Megamasers: Theory and Applications

Phys 595 Term Project



Since the discovery of cosmic masers by Gundermann (1965) and Weaver et al. (1965), detections of amplified microwave emission have been found in a variety of astronomical environments from numerous chemical species. “Maser” is an acronym for microwave amplification by stimulated emission of radiation, a phenomenon first discovered in laboratory settings by (Gordon 1955), just a decade before the first astronomical detections. The conditions required for maser emission occur only in environments out of thermal equilibrium (e.g., Elitzur, 1992). Typical conditions in the interstellar medium (ISM) are capable of inducing such conditions, primarily due to low densities of material (with respect to terrestrial conditions). Thus in many ISM environments, collisional processes do not dominate (e.g., Stahler et al., 2004).

Due to their non-thermal origins, masers have extremely high brightness temperatures ranging from \(T_{\mathrm{b}} = 10^{10}-10^{14}\) K (Lo, 2005). Such high brightness temperatures obviously do not correspond to the physical temperatures of the emitting material. Instead, the brightness temperatures correspond to level populations that do not follow a Boltzmann distribution (Elitzur, 1992). In the Rayleigh-Jeans limit, brightness temperature has the form: \[\label{eq:temp_bright} T_{\mathrm{b}} = \frac{S_\nu}{\Omega_{\mathrm{s}}} \frac{\lambda^2}{2k},\] These elevated brightness temperatures arise due to the small solid angle of the emission regions (\(\Omega_{\mathrm{s}}\)), and large surface brightnesses (\(S_\nu\)).

Maser emission has been detected in various astrophysical environments, such as around late-type stars, embedded protostars, HII regions, interactions between jets and the surrounding ISM, and comets (Lo, 2005). Typically, these emission lines can be classified as Type I masers, driven by collisional processes such as stellar winds or jets hitting dense gas, or Type II masers, due to radiative excitement from a nearby star or energetic source. These represent the source which provides the energy to invert the population levels of the masing species. In maser theory, these energy sources are the “pumping mechanisms”, which may be collisionally (Type I) or radiatively (Type II) driven (see §\ref{sec:maser_theory}).

In this report, I focus on the discovery, mechanisms, and applications of extragalactic mega-masers. It should be noted that no galactic mega-masers have been detected, and it is unlikely they occur within non-AGN or non-starburst galaxies (see §\ref{sub:oh_gal_props} & §\ref{sub:h20_agn}). Until recently, mega-masers had only been confidently detected from three species: OH, H\(_2\)O, and H\(_2\)CO. The vast majority of the detected mega-maser detection arises from the 22 GHz \(6_{16} \longrightarrow 5_{23}\) H\(_2\)O transition and the primary hyperfine ground-state OH lines (1665 & 1667 MHZ). Mega-masers were first detected serendipitously by Dos Santos et al. (1979), who found 22 GHz H\(_2\)O emission towards the nucleus of NGC 4945. They inferred an isotropic luminosity of \(\sim 85\) L\(_{\odot}\), \(~10^6\) times greater than any known galactic maser source, leading to the term “mega”-maser. Baan et al. (1982) reported the first OH mega-maser towards the peculiar galaxy IC 4553 with an inferred luminosity of \(\sim10^3\) L\(_{\odot}\). Baan et al. (1986) reported the lone detection of a formaldehyde (H\(_2\)CO) mega-maser in the 1\(_{10}\)-1\(_{11}\) (6.2 cm) transition. Recent results by, Wang et al. (2014) and Chen et al. (2015) have extended the mega-masing species to five with their detection of six transitions in methanol (CH\(_3\)OH; 36.2 GHz, 37.7 GHz, and four clustered at 96.7 GHz), and the silicon monoxide (SiO) J=2-1 (\(v=3\)) transition. It should be noted that there are detections of kilo-masers towards the nucleus of nearby galaxies (e.g., Ho et al., 1987), but it is unclear if these arise from the same processes of as mega-maser (Lo, 2005). Several properties of the observed mega-masers do not match those seen from the same species in galactic sources. This strongly suggests that mega-masers are powered by different energy sources.

