# The Impact of Organic Hazes and Graphite on the Observation of CO2-rich Sub-Neptune Atmospheres

Haixin Li, Chao He, Sai Wang, Zhengbo Yang, Yu Liu, Yingjian Wang, Xiao'ou Luo, Sarah E Moran, Cara Pesciotta, Sarah M Hörst, et al.

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Haixin Li, Chao He, Sai Wang, Zhengbo Yang, Yu Liu, et al. The Impact of Organic Hazes and Graphite on the Observation of CO2-rich Sub-Neptune Atmospheres. The Astrophysical Journal Letters, 2025, 990, 10.3847/2041-8213/adfa87. hal-05408835

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# The Impact of Organic Hazes and Graphite on the Observation of CO₂-rich Sub-Neptune Atmospheres

Haixin Li<fnref n="1" />, Chao He<fnref n="1" />, Sai Wang<fnref n="1" />, Zhengbo Yang<fnref n="1" />, Yu Liu<fnref n="1" />, Yingjian Wang<fnref n="1" />, Xiao'ou Luo<fnref n="1" />, Sarah E. Moran<fnref n="2" />,
Cara Pesciotta<fnref n="3" />, Sarah M. Hörst<fnref n="3" />,<fnref n="4" />, Julianne I. Moses<fnref n="5" />, and Véronique Vuitton<fnref n="6" />

Received 2025 July 18; revised 2025 August 5; accepted 2025 August 8; published 2025 September 10

## Abstract

Many sub-Neptune and super-Earth exoplanets are expected to develop metal-enriched atmospheres due to atmospheric loss processes such as photoevaporation or core-powered mass loss. Thermochemical equilibrium calculations predict that at high metallicity and a temperature range of 300-700 K, CO₂ becomes the dominant carbon species, and graphite may be the thermodynamically favored condensate under low-pressure conditions. Building on prior laboratory findings that such environments yield organic haze rather than graphite, we measured the transmittance spectra of organic haze analogs and graphite samples and computed their optical constants across the measured wavelength range from 0.4 to 25 µm. The organic haze exhibits strong vibrational absorption bands, notably at 3.0, 4.5, and 6.0 µm, while graphite shows featureless broadband absorption. The derived optical constants of haze and graphite provide the first data set for organic haze analogs formed in CO₂-rich atmospheres and offer improved applicability over prior graphite data derived from bulk reflectance or ellipsometry. We implemented these optical constants into the Virga and PICASO cloud and radiative transfer models to simulate transit spectra for GJ 1214b. The synthetic spectra with organic hazes reproduce the muted spectral features in the near-infrared observed by Hubble and general trends observed by JWST for GJ 1214b, while graphite models yield flat spectra across the observed wavelengths. This suggests haze features may serve as observational markers of carbon-rich atmospheres, whereas graphite's opacity could lead to radius overestimation, offering a possible explanation for superpuff exoplanets. Our work supplies essential optical to infrared data for interpreting observations of CO₂-rich exoplanet atmospheres.

*Unified Astronomy Thesaurus concepts: Exoplanet atmospheres (487); Exoplanet atmospheric composition (2021); Laboratory astrophysics (2004); Transmission spectroscopy (2133)*

## 1. Introduction

Super-Earths and sub-Neptunes are the most abundant exoplanet types discovered to date (e.g., A. W. Howard et al. 2012; N. M. Batalha et al. 2013; F. Fressin et al. 2013; L. Parc et al. 2024). These planets, with radii between Earth and Neptune, have no direct analogs in the present-day solar system, making them particularly important targets to improve our understanding of planetary atmospheres. A bimodal radius distribution—commonly referred to as the “radius valley”— suggests that many sub-Neptunes may evolve into super-Earths via their primordial hydrogen/helium envelopes loss through photoevaporation or core-powered mass loss (e.g., B. J. Fulton et al. 2017; V. Van Eylen et al. 2018; A. Gupta & H. E. Schlichting 2019; J. G. Rogers & J. E. Owen 2021).

The resulting stripped planets are expected to develop secondary atmospheres with high metallicity, often dominated by heavier molecules such as CO₂. These atmospheres may enter a graphite-stable regime, where graphite is predicted to be the thermodynamically stable solid end product among

carbon-bearing species (e.g., J. I. Moses et al. 2013; P. Woitke et al. 2021). Figure 1 illustrates the dominant carbon species as a function of temperature and metallicity with solar C/O, ~0.577 (K. Lodders et al. 2009), at 5 mbar as Hubble Space Telescope (HST)/JWST probe this region. Many observed sub-Neptunes and super-Earths have equilibrium temperatures of 300–800 K, overlapping with this regime. To investigate haze formation under such conditions, we simulate 2000× solar metallicity atmospheres at 300 and 500 K. In our companion study, we found that organic hazes rather than graphite form under such low-pressure CO₂-rich conditions (S. Wang et al. 2025). However, graphite may still condense in deeper, hotter atmospheric layers and be uplifted into the upper atmosphere, motivating a comparative study of the spectral impacts of both organic haze and graphite aerosols.

