Eciency of the top-down PAH-to-fullerene conversion in UV irradiated environments

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MNRAS 000,1–19 (2022) Preprint 21 October 2022 Compiled using MNRAS L

X style ﬁle v3.0

Eﬃciency of the top-down PAH-to-fullerene conversion in

UV irradiated environments

M. S. Murga1,2?, V. V. Akimkin1, D. S. Wiebe1

1Institute of Astronomy, Russian Academy of Sciences, Pyatnitskaya str. 48, Moscow 119017, Russia,

2Faculty of Chemistry, Lomonosov Moscow State University, Universitetsky pr. 13, Moscow 119234, Russia

Accepted today. Received tomorrow; in original form 21 October 2022

ABSTRACT

Polycyclic aromatic hydrocarbons (PAHs) and fullerenes play a major role in the physics and chemistry of the in-

terstellar medium. Based on a number of recent experimental and theoretical investigations we developed a model

in which PAHs are subject to photo-dissociation (carbon and hydrogen loss) and hydrogenation. We take into ac-

count that dehydrogenated PAHs may fold into closed structures – fullerenes. Fullerenes, in their turn, can be also

hydrogenated, becoming fulleranes, and photo-dissociated, losing carbon and hydrogen atoms. The carbon loss leads

to shrinking of fullerene cages to smaller ones. We calculate the abundance of PAHs and fullerenes of diﬀerent sizes

and hydrogenation level depending on external conditions: the gas temperature, intensity of radiation ﬁeld, num-

ber density of hydrogen atoms, carbon atoms, and electrons. We highlight the conditions, which are favourable for

fullerene formation from PAHs, and we conclude that this mechanism works not only in H-poor environment but

also at modest values of hydrogen density up to 104cm−3. We found that fulleranes can be formed in the ISM,

although the fraction of carbon atoms locked in them can be maximum around 10−9. We applied our model to two

photo-dissociation regions, Orion Bar and NGC 7023. We compare our estimates of the fullerene abundance and

synthetic band intensities in these objects with the observations and conclude that our model gives good results for

the closest surroundings of ionising stars. We also demonstrate that additional fullerene formation channels should

operate along with UV-induced formation to explain abundance of fullerenes far from UV sources.

Key words: infrared: ISM – dust, extinction – ISM: dust, evolution – astrochemistry

1 INTRODUCTION

Observations reveal signiﬁcant abundances of aromatic

molecules in the interstellar medium (Allamandola et al.

1985;Giard et al. 1994;Peeters et al. 2002;Draine et al. 2007;

Galliano et al. 2008). Two most straightforward representa-

tives of these compounds are polycyclic aromatic hydrocar-

bons (PAHs) and fullerenes. While the interstellar infrared

(IR) spectra do contain characteristic features of aromatic

species, speciﬁc PAHs have not yet been identiﬁed in the in-

terstellar medium (ISM), existence of interstellar fullerenes,

C60, C+

60, and C70, was demonstrated by observations of the

pertinent IR emission bands at 17.4 and 18.9µm (Cami et al.

2010;Sellgren et al. 2010) and absorption bands at 9577 and

9632 ˚

A (Campbell et al. 2015). It is believed that large car-

bonaceous molecules such as PAHs and fullerenes are formed

in carbon-rich asymptotic giant branch stars (Frenklach &

Feigelson 1989;Cherchneﬀ 2011,2012). However, these par-

ticles evolve further as they travel through the ISM, due

to ultraviolet (UV) irradiation, bombardment of highly en-

ergetic particles, etc., and their abundances change accord-

ingly (Hony et al. 2001;Galliano et al. 2008;Micelotta et al.

?E-mail: murga@inasan.ru

2010a;Boersma et al. 2012;Castellanos et al. 2014;Murga

et al. 2022) along with their ionisation state and molecular

structure (Allamandola et al. 1999;Montillaud et al. 2013;

Andrews et al. 2016;Peeters et al. 2017;Sidhu et al. 2022).

