arXiv subjects

Aigen Li

Publications and source records attributed to Aigen Li.

At least 55 records · Page 3Linked to original sources

arXiv2021

Interstellar Extinction and Elemental Abundances: Individual Sight Lines

While it is well recognized that both the Galactic interstellar extinction curves and the gas-phase abundances of dust-forming elements exhibit considerable variations from one sight line to another, as yet most of the dust extinction modeling efforts have been directed to the Galactic average extinction curve, which is obtained by averaging over many clouds of different gas and dust properties. Therefore, any details concerning the relationship between the dust properties and the interstellar environments are lost. Here we utilize the wealth of extinction and elemental abundance data obtained by space telescopes and explore the dust properties of a large number of individual sight lines. We model the observed extinction curve of each sight line and derive the abundances of the major dust-forming elements (i.e., C, O, Si, Mg and Fe) required to be tied up in dust (i.e., dust depletion). We then confront the derived dust depletions with the observed gas-phase abundances of these elements and investigate the environmental effects on the dust properties and elemental depletions. It is found that for the majority of the sight lines the interstellar oxygen atoms are fully accommodated by gas and dust and therefore there does not appear to be a "missing oxygen" problem. For those sight lines with an extinction-to-hydrogen column density $A_V/N_H$ $>$ 4.8$\times$10$^{-22}$ mag cm$^2$/H there are shortages of C, Si, Mg and Fe elements for making dust to account for the observed extinction, even if the interstellar C/H, Si/H, Mg/H and Fe/H abundances are assumed to be proto-solar abundances augmented by Galactic chemical evolution.

astro-ph.GA↗

arXiv2021

Excitation of Polycyclic Aromatic Hydrocarbon (PAH) Emission: Dependence on Size Distribution, Ionization, and Starlight Spectrum and Intensity

Using physical models, we study the sensitivity of polycyclic aromatic hydrocarbon (PAH) emission spectra to the character of the illuminating starlight, to the PAH size distribution, and to the PAH charge distribution. Starlight models considered range from the emission from a 3 Myr-old starburst, rich in far-ultraviolet (FUV) radiation, to the FUV-poor spectrum of the very old population of the M31 bulge. A wide range of starlight intensities is considered. The effects of reddening in dusty clouds are investigated for different starlight spectra. For a fixed PAH abundance parameter $q_{\rm PAH}$ (the fraction of the total dust mass in PAHs with $<10^3$ C atoms), the fraction of the IR power appearing in the PAH emission features can vary by a factor of two as the starlight spectrum varies from FUV-poor (M31 bulge) to FUV-rich (young starburst). We show how $q_{\rm PAH}$ can be measured from the strength of the 7.7$μ$m emission. The fractional power in the 17$μ$m feature can be suppressed by high starlight intensities.

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arXiv2021

Spectroscopic evidence for a large spot on the dimming Betelgeuse

During October 2019 and March 2020, the luminous red supergiant Betelgeuse demonstrated an unusually deep minimum of its brightness. It became fainter by more than one magnitude and this is the most significant dimming observed in the recent decades. While the reason for the dimming is debated, pre-phase of supernova explosion, obscuring dust, or changes in the photosphere of the star were suggested scenarios. Here, we present spectroscopic studies of Betelgeuse using high-resolution and high signal-to- noise ratio near-infrared spectra obtained at Weihai Observatory on four epochs in 2020 covering the phases of during and after dimming. We show that the dimming episode is caused by the dropping of its effective temperature by at least 170 K on 2020 January 31, that can be attributed to the emergence of a large dark spot on the surface of the star.

astro-ph.SR↗

arXiv2021

Magnetism of Fullerene C60 Compared with Graphene Molecule by DFT Calculation, Laboratory Experiment and Astronomical Observation

Magnetism of fullerene C60 was studied by three methods of the density functional theory (DFT) calculation, laboratory experiment and astronomical observation. DFT revealed that the most stable spin state was non-magnetic one of Sz=0/2. This is contrary to our recent study on void induced graphene molecules of C23 and C53 to be magnetic one of Sz=2/2. Two graphene molecules combined model suggested that two up-spin at every carbon pentagon ring may cancel each other to bring Sz=0/2. Similar cancelation may occur on C60. Molecular vibrational infrared spectrum of C60 show four major bands, which coincide with gas-phase laboratory experiment, also with astronomically observed one of carbon rich planetary nebula Tc1 and Lin49. However, there remain many unidentified bands on astronomical one. We supposed multiple voids on graphene sheet, which may create both C60 and complex graphene molecules. It was revealed that spectrum of two voids induced graphene molecule coincident well with major astronomical bands. Simple sum of C60 and graphene molecules could successfully reproduce astronomical bands in detail.

