Summary of the relevant theory of molecular spectroscopy

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Chapter 2 Organic molecules in space

What’s between stars, is there just a vacuum? Since quite long ago, people have been asking this question. At the end of the 18th century, the British astrophysicist William Herschel noticed the diffuse nebula between stars, and believed the dark “holes” and “cracks” in the Galaxy were the faint or very faint nebula which block visible light from stars (Xiang 2008, chap. 5; Herschel 1864). But this idea wasn’t widely accepted until the 1930s by the observation and analysis of molecular absorption spectra from space. These nebula are mainly the assemblies of interstellar gas with a density of more than 10 atoms (or ions, molecules) per cubic centimeter. Other than the interstellar gas, astrophysicists have also shown the presence of tiny solid dust particles between the stars. The gas and dust make up the interstellar medium (ISM), or in a simpler way, the ISM is the matter between the stars. The mass of the ISM accounts for nearly 10% of the total visible matter in the Galaxy, the density of the ISM can be 10-20 – 10-25 g/cm3. On average, the density is 10-24 g/cm3, equivalent to only 1 hydrogen atom per cubic centimeter, a much better vacuum than any that can be created in a laboratory on the Earth, whose value is about 32000 atoms per cubic centimeter. Nevertheless, the ISM plays a central role in the evolution of the Galaxy because it is made up of atoms created by nucleosynthesis in the previous generations of stars and also serves as the birthplace of future generations of stars in dense ISM regions (Tielens 2005, chap. 1). During the evolution of the Galaxy, chemical and physical processes can generate a suite of fundamental organic (i.e., carbon-based) molecules needed as modules for the synthesis of more complex organic matter allowing for an organization into “life” (Rehder 2011, chap. 7).

Interstellar medium and star formation

As stated above, the ISM can be characterized as interstellar gas and solid interstellar particles (called interstellar dust). If we take a more general definition, energy fields such as cosmic rays, the interstellar magnetic field and starlight, with a typical energy density of about 0.5 eV/cm3 could be incorporated as well, however they are not our main consideration here.
The gas and dust is visibly present as different objects of the ISM, for example: HII regions, reflection nebulae, dark clouds and supernova remnants. From the physical properties, the gas in the ISM is organized in different phases, which vary largely in density and temperature (as summarized in Table 2.1). Molecular gas appears in molecular clouds which are the densest parts of the ISM and surrounded by less dense envelopes of atomic gas. In the Milky Way, molecular clouds are mostly in the galactic plane, especially in galactic spiral arms, where numerous young stars can be found. The interstellar dust has a size distribution of roughly a power law, with an exponent of -3.5 (Tielens 2005, chap. 1). It plays an important role in astronomy, especially observational astronomy because of its emission spectrum providing an indicator of physical conditions and its radiated power bearing witness to populations of obscured stars of which we might otherwise be unaware (Draine 2011, chap. 21).

