CLV-HD Dataset: High-Res Transit Spectra

• CLV-HD Dataset is a comprehensive resource providing detailed center-to-limb variation maps from high-resolution transit spectra of the active star HD 189733.
• It employs UVES spectrograph observations during HD 189733 b’s transit, using precise calibration and data reduction to achieve a resolving power of approximately 60,000.
• The dataset enables robust correction of stellar contamination in planetary transmission spectroscopy, ensuring accurate interpretation of exoplanet atmospheric signals.

The CLV-HD dataset provides a densely sampled time series of high-resolution transit spectra for the active planet host star HD 189733, primarily designed to characterize the center-to-limb variation (CLV) across strong absorption lines, notably the Ca II H&K and Na I D1 and D2 Fraunhofer lines. Using the transit of the hot Jupiter HD 189733 b as a spatial probe via the UVES spectrograph at VLT-UT2, the dataset enables direct measurement of how the stellar specific intensity $I(\lambda, \mu)$ varies as a function of both wavelength ($\lambda$) and limb angle parameterized by $\mu = \cos\theta$. This mapping is essential both for advancing stellar atmosphere models and for correcting stellar contamination in planetary transmission spectroscopy.

1. Definitions and Notation

The core definitions underpinning the CLV-HD dataset are as follows:

• Limb angle ($\theta$): The angle between the surface normal and the line of sight.
• $\mu \equiv \cos\theta$: Disk center corresponds to $\mu=1$, the limb to $\mu=0$.
• $I(\lambda, \mu)$: Specific intensity at wavelength $\lambda$ and limb angle $\mu$.
• $C(\lambda, \mu)$: Normalized intensity, $$C(\lambda, \mu) = I(\lambda, \mu)/I(\lambda, \mu=1)$$, encapsulating the center-to-limb variation at each $\lambda$.

Normalized intensities $C$ provide the primary diagnostic of CLV by quantifying relative variation across the disk as a function of spectral feature.

2. Observational Setup and Spectral Data Acquisition

The observational campaign utilized the UVES spectrograph on VLT-UT2 (Kueyen, program 089.D-0701(A)), employing the Dic2 dichroic with the 437+760 nm setting. The instrumental setup and sampling parameters are summarized below:

Configuration Aspect	Specification	Remarks
Slit width	1.0″ (blue), 0.7″ (red)	Maximizes resolution
Resolving power	$R \approx 60\,000$	FWHM of isolated tellurics
Wavelength coverage	3732.1–4999.7 Å, 5655.1–7595.1 Å, 7564.3–9463.9 Å	Blue, lower red, upper red
Exposure/time sampling	244 spectra over 4.6 h; 30 s (first 29), 45 s (rest)	60 in-transit points
Wavelength binning	0.01 Å	Uniform grid

Spectra were reduced through the UVES pipeline with steps including bias subtraction, hot-pixel correction, optimal extraction, ThAr wavelength calibration, order merging, and continuum normalization via low-order polynomial fits outside strong lines. Telluric corrections leveraged cross-correlation with LBLRTM models and optional molecfit removal for H₂O and O₂, with typical impact on difference curves of less than $0.5 \times 10^{-3}$.

Barycentric, stellar-motion, and Rossiter–McLaughlin corrections were applied using cross-correlation in telluric-free spectral windows. All spectra are reported in absolute flux units [erg cm⁻² s⁻¹ Å⁻¹], on a common equidistant wavelength grid.

3. CLV Diagnostic Extraction Methodology

CLV diagnostics are extracted by constructing “difference curves” (DCs), exploiting narrow and wide feature/reference bands over key Fraunhofer lines:

• Ca II H & K lines (3933.66, 3968.47 Å):
  • Cores: $\pm$0.5 Å about each line center
  • Reference continua: [3891.67–3911.67] Å (H), [3991.067–4011.067] Å (K)
  • DC for cores: $$DC_{core}(t) = \tfrac{1}{2}[LC_K(t) + LC_H(t)] - \tfrac{1}{2}[LC_{C_K}(t) + LC_{C_H}(t)]$$
  • Wings: 3–5 Å from each line center, using four 2 Å intervals for each line
  • Wing DC: mean of four wing LCs minus mean of two reference continua
• Na I D doublet (5889.951, 5895.924 Å):
  • Central $\pm$0.3 Å excluded
  • Feature bands (wings): half-widths $p=0.6, 0.9, 1.5$ Å, excluding inner $\pm$0.3 Å
  • Reference bands: Wide ([5840–5860], [5925.875–5945.875] Å), shifted (+/–10 Å), and narrow ([5868–5872], [5910.5–5912.5] Å)
  • DC: $DC_{D_2}(t) = LC_{wing,D_2}(t) - LC_{ref}(t)$ (analogous for D1)

Uncertainties on per-point DC outside transit are of order $(2–5) \times 10^{-4}$, leading to difference-curve excess (DCE) fractional errors on the order of $±(0.2–0.5) \times 10^{-3}$.

