Absorption Coefficients of the Methane-Nitrogen Binary Ice System: Implications for Pluto
The methane-nitrogen phase diagram of Prokhvatilov and Yantsevich 16 indicates that at temperatures relevant to the surfaces of icy dwarf planets like Pluto, two phases contribute to the methane absorptions: nitrogen saturated with methane :CH and methane saturated with nitrogen :N. No optical constants are available so far for the latter component limiting construction of a proper model, in compliance with thermodynamic equilibrium considerations. New optical constants for solid solutions of methane diluted in nitrogen (N:CH) and nitrogen diluted in methane (CH:N) are presented at temperatures between 40 and 90 K, in the wavelength range 1.1–2.7 m at different mixing ratios. These optical constants are derived from transmission measurements of crystals grown from the liquid phase in closed cells. A systematic study of the changes of methane and nitrogen solid mixtures spectral behavior with mixing ratio and temperature is presented.
keywords:Ices, IR spectroscopy, Pluto, Trans-neptunian objects
Pluto, Eris, and Makemake, unlike most trans-Neptunian objects (TNOs) with water-ice rich or featureless surfaces 2, display infrared spectra dominated by methane ice 3. These three TNOs are often compared with Neptune’s large satellite Triton, since its spectrum is dominated by methane ice and it is thought to have formed similarly to Pluto, Eris, and Makemake, prior to its capture into a retrograde orbit around Neptune. In addition to methane ice, nitrogen ice has been directly detected on Pluto and Triton via the 2.148-m absorption band 6; 15. Additional evidence for nitrogen ice on Pluto and Triton comes from shifts of their methane absorption bands to shorter wavelengths, which occurs, as described by Quirico and Schmitt 18, when methane is dissolved at low concentrations in a matrix of solid nitrogen. Moderately high signal-to-noise spectra of Makemake and Eris show no evidence for the presence of the 2.148-m nitrogen absorption feature. Their methane bands do present subtle shifts, albeit smaller than the shifts measured in spectra of Pluto and Triton. A laboratory study by Brunetto et al. 5 showed that smaller shifts correspond to higher methane abundances. The lack of the 2.15-m nitrogen absorption band and the smaller methane wavelength shifts led several authors 4; 1; 13 to the conclusion that Eris and Makemake are not nitrogen dominated, contrary to Pluto and Triton.
Thermodynamic equilibrium dictates that if methane and nitrogen ices are both present, for most of the range of possible nitrogen/methane relative abundances, two distinct phases must coexist at temperatures relevant to the surfaces of these icy dwarf planets 16; 12: methane ice saturated with nitrogen and nitrogen ice saturated with methane.
Tegler et al. 21 demonstrated that the depth of the methane and nitrogen absorption bands and the wavelength shift of the observed methane absorption features should not be used as proxy for the methane-nitrogen mixing ratio. The phase composition as dictated by thermodynamic equilibrium must be taken into account. In particular, Tegler et al. 21 model each of the observed methane absorption bands with a binary mixture of methane ice saturated with nitrogen and nitrogen ice saturated with methane, according to the methane-nitrogen phase diagram of Prokhvatilov and Yantsevich 16. This technique, applied so far to the cases of Eris and Pluto only, results in the finding that the bulk volatile composition of Eris is similar to that of Pluto, with both objects being dominated by nitrogen ice. A correct modeling of the methane absorption bands has strong implications not only on the methane-nitrogen mixing ratio, but also enables exploration of stratification properties as well as heterogeneity of these targets 21; 22. Because of the lack of absorption coefficients for methane saturated in nitrogen and for nitrogen saturated in methane at the appropriate temperatures in the visible wavelength ranges, Tegler et al. 21 approximate the methane-dominated phase by using pure methane absorption coefficients and the highly diluted phase by shifting pure methane coefficients by amounts seen for highly diluted samples 18.
