission was inversely
correlated with the optical depth suggesting that the diffuse background
originated behind and was shadowed by the dense molecular cloud; a conclusion
later supported by observations from the SPEAR/FIMS instrument (Lee et al.,
2006).

We have used observations made by the Galaxy Evolution Explorer (GALEX) in two
bands (far-ultraviolet (FUV: 1350 - 1750 Å) and near-ultraviolet (NUV: 1750 -
2850 Å)) to study the diffuse UV radiation in and around the TMC. We will
describe the observations and our modelling below. Lim et al. (2013) performed
a similar analysis for a much larger region (the entire Taurus-Perseus-Auriga
complex of molecular clouds). However, that included areas with quite
different physical properties and we have chosen to focus on the TMC.

##  2 Data

Figure 1: GALEX FUV and NUV total exposure time per pixel are shown from left
to right. The exposure time are expressed in units of seconds.

Figure 2: GALEX FUV and NUV and Planck E(B-V) images are shown from left to
right with colour scales at the top. The UV images are in units of ph cm-2 s-1
sr-1 Å-1 and the E(B-V) is in magnitudes. The white crosses in the FUV image
show the positions of the UVX observations (Hurwitz, 1994). Regions with no
GALEX observations appear as black in the UV images.

GALEX, a NASA Small Explorer mission, was launched on April 28, 2003 with the
primary goal of studying galaxy evolution at low red-shift (Martin et al.,
2005) and completed its mission on June 28, 2013 (Bianchi, 2014). The final
data set of GALEX includes more than 44,000 observations (Murthy, 2014b) in
two ultraviolet bands. The data products from each observation have been
described by Morrissey et al. (2007) and are archived at the Mikulski Archive
for Space Telescopes (MAST).

We have shown an exposure time map of the observed region in the FUV and the
NUV bands in Fig. 1. There were a total of 159 FUV and 258 NUV visits near the
TMC region taken over a range of 9 years from 2003 to 2012 (2003 – 2007 for
the FUV). Most of the observations were taken as part of the AIS (All-sky
Imaging Survey) with an exposure time of about 100 seconds per visit but with
a few observations for specific science programs (eg Findeisen & Hillenbrand,
2010) with correspondingly greater exposure times. Murthy (2014b) has
calculated the diffuse Galactic background (DGL) values over the entire sky by
masking out point sources and binning to a resolution of $2^{\prime}$ and
these data are available from the MAST
archive111https://archive.stsci.edu/prepds/uv-bkgd/.

We have downloaded all the data within 8 degrees of the nominal centre of the
TMC (170.0, -14.0) and binned into 6$\arcmin$ bins, weighting each
observations by its exposure time. Edge effects contaminate the outer part of
the GALEX detector and we have only used the central $0.5\degree$ (radius) of
each observation. The resultant maps of the TMC in the FUV and the NUV are
shown in Fig. 2 along with the extinction map derived from Planck observations
(Planck Collaboration et al., 2014). There were no observations over
significant parts of the TMC, partly because of safety concerns for the
instrument (Findeisen & Hillenbrand, 2010) and partly because of the failure
of the FUV power supply.

Figure 3: Correlation between GALEX FUV and NUV intensity. Figure 4: Regions
with different relationship between FUV and E(B-V). The dotted region in red
colour on the right hand side of the image, is brighter in FUV and have little
dust. Figure 5: GALEX FUV (top) and NUV (bottom) intensity plotted against
Planck E(B-V).The black line separates the regions having different
relationship between UV and E(B-V).

There is a strong correlation (r $\sim$ 0.9) between the FUV and the NUV (Fig.
3). However, it is readily apparent that there is no correlation between the
extinction and the diffuse UV background; rather, the UV images appear to be
brighter to the right of the field where the extinction is least. This is
borne out by a weak anti-correlation between the E(B-V) and the FUV (r =
-0.25) and the E(B-V) and the NUV (r = -0.24). A more detailed examination of
the data suggests that there exist two separate regions, demarcated in Fig. 4
where the points in red are those that fall above the line in Fig. 5. There is
a positive correlation between the E(B - V) and the UV (FUV: r = 0.69; NUV: r
= 0.51) in this region. The remaining region, which encompasses most of the
TMC, has a negative correlation of r=-0.36 between the E(B - V) and the FUV
and r=-0.46 between the NUV and the E(B-V), as might be expected if the
radiation were shadowed by the dust in the TMC.

