Hydrostatic photoionization models of the Orion Bar

Abstract

Due to its proximity to the Earth and its nearly edge-on geometry, the Orion
Bar provides an excellent testbed for detailed models of the structure of HII
regions and the surrounding photon-dominated regions. In the present study, a
self-consistent model of the structure of the Orion Nebula in the vicinity of
the Bar is built under the assumption of approximate ionization, thermal, and
hydrostatic equilibrium. It is found that a fairly simple geometry is able to
describe the surface brightness profiles of the emission lines tracing the
ionized HII region with a remarkable accuracy, independent of the prescription
adopted to set the magnetic field or the population of cosmic rays. Although we
consider different scenarios for these non-thermal components, none of the
models is able to provide a fully satisfactory match to the observational data
for the atomic layer, and the predicted column densities of several molecular
species are always well above the measured abundances. Contrary to previous
studies, we conclude that a more elaborate model is required in order to match
all the available data.

Full text

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arXiv:1106.3990v1 [astro-ph.GA] 20 Jun 2011
Mon. Not. R. Astron. Soc. 000, 000–000 (0000) Printed 21 June 2011(MN LATEX style file v2.2)
Hydrostatic photoionization models of the Orion Bar
Y. Ascasibar, A. C. Obreja, and A. I. D´ ıaz
Departamento de F´ ısica Te´ orica, Universidad Aut´ onoma de Madrid, Madrid 28049, Spain
Draft version 2.0 (21 June 2011)
ABSTRACT
Due to its proximity to the Earth and its nearly edge-on geometry, the Orion Bar pro-
vides an excellent testbed for detailed models of the structure of Hii regions and the
surrounding photon-dominated regions. In the present study, a self-consistent model
of the structure of the Orion Nebula in the vicinity of the Bar is built under the as-
sumption of approximate ionization, thermal, and hydrostatic equilibrium. It is found
that a fairly simple geometry is able to describe the surface brightness profiles of the
emission lines tracing the ionized Hii region with a remarkable accuracy, independent
of the prescription adopted to set the magnetic field or the population of cosmic rays.
Although we consider different scenarios for these non-thermal components, none of
the models is able to provide a fully satisfactory match to the observational data for
the atomic layer, and the predicted column densities of several molecular species are
always well above the measured abundances. Contrary to previous studies, we conclude
that a more elaborate model is required in order to match all the available data.
Key words: ISM: HII regions – ISM: PDR – ISM: individual (Orion Nebula, M42,
NGC1976) – ISM: individual (Orion Bar)
1 INTRODUCTION
Hii regions are extended, low-surface brightness, diffuse neb-
ulae of photoionized gas. They are associated with regions of
ongoing star formation, most commonly found in the disks of
spiral galaxies, where young and bright stars provide the co-
pious amount of ionizing ultraviolet (UV) radiation required
for such regions to exist. The spectrum of these nebulae is
mainly composed of hydrogen recombination lines and for-
bidden lines of ions of common elements, superimposed on
a weak continuum. Hii regions can be used to trace star
formation from the solar neighborhood to the high-redshift
Universe, and their spectrum provides invaluable informa-
tion about the ionizing population of massive stars, as well
as the physical conditions of the interstellar medium.
The central source of such a region can be one or sev-
eral Population I stars of type O or early B, with effective
temperatures between 3 and 5 × 104K, that emit a large
number of photons with energies higher than the ionization
potentials of hydrogen and helium. Although these two ele-
ments are by far the most abundant ones, metal lines play
an important role because they provide the principal cooling
mechanism. At any point in the nebula, the degree of ion-
ization is determined by the equilibrium between electron
capture and photoionization. Ejected photoelectrons carry
the excess energy of the photon as kinetic energy, and they
contribute through electron-electron and electron-ion colli-
sions to maintaining a Maxwellian velocity distribution with
typical electron temperatures between 5000 and 20000 K.
The limit of the Hii region, an ionization front that
tends to expand into the surrounding neutral gas at sub-
sonic velocities, is usually approximated as a Str¨ omgren’s
sphere with typical radii of the order of parsec. The Hii re-
gion is surrounded by a neutral, photon-dominated region
(PDR), where the stellar UV radiation heats the gas and
partly dissociates the molecular hydrogen (hence the name
photo-dissociation region, which is also often used). Pho-
tons escaping far into the outer molecular region are also
absorbed by the dust present in the interstellar medium,
which gets thus heated to about 100 K, and re-emitted as
an infrared continuum.
