T he P hysical and C hem ical
E volution o f
Star Form ing R egions
A Thesis su b m itted for th e Degree
of
D octor of Philosophy of the U niversity of London
by
D eborah P atricia Ruffle
UCL
D epartm ent of Physics & A stronom y
U niversity College London
U niversity of London
ProQuest Number: U641922
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A b str a c t
A wide variety of molecular species are observed in regions of star form ation. The
chem istry is m easured to change between different sources; analysis of these observed
chem ical changes provides a probe of th e physical and chemical m echanism s occur
ring w ithin different regions. Of p articular im portance is th e gas-d u st interaction,
which affects th e physical and chemical properties of interstellar gas.
In this thesis, theoretical models of th e physics and chem istry in star forming
regions are applied to existing observational data, in a tte m p ts to deduce th e evolu
tionary history and physical conditions of such regions. In some cases, th e models
are used to suggest other species th a t could be observed to fu rth er explore the
dom inant mechanisms occurring in different regions.
An investigation into the initial support and collapse of diffuse clumps to form
dense cores suggests th a t a clump may require a m inim um column density for star
form ation to occur. For the first tim e the chemical evolution of a cloud th a t is
initially m agnetically supported against collapse perpendicular to th e field lines,
b u t is collapsing along the field lines, up to an unknown bu t critical density is
explored. It is shown th a t observations may reveal the value of th e critical density.
Study is m ade of the gas-dust interaction. Some m olecular species which have
been used as signposts of cloud evolution are dem onstrated to be indicative of both
early and late tim es; implications of this are discussed. The sulphur depletion
problem is explored; a simple model is suggested where S'*” is accreted rapidly onto
dust grains. In addition, th e elem ental depletions in star-form ing cores are exam ined
w ith reference to th e use of species to search for signatures of infall.
Finally, it is established th a t low tem p eratu re hom onuclear diatom ic molecules,
which are thought to be unobservable, should be detectable in cold interstellar
C on ten ts
1 In tr o d u c tio n 10
1 . 1 O verview ... 11
1 . 2 Clumpy Giant M olecular Cloud c o m p le x e s ... 18
1.3 Low-mass star form ation in a cluster of dense c o r e s ... 21
1.4 TM C- 1 ... 23
1.5 Collapse of dense cores in regions of low-mass star f o r m a ti o n ...25
1.6 Theoretical studies of the chem istry of dense core collapse in regions of low-mass star f o r m a tio n ... 31
1.7 S u m m a r y ... 33
2 C h e m is tr y and p h y sics o f c o lla p sin g in te r ste lla r clo u d s 35 2 . 1 Chem ical r e a c t i o n s ...35
2.1 . 1 Gas phase c h e m i s t r y ...36
2.1 . 2 Grain surface p ro d u c tio n ... 37
2.2 E lem ental a b u n d a n c e s ... 38
2.3 Ghemical n e t w o r k s ...40
2.3.1 Hydrogen and deuterium c h e m i s tr y ... 40
2.3.2 Garb on c h e m is try ... 41
2.3.3 Oxygen c h e m istry ... 42
2.3.4 Nitrogen c h e m i s tr y ... 43
2.3.5 Sulphur c h e m istry ... 44
2.4 The ionization s t r u c t u r e ... 44
2.5 Physics of collapsing clouds ... 46
2.5.2 C o lla p s e ...48
2.6 T he m o d e l... 48
3 I o n iz a tio n str u c tu r e and a critica l v isu a l e x tin c tio n for tu r b u le n t s u p p o r te d c lu m p s 52 3.1 In tr o d u c tio n ... 52
3.2 Fractional ionization as a function of A y , uh , ^ s , ^s\ and ...57
3.3 Collapse from A y = 3 ... 63
3.4 C o n c lu s io n s ... 69
4 C y a n o p o ly y n e s as in d ica to rs o f la te -t im e c h e m is tr y and d e p le tio n in sta r fo rm in g reg io n s 70 4.1 In tr o d u c tio n ... 70
4.2 Model a s s u m p tio n s ...75
4.3 R e s u lts ... 76
4.4 D is c u s s io n ... 80
4.5 New observations of TM C- 1 ... 84
4.6 New m easurem ent of the rate coefficient for th e reaction of N w ith Hs"*" 8 6 5 O n th e d e te c tio n o f in te r ste lla r h o m o n u clea r d ia to m ic m o le c u le s 88 5.1 I n tr o d u c tio n ... 89
5.2 V ibrational emission from N2 ...92
5.2.1 Calculating Einstein T - v a l u e s ... 95
5.2.2 C a s c a d e ...97
5.3 An estim ate of the detectability of the e m i s s i o n ... 102
5.4 C o n c lu s io n s ... 103
6 T h e su lp h u r d e p le tio n p ro b lem 105 6.1 In tr o d u c tio n ... 105
6.2 The m odel of sulphur c h e m is tr y ...108
6.3 R e s u lts ... 109
6.4 D is c u s s io n ... 113
7 S e le c tiv e d e p le tio n s and th e a b u n d a n ces o f m o le c u le s u se d to s tu d y
sta r fo r m a tio n 118
7.1 In tr o d u c tio n ... 118
7.2 The model and the r e s u l t s ... 120
7.3 D is c u s s io n ... 121
7.4 C o n c lu s io n s ... 126
8 C o n c lu sio n s and fu tu r e w ork 129
A F u rth er ta b le s o f resu lts for C h a p ter 7 133
A c k n o w le d g m e n ts 139
List o f Tables
1 . 1 Observed interstellar molecules ... 1 2
1 . 2 Observed interstellar i c e s ... 13
1.3 Im p o rtan t tim e s c a le s ... 17
1.4 Table of infall c a n d id a te s ... 28
2.1 Solar elem ental a b u n d a n c e s ... 39
2.2 Some model param eters ... 50
3.1 Examples of gas grain r e a c t i o n s ... 57
3.2 Fractional elem ental abundances used in th e ionization stru ctu re models 58 3.3 Fractional abundances as functions of ny for two collapse models . . . 67
4.1 Param eters for late-tim e chemistry m o d e l s ...79
4.2 Tim es of and fractional abundances at HC3N m a x im a ... 80
4.3 Observed fractional abundances in TMC-1 core D ... 84
5.1 Fractional abundance of O2 and N2 in interstellar c l o u d s ...89
5.2 V ibrational excitation cross-sections for N2 ... 93
5.3 V ibrational m atrix elements for N2 ...94
5.4 Spectroscopic d a ta for N2 ... 96
5.5 Transition wavelengths, A-value and num ber photons em itted in each tran sitio n of N2 ... 98
6.1 Elem ental abundances used in sulphur m o d e l s ...108
7.1 Standard elem ental abundances used in depletion m o d e l s ...120
7.2 D epletion model comparisons ...122
7.3 R otational constants for species used to detect in f a ll...127
List o f Figures
1.1 Map of the R osette Molecular C l o u d ... 18
1.2 Map of the Taurus-A uriga c o m p le x ... 20
1.3 m ap of B arnard 5 ...21
1.4 The evolution of uy for a cyclic model ...22
