Euclid Data Release 1 (DR1). NIR astrometric calibration

Introduction

Accurate astrometric calibration is essential for the success of the Euclid mission ([11]), which enables the precise mapping of celestial sources across its detectors. The astrometric calibration process ensures the reliable alignment of observed images with external reference catalogues, such as Gaia DR3 ([19]), and maintains internal consistency among multiple dithered images. Euclid’s Near-Infrared Spectrometer and Photometer (NISP: [8]) features three imaging channels: $Y_{\mathrm{E}}$, $J_{\mathrm{E}}$, and $H_{\mathrm{E}}$. An array of 16 HAWAII-2RG (H2RG) detectors, each with 2048×2048 pixels and a plate scale of 0.''3 pixel$^{-1}$, provides a field of view of 0.57 deg$^2$. We recall that within Euclid, a dithering sequence operating mode is termed a single observation, and the individual exposures (dithers) of each observation are archived under an Observation ID (OBSID hereafter). In the wide survey, each OBSID consists of four dithers; the self-calibration field consists of 76 dithers ([11, 13]). In DR1 ([17]), NISP calibrated images and associated catalogues are available for both single dithers and stacked products ([12]).

For the initial data releases (DR1 and DR2), the astrometric calibration requirement is set as a root mean square (RMS) of 200 mas for both RA and Dec, compared to the external reference (absolute astrometry), and 100 mas for the positions of the same sources observed within a dither sequence (relative astrometry). The ultimate aim of the final release (DR3) is to achieve an RMS of 30 mas on each axis for both relative and absolute astrometry, corresponding to 0.1 pixels. An additional requirement pertains to geometric distortion, which must be calibrated to within 0.015% over scales of 3 arcmin. This paper focuses on the methods used to model and correct instrumental distortions in images from the NISP photometric channel (NISP-P) and assesses the calibration quality achieved in the Euclid DR1, covering an area of 1900 deg$^2$ ([14]). The paper is organized as follows. Section 2 summarises the astrometric calibration module of the NIR processing function (NIR-PF) pipeline and its quality control tests. Section 3 presents the results obtained in the DR1, evaluating astrometric residuals against external catalogues and internal consistency metrics based on more than 1 year of Euclid operations. This analysis shows that the astrometric calibration meets the requirements on the RMS and on the geometric distortion accuracy, described in Sect. 3.3. The stability of the astrometric solution over time and its dependence on source properties and instrument configuration are also discussed in Sect. 3.3. Section 4 outlines the enhancements already implemented for Euclid Data Release 2, as well as additional improvements that may further refine the calibration accuracy and efficiency in later data releases. To support the use of the calibrated data products, for each parameter described in the text we also give the corresponding keyword in the NIR_AstrometricCalibration module of the NIR-PF (NIR_Astrometry hereafter).

Astrometric calibration of NISP images in Euclid

In the NIR-PF, NIR_Astrometry relies on the Scamp software ([1]) to compute the distortion and update the associated keywords in the headers of the FITS frames. This is done¹ for each dither, because the combined effect of the tilt in the NISP optics ([15]) and an offset of the filter centre from the optical axis, due to uncertainty in filter positioning, leads to variations in the distortion pattern that prevent us assuming a constant distortion across different exposures.

Scamp utilises the PV formalism (see e.g. [5, 21]), which calculates the distortion for each detector by mapping pixel coordinates $(x, y)$ from that detector to intermediate world coordinates $(\xi, \eta)$. The distortion is applied to the coordinates projected onto the focal plane as

The relevant quantities are defined as follows: $p_x$ and $p_y$ are the coordinates of the reference pixel, corresponding to the CRPIX keywords in the FITS files; $C_{ij}$ are the elements of the linear transformation matrix that accounts for pixel scale and rotation, stored in the CD keywords; and $a_{mn}$ and $b_{mn}$ are for each axis the coefficients of the polynomial with order $N$ describing the distortion, corresponding to the PV keywords. In NIR_Astrometry, the distortion (Figure 1) is represented by a polynomial with $N = 3$. This approach involves working in sky coordinates using a tangent-plane projection. In cases such as Euclid, where the detectors are not aligned with the celestial coordinates, the polynomial coefficients are dependent on the telescope rotation. In contrast, the SIP formalism ([22]) describes the distortion directly in the focal plane without relying on the tangent-plane projection. It uses polynomial distortion coefficients $A_{ij}$ and $B_{ij}$ (often encoded as SIP keywords) to model the optical and instrumental distortions that affect the pixel coordinates on the detector and transform them into intermediate world coordinates:

In this case, because the distortion is expressed purely in focal plane terms, it does not depend on the telescope rotation.

In DR1, the adopted external reference is the Gaia DR3 catalogue ([18, 23]), which is also the reference catalogue adopted for the astrometric calibration of the VIS channel. The positions from the VIS catalogue are not utilised for the following reasons. (1) Although there is a significant overlap between the VIS and NISP coverage in each exposure, it is not complete; therefore, incorporating additional adjacent VIS fields becomes necessary, but these fields are not guaranteed to be observed. (2) Point sources brighter than $I_{\mathrm{E}}=18.5$ are saturated in VIS normal exposures ([10]); as a consequence, a significant fraction of bright sources that are not saturated in NISP² and

therefore available for astrometric calibration with Gaia DR3 as reference, would be saturated in VIS and thus not usable with VIS as reference.

The Gaia DR3 celestial coordinates (epoch J2016.0) are propagated to the Euclid dither epoch through the application of proper motions. The final Euclid calibrated positions are in the barycentric ICRS.

Scamp processes the catalogues generated by SExtractor ([3]) in combination with PSFEx ([2]), optimising the precision of source centres through point-spread function (PSF) fitting. The implementation of PSF fitting in the NIR-PF is discussed in detail in [7]. Within Scamp, the quality maps produced by the NIR-PF ([13]) enable the exclusion of sources that are either saturated or compromised by issues like cosmic rays and persistence. The sources used for astrometric calibration have Gaia DR3 magnitudes, $G$, in the 15 to 21 range, corresponding to approximately 16 to 22.5 in the NIR bands.

The robustness of astrometric calibration can be enhanced by supplying Scamp with an initial estimate of the distortion (presolution). This approach is particularly advantageous for the detectors at the edges of the field of view (Figure 1), where distortion is more pronounced, thereby complicating the alignment with the external reference catalogue. In the current implementation, the presolution primarily serves as an initial input to Scamp, functioning as a preliminary estimate or starting point rather than delivering a highly precise outcome. In this implementation, because the presolution is primarily used to guide the matching of sources before further processing in Scamp, the demand for accuracy is relatively low (around $1''$). Although the distortion pattern is expected to vary among different exposures, deriving the presolution once is sufficient for the intended purpose of the current implementation. This derivation is based on the observations of the self-calibration field. The presolution initially contains distortion terms expressed in the Scamp PV format, along with the values encoded in the CD and CRPIX keywords. To facilitate its application to observations with varying telescope rotation angles, the presolution is initially transformed into the SIP format. Subsequently, it is converted back to the PV format, with modifications made to the CD matrix terms to accommodate the instrument rotation. Analytical expressions derived using the sympy package in Python are applied for all conversions between the PV and SIP formats. At this point, there may be an offset in the celestial coordinates of the tangent-point, defined by the CRVAL keyword in the images. Although Scamp corrects this offset before calculating the distortion, it is ineffective in situations such as a Fine Guidance Sensor (FGS) failure, which results in elongated source images, or when cosmic ray showers impact a significant number of pixels, necessitating the exclusion of the exposures regardless. Consequently, NIR_Astrometry initially employs Scamp exclusively to adjust the CRVAL values, followed by an initial alignment utilising the Gaia DR3 catalogue through the presolution. Subsequently, a series of tests is conducted for each dither, to identify those for which it is not possible to derive a reliable astrometric solution.

• If the median ellipticity of the matched sources (ASTRELL keyword) exceeds a threshold of $\epsilon_{\rm th} = 0.3$ or is more than twice the median across all dithers, it is highly likely that the dither is compromised owing to a failure in the FGS.

• If a detector records an abnormally low number of detections ($< 5$) or if the fraction of matched sources is too low compared to those in the external catalogue ($< 10\%$), it becomes impossible to reliably estimate the distortion.

The threshold values mentioned above are selected based on an analysis of a subset of dithers with known issues and may be refined in future data releases. For the dithers that successfully pass these evaluations, Scamp is executed once more to calculate the total distortion. One-third of the dithers identified as invalid in the NIR-PF [12] are marked as such through this step. § 3.1 presents an overview of the astrometric calibration results for dithers that pass the validity tests.

