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For isolated, free-flying nanoparticles or large molecules in many astrophysical environments, photon absorption is often the dominant excitation process. Prior to the absorption of an energetic photon, a molecule stays at the ground electronic state, which is S0 (the lowest singlet state) for neutrals and D0 (the lowest doublet state) for ions, containing very little vibrational energy. After photoabsorption occurs, the molecule is excited to an upper electronic state Sn for neutrals or Dn for ions (n > 1). The electronically excited molecule has 3 major competing decay channels to relax its energy: radiation, photoionization, and photodissociation. In this section we will focus on the radiation process and use PAHs as an example.

3.1. An Overview of the Photoexcitation and Emission Processes

Once the molecule is electronically excited, both radiative and radiationless transitions will occur between its vibrational modes, electronic and vibrational states (see Birks 1970 for detailed discussions on neutral molecules):

In addition, for highly isolated molecules, there could exist another two radiative energy decay channels - the inverse fluorescence (Leach 1987) and the recurrent fluorescence (Léger, Boissel, & d'Hendecourt 1988). The former results from a transition from a high vibrational level of a lower electronic state to a higher electronic state. The latter, also known as the Poincaré fluorescence, was postulated by Léger et al. (1988) as resulting from an inverse electronic conversion (i.e., the partial conversion of the vibrational energy of the ground electronic state into electronic excitation), followed by emitting a visible photon just like the ordinary (electronic) fluorescence process. However, the Poincaré fluorescence may have a quantum yield larger than one (i.e., several fluorescence photons can be emitted during one photoabsorption event since the molecule can oscillate many times between the electronic ground state and the excited state provided the absorbed energy is high enough; see Léger et al. 1988).

Figures 1 and 2 give a schematic overview of the above-described main processes following the absorption of an energetic photon respectively for a neutral molecule and a molecular cation.

Figure 1

Figure 1. Step ladder model of a large neutral molecule. The schematic energy levels involve an electronic part (singlets S0, S1, S2 ... and triplets T1, T2 ...) and a vibrational part (v1, v2, v3...). Upon absorption of an UV/visible photon, the molecule makes an electronic transition from the ground state S0 to an upper state Sn, followed by (1) radiationless internal vibrational redistribution, (2) radiationless electronic transitions (internal conversion [IC] and intersystem crossing [ISC]), (3) radiative electronic transitions (fluorescence and phosphorescence), (4) radiative inverse electronic transitions (inverse fluorescence, and Poincaré fluorescence resulted from the inverse internal conversion [IIC]), and (5) IR vibrational transitions.

Figure 2

Figure 2. Same as Figure 1 but for a large molecular cation (with one unpaired electron). The schematic energy levels involve an electronic part (doublets D0, D1, D2 ... and quartets Q0, Q1, Q2 ...) and a vibrational part (v1, v2, v3...). In comparison with neutral molecules, radiative electronic transitions (fluorescence and phosphorescence) for ions are not important since internal conversion quickly transfers almost all of the initial excitation energy to the vibrationally excited ground electronic state D0 (see Leach 1987; Allamandola et al. 1989). Therefore, IR emission becomes almost the only deactivation route.

The stochastic heating of ultrasmall grains has been extensively studied in literature (see Draine & Li 2001 and references therein). All studies prior to the identification of PAH molecules as the carrier of the "UIR" bands used the "thermal" approach (i.e., the vibrationally excited grain is described as a system having an internal temperature; see Section 3.3). The issue of "thermal" versus "non-thermal" arose when Léger and his coworkers used the "thermal" approach to model the vibrational excitation of PAHs to explain the "UIR" bands (Léger & Puget 1984; Léger, d'Hendecourt, & Défourneau 1989), while Allamandola, Tielens, & Barker (1985, 1989) took a statistical approach and questioned the validity of the "thermal" approximation. Barker & Cherchneff (1989), d'Hendecourt et al. (1989), Schutte, Tielens, & Allamandola (1993), and Cook & Saykally (1998) found that the thermal approximation was valid for computing thermal emission spectra. Below we will discuss the recent efforts we took to model the PAH excitation and de-excitation processes (Draine & Li 2001) using both the "exact-statistical" approach (Section 3.2) and the "thermal-approximation" approach (Section 3.3).

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