Recent observational and laboratory evidence increasingly supports the ubiquity of haze in sub-Neptune and super-Earth atmospheres (e.g., L. Kreidberg et al. 2014; C. He et al. 2018; S. M. Hörst et al. 2018; K. Ohno et al. 2025; N. L. Wallack et al. 2024; J. Teske et al. 2025). Hazes can alter a planet's thermal structure, albedo, and circulation, and suppress spectral features, complicating atmospheric characterization and habitability assessments (e.g., C. V. Morley et al. 2015; P. Gao et al. 2021). Their impacts are strongly dependent on

<figure><img src="image_3.png" /></figure>

Original content from this work may be used under the terms of the [Creative Commons Attribution 4.0 licence](https://creativecommons.org/licenses/by/4.0/). Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.

<footnote n="1">¹ State Key Laboratory of Lithospheric and Environmental Coevolution, School of Earth and Space Sciences, University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China; chaohe23@ustc.edu.cn</footnote>

<footnote n="2">² NHFP Sagan Fellow, NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA</footnote>

<footnote n="3">³ Department of Earth and Planetary Sciences, Johns Hopkins University, Baltimore, MD, USA</footnote>

<footnote n="4">⁴ Space Telescope Science Institute, Baltimore, MD, USA</footnote>

<footnote n="5">⁵ Space Science Institute, Boulder, CO, USA</footnote>

<footnote n="6">⁶ Univ. Grenoble Alpes, CNRS, IPAG, 38000 Grenoble, France</footnote>
<figure><img src="image_4.png" /><figcaption>**Figure 1.** Thermochemical equilibrium of carbon species. The calculations from the CEA code (S. Gordon & B. J. McBride 1994) at 5 mbar and solar C/O ratio, ~0.577 (K. Lodders et al. 2009), show the dominant carbon-bearing gas (CH₄, CO, or CO₂) as a function of temperature and metallicity. The shaded region indicates where solid graphite is thermodynamically favored. Red and blue stars mark the experimental conditions for the 500 and 300 K haze samples, both at 2000× solar metallicity. Pie charts illustrate the corresponding initial gas mixtures, composed of CO₂ (orange), CH₄ (red), N₂ (green), H₂O (blue), He (gray), and H₂ (purple), calculated from CEA without graphite in the list of species. The mean molecular mass of the 500 and 300 K cases are 27.4 and 28.2 g mol⁻¹, respectively.</figcaption></figure>

the optical properties, which vary greatly among different haze types (e.g., organics, soot, sulfur) and even within organic hazes formed under different conditions (C. V. Morley et al. 2015; P. Gao et al. 2017; L. Corrales et al. 2023; C. He et al. 2024). The atmospheric retrievals of exoplanet observations from advanced telescopes like JWST and the upcoming ARIEL mission (e.g., C. Beichman et al. 2014; G. Tinetti et al. 2018) also strongly rely on the optical properties of laboratory-derived hazes. However, only a limited set of laboratory-derived haze reference data are available, mostly derived from N₂- or H₂O-rich haze analogs (e.g., B. N. Khare et al. 1984; L. Corrales et al. 2023; T. Drant et al. 2024; C. He et al. 2024), leaving CO₂-rich hazes poorly constrained. Using mismatched haze data may lead to inaccurate retrievals of key molecular abundances (e.g., H₂O, CH₄), as well as particle size, potentially leading to broader misinterpretations of atmospheric properties.

Meanwhile, the optical constants of graphite remain uncertain, with large discrepancies across data sets due to variations in sample morphology and measurement methods (e.g., A. B. Djurišić et al. 2000; B. T. Draine 2003a, 2003b; A. B. Kuzmenko et al. 2008; R. J. Papoular & R. Papoular 2014; B. T. Draine 2016). Most existing data are derived from bulk solids or thin films, which do not accurately represent suspended atmospheric aerosols, limiting their utility to atmospheric modeling and retrievals. Therefore, new laboratory measurements under conditions relevant to planetary observations are necessary. In addition, measuring optical properties of organic hazes and graphite using the same method enables the direct comparison of their spectral impacts and provides a more reliable data set for modeling the potential spectral signatures of carbon-rich haze in exoplanet atmospheres.

This Letter is organized as follows: Section 2 describes the production and spectral measurement of haze analogs, along with optical constant computing and spectral modeling methods. Section 3 presents the transmittance spectra, computed optical constants, and their impact on observed planetary spectra. We compare organic haze and graphite cases to evaluate their spectral differences and implications for exoplanet atmospheric characterization. Section 4 summarizes the key findings and their relevance to interpreting muted or featureless spectra in carbon-rich atmospheres.

