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# Physical and Chemical Structure of the Disk and Envelope of the Class 0/I Protostar L1527

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Sub-millimeter spectral line and continuum emission from the protoplanetary disks and envelopes of protostars are powerful probes of their structure, chemistry, and dynamics. Here we present a benchmark study of our modeling code, RadChemT, that for the first time uses a chemical model to reproduce ALMA C$^{18}$O (2-1) and CARMA $^{12}$CO (1-0) and N$_{2}$H$^{+}$ (1-0) observations of L1527, that allow us to distinguish the disk, the infalling envelope and outflow of this Class 0/I protostar. RadChemT combines dynamics, radiative transfer, gas chemistry and gas-grain reactions to generate models which can be directly compared with observations for individual protostars. Rather than individually fit abundances to a large number of free parameters, we aim to best match the spectral line maps by (i) adopting a physical model based on density structure and luminosity derived primarily from previous work that fit SED and 2D imaging data, updating it to include a narrow jet detected in CARMA and ALMA data near ($\leq 75$au) the protostar, and then (ii) computing the resulting astrochemical abundances for 292 chemical species. Our model reproduces the C$^{18}$O and N$_{2}$H$^{+}$ line strengths within a factor of 3.0; this is encouraging considering the pronounced abundance variation (factor $> 10^3$) between the outflow shell and CO snowline region near the midplane. Further, our modeling confirms suggestions regarding the anti-correlation between N$_{2}$H$^{+}$ and the CO snowline between 400 au to 2,000 au from the central star. Our modeling tools represent a new and powerful capability with which to exploit the richness of spectral line imaging provided by modern submillimeter interferometers.
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Physical and Chemical Structure of the Disk and Envelope of the Class 0/I protostar L1527
Lizxandra Flores-Rivera,1, 2, 3 Susan Terebey,1, 2 Karen Willacy,2Andrea Isella,4Neal Turner,2and
Mario Flock2, 3
1Department of Physics & Astronomy, California State University at Los Angeles, Los Angeles, CA 90031, USA
2Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91109, USA
3Max-Planck Institute for Astronomy, K¨onigstuhl 17, 69117 Heidelberg, Germany
4Department of Physics & Astronomy, Rice University, 6100 Main Street Houston, TX, 77005
(Accepted December 7, 2020)
ABSTRACT
Sub-millimeter spectral line and continuum emission from the protoplanetary disks and envelopes
of protostars are powerful probes of their structure, chemistry, and dynamics. Here we present a
benchmark study of our modeling code, RadChemT, that for the ﬁrst time uses a chemical model
to reproduce ALMA C18O (2-1) and CARMA 12CO (1-0) and N2H+(1-0) observations of L1527,
that allow us to distinguish the disk, the infalling envelope and outﬂow of this Class 0/I protostar.
RadChemT combines dynamics, radiative transfer, gas chemistry and gas-grain reactions to generate
models which can be directly compared with observations for individual protostars. Rather than
individually ﬁt abundances to a large number of free parameters, we aim to best match the spectral
line maps by (i) adopting a physical model based on density structure and luminosity derived primarily
from previous work that ﬁt SED and 2D imaging data, updating it to include a narrow jet detected
in CARMA and ALMA data near (75au) the protostar, and then (ii) computing the resulting
astrochemical abundances for 292 chemical species.
Our model reproduces the C18 O and N2H+line strengths within a factor of 3.0; this is encouraging
considering the pronounced abundance variation (factor >103) between the outﬂow shell and CO
snowline region near the midplane. Further, our modeling conﬁrms suggestions regarding the anti-
correlation between N2H+and the CO snowline between 400 au to 2,000 au from the central star. Our
modeling tools represent a new and powerful capability with which to exploit the richness of spectral
line imaging provided by modern submillimeter interferometers.
Keywords: stars: low-mass protostars, L1527 — radiative transfer, stars: envelope collapse model —
spectral line emission
1. INTRODUCTION
In star formation theory, a low-mass protostar in its
earliest stage of order of 104years, is considered a Class
0 newborn star embedded in a dense core typically con-
taining a mass density of 1019 g cm3(Bergin &
Tafalla 2007). During the rotational-collapse process
at around 105years, the cloud conserves angular mo-
mentum where the low-angular-momentum parts form
a protostar, while the higher-angular-momentum parts
settle into a disk in orbit around the protostar (Tere-
Corresponding author: Lizxandra Flores-Rivera & Susan Terebey
lﬂor108@calstatela.edu, sterebe@calstatela.edu
bey et al. 1984); where the gas and dust spiral inward
through the disk and accrete onto the protostar.
Magnetic ﬁelds embedded in the initial cloud core can
resist the collapse, and remove angular momentum by
carrying the rotational energy of the core away into the
surrounding molecular cloud. However, if the cloud is
weakly-ionized, its coupling to magnetic ﬁelds is slight,
and magnetic ﬁelds can be ignored in the collapse. Sev-
eral recent reviews suggest that magnetic ﬁelds may play
a relatively small role during cloud collapse (Hull &
Zhang 2019;Krumholz & Federrath 2019). When mag-
netic ﬁelds are negligible, the collapse conserves angu-
lar momentum along streamlines. The density structure
in an initially-quiescent, isothermal, collapsing core can
arXiv:2012.05553v1 [astro-ph.SR] 10 Dec 2020
2Flores-Rivera et al. 2020
then be described by the Ulrich (Ulrich 1976;Cassen
& Moosman 1981) envelope model, hereafter UCM col-
lapse model, or the inside-out Terebey, Shu, Cassen,
hereafter TSC collapse model (Terebey et al. 1984).
These two models diﬀer from each other in terms of gas
pressure support and infall velocity, particularly out-
side the collapse radius (4000 au, see §2.2.1). The
whole picture of the protostellar system can be inferred
from dust continuum and spectral line emission, where
the age, luminosity, and mass of young protostar can
be determined (Kenyon & Hartmann 1995;Evans et al.
2009;Dunham & Vorobyov 2012;Jørgensen et al. 2013;
Frimann et al. 2016).
Predicting chemical abundances in envelopes and
disks of protostars provides a way to trace the chem-
ical inheritance of water and organics in planet forma-
tion; however, carrying out a realistic time-dependent
chemical model using 2D physical properties is techni-
cally challenging. An early chemical study by Ceccarelli
et al. (1996) assumed 1D (radial) physical structure for
the envelope, and by determining temperature via radia-
tive transfer, concluded that water would be abundant
at temperatures above 100K in protostellar envelopes.
Other studies, also using 1D physical models with ra-
diative transfer, further demonstrated the importance
of temperature, from showing extreme CO depletion in
cold outer envelopes, to the presence of simple organic
molecules in corinos, namely regions of warm gas near
the embedded protostar (Jørgensen et al. 2002,2005;
Ceccarelli et al. 2007;Yang et al. 2020). Time depen-
dence in the chemistry has also been used to predict
chemical signatures that result from episodic accretion
bursts in protostars (Jørgensen et al. 2015;Visser et al.
2015;Rab et al. 2017).
Subsequent studies have extended physical modeling
from 1D to 2D (Visser et al. 2009;Visser et al. 2011;
Drozdovskaya et al. 2014,2016) and focus on the time
history of a parcel of gas, in order to predict the abun-
dance of species such as CO, water, and methanol within
disks. Their conclusions on chemistry, while informa-
tive, are not compared with observations of protostars,
and moreover, make speciﬁc assumptions about lumi-
nosity evolution that are diﬃcult to test.
However, for comparision with observation, the previ-
ous studies have limitations, and in particular, they do
not model warm gas that is associated with outﬂows.
Many molecules show strong emission from gas in out-
ﬂows. For example, Kristensen et al. (2017) present data
for a protostar sample observed with Herschel; the veloc-
ity data for water and high-J CO lines show that these
spectral lines are clearly associated with the outﬂow. In
order to more reliably model molecules in the diﬀerent
spatial regions, a fully 2D description that includes out-
ﬂow dynamics is necessary. In this contribution, our
goal is to develop a fully 2D code that self-consistently
predicts abundances for many molecular species in pro-
tostars, and moreover that can be compared with high
spatial resolution spectral line data from ALMA. We try
to be parsimonious in the model, to generate realistic re-
sults that include a simple outﬂow description, and that
also minimize the inclusion of luminosity evolution, in
order to better understand the importance of these ef-
fects. In this paper, we do not intend to ﬁnd the best
ﬁtting parameters for the protostar L1527 but rather
use what has been previously determined by Tobin et al.
(2012) as initial parameters to explore the chemistry of
the envelope in L1527 using RadChemT, which com-
bines a physical and chemical model (see §2.2.4 and
§2.2.5 for more details).
We use the protostar L1527 to compare and vali-
date our chemical model calculations produced by Rad-
ChemT (see §2.1 for more details of the utility of this
package). L1527 is a typical dense core system classiﬁed
as a class 0/I protostar with an edge-on disk orientation
located 140 parsecs away in Taurus molecular cloud (Be-
ichman et al. 1986;Torres et al. 2007;Tobin et al. 2008;
Kristensen, L. E. et al. 2012). The edge-on orientation
is favorable for studying the velocity structure of the en-
velope and outﬂow that is important to later constrain
the mass of the protostar itself. Previous eﬀort by To-
bin et al. (2008,2010,2012) provided extensive ﬁtting,
through modeling and imaging, for the physical prop-
erties of the system, although the non-unique nature of
SED ﬁtting (Robitaille et al. 2006) means that there is
still a wide range in free parameters to play with. More
recently, Aso et al. (2017) constrained the radius and
mass of L1527 using high resolution data from Atacama
Large Millimiter/submillimiter Array (ALMA).
