JSTOR

1. INTRODUCTION

The advantages and disadvantages of lunar observatories have been discussed for a number of years (Lester et al., 2004). The case for lunar observatories compared to space-based instruments is far from clear in most instances. Experience operating the Hubble Space Telescope and other space-based instruments has shown that the problems of operation in space can be successfully overcome. Transportation costs, the presence of lunar dust, and our lack of experience make the operation of lunar observatories less clear.

However, there are certain cases where the moon may provide the best solution. One such case is a large liquid lunar telescope. A rotating liquid in a gravitational field naturally assumes the proper shape for a telescope mirror. Space-based optical telescopes, or lunar telescopes of standard design, are limited in size due to weight and size limitations for transport. A liquid lunar telescope can be assembled on site, allowing in principle a much larger telescope. The lower lunar gravity reduces the weight of the rotating portion, and therefore allows for a lighter overall design. The lack of atmosphere, which not only harms the seeing but can disturb the liquid surface, is also of great value. In a recent article in Nature, Borra et al. (2007) discuss the opportunities for science for such a telescope. These opportunities include studies of the first stars and formation of galaxies at redshifts of 15–20. With current NASA plans for a return to the moon, further study of the possibilities for a large lunar telescope seem worthwhile.

For a large diameter (tens of meters) telescope, a space-based telescope is unlikely in the foreseeable future, while a liquid lunar telescope is feasible. Such a telescope for visible wavelengths was discussed by Borra (1991). The particular advantage of a liquid lunar telescope is the simplicity of design and the lower mass. The expense and difficulty of transport make a lower mass essential. In addition, the lack of large delicate components to transport is also a benefit. Borra (1991) estimated that for a 4 m lunar telescope the mass could be less than the mass of the 2.4 m Hubble telescope mirror.

2. LIQUID MIRROR TELESCOPES

On the Earth, liquid mercury-based telescopes such as the Large Zenith Telescope have been successfully operated with sizes up to 6 m (Hickson et al. 2007; Hickson & Racine 2007). Extensive testing and actual operations of liquid telescopes have proved the concept workable. These telescopes are much cheaper and simpler to create than a telescope of standard design; the LZT cost only a few percent as much as a telescope with a standard mirror of similar size.

One obvious disadvantage of a liquid telescope is that it cannot be pointed in an arbitrary direction, but rather looks toward the zenith. On the other hand, eliminating steering capabilities simplifies the engineering design and reduces the weight. Such a telescope is best suited for cosmological studies of large redshift objects. For such studies, many of the interesting objects are in the IR. A location near the lunar polar region may be a good choice for looking at a small region of the sky.

The liquid used for the telescope needs to have several properties. First, it needs a high reflectivity over the wavelengths of interest. In addition, it is important that its vapor pressure is low enough that the loss of liquid to evaporation is small. Originally, liquid mercury or germanium was proposed for the operating fluid. However, mercury and germanium are only liquid at temperatures that are much too high to allow observations in the IR. To be useful in the IR, the lower the operational temperature the better.

Recently, Borra et al. (2007) have proposed using coated ionic liquids to serve as the mirror for a large visible/IR lunar telescope. Ionic liquids have a low vapor pressure, which is critical for operations in the lunar vacuum. The authors were able to coat an ionic liquid (1-ethyl-3methylimidazolium ethylsulphate) with chromium then silver and get reasonable reflectivities (∼70%). In addition, the coatings survived over periods of months without indications of degradation. Unfortunately, this substance only remains liquid to temperatures of 175 K, below which it freezes. A liquid with an operating temperature of 130 K or below is desired (Borra et al. 2007).

The fact that they were able to coat particles in ionic liquids with silver and get good reflectivity was a very interesting result in and of itself. And while they did not identify a suitable liquid, the large number of possible ionic liquids (10⁶ binary and 10¹⁸ ternary) make it plausible that there exists a suitable liquid that can (1) be coated, (2) be stable over time, and (3) have a sufficiently low melting temperature. However, we believe that a liquid metal ammonia solution may provide a simpler, more robust way to create such a telescope.

3. METAL AMMONIA SOLUTIONS

Liquid metals created by dissolving alkali metals in ammonia have been known for over 130 years (Weyl 1864). They have been extensively studied with a large number of techniques over many years. For an overview of the properties of these liquids see Thompson (1976). Of greatest interest for a liquid lunar telescope is the saturated solution of lithium in ammonia, Li(NH₃)₄. In these solutions, the outermost electron of the lithium dissociates from the metal, resulting in one nearly free electron for each lithium atom dissolved. Li(NH₃)₄ is a good liquid metal, with an electrical conductivity higher than liquid mercury. Importantly, it remains a liquid down to a temperature of 89 K (Thompson 1976) as shown in the phase diagram in Figure 1. Li(NH₃)₄ has the lowest melting temperature of any metal. The metal ammonia systems are examples of systems with strong electronic correlations, and recently have been used by the author to study the general properties of highly correlated systems (Burns et al. 1999, 2001, 2002; Said 2003).