In this paper we provide optical constants in the wavelength range 1.1–2.7 m of solid solutions of methane diluted in nitrogen, N:CH, and nitrogen diluted in methane, CH:N, at temperatures between 40 and 90 K and at different mixing ratios (http://www2.lowell.edu/users/grundy/abstracts/2015.CH4+N2.html), allowing a proper model to be constructed for any TNO where the methane/nitrogen ratio falls between the two solubility limits such that both saturated phases are present. Gaining more detailed knowledge of the methane/nitrogen mixing ratio and phase state of Pluto, Triton, Eris, and Makemake will enable a better understanding of the processes responsible for volatile loss and retention on TNOs 19. It will also help constrain the seasonal behaviors of their atmospheres, supported by vapor pressure equilibrium with surface ices. It will also shed light on the photolytic and radiolytic chemistry that can occur within the surface ices, since radicals produced by energetic radiation will encounter and react with different molecules within a nitrogen-dominated or a methane-dominated solid phase.
2 Laboratory Experiments
The experiments reported here were conducted in a new laboratory ice facility located in the Department of Physics and Astronomy of Northern Arizona University. A detailed description of this facility is given by Tegler et al. 21; Tegler et al. 22 and Grundy et al. 9. We used the closed cell technique for the ice sample preparation. This technique consists in the growth of crystals from the liquid phase in a closed cryogenic cell. Crystals are grown as follows. The sample is prepared in gas form in a 2 liter mixing volume. Here we report experiments obtained mixing methane (CH) and nitrogen (N). The purities of the gases used are 99.999% for CH and 99.9% for N, as reported by the vendors. The gas is set to flow into an empty cell, which is at a temperature slightly higher than the melting point of the ice sample. In the case of mixtures, the melting point depends on the mixing ratio of the gases and we use, as reference, the CH-N phase diagram of Prokhvatilov and Yantsevich 16. The gas, once in the cell, condenses immediately to liquid. The liquid is frozen by reducing the temperature in the cell at a rate of 0.1 K minute. A thermal gradient is maintained within the cell with the top and bottom heaters such that the crystal grows from the bottom to the top. Once the sample is frozen, the vertical thermal gradient is minimized. After the initial ice spectrum is recorded, the temperature is ramped down at 0.1 K minute. We recorded spectra at temperatures between 40 and 90 K.
A 5 mm cell, with sapphire (AlO) windows, was used (Figure 1). Thinner samples, needed in the case of mixtures with high CH content, were prepared by use of a transparent potassium bromide (KBr) or calcium fluoride (CaF) spacer between the windows. These KBr and CaF spacers occupied only part of the cell, enabling the choice of the full or reduced thickness, simply by moving the sample relative to the spectrometer beam. The thickness of the sample in absence of spacer is equal to the cell depth, , which is known. On the other side of the cell, due to the uncertainties on the depth of the KBr and CaF spacers, the sample has an unknown thickness, . This is computed with a liquid CH experiment. Two transmission spectra are recorded, and , by positioning the spectrometer beam away and in correspondence of the spacer, respectively. From the two transmission spectra, we compute the imaginary part of the refractive index, and , which will be function of and the unknown , respectively. Because the imaginary part of the refractive index, , is a property intrinsic to the material, we compute by setting = (see Section 3).
Spectra were recorded with a Nicolet Nexus 670 Fourier transform infrared (FTIR) spectrometer, covering the range 2799.9 – 12000.1 cm at a sampling interval of 0.24 cm, resulting in a spectral resolution of 0.6 cm (FWHM of unresolved lines). We averaged over 100 spectral scans to improve the signal-to-noise ratio.
3 Data Analysis
3.1 Calculation of n and k
The purpose of our measurements is to compute optical constants of methane-nitrogen ice mixtures, CH-N. The optical constants of a material are the real and imaginary part of the complex refractive index , and are both functions of the frequency . Let be the transmission spectrum of an ice sample within a cell of thickness (Figure 1), we compute the imaginary part of the refractive index, , via the Beer-Lambert absorption law:
In order to remove the flux distribution of the illumination source, the transmission function of the spectrometer and the cell, the detector spectral sensitivity function, and the water vapor contamination 10; 22, we compute the transmission spectrum as:
where and represent the transmission through the cell when filled by the sample and empty, respectively (Figure 2). Specifically, is the average of the transmission spectra through the empty cold cell recorded before and after the ice sample experiment.