1.5 C ontour map of the CCS emission from TM C- 1 ... 23
1.6 C ontour map of the NHg emission from TMC-1 ... 24
1.7 C ontour map of the HC3N emission from TMC-1 ...25
1 . 8 Collapse s ig n a t u r e s ... 26
1.9 The NH3 line profile of L1498 ... 30
2 . 1 Carbon chem istry n e tw o r k ...41
2.2 Oxygen chem istry n e tw o r k ...43
2.3 C hem istry controlling the ionization stru ctu re in a dark cloud . . . . 44
2.4 D iagram of HD f o r m a t i o n ...46
2.5 D iagram of DCO'*’ and HCO^ c h e m i s tr y ...46
3.1 R elation of peak ^^CO column density to clum p mass, for clumps in the RMC ... 53
3.2 Fractional ionization as a function of A y , Tg, Tg; and ...56
3.3 Fractional abundances of species as functions o f A y for t7h =1 0^ cm “ ^ 59 3.4 Fractional abundances of species as functions o f A y for nH=5xlO^ cm “ ^ ... 60
3.5 Fractional abundances during collapse from rzHc=2xlO'^ cm“ ^ ...65
4.2 Fractional abundances in model 1 ... 77
4.3 Fractional abundances in model 5 ... 78
4.4 Fractional abundances for potential observational pointers ... 83
6.1 M etallic depletion indices as a function of condensation te m p e ratu re . 106
6 . 2 Fractional abundances for D*=0.1 and D { S ' ^ ) = l... 110
C hapter 1
In trod u ction
Over th e last quarter of a century observations of interstellar m olecular emissions
have p erm itted the determ ination of the physical and chemical properties of star
form ing regions w ithin the Galaxy, and a basic picture of how stars form has been
developed. G iant M olecular Clouds, containing up to about 10® M© are sites of
stellar b irth and contain translucent clumps w ith masses ranging from of the order
of 1 0 M@ to 10® M© (W illiams, Blitz & Stark 1995). The translucent clumps possess
supertherm al turbulence th a t probably consists of a superposition of Alfvén waves
(Arons & Max 1975). The clumps are supported against gravitationally driven
collapse by the turbulence and by the large-scale m agnetic field. As described in
section 2.4, the decay rate of the turbulence due to ion-neutral friction and th e
evolution of th e large-scale m agnetic field depend on th e ionization stru ctu re, which
is governed by th e chemistry. The eventual collapse of a translucent clum p leads to
th e form ation of dense objects called dense cores. The therm al stru ctu re of m aterial
in translucent clumps and in th e dense cores is determ ined by m olecular processes.
Thus, the evolution of translucent clumps and dense cores leading to star form ation
'is controlled by, as well as traced through, chemical processes.
In this thesis we describe original work aim ed at th e exploitation of m olecular
diagnostics of star forming regions, to elucidate th e roles of chem istry in controlling
star form ation. P articular emphasis is placed on th e role of th e gas-d u st interaction
in affecting the chemical and physical properties of interstellar gas. We begin below
chemical mechanisms of im portance in it.
1.1
O v erv iew
Gas and dust are th e m ain constituents of interstellar clouds. (D ust contains roughly
1% of the mass.) In Table 1 . 1 we provide a list of all th e interstellar m olecular species
detected in th e gas phase (van Dishoeck 1998; NRAO list 1998). These species
have been observed in absorption lines against background stars and through their
emission lines at m illim etre wavelengths (van Dishoeck & Blake 1998; van Dishoeck
1998). The presence of interstellar dust grains is inferred from several observational
results, including the reddening of starlight (see the review by W illiam s & Taylor
1996). From th e observations of dust we can gain inform ation on its properties, such
as grain size and composition, which we discuss further in section 2.5.1.
T he gas is greatly modified through interactions w ith the dust grains. T he grain
surfaces provide sites for the formation of molecules. Indeed, m olecular hydrogen
m ust be produced on grain surfaces in order for its observed high abundance to
o b tain (W illiams & Taylor 1996). Gas phase species can accrete onto grain surfaces;
these molecules are adsorbed to th e surface, which leads to th eir depletion from th e
gas phase as they are now frozen-out onto the grain. We can m easure th e ex ten t to
which species are depleted from the gas phase, as described in section 2.2.
Species th a t have frozen-out onto a dust grain form an icy m antle around th e
grain core. We can observe molecules th a t are trap ped in icy m antles and in Table
1.2 we give a list of these species (van Dishoeck & Blake 1998; Tielens & W h itte t
1997). The molecules in ices are observed through th e absorption of radiation from
background stars. Once a species is frozen-out onto a g rain ’s surface it can be
ejected back into th e gas phase via desorption processes. Several possible desorption
m echanism s exist and these include chemical, radiative and high energy cosmic ray
processes (W illiams & Taylor 1996; see section 2.5.1).
A m easure of th e quantity of dust along a line of sight or in a cloud is th e visual
extinction. A y , m easured in m agnitudes. The visual extinction equals 1.086 tim es
Table 1.1: Table of observed interstellar and circum stellar molecules. We also de note th e wavelength ranges of the detections if they are not m ade at m illim etre wavelengths. From van Dishoeck (1998), NRAO list (1998).
Molecules with Two Atoms
AIF AlCl Cj(IR) CH CH+(VIS) CNf
CQf CQ+t CP* CSf CSP HCl
H2(IR) KCl NH(UV) NO NS NaCl
GRt PN SQt S0+ SiN* SiO
SiS HF
Molecules with Three Atoms
d (IR ,U V ) C2H C2O C2S CH2 HCNt
HCO HCO+t HCS+ HOC+ H2 0t H2St
H N d HNO MgCN MgNC N2H+ N2O
NaCN o c s^ s o | c-SiCz c o | NH|
Hj-(IR)
Molecules with Four Atoms
C-C3H I-C3H C3N C3O C3S C2H|(IR)
CH2D+? HCCN* HCNH+ HNCOf HNCS HO CO +
H2CO H2CN H jC St H30+t NRt
Molecules with Five Atoms
Q (IR ) C4H C4Si I-C3H2 C-C3H2 CH2CN
c hJ(i r) HC3N HC2NC HCOOH+ H2CHN H2C2O
H2NCN HNC3 SiH*(IR) H2COH+
Molecules with Six Atoms
CsH C5O C2H;(IR) CH3CNt CH3NC CHsOHt
CH3SH HC3NH+ HC2CHO HCONH2 I-H2C4
Molecules with Seven Atoms
CeH CH2CHCN CH3C2H HC5N HCOCH3 NH2CH3
C-C2H4O
Molecules with Eight Atoms
CH3C3N HCOOCH+ CH3COOH? C7H H2C6
Molecules with Nine Atoms
CH3C4H CH3CH2CN (CH3)20 CH3CH2OH HC7N CsH
Molecules with Ten Atoms
CH3C5N? (CH3)2C0 NH2CH2COOH? Molecules with Eleven Atoms
HCgN
Molecules with Thirteen Atoms HCiiN
* represents species observed only in circum stellar environm ents. ^ represents species also observed in comet Hale-Bopp.