Observervations of mega-masers show that most arise from emission regions on the order of milli-arcseconds in diameter. Coupled with their high surface-brightness, they make excellent VLBI targets. Most VLBI observations of mega-masers show that the majority of the flux is recovered using the VLBI alone, confirming that there is little mega-maser emission on scales larger than these compact source (Lo, 2005).

This report is arranged as follows. Section \ref{sec:maser_theory} presents the basics of Maser Theory: solutions to the radiative transfer equation and properties that result from those solutions. Section \ref{sec:OH} presents the observational results and applications of OH mega-maser emission, while Sections \ref{sec:h2o_mm} and \ref{sec:other} present the same for H\(_2\)O and other detected mega-masers, respectively. Section \ref{sec:conclusion} discusses the use of future surveys using the upcoming generation of radio telescopes.

Maser Theory


All maser emission arises when photons of specific frequencies incite an excited molecule to emit a photon of the same frequency. This causes a cascade of photons to be emitted within a region of excited molecules, resulting in exponential growth of the intensity of a ray of light. The process itself requires only a population inversion between two states in a molecule, which is provided by some pumping mechanism. In order to be detectable, the masering molecules must also be coherent in velocity (within the thermal width) to achieve a significant gain over the path length of the ray (Lo, 2005). This section explores the theory of maser emission based on these two requirements. A thorough treatment of modern maser theory can be found in a series of papers by Elitzur (Elitzur, 1990; Elitzur, 1990a; Elitzur, 1990; Elitzur, 1991).

Population Inversion & Radiative Transfer


In this section, I consider a two-level system of molecular energy levels and derive the exponential growth in the ray intensity in terms of the emitting region’s physical properties, and the properties of the emitting molecule. It should be noted that a proper treatment of any stimulated emission process requires a minimum of three energy levels, as is shown in the thorough derivations by (Elitzur 1992) and (Gray 2009). Here, I largely follow the simplified derivations presented in Chapter 4 of (Elitzur 1992) and Chapter 14 of Stahler et al. (2004), which implicitly treat levels unassociated with the maser transition as generic gain and loss rates.

Let there be an upper and lower state, such that the maser results from the transition from the upper to the lower. From the Boltzmann distribution, the excitation temperature is defined by \[\label{eq:level_pops} \frac{n_u}{n_{l}} = \frac{g_{u}}{g_{l}} \mathrm{exp}\left( \frac{\Delta E}{kT_{\mathrm{ex}}} \right)\] where \(n_u\) and \(n_l\) are the number densities in the respective upper and lower states, \(g_u\) and \(g_l\) are the degeneracies of those states, and \(\Delta E\) is the transition energy between them. The population levels become inverted when \(n_\mathrm{u}/g_\mathrm{u} \gt n_\mathrm{l}/g_\mathrm{l}\), which corresponds to a negative \(T_\mathrm{ex}\). Maintaining an inverted population requires an energy source, referred to as the pump\ref{sub:pumping}). Transistions in the microwave and radio require the smallest pump action, since \(n_\mathrm{u}/g_\mathrm{u} \approx n_\mathrm{l}/g_\mathrm{l}\) for kinetic temperatures of a few hundred kelvin, even when in thermal equilibrium. The role of the pump is to excite molecules into the upper and lower states of the maser transition, and is typically achieved through a collisional or radiative process. Without regard for the details of how the pump achieves this, let \(P_\mathrm{u}\) and \(P_\mathrm{l}\) be the rate per unit volume at which the pump adds molecules to the upper and lower states from other states of the molecule, respectively. Both states may also decay or be excited further into other energy states. Since this must depend on the population in the upper and lower levels, these loss rates per unit volume are \(n_u\Gamma_u\) and \(n_l\Gamma_l\), where \(\Gamma\) is the decay/excitation rate in each level. The level populations of the upper and lower states also depend on the Einstein A and B coefficients, representing spontaneous decay and absorption between the states, in the presence of a radiation field, \(\bar{J}\), the mean intensity. Finally, the molecules may collide with other molecules, giving collisional excitation (\(\gamma_{lu}\)) and deexcitation (\(\gamma_{ul}\)) rates. A schematic of the processes discussed here are presented in Figure \ref{fig:energy_diagram}.