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Fig. 1.— Phase diagram for lithium ammonia solutions in terms of temperature and the mole percent metal (MPM). At low concentrations the liquid is an insulator, there is a phase separation into a two component system over a certain temperature range, and the highly concentrated liquid is a good metal. The low temperature freezing point occurs at 89 K for the composition Li(NH₃)₄.

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Li(NH₃)₄ is not very suitable for earth-based telescopes. It has a high vapor pressure (∼0.8 bar) at room temperature. In addition, the mixtures react with air, harming the surface quality. However, these difficulties would not be present at low temperature under vacuum.

A plot of the theoretical reflectivity near melting (93 K), based on the assumption of reflection from a good metallic conductor, along with measured data (McKnight & Thompson 1975) at 195 K is shown in Figure 2. (The theoretical reflectivity changes less than 2% between 93 K and 195 K). Measured reflectivities are comparable to liquid mercury (∼77% at optical wavelengths), which is used in earth-based liquid telescopes. It is also possible that the true reflectivities will be closer to the theoretical values than the measurements shown in the figure. The measured reflectivities may have been reduced due to surface degradation at the interface between the liquid and the sample cells used (McKnight & Thompson 1975).

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Fig. 2.— Reflectivity of lithium ammonia. Theoretical curve (solid line) for the reflectivity of Li(NH₃)₄ at 93 K. Data at 195 K (squares) are from McKnight & Thompson (1975).

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Figure 3 shows the measured vapor pressure for lithium ammonia (Lo 1966) fit to a simple standard vapor pressure model (Dickerson 1979) which assumes that enthalpy and entropy do not vary with temperature over the range studied. Extrapolation of this fitting function to 93 K yields a vapor pressure ∼2.8 × 10^-8 mm Hg. At this vapor pressure, Langmuir’s equation for evaporation (Langmuir, 1913) predicts a loss of 7 × 10^-9 kg (m² s)^-1. A 50 m diameter telescope would have evaporation of about 1 kg of liquid (out of several metric tons) per day for operation. Liquid could be replenished in discrete steps, and it may even be feasible to trap the evaporating liquid so it is not lost. It may also be possible to reduce the vapor pressure by adding additional elements to the mix or creating a different layer on the surface. As an example, the vapor pressure of liquid mercury is reduced by over 5 orders of magnitude by the formation of a transparent surface layer that does not hinder the reflectivity (Hickson et al., 1993). Adding 1% excess Li to Li(NH₃)₄ at 230 K reduces the vapor pressure by over an order of magnitude (Lo 1966). One could also consider using some sort of window over the top, as is currently done with the Large Zenith Telescope (Hickson et al. 2007).

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Fig. 3.— Vapor Pressure of Li(NH₃)₄. Measured vapor pressure (squares) of Li(NH₃)₄ from Lo (1966) and fit to the data (solid line). For the vapor pressure fitting function, G is the free energy, T is the temperature, and C is a constant. Inset shows close-up of the region fit. Clearly more data at the low temperature end is needed to accurately determine the vapor pressure near melting.

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Li(NH₃)₄ has other valuable properties for a liquid telescope. A simple mixing of the constituents suffices to create the solution. It is also a very low density (∼0.5 g cm^-3) liquid. The low density minimizes the weight of liquid required for a given size telescope. For instance, a 50 m diameter telescope with a 2 mm thick liquid mirror would require about 2 metric tons of liquid. For comparison, a liquid mercury mirror of the same diameter and thickness would need a mass of about 54 metric tons. The low mass of the liquid reduces the demands on the support structure as well as transport costs.

Lithium ammonia has several advantages over the proposed ionic liquids. First, its density is lower by a factor of 2–3. In addition, there is no need for coating the liquid on site. This eliminates the weight of the coating equipment as well as the silver needed for the coating. Perhaps more importantly, it eliminates another step in the assembly procedure.

4. SUMMARY

A large liquid lunar telescope would offer many opportunities for studies of the early universe. Liquid Li(NH₃)₄ offers many potential advantages as the reflecting liquid for a rotating infrared lunar telescope. Further studies, in particular of its vapor pressure, its reflectivity, and the optical quality of its surface just above its melting temperature are needed to evaluate the suitability of this material.