? indicates th a t th e identification is unconfirmed.
dust. The value of Ay of a cloud is im portant in determ ining th e physical conditions
w ithin th e cloud, as we describe below.
The m ajor classes of interstellar clouds th a t this work deals w ith are ‘translucent
clum ps’ and ‘dense cores’. We can measure how dense th e different types of clouds
are, and define their num ber densities of H nuclei, uh, as
hh = n(H) + 2n(H2) (1.1)
where n(H ) and n (H2) are the num ber densities of hydrogen atom s and molecules
respectively. Diffuse clouds have the lowest num ber densities, typically of th e order
of n (H2 ) > 1 0 cm~^, and low visual extinctions ( T y ~ l m ag). Translucent clumps
have num ber densities of the order of n (H2) ~1 0^ -1 0^ cm “ ^ and visual extinctions
in th e range of 2 to 5 mag. Dense cores have num ber densities of n (H2) ~1 0^ -1 0®
cm “ ^ and much higher visual extinctions of i4 y > 5 mag.
R adiation from stars passes through the interstellar m edium and can interact
w ith th e gas and dust. A mean interstellar radiation field intensity was determ ined
by Draine (1978). Interstellar radiation can easily p en etrate the diffuse clouds and
translucent clumps, as these have low visual extinctions. However, dense cores have
m uch greater visual extinctions, and due to th e increased scattering and absorp
tion by grains their interiors are shielded from th e radiation. W hen radiation can
p e n etrate a cloud it can ionize atom s and molecules, in addition to dissociating
molecules. It is for this reason th a t only a lim ited set of molecules are observed in
diffuse clouds and translucent clumps (such as CO, CN, CH, CH+, H2 and OH),
as th e presence of the radiation inhibits th e form ation of complex species. On the
Table 1.2: Table of observed species in interstellar ices. Those in the second row only have upper limits on their abundances. From van Dishoeck & Blake (1998) and Tielens & W hittet (1997).
H2 0 CO CO2 o c s CH4 CH3OH XCN*
H2C0 HCOOH NH3 HCN SO2 H2S C2H2 C2H6
other hand, in dense cores we observe m any different complex species. In addition
to th e interstellar radiation field, cosmic rays (energetic protons) are another source
of ionization which contribute to the ionization in diffuse clouds and are th e m ajor
source in dense cores. In dense cores th e cosmic rays can directly in teract w ith
species to ionize and dissociate, in addition to inducing photons which can then
destroy species. The cosmic ray ionization of H2 results in an energetic electron
which then collides w ith and excites H2. W hen th e excited hydrogen molecule re
laxes it produces ultraviolet photons (Prasad & Tarafdar 1983; Gredel et al. 1989).
The direct cosmic ray ionization rate is lower th a n th a t of th e interstellar radiation
field, although its exact value is not clear as we discuss in section 2.4. The exact
ionization level or ‘stru c tu re ’ in a cloud is determ ined by th e chemistry, as we also
describe in section 2.4.
T he tem peratures of diffuse clouds, translucent clumps and dense cores also
differ. Typically, the tem p eratu re in a diffuse cloud is approxim ately 100 K and in
a translucent clum p or a dense core it is around 10-30 K. The tem p eratu re th a t
obtains is th e result of a balance between the heating and cooling m echanism s th a t
operate in a cloud. UV radiation and cosmic rays can heat a cloud by th e ionization
of species. The ionizing source im parts energy to the gas as the ejected electron
carries away excess energy. Photons, including those produced as a consequence of
cosmic-ray induced ionization, provide an additional heating source.
T he gas is cooled when radiation is em itted by the atom s and molecules th a t
comprise th e gas. Recom bination of an atom ic or m olecular ion w ith an electron
results in th e emission of a photon, which can then escape from th e gas; energy is
lost from th e system and the gas is cooled. The collisional excitem ent of an atom
or a molecule also results in the emission of a photon, as th e excited species decays
back to the ground state. B oth of these cooling mechanism s depend on th e num ber
density to th e power of two, which results in dense regions tending to be cooler th an
more diffuse environm ents. An additional loss m echanism is provided by th e grains,
which are heated when they absorb radiation. T he grains then radiate this energy in
th e infrared, which can then escape from the cloud. The dom inant coolant in both
only a few Kelvins. However, its effectiveness is reduced as its abundance rises in
denser clouds since the radiation em itted by one CO molecule can be absorbed by
another. This is a process called radiation trapping.
An im p o rtan t point to note is th a t in dense cores th e cosmic rays cannot m ain tain
th e tem p eratu res th a t are measured, when the cooling mechanisms are accounted
for. A nother heating process is needed. A potential source is some form of dynam ical
heating where movements w ithin the gas produce frictional heating.
Once we have determ ined the tem perature and num ber density of a cloud we
can consider its therm al pressure. Diffuse clouds and translucent clum ps have low
therm al pressures unlike dense cores which have therm al pressures around a hun
dred tim es greater. The m aterial between clumps and dense cores is referred to as
the interclum p m edium . The properties of th e interclum p m edium are poorly un
derstood but its to tal pressure m ust be com parable to th a t of a translucent clump.
(C ontributions to the to tal pressure include the therm al, tu rb u len t and m agnetic
pressures.) Pressure equilibrium between a translucent clum p and the interclum p
m edium should be established on roughly the tim escale for a fast-m ode m agnetic
wave to cross the clump; for an assumed fast-m ode speed of 3 km s " \ this is 10®
years for a clum p th a t is 3 pc across.
We now discuss how the gas is supported against collapse. We regard tran slu
cent clumps and dense cores as representing two different stages of star form ation:
th e translucent clumps collapse to form dense cores. Dense cores are identified as
th e direct progenitors of stars. Investigation into the star form ation process is con
ventionally divided into considerations of low-mass and high-mass star form ation
separately. Stars of low-mass (w ith masses less th an 4 M©) are thought to form as a
result of a gradual weakening of the m agnetic fields. However, higher mass stars are
believed to form because the ratio of the m agnetic flux to th e clumps mass is too
sm all for th e m agnetic field to prevent collapse when the pressure external to th e
clum p is increased above a critical value (e.g. Mouschovias 1987). High-mass star
form ation can therefore be triggered by increases in th e pressure of th e interclum p
m edium . Potential catalysts include winds and th e supernovae of other high-m ass
cerned w ith th e form ation of low-mass stars. Hence, all fu rth er descriptions, unless
stated otherwise, refer to low-mass star form ation only.