## 2. Methods

### 2.1. Sample Preparation

We performed laboratory simulations of CO₂-rich sub-Neptune atmospheres at 300 and 500 K using the Planetary Haze Research experimental setup. The gas mixture as shown in Figure 1 was exposed to AC glow discharge (cold plasma) for ~100 hr within the chamber. After each experiment, samples were collected as dry powders inside of the inert nitrogen glove box to avoid contamination from moisture or atmospheric oxygen. The setup and detailed experimental procedure have been described in previous studies (C. He et al. 2017, 2018, 2022, 2024; S. M. Hörst et al. 2018; S. Wang et al. 2025). The gas compositions shown in Figure 1 fall well within the graphite-stability regime and are predicted to form graphite based on thermochemical equilibrium modeling (J. I. Moses et al. 2013; P. Woitke et al. 2021).

### 2.2. Pellet Preparation and Spectral Measurements

We measured the transmittance spectra of the collected haze particles using the established KBr pellet method (C. He et al. 2024), whereby KBr is dried and powdered before mixing with
the desired material. KBr is used because it has a low opacity from the UV to mid-infrared. The samples and KBr were mixed at the desired ratio and then ground to 0.7–2.2 µm using a ball-mill grinder. Moreover, ~200 mg of the mixture was then pressed into a pellet using a pellet die, with pressure applied in three stages: 3 tons for 2 s, 7 tons for 30 s, and 10 tons for 120 s for both haze and graphite pellets. The mass concentration of the organic hazes/KBr pellets is ~0.3%, which has proved to be an appropriate concentration for optical constant retrieval of organic haze materials (C. He et al. 2024). For comparison, reference graphite pellets were prepared by mixing graphite powder (obtained from Sigma-Aldrich and ground to 0.7–2.2 µm) with KBr following the same procedure. Given the much stronger absorption of graphite, three graphite/KBr pellets with lower and varied mass concentrations (0.008%, 0.0016%, 0.03%) were made for accurate optical constant calculation.

For both organic haze and graphite pellets, the effective optical thickness d of each sample was calculated from

$$d = \frac{m}{\pi r^2 \rho}, \qquad (1)$$

where m is the mass of haze or graphite particles in the pellet, r is the pellet radius, and ρ is the measured density of the samples (S. Wang et al. 2025).

All spectral measurements were performed using a Bruker Vertex 70v vacuum Fourier-transform infrared spectrometer at room temperature (294 K). The system was operated under vacuum conditions (≤0.2 mbar) to eliminate spectral interference from atmospheric H₂O and CO₂. The instrument was equipped with two beamsplitters (quartz and KBr) and two detectors (silicon diode and DLaTGS) to cover the full range of 0.4–28.5 µm, encompassing the optical to mid-infrared regions relevant for exoplanetary observations. A total of 500 scans were collected for each spectrum at a resolution of 0.5 cm⁻¹. A pure KBr pellet, pressed under identical conditions, served as the reference to correct potential instrument shift and scattering loss. The sample transmittance was computed as the ratio of sample to reference intensities.

## 2.3. Calculation of Optical Constants

The imaginary part k(ν) of the complex refractive index was calculated from transmittance T(ν) via the Beer–Lambert law:

$$k(\nu) = \frac{\alpha}{4\pi\nu} = \frac{1}{4\pi\nu d} \ln\left(\frac{1}{T(\nu)}\right), \qquad (2)$$

where α is the absorption coefficient, d is the effective thickness of the sample, ν is the wavenumber in cm⁻¹, and T(ν) is the measured transmittance (T. Roush et al. 1991; A. Mahjoub et al. 2012). The real part n(ν) was computed using the subtractive Kramers–Kronig (SKK) relation:

$$n(\nu) = n_0 + \frac{2(\nu^2 - \nu_0^2)}{\pi} \mathcal{P} \int_0^\infty \frac{\nu'k(\nu')}{(\nu'^2 - \nu^2)(\nu'^2 - \nu_0^2)} d\nu'. \qquad (3)$$

In our analysis, the integral was divided into three regions: low-frequency (0–350 cm⁻¹), measured region (350–25,000 cm⁻¹), and high-frequency (25,000–∞). The measured region was numerically integrated using the trapezoidal rule, while the low- and high-frequency regions were extrapolated using literature

values of k(ν) (e.g., B. N. Khare et al. 1984; R. J. Papoular & R. Papoular 2014). To estimate the anchor point n₀ at a selected reference frequency ν₀, we analyzed interference fringes in the spectra of selected film samples measured at multiple incidence angles, following the methodology of C. He et al. (2024). The fringe spacings at two incidence angles were used to determine n₀ at anchor frequencies. To enhance clarity in interpreting the results, a more detailed description of the numerical solution is provided in Section 3.