The first observations of the diffuse UV in the TMC was done by Hurwitz (1994)
using the UVX instrument on the Space Shuttle followed by observations made by
using the SPEAR/FIMS (Lee et al., 2006; Lim et al., 2013). They observed the
same anti-correlation between the reddening and the UV flux and interpreted
this as due to the shadowing of a distant diffuse background by the molecular
cloud. We will explore this in the next section.

##  3 Modelling

Murthy (2016) has implemented a Monte Carlo model to predict the level of dust
scattered radiation throughout the Galaxy. He used stars from the Hipparcos
catalog (Perryman et al., 1997) along with model spectra for each spectral
type (Castelli & Kurucz, 2004) as sources for the stellar photons. Although we
are interested only in the emission from the vicinity of the TMC, we have
found that many of the scattered photons are from multiply scattered photons
from outside the TMC and have therefore modelled the entire Galaxy, but with
more detail in the vicinity of the TMC.

We have modelled the Galaxy as a 500x500x500 grid with a bin size of 2 pc on a
side and filled with a hydrogen density of 1 cm-3 at the Galactic Plane
falling off with a scale height of 125 pc (Marshall et al., 2006) from the
plane. We calculated an optical depth for each bin using the cross-section per
hydrogen atom tabulated by Draine (2003) for “Milky Way” dust. Welsh et al.
(2010) have found that there is a cavity of radius $\sim$ 80 pc (the Local
Bubble) around the Sun and we have incorporated this in the dust model.
However, this does not account for the complex structure in the TMC and we
have separately modelled the dust in that region.

Table 1: Properties of brightest stars near the TMC region with stellar flux contribution at three g values. HIP number | l | b | Spectral | V mag222From SIMBAD. | Distance333From Hipparcos catalogue. | % Total Flux 444At constant a =0.3 and at 1500 Å
---|---|---|---|---|---|---
| ($\degree$) | ($\degree$) | type |  | (pc) |  |  |
|  |  |  |  |  |  g=0.0 |  g=0.5 |  g=0.7
18246 | 162.3 | -16.7 | B1 | 2.84 | 301 | 7.7 | 14.7 | 23.8
18532 | 157.4 | -10.1 | B1.5 | 2.89 | 165 | 7.7 | 10.2 | 7.2
26727 | 206.5 | -16.6 | O9.7 | 1.79 | 226 | 4.3 | 4.3 | 2.2
24661 | 166.2 | 2.2 | — | 11.6 | 211 | 3.1 | 4.1 | 0.0
26311 | 205.2 | -17.2 | B0 | 1.69 | 412 | 2.7 | 3.8 | 2.3
25930 | 203.9 | -17.7 | B0 | 2.41 | 281 | 2.3 | 2.8 | 1.5
27366 | 214.5 | -18.5 | B0.5 | 2.06 | 221 | 2.3 | 1.7 | 0.8
4427 | 123.6 | -02.2 | B0.5 | 2.39 | 188 | 2.3 | 1.2 | 0.5
21881 | 176.7 | -15.1 | B3 | 4.26 | 123 | 2.2 | 1.8 | 2.0
24436 | 209.2 | -25.3 | B8 | 0.13 | 237 | 1.6 | 1.3 | 0.9
17448 | 160.4 | -17.7 | B1 | 3.84 | 452 | 1.3 | 2.6 | 4.6
17702 | 166.7 | -23.5 | B7 | 2.85 | 113 | 1.3 | 0.9 | 0.8
25336 | 196.9 | -16.0 | B2 | 1.64 | 75 | 1.3 | 0.3 | 0.2
26451 | 185.7 | -5.6 | B1 | 3.03 | 136 | 1.2 | 0.6 | 0.5
60718 | 300.1 | -0.4 | B1 | 0.81 | 98 | 1.2 | 0.3 | 0.1
18614 | 160.4 | -13.1 | O7.5 | 4.01 | 544 | 1.1 | 3.3 | 4.0
18724 | 178.4 | -29.4 | B3 | 3.41 | 114 | 1.1 | 0.5 | 0.0
30324 | 226.1 | -14.3 | B1 | 1.97 | 153 | 1.0 | 0.4 | 0.2
68702 | 311.8 | 1.3 | B1 | 0.60 | 161 | 1.0 | 0.3 | 0.1
26207 | 195.1 | -12.0 | O8 | 3.66 | 324 | 0.8 | 1.4 | 0.9

Figure 6: Correlation between Planck and GSF reddening.