Analysis of astrometric residuals

We present a summary of the astrometric residuals generated by NIR_Astrometry, both in relation to the Gaia DR3 catalogue and internally among the dithers. To accomplish this, we select 4000 OBSID from the Euclid Wide Survey in the Science Archive System (SAS) for each NISP filter, covering an area of 1950 deg$^2$ after removing overlaps (Sect. 3.2.4), over more than 1 year of operation (from February 2024 to May 2025).

To assess the quality of the astrometric calibration, we use the following quantities derived from the positional differences between the $N$ detections and their matched reference sources, $\Delta\alpha_i^* = (\alpha_i - \alpha_{\mathrm{ref},i})\cos\delta_{\mathrm{ref},i}$ in right ascension (RA) and $\Delta\delta_i = \delta_i - \delta_{\mathrm{ref},i}$ in declination (Dec). Quantities in RA marked with an asterisk indicate that they are multiplied by $\cos\delta$ to measure angular distances on the sky.

Average offset. The mean positional difference, which indicates the calibration bias, is given by

Standard deviation ($\sigma$). This measures the spread of the positional offsets around the mean, thereby indicating the calibration precision,

RMS offset. This is the square root of the mean squared positional differences, representing the total calibration accuracy (bias + precision),

Where the RMS or $\sigma$ represents the sum over both coordinates, it is expressed as $\mathrm{RMS}^2 = (\mathrm{RMS}_{\alpha^*}^2 + \mathrm{RMS}_{\delta}^2)/2$.

In NIR_Astrometry, the average offset relative to the reference catalogue is produced as an output and stored in the headers of the calibrated images using the keywords ASTROFF1 and ASTROFF2, corresponding to the RA and Dec coordinates, respectively. The keywords ASTRRMS1, ASTRRMS2 represent the standard deviation of the residuals for sources matched across different dithers; ASTRRMS1, and ASTRRMS2 refer to those compared to the reference catalogue. They are computed both for single detectors and the entire dither. Given that the average offset in each detector or dither is negligible, the standard deviation matches the RMS of the deviations. During the validation process, dithers are flagged if any value of ASTRIRMS1, ASTRIRMS2, ASTRRMS1, or ASTRRMS2 computed throughout the entire dither exceed 50 mas or if ASTRIRMS1 or ASTRIRMS2 exceed 50 mas in any detector.

Astrometric residuals in dithers

Figure 2 illustrates the distribution of average ellipticities, the number of matches with Gaia DR3 sources, and the residuals (offsets and standard deviations) in both the dithers (upper and middle rows) and individual detectors (bottom row). This confirms that, as anticipated in Sect. 3, the average offset to the reference catalogue is indeed negligible, being within 2 mas; the astrometric calibration accuracy is approximately 10 mas and remains below 20 mas for 99% of the dithers, in all bands. The RMS decreases from $Y_{\mathrm{E}}$ to $J_{\mathrm{E}}$ and $H_{\mathrm{E}}$, consistent with the stronger undersampling of the diffraction-limited PSF at shorter wavelengths [8] (Euclid Collaboration: da Silva et al. 2026). For individual detectors, mostly DET13 and DET14, a small fraction exhibits a standard deviation exceeding 60 mas and potentially reaching up to 150 mas. This fraction is at most 0.15% for $H_{\mathrm{E}}$ and is even lower in the other bands. As discussed in more detail in Sects. 3.6 and 4.1, the problem was identified as stemming from an excessively stringent exclusion of detections linked to the persistence flagging.

Figure 2 also confirms that, among the dithers that passed the initial selection, the average ellipticity is less than 0.16. In future data releases, a threshold lower than the current value ($\epsilon_{\mathrm{th}} = 0.3$) could be chosen to identify dithers affected by the FGS issue.

Analysis of stacked catalogues

To comprehensively assess the accuracy and robustness of the astrometric calibration of NIR images in the Euclid DR1, we present a series of diagnostic tests performed to investigate potential dependencies affecting the residuals. These tests examine variations in astrometric residuals as a function of Galactic extinction, source colour, observation time, and telescope rotation. Additionally, internal consistency checks analyse offsets between different filters and between the NISP and VIS bands, as well as comparisons with the Gaia DR3 catalogue. To accomplish this, we examine the stacked catalogues produced for

each OBSID rather than single dithers. Consequently, the results are independent of those derived from individual dithers during the astrometric calibration. A comparison of the residuals from the Gaia DR3 positions obtained on dithers in NIR_Astrometry and those from the stacked catalogues reveals consistency, with a median standard deviation $(\sigma_{\alpha},\sigma_{\delta})$ of approximately 10 mas, and 95% of the dithers falling within 15 mas.

The centroids of the sources in the stacked catalogues, obtained by PSF-fitting (Euclid Collaboration: Polenta et al. [13]), are cross-matched with the Gaia DR3 catalogue by applying the selection criteria described in Sect. 2. A strict mutual nearest-neighbour algorithm is adopted in the cross-match to minimise duplicate or incorrect assignments. First, we perform a forward match, identifying the nearest Gaia DR3 source for each target object in the stacked catalogue. Next, we perform a reverse match, identifying the nearest target object for every source in the Gaia DR3 catalogue. A cross-match is considered if two criteria are met: (1) the target object and the Gaia DR3 source are each other’s closest reciprocal matches; and (2) their angular separation does not exceed a maximum tolerance of 1″.

Astrometric residuals versus position angle and time

In the PV formalism, distortion changes with the instrument’s rotation relative to the sky. To test whether the position-angle-dependent distortion model introduces spurious residuals, we fitted, for each band, the RMS of the residuals per observation and their mean offsets in the instrument frame $(\Delta\xi,\ \Delta\eta)$ with a sinusoidal function of the position angle. The amplitude of the sinusoid is 0.08–0.14 mas for the RMS, compared with a median RMS of approximately 10 mas per observation, and at most 0.08 mas for the mean offsets, compared with their uncertainty of 0.5–0.8 mas per observation. The position-angle dependence of the distortion model therefore introduces no significant spurious residuals. Similarly, a linear fit of the RMS per observation as a function of time gives slopes of 0.04–0.11 mas yr$^{-1}$, i.e. a change of at most 0.2 mas over the period covered by the observations, which is again negligible.

Astrometric residuals versus focal plane position

To examine the discrepancies across the focal plane, we create an astrometric residual map for each filter. For this purpose, we first collect from all stacked catalogues the detections matched with Gaia DR3. When averaging frames with different rotations, offsets are diluted if derived from sky coordinates. For this reason here we compute offsets from the reference pixel ($u$, $v$ in Eq. (2)) converted to arcseconds with the pixel scale ($\xi$, $\eta$), and derive the NISP−Gaia DR3 residuals in the instrument frame ($\Delta\xi$, $\Delta\eta$). Since the scatter is nearly isotropic, the RMS is instead frame invariant ($\sigma_{\xi} \sim\sigma_{\alpha^\ast}$, $\sigma_{\eta} \sim\sigma_{\delta}$).

The mean offsets and the scatter of the residuals $\Delta\xi$ and $\Delta\eta$ are computed from the combined detections of all stacked catalogues, as a function of the position $\xi$, $\eta$ in the stack frame. For the two-dimensional maps (Figure 3 and Figure 4, top rows), the ($\xi$, $\eta$) plane is divided into non-overlapping cells of $2.5^\prime\times2.5^\prime$, each containing on average $10^4$ detections. In each cell, the mean and the standard deviation of $\Delta\xi$ and $\Delta\eta$ are computed after an iterative $3\sigma$ clipping of all the detections falling in it; cells with fewer than 100 detections after clipping are discarded. Each cell is represented by a whisker starting at the cell centre: its components are $\langle\Delta\xi\rangle$ and $\langle\Delta\eta\rangle$ for the mean offsets, and $\sigma_{\xi}$ and $\sigma_{\eta}$ for the scatter. To highlight trends along each axis, we also compute one-dimensional profiles (Figure 3 and Figure 4, bottom rows) in independent strips $1^\prime$ wide, running along $\xi$ and $\eta$ across the whole field, each containing on average $10^5$ detections; the same $3\sigma$-clipped statistics are applied. As a result of this analysis, across the focal plane offsets are below $\pm5$ mas in all bands; the standard deviation in both $\xi$ and $\eta$ does not vary significantly and, consistently with previous results, decreases from $Y_{\mathrm{E}}$, $J_{\mathrm{E}}$ ($\sim15$ mas) and $H_{\mathrm{E}}$ ($\sim10$ mas).