## 2.4. Spectral Modeling with Virga and PICASO

To simulate observational effects, we input the derived optical constants (n and k) into Virga, a cloud code (N. E. Batalha et al. 2019; C. M. Rooney et al. 2022), with the custom functionality originally developed for wavelength-dependent haze optical properties (C. He et al. 2024). For each haze or graphite sample, Virga was provided with the n(λ) and k(λ) values over the 0.5–15 µm wavelength range. The code uses PyMieScatt (B. J. Sumlin et al. 2018) to compute the scattering efficiency (Qsca), extinction efficiency (Qext), and asymmetry parameter (g) as functions of wavelength. These parameters were compiled into a Mie efficiency (mieff) file, formatted for use in the PICASO radiative transfer framework (N. E. Batalha et al. 2019; S. Mukherjee et al. 2023). PICASO was used to simulate transit spectra in a limb-viewing geometry appropriate for transiting exoplanets (N. E. Batalha et al. 2019; L. Alderson et al. 2023).

Each PICASO simulation was configured with a prescribed atmospheric temperature-pressure profile, planetary surface gravity, and stellar radius representative of the modeled exoplanet. Haze-free and hazy scenarios were both explored. In hazy simulations, the haze layer was implemented using the mieff file generated by Virga. Key input parameters included the haze upper and lower pressure layer bounds and total column-integrated number density (ndz, in cm⁻²). The haze layer was assumed to be vertically uniform in particle properties within its pressure bounds. For each case, the forward-modeled transit spectra were computed at a spectral resolution of R = 15,000. All model outputs were used to compare the spectral impact of organic haze versus graphite and assess their observational signatures across the near- and mid-infrared. Further modeling details, including gas opacities, particle sizes, and pressure–temperature (P–T) profiles, are described in Section 3.3.

# 3. Results

In this section, we present the key outcomes of our laboratory measurements and atmospheric modeling, aimed at quantifying the optical properties of carbon-rich hazes relevant to sub-Neptune and super-Earth atmospheres and evaluating their impact on the observed spectra.

## 3.1. Transmittance Spectra of Organic Haze and Graphite Samples

To assess the optical behavior of the organic haze analogs and standard graphite reference material, we measure their transmittance spectra over a broad wavelength range. Figure 2 presents the smoothed transmittance spectra for both classes of materials, where smoothing was performed using a Savitzky–Golay filter (A. Savitzky & M. J. E. Golay 1964) to reduce high-frequency noise while preserving spectral features. The
<figure><img src="image_5.png" /><figcaption>**Figure 2.** (a) Transmittance spectra of haze analogs produced at 300 (blue) and 500 K (red), exhibiting rich vibrational absorption bands (e.g., N-H, C-H, C≡N, C=O). Both samples have ~0.3% concentration of organic haze and share similar spectral features, with subtle differences in band intensity reflecting temperature-dependent composition. (b) Transmittance spectra of graphite pellets at three concentrations (0.008%, 0.016%, 0.03%), showing smooth, broadband absorption with consistent spectral shapes. (Note that graphite pellets were prepared at much lower concentrations due to the higher absorbance of graphite, and higher concentrations would result in saturated spectra.) Small features near 2.9, 5.8, and 6.1 µm may come from absorbed water in graphite structure and/or the byproducts during the commercial production process of graphite (B. L. Mojet et al. 2010; M. Bera et al. 2018), which likely arises from O-H stretching (2.9 µm), C=O stretching (5.8 µm), C=C stretching, or H-O-H bending (6.1 µm) vibrations.</figcaption></figure>

haze samples exhibit numerous well-defined molecular absorption bands, characteristic of organic hazes. Prominent features appear at 3.0 µm (N-H), 3.4 µm (C-H), 2.7-4.0 µm (O-H), 4.5 µm (C≡N), 6.0 µm (C=C, C=O, C=N, and NH₂), 6.9/7.2 µm (C-H), and near 8.1/9.0 µm (C-O or C-N; D. Lin-Vien et al. 1991). The presence of strong O-H, C≡N, N-H, and NH₂ features at shorter wavelengths indicates the incorporation of polar functional groups. Although the 300 and 500 K haze samples show similar absorption profiles, subtle differences in band intensities likely reflect different reaction pathways that alter functional group abundances in the two haze samples.

In contrast, the graphite spectra (Figure 2(b)) are largely featureless and exhibit a smooth, monotonic increase in absorption toward shorter wavelengths. This behavior is consistent with the delocalized electronic structure of crystalline graphite, where carbon atoms are arranged in extended sp²-bonded hexagonal lattices. The associated π-π* electronic transitions give rise to broadband absorption without discrete vibrational signatures, yielding a continuum-like transmittance spectrum (e.g., M. P. Conrad & H. L. Strauss 1985;

H. S. Skulason et al. 2010; B. T. Draine 2016). Note that weak absorption features near 2.9, 5.8, and 6.1 µm may come from absorbed water in graphite structure and/or the byproducts during the commercial production process of graphite (B. L. Mojet et al. 2010; M. Bera et al. 2018).