One of the major factors in the carbonaceous particle evo-

lution is their interaction with UV radiation. PAHs undergo

photo-processing in the diﬀuse ISM and photo-dissociation

regions (PDRs). In spite of their stability, they can lose hy-

drogen atoms and edged carbon atoms after absorption of a

UV photon (Jochims et al. 1994;Allain et al. 1996;Le Page

et al. 2001). In a reverse process, hydrogen atoms can be re-

attached (Rauls & Hornekær 2008;Goumans 2011). Thus,

PAH size and hydrogenation states are determined mainly

by two factors, which are intensity of UV radiation ﬁeld and

H atom number density. It is believed that the diﬀuse ISM

is mostly populated by compact PAHs with number of car-

bon atoms (NC) from ≈30 to 150, while the mean size of

PAHs increases closer to a UV radiation source (Andrews

et al. 2015;Croiset et al. 2016;Murga et al. 2022;Knight

et al. 2021). According to Montillaud et al. (2013); Andrews

et al. (2016), small PAHs (NC.50) are mostly dehydro-

genated in PDRs, medium-sized PAHs (50 .NC.90) can

be dehydrogenated under certain conditions, and larger PAHs

(NC&90) do not lose their hydrogen atoms and can even be

arXiv:2210.11156v1 [astro-ph.GA] 20 Oct 2022

2M. S. Murga et al.

super-hydrogenated. Until PAHs have lost all their hydrogen

atoms, the dissociation channel of H loss is more preferable

after photon absorption because the binding energy of C-H

bonds is smaller than that of C-C bonds. Once PAHs have

become dehydrogenated, they start losing carbon atoms. Car-

bon loss may lead to formation of defective pentagon rings,

bending of the molecule plane, and subsequent formation of

fullerenes (Chuvilin et al. 2010;Bern´e & Tielens 2012;Zhen

et al. 2014). Discovery of fullerenes and their relation with

PAHs in PDRs indicate that this process (‘top-down’ for-

mation) does occur in objects with enhanced UV radiation

ﬁeld (Castellanos et al. 2014;Bern´e et al. 2015). The top-

down fullerene formation from other carbonaceous grains is

also possible (Garc´ıa-Hern´andez et al. 2011;Micelotta et al.

2012).

Once formed, fullerenes can undergo the same evolution-

ary processes as PAHs, i.e. photo-dissociation and hydro-

genation. Activation energies of fullerenes are quite high

(≈7−11 eV (G luch et al. 2004)), where the highest en-

ergy belongs to C60. Therefore, their destruction is not ex-

pected to be eﬃcient except in the closest vicinity of UV

sources. The carbon loss likely leads to shrinking of cages

as it was described in Bern´e et al. (2015). Fullerenes were

shown to be highly reactive with hydrogen (Petrie et al.

1995), hence appearance of hydrogenated fullerenes (so-called

fulleranes) can be expected in the ISM. Fulleranes were sug-

gested to be possible carries of the emission bands near

3.5 µm (Webster 1992), anomalous microwave emission in

molecular clouds (Iglesias-Groth 2005,2006), the UV bump

at 2175 ˚

A and also diﬀuse interstellar bands (Iglesias-Groth

2004). Therefore, fulleranes are being searched both in the

ISM and in meteorites. In spite of their potential importance,

there are no conﬁdent detections of fulleranes, unlike pure

fullerenes, although some ﬁngerprints may indicate on their

presence (Heymann 1997;Palot´as et al. 2020;Sabbah et al.

2022).

To estimate abundance of diﬀerent fullerenes in a UV-

dominated environment, a detailed modelling is required that

includes all relevant evolutionary processes both for PAHs

and fullerenes. Bern´e et al. (2015) presented photo-chemical

evolutionary model of PAHs and fullerenes and estimated

abundance of C60 in the PDR NGC 7023. In this work,

we extend the model setup of Bern´e et al. (2015) by tak-

ing into account processes of hydrogenation and dehydro-

genation, adding C70, and calculating the ionisation state of

fullerenes. Our goal is to establish the range of conditions

favourable to fullerene formation from PAHs subject to UV

irradiation, and to check whether PAH dissociation is a suf-

ﬁcient source of fullerenes in objects with the enhanced UV

radiation.

2 MODEL OF EVOLUTION OF PAHS AND

FULLERENES

To describe the evolution of PAHs and fullerenes, we use the

system of kinetic equations similar to the one utilised in the

Shiva model (Murga et al. 2019) with modiﬁcations relevant

to the current task. Modiﬁcations regarding hydrogenation

and dissociation of super-hydrogenated PAHs have been al-

ready described in Murga et al. (2020,2022). In this work we

expand our model and consider isomerization of PAHs and

subsequent fullerene formation. Overall, the following pro-

cesses are included: photo-dissociation (C and H loss) and

hydrogenation of PAHs, bending of dehydrogenated PAHs

and folding into fullerene-like cages, photo-dissociation and

hydrogenation of fullerene cages. Schematically, the model is

illustrated in Fig. 1. Detailed information about the processes

is given below. Here we brieﬂy describe the main aspects of

the model. Three basic classes of molecules are considered:

PAHs, bowl-shaped PAHs (bPAHs), and fullerenes. PAHs

are subdivided into regular PAHs, dehydrogenated PAHs

(dPAHs), and super-hydrogenated PAHs (HPAHs). dPAHs

are produced from PAHs by H atom loss due to photo-

dissociation. Further, they transform to bPAHs and then to

fullerenes with some probability or undergo skeleton dissoci-

ation, remaining in the PAHs category. For technical conve-

nience, we describe bPAHs by equations separate from PAHs.