Notwithstanding with this simple picture, observations
of many Hii regions show signatures of dense neutral conden-
sations scattered in the ionized zone and turbulent motions
within the gas with velocities of the order of 10 km s−1.
The geometry of these nebulae is anything but spherical,
and theoretical models of their internal structure ought to
be constructed on case-by-case basis.
In this work, we attempt to build a self-consistent model
of the Orion Bar. The Orion Nebula (M42, NGC1976) is
part of the Orion Molecular Cloud Complex, at a distance
of 437 pc (Hirota et al. 2007), and it has been studied exten-
sively over the years across the entire electromagnetic spec-
trum. Most of the ionizing radiation comes from the star
θ1Orionis C, located roughly at the centre of the region.

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2Y. Ascasibar et. al.
The Orion Bar, situated at approximately 0.235 pc from the
central star towards the south-east, is a dramatic example of
the interface between the ionized gas and the PDR. Due to
its convenient orientation, allowing an almost edge-on per-
spective, and the rich variety of observations available in the
literature, the Orion Bar constitutes an ideal laboratory for
testing the PDR physics.
Recent studies (O’Dell et al. 2009; Shaw et al. 2009;
Pellegrini et al. 2009) highlight the importance of cosmic
rays and magnetic fields in determining the structure of
the PDR. In particular, it has been argued (Pellegrini et al.
2009) that a relatively strong magnetic field, as well as a pop-
ulation of cosmic rays in equipartition (and thus a density
that is much higher than the average galactic background),
must be present in the Bar in order to reproduce the ob-
served surface brightness profiles of the H2 line at 2.121 µm
and the12CO(J = 1 − 0) emission.
The presence of an important magnetic field is sup-
ported by polarization observations of the Orion Nebula
(Schleuning 1998) and the detection of a magnetic field in
Orion’s Veil with an intensity that is at least an order of
magnitude higher than the typical values measured in the
cold neutral medium of the Milky Way (Abel et al. 2006),
but the enhancement of the cosmic ray contribution above
the Galactic background is much more poorly constrained
from the observational point of view. A high cosmic-ray den-
sity is simply introduced as an additional heating source that
can act much deeper into the molecular cloud than the pho-
tons from the central star. As a result, the temperature of
the outer regions is considerably higher, providing a better
fit to the observed surface brightness profiles.
The present work represents an additional step towards
a self-consistent model of the internal structure of the Orion
Bar. As previous studies, it is based on the assumption that
the region is in approximate hydrostatic equilibrium: the
outward acceleration driven by the radiation field and the
pressure of the hot, ionized gas creates an expanding wind
that compresses the surrounding medium – and the mag-
netic field coupled to it – until the magnetic pressure is able
to halt the process. Radiative transfer across the different
gas phases is solved by the photoionization code Cloudy (last
described in Ferland et al. 1998), including all the relevant
processes affecting atoms, molecules, and dust grains, and
the predicted line intensities are computed by integrating
the physical properties of the gas along the line of sight, fol-
lowing an approach very similar in spirit to Morisset et al.
(2005).
The main improvements with respect to previous work
are the inclusion of a detailed treatment of the gravita-
tional acceleration and a more elaborate description of the
three-dimensional geometry of the system. As shown in
Ascasibar & D´ ıaz (2010), the gravitational force (both the
mass of the central object as well as the self-gravity of the
gas) plays an important role in the outer regions, setting the
total extent of the molecular layer and eliminating one free
parameter of the model. In addition, we propose a simple
parameterization of the geometry of the Hii region that is
able to provide a reasonable fit to the emission line data.
Emission from the atomic layer, though, as well as the col-
umn densities of several molecular species, remain difficult
to reproduce for any model, with or without gravity.
The details of our photoionization models are thor-
oughly described in Section 2, and their predictions are com-
pared with observational data in Section 3. Section 4 is de-
voted to the physical interpretation of our results, and a
brief summary and outlook are provided in Section 5.