Figure 7: Left: Planck dust distribution in terms of E(B-V) per 2 pc bin in
units of ‘mag’, as a function of distance along a representative line of
sight. Right: Modelled spatial distribution of the dust in the region.

We first used the 3-dimensional extinction map of Green et al. (2015) (GSF
hereafter) to characterize the dust distribution in the region finding that
the bulk of the dust is found between 140 and 200 pc in reasonable agreement
with the 140 – 160 pc from earlier results (Kenyon et al., 1994; Torres et
al., 2007; Lombardi et al., 2010). However, the total column density is
greater than that derived from the Planck data (Planck Collaboration et al.,
2014) (Fig. 6). The GSF measurements are along specific lines of sight while
the Planck measurements average over the $5^{\prime}$ beam of the instrument
and the larger values may be an indicator of clumping in the TMC. We have
therefore used a second model where we have taken the reddening along any line
of sight from the Planck data (Planck Collaboration et al., 2014) and
distributed the dust uniformly between 140 - 160 pc (Fig. 7). Although this
gives somewhat lower column densities than the GSF data, it does match the
extinction measurements of Arce & Goodman (1999). We tested the effects of
both models on our derived diffuse flux finding little difference between the
two. We therefore continue with only using the dust distribution as given by
the Planck model.

As has been standard in studies of interstellar dust, we used the Henyey-
Greenstein scattering function (Henyey & Greenstein, 1941) with the albedo (a)
and the phase function asymmetry factor(g) as free parameters to determine
each scattering.

##  4 Results

We have run a series of Monte Carlo models to predict the diffuse background
in both the FUV and the NUV bands for different combinations of a and g. We
used a baseline of 100 million ($10^{8}$) photons for the entire grid but used
simulations with 1 billion ($10^{9}$) photons for values of $a$ and $g$ near
the best fit values. We cannot compare the models directly to the GALEX data
on a pixel by pixel basis because of the noise intrinsic to the Monte Carlo
procedure and therefore used the root-mean-square (R.M.S) deviation of the
flux as a function of Galactic longitude as a metric of the goodness of fit of
the model (Fig. 8). We have plotted the R.M.S. deviations for both the FUV and
the NUV as a function of $a$ and $g$ in Fig. 9 finding that the best fit
occurs for an albedo of about 0.3 in both bands. Although this is in agreement
with Hurwitz (1994) and Lee et al. (2006) in the same region, it is lower than
the albedo found in other parts of the Galaxy (compiled in Table 4 of Murthy
(2016)). Witt & Gordon (1996) showed that a clumpy medium, as in the TMC
(Panopoulou et al., 2014), gives rise to a lower effective albedo and it is
likely that the “true” albedo is greater than our derived value.

We have listed the 20 stars which contribute the most to the diffuse flux at
$g=0$ in Table 1. The two stars which contribute the most flux at any value of
$g$ are near the right edge of Fig. 2 accounting for part of the rise in the
UV fluxes to lower longitudes. However, there are enough stars contributing
with a range of distances and positions that the dependence on $g$ is washed
out, as was found by Gordon et al. (1994) in the upper Scorpius region. We
have adopted $g=0.7$ which is consistent with most observations in the UV
(Draine, 2003).

Figure 8: Modelled FUV and NUV emission as a function of galactic longitude
for $a$ = 0.3 and $g$ = 0.7, over-plotted with the original FUV and NUV
emission.

Figure 9: Root mean square deviations as a function of albedo (a) and as a
function of phase function asymmetry factor (g). Figure 10: Correlation plot
between the modelled and the observed flux. The best fit lines are shown.
Figure 11: Comparison of absolute values between the UVX values from Hurwitz
(1994) and the GALEX intensity. 300 ph cm-2 s-1 sr-1 Å-1 have been subtracted
from the UVX data to account for molecular hydrogen emission. Figure 12:
Bright stars are marked as circles over the Planck dust reddening map. The
centre of the circles represents the location of the stars while its radius
proportional to contribution towards total flux. Figure 13: Mean E(B-V) as
function of galactic longitude in both GSF and Planck cases. Figure 14:
Fraction of total FUV scattered flux in the TMC as a function of distance from
the Sun.