Using RadChemT, we attempt to simultaneously
match the observed C18O(2-1), 12CO(1-0), and N2H+(1-
0) line strength and PV diagrams, together with contin-
uum data at infrared through millimeter wavelengths.
These molecules and transitions are of interest since they
are widely detectable by sub-millimeter interferometers.
12CO is an abundant species having strong transitions,
so it traces even the low-density gas in the outﬂow.
C18O probes higher gas density (107cm3) regions
that are aﬀected by photodissociation processes caused
by UltraViolet (UV) photons close to the disk surface
and is a very good tracer of the gas properties, struc-
ture and kinematics (Visser et al. 2009). The rotational
line emission of C18O has a much lower optical depth
than 12CO, thus probing in more detail the inner parts
of the envelope (Henning & Semenov 2013;Rab et al.
Physical and Chemical Structure of L1527 3
2017). Observations for some class I systems (Takakuwa
et al. 2012,2013;Takakuwa et al. 2017;Yen et al. 2013;
Murillo et al. 2015;Harsono, D. et al. 2013) have shown
that gaseous disks can be Keplerian, but understanding
their formation relies highly on what the spectral line
emission is telling us. Moreover, non-Keplerian dynam-
ics occurs in the cold outer disk boundary where the gas
motion is free-falling onto the disk, shocks are expected,
and there is the potential for a diﬀerent structural gas
ﬂow (Sakai et al. 2014). N2H+is one of the last species
depleted in prestellar cores, and traces the coldest, dens-
est material (107cm3).
We present the ﬁrst chemical calculations for L1527
using RadChemT. We provide a useful description of
the physical parameters and the chemical model used to
support the observations by Spitzer, Herschel, CARMA
and ALMA. As for the physical model description, we
compare the UCM and the TSC collapse models and
choose a density distribution to decide which one is more
compelling to describe what is happening at the line
center of the spectral data. We use the Hochunk3d
code (Whitney et al. (2013)) to determine the temper-
ature using continuum Monte Carlo Radiative Transfer
(MCRT). Then, we evolve a chemical network at each
cell to ﬁnd the molecular abundances, evaluating the re-
gions dominated by the UV ﬁeld and, ﬁnally, construct
synthetic spectral lines to compare against the interfer-
ometric dataset. In §2.2 we describe in detail the set up
of the physical model to simulate L1527 observations.
In §2.3 we present the essentials to model the chemistry
based on the temperature and density gathered from the
physical model. In §2.4 we present the tools to produce
images of L1527. In §3, we present the observational
parameters of ALMA and CARMA. In §4we present
the results and discussions of the physical structure and
chemical evolution using the tracers already mentioned
earlier for L1527, and outlining the new CARMA data
together with ALMA data for validation of the models.
Finally, in §5we present a summary of our ﬁndings.
2. METHODS
To make the modeling eﬀort tractable, the software
package we have assembled, RadChemT, breaks the
calculation into three parts with several key simpli-
fying assumptions. Step 1 carries out MCRT using
Hochunk3d, as described in §2.2, to calculate dust
temperature based on the current-time luminosity Lint
and 2D input physical model. Namely, for a given
snapshot in time, both density ρ(r, θ, φ) and velocity
v(r, θ, φ) are speciﬁed for the main components during
the dynamical collapse of the class 0/I system: outﬂow,
rotationally ﬂattened envelope, and disk. The physical
model is tuned to L1527, based on ﬁtting modeling and
imaging data from Tobin et al. (2008,2010,2012).
Step 2 performs a full time-dependent chemical abun-
dance calculation in a point model, i.e. locally for each
cell as described in §2.3, using the density and tempera-
ture from Step 1. As a simpliﬁcation, this ﬁrst version of
RadChemT does not track material along a gas stream-
line as a function of time. Instead, the abundance cal-
culations at each spatial grid point are time-dependent
but assume ﬁxed density and temperature. The assump-
tion is that current local conditions (ρ, T ) suﬃciently
describe earlier times. The assumption is most valid
in the outer envelope, where density and temperature
change the least for a moving gas parcel. There is an
initial (brief) transient behavior in the chemistry, from
starting with elements in atomic form, until molecular
cloud abundances are achieved. After this, the chemi-
cal age should be the same as the protostar age. The
age of an individual protostar can be estimated using
tage =M/˙
Menv, but the age of an individual object is
not well known during this early stage. We therefore
compare chemical abundance and morphology at two
time stamps, 104and 105years, that roughly span the
range of relevant ages for the Class 0/I phase. Predicted
abundance that are relatively constant over that time
span give conﬁdence that conclusions based on those
abundances will be robust.
Step 3 visualizes the protostar in a Position-Velocity
(PV) cube, making use of the Doppler eﬀect in spectral
line emission to sense the 3D velocity structure. This in-
vestigation uses RADMC-3D, as described in §2.4, to
perform spectral line radiative transfer assuming LTE.
The main inputs are the density, temperature, and ve-
locity grids from Step 1, combined with an abundance
grid from Step 2 for a selected molecule at t= 105years.
From the inputs RADMC-3D creates a synthetic model
PV cube in FITS format having units of Jy/pixel. The
primary and synthesized beam are then applied to the
model spectral line cube, in order to compare the model
with ALMA and CARMA submillimeter observations.
2.2. Physical model: Modiﬁcations of Hochunk3d
The physical structure of our representative Class 0/I
model is based on the Hochunk3d code (Whitney et al.
(2013)). This model uses an MCRT calculation to ob-
tain the temperature of the dust and the gas density
proﬁle. The 2D geometry considers the system in spher-
ical coordinates with axial symmetry and a logarithmic
the dust destruction radius, that is 10.04R, to the outer
edge of the envelope, Renv = 12,500 au. The meridional
4Flores-Rivera et al. 2020
(a) (b)
Figure 1. Lef t: Three color image of L1527. The north-south emission in green shows dense gas in the envelope as traced by
N2H+emission from CARMA. The outﬂow cavity lies east-west. In red, the Spitzer IRAC data at 4.5 µm traces the outﬂow
cavity in scattered light. Blue reveals the moderate velocity outﬂow shell as traced by CARMA 12CO emission. The size of the
panel is 16000×16000 (22,400 au at the distance of L1527). Right: Schematic representation of L1527. Regions are not drawn to
scale. Each west-east lobe is a low density region with two outﬂow cavities. The two outﬂow cavities are surrounded by a denser
outﬂow shell moving at 3 km s1outward, an approximated value obtained by ﬁtting the outﬂow shell of L1527 with the
channel maps of CARMA (See Appendix C). By contrast, in the envelope the velocity increases inwards towards the star due to
rotation-infall (collapse) motions. In addition, the direction of the rotation axis of the edge-on disk plus envelope is horizontal
(shown in the dashed black arrow), with red-shifted gas found north (top), and blue-shifted gas seen to the south (bottom) of
the protostar.
domain covers the full 180 degree. The model includes
a description of the density structure of the disk compo-
nent and of the envelope with an outﬂow cavity. Figure
1shows a schematic of the TSC geometry. Both the TSC
and UCM models have similar parameters to tune; Ta-
ble 1tabulates adopted values for L1527 to be described
more speciﬁcally in §2.2.4 and §2.2.5.
We adopt a dust model that is appropriate for proto-
stellar environments, based on a comparison of models
with observations (Huard & Terebey 2017). Speciﬁcally
we adopt the thinly ice-mantled, coagulated dust of Os-
senkopf & Henning (1994) (see their Table 1, 5th col-
umn), often referred to as “OH5” grains in the literature
(e.g., Evans et al. (2001); Shirley et al. (2005)), aug-
mented by the opacities of Pollack et al. (1994) at wave-
lengths shorter than 1.25 µm, as described in Dunham
et al. (2010). In the next subsections we explain how
the main components: envelope (§2.2.1), disk(§2.2.2),
and outﬂow cavities(§2.2.3), are structured in the model
and the physical parameters(§2.2.4 &§2.2.5) we chose
to model L1527.
2.2.1. Envelope prescription
Each region has its own density structure and its dis-
tribution proﬁle is semi-analytic. For the UCM collapse
model we incorporate the density structure of the en-
velope as implemented in Hochunk3d. We use a sep-
arate calculation to determine the envelope density for
the TSC collapse model (Terebey et al. 1984) that con-
sists of an infalling slowly rotating cloud that becomes
rotationally ﬂattened as it collapses. These two collapse
models are the same in the inner part of the envelope,
but diﬀer in the outer envelope due to the fact that
UCM neglects gas pressure support. For both collapse
models, we set the envelope radius to Renv and, for the
TSC model, the infall velocity is zero outside 4000 au,
which is the current boundary of the infall region and
it moreover has an infall rate of 3.0×106Myr1.
But for the UCM model, the infall velocity in this outer
region is not zero, but is given by the free-fall velocity
onto the 0.22 Mprotostar, with a mass infall rate of
5.0×106Myr1; moreover, UCM neglects any accel-
eration from the massive envelope (see Huard & Terebey
(2017) for additional discussion). Hence the UCM and
Physical and Chemical Structure of L1527 5
TSC models presented here have diﬀerent values for the
density of the envelope, but the spatial grid, as well as
the outﬂow and disk deﬁnitions, are the same for both
models. We expect the diﬀerence between the UCM and
TSC models to be greatest in the cold outer envelope,
where the infall speeds are lowest, less than about ﬁve
times the thermal line speed (see Table1). This cold gas
contributes signiﬁcantly to the emission near the core of
the spectral line, within about 1 km s1of line center.
