Cambridge Large Two 2020 113 ARTICLE TYPE Studying the internal structures of the central region of prestellar core_2
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Cambridge Large Two (2020), 1–13
ARTICLE TYPE
Studying the internal structures of the central region of prestellar core
L1517B in Taurus molecular cloud using ammonia (NH
3
) (1,1) and (2,2)
lines
Atanu Koley1
1Departamento de Astronomía, Universidad de Concepción, Casilla 160-C, Concepción, Chile
Author for correspondence: A. Koley, Email: atanuphysics15@gmail.com.
Abstract
Measurement of internal structures in the prestellar core is essential for understanding the initial conditions prior to star formation. In
this work, we study the ammonia lines (NH
3
) (J,K=1,1 and 2,2) in the central region of the prestellar core L1517B with the Karl G.
Jansky Very Large Array Radio Telescope (VLA, spatial resolution
∼
3.7
′′
). Our analysis indicates that the central region of the core is
close-to-round in shape obtained both from NH
3
(1,1) and (2,2) emissions. Radially averaged kinetic temperature (T
k
) is almost constant
with a mean value of
∼
9 K. A radially sharp decrease in kinetic temperature (T
k
) has not been observed inside the central dense nucleus
of this prestellar core. In addition, we also notice that there is an overall velocity gradient from north-east to south-west direction in this
region, which may be indicative of the rotational motion of the core. We then calculate the parameter
β
, which is defined as the ratio of
rotational energy to gravitational potential energy and find that
β
equals to
∼
5
×
10
–3
; which indicates that rotation has no effect at
least inside the central region of the core. We also perform the viral analysis and observe that the central region may be in a stage of
contraction. From this study, we also show that turbulence inside the central region is subsonic in nature (sonic Mach number, M
s
< 1)
and has no prominent length-scale dependence. Furthermore, we notice that the decrement of excitation temperature (T
ex
) and column
density of NH
3
from the centre of the core to the outer side with the peak values of
∼
5.6 K and
∼
10
15
cm
–2
respectively. In conclusion,
this work examines different physical and kinematical properties of the central region of the L1517B prestellar core.
Keywords: ISM: general – ISM: individual objects: L1517B – ISM: kinematics and dynamics – ISM: molecules – galaxies: star formation.
1. Introduction
Star formation is one of the fundamental processes in the cos-
mos. Stars are born in dense cold places called cloud cores.
Cores are classified as prestellar or protostellar depending on
whether they contain an embedded protostar. Along with
gravity, other effects like turbulence, magnetic field, rotation,
and temperature form a complex enviornment prior to the star
formation (Barranco and Goodman 1998; Kudoh and Basu
2014; Dunham et al. 2016; André 2017; Dobashi et al. 2018;
Caselli et al. 2019; Koley and Roy 2019; Dobashi et al. 2019;
Tokuda et al. 2020; Sahu et al. 2021; Koley et al. 2021; Koley
et al. 2022; Koley 2023). Therefore, studying these quan-
tities are very much essential for a complete understanding
of the star formation process. Dust continuum emission pro-
vides the line-of-sight averaged temperature of the core (Scott
Schnee et al. 2010). Apart from that, ammonia molecule is
also used to probe the temperature of the molecular cloud;
hence it is often called an
′′
interstellar thermometer
′′
. Am-
monia molecule exhibits several hyperfine lines. Here, due
to the several well-separated lines, measurements of essential
parameters like excitation temperature (T
ex
), kinetic temper-
ature (T
k
), optical depth (
τ
), column density (N), etc., have
been possible (Walmsley and Ungerechts 1983; Mangum and
Shirley 2015). In addition to these parameters, if one assumes
that the non-thermal broadening is caused due to turbulence,
then from this spectral study, turbulence measurement is also
possible; in particular, about the nature of the turbulence and
its scale-dependent behavior. For several decades, temperature
measurements have been carried out using ammonia molecules
in low and high mass prestellar cores and star-forming regions,
both from single-dish and from interferometric telescopes
(Barranco and Goodman 1998; Pillai et al. 2006; Dirienzo et
al. 2015; Krieger et al. 2017). Although from several studies, it
has been argued that in interferometric telescopes a significant
amount of flux is resolved out in the prestellar cores (Crapsi
et al. 2007; Roy et al. 2011; Koley 2022); for tracing the in-
ternal cold dense structures, interferometric observations are
generally more effective than single-dish studies (Barranco
and Goodman 1998; Crapsi et al. 2007; Dobashi et al. 2018;
Tokuda et al. 2020; Sahu et al. 2021).