We have run our model with $10^{10}$ photons for the best fit optical
constants ($a=0.3;g=0.7$) to improve the signal-to-noise and plotted the
modelled versus the observed fluxes in Fig. 10, where we have binned the data
into $0.2^{\circ}$ bins. The correlation between the observed and modelled FUV
is 0.55 with a slope of 0.68 and an offset of 980 ph cm-2 s-1 sr-1 Å-1. The
slope for the NUV is 0.48 with an offset of 1360 ph cm-2 s-1 sr-1 Å-1 and a
correlation coefficient of 0.51. If we look at these values in the broader
context of the diffuse radiation at low latitudes, Murthy (2016) found that
there was considerable scatter between the observed reddening and the UV flux,
which he attributed to an uncertain dust distribution. We believe that the
main source of scatter between our modelled fluxes and the data is the complex
structure of the TMC. However, we do find offsets similar to the 700 — 900 ph
cm-2 s-1 sr-1 Å-1 found by Murthy (2016) including 200 — 300 ph cm-2 s-1 sr-1
Å-1 from airglow Murthy (2014a), molecular hydrogen fluorescence in the FUV
(Hurwitz, 1994; Lim et al., 2013) and a possibly new, unknown component (Henry
et al., 2015; Hamden et al., 2013).

Finally, we return to the anti-correlation between the diffuse flux and the
reddening observed by Hurwitz (1994) and Lee et al. (2006), which they
interpreted as scattering from a more distant diffuse source extincted by the
TMC. Our data agree with both the UVX observations of Hurwitz (1994) (Fig. 11)
and the SPEAR observations of Lee et al. (2006) but we believe that the actual
situation is more complex. At least part of the brightening to lower
longitudes is coincidental because the two strongest contributing stars (Table
1) are near a longitude of 160∘ (Fig. 12) where the reddening is less (Fig.
13). These two B stars (HIP 18246 and HIP 18532) contribute 45% of the flux at
a Galactic longitude less than 165$\degree$.

Our model predicts that about 25% of the total scattered flux is from dust in
front of the TMC and another 25% behind the cloud with the remaining 50%
arising in the TMC itself (Fig. 14), as might be expected given that almost
all of the dust is in the TMC. However, our model is not well-suited to
explore the scattering within a dense molecular cloud where clumping may be
important. HIP 18246 is behind the TMC, as well as the other bright stars
which make much of the field unobservable by GALEX (Findeisen & Hillenbrand,
2010), and much of the flux from within the molecular cloud is due to the
scattering of the light from those stars by dust within the cloud. Self-
shielding within the cloud, itself, will yield the observed anti-correlation,
exacerbated by the coincidental position of the two bright stars at one edge
of the field.

##  5 Conclusions

We have modelled the diffuse radiation in the direction of the TMC using GALEX
data with a Monte Carlo model finding an albedo of $\approx 0.3$, but with no
constraints on $g$. The albedo is likely to be an underestimate because we do
not take clumping into effect.

About half of the scattered radiation originates in the body of the cloud with
self-shielding giving rise to an anti-correlation between the observed flux
and the reddening. The two brightest stars in the field are located in the
direction of least reddening which adds to the anti-correlation.

We find offsets of about 1000 ph cm-2 s-1 sr-1 Å-1 in both bands of which some
part may be due to foreground contributors such as airglow and some to an
unknown component (Henry et al., 2015).

## Acknowledgements

This work is based on the data from NASA’s GALEX spacecraft. GALEX is operated
for NASA by the California Institute of Technology under NASA contract
NAS5-98034. The dust extinction map obtained from PLANCK
(http://www.esa.int/Planck), an ESA science mission with instruments and
contributions directly funded by ESA Member States, NASA, and Canada. We thank
the anonymous referee for constructive suggestions which has resulted in a
better paper. Sathyanarayan would like to thank Dr. Sujatha and Ms. Jyothi for
their help during the early stages of this work.

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