Broadband spectroscopy of astrophysical ice analogues: IV. Optical constants of N$_2$ ice in the terahertz and mid-infrared ranges

TL;DR

This work delivers direct measurements of the broadband optical constants of N$_2$ ice from $0.3$ to $16$ THz by combining terahertz pulsed spectroscopy and Fourier-transform infrared spectroscopy, supported by DFT calculations. The data reveal two optically active phonon resonances at $1.47$ THz and $2.13$ THz, well described by a Lorentz dielectric model with parameters extracted from the measurements. DFT calculations of the α-N$_2$ vibrational modes corroborate the experimental translational phonons and validate the interpretation of the THz features. By providing a complete THz–IR optical constants dataset for N$_2$ ice, this study enhances radiative-transfer modeling for nitrogen-bearing environments in protoplanetary disks and helps bridge gaps in observational capabilities between JWST and ALMA, with implications for snowlines and disk mass estimates.

Abstract

Context. Understanding the optical properties of astrophysical ices is crucial for modeling dust continuum emission and radiative transfer in cold, dense interstellar environments. Molecular nitrogen (N$_2$), a major nitrogen reservoir in protoplanetary disks, plays a key role in nitrogen chemistry, yet the lack of direct terahertz (THz)--infrared (IR) optical constants for N$_2$ ice introduces uncertainties in radiative transfer models, snowline locations, and disk mass estimates. Aims. We present direct measurements of the optical properties of N$_2$ ice over a broad THz--IR spectral range using terahertz pulsed spectroscopy (TPS) and Fourier-transform infrared spectroscopy (FTIR), supported by density functional theory (DFT) calculations and comparison with literature data. Methods. N$_2$ ice was grown at cryogenic temperatures by gas-phase deposition onto a cold silicon window. The THz complex refractive index was directly reconstructed from TPS data, while the IR response was derived from FTIR measurements using Kramers--Kronig relations. The optical response was parameterized with a Lorentz dielectric model and validated by DFT calculations. Results. The complex refractive index of N$_2$ ice is quantified from $ν= 0.3$--$16$~THz ($λ= 1$~mm--$18.75~μ$m). Resonant absorption peaks at $ν_\mathrm{L} = 1.47$ and $2.13$~THz with damping constants $γ_\mathrm{L} = 0.03$ and $0.22$~THz are attributed to optically active phonons of the $α$-N$_2$ crystal. Conclusions. We provide a complete set of the THz--IR optical constants for \ce{N2} ice by combining TPS and FTIR spectroscopy. Our results have implications for future observational and modeling studies of protoplanetary disk evolution and planet formation.

Figures (4)

• Figure 1: Reference and sample spectra of N2 ice, measured by the TPS (solid lines) and FTIR (dashed lines) spectrometers at specified deposition steps, $t_\mathrm{dep}$, and normalized by the maximum of the corresponding reference spectrum (for convenience). The low-frequency gray-shaded area shows the spectral range where distortions are expected owing to the THz beam diffraction at the sample aperture AA.629.A112.2019. The orange-shaded area near $\simeq 2.0$ THz (enlarged in the inset for clarity) indicates where the TPS and FTIR data overlaps. Sensitivity of the TPS and FTIR measurements is characterized by the standard deviation of the corresponding instrumental noise, $\sigma_\mathrm{TPS}$ and $\sigma_\mathrm{FTIR}$ as described by 2022AA...667A..49G.
• Figure 2: Merging of the TPS and FTIR data for N$_2$ ice after the $54$-min-long deposition. (a) Amplitude of the complex transmission coefficient $\left| \widetilde{T} \left( \nu \right) \right|$ retrieved from the TPS (green markers) and FTIR (blue) data, and the resultant merged curve (red) see Eqs. (\ref{['eq:T_TPS']})--(\ref{['eq:T_FTIR']}) for the definitions of the transmission coefficients. (b) Zoom-in on the TPS and FTIR overlapping data. (c) Phase of the complex transmission coefficient $\phi\left( \nu \right)$, where the TPS phase $\phi_\mathrm{TPS}$ (green markers), FTIR-based Kramers-Kronig phase $\phi_\mathrm{K-K}$ (blue line), and resultant broadband phase (red) are shown. (d) Low-frequency behavior of the FTIR-based Kramers-Kronig phase $\phi_\mathrm{K-K}$.
• Figure 3: Broadband THz--IR optical properties of the N2 ice, deduced from the measurements of sample of different thicknesses $l$. The yellow solid lines show the mean values, the green shaded zones, the $\pm 1.5\sigma$ ($87$%) confidence intervals of the measurements, while the red solid lines, the complex dielectric permittivity model defined by Eq. \ref{['EQ:LorentzModel']} and Table \ref{['TAB']}. (a) Refractive index $n$. (b, c) Absorption coefficient $\alpha$ (by field) in the linear and logarithmic scales, respectively. In (c), the blue-shaded solid lines define the $3\sigma$ detection limits for the absorption $\delta \alpha$, calculated for the different ice thicknesses $l$ (measured with the $\sim0.01$ mm uncertainty). In (a)--(c), the vertical blue dashed lines define the frequencies of the $\alpha$-N2 vibrational modes predicted by the DFT method.
• Figure 4: The balls and sticks model of the $3 \times 3 \times 3$ cluster of $\alpha$-N2 ice is derived by cutting a $3 \times 3 \times 3$ repeated bulk using the same procedure adopted for obtaining the $2 \times 2 \times 2$ cluster model, which is also schematically reported here for comparison.