There are separate equations for fullerenes as well.

We consider an initial set of PAHs consisting of Nm=

15 molecules: C24H12, C32H14, C40H16, C48H18, C66H20,

C78H22, C96H24, C110H26, C130H28, C150H30, C170H32,

C190H34, C210H36, C294H42, C384H48. The set is supposed to

cover the whole range of PAH sizes, but is not meant to rep-

resent any speciﬁc family of PAHs. To describe evolution of

the PAHs in mathematical terms, we deﬁne PAH size bins by

the number of carbon atoms (NC, index i) and by the num-

ber of hydrogen atoms (NH, index j). In other terms, the bins

are determined by total mass of carbon and hydrogen atoms

in the molecule (miand mH

ij , correspondingly). The number

density of PAHs in each bin with corresponding miand mH

is designated as Nij . The scheme illustrating the considered

molecules and corresponding bins is presented in Fig. 2.

PAHs undergo evolutionary migration from a bin to a bin,

changing their carbon and hydrogen masses. The centres of

carbon mass bins correspond to the masses of carbon atoms

in molecules listed above. Hydrogenation or dehydrogena-

tion of PAHs preserves their iindex, while changing j. In

other words, the fraction of hydrogen atoms relative to car-

bon atoms (XH

ij ) varies. We designate the ratio of NHto NC

in the initial set as XH

ij,0. The range of hydrogen mass in

PAHs is divided into NHm = 5 bins. All the PAHs from the

initial set fall into bins with j= 3. The bins with j= 1,2

have XH

ij equal to (1/3XH

ij,0,2/3XH

ij,0). The bins with j= 4,5

have XH

ij equal to (1.5XH

ij,0,2XH

ij,0). Values of mH

ij are calcu-

lated from XH

ij . Borders of the bins by carbon and hydrogen

mass are designated as mb

iand mHb

ij , respectively, and are de-

ﬁned as the average values between miof neighbouring bins

with i−1 and i+ 1 in case of carbon and mH

ij of neighbour-

ing bins with i, j −1 and i, j + 1 in case of hydrogen. The

lower bounds mb

0and mHb

i0are zero. The upper bounds mb

and mb

NHm are determined as mNm+ (mNm−mNm−1/2) and

iNHm + (mH

iNHm −mH

iNHm−1/2). The initial number density

is calculated as dn/dm(mb

i+1 −mb

i) with the mass distribu-

tion dn/dm taken from Weingartner & Draine (2001b) (here-

inafter WD01).

We consider fullerene formation as a two step process.

First, some dPAHs can start to bend and turn to bPAHs pop-

ulation. Second, bPAHs can further lose their carbon atoms

completing the folding into fullerenes. The number density

of bPAHs is designated as Nb

k. In total, we consider Nb= 7

bPAHs (kfrom 1 to 7): C62, C64, C66, C72, C74 , C76, C78.

We assume that only dPAHs C66 and C78 (i= 5 and 6) can

MNRAS 000,1–19 (2022)

Fullerene evolution in the ISM 3

hν

e−H

IR photon

+/-

PAH - C2H2

C+

HPAHs

hν

C+

e−

dPAHs

dPAH - C2

+/- .C2

Fulleranes

photon

bPAHs

Figure 1. Schematic illustration of our model with all the considered processes.

turn to bPAHs population (with k= 3 and 7, correspond-

ingly). Certainly any dPAHs can undergo bending, but we

do not consider them as we focus only on formation chan-

nels of fullerenes C60 and C70 and their respective bPAHs

pre-cursors. Carbon loss in C66 and C78 leads to ﬁlling of the

bins with k= 1,2 and k= 4,5,6, correspondingly. Note that

not all dPAHs from i= 5,6 bins turn to bPAHs. Some of

them can undergo fragmentation without bending and stay

in dPAHs population.