In this work, we study the internal structures of the cen-
tral region of L1517B core with the Jansky Very Large Array
(VLA) radio telescope. This core was observed previously with
several single-dish telescopes using different molecules (Tafalla
et al. 2004a; Chitsazzadeh 2014; Megías et al. 2023), where the
field of view was larger than our study. Here, we particularly
concentrate on the central dense region of the core using the
high spatial resolution interferometric telescope.
In section 2, we present the observation and data analysis
of our work. In section 3, we mention the ammonia line
fitting using pyspeckit code (Ginsburg and Mirocha 2011). In
2 Atanu Koley1et al.
section 4, we discuss the main results. At last, in section 5, we
summarize our main findings.
2. Observation and data analysis
All the observational data were taken from the VLA archival
data center. These observations were carried out in 2013 from
March 20 to 26 over three observing sessions using the VLA
D configuration in the K band (proposal id: VLA-13A/394).
Right ascension (R.A.) and declination (Dec.) of the pointing
center is 04
h
55
m
18.00
s
and +30
◦
37
′
46.99
′′
respectively (epoch
J2000). The primary objective of this study is to analyse the
internal structures of the central region of the core using NH
3
(J,K=1,1 and 2,2) spectral lines. Rest frequencies of these lines
are 23.69449550 GHz and 23.722633600 GHz respectively.
The bandpass calibrator was 3C48 (0137+331) for this obser-
vation, whereas J0414+3418 was used as a phase calibrator.
Channel resolution was
∼
3.906 kHz (
∼
0.049 km sec
–1
) with
a total number of channels was 2048. For every 4 minutes 24
seconds of source observation, phase calibrator, J0414+3418
was observed for almost 1 minute 45 seconds. In each ob-
serving session, bandpass calibrator, 3C48 was observed for
∼
9 minutes 54 seconds. After observing almost 5 hours and
18 minutes on the source, the achieved RMS noise was
∼
2
mJy beam
–1
. This value of RMS noise represents the RMS
noise per channel. Initial flagging and calibration were done
using the scripted Common Astronomy Software Applications
(CASA) pipeline (scripted pipeline version 1.4.2) of the Na-
tional Radio Astronomy Observatory (NRAO)
a
. Additional
flagging was needed due to the bad amplitude gain of a few
antennas. We would like to emphasize that we have not done
the hanning smoothing of the UV data while calibrating using
the scripted pipeline. With the calibrated data produced by
the pipeline, we performed the cleaning with the CASA task
TCLEAN (CASA version 5.3.0). Please note that, we ran it
separately for the NH
3
(J,K=1,1) and NH
3
(J,K=2,2) lines.
Here, we used the deconvolver
′′
multiscale
′′
with the scales
3.2
′′
, 6.4
′′
, 12.8
′′
, 25.6
′′
, and 51.2
′′
respectively to pick up all
the structures. We used the robust parameter, ROBUST = +2
for natural weighting. The synthesized beam that is convolved
with the clean components is
∼
4.01
′′ ×
3.37
′′
with a position
angle of + 52.02
◦
. Final image cubes (both for 1,1 and 2,2
lines) produced after cleaning are used to study the core using
the simultaneous fitting of these lines. Here we would like
to point out that due to the use of interferometric-only ob-
servations, our data are lacking a contribution from extended
NH
3
emissions. This effect may affect the determination of
parameters that depend on the absolute intensity of the lines,
such as the column density of NH
3
. However, it may be less
severe for parameters that are dependent on the line ratio, such
as the kinetic temperature (Tk) of the gas.
a.
The National Radio Astronomy Observatory is a facility of the National
Science Foundation operated under cooperative agreement by Associated
Universities, Inc.
3. Line fitting
For fitting the NH
3
(J,K=1,1) and NH
3
(J,K=2,2) lines and in
turn obtaining different useful informations mentioned earlier,
we use the pyspeckit code (Ginsburg and Mirocha 2011). This
code is based on the nonlinear gradient descent algorithm (MP-
FIT, Markwardt 2009), where various useful parameters are
obtained after comparing the simulated and observed bright-
ness temperature (T
B
) of the lines. For a detailed discussion
regarding the fitting, we refer the study of Friesen et al. (2017).
Initial guesses in terms of kinetic (T
k
) or rotational tempera-
ture (T
rot
), excitation temperature (T
ex
), para column density
(N
para
), ortho ratio (F
ortho
), centre velocity (v
c
), and the veloc-
ity dispersion (
σtotal
) of the line have to be put in the fitting.