The transmission spectra, whether the cell is filled or empty, present a high frequency interference pattern due to the windows in the cell, which we remove using a Fourier filter. The resultant transmission spectrum is affected by subtle slopes from a variety of sources 10. In order to remove these slopes, we divide the spectrum by the fit to the continuum regions adjacent to the absorption bands to be analyzed. The continuum of our spectra is well fit by a third order polynomial.
Given the imaginary part of the refractive index, , we calculate from the Kramers-Kronig dispersion relation
where is the value of at the high-frequency end of the infrared, and the integration is over the infrared region of the spectrum. In the case of pure CH, is equal to 1.32 at 15800 cm 25. We will adopt the same value also for CH-N mixtures.
After computing and , we refine these calculations by taking into account first-order differences in transmission through boundaries between cell windows and vacuum in the case of empty cell, , and between cell windows and ice in the case of filled cell, . If the spectra are acquired by putting the beam on the side of the cell containing the KBr or CaF, we have to take into account the interfaces between the ice or vacuum and the KBr or CaF, as well (Figure 1). In this case, we have:
where represents the transmission across the boundary between the media with refractive index () and . Multiple reflections that are set up within the slab as the wave bounces back and forth at the top and bottom interfaces are considered negligible. For the case of normal incidence we have:
where and are given by:
The transmission spectrum and optical constants ( and ) of pure CH ice at 40 K are shown in four different bands in Figure 3.
3.2 Pure CH ice
Grundy et al. 11 present an exhaustive analysis of the temperature-dependent near-infrared absorption spectra of pure CH ice, available at temperatures between 30 and 93 K. Our measurements for pure CH ice at 40 K are compared with that by Grundy et al. 11 in Figure 4. The absorption spectra, , by Grundy et al. 11 have been converted for comparison purposes into the imaginary part of the refractive index, , by means of the dispersion relation . While the data by Grundy et al. 11 are obtained combining measurements acquired with different cell thicknesses, enabling measurement of the weakest and strongest CH absorptions, our data for pure CH ice correspond to a single sample of thickness 0.0252 cm. This prevents us from measuring absorption where it approaches zero or 100%. Therefore, we provide our results in narrow blocks of wavelengths covering regions of intermediate absorption. Differences in band strength between our measurements and those by Grundy et al. 11 are observed, as shown in Figure 4 for T= 40 K. Similar discrepancies between the two data sets are observed at all temperatures. This mismatch could be due to continuum removal, uncertainty in the sample thickness and/or temperature, transmission across the boundaries not taken into account when converting the absorption coefficients reported by Grundy et al. 11 into .
The general character of the temperature dependence of the pure CH ice absorption coefficients discussed by Grundy et al. 11 is confirmed by our data (Figure 5): lower temperature spectra exhibit narrower and higher peak absorptions which broaden and decrease in strength as the ice is warmed. Most of the CH ice bands do not show significant temperature-dependent wavelength shifts. Nevertheless subtle shifts occasionally arise; a good example can be seen at 6735 cm. Figure 6 displays the peak position of the +3 CH ice band centered around 6735 cm as a function of temperature. The peak position has been estimated as the average of the position where the maximum of the band occurs and the maximum of the gaussian function fit to the data around the band center. The error is the dispersion between the two estimates.
3.3 Ch-N Solid Mixtures
The methane and nitrogen stoichiometry of a CH-N solid mixture is estimated by dividing the integrated spectrum of the mixture by the corresponding integrated spectrum of pure CH ice. This results in the fraction of CH in the mixture. Given the temperature dependence of the pure CH ice optical constants (see Section 3.2), spectra of CH-N mixtures and pure CH acquired at the same temperature are compared. This procedure is applied in the frequency ranges from 5300 – 6440 cm, 6700 – 7650 cm, and 8100 – 9000 cm. in Table LABEL:tabA represents the CH fraction computed in the interval centered around . The values obtained at all temperatures and frequency ranges for a given CH-N mixture are averaged, resulting in the CH stoichiometry of our sample ( [%]). The mean CH content, [%], is listed in Table LABEL:tabA for all our experiments. The error on the concentration is given by the scatter of the values computed at all temperatures and frequency ranges and it is generally less than 5%.