Importantly, all three graphite spectra exhibit nearly identical spectral shapes, with only the absolute transmittance scaling with graphite's concentrations (0.008%-0.03%). This consistency confirms that the tested concentration range is well suited for optical constant derivation—sufficiently dilute to avoid saturation effects while still preserving the material's bulk spectral characteristics. A more detailed discussion on the applicability of our graphite samples to exoplanetary and astrophysical environments is provided later in Section 3.2.

Overall, the stark contrast in transmittance features between organic hazes and graphite materials highlights their fundamentally different optical responses. While the spectra of organic hazes reflect molecular vibrational modes of chemically diverse organic compounds in the hazes, graphite behaves as a broadband absorber with minimal molecular structure. These distinctions motivate the detailed computation
<figure><img src="image_6.png" /><figcaption>**Figure 3.** Complex refractive indices ($n$ and $k$) of haze analogs synthesized at 300 and 500 K. (a) Extinction coefficient $k(λ)$ retrieved from transmittance data using the Beer–Lambert relation. Both samples exhibit multiple absorption peaks associated with vibrational modes of organic functional groups. A dominant peak near 6.2 µm is present in both spectra, with $k$ values diverging beyond 7 µm. (b) Real part of the refractive index $n(λ)$ derived via the SKK method. A pronounced dip near 6 µm corresponds to the $k$ peak, while small but consistent differences between the 300 and 500 K samples appear across the spectrum.</figcaption></figure>

of complex refractive indices ($n$ and $k$) in the following section.

## 3.2. Optical Constants of Organic Hazes and Graphite

For the organic haze samples, the extinction coefficient $k(ν)$ was derived from the Beer–Lambert law (Equation (2)) using the effective sample thicknesses, determined to be $3.16 \times 10^{-4}$ cm for the 300 K haze and $2.91 \times 10^{-4}$ cm for the 500 K haze. The corresponding real part of the refractive index, $n(ν)$, was then obtained via the SKK integral transformation (Equation (3)). To ensure numerical stability and robustness, we computed $n(ν)$ over 31 evenly spaced reference frequencies $ν_0$ from 12,500 to 14,000 $cm^{-1}$ with $n_0$ determined using the fringe methods. The final $n$ spectrum was taken as the median of these solutions with the final anchor point $n_0 = 1.686$ at $ν_0 = 13,100$ $cm^{-1}$ for the 300 K sample and $n_0 = 1.631$ at $ν_0 = 13,100$ $cm^{-1}$ for the 500 K sample. Figure 3 displays the retrieved optical constants ($k$ and $n$) for the 300 K (blue) and 500 K (red) haze analogs. In the extinction coefficient panel (Figure 3(a)), both samples show a prominent absorption peak near 6.0 µm, accompanied by

several narrower features across the 3–10 µm region, corresponding to specific vibrational modes of different organic functional groups in the haze samples. Importantly, a clear divergence appears between the two haze samples beyond 7 µm, where the 300 K haze consistently exhibits higher $k$ values than the 500 K sample. In the refractive index profiles (Figure 3(b)), both samples show relatively smooth variations, with a distinct dip near 6 µm corresponding to the major $k$ peak. The two $n$ curves are generally similar in shape but exhibit subtle offsets throughout the spectrum. These distinctions indicate compositional differences arising from the experimental condition.

We derived the optical constants of commercial graphite from our measured transmittance spectra using two methods. The first method utilized the conventional single-pellet Beer–Lambert law (Equation (2)) to derive the extinction coefficient $k(ν)$ from each of the three graphite–KBr pellets (0.03%, 0.016%, and 0.008%), and the three $k$ values were averaged to yield a representative $k(ν)$ spectrum. The second method applied a multiconcentration linear fitting procedure to the same set of pellets, corresponding to effective graphite thicknesses of 19.89, 10.55, and 5.12 µm, respectively. Rather
<figure><img src="image_7.png" /><figcaption>**Figure 4.** Complex refractive indices (n and k) of graphite compared with previous studies. (a) Extinction coefficient k(λ) derived using two approaches: multiconcentration fitting (black) and single-pellet averaging (gray). Prior data sets from A. B. Djurišić et al. (2000, D & L 2000, brown), R. J. Papoular & R. Papoular (2014, P & P 2014, turquoise), and B. T. Draine (2016, D 2016, indigo) are overlaid for comparison, illustrating the wide variation in reported graphite optical constants. (b) Real part of the refractive index n(λ) retrieved via the SKK method. The fit-based result (black) shows better alignment with R. J. Papoular & R. Papoular (2014), while the averaged result (gray) displays a steeper rise. The discrepancies among all data sets reflect differences in material preparation, spectral methods, and analytical assumptions, underscoring the difficulty in constraining graphite's complex optical properties.</figcaption></figure>

than treating each pellet separately, we simultaneously modeled their transmittance spectra using the relation

$$-\ln T(\nu) = \alpha(\nu) \cdot d + b(\nu). \quad (4)$$

In this formulation, α(ν) represents the intrinsic absorption coefficient of graphite and b(ν) is a wavelength-dependent baseline term accounting for light scattering, reflection losses, or detector drift. A point-by-point linear regression was performed across all three data sets to extract α(ν), from which the extinction coefficient k(ν) was calculated using standard relations (Equation (2)).

