---
title: 'CLV-HD Dataset: High-Res Transit Spectra'
url: https://www.emergentmind.com/topics/clv-hd-dataset
type: topic
---

# CLV-HD Dataset: High-Res Transit Spectra

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.

Source: https://www.emergentmind.com/topics/clv-hd-dataset