2 A SIMPLE MODEL OF THE ORION BAR
Our model of the Orion Bar is based on the assumption that
the gas is in ionization, thermal, and hydrostatic equilibrium
at every point. Under these conditions, the physical prop-
erties of a cloud with plane-parallel or spherical symmetry
can be efficiently computed with the plasma physics code
Cloudy1(Ferland et al. 1998), a spectral synthesis program
designed for the study of low-density environments that are
ionized by an external radiation field. In this section, we
describe the parameters of our photoionization models and
discuss how the condition of hydrostatic equilibrium and the
non-spherical geometry of the Orion Nebula in the vicinity
of the Bar may be implemented.
2.1Model parameters
On input, Cloudy requires the user to specify the shape and
the intensity of the incident radiation field, the gas density,
its chemical composition, and the geometry of the cloud. For
consistency with previous studies, we follow Pellegrini et al.
(2009) and represent the incident continuum by the sum
of the cosmic microwave background, a Kurucz (1979) stel-
lar atmosphere with temperature T = 39600 K and ioniz-
ing luminosity Q(H) = 1049photons s−1, and a thermal
bremsstrahlung component with temperature T = 106K
and luminosity L = 1032.6erg s−1in the 0.5 − 8 keV band
(Feigelson et al. 2005). The gas density at the illuminated
face is set to n0 = 103.2cm−3, and a chemical composition
appropriate for Orion Nebula (Baldwin et al. 1991), includ-
ing dust grains and polycyclic aromatic hydrocarbons, is
used.
Unless otherwise specified, Cloudy assumes that the gas
density stays constant over the cloud, but many density and
pressure laws can be used instead. We model the Orion Bar
by enforcing hydrostatic equilibrium with the constant pres-
sure command. Contrary to what the name suggests, this
option does not keep the total pressure fixed, but adjusts its
value so that the total acceleration vanishes at every point,
1
ρ(r)
dP(r)
dr
= a(r) (1)
and therefore
P(r) = P0+
?r
0
ρ(x)a(x) dx(2)
where P0 denotes the initial pressure at the illuminated
face, and the acceleration to be balanced includes the terms
due to the absorption of photons (pushing the gas away
from the central star) and the gravitational force that
pulls the whole cloud towards the centre. The latter is
included by means of the gravity command, described in
1All our calculations have been preformed with version C08.00
of the code. The current stable release is publicly available at
http://www.nublado.org

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Hydrostatic photoionization models of the Orion Bar3
Ascasibar & D´ ıaz (2010). The gravitational acceleration is
calculated as g(r) = −4πGM(r)/r2, assuming spherical
symmetry, and the mass inside radius r includes the con-
tributions of both the gas and the stars in the cloud. The
distribution of the gas mass is computed self-consistently by
the code, Mgas(r) =?r
ple system is modeled as a point mass of 50 M⊙(Kraus et al.
2007) located at the centre of the region.
The total pressure
0ρ(x)4πx2dx, and the θ1Ori C multi-
P(r) = Pgas+ Pram+ Pturb+ Pmag+ Plines
(3)
that appears in equation (2) is the sum of the thermal
pressure of the gas Pgas = nkT, the terms Pram = ρv2
and Pturb = ρv2
lent motions, respectively, the magnetic pressure Pmag =
B2/8π, and the contribution Plines(Ferland & Elitzur 1984;
Elitzur & Ferland 1986) of the trapped emission lines. Al-
though winds are not considered in our model, it includes
a small turbulent velocity field of 2 km s−1. Regard-
ing the magnetic field, we consider the same scenarios as
Pellegrini et al. (2009). In the gas pressure model, only the
thermal pressure of the gas and the turbulent pressure terms
are taken into account. The magnetic pressure model adds
a tangled magnetic field whose intensity at the illuminated
face of the cloud is B0 = 8 µG, and its equation of state
is given by γ = 2 (i.e. B/B0 = n/n0). In both scenarios,
the density of cosmic rays is constant and equal to the aver-
age galactic background. The enhanced cosmic rays model
assumes the cosmic-ray density to be in equipartition with
the magnetic field, resulting in a much higher abundance of
relativistic particles.
