Probing Core B of the Massive Star Forming Region G35.20-0...

LEIDEN UNIVERSITY

MASTER THESIS

Probing Core B of the Massive Star FormingRegion G35.20-0.74N with ALMA and LIME

Author:Pim OVERGAAUW

Supervisors:Dr. Luke MAUD

Dr. Michiel HOGERHEIJDE

A thesis submitted in fulfilment of the requirementsfor the degree of Master of Science

at

Leiden Observatory

January 28, 2016

http://www.leidenuniv.nl

http://www.strw.leidenuniv.nl/~overgaauw

http://www.strw.leidenuniv.nl/~maud

http://www.strw.leidenuniv.nl/~michiel

http://strw.leidenuniv.nl

LEIDEN UNIVERSITY

AbstractFaculty of Science

Leiden Observatory

Master of Science

Probing Core B of the Massive Star Forming Region G35.20-0.74N with ALMA andLIME

by Pim OVERGAAUW

Massive stars (with masses> 8 M) play a key role in the evolution of the Universe.From the reionization of the universe, to the evolution of galaxies and the formation ofstars and planets, massive stars are able to impact a wide range of scales and processes.However, in contrast to low-mass star formation, the formation of these high-mass starsis still poorly understood. According to several proposed formation scenarios, theyform through disk accretion, but observational evidence remains sparse. Using datafrom the Atacama Large Millimeter Array (ALMA) we investigate a single massivestar forming core in the star forming region G35.20-0.74N. We model the region usingthe excitation and radiation transfer core LIME to gain further understanding of thegeometry, line emission and kinematics of this forming massive star. We find that asingle massive, Keplerian disk, as modelled in previous work, is not enough to fullyexplain the kinematics and geometry of this core.

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AcknowledgementsFirst of all, I would like to thank my supervisors, Michiel Hogerheijde and Luke

Maud, for allowing me to work on this project. Specifically Luke for the many hoursof meetings and for a continued push to improve my work. During this project I havelearned many things (amongst which the frustrations of CASA and LIME) and theyhad a big hand in that, for which I’m very thankful.

My HL1101 office mates deserve a massive shout out, in the first place for distract-ing me (too much) in the first 8 months of my project. But most of all for all the helpwith course work, cursing CASA (right, Ronniy?) and all the hilarious conversations.I’m not sure how they managed to deal with the endless amounts of Scrubs and Lordof the Rings references Josha and I managed to pump out in a day.

A big thanks to the FooBar, and it’s inhabitants, for being there at the end of the day.

Lastly I thank my lovely girlfriend for always believing in me and putting a smileon my face, for which I am eternally grateful.

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CONTENTS

Abstract iii

Acknowledgements v

1 Introduction 11.1 Stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Low-Mass Star Formation . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.3 Massive Star Formation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.3.1 Core Accretion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.3.2 Competitive Accretion . . . . . . . . . . . . . . . . . . . . . . . . . 41.3.3 Mass Assembly . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.3.4 Formation sequence . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.4 Interferometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61.5 CASA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71.6 Contents of this thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2 The Data 92.1 ALMA observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.2 G35.20-0.74N . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.3 Core B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.3.1 Line Emission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.3.2 Rotation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.4 Rotational Diagram Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 17

3 The Simulations 233.1 LIME . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233.2 Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3.2.1 Simulating ALMA observations . . . . . . . . . . . . . . . . . . . 243.2.2 The Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243.2.3 Model Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . 253.2.4 Results of Simulations . . . . . . . . . . . . . . . . . . . . . . . . . 26

4 Discussion 354.1 Comparing the Simulations with the Observations . . . . . . . . . . . . . 35

4.1.1 Drop in Emission . . . . . . . . . . . . . . . . . . . . . . . . . . . . 384.2 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

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4.2.1 Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 404.2.2 Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

5 Conclusions 41

Bibliography 43

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CHAPTER 1

INTRODUCTION

1.1 Stars

Ever since the dawn of man we have looked up at the night sky and wondered whatthe twinkling lights shining down upon us are. Whereas ancient societies saw theirancestors smiling down upon them, we now know that stars are great spheres of radi-ating gas and plasma, powered by nuclear fusion. Mysticism and religion have madeway for science and observation.

Through nuclear fusion, stars are able to synthesize heavy elements. Starting fromsimple hydrogen they are able to create helium, carbon, oxygen, silicon and even iron,to name a few. The very constituents of our own world and the bodies we live in. Asstated by Carl Sagan: “We are made of star stuff”. However, the road from interstellargas and dust to the specks of light that fill the night sky and drive our imagination isnot an easy path to take. In order to understand this path of formation, we must firstdiscuss the different classes of stars.

One of the simplest ways to classify different types of stars is by their mass (M?).According to their mass we can classify them as low-mass stars (M? ∼ 0.05 - 2 M),intermediate-mass stars (M? ∼ 2 - 8 M) and high-mass stars (M? ≥ 8 M). The high-mass stars are defined as such by their core mass (Mcore) exceeding the Chandrasekharlimit of ∼ 1.4 M at the end of their evolution. The deaths of these stars are accompa-nied by a catastrophic collapse of their core which results in the birth of a neutron star(M? ∼ 8-25 M) or a black hole (M? > 25 M).

We can classify stars in another way by looking at their formation. This is doneby comparing two timescales, the Kelvin-Helmholtz timescale (tKH ) and the accretiontimescale (tacc). The Kelvin-Helmholtz time is given by

tKH =GM2

RL(1.1)

where G is the gravitational constant and M , R and L the mass, radius and luminosityof the star, respectively. This timescale tells us how much time it would take for a starto emit its entire reserve of energy upon contraction, if its internal energy sources werecut off. It determines how long it takes for a star to contract to the main sequence, the

1

2 Chapter 1. Introduction

FIGURE 1.1: Path of evolution for low-mass stars. Figure by MagnusPersson.

point where nuclear fusion is “turned on” to power the star. Stars are born in greatclouds of gas and dust, the accretion timescale (tacc) determines the time it takes forthe star to acquire its mass from the cloud that envelopes the proto-star. After this timemost of the enveloping cloud is accreted or dispersed.

1.2 Low-Mass Star Formation

For low-mass stars tKH is typically on the order of 107 years. The time it takes forthem to accrete matter (tacc) is shorter, on the order of tacc ∼ 105 − 106 years (Evans etal. 2009 and Dunham et al. 2014), leading to a well-defined pre-main sequence phase.This allows us to study the formation process of low-mass stars in detail, as describedby McKee and Ostriker (2007) and presented graphically in Fig. 1.1 (made by Mag-nus Persson). The formation process starts when a dense pre-stellar core, embeddedin a dark molecular cloud, starts to undergo global infall under the effect of gravity.As the core collapses, the conservation of angular momentum results in the formationof a circumstellar disk (classes 0 and I). Most of the final stellar mass is accreted inthis stage from the cloud to the disk and from the disk to the central proto-star, andbipolar outflows appear. As this process progresses, the protostar becomes less andless embedded, as most of the surrounding gas is accreted and the envelope disap-pears (class II). Eventually, the outflow ceases and the proto-star slowly contracts tothe main sequence (class III). As stated before, the accretion time is shorter than theKelvin-Helmholtz time, dispersing the obscuring envelope before the star reaches themain sequence. This allows us to study the proto-star as it is still forming.

Chapter 1. Introduction 3

Mass Range (M) 0.5-1 1-2 2-4 4-8 8-16 16-32 32-64 64-128N 700 275 108 42 16.6 6.5 2.55 1

TABLE 1.1: Relative number of stars per mass interval according to theinitial mass function dN/dM ∼M−2.35, as adopted from Table 2 of Zin-necker and Yorke (2007). We can see that massive stars are rare com-

pared to their low-mass counterparts.

1.3 Massive Star Formation

For high-mass stars the two timescales are switched. The Kelvin-Helmholtz timescale(tKH ) is much shorter, only 104-105 years, meaning that massive stars enter the mainsequence much sooner, while the collapse of the dense core and subsequent accretionare still ongoing. This leads to difficulties in observing them, as the star is highly em-bedded for a large part of their short lifetimes (massive stars only live for a few millionyears).

There are several more difficulties in observing massive stars. Massive stars arerare compared to their low-mass counterparts. This follows from the mass distributionfunction of stars at birth, the Initial Mass Function (IMF), given by

dNdM∼M−α. (1.2)

This equation tells us how many stars can be found in a certain mass range. Salpeter(1955) first found that α = 2.35 is a good approximation for the upper range of the IMF,which is discussed and confirmed by, for example, Scalo (1998). In Table 1.1, takenfrom Zinnecker and Yorke (2007), we list the implications of this slope for the IMF. Aswe can see, there are many more low-mass stars than there are high-mass stars. Due tothis rareness, massive stars and the molecular clouds with enough mass to potentiallyform a massive star tend to be far away. The distances are on a kpc scale, they are ∼10 times farther away than low-mass objects (e.g., Cesaroni et al. 2007). If we want toprobe the environments of forming massive stars on a small scale we need high angu-lar resolution (∼ 1” or less) observations, specifically at wavelengths that can probe thegas and dust in which they are embedded (e.g., millimeter and submillimeter), whichis difficult (if not impossible) with single dish telescopes. Interferometry, which wewill discuss in Section 1.4, and the Atacama Large Millimeter Array (ALMA) in partic-ular, allows us to probe down to these scales in relevant wavelength regimes, hopefullysolving this problem.