Using the SKK relation (Equation (3)), we calculated the n(ν) values at 21 evenly spaced reference frequencies ν₀ from 5000 to 15,000 cm⁻¹ and took the median as the final n values. For the average method, the transformation was anchored at ν₀ = 9000 cm⁻¹ with n₀ = 2.8; for the fitting method, it was anchored at ν₀ = 7000 cm⁻¹ with n₀ = 2.8, following R. J. Papoular & R. Papoular (2014).

Figure 4 compares our computed complex refractive indices for commercial graphite using the two approaches—the averaged method (gray) and the fitting method (black)—alongside three representative literature data sets. In both methods, the extinction coefficient k(λ) rises toward longer wavelengths, consistent with π → π* electronic transitions in delocalized sp² carbon structures. Notably, the fitting method produces a smoother and more monotonic k spectrum, particularly in the 5–10 µm range. The fitted method corrects potential systematic errors like light scattering, reflection losses, or detector drift, and yields a reliable and physically meaningful refractive index. In contrast, the averaged k values overestimate absorption in this region, propagating into an inflated real refractive index n(λ) via the SKK relation. Therefore, the data calculated from the fitted method are used for the spectral modeling (Section 3.3). Note that we calculated the optical constants for the organic hazes using one concentration at 0.3%, as our previous study (C. He et al. 2024) has demonstrated that this concentration yields results
comparable to those obtained using the fitted methods for
similar organic haze materials.

Our fitted *k* values lie between those reported by R. J. Pap-
oular & R. Papoular (2014) and B. T. Draine (2016) across
most of the spectral range, while the B. T. Draine (2016) data
set exhibits significantly higher *k* values and a steep rise below
10 µm. This indicates a stronger absorption trend in the
A. B. Djurišić et al. (2000)'s results, likely influenced by
methodological differences. For the real refractive index *n*, our
fitted *n* values fall between the lower bound defined by
R. J. Papoular & R. Papoular (2014) and the higher bound of
B. T. Draine (2016), closely following the shape and slope of
R. J. Papoular & R. Papoular's (2014) curve throughout the
mid-infrared. In contrast, A. B. Djurišić et al. (2000) report
much higher *n* values with a sharp increase beyond 10 µm,
diverging from the more moderate trend seen in our computed
values.

The considerable variation in reported graphite optical constants underscores the persistent challenges in accurately determining graphite's optical properties. As stated in B. T. Draine (2016), optical constants are derived through a variety of experimental techniques, including reflectivity measurements, electron energy-loss spectroscopy (EELS), and photoemission at X-ray energies (e.g., E. D. Palik 1991; B. T. Draine 2016). Each method probes different energy regimes and may introduce systematic uncertainties depending on factors such as sample orientation, grain size, degree of anisotropy, and surface treatment. In this study, we derived the optical constants of graphite using the measured transmittance spectra of small, randomly oriented graphite particles (0.7–2.2 µm) dispersed in transparent KBr medium. The states of graphite particles in the measurement setting are more representative to graphite hazes in atmospheres or graphite grains in molecular clouds and the interstellar medium, compared to other methods such as reflectance spectroscopy on polished bulk samples, EELS, or thin-film ellipsometry. Moreover, our transmission measurements on dispersed particles better reflect the geometry and conditions relevant to transit or absorption spectroscopy. Therefore, the graphite optical constants derived here are more suitable for interpreting astronomical observations.

3.3. *Radiative Transfer Modeling with PICASO*

We employed Virga (N. E. Batalha et al. 2019; C. M. Rooney et al. 2022) and PICASO (N. E. Batalha et al. 2019; S. Mukherjee et al. 2023) to evaluate the radiative impact of the measured optical constants under conditions matching our laboratory experiments. The *P*–*T* profile used in the simulations is isothermal at 500 K, spanning 59 logarithmically spaced pressure layers from 10<sup>-10</sup> to 10<sup>2</sup> bar, consistent with the environment used in our haze production experiments. The atmospheric gas composition was consistent with the initial gas mixture used in the 500 K laboratory experiments (Figure 1), with volume mixing ratios of CO<sub>2</sub>, CH<sub>4</sub>, N<sub>2</sub>, H<sub>2</sub>O, He, and H<sub>2</sub> fixed vertically. These abundances were derived from Chemical Equilibrium with Applications (CEA) equilibrium modeling at 2000× solar metallicity and a solar C/O ratio and used directly in radiative transfer. For the opacities of the species, we use the V3 Zenodo Opacity Database (N. E. Batalha et al. 2025), with the most important gas phase absorbers being H<sub>2</sub>O (O. L. Polyansky et al. 2018), CH<sub>4</sub> (S. N. Yurchenko et al. 2013; S. N. Yurchenko &