Interstellar gas

In the Milky Way, the mass of ISM is found to be 99% in gas phase and 1% in dust, a ratio often referred as gas-to-dust ratio. The interstellar gas is composed principally of hydrogen and helium which can be divided into neutral atomic gas, ionized gas, molecular gas (including radicals) and coronal gas.
The atomic gas appears in two phases in thermal equilibrium: cold (~ 80 K) and dense (~ 50 cm-3) known as “Cold Neutral Medium, CNM” or warm (~ 8000 K) and diffuse (~ 0.5 cm-3) known as “Warm Neutral Medium, WNM”, proposed by (Field et al. 1969). The CNM could be also called HI regions, as hydrogen atoms in their ground state take the greatest majority. Astrophysicists use the 21 cm emission lines to observe hydrogen atoms from HI regions, through which the distribution of these regions can be mapped. 21 cm emission lines are transitions within the hyperfine structure of hydrogen atoms which are mainly caused by atomic collisions. The transition can hardly be observed because of too low transition probability on the Earth; however, large amounts of hydrogen atoms in these regions in space make the sum of this forbidden line non-negligible and also the dust is transparent to such a wavelength, hence the transition radiation is observable.
The ionized gas mainly gathers as two components in the Milky Way and other disk galaxies: HII regions and “Warm Ionized Medium, WIM”. The profiles of Hα emission of Balmer series (a specific line with a wavelength of 656.28 nm in air, occurring when a hydrogen electron falls from its third to second lowest energy level) distinguish the two components (detailed information, can for example refer to Madsen et al. 2006). Compared with HI regions, HII regions are closer to the central hot stars, with more energy for the ionization. HII regions have a temperature of about 104 K, and the densities range from 103 – 104 cm-3 for compact ones such as the Orion Nebula to ~ 10 cm-3 for more diffuse and extended nebulae such as the North America Nebula. HII regions are formed by young massive stars which emit copious amounts of photons beyond the Lyman limit (hν > 13.6 eV) ionize and heat their surrounding, nascent molecular clouds. Therefore, HII regions are signposts of sites of massive star formation in the Galaxy. The WIM is a diffuse (~ 0.1 cm-3), warm (~ 8000 K) component containing almost all the mass of the ionized gas. The source of ionization is not entirely clear; for the observations and models of the WIM readers can refer to for example the review (Haffner et al. 2009). Additionally, photo-ionized gas is also found in distinctive structures called planetary nebulae. When the central star experiences mass loss during its late stages of evolution, the radiation from this exposed core photo-ionizes the outflowing gas, exciting atoms besides hydrogen that can then emit radiation which contribute to colorful and magnificent views of the universe.
(McKee and Ostriker. 1977) extended the two-phase model (CNM and WNM) to a three-phase model by considering the contribution of stellar winds from early type stars or supernova explosions, the energy of which maintains a hot (~ 106 K) and rarefied (~ 10-3 cm -3) medium known as “Hot Intercloud Medium, HIM”. The hot gas can be traced through UV absorption lines and continuum or line radiation in the extreme ultraviolet and X-ray wavelength regions. The high-energy gas may have been vented by super bubbles created by the central star into the halo in the form of a galactic fountain, therefore, the gas is called “coronal gas”.
The CO 2.6 mm emission is commonly used as a tracer of molecular gas in the Galaxy, however H2 is thought to be the dominant molecular species, with a H2/CO ratio of 104 – 105 in mass. Much of the molecular gas in the Milky Way is localized in discrete Giant Molecular Clouds (GMCS), mixtures of numerous dust and gas particles with a mass of approximately 103 to 107 times the mass of the Sun. The temperature of GMCS is as low as about 10 K, in a diameter of 15 to 600 light-years. We have already identified thousands of GMCS in the Milky Way, and most of them are located in the spiral arms. Molecular clouds are characterized by high turbulent pressures as indicated by the large linewidths of emission lines. Molecular clouds are self-gravitating rather than in pressure equilibrium with other phases in the ISM. While they are stable over time scales of about 107 years, presumably because of a balance of thermal pressure, magnetic field, turbulence and gravity, molecular clouds are the sites of active star formation. Observation of molecular clouds through the rotational transitions of a variety of species allow a detailed study of their physical and chemical properties. Presently, some 200 different molecular species have been detected, mainly through their rotational transitions in the millimeter/submillimeter wavelength regions. Normal-propyl cyanide, is one of the largest molecules among these species, and our research is carried out under such a background.