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Astrometric residuals versus source colour

Figure 5 illustrates the standard deviations of the astrometric residuals measured in each stacked catalogue, as a function of the average Gaia DR3 BP − RP colours, with average redder colours corresponding to a higher Galactic extinction. A slight trend is noticeable, with a difference of less than 1 mas between stacks with average bluer and redder colours. A correlation between astrometric residuals and average source colours would be expected in the case of chromaticity effects in the PSF, where the measured centroid would be expected to vary with stellar colour and increase the astrometric scatter. A higher Galactic extinction shifts the selected Gaia DR3 stars towards redder colours and narrows the colour distribution: in the case of a PSF chromaticity, this would result in a smaller PSF variation across the sample than in fields with a low Galactic extinction, thus reducing the chromatic contribution to the astrometric scatter. A slight trend is noticeable, with a difference of less than 1 mas between stacks at lower and higher extinction levels. To further verify whether the astrometric calibration may be influenced by chromaticity effects, we examine the correlations between the residuals along the $x$ and $y$ axes of the detectors and Gaia DR3 colours (BP − RP). For this purpose, Gaia DR3 positions and those measured in the NISP stacks are first reprojected onto the focal plane, and the residuals along the detector axes ($\Delta\xi$, $\Delta\eta$) are computed and binned in BP − RP colours. The chromaticity terms, represented as $R_{\xi}$ and $R_{\eta}$, are defined as the slopes of these binned residuals against BP − RP: $R_{\xi} = \langle\Delta\xi\rangle_{\mathrm{bin}} / (\mathrm{BP} - \mathrm{RP})_{\mathrm{bin}}$, $R_{\eta} = \langle\Delta\eta\rangle_{\mathrm{bin}} / (\mathrm{BP} - \mathrm{RP})_{\mathrm{bin}}$ are finally derived. We find that for all filters, $R_{\xi} < 1$ mas mag$^{-1}$ and $R_{\eta} \ll1$ mas mag$^{-1}$.

Astrometric consistency across overlaps

Stacks of adjacent observations may overlap. This overlap enables us to assess whether the astrometric calibration remains consistent for the same sources that are detected in different stacks. To accomplish this, we select pairwise overlaps between stacks, with each having an overlap of at least $50\ \mathrm{arcmin}^{2}$, ensuring sufficient detections for a meaningful analysis. This results in a total area of $560\ \mathrm{deg}^{2}$. As shown in Figure 6, for 99% of the overlaps the standard deviation in both coordinates remains within 25 mas, while the median offsets are within 10 mas. This is in agreement with what derived in the previous sections.

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Geometric distortion: accuracy and stability

We verify whether the geometric distortion is calibrated within 0.015% over scales of $3'$, as in the requirement. To achieve this, for each stacked catalogue we extract within the matched sources the pairs separated by a distance $d_{\mathrm{ref}}$ between $2.'5$ and $3.'5$ in the Gaia DR3 catalogue, used as the reference. We then compare these pairs with the corresponding ones in the $Y_{\mathrm{E}}$, $J_{\mathrm{E}}$, and $H_{\mathrm{E}}$ catalogues, where the separation is $d_{\mathrm{NIR}}$, resulting in the fraction $\nu= \lvert d_{\mathrm{ref}} - d_{\mathrm{NIR}}\rvert/( \sqrt{2}d_{\mathrm{ref}})$. A factor of $\sqrt{2}$ is introduced to transform pair separations into single-source equivalents. In all the stacks examined here, the RMS of $\nu$ is less than 0.01%; in each stack, 95% of the considered pairs have $\nu< 0.02\%$. To ensure that this test accurately traces geometric distortions without being influenced by random centroiding noise, we conduct the analysis again on a $15^{\prime\prime}$ scale, where the impact of geometric distortion is minimal, and find the noise contribution to be negligible.

We then evaluate how well the assumption of a constant presolution aligns with the actual distortion observed in the dithers. For this purpose it is essential to separate the distortion, assumed to be constant, from the components that may vary across different observations: here we assume that they may be described by offset and linear terms. This is performed using a set of artificial source positions, following the procedure outlined below.

1. A list of artificial sources positioned on a grid $(x, y)$ that matches the detector’s size of $2048 \times2048$ pixels is created.

2. This list is transformed into intermediate world coordinates (IWC) using the PV distortion computed by NIR_Astrometry, yielding the reference coordinates $(\xi_{\mathrm{r}}, \eta_{\mathrm{r}})$.

3. The PV distortion model contained in the presolution is converted to SIP. Equation (2) is applied to transform pixel coordinates $(x, y)$ to intermediate coordinates $(U, V)$, using only the nonlinear terms of the SIP distortion $(i+j \geq2)$.

4. A least squares minimisation is performed to fit the $C_{ij}$ terms of the CD matrix (Eq. (1)) and an offset $(\Delta\xi, \Delta\eta)$:

5. The offset $(\Delta\xi, \Delta\eta)$ is converted back to pixel offsets $(\Delta U, \Delta V)$ by applying the inverse CD matrix:

Here $\lvert C\rvert= C_{11}C_{22} - C_{12}C_{21}$. The offsets $\Delta U, \Delta V$ replace the constant terms in the SIP polynomials, $A_{0,0}$ and $B_{0,0}$. Because the linear terms are now represented by the fitted CD matrix, the linear SIP terms $A_{1,0}$, $A_{0,1}$, $B_{1,0}$, and $B_{0,1}$ are set to zero to avoid redundancy.

6. The reference coordinates $\xi_{\mathrm{r}}, \eta_{\mathrm{r}}$ are compared with the coordinates $\xi_{\mathrm{n}}, \eta_{\mathrm{n}}$ obtained by applying the new distortion terms.

We analyse 15 observations of the self-calibration field, each comprising 76 dithers with varying rotation angles. This selection is made because of the notably stable distortion observed in these cases. The $(\xi_{\mathrm{r}}, \eta_{\mathrm{r}})$ values obtained from the pixel grid are compared with those derived by applying the Scamp distortion contained in the headers $(\xi_{\mathrm{r}}, \eta_{\mathrm{r}})$, and the offsets are analysed. Figure 7 illustrates the comparison between the standard deviation of these offsets and those computed by NIR_Astrometry with respect to the Gaia DR3 sources (ASTRRMS1, ASTRRMS2), based on the Scamp processing. In both methods, the median of the standard deviations is approximately 10 mas, and within 20 mas for 99% of them. These findings suggest that the distortion remains consistently stable over time, within a margin of approximately 10 mas. However, they also imply that the assumption that linear components can sufficiently account for the residual variations in distortion may not hold true, as further discussed in Sect. 4.2.

Effect of stellar aberration and plate-scale stability

The Gaia DR3 reference positions used in the astrometric calibration are barycentric and are propagated to the epoch of each exposure using proper motions only; no correction for stellar aberration due to the motion of Euclid is applied. To first order, aberration changes the apparent angular separations across the field by a factor $(1+\mathbf{v}\cdot\hat{\mathbf{n}}/c)$, where $\mathbf{v}$ is the barycentric velocity of Euclid, given by the VEL_X, VEL_Y, VEL_Z values in the frame headers, and $\hat{\mathbf{n}}$ the direction of the field, derived from the CRVAL1 and CRVAL2 values. Since the astrometric solution maps the observed pixel positions onto barycentric reference positions, this term is absorbed into the fitted plate scale $s$, which is then expected to vary by $\Delta s/s = \mathbf{v}\cdot\hat{\mathbf{n}}/c$ (see e.g. Cox & Gilliland [6]).

For each detector $d$ in a dither we compute the effective pixel scale, $s_d$, as the mean pixel size given by the full astrometric solution, including the distortion terms. To remove the differences in scale between detectors, caused e.g. by the optical distortion, we consider the fractional change $\Delta s_d/s_d$ relative to the median of $s_d$ over all dithers in all available fields. The scale change of a dither is the median of $\Delta s_d/s_d$ over the detectors, and the scale change, $\Delta s/s$, of a field is the median over its dithers. These values are then fitted as

where $k = 1$ if the scale changes are reproduced by aberration, and the constant accounts for the arbitrary zero point. To express the results as displacements on the sky, we convert the fractional scale change into the RMS displacement it produces over the NISP field of view, $\delta= (\Delta s/s)r$, where $r = 18'$ is the RMS distance of the detector pixels from the centre of the field, computed from the astrometric solution. Likewise, the predicted displacement is $\delta_{\mathrm{pred}} = r\,(\boldsymbol{v} \cdot\hat{\boldsymbol{n}}/c)$.