Despite the rare nature of massive stars, they play a much more important role thanlow-mass stars in influencing the interstellar medium (ISM), their parent galaxies andthe universe. Compared to low-mass stars, massive stars have immense luminosities(L ∼ M3), with which they are able to impact a vast range of scales and processesthrough, for instance, the dissociation/ionization of hydrogen and radiation pressure.Another way in which massive stars have a larger impact on their surroundings thanlow-mass stars is through their mechanical feedback from strong stellar winds (fromthe stellar surface) and proto-stellar outflows.


The intense radiation that massive stars emit also poses a problem in their forma-tion. The resulting radiation pressure and the ionizing nature of the UV part of theradiation is strong enough to halt accretion and generate HII regions. The former caneither be solved by introducing a very high accretion rate (McKee and Tan 2003) orthrough the “flashlight” effect (Yorke and Bodenheimer 1999). This effect is caused bya disk in the equatorial plane redirecting radiation to the polar directions, the radiationtaking the path of least resistance, reducing the pressure in the plane and allowing ac-cretion from the disk to the star.

Due to the above-mentioned problems, the first stages of the formation of high-mass stars are still poorly understood. However, a few theories have been proposed.The two most accepted theories are monolithic collapse and subsequent accretion ontoa single core, known as core accretion, and competitive accretion driven by a stellar cluster.Both these scenarios are discussed extensively by Zinnecker and Yorke (2007) and Tanet al. (2014) and references therein.

1.3.1 Core Accretion

The core accretion model is similar to the formation model outlined in Section 1.2.The principal assumption is that the initial conditions are gravitationally bound cores,scaled up in mass from the low-mass examples. A big difference is, however, that thelevel of turbulence in the high-mass cores is much higher due to their size (Myers andFuller 1992 and Caselli and Myers 1995), possibly dominating the internal pressure.This turbulence might be strong enough to provide enough pressure to support the coreagainst fragmentation before the massive star formation process proceeds. However,turbulence introduces density fluctuations, which could cause the core to fragment intosmaller, low-mass cores. This might be solved by a strong, large-scale magnetic fieldor by radiative feedback from surrounding lower-mass protostars with high accretionluminosities. This is an unsolved problem for this model.

1.3.2 Competitive Accretion

Competitive accretion (Bonnell et al. 2001 and Bonnell and Bate 2006) is different fromcore accretion in that it occurs when stars in a common gravitational potential accretematter from a large, distributed molecular gas cloud. This is in contrast to core accre-tion where the cores are more isolated and draw mass from their direct environments.Competitive accretion is most intuitively explained by Zinnecker and Yorke (2007),where the idea behind the model is compared to an economic one based on the real es-tate concept of “location, location, location” and on the capitalistic concept of “the richget richer”. Protostars located near the centre of the potential benefit from the gravita-tional attraction of the full potential, granting the central protostars access to the mostgas and allowing them to accrete at the highest rates in the cluster. As the mass ofthe protostar increases, the star becomes “richer”. With its increased mass over lowermass protostars in the cluster, it is able to draw in more and more gas as its gravita-tional sphere of influence keeps growing. The gas reservoir is limited, as it has a finitemass, so the protostellar cores will eventually have to compete for the gas. Hence thename of the model.


FIGURE 1.2: Path of evolution for high-mass stars. Figure by CormacPurcell.

1.3.3 Mass Assembly

The primary difference in the two models is when the mass is gathered. In the coreaccretion model the mass is assumed to be gathered before the star-formation processbegins, in the competitive accretion model the mass is gathered during the process. Asimilarity is that both formation theories suggest that accretion will occur via a disk.This has been seen in simulations (Hosokawa, Yorke, and Omukai 2010, Kuiper andYorke 2013), but only sparse evidence of Keplerian disks around O- and B-type starshas been found in observations (e.g. Cesaroni et al. 1999, Johnston et al. 2015).

1.3.4 Formation sequence

An evolutionary sequence, as described in Section 1.2 is not well established for mas-sive protostars. However, many aspects of the process are expected to be similar, or tovary gradually, as a function of protostellar mass as discussed by Tan et al. (2014) andpresented graphically in Fig. 1.2.

The process starts off in high mass starless cores (HMSC) within clumpy molecularclouds. Under the effect of gravity these cores start to collapse and flattened structuresand accretion disks are expected to form owing to conservation of angular momentum,likely accompanied by outflows. Up to this point, the evolution is theoretically ex-pected to be relatively similar to lower mass protostars, but observational confirmationhas yet to be made. As the density and temperature increase and the region becomesmore violent through outflows and shocks, complex organic molecules are formed,


leading to rich emission spectra (Herbst and van Dishoeck 2009). As the protostarcontracts to the main sequence and nuclear fusion starts to take place, UV radiationluminosities increase, ionizing the surrounding gas, and creating Hyper Compact andUltra Compact HII regions. These stages have all been observationally classified.

Massive stars spend a large portion of their evolution embedded in clouds of gas,which block light, making it more difficult to observe the inner workings of the sys-tem. As stated before, we have to obtain observations at millimeter and submillimeterwavelenghts in order to probe the inner workings of the system we are interested in.At these wavelengths we are able to look through the obscuring gas and dust. This iswhere interferometry comes into play. By combining multiple telescopes we are ableto achieve the necessary resolution.

1.4 Interferometry

The advent of interferometry has been a great leap forward for the study of star for-mation. An interferometer is able to obtain very high resolution observations by usinga technique called aperture synthesis, with which we are able to mix signals from anarray of telescopes. The final result is an image with the same angular resolution as atelescope with an aperture the size of the entire array. The angular resolution of a pairof telescopes ij is

θij ∼ λ/Bij , (1.3)

where Bij is the baseline between the pair: the projected separation between the twotelescopes. We can see that the resolution obtained from a pair of telescopes is muchlarger than the resolution of a single dish telescope, where the resolution is determinedby the size of the dish. For N number of telescopes, there are N(N − 1)/2 possiblebaselines. For each pair of telescopes the incident radiation is brought together forinterference, the interference being due to the wave nature of light. The electric fieldpropagates with different relative path lengths to where the beam is combined, hencealternately constructively and destructively interfering at different points, creating afringe pattern. This fringe pattern is directly related to the true sky brightness of theobject we aim to observe.The contrast between the fringes is historically called the visibility, given by

V =Imax − IminImax + Imin

=Fringe amplitudeAverage intensity

, (1.4)

where Imax and Imin are the maximum and minimum intensity of the fringes. This vis-ibility is related to a unique Fourier component of the true sky brightness observed bythe interferometer. Each pair of telescopes is sensitive to different size scales, depend-ing on their baselines. Large baselines (high resolution) sample small scales and shortbaselines sample large scales. To probe the structure of a source in detail we need manydifferent baselines.

As the Earth rotates, the projected baseline of each pair, and thus the spatial sensi-tivity and visibility, changes. An ensemble of different pairs of telescopes with differentprojections allows us to form a spatial sampling in the Fourier plane, or (u, v) plane.The true brightness distribution of the object is then reconstructed by performing a


Fourier transformation of the visibilities, allowing us to create an image with the reso-lution of effectively one very large telescope.

It is impossible to perfectly sample the entire Fourier plane. The unevenly-filledFourier plane can be thought of as a product of a completely-sampled Fourier planeand a spatial frequency mask which is equal to one where we have data and zero else-where. Since multiplication in Fourier space is identical to convolution in image space,we can take the Fourier transform of the spatial frequency mask to find a convolv-ing function we call the “dirty beam”. To recover the true sky brightness we have todeconcolve the “dirty image”, which is the (inverse) Fourier transform of the measuredvisibilities, by the dirty beam. This is done through a process called CLEAN (Högbom1974).

One of the problems with interferometers is that the largest spatial sensitivity isset by the smallest (u,v) sampling. Short baselines (telescopes that are close together)probe signals from large scales. This means that interferometers are blind to signalscoming from scales greater than the scales set by the shortest baselines. This can, how-ever, be solved by filling the gap with single dish observations. Here we only use(sub)millimeter interferometric observations. We will be blind to the large scale kine-matics of the region we investigate. This is not a problem for us, as we will focus onone star-forming core, as discussed in Sections 2.2 and 2.3.

Another problem with (sub)millimeter interferometry is the atmosphere affectingthe signals between antennas. Unfortunately for astronomical observations, the atmo-sphere through which light waves have to travel to reach our telescopes is not static.The atmosphere is turbulent and incoming light is corrupted as it propagates throughit. This is caused by variations in the column density of air along different paths andthe amount of water vapor in the air, which is not constant along the path of the ra-diation. To correct for atmospheric effects we use “calibrators”. These calibrators aresources with a known brightness and morphology. We can use, for instance, quasars(which are bright point sources) and objects in our own Solar System (which are well-characterized). By observing these known sources between observing science targetswe can determine how their radiation is affected and changed by the atmosphere asa function of time and frequency. We are then able to correct for these changes in thedata of our actual science target.

A full account of interferometry in astronomy is given by Monnier (2003).