The latter depends on the maximum recoverable spa-
tial scale of L1527. The model comparison is meant to
show whether the analytic UCM model is suﬃcient, or
whether it is necessary to include the additional com-
plexity of the TSC model in order to match the spectral
line proﬁles.
2.2.2. Disk-Envelope prescription
The boundary between the envelope and the disk is
not a well explored area, although it could be impor-
tant during the Class 0/I phase if infalling material goes
through a shock when it impacts the disk. In this ﬁrst
paper, we do not include shocks, however, as a ﬁrst
step towards including shocks we modiﬁed slightly the
shape in which the disk-envelope boundary is deﬁned
in Hochunk3d by including a ram pressure boundary
condition for motion perpendicular to the disk midplane.
The assumption is akin to that of infalling material hit-
ting a “brick wall” in the disk midplane. Expressing the
pressure in terms of the thermal sound speed as P=ρc2
s,
and the ram pressure as P+ρv2, then the disk-envelope
boundary is deﬁned by matching the disk and envelope
ram pressures:
ρdiskc2
sdisk =ρenv(c2
senv +v2
env ),(1)
where vrepresents the velocity component that is per-
pendicular to the disk midplane. The thermal sound
speed is calculated assuming cs= (kT /µmH)1/2and as-
suming that the dust and gas temperatures are equal,
which is a reasonable assumption for protostellar densi-
ties. The disk boundary that is found using this bound-
ary condition is no longer a ﬂared disk, but has fairly
constant opening angle out to the edge of the disk, as
described in §4.
2.2.3. Outﬂow cavities and outﬂow jet prescription
We use the prescription of Whitney et al. (2003a) for
the outﬂow cavity shape. The shape of both outﬂow cav-
ities are described by a polynomial function for L1527
which follows z($) =$bwhere \$= (x2+y2)1/2is the
cylindrical radius and b= (inner, outer) = (1.7,1.5) is
the cavity shape exponent. θ1and θ2are the opening
angle of the inner and outer cavity surface, respectively,
deﬁned at the maximum radius of the envelope. Only
the apex of θ1reach the source center, and θ2apex starts
after 75 au. The density inside the outﬂow cavities is set
to a constant value of 1.6×1020 g cm3.
2.2.4. Parameters
Initial values for the parameters were based on the
SEDs and image ﬁtting done by Tobin and collabora-
tors (Tobin et al. 2008,2010,2012,2013). The model-
ing of L1527 is primarily sensitive to Lint that depends
directly on the chosen values of Rand T(see Table 1),
the radius and temperature of the star, respectively. As
described in Whitney et al. (2013), to determine the
eﬀective temperature of the star, we specify spot pa-
rameters such as: two number of spots at 45 degrees in
latitude, and 0.10 as the fractional area. Deﬁning R
and T, we keep the internal luminosity Lint = 2.74 L
ﬁxed which is reasonable given the range of possible lu-
minosity values for L1527. For a Class 0/I protostar, the
protostar mass should be small. Therefore we looked at
lower mass values in the literature, and selected a cen-
tral star mass of M=0.22M, a mass that best ﬁt the
position-velocity diagram for 13CO (Tobin et al. 2012).
to 75 AU (Aso et al. 2017). The disk inner radius is the
dust destruction radius, a value that is set by the code
depending on the stellar luminosity.
Two important considerations are crucial to matching
both of the SED apertures, and for both TSC and UCM
for our modeled L1527. Using identical parameters leads
to somewhat diﬀerent looking SEDs; however we ﬁnd
that solely modifying ˙
Menv and Mdisk brings the SEDs
for UCM and TSC into reasonable correspondence, es-
pecially near 100 µm wavelength, near the far-infrared
peak of the SED. In this case, the reasonable parame-
ters found are Mdisk=0.006Mand a ˙
Menv of 5.0×106
Myr1for the UCM model. For the TSC model, on
the other hand, the mass of the disk chosen is 0.011M
and a ˙
Menv of 3.0×106Myr1. The second consid-
eration is the outﬂow; from newer data we ﬁnd there is
evidence in both the CARMA and ALMA 12CO data
for a narrow jet, plus a wide-angle bipolar outﬂow, with
a transition that happens at 75 au from the proto-
star. The ALMA data (Fig.8) show the inner region,
including the jet and outﬂow lobes in a representative
velocity channel. The CARMA 12 CO data in Fig.6and
Fig.9channel maps also display a narrow outﬂow struc-
ture near the protostar. We model this structure (Fig.3)
using a dual outﬂow cavity with the narrow “jet” ex-
tending to 75 au, a radius that is similar to the 85 au
suggested by a cavity modeling analysis from Tobin et al.
(2010). We also specify a small, but nonzero density in
6Flores-Rivera et al. 2020
Table 1. Physical Parameters.
Parameters Description TSC UCM
T(K) Stellar temperature 3,300 :
M(M) Stellar mass 0.22 :
Mdisk(M) Mass of the disk 0.011 0.006
Rdisk(au) Disk outer radius 75 :
˙
Mdisk(Myr1) Disk accretion rate 6.6×107:
˙
Menv(Myr1) Envelope infall rate 3.0×1065.0×106
θ1() Opening angle of the inner cavity surface 15 :
z(au) z-intercept, inner cavity surface at ω=0 75 :
θ2() Opening angle of the outer cavity surface 6 :
LIS RF (L) Luminosity due to ISRF 0.49 :
Quantities shown below are derived from input parameters above
Menv(M) Mass of the envelope 1.77 1.04
cs(km s1) Thermal sound speed using ˙
Menv = 0.975c3
s/G 0.23 0.27
Rcol(au) Inside-out collapse radius using Rcol =cstage 3800 n/a
L(L) Stellar luminosity 0.31 :
Lacc,star(L) Stellar hot spot accretion luminosity 2.14 :
Lacc,disk(L) Disk accretion luminosity 0.29 :
Lint(L) Internal luminosity 2.74 :
The symbol : means the UCM values are the same as TSC values.
the outﬂow cavity (1.6×1020 g cm3); adding a small
amount of material (having standard dust-to-gas mass
ratio of 0.01) to the outﬂow cavity produced a better
ﬁt to the SED from that shown in Tobin et al. (2010).
Our choice of outﬂow parameters removes the need for
the puﬀed up disk required by previous modeling (To-
bin et al. 2010). For the purposes of this paper we did
not attempt a detailed modeling of the jet length or the
cavity shape.
2.2.5. Luminosity
The internal luminosity is ﬁxed at Lint = 2.74 Lto
match the 2.74 Linternal luminosity found by Tobin
et al. (2008). The internal luminosity includes contri-
butions from the star L, plus the accretion luminosity
from material falling onto the star Lacc,star, and the ac-
cretion luminosity generated within the disk Lacc,disk,
as described in Whitney et al. (2013). For a Class 0/I
protostar, the protostar mass should be small and most
of the luminosity should be due to accretion. This led
to choosing a stellar radius of 1.70Rwith an eﬀec-
tive temperature of 3,300 K that gives a stellar lumi-
nosity of 0.31 L(see Table 1). One additional term
LIS RF contributes to the total luminosity of the sys-
tem, Ltot =Lint +LIS RF = 3.23 L; the term LI SRF is
due to external illumination by the Interstellar Radia-
tion Field (ISRF) and is based on the galactic value com-
puted near our solar system; see description in Huard &
Terebey (2017).
The largest luminosity term is due to the stellar hot
spot accretion luminosity, which is deﬁned as:
Lacc,star =GM˙
Mdisk(1
R1
Rtrunc
) (2)
where Rtrunc is the truncation radius where the disk
is truncated by the stellar magnetospheric ﬁeld and its
value is approximately the same as in Tobin et al. (2008).
The disk accretion rate ˙
Mdisk is an important parameter
that leads to the stellar accretion luminosity that encom-
passes about 66% of the total luminosity of the system.
The code determines that the value ˙
Mdisk=6.6×107
Myr1leads to an accretion luminosity onto the star
of 2.14 L.
We also include the disk accretion luminosity in terms
of the energy dissipated at the inner boundary of the
disk (see Shakura & Sunyaev 1977;Lynden-Bell &
Pringle 1974;Kenyon & Hartmann 1987;Whitney et al.
2003b, for more details). Table 1summarizes the values
of the diﬀerent luminosity terms.
2.3. Chemical model
We carry out local chemical evolution modeling to de-
termine the abundances of the molecules that have been
Physical and Chemical Structure of L1527 7
Table 2. Isotopic fractionation reactions used in the model. ∆E values
are taken from (Langer et al. 1984). ∆E values for reactions involving
17O are assumed to be the same as for the equivalent reaction of 18O, with
the pre-exponential factor in the rate calculation scaled by the reduced
mass (Young 2007).