Figure 8 shows the residuals between the measured and predicted ($k = 1$ in Eq. (8)) scale change, as a function of time and of the predicted displacement. We restrict the analysis to observations taken after July 2024, i.e. after the second thermal decontamination campaign (Euclid Collaboration: Schirmer et al. [16]), when Euclid had reached stable thermal conditions. In the self-calibration field, the displacement of stars due to aberration is close to its maximum, $\sim20''$, but it is a nearly uniform shift absorbed by the pointing. This field lies close to the North Ecliptic Pole, so the barycentric direction of its centre is almost perpendicular to the direction of motion of Euclid relative to the Solar System barycentre. The effect on the scale is therefore small, and corresponds to an absolute displacement of approximately 3 mas. Since the predicted displacement is small and the number of measurements lower, the constraint on $k$ is correspondingly weaker, but still consistent with $k = 1$ within uncertainties. In the wide survey fields, instead, the predicted aberration displacement is within $\pm100$ mas. The fit gives $k = 0.997 \pm0.001$, consistent within the uncertainties in the three bands. The measured scale changes thus follow the expected aberration; after removing it, 68% of the fields deviate from the prediction by less than 2 mas, with no significant mean offset.

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Parallax

As a further consistency check, we verify that the positions of stars in the self-calibration field observed at different epochs contain the parallax displacement expected for each star from Gaia DR3. Since the astrometric distortion is a smooth function of position on the detector, it can absorb a displacement common to all stars on a detector, but not the part that differs from star to star with their individual parallaxes. That part should remain fully in the calibrated positions, with the amplitude predicted from the Gaia DR3 parallax and the position of Euclid at each epoch. We test this with the observations of the self-calibration field, by measuring the parallax of individual stars from the calibrated positions alone and comparing it with Gaia DR3. The test is limited at faint magnitudes by the precision of the Gaia DR3 parallaxes and at bright magnitudes by saturation in NISP; since nearby red stars are brighter in the near-infrared than in the $G$ band, the effect of these limits is to remove the reddest and nearest stars, and keep mostly red dwarfs with parallax $\varpi_{\mathrm{Gaia}} \approx2$–5 mas, and few with larger parallaxes. Moreover, the visits of the self-calibration field span about 1 year, too short to separate parallax from proper motion, which is therefore fixed to the Gaia DR3 value. Since the self-calibration dither pattern has large offsets, a star falls on the detectors in only a fraction of the 76 dithers in a visit, from about 60% near the centre of the pattern to a few per cent at its edge.

Positions in the calibrated NISP catalogs are matched (within 0\farcs3) to Gaia DR3 stars brighter than $G = 20$, $r_{\mathrm{u}} < 1.4$ and astrometric_excess_noise $< 1$ mas (Lindegren et al. [20]) that are not flagged as duplicated sources, and the residual $\boldsymbol{r} = (\Delta\alpha^*, \Delta\delta)$ with respect to the Gaia DR3 position propagated with proper motion only is computed at each exposure epoch. The barycentric position of Euclid, $\boldsymbol{b}$, is taken as the barycentric position of the Earth plus the geocentric position of the spacecraft given in the POS_X/Y/Z header keywords. With $\boldsymbol{b} = (X,Y,Z)$ expressed in au in ICRS axes, the parallax factors of a star at $(\alpha,\delta)$, following the convention of the Gaia astrometric model,

so that a star of parallax $\varpi$ is displaced by $\varpi\boldsymbol{F} = \varpi(F_{\alpha^*},F_\delta)$ in $(\alpha^*,\delta)$.

Two sets of stars are used. Probe stars have a precise Gaia DR3 parallax ($\varpi> 2$ mas, $\varpi/\sigma_\varpi> 10$). Anchor stars are all other Gaia DR3 stars, regardless of their parallax. For each exposure and detector, the mean offset of the calibrated positions is computed from the anchors as $\boldsymbol{c} = \langle\boldsymbol{r} - \varpi_{\mathrm{Gaia}}\boldsymbol{F}\rangle$ (with $4\sigma$ clipping), i.e. after removing the parallactic displacement of each anchor predicted from its own Gaia parallax. Without this subtraction, the mean anchor parallax ($\approx$ a few tenths of a mas) would be absorbed by $\boldsymbol{c}$, biasing every probe parallax low by the same amount. The anchor-corrected probe offsets $\boldsymbol{y} = \boldsymbol{r} - \boldsymbol{c}$ and the parallax factors are then averaged over the dithers of each visit. For each probe with at least ten visits, $\varpi_{\mathrm{NISP}}$ is obtained by a least-squares fit of $y_i = \varpi_{\mathrm{NISP}}F_i + o$ to its visit means, where the constant $o$ absorbs the error of the propagated Gaia position, and its uncertainty $\sigma_{\mathrm{NISP}}$ from the scatter of the star’s own residuals about the fit.

Due to the significant uncertainty in individual parallaxes, the comparison relies on the entire probe sample. We fit

by least squares with weights $w_j = 1/(\sigma_{\mathrm{NISP},j}^2 + \sigma_{\varpi,\mathrm{Gaia},j}^2)$. A loss of part of the parallactic signal in the calibration would give $k < 1$, a zero-point offset would give $\delta\ne0$. The difference between the NISP and Gaia DR3 parallaxes can be expressed imately 30 per detector to just a few, which in turn results in less accurate astrometric calibration. Shortly after this issue was identified, a solution was implemented (Sect. 4.1); however, it could not be incorporated into DR1.

To better estimate the impact of these failures on DR1, the following analysis has been conducted. For each stacked catalogue generated in DR1 for a specific OBSID, detected sources are matched to the Gaia DR3 catalogue within a 5″ radius to account for astrometric failures. A similar procedure is employed to compare the NISP and VIS positions. In this case, VIS sources are initially selected with |spread_model| < 0.05 in the stacked VIS catalogues (Euclid Collaboration: McCracken et al. [10]) to exclude overly extended sources.

An RMS map is subsequently constructed utilising a 2D rolling window approach. The area covered by each stacked catalogue is divided into a grid with 30″ intervals: this step size is chosen to achieve a finer spatial resolution and more detailed data sampling across the observed area. At the centre of each grid cell, matched sources are gathered within a specified radius, selected to ensure that each cell contains at least 10 (20) matched Gaia DR3 (VIS) sources. This results in a radius of 4′ for Gaia DR3 and 2′ for VIS; in the latter case, the radius is smaller because aligning with the VIS catalogue increases the number of matches with fainter NISP sources. If a cell contains fewer than the minimum required matches, the radius is incrementally increased by 10″ until the requirement is met. On average, each cell contains 30, 50 matches with Gaia DR3 and VIS respectively.

This approach enables us to identify regions where the RMS surpasses a predetermined threshold without significantly increasing the computational time. For each OBSID, a specific RMS map is generated. assigning the highest RMS values observed across the NISP bands to each element of the map. The results of the comparison with VIS and Gaia DR3 (Figure 10) are consistent: the RMS exceeds 30, 60, and 90 mas in 3%, 0.3%, and 0.1% respectively of the total area, with a median RMS of approximately 20 mas. Finally, the same procedure is repeated using $H_\mathrm{E}$ as a reference and measuring the RMS in $J_\mathrm{E}$ and $Y_\mathrm{E}$. This produces results similar to those obtained previously, with RMS exceeding 30, 60, and 90 mas in 1%, 0.2%, and 0.1% respectively of the area for each of $J_\mathrm{E}$ and $Y_\mathrm{E}$ compared to $H_\mathrm{E}$.

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These tests indicate that despite this issue related to persistence masking, which will be resolved in Data Release 2 (Sect. 4.1), the astrometry remains consistent when compared to VIS and across the three NISP channels. The RMS is less than 30 mas (0.1 pixels) for at least 97% of the surveyed area when comparing VIS to NISP. Across the NISP bands, the RMS is less than 30 mas (0.1 pixels) for 99% of the area.