The measurements we present encompass both sides of the CH-N phase diagram of Prokhvatilov and Yantsevich 16, Figure 7 enabling us to characterize the spectral behavior of solid solutions of CH diluted in N (N:CH) and N diluted in CH (CH:N) at different temperatures and mixing ratios. Example optical constants of CH:N (92.04% CH) and N:CH (12.48% CH) at two different temperatures at low spectral resolution are reported in Table LABEL:OpticalConstantsTable.
Laboratory data of CH:N and N:CH at the solubility limits of CH and N in each other, which we indicate with :N and :CH respectively, give the means to generate optical constants of CH-N mixtures with any bulk composition between the solubility limits, at a given temperature (Figure 7). This is possible through the lever rule, which is a tool used to determine the molar percentage of each phase (in our case :N and :CH) in a two phase alloy in equilibrium. The molar percentage of the :N phase in a CH-N mixture is
where and represent the solubility limit of CH in the :N and :CH phases, respectively, and is the overall CH abundance in the mixture. At 55 K the solubility limits of CH in the CH-rich and N-rich saturated phases are close to 82.69% and 16.35%, corresponding to measurements of optical constants we made in the laboratory (filled diamond and open downward triangle in Figure 7). It is therefore possible to generate synthetically the optical constants of any CH-N mixture at 55 K. To a first order approximation our data behave consistent with expectation from the lever rule (see Figure 8).
Methane-nitrogen mixtures present a temperature-dependent behavior similar to that of pure CH (Section 3.2). We characterize the thermal broadening of CH ice absorption bands by measuring their full widths at half maximum (FWHM) as a function of temperature and stoichiometry (Figure 9). This analysis has been conducted for those CH-bands that are isolated, not influenced by the wings of adjacent bands. These are the , , and CH-band, centered, in a sample of pure CH at 90 K, at 4526, 5800, and 7487 cm, respectively. All bands we measured show a nearly linear dependence of FWHM with temperature, at all stoichiometries. Furthermore, the CH bands of CH:N samples broaden faster than those of N:CH, as expected given the higher CH content in CH:N than in N:CH mixtures.
The imaginary part of the refractive index, , of CH-N ice mixtures at different mixing ratios at T=60 K is shown in Figure 10. CH when dissolved in N presents absorption bands shifted toward shorter wavelengths compared to the central wavelengths of pure CH. This shift varies with the CH abundance in the mixture: the larger the CH concentration the smaller the blueshift. We estimate the spectral shift by means of a cross correlation technique. We shift a band in the pure CH spectrum relative to the same band in the mixture spectrum and for each shift a is computed. The versus shift behavior is fitted with a parabola, whose minimum position corresponds to the shift solution for the analyzed band. This method is described in detail by Tegler et al. 23. Another possible approach is, for a given band, to determine the difference between the peak positions in the CH-N and pure CH samples, with the peak position estimated as described in Section 3.2. The solutions obtained with these different techniques are averaged, and the dispersion between them is taken to be representative of the uncertainty. In order to correctly determine the blueshift of the CH-N bands relative to pure CH, spectra acquired at similar temperatures are compared, given the temperature dependent behavior of the CH bands peak position (Section 3.2).
The blueshift of four CH bands versus CH abundance is reported in Figure 11. For a given CH stoichiometry, different measurements correspond to different temperatures. No significant variations in the wavelength shift with respect to temperature are observed. Filled rightfacing triangles in Figure 11, contrary to the other symbols that represent samples generated in the laboratory (see legend in Figure 7 and Table LABEL:tabA), refer to optical constants computed synthetically by applying the lever rule at 55 K for a range of CH abundance between 30% and 70%, in 10% steps. The N-enriched and CH-enriched sides of the phase diagram present a different linear trend of the blueshift versus CH abundance (dashed and solid lines in Figure 7). Such trend varies from band to band.