The gas in translucent clumps is confined by th e pressure exerted by th e warm,
tenuous interclum p m edium as these objects are not gravitationally bound. They
are believed to be supported against collapse by m agnetic fields and m agnetohydro-
dynam ic (M ED ) waves which comprise th e turbulence (e.g. Mouschovias 1987; Shu,
A dam s & Lizano 1987). We describe the evidence for turbulence in section 1.2. The
M ED waves can be dissipated, and the dam ping ra te depends inversely on th e ion
num ber density. The ionization structure of a cloud is determ ined by th e chem istry
(see section 2.4). Eence, as the fractional ionization drops, th e ra te of wave dam ping
increases and th e clump will begin to collapse along th e m agnetic field lines. (In
C h ap ter 3 we investigate the nature of decreases in th e fractional ionization.) The
collapse of a translucent clump by this process leads to th e form ation of a dense
core.
By contrast, dense cores are supported by therm al pressure and m agnetic pres
sure. Waves are not im portant for their support (see C hapter 3). T heir fu rth er
collapse is governed by am bipolar diffusion, the drift of th e n eu tral com ponent of
th e gas relative to the charged component. The charged com ponent of the gas con
sists of ions and electrons, and th e grains which carry one negative charge (D raine
& Sutin 1987). The m agnetic field acts on the charged com ponents and tends to
push particles out of th e cloud. The m agnetic force does not act directly on th e
n eu tral com ponent. G ravity acts to pull the neutral com ponent inward. T he rela
tive m otions produce friction between the neutral and charged com ponents which
acts to reduce th eir relative velocities. The friction therefore leads to th e ‘m agnetic
re ta rd a tio n ’ of collapse (and may provide the additional heating source th a t is re
quired in order for dense cores to have their observed tem p eratu res, as m entioned
above, and as described by Scalo 1987). The tim e for which th e collapse of a cloud
rem ains m agnetically retarded is the tim e required for th e neutrals to drift through
th e charged particles due to gravity. This is the am bipolar diffusion tim escale. In
Table 1.3 we give approxim ate expressions for this and some of th e other im p o rtan t
Table 1.3: Some important timescales. From Hartquist
k
Williams 1998.Timescale Process Years
Collapse Gravity
Cooling Radiation 3x10^ (for 10 K)
Freeze-out Gas grain collisions 3xlO^/MH^
Ion-molecule chemistry Cosmic Ray ionization 3x10^
Ambipolar Diffusion Ion-neutral drift 4xl0^æ(z)/10-^
Desorption Chemically driven* 3xlO^[a:(CO)/10“ '^][lcm~^/n(H)]
nH =n(H )+2n(H2); a:(CO)=n(CO)/nH; x(i)=n(ions)/ nu * by H2 formation; S is the sticking probability.
The collapse of clumps probably occurs via free fall, and we can com pare the
free fall collapse tim escale to some of the other timescales given in Table 1.3. W ith
hh of 1 0^ cm~^ we obtain a free fall timescale of ~ 1 0® yrs. Com pare this to the
ion-molecule chem istry timescale, which is the tim escale on which th e n atu re of the
chem istry can be entirely changed (the tim e to ionize an am ount of H2 th a t equals
th e C and 0 gas phase abundance). This is about 3x10^ yrs and is independent of
hh. Consequently, it is possible th a t dynam ical changes can occur rapidly enough
so th a t some signatures of th e past physical conditions rem ains in the observable
chemistry. The freeze-out timescale (cf. section 2.5.1) for lO'^ cm “ ^ is 3x10^ yrs for
stan d ard assum ptions, but may be larger, and this is less th an th e free fall tim escale.
So molecules m ay be lost from the gas quickly com pared to the collapse tim escale,
unless desorption is also occuring.
T he rem ainder of the chapter provides a more detailed introduction to th e prob
lems th a t are th e concern of the following work. In section 1.2 we provide a more
com plete introduction to the structures of Giant M olecular Cloud complexes, which
contain m any of the G alaxy’s star forming regions. Each giant m olecular cloud is
gravitationally self-bound and is likely to have been formed from th e collision and
subsequent merging of clouds th a t were initially diffuse. Each contains structures on
several scales. Most of the mass is contained in translucent clumps. We will consider
th e initial support and collapse of one of these clumps leading to th e form ation of
dense cores, which can be identified as th e progenitors of stars. These dense cores
collection of several cores, which are close enough to one another th a t the birth of
even a low-mass star in one of the cores may then regulate the further evolution of
tlie other cores within the cluster. In section 1.3 we discuss the possible scenarios
for the development of core clusters, in which low-mass stars form. Another core
cluster, TM C -1, which is one of the closest and most thoroughly observed, is the
topic of section 1.4. TMC-1 consists of several dense cores which lie in a ridge in
the vicinity of a recently formed low-mass star. A chemical gradient is observed
along the ridge and is used to infer information on the dynamical properties of the
source. In section 1.5 we examine the observational studies of dense core collapse
which leads to the formation of stars. Finally in section 1.6 we treat the theoretical
studies of the collapse of dense cores. Section 1.7 is a summary, and also sets out
the content of the thesis.
1.2
C lum py G iant M olecu lar C loud co m p lex es
^ - 1.5
- 2
- 2.5
208.5 208 2 0 7 .5 2 0 7 2 0 6 .5 2 0 6 2 0 5 .5
G a la c t ic L o n g i tu d e ( ° )
Figure 1.1: Map of the Rosette Molecular Cloud in ^^CO(J=1-0) emission. 1° % 28 pc.
lAom Williams, Blitz & Stark (1995).
In tlie Milky Way the m ajority of the molecular m atter exists in Giant Molecular
('loud (CM C) complexes. These liave masses which are typically in the range of 1 0"^
to 1(F Mq and have linear extents of a loon t 30 to 1 0 0 pc. One such GMC is the
th e integrated ( J = l - 0 ) emission line m ap of the RMC. The ^^0 0 ( J = l - 0 ) and
^ ^ 0 0 ( J = l - 0 ) emission m aps of th e RMC have been analyzed in detail by W illiam s,
B litz & Stark (1995). Their work has provided inform ation on th e stru ctu re of this
p articular GMC complex. The projected cross section of th e RMC is about 2200
pc^, it has a mass of about 1-2x10^ M©, a m ean H2 column density of 4x10^^ cm “ ^
and a m ean H2 num ber density of 30 cm “ ^. Much of the m olecular m aterial in th e
RMC exists in approxim ately 70 clumps which have masses between about 30 and
2500 M©; th e num ber of clumps w ith masses between M a n d M + d M scales as
dM. Less massive clumps may also exist w ithin the complex, b u t only a few were
detected at the lim it of the sensitivity of th e observations.