Reactions
13C++ CO C++13CO ∆E=35K
13C++ C18 OC++13C18 O ∆E=36K
HCO++12CO CO + H13CO+∆E=9K
HCO++ C18OHC18 O + CO ∆E=14K
HCO++13C18 OH13C18 O++ CO ∆E=22K
H13CO++ C18 OHC18O++13 CO ∆E = 5K
H13CO++13 C18OH13 C18 O++13CO ∆E=13K
HC18O++13 C18OH13 C18 O++ C18O
observed. The chemical models are time-dependent, and
we focus on the results at two epochs 104and 105years
that span the range of possible ages for L1527.
Our chemical network is taken from the UMIST
database, RATE12 (D.McElroy et al. 2013). The re-
actions of the carbon and oxygen isotopes have been
added such that each reaction involving an atom of the
major isotopes will have an equivalent reaction involv-
ing the minor isotopes (see Willacy & Woods 2009, for
more details). Fractionation of the oxygen and carbon
isotopes can occur via the reactions listed in Table 2.
For reactions involving 17O the values of ∆E are taken
to be the same as the equivalent reaction of 18O, and
the pre-exponential part of the rate calculation is scaled
by the reduced mass (Young 2007).
The network also includes gas-grain reactions, i.e.
freezeout on the grain (Hasegawa & Herbst 1993), ther-
mal desorption (Hasegawa et al. 1992), as well as pho-
todesorption, and desorption by heating of grains by cos-
mic rays ( ¨
Oberg et al. 2009b,a). The freezeout and des-
orption reactions are also described in Woods & Willacy
(2009). Freezeout is assumed to occur with a sticking
coeﬃcient of 1.0 (Bisschop et al. 2006) for all species.
For desorption processes, the binding energies required
are taken from UMIST12. Cosmic ray heating rates are
given by
kcrh = 3.16 ×1019 ×exp(Eb/70.) (3)
(Hasegawa & Herbst 1993), where Ebis the binding en-
ergy of the accreted molecule. Photodesorption rates
are given by
kphotd =F Y < πa2ng>ΘX(4)
(Willacy & Langer 2000) where F is the UV ﬁeld (the
total of the stellar, interstellar and cosmic ray induced
ﬁelds in units of G0), Y is the yield per photon which
is taken to be 103for all species (Westley et al. 1995),
except for oxygen atoms (Y=104) and H2O (Y=103)
and Y = 2 ×103for desorption as OH (Hollenbach
et al. 2009). The dust is assumed to be well mixed with
the gas, ngis the number density of dust grains (ng
=1012 nH), and the average < πa2ng>= 2.1 ×1021
nH(standard interstellar value). ΘXis the surface cov-
erage of species X= (ns(x)/Σns(y)), where ns(x) is the
abundance of X in the ices and Σns(y) is the total abun-
dance of ices). The stellar UV ﬁeld is assumed to have a
typical T Tauri value of 500 G0at 100 au (unextincted)
from the star, where G0is the standard ISRF (Bergin
et al. 2003). The dense envelope generates signiﬁcant
extinction. To account for this, the local UV ﬁeld is
decreased to take into account the extinction calculated
along the line of sight of the star.
Grain surface reactions are included using the ap-
proach of Garrod (2011). Only atoms, H2and simple
hydrides (OH, CH, NH, and their isotopologues) are as-
sumed to be mobile on the grain surface.
Initially we assume all elements are in their atomic
form, except for carbon which is ionic and hydrogen
which is 95% molecular. The initial abundances used
are given in Table 4. We assume a cosmic ray ionization
rate of ζCR = 1.3 ×1017 s1.
For the photodissociation of CO (and its isotopo-
logues), and H2we use the self-shielding coeﬃcients
provided by Visser et al. (2009) assuming a doppler
width of 0.3 kms1and isotopic ratios of 12C/13 C =
89, 16O/18 O = 498 and 16O/17 O = 1988, which are
taken to be the same as local ISM values (Wouterloot,
J. G. A. et al. 2008). Abundances here are prescribed as
X, the fractional abundances relative to total hydrogen,
nX/(nH+ 2nH2).
8Flores-Rivera et al. 2020
Starting from t= 0, the molecular abundances grow
rapidly until t= 104years, when the abundance of 12CO
reaches its maximum achievable value of 7.22 ×105, a
value that is set by the assumed carbon abundance (Ta-
ble 4) and that is based on Taurus observations. There-
fore we chose t= 104yrs as our starting reference time
for the chemistry. The grid in the chemical model fol-
low the same structure as in the physical model (§2.2)
but, in order to speed up the computation, the chem-
istry was only computed on every 5th grid point in the
spatial grid. The solution of the chemical reaction net-
work reaches good convergence throughout most of the
spatial grid, including the disk, envelope, and outﬂow
shell. However, we exclude from consideration the low
density (n=4000 cm3) outﬂow cavity due to reduced
convergence in this mostly atomic region. There is little
impact on our study because the outﬂow cavity con-
tributes little to the molecular emission that is the fo-
cus of this investigation. However, we do capture the
chemistry that happens based on our prescription of the
outﬂow shell (see Fig.9) when we add constant velocity
in this region between the envelope and outﬂow, see §2.4
for more details.
2.4. Synthetic line images
Step 3 of RadChemT calculates the protostellar envi-
ronment in a PV cube. Because Hochunk3d did not
include spectral line emission we selected RADMC-3D,
version 0.41 (Dullemond et al. 2012) , to generate syn-
thetic spectral line emission assuming LTE. LTE im-
proves computational speed and holds in locations where
the gas density is above the critical density. The gen-
eration of synthetic line images takes into consideration
the density, temperature, and velocity grids from Step 1,
and the abundance grid from Step 2 at t= 104year and
t= 105year time stamps, all of which are translated
Finally, for each model density distribution and epoch,
we carry out line-of-sight radiative transfer calculations
using RADMC-3D to construct synthetic line and con-
tinuum observations, and compare these against the
multi-telescope data set for L1527.
source inclination i= 85, distance d= 140 pc, and vsys
= 6.0 km s1system velocity. For consistency the OH5
dust opacity law is the same as that used for the step
1 continuum radiative transfer. Standard and reason-
able assumptions for the protostellar environment are
Tdust =Tgas and 100 for the gas-to-dust ratio. The mi-
croturbulent velocity was ﬁxed at 0.1 km s1, a value
that is required for LTE and results in smoothing the
line proﬁle. A larger microturbulent velocity value could
aﬀect the hyperﬁne structures of the molecular spectrum
by causing line blending. However, data from CARMA
CO observations indicate somewhat larger values for the
microturbulence should be used for the outﬂow shell re-
gion. Based on the 12CO data presented in §4.5.1, and
in Appendix C, we chose a very simple outﬂow velocity
prescription having a constant outward radial motion
of 3 km s1in the outﬂow cavity and also in the out-
ﬂow shell. However a careful treatment of the outﬂow
shell lies outside the scope of this paper. From the in-
puts RADMC-3D creates a synthetic model PV cube
in FITS format having units of Jy pixel1.
Comparison with observations also requires apply-
ing telescope speciﬁc parameters. The velocity channel
width and spatial pixel size were speciﬁed as inputs to
RADMC-3D. The synthetic images are sampled in real
space in order to be able to see more clearly the varia-
tions in the chemical abundances and, therefore, the dy-
namical range of the system, in which in our models are
greater than the interferometric data. To compare with
millimeter interferometer data, the synthetic model im-
ages are multiplied by a Gaussian primary beam (peak
value normalized to unity), and then convolved with a
circular Gaussian synthesized beam (area normalized to
unity). See §3for ALMA and CARMA observational
parameters.
3. OBSERVATIONS
3.1. CARMA data
L1527 was observed on August and November 2009 us-
ing the Combined Array for Research in Millimeter-wave
Astronomy (CARMA) located at an altitude of 7200
feet on the Eastern California Inyo mountains. Obser-
vations were obtained in D- and C-array conﬁgurations,
which provide an uniform uv-coverage between 9 and
371 m. The CARMA correlator was set to observe the
12CO (1-0) emission line (ν= 115.271 GHz) in the up-
per side band, and the 13 CO (1-0) (ν= 110.201 GHz)
line in the lower side band. These two lines were ob-
served at a velocity resolution of 0.34 km s1in two 8
MHz spectral windows. The dust continuum emission
was observed in two 1 GHz windows separated by 3.6
GHz and centered at the mean frequency of 112.73625
GHz (λ= 2.66 mm). Here we do not use 13CO (1-
0) since it has higher optical depth than C18O, there-
fore, making it more diﬃcult to see the emission from
the disk. The band pass shape was calibrated by ob-
serving 3C84 and the ﬂux calibration was set by ob-
serving Uranus. The quasar 3C11 was observed every
12 minutes to correct for atmospheric and instrumental
eﬀects. The data reduction and the image reconstruc-
Physical and Chemical Structure of L1527 9
Table 3. CARMA observational parameters.
CARMA
12CO(1-0) N2H+(1-0)
Target, date L1527 IRS, August and November 2009
Coordinate Center R.A.(J2000)=4h39m53s.9000
Dec.(J2000)=2603010.000
Frequency 115.271 GHz 93.17378 GHz
Synthesized beam 3.3200×2.9500 10.9700 ×8.7300
Primary beam 5400 6700
Velocity resolution 0.34 km s10.26 km s1
Noise level (detected channel) 0.187Jy beam10.200Jy beam1
tion were obtained using the MIRIAD software package.
For N2H+data and model comparison, we convolve the
model using a geometric mean FWHM of 900 , namely,
b=p(bmax bmin) = 10.9700 8.7300 = 900 . The ob-
servational parameters are described in Table.3.
