ESPRESSO Transit Spectroscopy

• ESPRESSO transit spectroscopy is a high-resolution technique that uses the ESPRESSO spectrograph to capture subtle transit signals and extract detailed exoplanet properties.
• It measures minute Doppler shifts in the Rossiter–McLaughlin effect to detect atmospheric absorption, variability, and planetary oblateness in exoplanet transits.
• Combining high-cadence spectroscopic and photometric data, the method enhances our understanding of exoplanet interiors, rotation rates, and formation histories.

ESPRESSO transit spectroscopy refers to the use of the ESPRESSO (Echelle SPectrograph for Rocky Exoplanets and Stable Spectroscopic Observations) instrument at the ESO Very Large Telescope for high-resolution, high-precision time-series spectroscopy during exoplanet transits. This approach enables the extraction of detailed planetary properties—including atmospheric and physical parameters—by exploiting subtle changes in the stellar and planetary signals as the planet passes in front of its host star.

1. Definition and Core Capabilities

ESPRESSO is a fiber-fed, cross-dispersed echelle spectrograph capable of reaching radial velocity (RV) precisions down to ∼0.1 m s⁻¹, and a resolving power exceeding R ∼ 140,000 in its highest resolution modes. For transit spectroscopy, ESPRESSO’s precision and stability enable the disentangling of minute Doppler shifts and line profile variations associated with the Rossiter–McLaughlin (RM) effect, the planet’s atmospheric absorption, and any non-spherical planetary shapes.

The technique is uniquely positioned to detect spectroscopic signatures imprinted during transit—such as those arising from planetary oblateness, extended atmospheres, and atmospheric dynamics—by monitoring the distortions they induce in the stellar absorption lines and their temporal evolution.

2. Spectroscopic Detection of Planetary Oblateness

ESPRESSO is one of the few instruments capable of resolving spectroscopic RM anomalies induced by planetary oblateness. The spectroscopic effect is a time-variable RV anomaly that supplements the standard RM effect caused by a spherical transiting planet.

• Oblateness Parameterization: The projected oblateness $f = 1 - R_{\rm pol}/R_{\rm eq}$, where $R_{\rm pol}$ and $R_{\rm eq}$ are the planetary polar and equatorial radii, respectively, determines the distortion in transit chord geometry.
• Amplitude Scaling: The amplitude of the spectroscopic oblateness signature ($S_{\rm obl}^{\rm sp}$) scales as:

$$S_{\rm obl}^{\rm sp} \propto \left(\frac{v \sin i_\star}{5 \ {\rm km/s}}\right) \left(\frac{f}{0.098}\right) \left(\frac{\bar{R}_p}{0.1546}\right)^2$$

with $v \sin i_\star$ the projected stellar rotation velocity and $\bar{R}_p$ the geometric mean planetary radius.

• Detectability: For a Saturn-like oblateness ($f \approx 0.098$), $S_{\rm obl}^{\rm sp}$ can reach up to 1.1 m s⁻¹—above the single-exposure photon noise for bright targets ($m_V \lesssim 8–9$), making oblateness directly accessible with ESPRESSO (Akinsanmi et al., 2020).
• Measurement Precision: The achievable detection threshold is set by instrumental noise, stellar noise sources (granulation, oscillations), and the ability to co-add signals from multiple transits.

In some geometries, notably for rapid stellar rotation or nonzero spin–orbit misalignment (projected obliquity $\lambda \ne 0$), the oblateness-induced signal is amplified, providing optimal detection conditions.

3. Comparison: Photometric vs. ESPRESSO Spectroscopic Methods

Detection of planetary oblateness has traditionally relied on high-cadence photometry, probing minute deviations at ingress and egress caused by the altered limb geometry of an oblate planet. ESPRESSO spectroscopy provides a complementary and sometimes more sensitive axis of detection at specific transit orientations:

Method	Sensitivity (Example)	Timescale Resolution	Amplification Factors
Photometry	~272 ppm in $R_p^2/R_\star^2$	$\sim$2-minute integrations	Best for high-cadence ingress/egress
ESPRESSO RM	$\sim$1.1 m s⁻¹	Set by exposure and RV precision	Faster $v\sin i_\star$, large $f$, high misalignment

While photometric signatures are generally more sensitive due to higher temporal cadence, the spectroscopic approach can surpass photometry in detectability for transits across rapidly rotating stars or for planets with significant spin–orbit misalignment, where the RM effect is both locally and globally enhanced. Joint modeling of photometric and spectroscopic datasets is essential for breaking parameter degeneracies (e.g., between $f$ and $\theta$, the projected obliquity).