The clumps which have been identified occupy only approxim ately eight percent
of th e volume of th e RMC. In m ost clumps n (H2 ) ~ 2 0 0 cm “ ^; a variation of about
a factor of 4 in this value is found, b u t the m easured variation m ay be m ore lim ited
th a n th e real variation in density because CO is a poor tracer of denser gas. This is
due to the small dipole m om ent of CO resulting in th e CO rotational level population
distrib utio n becoming therm alized at values of n (H2) of several hundred cm “ ^. The
peak ^^CO column density through a clump scales roughly as and is about
10^® cm “ ^ for M =10^ M©; th e H2 column density is assum ed to be a factor of 5x10^
larger. T here are seven em bedded stars which exist in th e three m ost massive and
th e fifth, seventh, eleventh, and eighteenth most massive clumps. T he clumps th a t
contain stars are all amongst the 16 clumps having th e highest ^^CO colum n densities
of about 1 0^® cm “ ^ and more.
For a feature formed in an individual clump the line of sight full w idth at half
m axim um lies in th e range of about 0.9 to 3.3 km s“ L For com parison, the value
for ^^CO th a t is therm ally broadened only and is at 30 K (which is roughly th e
m axim um tem p eratu re obtaining in th e clumps) is only 0.22 km s~^. It has been
inferred th a t about half of the clumps are not bound by th eir own gravitational fields,
from the comparison of the velocity dispersion w ith th e escape velocity estim ated
from th e mass and radius of each clump. This is a result th a t appears to also apply
to clumps in other GMCs (Bertoldi & McKee 1992). A clump th a t is not bound
m ay consist prim arily of gas at about 10^ K.
The clumps have m agnetic fields which are im p o rtant for their support (e.g.
Mouschovias 1987). Turbulent pressure, which is associated w ith th e broad lines
th a t are observed, is im portant for clump support and acts along th e m agnetic field
lines. The form of th e turbulence is a superposition of Alfvén waves (Arons & Max
1975; Mouschovias & Psaltis 1995).
In C hapter 3 we examine th e collapse of a clum p to form a dense core. We argue
th a t collapse m ay begin if a critical column density is exceeded, and th a t this is
directly related to the extent of turbulent support in a clump.
30*1- LI5I7
28*,
26*
MCI
TMC2
— CO EMISSION • DENSE CORE + OBSCURED STAR
• T TAURI S T A R /^
L I5 3 6
2 0*,
18"
16' _ _
4*’5 5 ' 4 5 35"' 25"' 4 " 0 5
RIGHT A SC E N SIO N ( 1 9 5 0 )
Figure 1.2: The distribution of dark cores and low-mass stars in the Taurus — Auriga
1.3
L ow -m ass star fo rm a tio n in a c lu ste r o f d en se
cores
30
20
I R S 4
10
2.0
UJ
IR S 2
10
w
0 . 2 5
- 2 0
- 3 0
30 2 0 10 0 - 1 0 -20 - 3 0
RA OFFSET ( o r e min )
Figure 1.3: contour map of B5. The positions of four infrared sources (IRSl-4)
associated with young stars are shown. From Goldsmith, Langer & Wilson (1986).
W hen a clump like one of those observed in th e RMC collapses, it fragm ents and
objects known as dense cores form (e.g. Myers 1990). A m m onia emission has been
used to m ap m any of th e dense cores (e.g. Benson & Myers 1989). Dense cores
typically have masses of one to several tens of solar masses each, num ber densities
n (H2) ~1 0^ —10^ cm~^ and tem peratures of ~ 1 0 —30 K. However, some dense cores
are observed to have num ber densities of up to roughly 1 0^ cm “ ^ and masses of
more th an one hundred solar masses, particularly in regions where massive stars
form. In Fig. 1.2 th e dense core distribution in th e Taurus — A uriga complex is
shown. A pproxim ately half of all dense cores are associated w ith young low-mass
stars. Dense cores are considered to be the direct progenitors of protostars.
Figure 1.2 shows th a t m any (but not all) of the dense cores are near other dense
low-CLUMP COLLAPSE ABLATION AND SHOCK
•H
BUBBLE TBAVEBSAL
Figure 1.4: The evolution of nu for a parcel of gas in a cyclic model. At point A collapse of the interclump medium begins; the collapse continues until a more slowly evolving core is formed. At point B the parcel is ablated from the dense core by a stellar wind. H'*' and He"*" are assumed to mix from the wind into the ablated gas as it is accelerated. At point C the ablated gas is fully incorporated into the wind. The ablated gas-stellar wind mixture expands freely until at point D it passes through a termination shock inside the interface of the mixture and the ambient intercore medium. The density of the decelerated mixture increases as it cools; after cooling is complete the mixture becomes part of the cool phase of the ambient intercore medium. The parcel of gas may then pass through a qualitatively similar cycle again. Adapted from Charnley et al. (1988). Note the time axis is not to scale.
mass stars. Figure 1.3 shows a emission line m ap of B5. The gravitationally
induced collapse of a core is an im portant step in the form ation of a star, bu t
once young stars have formed in a region their winds m ay affect th e collapse of the
neighbouring cores. In Fig. 1.4 we present an illustration of a m odel of cyclic clump
evolution, which is a modified version of one developed by N orm an & Silk (1980). In
this scenario, a core is ablated by the supersonic wind of a nearby young low-mass
star, to create a stellar w ind-ablated m aterial m ixture. This m ixture then moves
supersonically u ntil it collides with the sim ilarly m ass-loaded winds of th e other
nearby stars, where it is decelerated and passes through a shock. T he shocked gas
is then radiatively cooled leading to the form ation of irregular shells separating th e
winds of different stars. As a result, an intercore m edium of regions of supersonic
w ind-ablated m aterial m ixtures and shells of decelerated m ixtures is produced. The
form ation of subsequent generations of cores could occur if th e shells fragm ent.
to form stars, before they can be significantly eroded. The m aterial th a t was in a
core l)iit does not go into a star may then be blown to a large enough distance from
the cluster of cores, by the stellar winds, such th at it cannot be considered to be
associated with the cluster.
1.4
T M C -1
.y*)CCS {t>)CCS J{^=2i -1Q
Beam Slz#
(HPÏWV)
5 0 - 5
*r,(arcmin)
B eam S ite
iVIPSW)
-1 0 5 0 - 5
io(arcmin)
higure 1.5: Contour map of the CCS emission from TMC-1. The filled triangle and
circle represent the positions of the ammonia and cyanopolyyne peaks respectively. From
I lirahara et al. (1992).
TM C- 1 (Taurus Molecular Cloud-1) is one of the most thoroughly observed dense
core sources. It is located within the Taurus - Auriga complex (see Fig. 1.2), at
a distance of 140 pc. Figure 1.5, a map of CCS emission, shows th a t TAlC- 1 is a
ridge which contains 5 dense cores th at are aligned on the plane of the sky, which
are labelled A to E (H irahara et ah 1992). There is a sixth core th a t lies to the side
of the Northern most core, core X which contains a star (its position is given in
f ig. 1.6). TMC-1 has an estim ated mass of approxim ately 1 0 M@ and an average
tem perature of about 1 0 K, in addition to being the site where some of the largest
detected molecules (lICgN, IIC uN ) have been found.