astro-ph.GA↗

arXiv2021

Void defect induced magnetism and structure change of carbon material-3, Polycyclic aromatic hydrocarbon

Void-defect induced magnetism of graphene molecule was recently reported in our previous paper of this series study. This paper investigated the case of hydrogenated graphene molecule, in chemical term, polycyclic aromatic hydrocarbon (PAH). Molecular infrared spectrum obtained by density functional theory was compared with astronomical observation. Void-defect on PAH caused serious structure change. Typical example of C23H12 had two carbon pentagon rings among hexagon networks. Stable spin state was non-magnetic singlet state. This is contrary to pure carbon case of C23, which show magnetic triplet state. It was discussed that Hydrogen played an important role to diminish magnetism by creating an SP3-bond among SP2-networks. Such a structure change affected molecular vibration and finally to photoemission spectrum in infrared region. The dication-C23H12 showed featured bands at 3.2, 6.3, 7.7, 8.6, 11.2, and 12.7 micrometer. It was surprising that those calculated bands coincided well with astronomically observed bands in many planetary nebulae. To confirm our study, large size molecule of C53H18 was studied. Calculation reproduced again similar astronomical bands. Also, small size molecule of C12H8 showed good coincidence with the spectrum observed for young stars. This paper would be the first report to indicate the specific PAH in space.

astro-ph.GA↗

arXiv2021

Deuterated Polycyclic Aromatic Hydrocarbons in the Interstellar Medium: The C--D Band Strengths of Multi-Deuterated Species

Observationally, the interstellar gas-phase abundance of deuterium (D) is considerably depleted and the missing D atoms are often postulated to have been locked up into carbonaceous solids and polycyclic aromatic hydrocarbon (PAH) molecules. An accurate knowledge of the fractional amount of D (relative to H) tied up in carbon dust and PAHs has important cosmological implications since D originated exclusively from the Big Bang and the present-day D abundance, after accounting for the astration it has experienced during the Galactic evolution, provides essential clues to the primordial nucleosynthesis and the cosmological parameters. To quantitatively explore the extent to which PAHs could possibly accommodate the observed D depletion, we have previously quantum-chemically computed the infrared vibrational spectra of mono-deuterated PAHs and derived the mean intrinsic band strengths of the 3.3 $μ$m C--H stretch (A$_{3.3}$) and the 4.4 $μ$m C--D stretch (A$_{4.4}$). Here we extend our previous work to multi-deuterated PAH species of different deuterations, sizes and structures. We find that both the intrinsic band strengths A$_{3.3}$ and A$_{4.4}$ and their ratios A$_{4.4}$/A$_{3.3}$ not only show little variations among PAHs of different deuterations, sizes and structures, they are also closely similar to that of mono-deuterated PAHs. Therefore, a PAH deuteration level (i.e., the fraction of peripheral atoms attached to C atoms in the form of D) of ~2.4% previously estimated from the observed 4.4 $μ$m to 3.3 $μ$m band ratio based on the A$_{4.4}$/A$_{3.3}$ ratio of mono-deuterated PAHs is robust.

astro-ph.GA↗

arXiv2021

Compact pebbles and the evolution of volatiles in the interstellar comet 2I/Borisov

The interstellar traveler, 2I/Borisov, is the first clearly active extrasolar comet, ever detected in our Solar system. We obtained high-resolution interferometric observations of 2I/Borisov with the Atacama Large Millimeter/submillimeter Array (ALMA), and multi-color optical observations with the Very Large Telescope (VLT) to gain a comprehensive understanding of the dust properties of this comet. We found that the dust coma of 2I/Borisov consists of compact "pebbles" of radii exceeding ~1 mm, suggesting that the dust particles have experienced compaction through mutual impacts during the bouncing collision phase in the protoplanetary disk. We derived a dust mass loss rate of >= 200 kg/s and a dust-to-gas ratio >=3. Our long term monitoring of 2I/Borisov with VLT indicates a steady dust mass loss with no significant dust fragmentation and/or sublimation occurring in the coma. We also detected emissions from carbon monoxide gas (CO) with ALMA and derived the gas production rate of Q(CO) (3.3+/-0.8)x10^{26} mole/s. We found that the CO/H$_2$O mixing ratio of 2I/Borisov changed drastically before and after perihelion, indicating the heterogeneity of the cometary nucleus, with components formed at different locations beyond the volatile snow-line with different chemical abundances. Our observations suggest that 2I/Borisov's home system, much like our own system, experienced efficient radial mixing from the innermost parts of its protoplanetary disk to beyond the frost line of CO.