Best et al. [4] in units of their uncertainties, $z = (\varpi_\mathrm{NISP} - \varpi_\mathrm{Gaia})/(\sigma_\mathrm{NISP}^{2} + \sigma_{\varpi,\mathrm{Gaia}}^{2})^{1/2}$

Figure 9 compares the NISP and Gaia DR3 parallaxes for 152, 126, and 157 probe stars in $Y_\mathrm{E}$, $J_\mathrm{E}$ and $H_\mathrm{E}$. In $J_\mathrm{E}$ and $H_\mathrm{E}$ we find $k = 1.03 \pm0.11$ and $1.12 \pm0.16$: the full parallactic amplitude is recovered. The same fits indicate a zero-point offset $\delta\approx-1$ mas in these bands ($-0.92 \pm0.49$ and $-1.18 \pm0.52$ mas), significant at about $2\sigma$ in each band. In $Y_\mathrm{E}$, the most undersampled band and hence the one with the lowest astrometric precision, the constraints are weaker ($k = 0.73 \pm0.29$, $\delta= +1.0 \pm0.9$ mas) and consistent both with $k = 1$, $\delta= 0$ and with the $J_\mathrm{E}$ and $H_\mathrm{E}$ values. The median of $z$, with uncertainties bases on bootstrap resampling, is $+0.01 \pm0.09$ ($Y_\mathrm{E}$), $-0.47 \pm0.12$ ($J_\mathrm{E}$), and $-0.43 \pm0.18$ ($H_\mathrm{E}$), consistently with with the slight offset found above. The robust RMS is 1.07, 1.31, and 1.67 respectively. The negative medians in $J$ and $H$ reflect the zero-point offset discussed below.

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We conclude that the NISP astrometric calibration preserves the stellar parallax: over the probe sample, the parallaxes recovered from the calibrated positions have an amplitude consistent with that of Gaia DR3, to 11–16% in $J_\mathrm{E}$ and $H_\mathrm{E}$, the two bands that constrain it best, and at most $\approx20\%$ of the signal could have been lost ($2\sigma$). The possible zero-point offset of $\approx-1$ mas is marginal and well within the astrometric accuracy.

Inaccuracies due to persistence masking

As anticipated in Sect. 3.1, the validation of the DR1 data products indicated that, for a specific number of dithers, the residuals in certain detectors, particularly DET13 and DET14, are higher than those in other detectors, exceeding 100 mas. A comprehensive analysis revealed that, in these instances, the flagging of pixels is affected by persistence. Persistence can cause false detections, and as detailed in Euclid Collaboration: Polenta et al. [12], pixels in the persistence image that exceed a threshold of 2 e⁻ are considered invalid in the NISP images. However, this choice leads to a notable decrease in the number of sources with matches in the Gaia DR3 catalogue, reducing from approximately 30 per detector to just a few, which in turn results in less accurate astrometric calibration. Shortly after this issue was identified, a solution was implemented (Sect. 4.1); however, it could not be incorporated into DR1.

Improvements for DR2 and beyond

Reducing the impact on astrometry of the persistence masking

Although it was not feasible to rectify the persistence issue in DR1, a solution has been developed and applied to subsequent processing. Astrometric calibration can be influenced by persistence, either through false detections that result in spurious matches or by false detections near real sources that disrupt the centroid estimate. The impact of persistence flagging can be mitigated if a detection is discarded only when the pixels within a defined radius $R_\mathrm{p}$ from the detection centre exceed a specified persistence threshold $I_\mathrm{p}$. This ensures that only genuinely spurious detections are rejected, or those detections whose centre estimates may be compromised by persistence features. The values of $I_{\mathrm{p}}$ and $R_{\mathrm{p}}$ are determined following an analysis conducted on a subset of dithers: $I_{\mathrm{p}} = 5\mathrm{e}^{-}$ (see also Euclid Collaboration: Kubik et al. [9]) and $R_{\mathrm{p}} = 5$ pixels. Figure 11 demonstrates the impact of the fix on the astrometric residuals on a single observation ID.

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Exploring a simplified distortion model: preliminary Investigation

In DR1, the presolution is merely utilised in Scamp to enhance the initial matching of detected and Gaia DR3 sources. As discussed in Sect. 3.3, the distortion appears to be stable enough to consider keeping it constant while fitting only the linear terms.

This alternative approach involves directly applying the presolution distortion model, assumed to be constant, to the source positions, followed by the computation of only the linear terms that are specific to each dither. This simplified model would reduce computational complexity and minimise the sensitivity of the astrometric calibration to noise or spurious variations, potentially mitigating the risk of overfitting.

The underlying assumption here is that the linear corrections capture the residual variations due to the NISP optics (Sect. 2). To initially evaluate the validity of this assumption, we developed a modified version of NIR_Astrometry employing an approach similar to that outlined in Sect. 3.3, and conducted a pilot study based on a limited set of 10 observations (40 dithers): initially, the presolution is converted into the SIP formalism, which is then employed to remove distortion from the pixel coordinates in the SExtractor catalogue. Scamp is subsequently executed on this modified catalogue. Two options are considered: (1) no additional distortion is computed in this second step, with only the linear terms being refitted, and (2) a polynomial of order 2 is fitted. Figure 12, which illustrates the RMS of the residuals, supports the conclusions presented in Sect. 3.3: relying solely on linear terms results in an increased RMS of the residuals. To achieve RMS values comparable to those obtained with the full fitting (10 mas), it is necessary to incorporate an additional second-order component. A simplified distortion model with fewer free parameters would still allow for a reduction in the computational complexity; however, further comprehensive testing across a larger dataset is required before considering potential integration into the pipeline.

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Conclusions

This paper has presented the methodology and results of the astrometric calibration applied to the NISP data in Euclid DR1. The calibration pipeline employs the Scamp software to model and correct instrumental distortions on a per-dither basis, using a polynomial distortion representation within the PV formalism. The Gaia DR3 catalogue serves as the external astrometric reference, with source selections and quality controls implemented to ensure robust matching and calibration accuracy.

Analysis of 4000 observations covering $1950\,\mathrm{deg}^2$ and over 1 year of observations demonstrates that the NIR astrometric calibration achieves an average precision of approximately 10 mas, with 99% of the dithers exhibiting residuals below 20 mas in each detector. This corresponds to less than 0.1 pixels, and is within the requirement of 30 mas. The average offsets relative to Gaia DR3 are negligible (within 2 mas), confirming the absence of significant systematic biases.

The analysis of the stacked catalogues confirms these values, allowing further tests. Spatial mapping of the residuals across the focal plane shows stable performance, with minor variations at the edges attributed to the dithering patterns. The astrometric consistency among the neighbouring dithers is confirmed by matching sources in overlapping areas across the stacks. The chromaticity effects on astrometry are minimal, with slopes below 1 mas mag$^{-1}$, and no significant temporal or telescope rotation dependencies is observed. The distortion pattern is stable over time within approximately 10 mas, supporting the potential for a constant distortion model supplemented by an additional correction to capture the residual variations. However, tests indicate that fitting only linear terms increases the residuals, and a second-order polynomial fit is necessary to maintain a calibration accuracy comparable to that of the full polynomial model.

A limitation identified in DR1 is the impact of persistence masking on astrometric accuracy, particularly affecting detectors DET13 and DET14. Excessive flagging of pixels due to persistence reduces the number of matched sources and may locally degrade the calibration precision. Upon comparison with the VIS detections, it is found that this issue (RMS $>$ 30 mas) impacts less than 5% of the surveyed area. This test also allows us to verify the astrometric consistency across the different NISP bands. A mitigation strategy involving a refined persistence flagging criterion based on persistence intensity and radius around detections has been developed and applied in subsequent processing, effectively restoring astrometric accuracy in the affected regions.

For future data releases, improvements include a refined persistence masking approach and exploration of alternative distortion evaluation methods that reduce the complexity of the distortion model while preserving the calibration quality. These enhancements aim to increase the calibration robustness and computational efficiency.

In conclusion, the Euclid NISP astrometric calibration in DR1 demonstrates high precision and stability, with well-characterised residuals and identified pathways for further improvement. The results provide a solid foundation for subsequent data releases, ensuring accurate celestial source positioning, which is essential for the mission’s scientific objectives.

Acknowledgements. The Euclid Consortium acknowledges the European Space Agency and a number of agencies and institutes that have supported the development of Euclid, in particular the Agenzia Spaziale Italiana, the Austrian Forschungsförderungsgesellschaft funded through BMIMI, the Belgian Science Policy, the Canadian Euclid Consortium, the Deutsches Zentrum für Luft- und Raumfahrt, the DTU Space and the Niels Bohr Institute in Denmark, the French Centre National d’Etudes Spatiales, the Fundação para a Ciência e a Tecnologia, the Hungarian Academy of Sciences, the Ministerio de Ciencia, Innovación y Universidades, the National Aeronautics and Space Administration, the National Astronomical Observatory of Japan, the Nederlandse Onderzoekschool voor Astronomie, the Norwegian Space Agency, the Research Council of Finland, the Romanian Space Agency, the Swiss Space Office (SSO) at the State Secretariat for Education, Research, and Innovation (SERI), and the United Kingdom Space Agency. A complete and detailed list is available on the Euclid web site (www.euclid-ec.org/consortium/community/). This work has made use of the Euclid Data Release 1 (DR1) from the European Space Agency (ESA) mission Euclid, available at https://www.cosmos.esa.int/web/euclid/data-release-dr1. This research makes use of ESA Databases (databases.esa.int), an initiative by ESA’s Data Science and Archives Division in the Science and Operations Department, Directorate of Science. This work has made use of data from the European Space Agency (ESA) mission Gaia (https://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing and Analysis Consortium (DPAC, https://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for the DPAC has been provided by national institutions, in particular the institutions participating in the Gaia Multilateral Agreement.