For each scenario, we ran a grid of Cloudy models with
initial distances from θ1Ori C ranging from 0.05763 to
0.5763 pc in logarithmic steps of 0.01. A sample Cloudy
script used in the preparation of our model grids is shown
in Appendix A. Each model saves the emissivities of two
emission lines from the ionized region ([Sii]λλ6716+6731
and Hα) and one emission line produced in the atomic layer
(H22.121 µm), the extinction towards the end of the cloud,
and the volume densities of six molecular species (CO+, SO,
CN, CS, SO+, and SiO), all of them as a function of depth
into the cloud (i.e. the distance from the illuminated face).
wind
turb/2 induced by the uniform and turbu-
2.2Geometry
One of the aims of the present work is to show that the over-
all geometry of the Orion Nebula plays an important role on
its physical conditions and observable properties, which can
be exquisitely probed in the region near the Bar due to its
privileged orientation. Previous studies have constrained the
geometry of the cloud using the surface brightness profile of
the emission lines associated to the Hii region. More specif-
ically, the [Sii]λλ6716+6731 line displays a sharp peak at
the interface between the ionized and the neutral layers, thus
providing an excellent tracer of the position of the ionization
front (see e.g. Baldwin et al. 1991; Wen & O’dell 1995).
In the vicinity of the Bar, the projected distance be-
tween the maximum of the observed emission and the central
star is 111 arcsec (0.235 pc, assuming a distance of 437 pc).
Approximating the Bar as a plane-parallel slab of thickness
h, located at a distance R0 from θ1Ori C with an incli-
nation angle β with respect to the line of sight, the data
Figure 1.
scribed by the parameters R0, α, β, δ, and h (see text for a de-
tailed explanation). The x- and y-axes represent the offset with
respect to θ1Ori C and the coordinate along the line of sight,
respectively.
Geometry of the illuminated face of the cloud, de-
suggest the values h ∼ 0.115 pc, R0 ∼ 0.114 pc, and β ∼ 7◦
(Pellegrini et al. 2009).
We consider a very similar layout, depicted in Figure 1,
that also includes the contribution of the adjacent regions of
the Orion Nebula. The interior region, towards the central
star, is approximated as a sphere of radius R0 centered at
the location of θ1Ori C, which we take as the origin of
coordinates. The transition between the spherical region and
the Orion Bar takes place at an angle α with respect to
the plane of the sky, which is an additional free parameter
of our model. The Bar itself, as well as the outer region,
are modeled as straight lines whose angles with respect to
the line of sight are denoted by the parameters β and δ,
respectively. The length of the Bar region is specified by
the parameter h, whereas the outer region is assumed to
continue well beyond the observed field.
The region interior to this curve is empty, or, more pre-
cisely, filled by a hot, tenuous gas that can be detected in
X-rays (G¨ udel et al. 2008) and provides thermal pressure
support for the warm (T ? 104K) dense gas that is respon-
sible for the optical and infrared emission in which we are
interested. In Cloudy parlance, the curve depicted in Fig-
ure 1 defines the illuminated face of the cloud. For the outer
region to receive direct illumination from θ1Ori C, as as-
sumed by our models, it must not be behind the shadow
cast by the Bar (angle ψ in Figure 1). Thus, we chose the
parameterization
δ = η
?π
2+ ψ
?
+ (1 − η) β(4)
where 0 < η < 1.
This geometry is implemented as a summation over a
grid of Cloudy models with spherical symmetry and different
distances between the illuminated face of the cloud and the
central star (light dashed lines in Figure 1 illustrate the sep-

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4 Y. Ascasibar et. al.
aration between models). The spherical region corresponds
to a single Cloudy model, fully characterized by the value of
R0, while both the Bar and the outer region involve many
models each.
The column density of a given species i is given by the
integral along the line of sight
Ni(x) =
?∞
−∞
ni(x,y) dy (5)
where the volume density ni(x,y) is evaluated from the out-
put of the Cloudy model that is appropriate for each posi-
tion. Surface brightness profiles of the emission lines have
been computed as
Si(x) =
?∞
−∞
εi(x,y)
4π
10−0.4Ai(x,y)dy (6)
where ǫi(x,y) denotes the emissivity per unit volume of the
line, and the amount of dust extinction
Ai(x,y) =
?y
−∞
∂Ai
∂y′(x,y′) dy′
(7)
includes all the foreground material between any given point
and the observer. The differential extinction
estimated from the radial increment of the total extinction
in the V band output by Cloudy and then converted to the
rest wavelength of the line.