4. Technical Implementation: Formulas and Workflow

ESPRESSO transit spectroscopy for constraining oblateness requires detailed time-series modeling of the observed radial velocities and the stellar line profile variations.

Key formulas:

• Planet Mean Radius:

$\bar{R}_p = R_{\rm eq} \sqrt{1-f}$

• Rotation Period (with internal structure):

$$P_{\rm rot} = 2\pi \sqrt{\frac{R_{\rm eq}^3}{G M_p (2f - 3J_2)}}$$

where $J_2$ is the quadrupole moment and $M_p$ is the planet mass.

Workflow:

1. Data acquisition: High-cadence spectra throughout the transit, prioritizing cadence during ingress and egress.
2. Data reduction: Correction for telluric and instrumental systematics; extraction of high-S/N cross-correlation functions (CCFs).
3. RM modeling: Simultaneous fitting of the classical RM effect and oblateness-induced residuals as a function of time.
4. Signal isolation: Disentangling the planetary RM signature from stellar activity-induced RVs via modeling or data-driven corrections.
5. Parameter estimation: Joint photometric–spectroscopic MCMC sampling to constrain $f$, $\theta$, and possibly $P_{\rm rot}$.

Figures in (Akinsanmi et al., 2020) map the RM anomaly amplitude across impact parameter, $\theta$, and $\lambda$, serving as guides for system selection.

5. Implications for Planetary Rotation and Interior Structure

Detection of oblateness via ESPRESSO transit spectroscopy provides a direct probe of planetary rotation rates and internal density profiles. Measurement of $f$ enables estimation of $P_{\rm rot}$, placing constraints on tidal evolution timescales and core mass (since $J_2$ is linked to the mass distribution).

For long-period giant planets that have not undergone strong tidal synchronization, the oblateness signature measured by ESPRESSO offers a window into primordial rotation and, by extension, planet formation scenarios and interior structure models.

6. Practical Considerations, Limitations, and Future Prospects

• Target Selection: Bright host stars ($m_V \lesssim 8-9$) and planets with $R_p/R_\star \gtrsim 0.15$, orbiting rapid rotators and exhibiting spin–orbit misalignment, offer best prospects for detection.
• Noise Sources: Stellar oscillations, granulation, and activity dominate the RV noise floor; advanced modeling of these effects (and possibly Gaussian process regression) is advised.
• Cadence/Co-addition: Multiple-transit co-addition is sometimes required for sub-m/s precision in challenging systems or those with low oblateness.
• Instrumental Stability: ESPRESSO’s RV zero-point stability and repeatability are critical; instrumental systematics must be matched or outperformed by photon noise.

Looking forward, the ESPRESSO methodology is expected to be further enhanced by upcoming high-S/N photometric instruments (e.g., TESS, CHEOPS, PLATO, JWST) and by the advent of ELT-class spectrographs, which will push detection thresholds into the regime of smaller, possibly Neptune-class planets. Improvements in line-by-line RV extraction, telluric correction, and stochastic modeling of stellar activity will further increase the sensitivity to oblateness-induced RM anomalies.

7. Significance Within Exoplanet Research

ESPRESSO transit spectroscopy thus expands exoplanet characterization beyond basic physical and orbital parameters to include constraints on rotational and interior properties via spectroscopic oblateness signatures. By leveraging simultaneous photometric and spectroscopic datasets, this methodology alleviates degeneracies intrinsic to single-technique analyses, providing a more robust and precise measurement of planetary figures. This, in turn, enables new insights into planetary evolution, angular momentum history, and the population statistics of planetary shapes and rotational states within the exoplanet census (Akinsanmi et al., 2020).