Interstellar dust

The total mass of interstellar dust makes up only a small percentage of the whole ISM (~ 1%). Generally, interstellar dust has a broad size distribution, extending through some 0.01 – 0.2 μm (Draine 2011, chap. 21) and comprises 20 – 100 atoms. The composition can be classified as:
1. Solid-state H2O, CH4, NH3 for example; 2. minerals such as SiO2, Fe2O3 and FeS; 3. small graphite grains. Larger particles may have particular structures: their cores may consist of silicide or carbide, surrounded by layers of mantles.
Interstellar dust has very significant effects on optical observations including interstellar extinction and reddening. Extinction, or wavelength-dependent attenuation, comes from the dust’s absorption and scattering of starlight, so that the stars look darker. According to the Rayleigh scattering law, light with a longer wavelength has a smaller scattering and absorption cross section than shorter wavelengths, so red light can transmit more. Interstellar dust is very significant in the formation and conservation of molecules: it provides an appropriate site for their formation and plays a role of catalyst to accelerate reactions. Dust extinction prevents stellar radiation from penetrating dense clouds so that molecules are protected against photo-dissociation and are enriched in the dense clouds (Elmegreen 1985, 1993). Besides the chemical functions, dust also plays many critical roles physically in galactic evolution, as it adjusts temperature of surrounding gas, communicates radiation pressure from starlight to the gas and couples magnetic field to the gas in regions of low fractional ionization.
It should be noted that, there exists a population of large molecules in the ISM. Broad infrared emission at mid-IR wavelengths is attributed to the presence of polycyclic aromatic hydrocarbons (PAH). Besides PAH, different large molecules with 10 – 50 carbon atoms are proved by prominent absorption features in visible spectra and seem to represent the extension of the interstellar gain size distribution into the molecular domain.
Concerning the evolution of interstellar dust, there is no universal dust model that can be applied to a galaxy as a whole, or to galaxies with different evolutionary histories. However, several well-distinguished populations can be listed as stellar outflow dust, dust in the diffuse ISM, dust in dense cool clouds and circumstellar dust around young stellar objects. These different populations provide special environments for the formation and/or decisively modification of interstellar dust. Several detailed aspects can be found in the review (Dorschner & Henning 1995), however, the interstellar dust here is not limited to those only in diffuse ISM.