Figures 1.6 and 1.7 show maps of the NII3 (.7, A') = ( l , l ) inversion emission and
. NH3 (J,KH1,1)
10
5 8 1+2 5 4 0)
<c
0
B e a m S iz e (HPBW)
-5
0
5 5 -10
Aa{arcmin)
I'^igure 1.6: Contour map of the NII3 emission from TM C-1. The location of a star is
indicated. From Hirahara et al. (1992).
IIC3N .7=5-4 emission (H irahara et al. 1992). One can see th a t core B is the site of
t he peak in the NII3 emission, whilst the cyanopolyyne emission peaks at core D.
H irahara et al. (1992) have estim ated the densities of the various cores from single
dish observations of C^'^S (.7=1-0 and 2-1) and C2S (.7^ =4 3 - 8 2 and 2i -1q) emissions
and found ?7.(H2) ~4x 1 0'* cm"^, 2.4x10^ cm “^, and 4x10^ cm “^ in cores D, C and
B respectively. From interferornetric studies of core D using C2S emission, Langer
et al. (1995) found core D to be fragmented, with 77(H2) ranging from roughly 3 to
8 x1 0'* cm “ ^ in the largest fragments, to 1 0*^ cm~^ in the smallest.
An understanding of the chemical variations along TM C- 1 would lead to insight
into how TMC-1 has reached its present physical state and, more generally, into
dense core formation and evolution during the process of stellar birth. There are
several different ways in which the variations of the HC3N fractional abundance along
FMC-1 might have arisen. In Chapter 4 we examine in detail the many different
explanations for the observed chemical gradient along TM C- 1 and the assum ption
HC3 N J=5-4
( g
B e a m S i z e T J
(HPBW )
5 0
Aa(arcmin)
-5 -10
I’ igurc 1.7: C'oiitour map of IK^gN emission from TMCl-l. From llirahara et al. (1992).
'riien in (llia])tcr 5 we explore wliether it may be possible to observe molecular
nitrogen and oxygen in such regions, and thereby provide a direct measure of the
nitrogen and oxygen budgets in star forming regions and a limit on the theoretical
chemical models.
1.5
C ollap se o f d en se cores in region s o f low -m ass
star form ation
As described previously, dense cores are thought to be the im m ediate progenitors
of protostars, which has fueled efforts to detect signatures in molecular emission
line profiles of the collapse of such cores. In the search for evidence of collapse,
comparisons are normally made between line ])rohles from both optically thick and
1 hin lines. The o])tically thin lines probe higher density and tem perature regions and
as a residt are broadened (transitions between higher rotational levels are needed).
The o]M ically thin lines are symmetric and have a single peak. Therefore, such lines
Static E nvelope
Infall Region
+V
O b served Spectrum
Velocity
A ntenna
Figure 1.8: Collapse signatures: the formation of asymmetric, double-peaked, self
absorption line profiles in optically thick lines. From Rawlings (1996).
used to search for the infall signatures. The signatures th a t observers search for
are asym m etric, narrow and double-peaked line profiles. Figure 1.8 depicts how th e
characteristic infall signature is produced (Rawlings 1996). As the line is optically
thick we preferentially ’see’ emission from the parts of th e blue-shifted and red-
shifted hemispheres th a t are closest to us. In the red-shifted case, this emission
will be from th e outer p art of the infall region, which is cooler and has a low infall
velocity. However, the blue-shifted part of the emission comes from a m ore central
region of the infall, which will be moving faster th an th e outer regions, and will also
be denser and hotter; consequently this emission is brighter th a n th a t produced in
th e red-shifted hemisphere. The surrounding envelope of m aterial, which is static,
absorbs some of th e emission and hence a self-absorption dip at th e center of the
profile is produced.
The requirem ents to produce such asym m etric line profiles are th a t i) th e line
is optically thick in both hemispheres of emission; ii) a velocity gradient is present
th e core centre); iii) the observed species is also present in th e static outer envelope;
and iv) a positive tem p eratu re gradient towards the cloud centre exists.
O bservational detections of this sort of blue-red asym m etric self-absorption were
m ade for a num ber of clouds in CO emission line profiles by Snell & Loren (1976), b u t
these results were challenged by Leung & Brown (1977) who argued th a t th e infall
explanation for the origin of the asym m etric features was not unique. (Turbulence,
ro tatio n and outflows also produce double-peaked profiles. However, as described
by Zhou (1997), these motions should produce equal am ounts of blue-shifted and
red-shifted emission.) Walker et al. (1986) reported th e detection of infall in IRAS
16293-2422 using a CS emission line study. However, M enten et al. (1987) showed
th a t th e observed line profiles could be explained using a model in which the emission
from a rapidly rotating core undergoes foreground absorption.
In an a tte m p t to establish more thoroughly w hat th e characteristics of spectral
line profiles formed in collapse models are, Zhou (1992) perform ed radiative transfer
calculations based on simplifying approxim ations. One particu lar collapse model
th a t Zhou (1992) used is one studied analytically by Shu (1977). Shu (1977) showed
th a t an initially static, singular isotherm al sphere (w ith n ~ r “ ^) will undergo self
sim ilar collapse w ith the collapse wave propagating out from the centre where the
collapse velocity and the density are infinite. Collapse in which th e infall speed
decreases w ith radius and th e outer radius of the collapsing region, Tout, increases
w ith tim e has come to be known as “inside-out” collapse. C om putations like those
of Zhou (1992) and the more accurate M onte-Carlo calculations of Choi et al. (1995)
give results th a t imply th a t for cores undergoing inside-out collapse and in which
th e te m p eratu re decreases w ith radius:
1. optically thick lines show the blue-red self-absorption asym m etry,
2. for fixed angular resolution and equal optical depths th e w idth of a line of a
tran sitio n for which the critical density is large is greater th a n th e w idth of a
line of a transition for which the critical density is small,
3. th e self-absorption and linew idth of a line appear to increase w ith increasing
Table 1.4: Table of infall candidates.
Collapse Candidates Authors
B335 Zhou et al. (1993); Choi et al. (1995) CB3, CB54, CB244 Wang et al. (1995)
HR 25MMS, IRAS 20050 Gregersen et al. (1997)
IRAS 16293-2422 Walker et al. (1986); Zhou (1995); Mardones et al. (1997)
IRAS 03256+3055 Mardones et al. (1997)
IRAS 13036-7644 Lehtinen (1997); Mardones et al. (1997)
L483 Myers et al. (1995)
L1157 Gueth et al. (1997); Mardones et al. (1997) L1251 Myers et al. (1996); Mardones et al. (1997) L1527 Myers et al. (1995); Zhou et al. (1996)
L1544 Myers et al. (1996)
NGC 1333 IRAS 2 Ward-Thompson et al. (1996)
NGC 1333 IRAS 4A/4B Gregersen et al. (1997); Mardones et al. (1997) S6 8N Hurt et al. (1996); Mardones et al. (1997) Serpens SMM4 Hurt et al. (1996); Gregersen et al. (1997);
Mardones et al. (1997) Serpens SMM5 Mardones et al. (1997)
VLA 1623 Mardones et al. (1997)
WL22 Mardones et al. (1997)
W ith these three points in m ind, Zhou et al. (1993) dem onstrated th a t H2CO and
CS emission profiles (both are optically thick) originating in B335 show th e charac
teristic shapes associated w ith infall. B335 is a low-mass star forming core w ith an
em bedded 3 L@ infrared source and a collimated outflow. High resolution (3" to 5")
ap erture synthesis maps of and emissions also support th e hypothesis
th a t B335 is still undergoing collapse (Chandler & Sargent 1993).