Authors and affiliations

Euclid Collaboration: M. Radovich{sup}⋆1, R. da Silva^{2, 3}, G. Polenta³, A. Alavi⁴, H. Aussel⁵, P. Awad⁶, A. Bonchi³, L. Bramante⁷, S. Conseil^{8, 9}, M. Correnti^{2, 3}, L. V. Costa⁷, I. Das⁴, F. Faustini², M. Frailis¹⁰, Y. Fu^{6, 11}, T. Gasparetto², W. Gillard¹², S. Hemmati⁴, J. Jacobson⁴, K. Jahnke¹³, B. Kubik⁹, C. Macabiau⁹, P. W. Morris¹⁴, K. Paterson¹³, M. Schirmer¹³, H. I. Teplitz¹⁵, A. Troja¹⁰, B. Altieri¹⁶, S. Andreon¹⁷, N. Auricchio¹⁸, C. Baccigalupi^{19, 10, 20, 21}, M. Baldi^{22, 18, 23}, A. Balestra¹, P. Battaglia¹⁸, A. N. Belikov^{11, 24}, A. Biviano^{10, 19}, M. Bolzonella¹⁸, E. Branchini^{25, 26, 17}, M. Brescia^{27, 28}, J. Brinchmann^{29, 30, 31}, S. Camera^{32, 33, 34}, G. Cañas-Herrera⁶, V. Capobianco³⁴, C. Carbone³⁵, J. Carretero^{36, 37}, M. Castellano², G. Castignani¹⁸, S. Cavuoti^{28, 38}, A. Cimatti³⁹, C. Colodro-Conde⁴⁰, G. Congedo⁴¹, C. J. Conselice⁴², L. Conversi^{43, 16}, Y. Copin⁹, A. Costille⁴⁴, H. M. Courtois⁴⁵, A. Da Silva^{46, 47}, H. Degaudenzi⁴⁸, G. De Lucia¹⁰, H. Dole^{49, 50}, F. Dubath⁴⁸, C. A. J. Duncan⁴¹, X. Dupac¹⁶, S. Dusini⁵¹, S. Escoffier¹², M. Farina⁵², S. Farrens⁵, S. Ferriol⁹, F. Finelli^{18, 53}, S. Fotopoulou⁵⁴, N. Fourmanoit¹², E. Franceschi¹⁸, M. Fumana³⁵, L. Gabarra⁵⁵, S. Galeotta¹⁰, K. George⁵⁶, B. Gillis⁴¹, C. Giocoli^{18, 23}, J. Gracia-Carpio⁵⁷, A. Grazian¹, F. Grupp^{57, 58}, L. Guzzo^{59, 17, 60}, W. G. Hartley⁴⁸, S. V. H. Haugan⁶¹, H. Hoekstra⁶, W. Holmes⁶², I. M. Hook⁶³, F. Hormuth⁶⁴, A. Hornstrup^{65, 66}, M. Jhabvala⁶⁷, S. Kermiche¹², A. Kiessling⁶², R. Kohley¹⁶, M. Kümmel⁵⁸, M. Kunz⁶⁸, H. Kurki-Suonio^{69, 70}, A. M. C. Le Brun⁷¹, D. Le Mignant⁴⁴, S. Ligori³⁴, P. B. Lilje⁶¹, V. Lindholm^{69, 70}, I. Lloro⁷², M. Magliocchetti⁵², G. Mainetti⁷³, O. Mansutti¹⁰, S. Marcin⁷⁴, O. Marggraf⁷⁵, M. Martinelli^{2, 76}, N. Martinet⁴⁴, F. Marulli^{77, 18, 23}, R. J. Massey⁷⁸, N. Mauri^{39, 23}, H. J. McCracken⁷⁹, C. J. R. McPartland^{66, 80}, E. Medinaceli¹⁸, S. Mei^{81, 82}, M. Melchior⁸³, M. Meneghetti^{18, 23}, E. Merlin¹, G. Meylan⁸⁴, P. Monaco^{85, 10, 20, 19}, A. Mora⁸⁶, M. Moresco^{77, 18}, C. Moretti^{10, 19, 20}, L. Moscardini^{77, 18, 23}, R. Nakajima⁷⁵, C. Neissner^{87, 37}, R. C. Nichol⁸⁸, S.-M. Niemi⁸⁹, C. Padilla⁸⁷, S. Paltani⁴⁸, F. Pasian¹⁰, W. J. Percival^{90, 91, 92}, V. Pettorino⁸⁹, A. Pezzotta¹⁷, M. Poncet⁹³, L. A. Popa⁹⁴, F. Raison⁵⁷, A. Refregier⁹⁵, A. Renzi^{96, 51, 18}, J. Rhodes⁶², G. Riccio²⁸, I. Risso^{25, 26, 17}, H.-W. Rix¹³, F. Rizzo¹⁰, E. Romelli¹⁰, C. Rosset⁸¹, B. Rusholme⁴, R. Saglia^{58, 57}, Z. Sakr^{97, 98, 99}, A. G. Sánchez⁵⁷, D. Sapone¹⁰⁰, B. Sartoris¹⁰¹, P. Schneider⁷⁵, A. Secroun¹², E. Sihvola^{69, 70}, C. Sirignano^{96, 51}, G. Sirri²³, L. Stanco⁵¹, P. Tallada-Crespí^{36, 37}, A. N. Taylor⁴¹, I. Tereno^{46, 47}, N. Tessore¹⁰², S. Toft^{104, 105}, R. Toledo-Moreo^{37, 36}, F. Torradeflot^{37, 36}, Y. Tsang¹⁰⁶, I. Tutsau^{107, 108, 98}, J. Valiviita^{69, 70}, T. Vassallo^{10, 56}, A. Veropalumbo^{17, 26, 25}, Y. Wang⁴, J. Weller^{58, 57}, A. Zacchei^{10, 19}, G. Zamorani¹⁸, F. M. Zerbi¹⁷, E. Zucca¹⁸, I. T. Andika⁵⁸, M. Ballardini^{109, 110, 18}, P. Bergamini¹⁸, S. Borgani^{85, 19, 10, 20, 111}, E. Bozzo⁴⁸, C. Burigana^{112, 53}, R. Cabanac⁹⁸, M. Calabrese^{113, 35}, A. Cappi^{101, 18}, F. Caro², T. Castro^{114, 10, 19}, D. Di Ferdinando²³, J. A. Escartin Vigo⁵⁷, G. Fabbian⁴⁹, J. García-Bellido⁹⁷, C. M. Gutierrez^{40, 115}, A. Hall⁴¹, Y. Kang¹¹⁶, L. Loureiro^{117, 118}, J. Macias-Perez¹¹⁹, R. Maoli^{120, 2}, R. B. Metcalf^{77, 18}, M. Pöntinen⁹, E. Sarpa¹⁰, V. Scottez^{121, 122}, M. Sereno¹²³, K. Tandid²³, M. Tenti²³, M. Tucci⁴⁸, M. Viel^{19, 10, 21, 20, 111}, M. Weissmann⁶¹, J. A. Acevedo Barroso⁹⁷, Y. Akrami^{108, 109}, S. Anselmi^{51, 96, 125}, M. Archidiacono^{59, 60}, G. Aricò²³, F. Atrio-Barandela¹²⁶, M. Aubert⁹, M. Baes¹²⁷, L. Bazzanini^{109, 18}, J. R. Bermejo-Climent^{128, 129}, D. Bertacca^{96, 1, 51}, M. Bethermin¹³⁰, F. Beutler⁴¹, A. Blanchard⁹⁸, F. Bouché^{131, 38}, M. L. Brown⁴², S. Bruton¹⁴, A. Calabro², B. Camacho Quevedo^{19, 21, 10}, P. Carrilho¹³², C. S. Carvalho¹³³, Y. Charles⁴⁴, F. Cogato¹⁸, T. E. Collett¹³⁴, A. R. Cooray¹³⁵, P. Corcho-Caballero¹¹, B. Csizi¹¹⁶, O. Cucc iati¹⁸, T. de Boer¹³⁶, G. Desprez¹¹, A. Díaz-Sánchez¹³⁷, S. Di Domizio^{25, 26}, J. M. Diego¹³⁸, V. Duret¹², A. Enia¹³⁹, Y. Fang⁵⁸, A. Farina^{17, 26}, A. M. N. Ferguson⁴¹, A. Figuenov⁶⁹, A. Franco¹⁰, A. Fumagalli¹⁰, K. Ganga⁸¹, Y. Gavazzi^{44, 79}, E. Geach^{107, 108, 134}, Z. Ghaffari^{10, 19}, F. Giannotti²³, G. Gozaliasl^{43, 69}, A. Gruppuso^{18, 23}, M. Guidi^{22, 18}, C. Hernández-Monteagudo^{115, 40}, T. Heuberger⁷⁴, H. Hildebrandt¹⁴⁴, J. Hjorth¹⁴⁵, M. Jauzac^{146, 78, 147, 148, 98}, J. J. E. Kajava^{149, 150, 151}, V. Kansal^{152, 153}, J. Kim⁵⁵, C. C. Kirkpatrick¹⁵⁴, A. Kovács^{129, 128}, I. Kovačić¹²⁷, K. Koyama¹³⁴, S. Kruk¹⁶, M. C. Lam⁴¹, M. Lattanzi¹¹⁰, S. Lee^{155, 62}, L. Legrand^{156, 49}, M. D. Lepinzan¹⁰, G. Leroy^{146, 78}, J. Lesgourgues¹⁵⁷, T. I. Liaudat¹⁵⁸, L. Linke¹¹⁶, S. J. Liu⁵², G. Maggio¹⁰, F. Mannucci¹⁵⁹, F. R. Marleau¹¹⁶, C. J. A. P. Martins^{160, 29}, M. Miluzio^{16, 161}, G. Morgante¹⁸, S. Nadathur¹⁹, K. Naidoo^{134, 13}, P. Natoli^{159, 11}, A. Navarro-Alsina⁷⁵, S. Nessis⁹, F. Oppizzi^{26, 51}, F. Pace^{32, 33, 34}, D. Paoloetti^{18, 53}, F. Passalacqua⁵¹, L. Patrizii²³, C. Pattison¹³⁴, A. Pisani¹², L. Pizzuti¹⁶², D. Potter¹⁶³, M. Poulain¹⁶⁴, G. W. Pratt⁵, S. Quaii^{77, 18}, G. Rodighiero^{96, 1}, W. Roster⁵⁷, M. Sahlén¹⁶⁵, D. B. Sanders¹³⁶, A. Schneider¹⁶³, M. Schultheis¹⁰¹, D. Sciotti^{2, 76}, E. Sellentin^{166, 6}, S. Serjeant¹⁶⁷, L. C. Smith¹⁶⁸, J. G. Sorce^{169, 49}, I. Szapudi¹³⁶, M. Talia^{77, 18}, F. Tarsitano^{170, 95}, G. Testera²⁶, R. Teyssier¹⁷¹, S. Tosi^{25, 17, 26}, C. Uhlemann^{172, 173}, C. Valieri²³, A. Venhola¹⁶⁴, D. Vergani¹⁸, P. Vielzeuf¹², E. Velijanius¹⁶⁸, S. Vinciguerra⁴⁴, M. von Wietersheim-Kramsta^{78, 146}, N. A. Walton¹⁶⁸, A. H. Wright¹⁴⁴, and D. Scott¹⁷⁴