∂Ai
∂y′(x,y′) is
3COMPARISON WITH OBSERVATIONS
3.1Hii region
As will be shown below, the observational properties of the
ionized region (more precisely, the surface brightness profiles
of its emission lines) are not very sensitive to the details of
the magnetic field or the prescription adopted to establish
the population of cosmic rays. The exact position of the
ionization front depends on a combination of the gas density
at the illuminated face, the intensity of the ionizing radiation
from θ1Ori C, and the distance to the Orion Nebula. Once
these (degenerate) parameters are specified, the shape of the
emission profiles is entirely determined by the geometrical
configuration of the system.
In our model, this geometry (the distance from the cen-
tral star to the illuminated face) is described by the values
of five free parameters: the radius of the inner region R0,
the transition to the Bar α, its inclination with respect to
the line of sight β, its length h, and the angle δ – or, equiv-
alently, the parameter η defined in expression (4) – that
defines the orientation of the outer region with respect to
the line of sight. We estimate the values of these parame-
ters by fitting the observed surface brightness profiles of the
[Sii]λλ6716+6731˚ A and Hα emission lines.
The surface brightness profile of the [Sii]λλ6716+6731
line across the bar has been obtained from two narrow-band
images, taken by Pellegrini et al. (2009) with the Southern
Astrophysical Research Telescope, centered at λ = 6723 and
6850˚ A with bandwidths of 45 and 95˚ A, respectively. For
the Hα line, we use the observations of Wen & O’dell (1995).
Both data sets were constructed as continuum-subtracted
averages over 20 arcsec-wide swathes, using similar cuts.
Figure
[Sii]λλ6716+6731 and Hα emission lines (dots), compared to the
theoretical model predictions. The gas pressure, magnetic pres-
sure, and enhanced cosmic rays models have been plotted as dot-
ted, dashed, and solid lines, respectively, but they lie virtually on
top of each other.
2.Observedsurfacebrightnessprofilesofthe
Since these data have already been corrected for dust ex-
tinction, we set Ai = 0 when modelling both emission lines.
The best-fitting values of R0, α, β, η, and h have
been found by means of the FiEstAS sampling technique
(Ascasibar 2008), a Monte Carlo integration scheme based
on the Field Estimator for Arbitrary Spaces (FiEstAS;
Ascasibar & Binney 2005; Ascasibar 2010). In order to
quantify the quality of the fit to the observational data, we
compute the reduced χ2as
χ2=
1
Nobs
Nobs
?
j=1
[Sobs(xj) − Smodel(xj)]2
σ2
j
(8)
where Sobs(xj) denotes the observations at a projected dis-
tance xj from the central star, Smodel(xj) are the cor-
responding model predictions, and the sum over the in-
dex j corresponds to the Nobs observational data points,
whose errors have been characterized by a standard devia-
tion σj = 5 × 10−14and 5 × 10−13erg s−1cm−2arcsec−2
for the [Sii]λλ6716+6731 and the Hα lines, respectively.
The results are shown in Figure 2, where the surface
brightness profiles obtained for R0 = 0.122 pc, α = 28.3◦,
β = 2.3◦, h = 0.05 pc, and δ = 45.15◦are compared with
the observational data points. Our three scenarios for the
magnetic field and cosmic rays yield exactly the same pre-
diction for the emissivities within the ionized region of the
nebula. Although the value of the best-fit χ2= 0.62 is some-
what arbitrary, since it depends on the adopted σi, we judge
from Figure 2 that the proposed geometry is able to provide
a reasonable description of the Orion Bar up to the ioniza-
tion front, regardless of the assumptions made concerning
the non-thermal components.

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Hydrostatic photoionization models of the Orion Bar5
3.2Atomic region
In order to test the ability of our models to describe the
structure and physical properties of the atomic layer, we
will now focus on the H2 S(1 − 0) transition at 2.121 µm,
comparing the model predictions with the observational
data reported in van der Werf et al. (1996). The spatial cut
from which the H2 data were obtained is different from
that of the [Sii] and Hα lines. Although the [Sii] pro-
file shows little variation (see e.g. Henney et al. 2005), it
has been shown (van der Werf et al. 1996; Young Owl et al.