As the line modeling crucially depends on the centre velocity
(v
c
), its initial guess has been calculated from the moment map
of the cube before the fitting. We note that the final results do
not alter as long as the initial parameters are within a reliable
range. We would also like to point out that we took only those
pixels where the signal-to-noise ratio (SNR) of the NH
3
(1,1)
emission is greater than 5.5. In the modeling, it is assumed
that T
ex
is the same for both (1,1) and (2,2) lines. Out of differ-
ent types of fitters, we use the fittype =
′
cold
_
ammonia
′
, which
makes the assumption that for typically low temperature in the
prestellar cores, only (1,1), (2,2) and (2,1) lines of para-NH
3
are occupied (Krieger et al. 2017; Pineda et al. 2021). It is also
assumed that the ortho-to-para ratio of ammonia is 1. This
code fits pixel-wise spectra and finally forms a cube, where
various fitted parameters and their associated errors are stored
in different planes, which are further used for detailed ana-
lyzing the core. For a detailed understanding of the different
energy levels of NH
3
lines, we refer the works of Walmsley
and Ungerechts (1983) and Mangum and Shirley (2015).
4. Results
4.1 Integrated intensity emission & column density
Left panel of Fig. 1shows the overplot of integrated intensity
map of NH
3
(1,1) emission both in color and contour plots.
Likewise, the right panel of Fig. 1shows the overplot of
integrated intensity map of NH
3
(2,2) emission both in color
and contour plots. Based on these figures, it is apparent that
NH
3
(2,2) emission is less spread than NH
3
(1,1) emission.
This is supported by the previous single-dish observation of
this core (Chitsazzadeh 2014). From these figures, it is also
noticeable that NH
3
(1,1) and (2,2) emissions are centrally
concentrated, but the peak positions of the integrated intensity
maps have a slight offset compared to the dust and H
2
column
density maps where the peaks of them are identical (Tafalla et
al. 2004a; Megías et al. 2023). The location of the dust peak is
04
h
55
m
17.60
s
, +30
◦
37
′
44.00
′′
, whereas the peaks of the NH
3
(1,1) and (2,2) integrated intensity maps are 04
h
55
m
18.31
s
,
+30
◦
37
′
42.38
′′
and 04
h
55
m
18.06
s
, +30
◦
37
′
41.34
′′
respectively.
It is interesting to note that, the central region of the core is
close-to-round in shape, rather than a filament-like structure
(Kauffmann et al. 2008; Dobashi et al. 2018). Since the shape
of the central region of the core is round, an average of various
Cambridge Large Two 3
essential parameters can be calculated over concentric circles to
obtain the radially averaged profiles of the essential parameters.
On the other hand, if the structure had elongated, an average
would have to be performed over successive ellipses (with a
fixed aspect ratio and position angle). From the line fitting
using pyspeckit code, we obtain the column density map of
ammonia emission in the L1517B core, which is shown in
the left panel of Fig. 2. Using this distribution, we obtain
the radially averaged profile of column density in the core.
Here, we would also like to point out that, we consider the
peak position of the dust continuum emission as the centre of
the core. This is because the peak of dust and the peak of H
2
column density match well in this core (Megías et al. 2023).
And for converting the angular scale into the physical distance
on the plane of the sky, we take 159 pc distance of the L1517B
core (Galli et al. 2019). Right panel of Fig. 2represents the
radially averaged column density profile. From this figure, it
indicates that the peak column density of NH
3
is
∼
10
15
cm
–2
and decreases towards the outer edge. We also note that the
distance where the column density decreases by a factor of 2
of its peak value is at radius ∼0.016 pc.
4.2 Spectral properties across the core
In Fig. 3, we show the spectra of NH
3
(1,1) and (2,2) lines
towards different positions inside the core. For example, we
show the spectra towards the dust peak position. Similarly, we
also plot the spectra towards the peaks of NH
3
(1,1) and (2,2)
emissions. Here, it is interesting to note that the blue-skewed
profile that is observed in the (1,1) spectra is not due to the col-
lapse (Myers et al. 1996) or any other cloud dynamics (Evans
1999), rather it is the intrinsic closely separated lines caused
by the hyperfine splitting. Here, we would like to point out
that all the calibrated data and the pyspeckit results are obtained
from the original data. No hanning smoothing has been per-
formed in the entire analysis except for these spectra in Fig. 3.
As a simple matter of making the spectra more visible, we use
the CASA viewer task to smooth the spectra in Fig. 3.