Star formation and interstellar molecules

Most of the star formation in galaxies occurs in dense interstellar gas at spiral arms, which are marked primarily by their concentrations of luminous young stars and associated glowing clouds of ionized gas. Stars also form near the centers of some galaxies, but this center-area star formation is often obscured by interstellar dust and its existence is inferred only from the infrared radiation emitted by dust heated by the embedded young stars. The gas from which stars form, whether in spiral arms or in galactic nuclei, is concentrated in massive and dense molecular clouds. The internal structure and also the irregular boundaries of molecular clouds favor fractal models resembling these surfaces supported in turbulent flows, and this suggests that the shapes of molecular clouds may be created by turbulence.
When we say star formation, a traditional classifications should be followed: low-mass star formation and high-mass star formation. The distinction between the two is whether the time taken in the formation is respectively smaller than or larger than the star’s future life. Many stars are smaller than 8 solar masses, and can be broadly classified as low-mass. Low-mass stars form from the collapse of prestellar cores, which are denser, gravitationally bound gas globules in the molecular clouds. These cores typically have a density of 104 – 10 5 cm-3 (around 105 times the average density of the entire GMC), and a temperature as low as 10 K. The thermal coupling effect by interstellar dust, because of its strongly temperature-dependent thermal emission, maintains its low temperature over a quite wide range of densities. The low-temperature and high-density make the thermal pressure of the cores small. Therefore self-gravity, which is the gravitational force allowing a body or a group of bodies to be held together, dominates over the thermal pressure by a large factor. However the thermal pressure is not the only force opposing gravity, there is a widely held view that additional effects such as turbulence or magnetic fields support these clouds in near-equilibrium against gravity and prevent a rapid collapse and the collapse of prestellar cores in this view is a dynamic process rather than a quasi-static fashion. For high-mass stars, it is not clear whether the prestellar stage exists or not: their formation from either prestellar mergers or accretion were explored and contrasted in (Bally & Zinnecker, 2005); the high-mass analogs of prestellar dense cores were not discovered toward Cygnus X supporting a short statistical prestellar lifetime (Motte et al. 2007)).
Very few GMCs are known that are not forming stars, and the most massive and dense ones all contain newly formed stars. Therefore, the lifetime of a molecular cloud can be estimated by the age span of the associated young stars and clusters, which is never more than 107 years, a timescale of a stable GMC. On the other hand, stars and clusters older than 107 years no longer have any associated molecular gas. In this way, molecular clouds can be considered “short-lived” (on the scale of the universe) and are soon destroyed or become no longer recognizable. The chemistry of molecules in the clouds also suggests the short life time of the latter, since the observed abundances of various molecules are far from chemical equilibrium in the cloud-evolution stage (van Dishoeck & Blake 1998; Brünken et al. 2014). The fragmentation of molecular clouds to form denser clumps and cloud cores could be regarded as the starting line for star formation. The process leading to a hierarchy of clumps of various size may be caused by density fluctuations in molecular clouds that are amplified by their self-gravity and supersonic turbulent motions that compress the gas in shocks.
Then the collapse of prestellar cloud cores occurs. The collapse is not fully understood, however, two kinds of models have been widely studied to illustrate how the collapse of a spherical cloud core might be initiated. One possibility is a continuation on the fragmentation model of self-gravity that the collapse begins with an unstable or marginally stable clump of gas in which gravity prevails the thermal pressure and causes a collapse. The second model is based on the assumption that prestellar cores are initially magnetically supported and condense gradually by ambipolar diffusion, whereby the gas contracts slowly across the field lines. No matter which model or their combined effects, a major consensus is that only a very small fraction of the mass of a collapsing cloud core first attains densities high enough to form a star, while most of the mass remains behind in an extended infalling envelope. Most star-forming cloud cores are observed to be rotating, arising from the turbulence in molecular clouds. Therefore rotation plays an important role as angular momentum in the whole process should be conserved. However the observed angular momentum of prestellar cores is about three orders of magnitude more than can be contained in a single star. Thus, in most cases, collapse with rotation probably results in the formation of a binary or multiple system of stars whose orbital motions can account for much of the initial angular momentum. During the collapse, the thermal pressure counters gravity to control the development of the very central denser region. The evolution of thermal pressure continues until the central region possesses optical depth large enough, opaque in another word, to weaken the radiative cooling substantially. Therefore the prestellar core evolves from the initial isothermal phase to an adiabatic phase when the central temperature rises rapidly and pressure grows faster than gravity to retard the collapse until it is completely adiabatic. Thus an embryonic star or “protostar” forms with characteristics of the central region in the form of hydrostatic equilibrium which consists mostly of molecular hydrogen. This is the first hydrostatic core which continues to grow in mass as matter continues to fall onto it through accretion. The first hydrostatic core is pressure supported which is a transient feature. Then a second phase collapse begins and the central temperature rises above 2000 K, causing hydrogen molecules to dissociate. The dissociation leads to the decrease of the ratio of specific heats in the center, therefore, the temperature climbs sharply and the central density peak again quickly grows. The central temperature which is high enough to ionize the central hydrogen halts the rapid collapse and this gives birth to a second hydrostatic core bounded again by an accretion shock into which matter continues to fall. At first the matter falling onto the newborn core is still optically thick and the shock is therefore adiabatic, which strongly heats the outer layers of the protostar. After the material of the first hydrostatic core has been accreted, the opacity of the matter outside the second core drops rapidly and radiation begins to escape freely. This radiative energy loss stops the protostar’s expanding and it subsequently maintains an almost constant radius of about 4 solar radiuses during the remainder of the accretion process. During accretion, most protostars also drive powerful jet-like bipolar outflows which may rise from the rotation and magnetic fields working on the gravitational energy of the matter accreted. Once enough mass in dynamic equilibrium, the accretion process ceases to be important.