3 Space Science Data Center, Italian Space Agency, via del Politecnico snc, 00133 Roma, Italy

4 Caltech/IPAC, 1200 E. California Blvd., Pasadena, CA 91125, USA

5 Université Paris-Saclay, Université Paris Cité, CEA, CNRS, AIM, 91191, Gif-sur-Yvette, France

6 Leiden Observatory, Leiden University, Einsteinweg 55, 2333 CC Leiden, The Netherlands

7 Aerospace Logistics Technology Engineering Company, Corso Marche 79, 10146 Torino, Italy

8 Centre de Recherche Astrophysique de Lyon, UMR5574, CNRS, Université Claude Bernard Lyon 1, ENS de Lyon, 69230, Saint-Genis-Laval, France

9 Université Lyon 1, CNRS/IN2P3, IP2I Lyon, Villeurbanne, France

10 INAF-Osservatorio Astronomico di Trieste, Via G. B. Tiepolo 11, 34143 Trieste, Italy

11 Kapteyn Astronomical Institute, University of Groningen, PO Box 800, 9700 AV Groningen, The Netherlands

12 Aix-Marseille Université, CNRS/IN2P3, CPPM, Marseille, France

13 Max-Planck-Institut für Astronomie, Königstuhl 17, 69117 Heidelberg, Germany

14 California Institute of Technology, 1200 E California Blvd, Pasadena, CA 91125, USA

15 Infrared Processing and Analysis Center, California Institute of Technology, Pasadena, CA 91125, USA

16 ESAC/ESA, Camino Bajo del Castillo, s/n., Urb. Villafranca del Castillo, 28692 Villanueva de la Cañada, Madrid, Spain

17 INAF-Osservatorio Astronomico di Brera, Via Brera 28, 20122 Milano, Italy

18 INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Piero Gobetti 93/3, 40129 Bologna, Italy

19 IFPU, Institute for Fundamental Physics of the Universe, via Beirut 2, 34151 Trieste, Italy

20 INFN, Sezione di Trieste, Via Valerio 2, 34127 Trieste TS, Italy

21 SISSA, International School for Advanced Studies, Via Bonomea 265, 34136 Trieste TS, Italy

22 Dipartimento di Fisica e Astronomia, Università di Bologna, Via Gobetti 93/2, 40129 Bologna, Italy

23 INFN-Sezione di Bologna, Viale Berti Pichat 6/2, 40127 Bologna, Italy

24 ATG Europe BV, Huygensstraat 34, 2201 DK Noordwijk, The Netherlands

25 Dipartimento di Fisica, Università di Genova, Via Dodecaneso 33, 16146, Genova, Italy

26 INFN-Sezione di Genova, Via Dodecaneso 33, 16146, Genova, Italy

27 Department of Physics "E. Pancini", University Federico II, Via Cinthia 6, 80126, Napoli, Italy

28 INAF-Osservatorio Astronomico di Capodimonte, Via Moiariello 16, 80131 Napoli, Italy

29 Instituto de Astrofísica e Ciências do Espaço, Universidade do Porto, CAUP, Rua das Estrelas, PT4150-762 Porto, Portugal

30 Faculdade de Ciências da Universidade do Porto, Rua do Campo de Alegre, 4150-007 Porto, Portugal

31 European Southern Observatory, Karl-Schwarzschild-Str. 2, 85748 Garching, Germany

32 Dipartimento di Fisica, Università degli Studi di Torino, Via P. Giuria 1, 10125 Torino, Italy

33 INFN-Sezione di Torino, Via P. Giuria 1, 10125 Torino, Italy

34 INAF-Osservatorio Astrofisico di Torino, Via Osservatorio 20, 10025 Pino Torinese (TO), Italy

35 INAF-IASF Milano, Via Alfonso Corti 12, 20133 Milano, Italy

36 Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas (CIEMAT), Avenida Complutense 40, 28040 Madrid, Spain

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38 INFN – Sezione di Napoli, Via Chiatia 6, 80126, Napoli, Italy

39 Dipartimento di Fisica e Astronomia "Augusto Righi" - Alma Mater Studiorum Università di Bologna, Viale Berti Pichat 6/2, 40127 Bologna, Italy

40 Instituto de Astrofísica de Canarias, E-38205 La Laguna, Tenerife, Spain

41 Institute for Astronomy, University of Edinburgh, Royal Observatory, Blackford Hill, Edinburgh EH9 3HJ, UK

42 Jodrell Bank Centre for Astrophysics, Department of Physics and Astronomy, University of Manchester, Oxford Road, Manchester M13 9PL, UK

43 European Space Agency/ESRIN, Largo Galileo Galilei 1, 00044 Frascati, Roma, Italy

44 Aix-Marseille Université, CNRS, CNES, LAM, Marseille, France

45 Université Lyon 1, CNRS/IN2P3, IUF, IP2I Lyon, Villeurbanne, France

46 Departamento de Física, Faculdade de Ciências, Universidade de Lisboa, Edifício C8, Campo Grande, PT1749-016 Lisboa, Portugal