J. Tennyson 2014), and CO₂ (X. Huang et al. 2014) given our
model atmosphere compositions.

The particle size distribution followed a log-normal form with radii spanning 20–200 nm (C. He et al. 2024). Organic haze layers were implemented with a constant number density of 50 cm⁻³ between 0.1 bar and 1 nbar, corresponding to a total column density of 1.5 × 10¹⁰ cm⁻². A representative sub-Neptune exoplanet, GJ 1214b, was chosen as the benchmark due to its well-characterized transit spectra and hypothesized haze-rich atmosphere. Planetary parameters adopted were mass 8.17 M<sub>⊕</sub>, radius 2.742 R<sub>⊕</sub>, and equilibrium temperature ~596 K from R. Cloutier et al. (2021) and stellar radius 0.2162 R<sub>☉</sub> from A. S. Mahajan et al. (2024).

Figure 5 presents the synthetic spectra and the observational data for GJ 1214b from L. Kreidberg et al. (2014), E. M. R. Kempton et al. (2023), and E. Schlawin et al. (2024) for comparison. To facilitate visual comparison of model features and different data sets, we apply an offset of 0.012% in transit depth to the data from E. Schlawin et al. (2024). The synthetic spectrum of the clear atmosphere shows pronounced absorption features from key gases such as H₂O, CH₄, and CO₂. In contrast, the hazy scenarios exhibit substantial muting of molecular features across the spectrum, particularly below 2 µm, where the spectra become nearly flat. Between 3 and 7 µm, distinct differences emerge: both organic haze models suppress gas features to varying degrees, while simultaneously introducing new spectral features at 3.0, 4.5, 4.7, and 6.0 µm—attributable to organic functional groups in the hazes. Across all four features, our 500 K haze consistently shows stronger absorption than the 300 K case, suggesting that elevated formation temperatures promote haze species with greater infrared activity.

Notably, the synthetic spectrum for graphite at a number
density (50 cm⁻³) is nearly featureless, with atmospheric gas
absorption features almost entirely suppressed and a consistent
uplift in transit depth (0.025%). This flat, absorbing behavior
highlights the broadband opacity of graphite and suggests that if
such material dominates the aerosol composition, spectral
signatures could be entirely masked. Even at a much lower
number density (5 cm⁻³), graphite introduces stronger masking
effects than the organic hazes at 10 times the number density
(50 cm⁻³), allowing only a few molecular features to emerge.

A comparison between our synthetic spectra and GJ 1214b
observations shows that organic haze models capture several
qualitative features present in the data. The organic haze
models are broadly consistent with the flat near-infrared
spectrum reported by L. Kreidberg et al. (2014) in the near-
infrared region (1.1–1.6 µm; HST/WFC3), supporting the
presence of high-opacity hazes in this region. In the
2.8–5.1 µm region reported by E. Schlawin et al. (2024;
JWST/NIRSpec), some haze-specific absorption features—
especially near 4.7 µm—partially align with our simulations,
though the observed band intensities differ, suggesting
possible compositional or abundance variations. For the mid-
infrared data (5.2–11.7 µm; E. M. R. Kempton et al. 2023),
overall trends are broadly consistent but exhibit larger
uncertainties. E. Schlawin et al.’s (2024) spectrum shows
strong absorption near 4.3 µm, matching the CO₂ feature in
our clear and hazy model and indicating CO₂ present in the
atmosphere on GJ 1214b.

We use GJ 1214b as an example to demonstrate the effect of
different haze optical constants on the observed spectra. Our
aim is not to reproduce the observed spectrum in detail but
<figure><img src="image_8.png" /><figcaption>**Figure 5.** Modeled transit spectra of GJ 1214b including haze and graphite scenarios. Planet mass 8.17 $M_⊕$, radius 2.742 $R_⊕$, and equilibrium temperature ~596 K are adopted from R. Cloutier et al. (2021). The stellar radius, 0.2162 $R_⊕$, is adopted from A. S. Mahajan et al. (2024). Simulations include a cloud-free atmosphere (cyan), haze analogs produced at 300 (blue) and 500 K (red), graphite-based aerosols (dark gray), and the graphite-based aerosols using 10% of the number density (5 cm⁻³ volumetric; light gray) overlaid with observational data from L. Kreidberg et al. (2014), E. M. R. Kempton et al. (2023), and E. Schlawin et al. (2024). The upper panel shows the full wavelength range (0.5–15 µm), while the lower panel provides a magnified view of the visible to near-infrared region (0.5–7 µm), emphasizing haze-induced modulations and absorption features. Hazy scenarios suppress molecular absorption bands and introduce new spectral signatures (e.g., at 3.0, 4.5, 4.7, and 6.0 µm). Graphite shows extreme flattening due to its broadband opacity.</figcaption></figure>

rather to isolate and demonstrate the spectral impact of haze composition under otherwise fixed model conditions. These haze particles are not necessarily present in GJ 1214b's atmosphere, but their characteristic absorption features may serve as diagnostic signatures in future observations of carbon-rich exoplanet atmospheres.