astro-ph.EP↗

arXiv2021

Void defect induced magnetism and structure change of carbon material-2, Graphene molecules

Void-defect is a possible origin of ferromagnetic feature on pure carbon materials. In our previous paper, void-defect on graphene-nanoribbon show highly polarized spin configuration. In this paper, we studied cases for graphene molecules by quantum theory, by astronomical observation and by laboratory experiment. Model molecules for the density functional theory are graphene molecules of C23 and C53 induced by a void-defect. They have carbon pentagon ring within a hexagon network. Single void has three radical carbons, holding six spins. Those spins make several spin-states, which affects to molecular structure and molecular vibration, finally to infrared spectrum. The stable spin state was triplet, not singlet. This suggests magnetic pure carbon molecule. It was a surprise that those molecules show close infrared spectrum with astronomically observed one, especially observed on carbon rich planetary nebulae. We could assign major band at 18.9 micrometer, and sub-bands at 6.6, 7.0, 7.6, 8.1, 8.5, 9.0 and 17.4 micrometer. Also, calculated spectrum roughly coincides with that of laboratory experiment by the laser-induced carbon plasma, which is an analogy of cosmic carbon creation in interstellar space.

astro-ph.GA↗

arXiv2021

Optical properties of elongated conducting grains

Extremely elongated, conducting dust particles (also known as metallic "needles" or "whiskers") are seen in carbonaceous chondrites and in samples brought back from the Itokawa asteroid. Their formation in protostellar nebulae and subsequent injection into the interstellar medium have been demonstrated, both experimentally and theoretically. Metallic needles have been suggested to explain a wide variety of astrophysical phenomena, ranging from the mid-infrared interstellar extinction at ~3--8 micron to the thermalization of starlight to generate the cosmic microwave background. To validate (or invalidate) these suggestions, an accurate knowledge of the optics (e.g., the amplitude and the wavelength dependence of the absorption cross sections) of metallic needles is crucial. Here we calculate the absorption cross sections of iron needles of various aspect ratios over a wide wavelength range, by exploiting the discrete dipole approximation, the most powerful technique for rigorously calculating the optics of irregular or nonspherical grains. Our calculations support the earlier findings that the antenna theory and the Rayleigh approximation, which are often taken to approximate the optical properties of metallic needles are indeed inapplicable.

astro-ph.GA↗

arXiv2020

Interstellar Extinction and Elemental Abundances

Elements in the interstellar medium (ISM) exist in the form of gas or dust. The interstellar extinction and elemental abundances provide crucial constraints on the composition, size and quantity of interstellar dust. Most of the extinction modeling efforts have assumed the total abundances (both in gas and in dust) of the dust-forming elements---known as the "interstellar abundances", the "interstellar reference abundances", or the "cosmic abundances"---to be solar and the gas-phase abundances to be independent of the interstellar environments. However, it remains unclear if the solar abundances are an appropriate representation of the interstellar abundances. Meanwhile, the gas-phase abundances are known to exhibit appreciable variations with the local interstellar environments. In this work we explore the viability of the abundances of B stars, the solar and protosolar abundances, and the protosolar abundances augmented by Galactic chemical enrichment (GCE) as an appropriate representation of the interstellar abundances by quantitatively examining the extinction and elemental abundances of ten interstellar lines of sight for which both the extinction curves and the gas-phase abundances of all the major dust-forming elements (i.e., C, O, Mg, Si and Fe) have been observationally determined. Instead of assuming a specific dust model and then fitting the observed extinction curves, for each sightline we apply the model-independent Kramers-Kronig relation, which relates the wavelength-integrated extinction to the total dust volume, to place a lower limit on the dust depletion. This, together with the observationally-derived gas-phase abundances, allows us to rule out the B-star, solar, and protosolar abundances as the interstellar reference standard. We conclude that the GCE-augmented protosolar abundances are a viable representation of the interstellar abundances.