1.5 CASA

In order to calibrate and image the interferometric ALMA data we use the CASA1 pack-age (McMullin et al. 2007). CASA is a suite of astronomical data reduction tools andtasks that can be run via the IPython interface in Python. CASA has useful tools to cal-culate and perform calibrations (e.g. gaincal), carry out (u, v)-plane continuum fittingand subtraction (uvcontsub), and to calculate a deconvolved image with a selected cleanalgorithm (clean).

1The Common Astronomy Software Applications (CASA) software can be downloaded athttp://casa.nrao.edu


1.6 Contents of this thesis

In this thesis we use ALMA data, obtained in ALMA Cycle 0 between May 8th andJune 3rd 2012, to study and subsequently model a protostellar core in the massive starforming region G35.20-0.74N. We will investigate the possible presence of a circum-stellar disk, and discuss the implications for the proposed formation sequences. InChapter 2 we describe the data and investigate simple fits and parameters. In Chapter3 we discuss how we create simulated observations based on source models using theexcitation and radiation transfer code LIME and how these simulations would be ob-served with ALMA. In Chapter 4 we will give a final discussion and we will concludethis report in Chapter 5.

CHAPTER 2

THE DATA

In this chapter we will discuss the observed data. Our target is core B of the starforming region G35.20-0.74N, described in detail by Sánchez-Monge et al. (2013) andSánchez-Monge et al. (2014), and is located at a distance of 2.19+0.24

−0.20 kpc (Zhang et al.2009). We discuss how the observations were carried out, what molecular species andtransitions we use in our analysis and what we can conclude from the distribution ofemission.

2.1 ALMA observations

The radio-interferometer ALMA was used to observe the G35.20-0.74N region in thesub-millimeter continuum and line emission in Band 7 (∼ 350 GHz). The observations,which have the proposal ID 2011.0.00275, took place in Cycle 0 between May 8th andJune 3rd 2012. The source was observed with 21 antennas of the array in the extendedconfiguration, with baselines ranging between 21 and 400 m, providing a spatial sensi-tivity down to structures of∼ 0.44”. The observations consist of four spectral windowswith a width of 1875 MHz (covered by 3840 channels) each, providing a resolution of∼ 0.4 km s−1. The four spectral windows cover the frequency ranges [336 858.049 -338 733.048] MHz, [334 974.167 - 336 849.166] MHz, [348 853.074 - 350 728.073] MHzand [346 900.537 - 348 755.536] MHz. The phase center of the observations is α(J2000)= 18h58m13s.03, δ(J2000) = +0140′36′′. Flux, gain and bandpass calibrations were ob-tained through observations of Neptune and J1751+096. The data were calibrated andimaged using CASA.

2.2 G35.20-0.74N

G35.20-0.74 is a star-forming complex located at a distance of 2.19+0.24−0.20 kpc (Zhang et al.

2009) and was first reported in a large survey of the galactic plane by Altenhoff et al.(1979). The main site of high-mass star formation is known as G35.20-0.74N. This site isassociated with the IRAS source 18556+0136 and estimates of its bolometric luminosityrange from ∼ 104 L (Gibb et al. 2003) to larger values of 0.7 − 2.2 × 105 L (Zhanget al. 2013).

9

10 Chapter 2. The Data

Subsequent work and technical advances have furthered our understanding of G35.20-0.74N. Early observations (e.g. Dent et al. 1985) revealed a well-collimated bipolaroutflow in 12CO. It appears that precession of this outflow (e.g. Gibb et al. 2003 andSánchez-Monge et al. 2014) is the cause of a large, butterfly shaped bipolar outflow witha NE-SW orientation, which dominates the infrared (see Fig. 1a in Sánchez-Monge etal. 2014). Observations with dense gas tracers and continuum emission at millime-ter wavelengths (e.g. Little et al. 1985 and López-Sepulcre et al. 2009) show a denseelongated structure, with a velocity gradient perpendicular to the above mentionedoutflow. This velocity gradient was at first thought to originate from a large (∼ 0.6 pc)flattened structure rotating about the axis of the NE-SW outflow. However, Gibb et al.(2003) proposed that the structure might actually be a fragmented rotating envelope,containing multiple young stellar objects. With the advent of ALMA, the resolution ofmillimeter observations greatly improved. Sánchez-Monge et al. (2014) showed thatthe elongated structure is indeed highly fragmented into a number of individual cores,as can be seen in Fig. 2.1, where we show a continuum emission map of the region.

There are a total of six cores in the necklace, named cores A, B, C, D, E and F inSánchez-Monge et al. (2013). Three of these cores, cores A, B and C, show strong emis-sion in complex organic molecules (e.g. CH3CN, CH3OH), which is typical of the hotcore phase in star formation. The other three cores do not show a high amount ofemission from these molecular species (see Fig. 2 in Sánchez-Monge et al. 2013), whichcould indicate that they are at earlier stages in their formation. The two strongest cores,core A and core B, are found close to the center of the structure. Rotation has been seenin both these cores. For core B this has been modelled as Keplerian rotation about acentral mass of ∼ 18 M by Sánchez-Monge et al. (2013). In this report, we will inves-tigate this core and its rotation further to understand the geometry, line emission andkinematics of this forming massive star.

2.3 Core B

2.3.1 Line Emission

CH3CNIn Fig. 2.2 we show a part of the spectrum of core B. We can see that there are sev-eral clear emission peaks. These emission peaks correspond with transitions of methylcyanide (CH3CN) between certain rotational energy levels. The rotational energy levelscan be described with two quantum numbers, J and K. J is the total angular momentand K is the projection of J along the axis of symmetry. Individual J → (J - 1) transi-tions are grouped into ‘rotational ladders’, which are labelled by their K values. Thecoloured peaks in Fig. 2.2 correspond to different K values of the CH3CN J = 19K−18Ktransition, namely the K = 2, 4, 5, 6, 7 and 8 transitions, which we will use for furtheranalysis of the core. We exclude the double peak on the far right, which are the K = 0and K = 1 transitions blended together, from our analysis. We also exclude the K = 3transition (visible as the grey peak in between the green and blue peaks); on closer in-spection this line appears to be blended with an ethyl cyanide line, making it unsuitedfor our analysis.

Several studies (Cesaroni et al. 1994, Furuya et al. 2008 and Beltrán et al. 2011), haveshown that CH3CN is a particularly useful tracer of rotation in circumstellar disks ortori, around massive proto-stars. This is due to the fact that CH3CN has favourable

Chapter 2. The Data 11

FIGURE 2.1: ALMA 870 µm continuum emission map of the star formingregion G35.20-0.74N. The contour levels correspond to 5, 10, 20 and 40times the rms value (1.21 mJy/beam). The synthesized beam (0.′′468 x

0.′′409, PA = 50) is shown in the bottom-right corner.


349.0 349.1 349.2 349.3 349.4Freq (GHz)

0

1

2

3

4

5

6

7

8

Flu

xde

nsit

y(J

y)

FIGURE 2.2: Spectrum of core B taken with the large area as shown inFig. 2.7a. Coloured lines show the CH3CN J = 19K − 18K ladder for K= 2 (blue), 4 (green), 5 (red), 6 (cyan), 7 (purple), 8 (yellow). The K = 3 lineis excluded from our analysis because on close inspection it appears tobe blended with an ethyl cyanide line. The K = 0 and K = 1 lines areexcluded as well, as they are blended together. They can be seen to the

right of the blue K = 2 line.

abundance and excitation in warm (> 150-300 K) and dense (≥ 107 cm−3) regions (e.g.Blake et al. 1987), conditions that can be expected in the immediate vicinity of mas-sive proto-stars. This favourable abundance and excitation is thought to be caused byits possible formation scenarios; e.g. reactions between species evaporated from dustgrain mantles (Millar, MacDonald, and Gibb 1997) and gas phase chemistry in the en-velope around massive young stars (Mackay 1999). Furthermore, for each J → (J-1)transistion (as discussed in the first paragraph of this section) selection rules prohibitradiative transfer between the different K-ladders. This means that their relative pop-ulations are strictly determined by collissional excitation. If we assume local thermalequilibrium (LTE) and optically thin lines, we can determine the kinetic temperatureand column density using the rotation diagram method (e.g., Goldsmith and Langer1999). We will discuss this method further in Section 2.4.

H13CO+

Another line of interest is the line produced by the H13CO+ J = 4 - 3 transition. Emissionfrom this transition is a great illustration of the complexity of the region surroundingcore B. In Fig. 2.3 we show the emission from this transition in different velocity ranges.The region of emission curves around core B from a high systemic velocity to a lowerone. The structure appears similar to the spiral infall in the OB cluster-forming regionG33.92+0.11 in DCN 3-2 and 13CS 5-4 line emission (Liu et al. 2015). This could indicatean infalling gas stream, feeding core B, but further research (beyond the scope of thisreport) is needed to confirm this suspicion.