Moreover, the near-flat spectrum with graphite haze indicates that graphite is not the dominant haze in the atmosphere of GJ 1214b. While laboratory results show that graphite does not form under atmospheric conditions of 500/300 K and 5 mbar (S. Wang et al. 2025), graphite could form in deep, hot regions of the atmosphere and be lofted into observable altitudes. Such a spectrally flat, broadband absorber could obscure molecular features and mimic the effect of a

planetary surface on transit geometry. In this scenario, the top of the graphite haze layer may be interpreted as the true planetary radius, leading to an overestimated radius and, consequently, an underestimated bulk density. This mechanism offers a plausible explanation for superpuff planets (e.g., P. Gao & X. Zhang 2020; K. Ohno & Y. A. Tanaka 2021), whose anomalously low densities may be apparent rather than intrinsic.

## 4. Conclusion

In summary, our results reveal distinct spectral differences between haze and graphite. The organic haze exhibits identifiable absorption features from various functional
groups, while graphite displays featureless, broadband absorp-
tion that strongly masks molecular features in simulated transit
spectra.

This study provides the first set of optical constants for organic hazes formed in CO₂-rich, high-metallicity environments, filling a key gap in existing aerosol data sets. The results are expected to be representative for organic hazes formed in CO₂-rich sub-Neptune atmospheres within the graphite-stability regime, spanning from 2000 to 10,000× metallicity with C/O ratios from 0.5 to 0.85, as predicted by thermochemical equilibrium modeling (CEA). Our graphite data, derived via spectra of randomly oriented and dispersed submicron particles, better represent the particulate state of atmospheric or interstellar graphite than measurements based on bulk or film samples. Compared to previous data sets based on reflectance, ellipsometry, or EELS measurements on bulk or oriented samples, our approach is more directly applicable to astronomical observations relying on transmission geometry.

Using the derived optical constants, we simulated transit spectra of a representative sub-Neptune atmosphere using Virga and PICASO. The haze models reproduce several spectral features that are potentially consistent with those observed in GJ 1214b, suggesting the widespread presence of high-opacity photochemical hazes. Additionally, the distinctive haze absorption features (e.g., near 3.0, 4.5, 4.7, and 6.0 µm) provide potential diagnostic markers for future observations aiming to identify haze compositions in carbon-rich atmospheres.

Meanwhile, the graphite model yields a nearly flat spectrum,
effectively masking molecular features and mimicking the
spectral signature of a solid planetary surface, offering a
plausible explanation for the anomalously low densities of
superpuff exoplanets like Kepler 51d.

Overall, our study presents an experimentally grounded optical data set for both haze and graphite relevant to CO₂-rich sub-Neptune atmospheres, enabling more accurate spectral retrievals and informing the interpretation of muted and featureless exoplanet spectra. A full model parameter study is required to understand the effects of the organic hazes on exoplanet observations.

Acknowledgments

The authors thank the anonymous referee for their valuable comments that enhanced the presentation of this Letter. The authors gratefully acknowledge the supports from the National Natural Science Foundation of China (42475132), the U.S. National Science Foundation (2206245), and the National Aeronautics and Space Administration (80ARC0M0008). S.E. M. is supported by NASA through the NASA Hubble Fellowship grant HST-HF2-51563 awarded by the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., for NASA, under contract NAS5-26555. V.V. acknowledges support from the French National Research Agency in the framework of the “Investissements d’Avenir” program (ANR-15-IDEX-02), through the funding of the Origin of Life project of the Université Grenoble Alpes and the French Space Agency (CNES) under their “Exobiologie, Exoplanètes et Protection Planétaire” program.

ORCID iDs

Haixin Li https://orcid.org/0009-0009-2660-1764

Chao He https://orcid.org/0000-0002-6694-0965

Sai Wang https://orcid.org/0009-0001-9044-7927

Yu Liu https://orcid.org/0000-0002-6085-9365

Sarah E. Moran https://orcid.org/0000-0002-6721-3284

Cara Pesciotta https://orcid.org/0009-0007-6910-6347

Sarah M. Hörst https://orcid.org/0000-0003-4596-0702

Julianne I. Moses https://orcid.org/0000-0002-8837-0035

Véronique Vuitton https://orcid.org/0000-0001-7273-1898

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