While observed masers may vary on time-scales ranging from days to months (e.g., Elitzur, 1992), I make the assumption that the maser mechanism is generally in a steady-state. The steady state populations of the upper and lower levels are then given by, \[\label{eq:ss_pops} 0 = P_u - n_u \Gamma_u - \left( n_u B_{ul} - n_l B_{lu} \right)\bar{J} - \left( n_u \gamma_{ul} - n_l \gamma{lu} \right) n_{\mathrm{tot}} - n_u A_{ul} \\ 0 = P_l - n_l \Gamma_l + \left( n_u B_{ul} - n_l B_{lu} \right)\bar{J} + \left( n_u \gamma_{ul} - n_l \gamma{lu} \right) n_{\mathrm{tot}} + n_u A_{ul}\] Here, \(n_{\mathrm{tot}}\) is the number density of the background gas. The \(B\)-coefficients are related by \(g_lB_{lu}=g_uB_{ul}\), and the collisional coefficients approximately follow \(\gamma_{ul}g_u \approx \gamma_{lu}g_l\), since \(T_{\mathrm{kin}} \gg \Delta E / k_{\mathrm{B}}\) for the relevant energy transitions for masers (Stahler et al., 2004).

The relevant quantity for understanding the radiative transfer of a maser is the degree of inversion of the population levels. To derive this, Stahler et al. (2004) make two simplifying assumptions: the loss rates are equal (\(\Gamma=\Gamma_u=\Gamma_l\)), and, in practice, spontaneous emission is negligible compared to the loss rates for the transitions of interest(\(\Gamma \gg A_{ul}\)) (Elitzur, 1992). Assuming equal loss rates does not change the form of the final result of the derivation. Using these assumptions, and the aforementioned relation, the population inversion can be described in terms of the properties of the two states: \[\label{eq:pop_inverse_full} \Delta n \equiv \frac{n_u}{g_u} - \frac{n_l}{g_l} \\ = \frac{P_u/g_u - P_l/g_l}{\Gamma + \left( 1 + g_u/g_l \right)\gamma_{ul} n_{\mathrm{tot}}}\] This difference, from the Einstein theory, is the criterion for stimulated action (Gray, 2009). As is done in Stahler et al. (2004), I define the population inversion due to only collisional processes (ie. \(\bar{J}=0\)), as \(\Delta n^{\circ}\). Equation \ref{eq:pop_inverse_full} can then be expressed as: \[\label{eq:pop_inverse} \Delta n = \frac{\Delta n^{\circ}}{1 + \bar{J}/\bar{J}_s}\] \(\bar{J}_s\) is the saturation intensity, representing the intensity where the transition will begin to become thermalized due to collisional excitation: \[\label{eq:sat_intensity} \bar{J}_s \equiv \frac{\Gamma + \left( 1 + g_u/g_l \right)\gamma_{ul}n_{\mathrm{tot}}}{\left( 1 + g_u/g_l \right)B_{ul}}\] Equation \ref{eq:pop_inverse} shows that the population inversion is not affected greatly by radiation (\(\bar{J}\)), until it exceeds \(\bar{J}_s\) and quickly declines. This makes the maser mechanism self-limiting, since \(\bar{J}\) is amplified by the process. The value of \(\bar{J}_s\), as will be shown below, sets the maximum intensity that the maser mechanism can produce, and distinguishes between the unsaturated and saturated regimes (Elitzur, 1992).

For spectral line emission, the emission and absorption coefficients are related to the Einstein \(A\) and \(B\) values of the transition: \(j_\nu = h \nu_0 n_u A_{ul}\phi(\nu)\) and \(\alpha_\nu = h\nu_0 \left( n_l B_{lu} - n_u B_{ul} \right)\phi(\nu)/4\pi\), respectively. Here, \(\phi(\nu)\) is a normalized Doppler profile, corresponding to the ambient temperature, and \(\nu_0\) is the central frequency. The radiative transfer