2000; Walmsley et al. 2000; Allers et al. 2005) that the sur-
face brightness of the H2 line may change considerably when
using different cuts perpendicular to the Bar, which intro-
duces some uncertainty in the comparison. Moreover, the
data represent a summation parallel to the bar, whereas the
H2 emission is actually concentrated in rather thin filaments
with typical widths of ∼ 8 arcsec, about 0.016 pc.
Another potential issue is the estimation of the amount
of dust extinction in the models.
models may overestimate the value of AV, perhaps due to
the assumed cross-section for dust attenuation (Allers et al.
2005) and/or an excessive amount of dust in the atomic
region. On the other hand, the conversion between the visual
extinction AV returned by Cloudy and the extinction at the
infrared wavelength λ = 2.121 µm of the H2 emission line
On the one hand, our
A2.121 µm ≈ 0.14AV
(9)
may be obtained by applying a Cardelli et al. (1989) red-
dening curve with R = 5.5, in accordance with observations
of the Orion Nebula. This estimate is based on the observed
reddening curve of stellar spectra, where the extinction in-
cludes both the absorption and scattering of light by the
dust grains. For an extended source, like the Orion Nebula,
a large fraction of the photons (those that are scattered a
small angle away from the light of sight) will be compensated
by similar small-angle events affecting nearby rays, and the
effective scattering opacity
σscat = σs (1 − g)(10)
will be given by the product of the total scattering cross-
section σs and the grain asymmetry factor g, defined as the
average ?cosθ? over the angle θ between the incident and
the scattered photon. Since the wavelength dependence of
the asymmetry factor is determined by the chemical compo-
sition, shape, and size distribution of the dust grains, and
these variables may vary with the spatial location within the
nebula (they depend, for instance, on the gas density and
the high-energy radiation field), there is some uncertainty
associated to equation (9).Nevertheless, an independent
estimation of the nebular extinction in the Orion Nebula
based on the hydrogen recombination lines from the Balmer,
Paschen, and Brackett series (Bautista et al. 1995) is com-
patible with A2.121 µm = 0.14AV, suggesting that the effects
of scattering are not very important in this case.
Thepredicted surface
H22.121 µm line for the gas pressure, magnetic pressure,
and enhanced cosmic rays models are shown on the different
panels in Figure 3. It is worth noting that, while the emis-
sion lines of the ionized region have been used to constrain
the free parameters that set the geometry of the illuminated
brightnessprofiles of the
Figure 3. Surface brightness profiles of the H22.121 µm emission
line predicted by the gas pressure (top), magnetic pressure (mid-
dle), and enhanced cosmic rays (bottom) models. Dotted lines
show the total, unextincted emission. Dashed and solid lines cor-
respond to A2.121 µm = 0.028AVand A2.121 µm = 0.14AV, re-
spectively.
face, the surface brightness profile of the H2 line is a genuine
prediction of the models.
Our results suggest that none of the scenarios we have
considered is able to reproduce the observed emission at the
quantitative level. In particular, all models underestimate
the maximum intensity of the H2 line by more than a fac-
tor of three. We have verified that the discrepancy between
models and data is not a consequence of the prescription
adopted for dust extinction. In the gas pressure scenario,
the separation between the peaks of the [Sii] and the H2
emission is always too small, whereas the magnetic pressure
model fails to explain the observed surface brightness even
for A2.121 µm = 0. The enhanced cosmic rays model seems
slightly more promising, but the precise amount of dust ex-
tinction is critical. In addition, the density gradient in the
molecular region should be much steeper than predicted by
our gravitational models in order to reproduce the observed
lack of emission outside the main peak.
3.3Molecular region
The
vide
cal conditions
Pellegrini et al. (2009), we compare the column density pro-
files predicted by the models with observations of CO+
(Stoerzer et al. 1995; Fuente et al. 2003), CN (Simon et al.
1997), SO+(Fuente et al. 2003), SO (Jansen et al. 1995),
CS (Simon et al. 1997; Hogerheijde et al. 1995), and SiO
(Schilke et al. 2001).
Observed column densities should, however, be treated
with some caution, given the many assumptions involved
in their derivation. For instance, Fuente et al. (2003) as-
sume a constant rotational temperature of 10 K for all the
molecular levels, and all lines are considered to be opti-
abundances
a direct
ofdifferent
of
molecular
extent
species
the
layer.
pro-
physi-
As in
probe
of the outer, molecular
theand