FIGURE 2.3: Overlay of the 870 µm continuum emission (white con-tours) on the H13CO+ J = 4 - 3 emission in different velocity ranges.The ranges are 35.4-38.4 km s−1, 34.2-36.0 km s−1, 32.4-34.2 km s−1 and28.8-31.2 km s−1 for the top-left, top-right, bottom-left and bottom-rightimages, respectively. The contours are the same as in Fig. 2.1. The syn-thesized beam of the H13CO+ J = 4 - 3 data (0.′′48 x 0.′′42, PA = 37) isshown in the bottom-left corner. The distribution of the H13CO+ J = 4 -

3 emission gives us a good example of how complex the region is.


(A) Integrated intensity. (B) Velocity field

FIGURE 2.4: Moment maps for J = 19K - 18K , K = 2. Contour levels areat 25%, 50% and 75% of the peak emission of 3.64 Jy beam−1 km s−1.The synthesized beam of the CH3CN J = 192 - 182 data (0.′′469 x 0.′′420,PA = 41.41) is shown as the filled ellipse in the bottom-right corner. Theemission visible in the upper-right corner of both images is emissionfrom core A, which we will not further discuss in this report. A cleargradient can be seen in the velocity structure, possibly due to Keplerian

rotation.

2.3.2 Rotation

The velocity pattern of Core B was studied by Sánchez-Monge et al. (2013). Fitting thepeaks of CH3CN J = 192 − 182 in each velocity channel with a 2D Gaussian they wereable to model the velocity field with a Keplerian disk rotating about a central mass of18 M, with a radius of ∼ 2600 AU and inclined 19 with respect to the plane of thesky. Keplerian rotation is rotation which follows

v(r) =

√GM

r, (2.1)

where G is the gravitational constant, M the central mass and r the distance from thatmass. To verify the rotation, found by Sánchez-Monge et al. (2013), we can make sev-eral plots. First of all we make moment maps of the region. The zeroth moment is thesum of emission along the frequency (or velocity) axis at each pixel. This shows usthe extend of the emission. The first moment is the intensity-weighted frequency (orvelocity), this shows us the rotation of the emitting region. In Fig. 2.4 we show mapsof core B for the first two moments.

In Fig. 2.4b we can see a clear gradient in the velocity, ranging from ∼ +29 kms−1 to ∼ +35 km s−1. To investigate if this velocity gradient traces Keplerian rotationwe can make a Position-Velocity (PV) diagram. A PV-diagram is obtained by takinga certain slice through an image cube. An image cube consists of three dimensions,two dimensions are the right ascension (RA) and declination (Dec) and the third is the


FIGURE 2.5: Example of a channel map for two velocity channels. Thesynthesized beam of the continuum data (0.′′478 x 0.′′411, PA = 39.83) isshown as the filled ellipse in the bottom-left corner of the right image, itis the same for both images. We can clearly see how the distribution ofemission changes with the velocity. We can see it move from SE to NW,

coinciding with the gradient in Fig. 2.4b.

velocity. For a channel map (position-position diagram) we select a RA-Dec slice forcertain values of the velocity. An example is shown in Fig. 2.5. In the figure we can seethe emission of CH3CN J = 192 − 182 for two velocity channels, we can clearly see howthe distribution of emission changes with the velocity.

For a PV diagram we draw a line in the RA-Dec plane and take a slice throughall the velocity channels. In this way we can visualize the velocity structure of theobject, allowing us to determine if it is Keplerian. An analysis of the appearance ofPV-diagrams produced by Keplerian protostellar disks is given by Richer and Padman(1991). They show that the PV-diagrams have a distinct shape, which is referred toas a ’butterfly’ pattern. This pattern can be seen in real observations of disks rotatingaround low mass proto-stars as discussed by, for example, Ohashi et al. (2014) and Yenet al. (2014) and around more massive stars as discussed by Johnston et al. (2015).

In Fig. 2.6 we show PV-diagrams for the CH3CN J = 19K - 18K K = 2, 4, 5, 6, 7and 8 transitions. In the plots we show several black outlines, which encompass theregion where emission is expected for an idealized, thin Keplerian disk that is inclinedwith 19 with respect to the sky with a radius of 2600 AU and with various masses. Allthese patterns seem roughly consistent with the data, taking into account that the blacklines are obtained for zero line width and infinite angular resolution and our data hasnon-zero line width and finite angular resolution. As we can see, a PV-diagram alonecan give us a rough estimate of the mass of the central mass and the size of the rotatingstructure, but it lacks conclusiveness and uniqueness.


25

30

35

40

v LSR

(m/s

)

K = 20.0e+001.0e-012.0e-013.0e-014.0e-015.0e-016.0e-017.0e-01

K = 40.0e+008.0e-021.6e-012.4e-013.2e-014.0e-014.8e-015.6e-016.4e-01

26

28

30

32

34

36

38

40

v LSR

(m/s

)

K = 50.0e+008.0e-021.6e-012.4e-013.2e-014.0e-014.8e-015.6e-01

K = 60.0e+008.0e-021.6e-012.4e-013.2e-014.0e-014.8e-015.6e-01

0.0 0.5 1.0 1.5 2.0Offset (arcsec)

26

28

30

32

34

36

38

40

v LSR

(m/s

)

K = 7 0.0e+005.0e-021.0e-011.5e-012.0e-012.5e-013.0e-013.5e-01

0.0 0.5 1.0 1.5 2.0Offset (arcsec)

K = 80.0e+003.0e-026.0e-029.0e-021.2e-011.5e-011.8e-012.1e-01

FIGURE 2.6: Position-velocity plots along the direction with PA = 157

towards core B for different transitions of CH3CN, as in Sánchez-Mongeet al. (2014). The black lines mark the border of the region where emis-sion is expected for a Keplerian disk, inclined 19 with respect to theplane of the sky and of radius 1.′′2 (2600 AU) rotating about different cen-tral masses. The dashed, solid, dotted and dash-dotted lines are plottedfor a central mass of 25 M, 21 M, 18 M and 15 M, respectively. Allof these lines appear to be consistent with the data. The cyan dots arethe points of peak emission per velocity channel, as discussed by Richer

and Padman (1991). Units on the colourbar are given in Jy/beam.


Furthermore, in Fig. 2.6 we plot the peak of emission for every velocity channel, asdiscussed by Sargent and Beckwith (1987) and Richer and Padman (1991). This curvehas a distinct “S" shape in models of disks rotating in Keplerian fashion, this patterncan be clearly seen in the K = 2, 4 and 5 transitions but gets distorted as we go up in theK-ladder. In all the PV-diagrams the emission is largely restricted to only one side ofthe disk. This suggests that the region is not axially symmetric (Sánchez-Monge et al.2014), similar to the case of the disk around the B-type protostar IRAS 20126+4104 (Ce-saroni et al. 2014).

To gain further understanding of core B we will use the Line Modelling Engine(LIME), which we will discuss in Section 3.1, to simulate the line emission of the region,allowing us to further delve into the dynamics of the core.

2.4 Rotational Diagram Analysis

To be able to build a model of core B with LIME we need to know the temperature andcolumn density of CH3CN J = 19K − 18K . To estimate these two quantities, we use theRotational Diagram (RD) analysis, which was first introduced by Hollis (1982). Severalauthors have expanded this method (Loren and Mundy 1984, Turner 1991, Goldsmithand Langer 1999, Araya et al. 2005) and a brief summary is given by Purcell et al. (2006).In the following section we explain this method, closely following the summary of Pur-cell et al. (2006).

To obtain a relation between the upper-state colum density, Nu, and the measuredline intensity,

∫∞−∞ Tbdν, we have to solve the radiative transfer equation

dIν = −Iνκνds+ jνds, (2.2)

where Iν is the intensity of the radiation, κν is the attenuation coefficient and jν is theemissivity. If we assume low optical depth (i.e. τ 1), we arrive at,

Nu =8πkν2

ul

hc3Aul

∫ ∞−∞

Tbdν, (2.3)

where νul is the frequency of the transition, Aul is the Einstein A coefficient and the lineintensity is in units of K km s−1. All others constants are in SI units. The line intensityoutput of the real data we receive from CASA is not in K km s−1, but in Janksy (Jy).To convert this to K km s−1 we use

IΩ =2k

λ2TR, (2.4)

where IΩ is given in J s−1 m−2 Hz−1 sr−1 and 1 Jy = 10−26 J s−1 m−2 Hz−1.If we now assume that the system is in Local Thermodynamic Equilibrium (LTE),which means that the energy levels are populated according to a Boltzmann distri-bution characterized by a single temperature, T ,

nunl

=gugle[El−Eu]/kT , (2.5)


K 2 4 5 6 7 8

ν (GHz) 349.42685 349.34634 349.28601 349.21231 349.12529 349.02497log(Aul) -2.59590 -2.61106 -2.62274 -2.19251 -2.65552 -2.67727Eu/k 196.30319 281.98433 346.21972 424.69973 517.40633 624.31945∫

Tb dν(a) 90.25 ± 4.61 63.79 ± 3.41 52.52 ± 2.72 46.98 ± 2.57 12.40 ± 1.00 9.31 ± 0.61∫Tb dν(b) 109.21 ± 9.11 82.26 ± 7.04 72.35 ±5.82 64.04 ±5.53 22.10 ± 2.72 15.94 ± 1.41

N(a)u (×1013cm−2) 8.45 ± 0.43 6.18 ± 0.33 5.22 ± 0.27 1.73 ± 0.09 1.33 ± 0.11 1.05 ± 0.07