astro-ph.GA↗

arXiv2020

On the Absorption Properties of Metallic Needles

Needle-like metallic particles have been suggested to explain a wide variety of astrophysical phenomena, ranging from the mid-infrared interstellar extinction to the thermalization of starlight to generate the cosmic microwave background. These suggestions rely on the amplitude and the wavelength dependence of the absorption cross sections of metallic needles. On the absence of an exact solution to the absorption properties of metallic needles, their absorption cross sections are often derived from the antenna approximation. However, it is shown here that the antenna approximation is not an appropriate representation since it violates the Kramers-Kronig relation. Stimulated by the recent discovery of iron whiskers in asteroid Itokawa and graphite whiskers in carbonaceous chondrites, we call for rigorous calculations of the absorption cross sections of metallic needle-like particles, presumably with the discrete dipole approximation. We also call for experimental studies of the formation and growth mechanisms of metallic needle-like particles as well as experimental measurements of the absorption cross sections of metallic needles of various aspect ratios over a wide wavelength range to bound theoretical calculations.

astro-ph.GA↗

arXiv2020

Deuterated Polycyclic Aromatic Hydrocarbons in the Interstellar Medium: The C--D Band Strengths of Mono-Deuterated Species

Deuterium (D) is one of the light elements created in the big bang. As the Galaxy evolves, the D/H abundance in the interstellar medium (ISM) decreases from its primordial value due to "astration". However, the observed gas-phase D/H abundances of some interstellar sightlines are substantially lower than the expected reduction by astration alone. The missing D could have been depleted onto polycyclic aromatic hydrocarbon (PAH) molecules which are ubiquitous and abundant in interstellar regions. To quantitatively explore the hypothesis of PAHs as a possible reservoir of interstellar D, we compute quantum-chemically the infrared vibrational spectra of mono-deuterated PAHs (and their cations) of various sizes. We find that, as expected, when H in PAHs is replaced by D, the C-H stretching and bending modes at 3.3, 8.6 and 11.3 $μ$m respectively shift to longer wavelengths at $\sim$4.4, 11.4 and 15.4 $μ$m by a factor of $\sim$$\sqrt{13/7}$, the difference in reduced mass between the C-H and C-D oscillators. We derive from the computed spectra the mean intrinsic strengths of the 3.3 $μ$m C-H stretch and 4.4 $μ$m C--D stretch to be $\langle A_{3.3} \rangle \sim 13.4$ km/mol and $\langle A_{4.4} \rangle \sim 7.4$ km/mol for neutral deuterated PAHs which would dominate the interstellar 3.3 and 4.4 $μ$m emission. By comparing the computationally-derived mean ratio of $\langle A_{4.4}/A_{3.3} \rangle \sim 0.56$ for neutral PAHs with the mean ratio of the observed intensities of $\langle (I_{4.4}/I_{3.3})_{\rm obs} \rangle \sim 0.019$, we estimate the degree of deuteration (i.e., the fraction of peripheral atoms attached to C in the form of D) to be ~2.4\%, corresponding to a D-enrichment of a factor of ~1200 with respect to the interstellar D/H abundance.

astro-ph.GA↗

arXiv2020

Graphene Molecules Contributing to the Infrared Bands of Carbon Rich Planetary Nebulae

It is well known since 2010 that fullerene C60 is widespread through the interstellar space. Also, it is well known that graphene is a source material for synthesizing fullerene. Here, we simply assume the occurrence of graphene in space. Infrared spectra of graphene molecules are calculated to compare both to astronomical observational spectra and to laboratory experimental one. Model molecules for DFT calculation are selected by one astronomical assumption, that is, single void in charge neutral graphene of C13, C24 and C54, resulting C12, C23 and C53. They have a carbon pentagon ring within a hexagon network. Different void positions are classified as different species. Single void is surrounded by 3 radical carbons, holding 6 spins. Spin state affects molecular configuration and vibrational spectrum. It was a surprise that the triplet state is stable than the singlet. Most of charge neutral and triplet spin state species show closely resembling spectra with observed one of carbon rich planetary nebulae Tc1 and Lin49. We could assign major bands at 18.9 micrometer, and sub-bands at 6.6, 7.0, 7.6, 8.1, 8.5, 9.0 and 17.4 micrometer. It is interesting that those graphene species were also assigned in the laboratory experiments on laser-induced carbon plasma, which are analogies of carbon cluster creation in space. The conclusion is that graphene molecules could potentially contribute to the infrared emission bands of carbon-rich planetary nebulae.