3.2. ALMA data
The observational data presented for C18 O (2-1) and
having 0.9600 ×0.7300 (that is the geometric beam) spa-
tial resolution and a maximum recoverable scale of
1500 are based on data from the ALMA archive that
was taken during cycle 0 on 2012 August 26 (Project
code: 2011.0.00210.S). Higher spatial resolution ALMA
data exist: however they resolve out much of the 1000
emission that is relevant to this study. We convolve the
model using the same geometric mean formulation as in
CARMA, giving b= 0.800 for the ALMA spatial reso-
lution. The model is also multiplied by the ALMA pri-
mary beam, which was taken to be a smooth 2800 FWHM
Gaussian image. Table 5summarizes observational pa-
calibration is given in Table 1. in Ohashi et al. (2014).
4. RESULTS AND DISCUSSIONS
4.1. L1527 SED ﬁts
We present a comparison of the ﬂux density of the
simulated L1527 for both UCM and TSC models. The
simulated L1527 SEDs are shown in Figure 2plotted
at 85edge-on (pink), the appropriate inclination of
L1527 (Oya et al. 2015). Panel (a) and (b) show the
model SEDs computed for a 1000 au (7.1400 ) aperture
and a larger 10,000 au (71.400) aperture, respectively.
We also include a plot to illustrate the strong eﬀect of
source inclination on the SED model curves. We re-
generate SEDs for L1527 by including the ﬂux density
values from (Tobin et al. 2008) plus we added ﬂux den-
sity values from Herschel (see Table 6and 7), that come
mostly from the thermal radiation of the envelope. The
archive. Since the Herschel CDF spectrum (Green et al.
2016) and HPPSC catalog ﬂux density points (Marton
et al. 2017a) have apertures of 61400 , namely that lie in
between the model 7.1400 and 71.400 apertures, we chose
to show the Herschel data on both SED aperture plots.
Although we do not intend to redo the best parameter ﬁt
for L1527, here we revisit the outskirts of the envelope
where the emission is also important for the chemistry.
Overall, both the UCM and TSC models provide rea-
sonable SED ﬁts, with the TSC model providing a bet-
ter ﬁt for the 10,000 au aperture that is consistent with
the large spatial extent of the system. Another regime
that supports our later statement is the region where
the disk emits, this is between 2.16 and 8.0 µm. We ﬁnd
that the TSC is a closer ﬁt to the ﬂux points although
not perfectly due the diﬀerent dust opacity population
and density that lies in here which not necessarily is in
accordance with the dust opacity model we use for the
envelope. The PACS data are also of particular interest
because they occur near the peak of the SED distribu-
tion. The Herschel PACS HPPSC data have an aperture
of 6 00at 70 µm and 100 µm, and 1200 at 160 µm. The
PACS data at 70 µm and 100 µm have a spatial resolu-
tion that is comparable with the 7.14 00aperture model
(Fig.2, Panel(a)) and moreover, the ﬂux density values
do not deviate much from the modeled ones. However,
for PACS >100 µm it is slightly oﬀset since the discrep-
ancy in aperture size is greater. The Herschel spectrum
does not match the Herschel photometry points either,
so the Herschel data are not consistent with each other
at around 100 µm and longer wavelengths. Some possi-
ble explanations can be that: a) the source is extended,
which might mean the data calibration is oﬀ/incorrect
10 Flores-Rivera et al. 2020
(a) (b)
(c)
Figure 2. Spectral Energy Distribution (SEDs) of L1527 is plotted at 85source inclination for both the UCM (dashed pink
line) and TSC (solid pink line) collapse models. Panel (a) and Panel (b) show the ﬂux density data obtained from Tobin et al.
(2008) as diamond icons for a model aperture size of 1000 au (7.1400 ) and as squared icons for a model aperture size of 10,000 au
(71.400), respectively. Except; the Herschel CDF spectrum (solid black line) and HPPSC data (triangles) plotted near 100 µm
are the same in all three panels. See Appendix B, Table 6and Table 7for a detailed description. To illustrate the eﬀect of
diﬀering source inclination, panel (c), in particular, shows 10 inclinations (pole-on green, edge-on pink).
(data issue) or b) the source is varying in luminosity
(source variability).
The properties of the central region were chosen care-
fully (see §2.2.4) to best describe the physical structure
of L1527 as constrained by imaging data and the SED
photometry. We estimated these stellar properties prop-
erly describing L1527 based on Tobin et al. (2008,2010,
2013). We also adjusted the description of the outﬂow
cavity to transition from jet to wide-angle outﬂow based
on ALMA CO data (Fig.8) at 75 au (see §2.2.4). For the
ﬁxed protostellar parameters listed in Table 1and de-
scribed in §2.2.4 and §2.2.5, we varied the mass infall
rate and disk mass, ﬁnding the mass infall rate, ˙
Menv,
to be 5×106Myr1and 3×106Myr1for the
UCM and TSC models, respectively. Based on the mag-
nitude of ˙
Menv chosen, the age of the simulated L1527 is
estimated to be 0.22M
that L1527 is in the protostar collapse phase with an
age of t'105yrs.
To further assess the self-consistency of the model, we
note that in every evolutionary stage of the star for-
mation process, the mass budget of the infalling en-
velope and accreting disk have to be consistent with
the feedback of the outﬂows and winds. In the ab-
sence of any outﬂow, then ˙
Menv =˙
Mdisk, all of which
falls onto the central star. As discussed in section 2.2.5
and shown by Equation (2), the disk accretion ˙
Mdisk
leads to generous Lacc,star accretion luminosity, which
Physical and Chemical Structure of L1527 11
is ﬁt by the modeling procedure. Therefore a mis-
match in the two accretion rates is related to outﬂow
feedback. The infall eﬃciency is given by the ratio of
the accretion rates; for L1527 our model value of ˙
Mdisk
˙
Menv
= 6.6×107Myr1/3×106Myr1= 0.22. We
point out that this value is similar to the value of 0.25
estimated for the protostar TMC-1 (Terebey et al. 2006).
These values diﬀer from unity, and provide interesting
constraints to theoretical discussions of star formation
eﬃciency. See Matzner & McKee (2000), and in the
context of high mass star formation, Zhang et al. (2014)
for an extensive treatment of outﬂow feedback, and its
relation to star formation eﬃciency.
Next, for comparison purposes with van ’t Hoﬀ et al.
(2018), we produced a second UCM run by increas-
ing the stellar mass to 0.45 Mand the disk radius
to 125 au. The untuned model produced SED ﬁts that
were worse but still reasonable. No signiﬁcant diﬀer-
ence could be discerned in the density, temperature, or
resultant chemistry. However, the velocities increased
by 2 due to higher gravity from the larger mass. The
eﬀect was clearly seen in model spectral line proﬁles and
PV diagrams (see further in §4.5.2), therefore, turning
it into a promising venue to investigate the dynamical
mass of L1527 in future studies.
4.2. Temperature and density maps
Figure 3presents the dust temperature (top panels)
and gas density (bottom panels), computed using the
RadChemT package, as meridional cuts through the en-
velope + disk + bipolar outﬂow cavity. Three diﬀerent
zoomed views are shown from left to right. The cen-
tral star is located at the origin, the outﬂow cavities
extend horizontally, and the edge-on disk (vertical) is
oriented 90with respect to the outﬂow cavities. The
dust temperature is calculated from the radiative equi-
librium solution using Hochunk3d and its distribution
goes as the power r0.5in optically thick regions, and as
the power r0.33 in optically thin regions (S.J. Kenyon
1993). Near the protostar, the temperature reaches the
sublimation temperature of 1600 K inside the outﬂow
cavities, and the small amount of dust sublimates due
to exposure from stellar radiation in this region, making
it feasible for the atomic gas to be present at vibrational
energy levels. The radius of the collapsing region (i.e.
expansion wave) is 3,800 au, and grows larger in time
at the sound speed. Outside the collapse radius, the
distribution of the envelope is a power-law function of
sity distribution becomes ﬂat, transitioning at smaller
radius to the free-fall zone where the density behaves
as ρr3/2well outside the disk (Shu 1977;Terebey
et al. 1984). Contour lines in white show T= 25 K (top
panels), our deﬁnition of the evaporation temperature of
CO(e.g, Qi et al. (2015,2019); Wiebe et al. (2019), and
number density n= 109cm3(bottom panels). The
shape of the dual outﬂow cavity is seen most clearly in
the lower middle density panel in blue; near 75 au the
narrow outﬂow/jet opens into a wide-angle outﬂow. The
circle in the lower right shows the (small) 1000 au radius
aperture (7.1400 ) that is used for aperture photometry.
Note that this aperture covers a small portion of L1527
making necessary to compare PACS data points with
71.400 (10,000 au) that covers a much larger region.
the envelope, 75 au, and the disk-envelope boundary is
wedge-shaped due to the ram pressure boundary condi-
tion (see §2.2). The highest density region is found at
the disk midplane with the number density on the or-
der of 1014 cm3. At this high density region inside
50 au, the temperature in the disk midplane is slightly
higher than 30 K. Beyond 75 au, the midplane is shielded
freeze-out onto dust grains until T= 25 K at 225 au,
where the CO snowline lies and freeze-out is expected
to happen more rapidly. Beyond the T= 25 K contour
line, the temperature decreases until reaching the typi-
cal temperature of the envelope, T= 10 K. Since we do
not include shocks, there is no increase in the temper-
ature proﬁle due to them. The luminosity that shocks
can produce is a small fraction compared to the stellar
luminosity, however, it is been suggested that can be
enough to liberate molecules from grains (Sakai et al.