N(b)u (×1013cm−2) 10.22 ± 0.85 7.97 ± 0.68 7.20 ± 0.58 2.36 ± 0.20 2.37 ± 0.24 1.80 ± 0.16

∆ν (km s−1) 4.16 4.01 4.59 3.87 2.69 3.66τ (a) 0.117 ± 0.020 0.086 ± 0.015 0.062 ± 0.011 0.066 ± 0.011 0.025 ± 0.005 0.014 ± 0.002τ (b) 0.116 ± 0.025 0.091 ± 0.020 0.070 ± 0.015 0.073 ± 0.016 0.036 ± 0.008 0.019 ± 0.004

TABLE 2.1: Data for the K-ladder of the CH3CN J = 19-18 transition. (a)

Obtained with the large region as defined in Fig. 2.7. (b) Obtained withthe small region as defined in Fig. 2.7. Errors are calculated using the

rms error of the background emission.

the upper-state column density is related to the total column density, N , by

Nu =NguQ(T )

e−Eu/kT , (2.6)

where gu is the degeneracy of the upper state, Eu is the energy of the upper state andQ(T ) is the partition function. rearranging and taking the natural logarithm of bothsides we find

ln

(Nu

gu

)= ln

[N

Q(T )

]− EukT

. (2.7)

A straight line fitted to a plot of ln(Nu/gu) versus Eu/k will have a slope of 1/T andan intercept of ln[N/Q(T )]. Temperatures found from this method are referred to asrotational temperatures Trot. In our analysis we use the partition function for CH3CNderived by Araya et al. (2005)

Q(T ) =3.89T 1.5

rot

(1− e−524.8/Trot)2. (2.8)

As stated before, this method only works if the emitting region is optically thin. If this isnot the case, the measured line intensities will not correctly reflect the column densitiesof the levels. As stated by Goldsmith and Langer (1999), optical depth effects will beevident in the RD as deviations from a straight line, the estimate of the column densitywould appear to be too small. This would cause a flattening of the slope, leading to anoverestimate of Trot. Assuming Gaussian line profiles, the line-centre optical depth isgiven by,

τ =c3√

4ln2

8πν3√π∆v

NuAul(ehν/kTrot − 1), (2.9)

where ∆v is the FWHM of the line profile in km s−1. To find the FWHM we fit thespectrum shown in Fig. 2.2. The values are shown in Table 2.1. We see that all valuesare 1, so we do not need to correct for optical depth effects. As Purcell et al. (2006)state, this analysis also requires that the source fills the beam. As we can see in Fig.2.4a, this is the case.


(A) K = 2. (B) K = 8.

FIGURE 2.7: Moment 0 maps for J = 19K - 18K , K = 2 and 8. The smalland large white contours coincide with the 25% peak value in core B forK = 8 and K = 2, respectively. The regions defined by these contours areused for the determination of the column density and rotational tem-perature of CH3CN. The synthesized beam of the CH3CN J = 192 - 182

data (0.′′469 x 0.′′420, PA = 41.41) is shown as the filled ellipse and thesynthesized beam of the CH3CN J = 198 - 188 data (0.′′468 x 0.′′419, PA= 44.59) is shown as the open ellipse, both in the bottom-left corner of

their respective images.

To determine how the density and temperature of the core B depend on the radiuswe calculate two rotational diagrams; one for a region with a large radius and one fora region with a smaller one. These regions are shown in Fig. 2.7. The large and smallregions, shown as white contours, are determined using the moment 0 map of the J= 192-182 and J = 198-188 emission lines, respectively, and coincide with the 25% peakvalue of the two different maps, roughly corresponding to 20 times the rms noise of thebackground for the K = 2 transition. For lower values the K = 2 region starts to blendwith core A. The larger region reaches a distance of∼ 2080 AU from the centre, and thesmaller region reaches a distance of ∼ 1380 AU from the centre. The fact that the K = 2region is larger than the K = 8 region is the result of the difference in energy requiredto excite CH3CN to the upper state (either J = 192 or J = 198). The upper-level energy ofJ = 198 is much higher than the upper-level energy of J = 192, Eu/k = 624.32 comparedto Eu/k = 196.30, which means that a higher temperature is needed for the J = 198-188

transition and it is thus confined to an area closer to the central star.

With these two regions we can determine the rotational diagrams, using data fromTable 2.1. The RD are shown in Fig. 2.8. We find a temperature of T = 220.05± 41.63 Kand a column density of N = 1.01× 1017 ± 3.79× 1016 cm−2 for the small region and atemperature of T = 182.18±28.32 K and a column density ofN = 7.11×1016±2.04×1016

cm−2 for the large region. The volume densities are then 5.49×1013 cm−3 and 2.56×1013

cm−3 for the small and large region, respectively. As we can see, the temperature andcolumn density do indeed appear to increase as we get closer to the centre of the core,as we expected.


0 100 200 300 400 500 600 700Eu /k

25.5

26.0

26.5

27.0

27.5

28.0

28.5

29.0

29.5

30.0ln

(Nu/g u

)

T = 182.18±28.32 KN = 7.11e+16±2.04e+16 cm−2

(A) K = 2.

0 100 200 300 400 500 600 700Eu /k

25.5

26.0

26.5

27.0

27.5

28.0

28.5

29.0

29.5

30.0

ln(N

u/g

u)

T = 220.05±41.63 KN = 1.01e+17±3.79e+16 cm−2

(B) K = 8.

FIGURE 2.8: Rotational diagram determined using the regions shown inFig. 2.7. Error bars denote five times the rms error in the real data. Theerrors given for the temperature (T) and the column density (N) are one

standard deviation from the fit.


The values we find for the temperature and column density of core B are differentfrom the ones that Sánchez-Monge et al. (2014) find. They find a temperature of ∼ 148K and a column density of ∼ 1 × 1016 cm−2 using fitted spectra with the CASA inter-face of the XCLASS software called myXCLASS (Comito et al. 2005) and with MAGIX(Modeling and Analysis Generic Interface for eX-ternal numerical codes; Bernst et al.2011). However, these values appear to be mean values of the entire core, not givingus enough information to re-construct the spectrum with LIME. Furthermore, we donot know what region they used for their analysis. It could possibly be a larger region,skewing the values.

Using the two estimates we found for the density and temperature, and convertingthe CH3CN column density to the H2 number density that LIME requires, we will fitboth with a simple radial gradient, using a simple linear fit.

First we will model the region with constant values, based on the two regions, wethen compare those results with a simple linear gradient. The constant values we willuse are T = 182.18 K and N = 7.11×1016 cm−2 for the large region and T = 220.05 K andN = 1.01 × 1017 cm−2 for the small region. We will discuss the simulations in Chapter3.

CHAPTER 3

THE SIMULATIONS

In this chapter we will discuss how we have simulated the CH3CN 19K−18K emissionof core B in the star forming region G35.20-0.74N. We have made use of the excitationand radiation transfer code LIME (Brinch and Hogerheijde 2010). We will discuss thedifferent geometries we use, the different density and temperature profiles and theconclusions we can draw from our results.

3.1 LIME

The Line Modelling Engine (LIME) is an excitation and radiation transfer code that canbe used to predict line and continuum radiation from an astronomical source model.A full description is given in Brinch and Hogerheijde (2010). LIME models are writ-ten in C and can be given a large number of parameters and model functions. A fewexamples of possible parameters are the radius of the model, the smallest size that issampled and the path to the specific molecular data file. Molecular data files containthe energy states, Einstein coefficients, and collisional rates for the specified molecularspecies, which are needed by LIME to solve the excitation.

We can specify a physical model in almost every way we want with seven subrou-tines: density, molecular abundance, temperature, systemic velocities, random veloci-ties, magnetic field and the gas-to-dust ratio.

LIME can output a number of images per run to visualize the output of the sim-ulation. For instance, we can set the distance to the source, the image resolution, theviewing angle and the number of velocity channels. With LIME we have a powerfultool to help us gain a better understanding of the physical conditions in core B of thestar forming region G35.20-0.74N.

3.2 Simulations

Given the resolution of the observations, as discussed in Chapter 2, we can not tell forcertain at what stage of its evolution core B currently is or delve deeper into its kine-matics. It could be in an early stage where it is still largely obscured by a sphericalcloud, or it might be further along and have a more disk-like structure.

23

24 Chapter 3. The Simulations

To explore what kind of kinematical model with the parameters as discussed inthe previous chapter can reproduce the observed velocity pattern and molecular linespectra, we construct a range of models, calculate the resulting emission using the exci-tation and radiative transfer code LIME (described in Section 3.1) and determine whichof the models fits the data best.

Our models consist of a sphere, a sphere with an empty cavity and a simple thindisk, which we will discus in Section 3.2.2. We will run different versions of these threemodels. In our first simulations we will adopt a constant temperature and density. Inthe second set of simulations we will adopt a parametrized description of the tempera-ture and density, as determined in Section 2.4. For all models we will adopt Keplerianrotation around a core of 18 M and a radius of 2600 AU, inclined with 19 with respectto the sky, found by Sánchez-Monge et al. (2013), as a starting point.