Newly formed low-mass stars have similar radii when accretion becomes unimportant. This radius hence represents the “birthline” or the moment when the star is considered to be born. The star is then stable for a time and called a normal pre-main sequence star which has a convective envelope. This phase is also the first time they are visibly observable after emerging from their birth clouds. Then, stars get their luminosity from gravitational contraction. This is the Kelvin-Helmholz contraction, which comes from the cool surface of the early star causing unbalance between the thermal pressure and its gravity. The contraction lasts a few tens of millions of years until the star becomes hot enough at its center to start nuclear fusion reactions. The star then becomes a long-lived main-sequence star in the Hertzsprung-Russell diagram (Larson 2003; McKee & Ostriker 2007).
The research on molecular lines has shown their importance in relation to star-formation theory. Some cases can be considered. As discussed above, supersonic turbulence may play a role in structuring molecular clouds, and therefore influence their fragmentation. Through molecular lines, “size-linewidth relations” have been proposed, such as (Goodman et al 1998) tested the conclusion that dense cores represent the inner scales of a molecular cloud by measurements of the emission of OH, C18O, 12CO, 13CO and NH3 after a previous publication (Barranco & Goodman 1998) in which the method was detailed. (Myers 1999) also gave examples of easily observable molecular lines to define dense cores and cores with lesser density. Some publications reported the detection of rotational transitions of some specific molecule or molecular family, with which, the age of their environments could be derived and also the duration for such a phase in star evolution. An example is (Stahler 1984), in which, the author used cyanopolyynes (HC2k + 1N, k = 0, 1, 2…) to probe the ages of four dark molecular clouds and deducted they are either in a state of hydrostatic balance or have only recently begun to collapse. (Suzuki et al. 1992) proposed the abundance ratio of CCS/NH3 as a possible indicator of cloud evolution and star formation by systematical study of the molecular rotational lines toward 49 dark cloud cores. The ratio can be reproduced quantitatively in models that start from diffuse gas and from dense cores over a period of 105 to 2 ×106 years. An important role that molecules play in star formation is the dissipation of energy by their radiation because the small energy differences between states (mainly vibrational and rotational) leads to a long wavelength, which can benefit the energy loss through clouds. This method is also applied for detection of highly obscured objects. (Giannini et al. 2001) found that the pure rotational lines of abundant molecules (CO, H2O, OH and [O I]) arise from small, warm and dense regions compressed after passage of shocks in Class 0 sources, the youngest protostars in the sequence, with dominant submillimeter continuum emission in the spectra observed. In addition, they tested the total far-infrared line cooling (luminosity) which is roughly equal to the outflow kinetic luminosity demonstrating the radiation lines a valid measure of the power deposited in the outflow. A widely used model to explain the radiative cooling of warm gas by rotational and vibrational transitions of H2O, CO and H2 is NK93 published in (Neufeld & Kaufman 1993). The authors derived the cooling rate for each molecule as function of temperature, density and an optical depth parameter. With this model, they concluded H2O rotational transitions are found to dominate in different regions with realistic astrophysical conditions. The model was updated by (Morris et al. 2009) to study the relation of cooling rate and dust grains. Finally they obtained the cooling mechanism by H2O emission in the nebular shocked region in protoplanetary disks. In addition to the fact that the density distribution has been well modeled in prestellar cores (Bacmann et al. 2000), the observed abundances of molecules by line emission can also be used to probe physical dynamics and chemical kinetics in these regions. (Aikawa et al. 2003) found that various molecular column densities of L1544 (a prestellar core) could be consistent with those predicted for rapidly collapsing cores, but not the strongly delayed one by magnetic or other effects as we discussed in the prestellar collapsing model.
Another aspect of the research on interstellar molecules is to understand the routes that lead to their synthesis and to follow the evolution of nebulae and related celestial bodies based on the abundance of these molecules. The number of different interstellar molecules, their isotopologues and vibrational states is very large (a constantly updated list of detected molecules can be found at http://www.astro.uni-koeln.de/cdms/molecules); the environments they are located and formed in are various, and therefore, the reactions between interstellar molecules are complex. A very interesting question may be, how the first molecule formed. When the universe cooled down to about 4000 K, electrons and nuclei began binding to form neutral hydrogen atoms, and then gave rise to the decoupling between matter and radiation. The first molecules in space were hydrogen molecules. Other surplus ions and electrons facilitated the molecular formation through two possible mechanisms as 2.1 and 2.2. It is the case in the recombination epoch but not the present situation, in which the gas phase hydrogen molecules are efficiently formed on interstellar dust and then evaporated into the space. Hydrogen molecules can efficiently dissipate energy for primordial gas through ro-vibrational lines, therefore they played important roles to form the first-generation stars (Abel et al. 2002).