2014). Comparing the UCM and TSC models, the tem-
perature and the density distribution from both show
very little diﬀerence in terms of structure.
4.3. C18O abundance distribution
both the temperature and density (Hartmann et al.
2004), which vary throughout the cloud. The chem-
istry at the outer boundary of the cloud is determined
by the cold temperature, low density, and exposure to
the ISRF. Within the cloud envelope, at ﬁrst the rapid
increase of density inwards dominates, so that molecules
freeze out onto grains in regions of low temperature and
high density. Nearer the protostar the temperature rises
above the desorption temperature, at which point the
behavior changes, and molecules come oﬀ the grains and
are released into the gas phase. The chemistry is also
aﬀected by the UV radiation ﬁeld from the protostar.
Dust extinction shields regions near the midplane from
the protostellar UV ﬁeld.
12 Flores-Rivera et al. 2020
Figure 3. Meridional (zvs. cylindrical r) temperature (top) and gas density (bottom) panels for the disk + envelope + outﬂow
using TSC model of L1527. The edge-on disk is oriented vertically in the ﬁgure, and rotated by 90with respect to the outﬂow
cavity. The shape of the dual outﬂow cavity is evident in the lower middle panel in blue. White line contours: T = 25K (top
panels) and n= 109cm3(ﬁrst two bottom panels). The white line contour in the third bottom panel shows the radius for the
1,000 au aperture size. The colorbar temperature wedge is log10 (T/Kelvin), and the density wedge is log10(ρ) where ρis the
mass density in g cm3.
The dense gas distribution is often traced using iso-
topologues of CO, like C18O, which are less likely to
be optically thick than CO itself. For both time steps,
t= 104years and t= 105years, high C18O abundances
(107relative to hydrogen) are primarily coming from
the disk and envelope at radii smaller than 400 au, where
the temperature is 25 K (see Fig. 3) and the chemistry
can be dominated by thermal desorption reactions and
perhaps photodesorption reactions due to the capture
of stellar radiation. Due to the lower abundance and
optical depth of C18O, the eﬀect of photodissociation is
visible by a drop of 10×in C18O abundance already in
the outer envelope (8000 AU) at t= 105years. But in
terms of spatial extension, the C18O is similar to 12 CO,
as seen in Fig.4panel a, but diﬀerent for absolute abun-
dance. We found no signiﬁcant diﬀerence between UCM
and TSC model for chemical abundances, and therefore
limit the discussion to the TSC model abundances.
Our chemistry matches expectations in the envelope
outside the edge of the disk, where we expect lower con-
centrations of C18O (108) due to the high density
area that is shielded from stellar radiation, and thus,
cooler in this region. An abundance gap in the midplane
beyond 300 au is present for both t= 104and t= 105
years, and is consistent with the depletion expected in
the region beyond the CO snowline (T25 K) in the
disk and envelope midplane. At t= 105years there
is a steep drop in the C18O abundance between 400
au and 4000 au due to the short freeze-out timescale
compared with the outermost part of the cloud where
the freeze-out timescale becomes longer (i.e., Caselli, P.
et al. 1999).
Physical and Chemical Structure of L1527 13
(a)
(b)
Figure 4. Evolution of 12 CO (Panel a) and of N2H+(Panel b) gas phase abundance both for the TSC model. In Panel a, the
black contour line shows the maximum 12CO abundance, divided by 10. In Panel b, the black contour line shows the maximum
N2H+abundance, also divided by 10. The purple dashed line in the ﬁrst panel shows the disk. The maximum CO abundance
is 7.22×105. The colorbar is in logarithmic scale.
14 Flores-Rivera et al. 2020
In the outermost region in the envelope (r > 4000 au),
the temperature drops to T= 10 K; the light enhance-
ment of C18O abundance (108) in this region is inﬂu-
enced by photodesorption reactions such as CRs coming
from outside the cloud.
The chemistry results presented here for 12CO, C18O,
and also for N2H+(next section §4.4) represent a small
subset of molecular abundances that are available for
comparison with observations. Our RadChemT model
includes a chemical network that provides abundance
predictions for 292 chemical species; this number in-
cludes carbon and oxygen isotopologues and 90 grain
surface abundances, a promising venue for further stud-
ies.
4.4. N2H+as CO snowline tracer
Snowlines, such as those for water and CO, are impor-
tant because they can inﬂuence the eﬃciency of planet
formation within the cold shielded regions of disks. Be-
cause CO line emission is optically thick thus making
it diﬃcult to observe the dense interior regions, recent
studies by Aikawa et al. (2015) and van’t Hoﬀ et al.
(2017) suggest that it is necessary to derive the location
of the CO snowline from N2H+observations. Obser-
vations have established that the N2H+abundance is
anti-correlated with CO abundance in systems ranging
from starless cores (i.e, Tafalla et al. (2004)), to class
0 protostars (i.e. Jørgensen (2004)), to protoplanetary
disks (i.e. Qi et al. (2013,2015,2019); Wiebe et al.
(2019)).
Our chemistry results show a general predicted trend,
that gas phase 12CO and N2H+are anti-correlated in
the envelope. In Figure 4(Panel a, top middle and
right) at t= 104years the 12CO is depleted from the
gas phase and at t= 105years (Panel a, bottom middle
and right) the 12CO depletion region increases outwards.
The increase of N2H+concentration, beyond 400 au, is
consistent with the 12CO depletion to t= 105years
(Figure 4(Panel b, bottom middle and right). Inside
320 au, 12CO is enhanced since T>25 K in this region
(see the ﬁrst two top panels in Fig.3) due to thermal
and photodesorption reactions whereas N2H+is absent.
Therefore, the 12CO snowline is present and the best
anticorrelation takes place at T25 K in the midplane.
The predicted anti-correlation covers a larger region
at t= 105years, which is the nominal age of L1527, and
shows that the N2H+concentration grows and extends
from 400 au to 2000 au (close to the midplane). The
N2H+is present in the outer envelope at larger abun-
dances at t= 105years compared to t= 104years.
Thus, our models show a general predicted trend, that
gas phase 12CO and N2H+are anti-correlated in the
envelope. Although the CO depletion timescale diﬀers
somewhat from the N2H+growth timescale, the N2H+
abundance increase should closely follow the slow deple-
tion of 12CO since gas-phase timescales are much less
than freeze-out timescales. The chemistry models are
thus consistent with N2H+being a good tracer for the
12CO snowline. Note that the abundances in the outﬂow
cavity are excluded from consideration (see §2.3). The
jagged boundary between outﬂow cavity and envelope is
due to grid sampling eﬀects mentioned in §2.3.
4.5. Spectral line comparison: models versus
observations
In order to compare our models with observations, we
generate synthetic model spectral line images of N2H+
for CARMA and compare its anti-correlation with 12CO
CARMA data (§4.5.1). In order to convey the validation
of RadChemT, we generate a synthetic spectral line for
C18O, from which we extract synthetic P-V diagrams to
compare with ALMA observations (§4.5.2). Each model
spectral line data cube is based on the density, temper-
ature, velocity grids, and chemical abundances analyzed
from previous sections.
4.5.1. N2H+and 12CO CARMA
Figure 5presents the RadChemT model in the form of
an integrated intensity map of N2H+at t= 105years.
The best N2H+and 12CO anticorrelation takes place
at t= 105years, where the greater extension of the
N2H+abundance (see Panel ain Fig. 4) is more consis-
tent with the CARMA data than at t= 104years. In
Figure 5we predict the spatial extension of the N2H+
intensity. By not convolving the modeled emission of
Figure 5with the beam, we are able to see in more de-
tail the spatial structure of the N2H+emission in the
envelope, otherwise, the X-shape emission would disap-
pear looking more like a vertical bar, very similar to how
it looks in Figure 6Panel (a). As previously discussed
in §4.4, the predicted N2H+emission traces cold dense
gas in the envelope between 400 au and 3000 au, ex-
tending north-south along the midplane. The predicted
emission is seen to peak north and south of the proto-
star position, with less emission at 400 au, or about
300 in radius, where Figure 4predicts that N2H+should
be absent. Although less visually prominent, there is
also extended N2H+that corresponds to the outer en-
velope, that is faintly seen in Figure 5at the level of
0.002 Jy pixel1, extending across the simulated im-
age.
The N2H+spectrum is constructed by integrating over
the entire 10,000 au image, and which moreover includes
and conﬁrms the hyperﬁne components seen in Figure 6
Panel (b). The red solid line (model) and green plus
Physical and Chemical Structure of L1527 15
Figure 5. The predicted model emission of N2H+at t= 105years in units of Jy/pixel, having 0.6700 pixel size. The + symbol
at the center shows the protostar position. The disk diameter is only 1 pixel (smaller than the + symbol). Velocity channels
covering the main hyperﬁne complex from 4.9 to 7.0 km s1contribute to the integrated intensity. The model was not convolved
with the 900 beam in order to more clearly show the spatial structure. Notice that the predicted N2H+emission peaks north
and south of the protostar position.