3.2.1 Simulating ALMA observations

The output of our LIME simulations is an idealized version of what we would hope toobserve. Our data is not ideal. The observations are limited by the uv-coverage andthe size of the beam of ALMA, amongst other factors. To simulate the observationsof ALMA we use the CASA task simobserve. This task takes an input model image(our LIME output), and simulates a particular ALMA observation for which we canset, for example, the total integration time and the antenna configuration. A detailedexplanation of the task is given in the CASA cookbook.The output contains a visibility file, with the same sampling and coordinates (the LIMEoutput is centered on α(J2000) = 0h0m0s, δ(J2000) = 00′0′′ , the real data coordinates ofcore B are α(J2000) = 18h58m13s.025, δ(J2000) = +0140′35.92′′) as the real data, whichwe can run through the CASA clean task to create an image. With the simobserve outputwe can compare our simulations with the real data in the most similar way.

3.2.2 The Models

The models we use roughly represent different stages in the evolution of massive stars,as discussed in Section 1.3.4. The first model being a simple sphere, one of the earliestphases. The second model, further along the evolution, being a sphere where a cav-ity has been carved out of by possible outflows, but where most of the region is stillenveloped by the contracting sphere. For the cavity model we need to determine theopening angle of the cavity. The opening angle is determined using Figures 15 and 16in Sánchez-Monge et al. (2014). They show that H2 2.12 µm line emission outlines abipolar structure, which seems to roughly align with a precessing jet emanating fromcore B. Note, however, that the bipolar structure is not fully explained by the singleprecessing jet. The region is complex and the large scale bipolar outflow could be theresult of several outflows in the region. Using the two figures, we estimate an openingangle of ∼ 90 for the large scale outflow. In the literature a large range of openingangles can be found for cavities carved out by bipolar outflows (e.g. Cesaroni et al.1999, Arce et al. 2007 and references therein) and the degree of collimation is also likelydependent on the age of the driving star and degree of turbulence in the environment,making us unable to set a well-founded average opening angle. Because of this we willstick to our crudely determined cavity angle of ∼ 90 for this model.

Chapter 3. The Simulations 25

FIGURE 3.1: Density profiles for the linear gradient models. The top-left figure shows the spherical model, the top-right figure shows thesphere with a cavity model. The bottom two figures show the thin diskmodel. Units on the colourbar are H2 density in cm−3. The figures onthe bottom-right is a zoomed-in version of the thin disk model. In thebottom-right figure we can see that the thin disk is not sampled correctly;it is not confined to a height of 26 AU. This is a known LIME problem

for geometrically thin structures, which we were unable to solve.

The last model is a fully formed, thin disk, where the entire sphere has contracted.For a thin disk model the height of the disk is much smaller than the radius of the disk,H R. For this model we set the height of the disk, which is constant across the entiredisk, to 1% of the outer disk radius. This gives us a height of 26 AU.

To see which profiles can reproduce the spectrum of core B, shown in Fig. 2.2, weinvestigate several density and temperature profiles. We start with a constant distribu-tion for both the density and the temperature, and compare them with a simple linearfit between the values we found in Section 2.4. As stated at the end of Section 2.4,we will use the temperature and density of both the small and the large region for theconstant profiles, T = 220.05 and N = 1.01 × 1017 ± 3.79 × 1016 cm−2 and T = 182.18 Kand N = 7.11× 1016 cm−2, respectively, and compare the results with the linear fit. Thegradient density profiles are shown in Fig. 3.1 to illustrate the geometry of the models.

3.2.3 Model Parameters

As stated before, LIME gives us an idealized output. We can set, for example, the res-olution per pixel, the number of velocity channels, the smallest scale that is sampledand we have to set the number of grid points in the model. However, there is a trade-off between the parameters and the computation time. The number of grid points, theresolution and number of channels all increase the time it takes for the simulations tocomplete. They also increase the time it takes for CASA to process the results. How-ever, we do want to set the parameters as high as possible to obtain the highest qualitysimulations.


The simulations are centered on 349152.100 MHz with a bandwidth of 619.000 MHz,covered by 635 channels. This gives us a channel width of 0.837 km s−1, comparable tothe 0.6 km s−1 we use for the data. With the provided central frequency and bandwidthwe cover the full range of the CH3CN K-ladder we use in the analysis of our real data,as discussed in Section 2.3. The resolution is 0.01 arcsecond per pixel, much higher thanthe ∼ 0.44 arcsecond data resolution. The number of grid points for all simulations isset to 104, with uniform logarithmic sampling. With these parameters the simulationstook between one and two days. We used a single processor on the helada computer inthe Allegro group (Intel Xeon E5-2640 v3).

3.2.4 Results of Simulations

EmissionIn Figures 3.2, 3.3, 3.4 and 3.5 we show the moment 0 maps (the distribution of emis-sion) for the simulated data. We show moment 0 maps for the K = 4 and the K = 8transitions. We use the K = 4 transition, instead of the K = 2 transition we used for theobservations, because the K = 2 transition appeared slightly blended in the simulations,skewing the results. The K = 1 and K = 2 lines are close together; the channel widthof 0.837 km s−1 we choose for the simulations is not quite small enough, leading to aslight blending of the two. We decided to keep the channel width as it is due to timeconstraints. Using the K = 4 line will not change our analysis significantly, as the K = 4transition shows strong emission and the same trend as the K = 2 transition.

One thing that stands out in the moment 0 maps is that the emission is not sam-pled correctly in the thin disk models, the output emission does not appear uniformlydistributed. We will discuss this later on as we look at the PV-diagrams and in the dis-cussion in Chapter 4.

The emission resulting from the sphere and the sphere with cavity models appearsroughly similar. It is difficult to distinguish between the two by eye based on the mo-ment 0 maps. There is a slight difference discernible at the poles (the top and the bot-tom) in Figures 3.2 and 3.3; there appears to be less emission in the sphere with cavitymodel, as expected. In Figures 3.4 and 3.5 we can see that the sphere with cavity modelis slightly more flattened than the spherical model.

For all models there is a clear difference between the constant density and tem-perature profiles and the linear gradient profiles. The constant models have higheroverall emission, but for the gradient models the center has a higher peak emission.This makes sense, as in the constant profiles there are more molecules overall to un-dergo transitions and emit radiation. There is a high density out to a large radius, witha relatively high temperature. More molecules get excited, leading to more emission.However, the gradient models have a higher density and temperature in the center,which drops off towards higher radii.

Another clear difference can be seen between the different geometries. The sphereand the sphere with cavity models show a lot more emission than the thin disk model.This makes sense for the same reason as in the previous paragraph; in the two sphericalmodels there are many more molecules to get excited, leading to more emission. Thisdifference is clearly seen in the spectra as well, which we will discuss in the next section.


Only a slight difference can be seen between the K = 4 and K = 8 moment maps. Thesimulated lines seem to be excited in roughly similar-sized regions. This is in contrastwith the observations. There is a major difference between the two observed emissionlines; this suggest that the regions in which they are emitted vary greatly, as can be seenin Fig. 2.7 for the K = 2 and K = 8 lines.

A clear difference is seen between the pre-simobserve and post-simobserve images.The simobserve task convolves the idealized LIME output with the ALMA beam, ‘blur-ring’ the ideal emission.

SpectraAs with the real data we plot the spectra of the simulations. The region we use to obtainthe spectra for the post-simobserve spectra is the same as the region we use for the realdata, rotated to the correct PA. Core B in the data has a PA of ∼ 157, unfortunately wecould not reproduce this in LIME, so we had to correct for it in the region used to ob-tain the spectrum. For the pre-simobserve LIME data, which is in different coordinatesthan the real data as stated in Section 3.2.1, we use an ellipse with a major and minoraxis based on the maximum width and heigth of the real data region, as we were un-able to re-grid the CASA region file used to obtain the spectra. We plot the spectrum ofthe LIME output, Fig. 3.6 (pre-simobserve), and the spectrum of the simobserve output(post-simobserve), Fig. 3.7, for all nine models discussed so far.

The general trend in the spectra does not change much from the pre-simobservedata to the the post-simobserve data. What is clear, however, is that the post-simobservespectra have lower values of peak emission, this is due to the limited ALMA uv-coverage we put through simobserve. As stated in Section 3.2.1, this is needed to beable to compare the real data with our simulations in the most similar way. We will dis-cuss the differences between the simulated spectra and the observed spectra in Chapter4.

PV-diagramsBefore going in to comparing the simulations with the observations we will investigatethe PV-diagrams. In Figures 3.8, 3.9, 3.10 and 3.11 we show the PV-diagrams of oursimulated data. As stated before, we show our results for the K = 4 and the K = 8 tran-sitions.

As in Fig. 2.6 we show several black outlines; these outlines encompass the regionwhere emission is expected for an idealized, thin Keplerian disk that is inclined with19 with respect to the sky with a radius of 2600 AU and with various masses. Themass we set for the simulations is a central mass of 18 M, which we are certain of (incontrast to the fitted mass in the observations); still all patterns seem comparable to thedata, again showing that a PV-diagram alone can only give us a rough estimate of themass of the central object and the size of the rotating structure. In the post-simobservePV-diagrams (Figures 3.10 and 3.11) we show the points of peak emission per veloc-ity as cyan dots; they show the distinct “S”-shape pattern, as discussed by Richer andPadman (1991).