Now, we discuss the Left panel of Fig. 4, where we show
the velocity field across the region. From this figure, it appears
that there is an indication of overall velocity gradient from
north-east to south-west direction. This might be caused due
to the rotational motion of the core. However, the exact pat-
tern is more complex than a continuous increase or decrease
in velocity of equal magnitude. Velocity gradient across the
core was noticed in the earlier single-dish observations with
the NH
3
(1,1) and N
2
H
+
(1-0) lines where the fields of view
were larger than our study (Goodman et al. 1993; Tafalla et
al. 2004a; Chitsazzadeh 2014). Right panel of Fig. 4shows the
overplot of the local velocity gradient and velocity field across
the region. Here, in the color plot we subtract the systematic
velocity of the core (+ 5.79 km sec
–1
) from the velocity field.
Now, in order to measure the overall velocity gradient, we
first calculate the velocity gradient at each position and finally
obtain the overall gradient in this region. Detailed discussion
regarding the calculation of local and overall velocity gradient
is mentioned in Appendix 1. From the analysis, we obtain the
overall velocity gradient,
ψ∼
1.10 km sec
–1
pc
–1
and direction,
θˆ
ψ∼
127
◦
west of north. This value is similar to the earlier
single-dish observations studied by Goodman et al. 1993 and
Tafalla et al. 2004a, where the measured values were 1.52 and
1.10 km sec
–1
pc
–1
respectively. However, this value is one
order smaller than the L1544 core, where the value is
∼
9.0
km sec
–1
pc
–1
based on the interferometric (VLA) observations
of NH3(1,1) and (2,2) lines (Crapsi et al. 2007).
If there is a strict continuous velocity gradient of equal magni-
tude across the region, it is possible to conclude strongly that
the region is rotating. However, in our region, both visually
and in terms of the magnitude of the overall velocity gradient,
it appears to be a rotation, despite not meeting the strict criteria
of smooth and continuous velocity variation. It is also true
that there are many challenges associated with the analysis and
fitting of real astronomical data. Consequently, obtaining a
smooth variation of velocity across the region is extremely
difficult. Therefore, in the following, we calculate the ratio of
rotational energy to gravitational potential energy, assuming
that the velocity gradient is the cause of rotation. This enables
us to gain a rough understanding of the role of rotation in this
region if the overall velocity gradient is caused by the rotation.
The parameter
β
, which is the ratio of the rotational energy
to the gravitational energy (Goodman et al. 1993) is defined
by the formula:
β=
1
2Iω2
qGM2
R
=1
2
p
q
ω2R3
GM (1)
Here, Iis the moment of inertia,
ω
is the angular velocity,
Gis the gravitational constant, Mis the mass, Ris the radius of
the core, pand qare unit-less numbers, which vary depending
on the geometry and the density profile of the system (Kauff-
mann, Pillai, and Goldsmith 2013). The value of (
p
q
) is 0.66 for
a constant density sphere. However, when the density profile
varies as r
–2
with fixed Mand R, this value is 0.22, which is
one third of the earlier one (see Appendix 2). From the fitting
of observed continuum emission, Tafalla et al. (2004a) showed
that the number density of this core is not constant rather fol-
lows a power law: n(r) =
n0
1+( r
r0)2.5
. Here, ris the radial distance,
n
0
= 2.2
×
10
5
cm
–3
and r
0
= 35.00
′′
or 0.027 pc. Since we
are only analyzing the central 0.025 pc region inside the core,
we consider
p
q
= 0.66 for our analysis, which will not lead to
a significant difference in the result. Likewise, we consider
only the enclosed mass within the radius of 0.025 pc. From
the work of Benson and Myers 1989, the mass of the core
is
∼
0.50
M⊙
, where it was assumed a radius of
∼
0.068 pc
(assuming 159 pc distance) based on the observation of NH
3
(1,1) line. Now, according to the power-law of density (r
–2.5
),
the mass enclosed in a radius of 0.025 pc is
∼
0.30
M⊙
. Fur-
thermore, the value of
ω
is obtained from
ψ
after considering
the inclination angle (i) of
ω
to the line-of-sight. However,
for a single measurement, we have not taken into account this
statistical correction. This correction factor is small and will
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CambridgeLargeTwo(2020),1–13ARTICLETYPEStudyingtheinternalstructuresofthecentralregionofprestellarcoreL1517BinTaurusmolecularcloudusingammonia(NH3)(1,1)and(2,2)linesAtanuKoley11DepartamentodeAstronomía,UniversidaddeConcepción,Casilla160-C,Concepción,ChileAuthorforcorrespondence:A.Koley,Email:atanuph...
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时间：2025-04-30
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