PRIN Large Scale Lab (LaScaLa)

To achieve its ambitious scientific goals, the European Space Agency Euclid satellite mission needs to reach an accuracy for its data handling and calibrations procedures that is one order of magnitude better than what was previously achieved on data with similar quality, while maintaining this unprecedented accuracy over a dataset which is almost two orders of magnitude larger than what was produced by precedent astronomical surveys.

In particular, the precise mapping of galaxies' large-scale distribution, which is one of the primary tools used in modern cosmology to build an accurate description of our Universe, is one of two main cosmological probes for the Euclid satellite mission. This mapping relies on the usage of Hubble’s law, relating galaxy distances to their redshift, i.e., the speed with which they are moving away from our own galaxy within an expanding Universe. It is therefore mandatory for the Euclid mission to produce as accurate as possible redshift measurements for the tens of millions of galaxies that the satellite is observing as part of its six-year mission to explore the secrets of our Universe.

As these measurements are obtained starting from the Euclid spectroscopic observations, taking advantage of the Doppler effect created by the relative motion between the distant galaxies and our own Milky Way Galaxy, which results in a wavelength shift for the observed spectra towards longer wavelengths (hence the name red-shift), there are three main factors that contribute to the accuracy of redshift measurements:

• The quality of each individual spectrum: spectra with lower noise facilitate the precise determination of the observed spectrum shape, and consequently its comparison with a non-redshifted spectral template to measure the shift.
• The prominence of certain features in each individual spectrum: hot gas in star-forming spiral galaxies produces strong, easily identified emission peaks in the corresponding galaxy spectra, whereas the spectra of non-star-forming elliptical galaxies are devoid of such peaks, making the determination of the shift for these spectra significantly harder.
• The overall accuracy of the wavelength calibration: the precise determination of the wavelengths within each observed spectrum is a primary component in the accuracy of the shift to be measured between such spectrum and the reference spectral template.

While the first two factors are completely beyond our control, as they depend only on the physical properties of the galaxies being observed, the accuracy of the wavelength calibration for the Euclid spectroscopic data is the primary factor where we can intervene to ensure the best possible quality for the Euclid spectroscopic dataset.

The NISP Instrument and Calibration Strategy

The implementation of this wavelength calibration is dictated in large part by the characteristics of the NISP spectrograph on board the Euclid satellite. NISP is a slitless spectrograph, where the light of all astronomical sources visible in its focal plane is dispersed by the instrument optics, instead of limiting the selection of sources via an opaque mask with transparent "holes," as is done with the majority of multi-object spectrographs (MOS).

Figure 1: Observed spectrum of a planetary nebula. The distinct emission peaks serve as high-precision anchors for wavelength calibration (Hora et al. 1999).

As a result, spectra can be obtained from a source at any position in the NISP focal plane, making it mandatory to extend the wavelength calibration to the full focal plane. To achieve this, the NISP calibration team derives the calibration via specific observations of a planetary nebula, positioned over a grid of points, and then interpolates the results across the entire focal plane. Planetary nebulae are used because their spectra contain many bright emission peaks with accurately known wavelengths.

The grid of observations is composed of 80 spectra (5 points for each of the 16 NISP detectors). These solutions are then interpolated using 2D Chebyshev polynomials to provide an overall wavelength calibration accuracy of 5.4 Angstrom.

Advancing Calibration Precision

Figure 2: Enhanced detection of faint stellar absorption lines used to refine the astrometric localization model. Highlighted in yellow is an image artifact correctly rejected by the algorithm, while the green marker at the center indicates the accurately measured absorption feature

Within the framework of the Large Scale Lab (LaScaLa), we have carried out extensive work to produce significant improvements in the accuracy of the Euclid spectroscopic wavelength calibration. One of the primary challenges in slitless spectroscopy is the precise localization of celestial objects. This initial step is critical, as any error in localization translates directly into a shift in the measured wavelength. To address this, we use a calibration model based on astronomical coordinates, refined by measuring specific absorption features, such as the magnesium line, in the spectra of bright stars.

However, detecting these features is difficult, as they appear as faint signals embedded in noisy images. Part of our work focused on enhancing the measurement accuracy of these subtle absorptions, leading to a significant refinement of the underlying "astrometric" localization model.

Once localized, we measure the positions of the emission lines in planetary nebulae. By comparing observed positions with cataloged wavelengths, we calculate wavelength solutions for 80 specific points across the Field of View (FOV). We then apply a global fit to these coefficients, to extrapolate the solution everywhere in the FOV. However, these mathematical fits often diverge at the edges of the field, leading to models that do not accurately represent the data near the boundaries.

The research funded by this project investigated regularization techniques to stabilize these solutions. By applying these regularization methods, we produced smoother, more reliable surfaces that ensure consistent and accurate calibration across the entire Field of View, preventing divergence at the edges.

Figure 3: Wavelength calibration maps. The original model (left) shows instability and divergence at the focal plane boundaries. The improved model (right) utilizes LaScaLa regularization techniques to achieve high stability and accuracy across the entire FOV.