(a) (b)
Figure 6. Lef t: L1527 composite from CARMA data. Image size is 71.400 (10000 au). The color image shows integrated
12CO emission, which is seen to trace the outﬂow in the east-west direction. The red contour lines are dust continuum emission
centered on the protostar position. The blue contour lines show the dense gas distribution in N2H+emission, which extends
north-south. Notice that the N2H+emission peaks at roughly 1000 north and south of the protostar position. The CO and N2H+
beams are drawn in the lower left corner of the image. Right: shows the N2H+(1-0) spectrum, including hyperﬁne components,
constructed using a 10,000 au size box centered on the protostar position. Green plus symbols are CARMA data, and red line
symbols (data) show good correspondence at t= 105years. Note that the extended (faint) emission con-
16 Flores-Rivera et al. 2020
tributes signiﬁcantly to the predicted spectrum. For
the two emission peaks from the inner envelope (two
red peaks in Fig.5), there is a discrepancy between the
spatial extent of our prediction (Fig. 4and Fig. 5) and
the observation (Fig.6) that we conjecture might be im-
proved by increasing the collapse age of the system in
terms of changing the dynamics so that Rcol leads to a
larger collapsing region. This is a good motivation to
follow a time-dependent evolutionary parcel and, thus,
conﬁrm the spatial extension. Overall, the strength of
the observed N2H+emission is consistent with the model
prediction as seen in the spectrum.
Figure 6also presents the integrated intensity maps
of 12CO (1-0) from CARMA that cover the same 71.400
(10,000 au) ﬁeld of view and that shows out-ﬂowing CO
gas that extends east-west, perpendicular to the N2H+
emission. The dust continuum emission (red contours)
is centered on the protostar position. In 12 CO a nar-
row “jet” extends east-west from the protostar, merging
into a wide-angle outﬂow on both sides of the protostar.
The narrow “jet” is also conﬁrmed by ALMA (Fig.8),
therefore, supporting the inclusion of an inner outﬂow
jet in our model. Fig.9in Appendix C contains the
12CO velocity channel maps, that further show that the
emission arises in an (±3 km s1) outﬂow shell. None
of the emission extends north-south, since the high op-
tical depth of 12CO blocks any meaningful view of the
low-velocity envelope.
We conclude that the N2H+emission shows evidence
for the predicted anti-correlation with 12CO. The N2H+
appears to be missing within 400 au of the protostar,
just where full strength 12CO emission is predicted. One
diﬀerence is that our predicted emission is less extended
compared with the data (Fig. 5), that extends out to
3000 (4200 au). However, the data agree in show-
ing N2H+enhancement at ±1800 2500 au from the
protostar, where the model predicts there is severe de-
pletion for 12CO (see Fig.4). A factor that might help to
further improve the comparison is to increase Rcol and
follow the evolutionary process of the chemical parcel
spatially.
4.5.2. C18O ALMA
We focus on C18 O (2-1) observations from ALMA in
order to investigate the kinematics of the dense gas dis-
tribution in the disk and inner envelope in a spectral line
tracer that is (nearly) optically thin. The orientation
of the rotating and infalling material is extended from
north-south (as seen in Fig. 1) and C18O probes dense
gas near the protostar. The edge-on inclination of L1527
means that a north-south cut along the midplane will
minimize the contamination of the dense gas emission
by the outﬂow. However, the central 0.800 beam, mean-
ing ±0.400 centered on the protostar, can still contain
some outﬂow emission. The 12CO emission (Fig.8) for
the same size region is optically thick and traces lower
density gas extending east-west in the outﬂow shell.
To compare with the ALMA data we make a syn-
thetic model spectral line cube that matches the ALMA
data ﬁle. Namely, we generate velocity channel maps
for C18O (2-1) with a velocity spacing of 0.167 km s1
and 0.1700 pixel size. We convolve the model with the
0.800 eﬀective beam, and apply the 2800 primary beam,
as described in §2.4. Note that RadChemT includes
a basic description of the outﬂow velocity prescrip-
tion of 3 km s1in the model, since RadChemT self-
consistently computes both the abundances of 12CO and
C18O as well as the radiative transfer of the two species
(LTE is assumed).
The edge-on inclination of L1527 means that a PV
diagram is well-suited for viewing the kinematics of ro-
tation and infall in the central envelope and disk. Fig-
ure 7presents PV diagrams for C18O (2-1), where panel
ashows the ALMA data that is also presented in Ohashi
et al. (2014). These data are sampled in real space to
clearly see the cloud features in more detail. Panel b
shows the simulated L1527 as modeled using the TSC
model and, panel cshows the simulated L1527 as mod-
eled using the UCM model. Each horizontal row in
Fig. 7corresponds to a spectrum that is spatially oﬀ-
set from the protostar, in the north-south direction. The
horizontal solid white line marks the position of the pro-
tostar, which is located at 000 oﬀset. The eﬀective width
of the position slice is the 0.800 beam (=112 au @140pc)
and the units are Jy beam1. The vertical solid white
ity of L1527.
The data (panel a) show that C18O is self-absorbed
at the protostar position, where the solid white lines
meet at the center of the PV diagram. This indicates
that the C18O is optically thick at line center, consis-
tent with the ﬁnding of van ’t Hoﬀ et al. (2018). How-
ever, our model does not currently reproduce the self-
absorption feature, seen to occur within ±0.5 km s1
from line center (6.0 km s1). In a later paragraph we
further discuss the self-absorption. The data (panel a)
also show an artifact that is common to interferometers.
The cloud emission from L1527 is spatially extended
and therefore resolved-out by the interferometer at the
6.0 km s1cloud velocity, resulting in no/little emission
from the cloud near the vertical line. However, the Rad-
ChemT images retain the low-velocity cloud emission at
6.0 km s1, and do not mimic this artifact of the data.
Physical and Chemical Structure of L1527 17
(a) (b) (c)
(d)
Figure 7. Position-Velocity (PV) diagrams that show the velocity of C18 O versus position oﬀset along the north-south direction.
Each horizontal row corresponds to a spectrum at the indicated spatial oﬀset. Panel (a) shows the ALMA C18O observational
data. The P-V diagram obtained from the RadChemT chemical model is shown in panel (b) for the TSC collapse model and
panel (c) for the UCM collapse model. The white solid line in each panel shows the system radial velocity (vertical) and central
protostar position (horizontal). Dashed white lines represent ±125au, the maximum disk size considered. Keplerian rotation
curves are included for reference. The solid black line represents the ﬁducial model with M=0.22 Mand Rdisk=75 au. The
dashed black line is M=0.45 Mand Rdisk=125 au. Panel (b) and Panel (c) shows diﬀerent color scale bar due to the higher
density of UCM in the inner envelope. Panel (d) shows the C18O (2-1) spectrum, integrated over a 3.4 00×3.4 00 box centered
on the protostar. Green plus symbols are ALMA data; red triangles show the RadChemT TSC collapse model, multiplied by a
3.0×scaling factor.
18 Flores-Rivera et al. 2020
At large spatial oﬀsets (>400) the spectral line has
a narrow width that approximates the thermal sound
speed of the cloud. The range of velocities vin each
spectrum (i.e. horizontal row) increases towards the pro-
tostar (i.e. smaller R and smaller position oﬀset), as is
expected for gravitational motion where vpGM/R.
The emission occurs mainly in the lower left and upper
right quadrants, which is the expected signature of ro-
tational motion in a disk. Emission that occurs in the
“forbidden” quadrants (upper left and lower right) is not
from the rotating disk, but instead is a signature of the
rotating and infalling envelope (i.e. Ho & Keto (2007)).
Comparison of the PV diagrams in Fig. 7shows an
overall correspondence of the data with the RadChemT
models that is encouraging. Visually, the TSC model
(panel b) is a better ﬁt than the UCM model (panel c).
One diﬀerence between data and model is that the peak
brightness values are symmetric in the models but not
symmetric in the data. The data (panel a) show stronger
blue shifted peak emission (lower left quadrant) than red
shifted (upper right quadrant), which is a signature of
optically thick emission. To improve the model ﬁt, this
suggests that the model envelope density (or abundance)
should be increased over the ﬁducial value.
Recent analyses of L1527 in the literature using dif-
ferent datasets ﬁnd M= (0.19,0.45,0.45 M) and
Rdisk= (125,75,125 au), respectively (Tobin et al. 2012;
Aso et al. 2017;van ’t Hoﬀ et al. 2018). In our ﬁdu-
cial model we adopted the Tobin et al. (2012) values of
M= 0.22 Mand Rdisk = 75 au as a starting point
to test the capabilites of RadChemT on reproducing the
chemical abundances of L1527. Our ﬁducial numbers fall
at the lower end of recent determinations. The analysis
by van ’t Hoﬀ et al. (2018) is the most similar to our
modeling, although it assumes but does not compute
the astrochemical abundances, and moreover restricts
attention to the inner 100(140 au).
In all three PV diagrams, the dashed white line repre-
sents the maximum size of the disk. Everything outside
of the dashed white lines, at >100 position oﬀset, is
emission coming purely from the envelope. The emis-
sion coming from inside these lines is therefore due to
a combination of envelope and disk emission. Keplerian
rotation curves are presented as a guide for the eye, and
represent the maximum velocity expected from a rotat-
ing Keplerian disk. The solid black line represents the
ﬁducial model with M=0.22 Mand Rdisk =75 au. The
dashed black line is M=0.45 Mand Rdisk=125 au, a
model that is considered in van ’t Hoﬀ et al. (2018).