astro-ph.GA↗

arXiv2020

Spitzer's perspective of polycyclic aromatic hydrocarbons in galaxies

Polycyclic aromatic hydrocarbon (PAH) molecules, as revealed by the distinctive set of emission bands at 3.3, 6.2, 7.7, 8.6, 11.3 and 12.7 $μ$m characteristic of their vibrational modes, are abundant and widespread throughout the Universe. They are ubiquitously seen in a wide variety of astrophysical regions, ranging from planet-forming disks around young stars to the interstellar medium (ISM) of the Milky Way and external galaxies out to high redshifts at z>4. PAHs profoundly influence the thermal budget and chemistry of the ISM by dominating the photoelectric heating of the gas and controlling the ionization balance. Here, we review the current state of knowledge of the astrophysics of PAHs, focusing on their observational characteristics obtained from the Spitzer Space Telescope and their diagnostic power for probing the local physical and chemical conditions and processes. Special attention is paid to the spectral properties of PAHs and their variations revealed by the Infrared Spectrograph (IRS) on board Spitzer across a much broader range of extragalactic environments (e.g., distant galaxies, early-type galaxies, galactic halos, active galactic nuclei, and low-metallicity galaxies) than was previously possible with the Infrared Space Observatory (ISO) or any other telescope facilities. Also highlighted is the relation between the PAH abundance and the galaxy metallicity established for the first time by Spitzer.

astro-ph.GA↗

arXiv2020

On Carbon Nanotubes in the Interstellar Medium

Since their discovery in 1991, carbon nanotubes (CNTs) -- a novel one-dimensional carbon allotrope -- have attracted considerable interest worldwide because of their potential technological applications such as electric and optical devices. In the astrophysical context, CNTs may be present in the interstellar space since many of the other allotropes of carbon (e.g., amorphous carbon, fullerenes, nanodiamonds, graphite, polycyclic aromatic hydrocarbons, and possibly graphene as well) are known to be widespread in the Universe, as revealed by presolar grains in carbonaceous primitive meteorites and/or by their fingerprint spectral features in astronomical spectra. In addition, there are also experimental and theoretical pathways to the formation of CNTs in the interstellar medium (ISM). In this work, we examine their possible presence in the ISM by comparing the observed interstellar extinction curve with the ultraviolet/optical absorption spectra experimentally obtained for single-walled CNTs of a wide range of diameters and chiralities. Based on the absence in the interstellar extinction curve of the ~4.5 and 5.25 eV $π$-plasmon absorption bands which are pronounced in the experimental spectra of CNTs, we place an upper limit of ~10 ppm of C/H (i.e., ~4% of the total interstellar C) on the interstellar CNT abundance.

astro-ph.GA↗

arXiv2020

Superhydrogenated Polycyclic Aromatic Hydrocarbon Molecules: Vibrational Spectra in the Infrared

Superhydrogenated polycyclic aromatic hydrocarbons (PAHs) may be present in H-rich and ultraviolet-poor benign regions. The addition of excess H atoms to PAHs converts the aromatic bonds into aliphatic bonds, the strongest of which falls near 3.4 $μ$m. Therefore, superhydrogenated PAHs are often hypothesized as a carrier of the 3.4 $μ$m emission feature which typically accompanies the stronger 3.3 $μ$m aromatic C--H stretching feature. To assess this hypothesis, we use density function theory to compute the IR vibrational spectra of superhydrogenated PAHs and their ions of various sizes (ranging from benzene, naphthalene to perylene and coronene) and of various degrees of hydrogenation (ranging from minimal hydrogenation to heavy hydrogenation). For each molecule, we derive the intrinsic oscillator strengths of the 3.3 $μ$m aromatic C--H stretch ($A_{3.3}$) and the 3.4 $μ$m aliphatic C--H stretch ($A_{3.4}$). By comparing the computationally-derived mean ratio of $\langle A_{3.4}/A_{3.3}\rangle\sim1.98$ with the mean ratio of the observed intensities $\langle I_{3.4}/I_{3.3}\rangle\sim0.12$, we find that the degree of superhydrogenation --- the fraction of C atoms attached with excess H atoms --- is only $\sim2.2\%$ for neutral PAHs which predominantly emit the 3.3 and 3.4 $μ$m features. We also determine for each molecule the intrinsic band strengths of the 6.2 $μ$m aromatic C--C stretch ($A_{6.2}$) and the 6.85 $μ$m aliphatic C--H deformation ($A_{6.85}$). We derive the degree of superhydrogenation from the mean ratio of the observed intensities $\langle I_{6.85}/I_{6.2}\rangle\sim0.10$ and $\langle A_{6.85}/A_{6.2}\rangle\sim1.53$ for neutrals and $\langle A_{6.85}/A_{6.2}\rangle\sim1.23$ for cations to be $\lesssim 3.1\%$ for neutrals and $\lesssim 8.6\%$ for cations. We conclude that astrophysical PAHs are primarily aromatic and are only marginally superhydrogenated.