4. Quantitative Results: Modeled and Observed CLV Strengths

Model tables present DCE values across effective temperatures, e.g., for Charbonneau bands:

$T_{eff}$ (K)	$n=0.75$ Å	$m=3.0$ Å	$w=12$ Å
4000	49.2	6.1	2.5
...	...	...	...
7000	0.57	0.08	0.15

For HD 189733 (5040 K), peak-to-peak DC amplitudes for Ca wings reach $\sim 5 \times 10^{-3}$, while Na wings (p=0.6 Å) are $\sim 1 \times 10^{-3}$, decreasing with broader bands. Analytic limb-darkening (quadratic law) fits perform poorly across line wings compared to full CLV computation with $C(\lambda, \mu)$ from synthetic intensities.

Fits of observed DCs with synthetic DCs from Kurucz-based models yield reduced $\chi^2$ values consistent with no residual amplitude (e.g., Ca wings: $\chi^2_{red}=1.31 \rightarrow 1.02$ with synthetic DC), showing CLV accounts for the entire transit-shaped signal in these bands.

Residuals exhibit correlated structure at the $\pm 2\times 10^{-4}$ level, likely associated with instrumental blaze/merging effects or residual stellar activity.

5. Structure and Content of the CLV-HD Dataset

The CLV-HD dataset is structured as follows:

• Format: ASCII or FITS tables, one per spectral order/chunk
• Columns for $C(\lambda, \mu)$ files:

1. Wavelength $\lambda$ [Å]
2. $\mu$-grid index or explicit $\mu$ axis
3. $C(\lambda, \mu)$ (dimensionless)
4. $\sigma_C(\lambda, \mu)$ (typical 1–2 %, combines photon noise and normalization error)

• Time-series DC files:
  • Columns: time [BJD_UTC], orbital phase, $DC_{core}$(Ca), $DC_{wing}$(Ca), $DC_{D_2}(p)$, $DC_{D_1}(p)$, reference LC levels
  • All spectra: 0.01 Å wavelength grid, flux in erg cm⁻² s⁻¹ Å⁻¹

Time and wavelength grids are fully standardized, enabling direct use in modeling and comparison.

6. Guidance for Data Application and Correction of Planetary Transmission Spectra

To reconstruct observed DCs from scratch:

1. Generate $C(\lambda, \mu)$ using a 1D-LTE Kurucz model ($T_{eff}=5040$ K, $\log g=4.587$, $[\rm Fe/H]=-0.04$), sampled at $\mu=0.001,0.05,\ldots,1.0$ and 0.01 Å grid.
2. Discretize the stellar disk into $\sim 250,000$ elements (Vogt et al. 1987), each with assigned $\mu$ and projected area.
3. At each transit epoch $t_i$, occult elements by the planet with parameters $R_p/R_s=0.15463$, $a/R_s=8.81$, $i=85.58^\circ$.
4. Compute $$F(\lambda, t_i) = \sum_{\text{visible}} I(\lambda, \mu_k)\Delta A_k$$ and integrate across defined feature and reference bands to get $f_f(t_i)$, $f_r(t_i)$.
5. Normalize light curves $n_X = f_X/\langle f_X(\rm oot)\rangle$ and build $DC(t_i) = n_f - n_r$.
6. Compare to observed DCs and subtract the modeled CLV-induced DC to correct for stellar contamination.

For exoplanet atmospheric analyses, it is critical to model and subtract CLV-induced DC from observed signals, especially for narrow bands around strong absorption lines where uncorrected CLV effects can reach $\sim 10^{-3}$. Only matched temporal sampling, resolution, and bandpass definitions ensure robust correction.

7. Significance and Implications in Exoplanet Spectroscopy

The CLV-HD dataset demonstrates that the strength of CLV-induced effects in the wings of strong Fraunhofer lines is comparable to the amplitude of hot Jupiter atmospheric signals. This establishes the necessity of wavelength-resolved CLV modeling when interpreting transmission spectra, especially when using narrow bands centered on lines such as Na I or Ca II. Quadratic limb-darkening laws parametrized in the broad continuum are inadequate in the spectral line wings, which require explicit modeling through $C(\lambda, \mu)$ profiles derived from stellar atmosphere models. A plausible implication is that systematic uncorrected CLV effects could yield false-positive planetary atmospheric detections if not rigorously accounted for. Researchers are thus advised to employ CLV-HD or equivalent datasets and modeling procedures as an integral part of exoplanet transmission spectroscopy to ensure astrophysical interpretations are robust to stellar contamination.