Almost no difference can be discerned between the sphere and the sphere with acavity in the PV-diagrams.


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FIGURE 3.2: Moment 0 map for our simulations (pre-simobserve) forthe K = 4 transition. We show the simulations with constant T and Nbased on the small region on the left and based on the large region in themiddle. On the right side we show the simulations with a gradient inT and N. From top to bottom we show the thin disk, the sphere with acavity and the sphere. Units on the colourbar are given in Jy/pixel km/s

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FIGURE 3.3: Moment 0 map for our simulations (pre-simobserve) forthe K = 8 transition. We show the simulations with constant T and Nbased on the small region on the left and based on the large region in themiddle. On the right side we show the simulations with a gradient inT and N. From top to bottom we show the thin disk, the sphere with acavity and the sphere. Units on the colourbar are given in Jy/pixel km/s


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FIGURE 3.4: Moment 0 map for our simulations (post-simobserve) forthe K = 4 transition. We show the simulations with constant T and Nbased on the small region on the left and based on the large region inthe middle. On the right side we show the simulations with a gradientin T and N. From top to bottom we show the thin disk, the sphere witha cavity and the sphere. Units on the colourbar are given in Jy/beam

km/s.

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FIGURE 3.5: Moment 0 map for our simulations (post-simobserve) forthe K = 8 transition. We show the simulations with constant T and Nbased on the small region on the left and based on the large region inthe middle. On the right side we show the simulations with a gradientin T and N. From top to bottom we show the thin disk, the sphere witha cavity and the sphere. Units on the colourbar are given in Jy/beam

km/s.


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FIGURE 3.6: Spectrum of core B (coloured lines) overlaid on the spec-trum of our simulations (pre-simobserve, grey lines). Coloured linesshow the CH3CN J = 19K − 18K ladder for K = 2 (blue), 4 (green), 5 (red),6 (cyan), 7 (purple), 8 (yellow). We show the simulations with constant Tand N based on the small region on the left and based on the large regionin the middle. On the right side we show the simulations with a gradientin T and N. From top to bottom we show the thin disk, the sphere with

a cavity and the sphere.


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FIGURE 3.7: Spectrum of core B (coloured lines) overlaid on the spec-trum of our simulations (pre-simobserve, grey lines). Coloured linesshow the CH3CN J = 19K − 18K ladder for K = 2 (blue), 4 (green), 5 (red),6 (cyan), 7 (purple), 8 (yellow). We show the simulations with constant Tand N based on the small region on the left and based on the large regionin the middle. On the right side we show the simulations with a gradientin T and N. From top to bottom we show the thin disk, the sphere with

a cavity and the sphere.


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FIGURE 3.8: PV diagrams for K = 4, pre-simobserve. The order of thefigures is the same as in Figures 3.6 and 3.7. On the left side we showthe simulations with constant T and N, on the right side we show thesimulations with a gradient in T and N. From top to bottom we showthe thin disk, the sphere with a cavity and the sphere. The black linesmark the same regions as in Fig. 2.6. Units on the colourbar are given in

Jy/beam.

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FIGURE 3.9: PV diagrams for K = 8, pre-simobserve. The order of thefigures is the same as in Figures 3.6 and 3.7. On the left side we showthe simulations with constant T and N, on the right side we show thesimulations with a gradient in T and N. From top to bottom we showthe thin disk, the sphere with a cavity and the sphere. The black linesmark the same regions as in Fig. 2.6. Units on the colourbar are given in

Jy/beam.


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FIGURE 3.10: PV diagrams for K = 4, post-simobserve. The order of thefigures is the same as in Figures 3.6 and 3.7. On the left side we showthe simulations with constant T and N, on the right side we show thesimulations with a gradient in T and N. From top to bottom we showthe thin disk, the sphere with a cavity and the sphere. The black linesmark the same regions as in Fig. 2.6. The cyan dots are the points ofpeak emission per velocity channel, as discussed by Richer and Padman

(1991). Units on the colourbar are given in Jy/beam.

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FIGURE 3.11: PV diagrams for K = 8, post-simobserve. The order of thefigures is the same as in Figures 3.6 and 3.7. On the left side we showthe simulations with constant T and N, on the right side we show thesimulations with a gradient in T and N. From top to bottom we showthe thin disk, the sphere with a cavity and the sphere. The black linesmark the same regions as in Fig. 2.6. The cyan dots are the points ofpeak emission per velocity channel, as discussed by Richer and Padman

(1991). Units on the colourbar are given in Jy/beam.

CHAPTER 4

DISCUSSION

In this chapter we will discuss the results of our simulations and how they compare tothe observations. We will discuss some caveats of our simulations and briefly touch onpossible future work.

4.1 Comparing the Simulations with the Observations

EmissionA clear difference between the moment 0 maps of the simulated data and the observeddata is the level of symmetry. The observed distribution of emission, as shown in Fig.2.7, is not symmetric, whilst the simulated distribution is. There is, however, a highlevel of asymmetry in the thin disk model; this is due to poor sampling of the emis-sion in LIME. This is a known LIME problem for geometrically thin structures, whichwe were unable to solve. We attempted to solve this by increasing the number of gridpoints in the thin disk simulations from 104 to 2×104. This changed the outcome of thesimulation slightly, but the thin disk is still poorly sampled and the resulting spectrumis almost indistinguishable from the model with 104 grid points, as can been seen inFig. 4.1.

The symmetry in the spherical models is due to the fact that we model an idealizedsingle source, not influenced by neighbouring regions. The entire star forming regionG35.20-0.74N, as discussed in Chapter 2, is a complex region. Several cores are close toeach other, influencing their neighbours. As we stated in Section 2.4, when discussingthe different regions we use for the RD-analysis based on the K = 2 and K = 8 emission,the K = 2 emission surrounding core B starts to blend with the emission of core A aswe go down to lower levels of emission; this can be clearly seen in Fig. 4.2. At ∼ 20times the rms noise of the background the two cores are clearly separated, but alreadyat ∼ 10 times the rms value the emission starts to blend together. This blending doesnot happen in the K = 8 emission, even as we go down as low as 3 times the rms ofthe background. This could suggest that the core is not a large (R ∼ 2600 AU) rotatingstructure, but a smaller rotating structure embedded in a cloud of cooler, less densematerial that is still hot and dense enough to excite the lower rungs of the K-ladder.

35

36 Chapter 4. Discussion

349.05 349.15 349.25 349.35 349.45Freq (GHz)

0.0

0.5

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1.5

2.0

2.5

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4.0

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y)

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(A) Spectra for the linear gradient thin disk models.

2.5 1.5 0.5 -0.5 -1.5 -2.5Offset (arcsec)

-2.5

-1.5

-0.5

0.5

1.5

2.5

Off

set

(arc

sec)

0.0e+00

2.0e-03

4.0e-03

6.0e-03

8.0e-03

1.0e-02

1.2e-02

1.4e-02

1.6e-02

1.8e-02

2.0e-02

2.5 1.5 0.5 -0.5 -1.5 -2.5Offset (arcsec)

0.0e+00

2.0e-03

4.0e-03

6.0e-03

8.0e-03

1.0e-02

1.2e-02

1.4e-02

1.6e-02

1.8e-02

2.0e-02

(B) Moment 0 maps (K = 4) for the linear gradient thin disk models.

FIGURE 4.1: Comparison of the thin disk model, with a linear gradientin both density and temperature, for a different number of grid points..In the left two figures we show the spectrum and moment 0 map for themodel with 2 × 104 grid points. In the right two figures we show thespectrum and moment 0 map for the model with 104 grid points, thenumber of grid points we have used for the other models as well. There

is almost no difference discernible between the two cases.

Chapter 4. Discussion 37

(A) Moment 0 map for K = 2. (B) Moment 0 map for K = 8.

FIGURE 4.2: Moment maps for J = 19K - 18K , K = 2 (left) and K = 8(right). Contour levels are at 5, 10, 15 and 20 times the rms noise of thebackground in both images, 0.042 Jy/beam km/s for K = 2 and 0.014Jy/beam km/s for K = 8. The synthesized beams are shown in thebottom-left corner of both images (0.′′469 x 0.′′420, PA = 41.41 for K =2 and 0.′′468 x 0.′′419, PA = 44.59 for K = 8). The K = 2 emission sur-rounding core B starts to blend with core A at ∼ 10 times the rms value

of the background.

SpectraJudging the spectra shown in Figures 3.6 and 3.7 by eye it appears that the thin diskmodels are most similar to the observed data, out of the three different geometries. Theoverall emission strength for the sphere and the sphere with cavity models is muchhigher. However, there is a major difference between the observed spectra and thespectra from the simulated data. The data has a clear drop in the strength of the emis-sion from the K = 2 to K = 8 transitions; this drop is not as pronounced in the simulateddata. To compare the spectra of the observations with the simulated data, we show thevalues of peak emission for the CH3CN J = 19 - 18 K-ladder in Table 4.1. In the observeddata there is a ∼ 89 % drop in the peak emission strength from K = 2 to K = 8. For thesimulated thin disk data this drop is only ∼ 21-35 %. We will attempt to reproduce thisdrop in emission in Section 4.1.1.