astro-ph.GA↗

arXiv2019

Fragmentation and isomerization of polycyclic aromatic hydrocarbons in the interstellar medium: coronene as a case study

Aims. Due to the limitations of current computational technology, the fragmentation and isomerization products of vibrationally-excited polycyclic aromatic hydrocarbon (PAH) molecules and their derivatives are poorly studied. In this work, we investigate the intermediate products of PAHs and their derivatives as well as the gas-phase reactions relevant to the interstellar medium, with coronene as a case study. Methods. Based on the semi-empirical method of PM3 as implemented in the CP2K program, molecular dynamics simulations are performed to model the major processes (e.g., vibrations, fragmentations, and isomerizations) of coronene and its derivatives (e.g., methylated coronene, hydrogenated coronene, dehydrogenated coronene, nitrogen-substituted coronene, and oxygen-substituted coronene) at temperatures of 3000 K and 4000 K. Results. We find that the anharmonic effects are crucial for the simulation of vibrational excitation. For the molecules studied here, H2, CO, HCN, and CH2 are the major fragments. Following the dissociation of these small units, most of the molecules could maintain their ring structures, but a few molecules would break completely into carbon chains. The transformation from hexagon to pentagon or heptagon may occur and the heteroatomic substitutions (e.g., N- or O-substitutions) facilitate the transformation.

astro-ph.GA↗

arXiv2019

The infrared bands of polycyclic aromatic hydrocarbons in the 1.6-1.7 μm wavelength region

Context. The 3.3 $μ$m aromatic C-H stretching band of polycyclic aromatic hydrocarbon (PAH) molecules seen in a wide variety of astrophysical regions is often accompanied by a series of weak satellite bands at ~3.4-3.6 $μ$m. One of these sources, IRAS 21282+5050, a planetary nebula, also exhibits a weak band at ~1.68 $μ$m. While the satellite features at ~3.4-3.6 $μ$m are often attributed to the anharmonicities of PAHs, it is not clear whether overtones or combination bands dominate the 1.68 $μ$m feature. Aims. In this work, we examine the anharmonic spectra of eight PAH molecules, including anthracene, tetracene, pentacene, phenanthrene, chrysene, benz[a]anthracene, pyrene, and perylene, to explore the origin of the infrared bands in the 1.6-1.7 $μ$m waveelngth region. Methods. Density Functional Theory (DFT) in combination with the vibrational second-order perturbation theory (VPT2) is utilized for computing the anharmonic spectra of PAHs. To simulate the vibrational excitation process of PAHs, the Wang-Landau random walk technique is employed. Results. All the dominant bands in the 1.6-1.7 $μ$m wavelength range and in the 3.1-3.5 $μ$m C-H stretching region are calculated and tabulated. It is demonstrated that combination bands dominate the 1.6-1.7 $μ$m region, while overtones are rare and weak in this region. We also calculate the intensity ratios of the 3.1-3.5 $μ$m C-H stretching features to the bands in the 1.6-1.7 $μ$m region, $I_{3.1-3.5}/I_{1.6-1.7}$, for both ground and vibrationally excited states. On average, we obtain $\langle I_{3.1-3.5}/I_{1.6-1.7} \rangle$ $\approx$ 12.6 and $\langle I_{3.1-3.5}/I_{1.6-1.7} \rangle$ $\approx$ 17.6 for PAHs at ground states and at vibrationally excited states, respectively.

astro-ph.IM↗