HARPS Spectrograph: Exoplanet Detection Tool

• HARPS Spectrograph is a fiber-fed echelle instrument with a resolving power of ≈115,000, optimized for ultra-stable radial velocity measurements across 3800–6900 Å.
• It employs dual fibers, octagonal light scrambling, and advanced calibrations with ThAr lamps, Fabry–Pérot etalons, and laser frequency combs to minimize systematic errors.
• Its data reduction techniques, including cross-correlation and template-matching, achieve 0.5–1 m/s precision, driving discoveries of low-mass exoplanets and detailed stellar studies.

The High Accuracy Radial Velocity Planet Searcher (HARPS) spectrograph is a fiber-fed cross-dispersed echelle spectrograph optimized for sub-meter-per-second radial velocity precision. Installed at the ESO 3.6 m telescope at La Silla Observatory in Chile, HARPS has set the benchmark for high-resolution, ultra-stable spectroscopic measurements, underpinning fundamental advances in exoplanet detection, stellar physics, and time-domain astrophysics.

1. Instrument Architecture and Key Specifications

HARPS is designed for high-resolution spectroscopy, achieving a resolving power R ≈ 115,000 over an optical bandpass from 3800 Å to 6900 Å. The spectrograph operates in a temperature- and pressure-stabilized vacuum vessel to minimize environmental drifts. It features a dual-fibre design: one fiber conveys starlight while the second can be used for simultaneous reference exposures or sky background subtraction (Barbieri, 2023).

The optical layout consists of a fiber injection module feeding a large parabolic collimator, an echelle grating for primary dispersion, a cross-dispersing grism, and a camera objective imaging the spectrum onto a CCD mosaic comprising two 2k × 4k EEV44-82 devices (&&&1&&&). The dual input (science + reference) allows for continuous monitoring of instrumental stability and efficient calibration routines.

Critical to its performance is the use of octagonal fibers (introduced after 2015) that improve near-field light scrambling, substantially stabilizing the illumination pattern at the spectrograph entrance and further reducing instrumental profile variations (Trifonov et al., 2020).

2. Wavelength Calibration and Long-Term Stability

Wavelength calibration in HARPS is based on fiber-fed reference spectra obtained primarily from ThAr hollow cathode lamps, and, since 2011, Fabry–Pérot etalons and laser frequency combs (LFCs) (Coffinet et al., 2019, Probst et al., 2020).

A key limitation identified is the “block-stitching” effect of its CCD mosaic. Each 2k×4k chip is comprised of stitched 512-pixel blocks, resulting in non-uniform pixel sizes at the block boundaries. Spectral lines crossing these stitchings experience mapping errors, leading to spurious radial velocity signals with one-year periodicity due to Earth's barycentric motion (Dumusque et al., 2015, Coffinet et al., 2019). Correction requires precise flat-field mapping of pixel area anomalies and integration with the wavelength solution:

• Gap size estimation from flat-fields:

$$L_\text{gap}/L_\text{nom} = (F_\text{meas}/F_\text{exp}) - 1$$

• Gap-corrected mapping for calibration lines:

$X_i = x_i + \sum_{j=1}^G \_{i,j} \, g_j$

(where $\_{i,j}$ = 1 if line i is right of gap j, $g_j$ is gap width)

• Polynomial wavelength fit in physical CCD coordinates:

$\sum_{k=0}^P a_k (X_i)^k = \lambda_i$

Application of these corrections, especially when combined with high-density LFC calibrators (providing known comb line frequencies $f_n = n f_\mathrm{rep} + f_0$), has reduced systematic errors to a few cm/s, crucial for detecting Earth-mass planets (Probst et al., 2020).

3. Radial Velocity Extraction and Data Reduction

Radial velocity (RV) measurement in HARPS data is traditionally performed via cross-correlation function (CCF) techniques. The spectrum is multiplied by a numerical “mask”—a binary function reflecting the locations of stellar absorption features for a given spectral type—and the velocity shift corresponding to the CCF minimum is identified as the star’s RV. This process is integrated in the HARPS Data Reduction Software (DRS), yielding a typical precision of 0.5–1 m/s (Barbieri, 2023).

More recently, template-matching strategies have demonstrated improvements, particularly for M dwarfs and stars with crowded molecular spectra. HARPS–TERRA, for example, performs least-squares matching between each observed spectrum and a high S/N template, built from coadded observations, while modeling blaze function variations with low-order polynomials. This approach leverages the full pixel-level Doppler information (Anglada-Escudé et al., 2012). Similar advances are implemented in SERVAL (Trifonov et al., 2020), which differentially measures the RV between template and observation by minimizing

$$\chi^2(\Delta \text{RV}) = \sum_i \frac{[f_\text{obs}(\lambda_i) - T(\lambda_i + \Delta \text{RV})]^2}{\sigma_i^2}$$

Systematic residuals observed at the 1–3 m/s level (arising from system throughput, intra-night drifts, and zero point offsets) are mitigated by the calculation and application of nightly zero-point corrections (NZPs), derived from quiet stars (Trifonov et al., 2020). Fiber interventions (2015) introduced spectral-type dependent RV offsets (up to +14 m/s in F-type, –3 m/s in M-type), necessitating epoch-dependent corrections for merged time-series data.