Interstellar organic molecules and possible links with the origin of life

What is the origin of life, when and how did life begin? These three fascinating questions have for a long time encouraged scientists to explore and doubt. The consideration on life’s origin can be on three levels: monomers, polymers, and gene-loading. All of the three show commonality for all known life forms: monomers such as amino acids, sugars, purines, consisting of elements C, H, O, N, S, P to build large molecules, polymers such as carbohydrates, proteins and DNA. In living organisms, there are only a few kinds of polymers which are all slender threadlike strands made up of simple subunits. The process to form polymers is completed by cells, and together with all their other work and organization, is directed by genes. Summarizing some consensus achieved for the origin of life, we can list:
1. Life appeared relatively soon after the Earth’s birth: the widely accepted evidence of the earliest life on Earth is in rocks with age of about 3.45 billion years (Allwood et al 2018). Now the most widely accepted view is that our earth was formed about 4.54 billion years ago.
However, the downside of the fact is that the evidence of life’s beginning and the life-generating events are too rare to tell the story.
2. Living and non-living matter are not sharply divided, or in other words, the transition to form primitive life can be from non-living matter by prebiotic chemical evolution. Laboratory work shows that all crucial monomers forming life could easily have formed in a variety of settings on the primordial Earth.

Table of contents :

Chapter 1 Introduction
Chapter 2 Organic molecules in space
2.1 Interstellar medium and star formation
2.1.1 Interstellar gas
2.1.2 Interstellar dust
2.1.3 Star formation and interstellar molecules
2.2 Interstellar organic molecules and possible links with the origin of life
2.3 Observation of interstellar molecules by telescopes
2.4 Research in radio astronomy on molecules in vibrationally excited states
Chapter 3 Summary of the relevant theory of molecular spectroscopy
3.1 Introduction to molecular energy levels and spectroscopy
3.2 Molecular Schrodinger equation and the Born-Oppenheimer approximation
3.3 Rotational energy levels and rotational spectroscopy
3.3.1 Rigid linear rotors
3.3.2 Symmetric rotors
3.3.3 Asymmetric rotors
3.3.4 Non-rigid rotors and centrifugal distortion perturbation
3.4 Nuclear hyperfine splitting in molecules
3.5 Hindered internal rotation
3.6 Coriolis interaction and Fermi resonance
3.7 Partition function
Chapter 4 Measurements and analysis procedure
4.1 Radiation sources
4.2 Absorption cell
4.3 Detection chain
4.4 Control and acquisition
4.5 Analysis with SPFIT and SPCAT
4.6 The start and improvement of the fits
Chapter 5 n-propyl cyanide in the ground vibrational states
5.1 n-propyl cyanide and its laboratory rotational spectroscopy
5.2 The summary of the fitting for n-PrCN in its ground vibrational states
5.3 Reliability of predictions on the ground states of n-PrCN
Chapter 6 Vibrationally excited states of n-propyl cyanide
6.1 Review of the vibrationally excited molecules detected in space
6.2 Review of our first spectroscopic work and observations
6.3 The gauche conformer of n-propyl cyanide
6.3.1 v30 = 1 and 2 of g-n-PrCN
6.3.2 v29 = 1 of g-n-PrCN
6.3.3 v28 = 1 of g-n-PrCN
6.3.4 v29 = v30 = 1 of g-n-PrCN
6.4 The anti conformer of n-propyl cyanide
6.4.1 v30 = 1 of a-n-PrCN
6.4.2 v30 = 2 and v18 = 1 of a-n-PrCN
6.4.3 v29 = 1 of a-n-PrCN
6.4.4 v18 = v30 = 1 of a-n-PrCN
Chapter 7 Conclusion and outlook
7.1 Conclusion
7.2 Outlook
Conclusion (en français)

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