In order to confirm these initial encouraging results th ere is a need to:
a) observe more molecules and transitions
b) consider the effects of the outflow on the profiles
c) detect outflows in more sources.
et al. (1994), Mardones et al. (1994), Myers et al. (1995), Velusamy et al. (1995),
Wang et al. (1995), Zhou et al. (1996), Myers et al. (1996), Gregersen et al. (1997)
and M ardones et al. (1997). Many new infall candidates have been discovered and
are listed in Table 1.4. The characteristic infall signatures have been observed in a
variety of m olecular lines: (2-1), C3H2 (2i,2-lo ,i), C2S (2 i-lo ), HCO+, ^^0 0
and HCN, besides H2CO and CS. However, point (b) is a difficult one to address be
cause it fu rth er complicates already sophisticated models. Myers et al. (1996) have
developed a simple analytic model of radiative transfer in which th e contribution
of outflowing gas to spectral line profiles from contracting clouds is also considered.
This model provides a simple way to quantify characteristic infall speeds, and its
use to in terp ret d a ta strongly suggests th a t the inward m otions derived from the
line profiles are gravitational in origin.
One way to avoid complications due to the presence of stellar outflows is to
observe starless cores which, presumably, do not have outflows. Some of these
objects m ay be collapsing, yet are starless due to insufficient developm ent tim e. To
d ate, only one starless core L1544 has shown evidence of infall asym m etry profiles
which strongly suggest infall motions (Myers et al. 1996; Tafalla et al. 1998). The
m easured linew idths in L1544 are extrem ely small (~0.3 km s“ ^) and im ply th a t
therm al pressure is playing an im p o rtan t role in th e dynamics. In addition, it is one
of the m ost opaque cores in the Taurus Molecular Cloud, suggesting th e presence of
high colum n densities. Myers and collaborators have therefore defined L I544 as the
m o s t evolved starless core. L1498 is another interesting starless core which shows
an intriguing double-peaked CS feature w ith th e blue peak stronger th a n th e red
peak (L em m eet al. 1995). However, L1498 has a com plicated physical and chemical
stru ctu re which hinders an easy interp retatio n of observational d a ta (see K uiper,
Langer & Velusamy 1996). Figure 1.9 shows th e shape of an NH3 emission line
feature arising in the dense core L1498 (Myers & Benson 1983). As th e source was
observed in two separate lines a tem p eratu re could be derived. The NH3 emission
profile shows very little deviation from th a t expected from a static core w ith very
subsonic turbulence. There are no broad wings like those th a t m ight be expected to
m agnetic effects are negligible, in the fastest (supersonically) infalling m aterial.
High sensitivity and high spectral resolution interferom etric observations are
providing a new window to the innerm ost p arts of low-mass star form ing cores,
and are helping to establish infall from outflow m otions (e.g. Ohashi et al. 1997).
Interferom eters are also needed to identify which p a rt of th e cloud is traced by
th e chosen m olecular species. For exam ple, C2S in B335 is tracing th e outer p arts
of th e collapsing envelope of the core (Velusamy et al. 1995), whereas H2CO and
CS emission is coming from deeper regions. A sim ilar result has been found from
high resolution observations toward L1498 (K uiper et al. 1996). This starless core
shows a chemically differentiated onion-shell stru ctu re, w ith the NH 3 in th e inner
and th e C2S in th e outer part of the core; the CS and C3H2 emission seems to lie
betw een these. The chemical and physical properties of L1498 have been in terp reted
by K uiper et al. in term s of a “slowly contracting” dense core in which th e outer
envelope is still growing.
LI498
0.075 KM S -' RESOLUTION
^ 0.8
H 0.6
> 0 .4
OBSERVED NH3 LINE
COLLAPSE 10 K 0.2
1.2.3 STATIC
10 K
0.0
-0.4 -0.2 0.0 0.2 0 .4
V L S R -< V L S R > (K M S * ')
Figure 1.9: The NH3 line profile of L1498. The curve associated with the dots is the observed profile. That marked static is the one expected from lOK gas th a t is not turbulent and experiences no systemic motion. The curve marked collapse is the profile expected if the fractional abundance of NH3 is constant and the core is undergoing collapse governed by a particular solution of the class th at Shu (1977) investigated. From Myers & Benson (1983).
Some questions arise
cloud core collapse:
1. How deeply in the core are infalling motions traced by H2CO and CS obser
vations? These are th e species used most for this kind of study.
2. How strongly do stellar outflows affect the abundance and th e excitation of
th e above molecular species?
3. W hy does NH3 not reveal infall signatures?
4. W hy do CS and C2S seem to trace “envelope” m aterial, even though they are
bo th high density tracers? They should trace densities higher th a n NH3 but
their emission seems to be external to am m onia emission.
5. W hat is happening to molecular m aterial in a region im m ediately surrounding
th e accreting young star, and can depletion onto grains occur in spite of the
proxim ity of a central source?
More high sensitivity and high resolution observations are required to answer
these questions, to b etter understand the physics of gravitational collapse in cloud
cores, and the chemical processes in star forming regions.
1.6
T h e o r e tic a l stu d ie s o f th e c h e m istr y o f d en se
core co lla p se in regions o f lo w -m a ss sta r for
m a tio n
Analysis of dense cores have revealed variations in th eir chemical com position and
these have effects on the profiles of lines observed to study core collapse. In order
to obtain th e m axim um inform ation from the profiles about th e dynam ics of core
collapse, the observed variations in chemical com position m ust be understood theo
retically so th a t their effects on the profiles can be reliably deconvolved from those
of th e dynamics.
As m entioned in the previous section, a key problem associated w ith dense
core observations is the absence of infall signatures in NH3 line profiles. M enten
is not observable in it. This suggestion was taken by Rawlings et al. (1992) to be
th e startin g point for a theoretical exam ination of chem istry in dense core collapse.
H artq u ist & W illiams (1989) argued th a t for some ranges of depletion, some species
should have gas phase fractional abundances th a t increase as depletion occurs (see
C h ap ter 4). Following these findings of H artquist & W illiams (1989), Rawlings
et al. (1992) a tte m p ted to identify gas phase species th a t have non-dim inishing or
at m ost slowly diminishing fractional abundances during some stages of depletion.
T he proposal by Rawlings et al. (1992) was th a t the lines of such species would be
th e m ost suitable ones to observe when attem p tin g to discover unam biguous spec
tra l signatures of ongoing collapse, such efforts having been unsuccessful up to th a t
tim e.