4 Applications to Pluto
Efforts to quantitatively model Pluto’s spectrum over the course of the years identified several important issues. The first concerns the state of CH ice on Pluto’s surface. Seen at high spectral resolution, the CH bands in Pluto’s spectrum are shifted toward shorter wavelengths compared to the central wavelengths of pure CH obtained in the laboratory, implying CH being dissolved at low concentrations in a matrix of solid N 20; 18. Additionally, the identification of the 1.69-m band in Pluto’s spectrum has been interpreted so far as the evidence of the presence of pure CH on Pluto. Indeed, the 1.69-m CH feature has never been observed in any sample of CH diluted at low concentrations in N (neither in - or -N phases) at any temperature. These considerations together with the lack of optical constants for CH with a small fraction of N are the main arguments behind the approach taken in analyzing Pluto spectra in the last decade e.g., 8; 14; 17, employing pure CH and CH diluted at low concentrations in N.
The set of optical constants presented in this work enable us to compare and contrast samples with CH dissolved at low concentrations in a matrix of solid N (N:CH), and CH with a small fraction of N (CH:N). These data reveal that the 1.69-m band of Pluto’s spectrum can no longer be considered as evidence for the presence of pure CH on Pluto’s surface, as this feature is observed not only in samples of pure CH (at temperatures below 60 K, Figure 5), but also in CH:N samples (Figure 10). Also, the wavelength shift of Pluto’s CH bands with respect to that of pure CH, does not necessarily imply the presence of CH being dissolved at low concentrations in a matrix of solid N, as the wavelength shift is a linear function of the CH abundance (Figure 11).
The quantitative analysis of the wavelength shift versus abundance indicates that the wavelength shift of the CH bands is indeed a good dilution indicator. The linear fits of the wavelength shift as a function of CH abundance for different CH bands provide the tools to infer the CH-N mixing ratio on the surface of Pluto, or any TNO covered by CH and N. Also, it is extremely important to stress that the linear dependency of the shift versus CH abundance changes from band to band. This needs to be taken into account when comparing the shift of deeper and shallower bands to address stratification properties 13.
Our new optical constants enable us to model for the first time Pluto’s near-infrared spectroscopic measurements in compliance with thermodynamic equilibrium, superseding more than a decade of work in which Pluto’s spectrum was interpreted in terms of a combination of “diluted” and “pure” CH components. To account for thermodynamic equilibrium on Pluto’s surface, we need instead to consider methane saturated with nitrogen, :N, and nitrogen saturated with methane, :CH, as dictated by the N-CH binary phase diagram Figure 7, 16 and suggested by Trafton 24 and Cruikshank et al. 7. Specifically, for a plausible Pluto volatile ice temperature of 40 K 26, the diagram shows that the solubility limits of CH and N in each other are about 5% (:CH, with 5% CH) and 3% (:N with 3% N). While we have optical constants available for the former phase (see Figure 7), the latter is not available yet. However, we have laboratory data covering a wide range of temperatures and mixing ratios to synthetically reproduce the lacking set of optical constants. The laboratory measurements presented in this work cover the wavelength range of the LEISA spectrometer on board of the New Horizons spacecraft 27, which will flyby Pluto in July 2015 and therefore will help to improve the scientific outcome of this mission.
The authors gratefully thank NASA’s Outer Planets Research program (grant #NNX11AM53G) for funding that supported this work and the Mt. Cuba Astronomical Foundation for hardware upgrades used in the experiments described in this paper. J. Bergonio thanks the National Science Foundation’s Research Experience for Undergraduates grant AST-1004107 to Northern Arizona University that enabled his contribution. We also thank two anonymous reviewers for their constructive suggestions that helped to improve this paper and M. Adamkovics for valuable pointers on implementation of the Kramers-Kronig calculation. Finally, we thank the free and open source software communities for empowering us with key software tools used to complete this project.
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