PV-diagramsThe post-simobserve PV-diagrams look similar to the observations, but, in contrast tothe observations as shown in Fig. 2.6, they are too symmetric. The PV-diagram for thedisk is, again, most similar and there is some asymmetry. This asymmetry is due tothe fact that the emission is not sampled perfectly in our thin disk simulation in LIME,causing an asymmetry in the emission.


K 2 4 5 6 7 8 DecreaseReal data 3.43 2.53 1.99 1.96 0.65 0.39 -88.6%Constant disk(a)(c) 3.95 3.82 3.47 3.56 3.17 3.11 -21.1%Constant disk(b)(c) 2.23 2.06 2.12 2.21 1.80 1.45 -34.8 %Gradient disk(c) 3.29 3.13 2.88 2.94 2.53 2.22 -32.5%Constant sphere with cavity(a)(c) 26.63 25.96 25.04 26.02 23.48 22.76 -14.5%Constant sphere with cavity(b)(c) 20.55 19.90 18.60 19.25 17.19 16.55 -19.5%Gradient sphere with cavity(c) 18.29 17.75 17.09 17.23 15.84 15.06 -17.7%Constant sphere(a)(c) 27.33 26.77 25.31 26.21 24.13 24.00 -12.2%Constant sphere(b)(c) 21.24 20.62 19.47 20.06 18.07 17.56 -17.3%Gradient sphere(c) -18.78 18.26 17.47 17.53 16.43 15.52 17.4%Constant disk(a)(d) 3.54 3.43 3.10 3.10 2.84 2.80 -21.1%Constant disk(b)(d) 2.55 2.45 2.34 2.54 1.98 1.95 -23.4%Gradient disk (d) 2.82 2.69 2.48 2.53 2.20 2.03 -28.1%Constant sphere with cavity(a)(d) 17.19 16.80 16.41 16.59 15.43 14.85 -13.6%Constant sphere with cavity(b)(d) 11.88 11.62 11.26 11.34 10.61 10.10 -15.0%Gradient sphere with cavity (d) 11.93 11.60 11.49 11.76 11.38 11.49 -3.6%Constant sphere(a)(d) 17.01 16.69 16.32 16.46 15.47 15.03 -11.6%Constant sphere(b)(d) 11.51 11.24 10.90 10.98 10.26 9.85 -14.1%Gradient sphere (d) 10.76 10.80 10.82 10.81 10.84 10.89 +1.1%

TABLE 4.1: Peak emission for the different CH3CN J = 19K − 18K tran-sitions. (a) Obtained with the small region as defined in Fig. 2.7. (b)

Obtained with the large region as defined in Fig. 2.7. (c) Pre-simobservedata. (d) Post-simobserve data. In the final column we show the decrease

in line strength between the K = 2 and K = 8 transition.

4.1.1 Drop in Emission

In Section 4.1 we stated that the thin Keplerian disk model is most like the real obser-vations out of the nine models we tested, apart from one big difference. We do not seethe same decrease in the strength of emission from the K = 2 to the K = 8 transitions,using either a constant density and temperature of a linear gradient fitted to the valueswe found in Section 2.4.

To attempt to replicate the decrease in the line emission, we investigate severaldensity and temperature profiles. We test simple power-laws as a function of radius(R), starting with a power-law used in flared disk models (as we will discuss in Section4.2.1) and progressing to more exaggerated R-dependencies. For all these density andtemperature profiles we use the thin disk model, as it resembles the observations themost so far. The density and temperature profiles are given by

T (R) ∼ T0

(R

R0

)α, (4.1)

n(R) ∼ n0

(R

R0

)β, (4.2)

with T0 = 220.05 K, n0 = 5.49 × 1015 cm−3 and R0 = 1379.5 AU. In Fig. 4.3 we showthe resulting spectra for different values of α and β.

Chapter 4. Discussion 39

0

1

2

3

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7

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y)

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0

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0

1

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5

6

7

Flu

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y(J

y)

α = -0.5, β = -1.25

349.05 349.15 349.25 349.35 349.45Freq (GHz)

α = -0.5, β = -1.75

FIGURE 4.3: Spectrum of core B (coloured lines) overlaid on the spec-trum of the density and temperature profile tests for a thin, Kepleriandisk (pre-simobserve, grey lines). Coloured lines show the CH3CN J =19K − 18K ladder for K = 2 (blue), 4 (green), 5 (red), 6 (cyan), 7 (purple),8 (yellow). The values for α and β, as given in Equations 4.1.1 and 4.1.1.None of the models reproduce the gradient in the strength of the emis-

sion from the K = 2 to K = 8 transitions as seen in the observations.


ResultsNone of the models reproduce the decrease in the strength of the emission from the K= 2 to K = 8 transitions as seen in the observations; for these six models the decreasein emission strength ranges from 18.2 % to 28.8 %. In addition to the above mentionedmodels, we simulate the α = −0.5 and β = −1.5 for two cases with a lower T0, T0 =140 K (similar to the temperature from Sánchez-Monge et al. 2014) and T0 = 173 K (thelower bound in the K = 8 region, as shown in Fig. 2.8), to investigate if the overall tem-perature of the region is too high, exciting all transitions equally. We find a decrease of∼ 22% in the levels of emission. The only thing that changes is the strength of each line,in roughly equal measure; the decrease appears unchanged. This leads us to believethat the region is not well described by a single, large rotating structure with a radiusof 2600 AU, as found in previous work, but possibly by a smaller disk in an asymmetricenvelope of lower density and temperature.

Rotating disks and toroids in high mass (proto-)stars are found with a large rangeof different sizes, with radii ranging from ∼ 290 AU to ∼ 14400 AU (Beltrán et al.2011). It is possible that a possible disk surrounding core B of the star forming regionG35.20-0.74N is smaller than the 2600 AU we have used for our models so far. Futurework would include not only varying the density and temperature gradient and thegeometry (sphere, sphere with a cavity or a thin disk), but also varying the size.

4.2 Future work

4.2.1 Models

In our simulations and analysis we used idealized models of a perfect sphere, a per-fectly defined cavity and a perfect thin disk. In future work we hope to test morerealistic models. One of the models that we had hoped to include in our analysis, butwe could not test to its full potential, is a flared disk model. Flared disk models areoften invoked in the literature (Chiang and Goldreich 1997, Dullemond and Dominik2004a) for low-mass stars and is used as the prime example in Brinch and Hogerhei-jde (2010). In LIME we were unable to scale the model to the scales we used for ourother models. Due to issues with the triangulation of the grid we were not able to plotthe density and temperature structure of this model, making us unable to confirm ifthe LIME output matched the input parameters. Possible follow up research wouldinclude delving further into this model.

4.2.2 Observations

Furthermore, higher resolution observations are needed to confirm the geometry andsize of the region we have studied. The maximum ALMA baseline used for the obser-vations was ∼ 400 m (Section 2.1). ALMA observing cycle 3 has baselines of up to 5km for Band 7 (∼ 350 GHz), possibly allowing us to probe down to an angular scaleof ∼ 0.04”, ten times smaller than the current observations. In future work we hopeto explore models with varying sizes to model the emission of core B in the star form-ing region G35.20-0.74N. High resolution observations are required to confirm thosemodels.

CHAPTER 5

CONCLUSIONS

We investigated a massive star forming core in the star forming region G35.20-0.74Nusing ALMA data obtained in the spring of 2012. We subsequently modelled the re-gion using the excitation and radiation transfer code LIME. Our conclusions can besummarized as follows.

1. Emission from the CH3CN J = 19K - 18K K = 2 transition shows a clear gradientin the rotation of the core. Based on Position-Velocity diagrams for K = 2, 4, 5,6, 7 and 8 this rotation appears to be of Keplerian nature for low values of K. Inaddition to the Keplerian structure becoming increasingly unclear as we go up tohigher values of K, the level of asymmetry of the core increases as well.

2. A clear gradient is seen in the emission strength of the CH3CN J = 19K - 18K K = 2,4, 5, 6, 7 and 8 transitions. Allowing us to determine the temperature and densitywith the Rotational Diagram method. We defined two regions based on the K =2 and K = 8 emission and found a column density of 7.11 × 1016 ± 2.04 × 1016

cm−2 and temperature of 182.18±28.32 K at a radius of∼ 2080 AU and a columndensity of 1.01× 1017 ± 3.79× 1016 cm−2 and temperature of 220.05± 41.63 K ata radius of ∼ 1380 AU.

3. We initially simulated the region with nine models: a sphere, a sphere with a cav-ity and a thin disk, with either a linear gradient density and temperature profileor a constant density and temperature profile. The thin disk model resembled theobserved region the most, but none of the models reproduced the decrease seenin the emission strength of the CH3CN J = 19 - 18 K-ladder in the observations.Exploring the thin disk model further with several power-law density and tem-perature profiles, we were still unable to reproduce the observed decrease.

4. Judging by the asymmetry in the PV-diagrams, the blending together of core Aand B in the CH3CN J = 19 - 18 K = 2 emission and the fact that we are unable torecreate the spectrum with a single large rotating core, we suggest that the densestar forming core is much smaller than the proposed ∼ 2600 AU (as found in pre-vious work), surrounded by a less dense, asymmetric envelope. High resolutionobservations, possible with ALMA cycle 3, are required to confirm this.

41

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