T he m odel of collapse adopted was th a t of th e inside-out collapse of a singular
isotherm al sphere due to Shu (1977), as described in 1.5. Rawlings et al. (1992) cal
culated tim e-varying profiles for optically thin lines of a num ber of species. T he line
profiles were calculated for angular resolutions obtainable w ith existing single dish
telescopes and for an object at the distance of L1498. Species found to have notice
ably broader line profiles th an NH3 included HCO, HNO, N2H"^, HCO"^, HS, CH and
H2S. For a num ber of these species the prim ary cause for their greater w idths was
th a t as depletion occurs the reduction of the high gas phase H2O fractional abun
dance (which was an artifact of the initial conditions used in th e model) decreases
th e ra te of th e prim ary removal mechanism of th e species itself or a species th a t is
a progenitor of it. It was concluded th a t the suggestion of M enten et al. (1984) is
plausible, and th a t the proposal may be further tested by study of th e line profiles
of th e additional species listed above.
U nfortunately, Rawlings et al. (1992) did not follow th e behaviour of CS. The
behaviour of th e sulphur depletion is a key unanswered question in star form ation.
Sulphur is observed to be practically undepleted in diffuse clouds, yet it is heavily
depleted in dense cores even when carbon, nitrogen and oxygen are not (Taylor
et al. 1996). It is not known w hether the depletion of S increases where C and 0
depletions are m ore substantial, but it is apparent th a t S depletes in a very different
detail and propose a potential mechanism to explain th e unusual behaviour of S.
Various models of the ways in which m agnetic fields and am bipolar diffusion
affect dense core collapse exist (e.g. Ciolek & Mouschovias 1995). It is som etim es
valuable to adopt a simple description of the dynamics or even assume a fixed den
sity to explore th e effects of depletions in models w ith varying initial conditions,
ra th e r th a n perform ing complex calculations for detailed dynam ical models. N ejad,
H artq u ist & W illiams (1994) studied the chemical evolution in a single parcel of gas
undergoing cycling in one cyclic model. Species found to have fractional abundances
increasing w ith tim e or at least rem aining fairly level w ith tim e included CH, OH,
C2H, H2CO, HCN, HNC and CN, for model tim es when some im p o rtan t TMC-1
fractional abundances were reasonably well m atched by the model fractional abun
dances. These species might be good candidates to observe in studies of infall, as
H2CO has, in fact, proven to be (Zhou et al. 1993). We investigate the dependences
of th e fractional abundances of a num ber of species on the selective depletions of
elem ental carbon, nitrogen, oxygen and sulphur, as well as m etals in C h ap ter 7.
1.7
S u m m ary
In th e previous sections we have outlined some fundam ental questions th a t inhibit
our understanding of the star form ation process. In the following chapters we ex
am ine these problems in detail.
In C hapter 2 we discuss further th e chem istry and physics of star form ing re
gions, and provide an introduction to the model which is employed in th e rem aining
chapters. We investigate th e initial support and collapse of translucent clum ps to
form dense cores in C hapter 3. In C hapter 4 we study th e effects th a t th e gas
grain interaction has on observable molecular species and the assum ption th a t cer
ta in types of molecules are indicative of a specific evolutionary epoch in a clouds
lifetim e.
In an a tte m p t to test the accuracy of the models th a t we use, we exam ine th e
feasibility of a novel proposal to observe molecular nitrogen in a dark, dense core
why is S observed to be much m ore depleted in dense cores th an carbon, nitrogen
and oxygen are? In C hapter 7 we investigate th e suitability of different m olecular
species for use in attem p ts to observe regions of infall.
Finally in C hapter 8 we sum m arise the results presented in the preceeding chap
ters and explore the future avenues of research th a t th e work presented here indi
C hapter 2
C h em istry and physics o f
collapsing interstellar clouds
In this chapter we provide an introduction to the chemical and dynam ical modelling
employed in this work. In section 2.1 we describe th e basic chemical reactions th a t
occur in both the gas phase and grain surface production schemes. Section 2 . 2
concerns th e relative abundances of the elem ents, values of which need to specified
in a model. In section 2.3 we exam ine th e chemical networks for a few selected
elem ents and in section 2.4 we discuss how the ionization stru ctu re is determ ined by
th e chemistry. We sum m arise the physics th a t is involved in th e m odel in section
2.5. Finally in section 2.6 we describe in detail th e m ethod of using th e m odel and
producing values for the evolution w ith tim e of th e abundances of species in the
model.
2.1
C h em ica l rea ctio n s
M any different models have been used in attem p ts to explain th e observed inter
stellar m olecular species and their abundances. There are two basic schemes for th e
form ation of molecules th a t have been established. The first scheme involves reac
tions taking place in the gas phase (Bates & Spitzer 1951; H erbst & K lem perer 1973;
Black & Dalgarno 1973), and the second involves reactions on interstellar grain sur
from recent observations of an increasing num ber of molecular species th a t both gas
phase and grain surface production of molecules m ust be included into models (e.g.
W illiam s & Taylor 1996; Crawford & W illiams 1997). We exam ine these different
schemes in turn.
2 .1 .1
G a s p h a se c h e m istr y
Molecules can be formed via ion-molecule or neutral-neutral reactions. The rates of
these reactions are given by k n ( X ) n { Y ) in cm~^ s“ ^, where k is th e reaction rate
coefficient (in cm^ s“ ^) and n is the num ber density of th e species (in cm “ ^). The
reactan ts X and Y could be any of th e following: atom s, molecules, atom ic ions or
m olecular ions.
Ion-molecule reactions are particularly effective in forming increasingly complex
species, and the reactions are rapid even at the low tem p eratu re conditions of in ter
stellar clouds. If the reaction is exotherm ic then from Langevin theory th e reaction
ra te coefficient will be independent of tem p eratu re, and will depend only on th e
reduced mass of th e system and the polarizability of th e molecule. R ate coefficients
for ion-molecule reactions are typically of the order of cm “ ^ s“ ^. However,
if th e molecule has a perm anent dipole (e.g. H2O), then the enhanced long range
a ttra c tio n leads to rate coefficients of between ten to a hundred tim es larger.
B oth an ion and a molecule are required to in itiate this chemistry. The starting
molecule is H2, and when H2 is present the effectiveness of ion-molecule chem istry is
directly related to the ion form ation rate. Ionization can be induced by ultraviolet
radiation or cosmic rays (cf. section 1.1).
Various loss mechanisms exist to hinder th e build up of complex species. These
include dissociative recom bination of molecular ions and radiative recom bination of
atom ic ions. B oth of these processes also control th e ionization level w ithin a cloud.
Photodissociation of molecules is another destructive mechanism . This last process
can be caused by photons from the background interstellar radiation field or by
photons which are generated as a result of cosmic ray ionization (see section 1.1).
N eutral-neutral reactions can also occur. N eutral exchanges are th e m ost im