4. Spectro-Polarimetric and Extended Capabilities

The integration of a polarimetric module—HARPSpol—enables high-precision full-Stokes spectropolarimetry (Snik et al., 2010). HARPSpol employs a compact dual-beam polarimetric module using a custom Foster prism (modified Glan–Thompson design) and superachromatic rotating wave plates (QWP for circular, HWP for linear polarization). Differential beam analysis and double-ratio demodulation yield a polarimetric sensitivity $\sim10^{-5}$, with negligible instrumental polarization, allowing Zeeman–Doppler imaging and detailed magnetic field topology mapping at HARPS’s high spectral resolution.

A slider mechanism and compact module ensure quick transitions between polarimetric modes and minimal perturbation of the native HARPS configuration. The synergy with the southern hemisphere’s target field makes HARPSpol particularly valuable for stellar magnetic field and exoplanet studies.

5. Precision, Systematics, and Error Budget

HARPS’s instrumental stability over a decade is manifested by consistent sub-meter-per-second RV precision across time (Udry et al., 2017). Nevertheless, several systematic noise sources have been identified:

• CCD block-stitching-induced annual RV artefacts (typically anti-correlated with barycentric variations) (Dumusque et al., 2015, Coffinet et al., 2019)
• Charge transfer inefficiency (CTI) in the CCD leading to flux-dependent centroid shifts; mitigated by empirical correction functions based on detailed moment analysis of LFC lines (Zhao et al., 2020)
• Telluric (atmospheric) contamination, especially from water vapor lines, degrading RV precision at times or in certain orders; practical mitigation requires per-order SNR and telluric EW thresholding (Lisogorskyi et al., 2019)

Mitigation strategies have involved both instrumental (flat-field mapping, LFC calibration) and data-driven (mask cleaning, NZP correction, template matching) innovations. On carefully selected data, overall RV rms for bright, quiet stars can routinely reach 0.5–1 m/s, supporting low-mass planet detection and asteroseismic studies (Barbieri, 2023).

6. Data Products and Legacy

HARPS observational campaigns have led to large public time-series datasets—most notably the ESO/HARPS Radial Velocities Catalog (Barbieri, 2023). This release comprises $\sim 290{,}000$ observations of 6488 unique objects (2003–2023), with cross-identifications in SIMBAD, associated photometry, astrometry, and both high-precision (DRS) and H$\alpha$-derived (Lorentzian profile fitting) RVs. The H$\alpha$ measurements, though less precise ($\sim$300 m/s error), enable kinematic and atmospheric studies in stars where the CCF method is less effective.

Metadata include instrumental configuration, S/N, CCF parameters, observation time, and ancillary activity indices, making the archive invaluable for studies of exoplanet populations, stellar dynamics, activity cycles, and time-domain trends.

7. Impact and Scientific Contributions

HARPS has been central to the discovery of low-mass exoplanets, in particular super-Earths and Neptunes with small RV signatures (Curto et al., 2013, Udry et al., 2017). Its long-duration, high-cadence surveys, frequently employing complementary activity indicators and sophisticated statistical modeling (GLS periodograms, MCMC orbital fits, F-tests), have refined occurrence rates, improved dynamical analyses, and aided asteroseismic investigations (Poretti et al., 2012, Datson et al., 2014).

Instrumental innovations—polarimetric modules, LFC calibration (Probst et al., 2020), template-matching pipelines (Anglada-Escudé et al., 2012, Trifonov et al., 2020)—have ensured enduring relevance, while its datasets and calibration approaches continue to inform the next generation of instruments (HARPS3, ESPRESSO, RISTRETTO). The rigorous characterisation of systematics (e.g., annual signals, CTI, tellurics) has established best practices and defined error budgets for precision RV and spectroscopic studies.

Table: HARPS Precision, Data Products, and Systematics

Parameter	Value / Description	Notes
Spectral Resolution (R)	115,000	$3800$–$6900$ Å range
Typical RV precision	0.5–1 m/s	DRS, after correction (quiet stars)
Polarimetric sensitivity	$\sim10^{-5}$	Full-Stokes, after LSD line addition
Systematic RV offsets	1–3 m/s (NZP, annual, fiber step)	Correction required; fiber change 2015
Main datasets	ESO/HARPS RV Catalog, HARPS-RVBank	(Barbieri, 2023, Trifonov et al., 2020)
Calibration innovations	LFC, gap mapping, multi-source comb.	(Coffinet et al., 2019, Probst et al., 2020)
Correction methods	Mask cleaning, NZP, template-matching	(Dumusque et al., 2015, Trifonov et al., 2020, Anglada-Escudé et al., 2012)

These empirical and technical advances, in combination with open data releases, ensure that HARPS remains a foundational facility for the quantitative analysis of extrasolar planets and other precision astrophysical phenomena.