The number density of fullerenes is designated as Nful

lp . We

consider Nful = 7 fullerene molecules: C58, C60, C62, C64,

C66, C68, C70. The index lpoints to the cage size. The index p

indicates the number of attached hydrogen atoms. The index

varies from 1 to NHm,ful = 10, thus, the fullerenes can be

hydrogenated and have up to nine hydrogen atoms1. When

bPAHs C62 and C72 (k= 1 and 4) lose their C2they transit to

1Certainly the more number of hydrogen can be attached to

fullerenes. However, we limited the number by 9 atoms, hence we

have 10 equations corresponding to diﬀerent hydrogenation state

of each fullerene. The more number of equations, the more model

becomes time-consuming. Looking ahead we can conclude that

this limitation does not aﬀect the ﬁnal results as fullerenes can

be hardly hydrogenated up to 9 atoms, especially more than that.

So, we suppose that our limitation is justiﬁed.

fullerene bins with l= 2 and 7, respectively, herewith p= 1.

As the evolution goes, fullerene bins with l= 1,3−6 can be

populated.

MNRAS 000,1–19 (2022)

4M. S. Murga et al.

C atom grid, i =1..15

initial

H/C ratio grid

j = 1..5

С22 С384 dPAHs

HPAHs

C2 loss

H loss/gain

С66 С78

fullerenes

С66 С72 С74 С76 С78

С64

С62

... ... ...

С62 С64 С66 С68 С70

С60

С58

bowl-shaped

PAHs

k = 1..7

H atom number

p = 1..10

bending

C2 loss & folding

С32 С40 С48 С96 С110 С130 С150 С170 С190 С210 С294

C atom grid, l = 1..7

fulleranes

Figure 2. Considered populations of PAHs, bowl-shaped PAHs and fullerenes and involved evolutionary processes – C2loss,

(de)hydrogenization, dPAHs bending, C2-loss-induced fullerene folding.

The system of kinetic equations for Nij ,Nb

kand Nful

lp is











dNij

dt =A(1)

ij+1Nij+1 −A(1)

ij Nij

| {z }

H loss due to photo-dissociation

+Bi+1jNi+1j−Bij Nij

| {z }

C loss due to photo-dissociation

+A(2)

ij−1Nij−1−A(2)

ij Nij

| {z }

H addition to PAHs

−X

IijkNij

| {z }

transition to bPAHs

dNb

dt =P

IijkNij +Bk+1Nb

k+1 −BkNb

| {z }

C loss due to photo-dissociation

dNful

dt =X

FklpNb

| {z }

transition to fullerenes

+A(1)

lp+1Nful

lp+1 −A(1)

lp Nful

| {z }

H loss due to photo-dissociation

+Bl+1Nful

l+1p−BlNful

| {z }

C loss due to photo-dissociation

+A(2)

lp−1Nful

lp−1−A(2)

lp Nful

| {z }

H addition to fullerene cages

(1)

where A(1,2)

index and Bindex are rate coeﬃcients of change the H

and C mass, respectively, for the bins with indices ij,kor

lp depending on a molecule type, Iijk is the rate coeﬃcient

of transition of ijth PAH bin into the kth bin of bPAHs due

to PAH sheet bending, and Fklp is the rate coeﬃcient of the

transition of the kth bin of bPAHs to the lpth fullerene bin.

The expressions for A(1,2)

ij and Bij and their boundary val-

ues were given in Murga et al. (2020,2022) (Eqs. 2, 4 and

related Eqs. 3, 5, 6). The same expressions are used in this

work although here we also calculate rates for bPAHs (in-

dices k) and fullerenes (lp) instead of PAHs and indices ij.

The calculations for all molecules are similar with only diﬀer-

ence in parameters of reactions. The generalised expression

for A(1,2)

index is

A(1,2)

index =ε(1,2)

index

∆mH

index

,(2)

where ε(1,2)

index is the rate of H mass change, ∆mH

index is the

H mass interval of the bin which is mHb

ij+1 −mHb

ij for PAHs,

and mHfor fullerenes. A(1)

index is set 0 if j= 1 or j>NHm

and if p= 1 or p>NHm,ful.A(2)

index is set 0 if j>NHm or

MNRAS 000,1–19 (2022)

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MNRAS000,1{19(2022)Preprint21October2022CompiledusingMNRASLATEXstylelev3.0Eciencyofthetop-downPAH-to-fullereneconversioninUVirradiatedenvironmentsM.S.Murga1;2?,V.V.Akimkin1,D.S.Wiebe11InstituteofAstronomy,RussianAcademyofSciences,Pyatnitskayastr.48,Moscow119017,Russia,2FacultyofChemistry,Lomonosov...

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Eciency of the top-down PAH-to-fullerene conversion in UV irradiated environments

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