Comparison of the model PV diagram with the data in
Fig. 7suggests the higher protostar mass would be pre-
ferred over the ﬁducial value. However, detailed model
ﬁtting of the disk dynamics lies outside the scope of the
current work.
The strength of the observed C18O(2-1) emission is
about a factor of 3.0 higher than the model prediction for
the TSC model. Figure 7(panel d) shows the C18O spec-
trum that is constructed by integrating over a 3.400 ×3.400
box (475 au ×475 au). The red triangles (model) and
green plus symbols (data) show reasonable correspon-
dence in terms of proﬁle shape. The overall emission of
the UCM model is about (50%) brighter; this diﬀerence
is understandable as due to the higher density of UCM in
the inner envelope for our choice of physical parameters;
an approximate estimate of the density ratio expected
between UCM and TSC is 5/3, and is simply obtained
from the ratio of ˙
Menv that are given in Table 1.
The fact of not reproducing the self-absorption at the
protostar position in our modeled C18 O spectrum does
not preclude the ability of the models to explain what
is happening at the center of the spectral line. The
observed self-absorption is consistent with a high den-
sity region, grains with millimeter size or greater, in the
disk that suggests a promising avenue for future studies
to increase the density between the envelope and disk.
Considering a diﬀerent type of dust opacity that is more
suitable for the inner parts is also encouraging. On the
model processing side, performing the spectral tracing
using non-LTE may also lead to improvement. In sum-
mary, the RadChemT model was not tweaked to match
the C18O emission, so the initial match between model
and data to within the factor of 3.0 is encouraging.
From Figure 7we see that our prediction of C18O us-
ing the TSC model is better at representing the actual
envelope structure of L1527 when compared with C18O
ALMA data. Due to the fact that UCM neglects pres-
sure eﬀects in the outer layers of the envelope, we see
that at spatial oﬀsets >100 (150 au), the UCM enve-
lope shows too much gas at higher velocity, resulting
in a rectangular rather than bowtie shape around the
green perimeter showing the fainter emission. In gen-
eral, we conclude that the predicted C18O(2-1) emission
from the RadChemT model reproduces the main fea-
tures of the PV diagram (Fig. 7) for both the envelope
and disk emission. Moreover, these initial results sug-
gest that RadChemT can be used as a tool to investigate
the protostar dynamical mass, the disk radius, and the
unknown dynamics of the outer disk. Future improve-
ments to RadChemT to speciﬁcally model L1527 better
could include: 1)increasing the density and opacity pro-
ﬁle in the disk and performing non-LTE spectral line
radiative transfer (i.e., Evans (1999)), 2)changing the
physical conditions as a function of time to follow col-
lapse motions, and 3)including shock physics and adding
Physical and Chemical Structure of L1527 19
sulfur chemistry to study the suggested enhancement of
SO at the disk-envelope interface.
5. SUMMARY AND CONCLUSIONS
RadChemT is a method for modeling embedded pro-
tostars to compare with both, continuum and molec-
ular line observations. The method combines a two-
dimensional, varying both with distance from the star
and angle from the rotation axis, axisymmetric cloud
collapse solution with MCRT and the solution of an as-
trochemical reaction network. The resulting gas phase
abundances are transformed via LTE radiative trans-
fer into simulated Position-Velocity cubes to compare
with spectral line observational data. This pilot study
with RadChemT uses a model of the central star and
surrounding gas density distribution obtained by To-
bin et al. (2008,2010,2012) for the protostar L1527.
In the current implementation, a protostar of a given
age has time-steady density and temperature distribu-
tions, while the chemical abundance calculation is time-
dependent. There are pronounced spatial variations in
the abundances. Abundances are enhanced in the out-
ﬂow shell and decreased in the cold regions near the
midplane, varying by more than a factor of 103in the
case of CO. In order to validate RadChemT, we generate
PV diagrams for the inner 1,000 au (14.200), and com-
pare with ALMA C18O observations. We also present
CARMA data for 12CO and N2H+on a larger 10,000 au
scale, and compare with our predicted abundances for
L1527. We report our highlights as follows:
1. The TSC and UCM collapse models give compa-
rable ﬁts to the SEDs, both for aperture size of
10,000 au and 1,000 au. Similarly, there is little
qualitative diﬀerence for the predicted molecular
abundances. However, the TSC model better cor-
responds to the observed PV diagrams. In the
case of UCM, which neglects pressure forces, the
envelope shows too much gas at higher velocity,
particularly at spatial oﬀsets greater than 150 au.
2. The ALMA C18O (2-1) spectrum is about 3.0
times brighter than our C18O prediction. This is
reasonable agreement given that the astrochemi-
cal computation has not been “tuned” to improve
the ﬁt. However, increasing the density in the en-
velope and the opacity proﬁle in the disk could
be fruitful, since the C18O abundance is sensitive
to them. The dynamics of the C18 O gas imply
that the protostar mass and disk radius are some-
what larger than the ﬁducial values of 0.22 M
and 75 au, respectively.
3. The CARMA 12CO (1-0) data conﬁrms that there
is strong emission with the morphology of an out-
ﬂow shell. The ALMA 12 CO (2-1) data deﬁnitively
establish that a narrow jet-like structure connects
the two outﬂow lobes inside 75 au. For the physi-
cal model we therefore include a swept-up outﬂow
shell with a constant outward velocity of 3 km s1
(Fig.9) as a proof of concept. The chemistry im-
plies that the 12CO abundances are low in the in-
ner envelope from 400 au <Renv <2,000 au at
t=105yrs, indicative of freeze out onto grains.
4. In the CARMA N2H+(1-0) data, emission is elon-
gated north-south, with the peak emission oﬀset
1000 from the central star. In our chemical
model, N2H+is also oﬀset, by about 1000 north
of the central star. This is indirect but strong
evidence of signiﬁcant 12CO freeeze out in the
same region. As found in many previous studies,
the chemistry implies that N2H+is anti-correlated
with CO abundance. In the case L1527, Rad-
ChemT predicts that N2H+is enhanced in the en-
velope over 500 au <Renv <2,000 au at t=105
years.
Facilities: ALMA, CARMA, HERSCHEL, IRSA,
Spitzer, TIFKAM, IRAC, MIPS, SCUBA, JCMT/UKT,
NMA
ACKNOWLEDGMENTS
I am very thankful to Dr. Susan Terebey, who helped
tirelessly on this project. Very special thanks to all
my co-authors as well. To Dr. Hengchun Ye and
Dr. Krishna Foster for sponsoring through the NASA-
DIRECT STEM program (Grant: NNX15AQ06A) and
through the MORE RISE-to-PhD program (Grant:
2R25GM061331-18). This work was also carried
out in part at the Jet Propulsion Laboratory, un-
der contract with NASA and with the support of
Exoplanets Research Program grain 17-XRP17 2-0081.
This project received support from the European Re-
search Council (ERC) under the European Union0s
Horizon 2020 research and innovation programme
(grant agreement 757957). To Dr. Andrea Isella
(RICE) for providing the CARMA observational data.
This paper makes use of the following ALMA data:
ALMA is a partnership of ESO (representing its mem-
ber states), NSF (USA) and NINS (Japan), together
with NRC (Canada), MOST and ASIAA (Taiwan), and
KASI (Republic of Korea), in cooperation with the Re-
public of Chile.
20 Flores-Rivera et al. 2020
The Joint ALMA Observatory is operated by ESO,
AUI/NRAO and NAOJ. The National Radio Astron-
omy Observatory is a facility of the National Science
Foundation operated under cooperative agreement by
Associated Universities, Inc.
APPENDIX
A. 12CO (2-1) ALMA CHANNEL MAP
Figure 8. Snapshot of a 12 CO(2-1) ALMA channel map at 9.9 km s1that shows the inner region of the outﬂow. The 12 CO
emission is shaded in white and shows two outﬂow shells lying in the east-west direction that are connected by a narrow jet.
This orientation matches with Fig.1, Panel (b). The data have a spatial resolution of 0.800and the star position is at the center
of the 1000(1400 au) image.
B. CARMA 12CO CHANNEL MAPS
C. INITIAL ABUNDANCES
D. ALMA OBSERVATIONAL PARAMETERS
E. PHOTOMETRY
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C18O(2-1)
Target, date L1527 IRS, 26 August 2012
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Frequency 219.5603 GHz
Synthesized beam 0.9600 ×0.7300(+11)
Primary beam 28.600
Velocity resolution 0.17 km s1
Noise level (detected channel) 8.0mJy beam1
Minimum baseline 18m
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Physical and Chemical Structure of L1527 23
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3.6 6.936±0.69 7.14 1
4.5 22.75±2.28 7.14 1
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3.6 141.8±16.2 71.4 1
4.5 225.1±16.3 71.4 1
5.8 149.5±45.0 71.4 1
8.0 54.5±25.0 71.4 1
25 743.6±70.0 23×150c7
60 17770.0±1600.0 45×150c7
70 160b22000-64000±500-7000 14 2
70b16746.0±49.0 6 3
70 24170.0±4834.0 75 1
100 73260.0±11700.0 90×150c7
100b28942.0±653.0 6 3
160b47011.0±16291.0 12 3
160 94000.0±38000.0 60 8
350 44000.0d±20000.0d45-60e1
450 33125.0d±20900.0d40-120e1
750 8400.0±1100.0 45 9
800 1400.0±560.0 60 8
850 6167.0d±480.0d40-120e1
1300 1110.0d±110.0d30-40e1
2700 47.0±5.6 3.2c5,6
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