47 Instituto de Astrofísica e Ciências do Espaço, Faculdade de Ciências, Universidade de Lisboa, Campo Grande, 1749-016 Lisboa, Portugal

48 Department of Astronomy, University of Geneva, ch. d’Ecogia 16, 1290 Versoix, Switzerland

49 Université Paris-Saclay, CNRS, Institut d’astrophysique spatiale, 91405, Orsay, France

50 Institut universitaire de France (IUF), 1 rue Descartes, 75231 PARIS CEDEX 05, France

51 INFN-Padova, Via Marzolo 8, 35131 Padova, Italy

52 INAF-Istituto di Astrofisica e Planetologia Spaziali, via del Fosso del Cavaliere, 100, 00100 Roma, Italy

53 INFN-Bologna, Via Irnerio 46, 40126 Bologna, Italy

54 School of Physics, HH Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol, BS8 1TL, UK

55 Department of Physics, University of Oxford, Keble Road, Oxford OX1 3RH, UK

56 University Observatory, LMU Faculty of Physics, Scheinerstr. 1, 81679 Munich, Germany

57 Max Planck Institute for Extraterrestrial Physics, Giessenbachstr. 1, 85748 Garching, Germany

58 Universitäts-Sternwarte München, Fakultät für Physik, Ludwig-Maximilians-Universität München, Scheinerstr. 1, 81679 München, Germany

59 Dipartimento di Fisica "Aldo Pontremoli", Università degli Studi di Milano, Via Celoria 16, 20133 Milano, Italy

60 INFN-Sezione di Milano, Via Celoria 16, 20133 Milano, Italy

61 Institute of Theoretical Astrophysics, University of Oslo, P.O. Box 1029 Blindern, 0315 Oslo, Norway

62 Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA, 91109, USA

63 School of Physics and Astronomy, Lancaster University, Lancaster, LA1 4YB, UK

64 Felix Hormuth Engineering, Goethestr. 17, 69181 Leimen, Germany

65 Technical University of Denmark, Elektrovej 327, 2800 Kgs. Lyngby, Denmark

66 Cosmic Dawn Center (DAWN), Denmark

67 NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA

68 Université de Genève, Département de Physique Théorique and Centre for Astroparticle Physics, 24 quai Ernest-Ansermet, CH-1211 Genève 4, Switzerland

69 Department of Physics, P.O. Box 64, University of Helsinki, 00014 Helsinki, Finland

70 Helsinki Institute of Physics, Gustaf Hällströmin katu 2, University of Helsinki, 00014 Helsinki, Finland

71 Laboratoire d’etude de l’Univers et des phenomenes eXtremes, Observatoire de Paris, Université PSL, Sorbonne Université, CNRS, 92190 Meudon, France

72 SKAO, Jodrell Bank, Lower Withington, Macclesfield SK11 9FT, UK

73 Centre de Calcul de l’IN2P3/CNRS, 21 avenue Pierre de Coubertin 69627 Villeurbanne Cedex, France

74 University of Applied Sciences and Arts of Northwestern Switzerland, School of Computer Science, 5210 Windisch, Switzerland

75 Universität Bonn, Argelander-Institut für Astronomie, Auf dem Hügel 71, 53121 Bonn, Germany

76 INFN-Sezione di Roma, Piazzale Aldo Moro, 2 - c/o Dipartimento di Fisica, Edificio G. Marconi, 00185 Roma, Italy

77 Dipartimento di Fisica e Astronomia "Augusto Righi" - Alma Mater Studiorum Università di Bologna, via Piero Gobetti 93/2, 40129 Bologna, Italy

78 Department of Physics, Institute for Computational Cosmology, Durham University, South Road, Durham, DH1 3LE, UK

79 Institut d’Astrophysique de Paris, UMR 7095, CNRS, and Sorbonne Université, 98 bis boulevard Arago, 75014 Paris, France

80 Niels Bohr Institute, University of Copenhagen, Jagtvej 128, 2200 Copenhagen, Denmark

81 Université Paris Cité, CNRS, Astroparticule et Cosmologie, 75013 Paris, France

82 CNRS-UCB International Research Laboratory, Centre Pierre Binétruy, IRL2007, CPB-IN2P3, Berkeley, USA

83 University of Applied Sciences and Arts of Northwestern Switzerland, School of Engineering, 5210 Windisch, Switzerland

84 Institute of Physics, Laboratory of Astrophysics, Ecole Polytechnique Fédérale de Lausanne (EPFL), Observatoire de Sauverny, 1290 Versoix, Switzerland

85 Dipartimento di Fisica - Sezione di Astronomia, Università di Trieste, Via Tiepolo 11, 34131 Trieste, Italy

86 Telespazio UK S.L. for European Space Agency (ESA), Camino bajo del Castillo, s/n, Urbanizacion Villafranca del Castillo, Villanueva de la Cañada, 28692 Madrid, Spain

87 Institut de Física d’Altes Energies (IFAE), The Barcelona Institute of Science and Technology, Campus UAB, 08193 Bellaterra (Barcelona), Spain

88 School of Mathematics and Physics, University of Surrey, Guildford, Surrey, GU2 7XH, UK

89 European Space Agency/ESTEC, Keplerlaan 1, 2201 AZ Noordwijk, The Netherlands

90 Waterloo Centre for Astrophysics, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada

91 Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada

92 Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada

93 Centre National d’Etudes Spatiales – Centre spatial de Toulouse, 18 avenue Edouard Belin, 31401 Toulouse Cedex 9, France

94 Institute of Space Science, Str. Atomistilor, nr. 409 Măgurele, Ilfov, 077125, Romania

95 Institute for Particle Physics and Astrophysics, Dept. of Physics, ETH Zurich, Wolfgang-Pauli-Strasse 27, 8093 Zurich, Switzerland

96 Dipartimento di Fisica e Astronomia "G. Galilei", Università degli di Padova, Via Marzolo 8, 35131 Padova, Italy

97 Instituto de Física Teórica UAM-CSIC, Campus de Cantoblanco, 28049 Madrid, Spain

98 Institut de Recherche en Astrophysique et Planétologie (IRAP), Université de Toulouse, CNRS, UPS, CNES, 14 Av. Edouard Belin, 31400 Toulouse, France

99 Université St Joseph; Faculty of Sciences, Beirut, Lebanon

100 Departamento de Física, FCFM, Universidad de Chile, Blanco Encalada 2008, Santiago, Chile

101 Université Côte d’Azur, Observatoire de la Côte d’Azur, CNRS, Laboratoire Lagrange, Bd de l’Observatoire, CS 34229, 06304 Nice cedex 4, France

102 Mullard Space Science Laboratory, University College London, Holmbury St Mary, Dorking, Surrey RH5 6NT, UK

103 Cosmic Dawn Center (DAWN)

104 Universidad Politécnica de Cartagena, Departamento de Electrónica y Tecnología de Computadoras, Plaza del Hospital 1, 30202 Cartagena, Spain

105 European University of Technology EUt+, European Union

106 Centre for Information Technology, University of Groningen, P.O. Box 11044, 9700 CA Groningen, The Netherlands

107 Institute of Space Sciences (ICE, CSIC), Campus UAB, Carrer de Can Magrans, s/n, 08193 Barcelona, Spain

108 Institut d’Estudis Espacials de Catalunya (IEEC), Edifici RDIT, Campus UPC, 08860 Castelldefels, Barcelona, Spain

109 Dipartimento di Fisica e Scienze della Terra, Università degli Studi di Ferrara, Via Giuseppe Saragat 1, 44122 Ferrara, Italy

110 Istituto Nazionale di Fisica Nucleare, Sezione di Ferrara, Via Giuseppe Saragat 1, 44122 Ferrara, Italy

111 ICSC - Centro Nazionale di Ricerca in High Performance Computing, Big Data e Quantum Computing, Via Magnanelli 2, Bologna, Italy

112 INAF, Istituto di Radioastronomia, Via Piero Gobetti 101, 40129 Bologna, Italy

113 Astronomical Observatory of the Autonomous Region of Aosta Valley (OAVdA), Loc. Lignan 39, I-11020, Nus (Aosta Valley), Italy

114 Department of Mathematical Physics, Institute of Physics, University of São Paulo, R. do Matão 1371, 05508-090, São Paulo, SP, Brazil

115 Universidad de La Laguna, Dpto. Astrofísica, E-38206 La Laguna, Tenerife, Spain

116 Universität Innsbruck, Institut für Astro- und Teilchenphysik, Technikerstr. 25/8, 6020 Innsbruck, Austria

117 Oskar Klein Centre for Cosmoparticle Physics, Department of Physics, Stockholm University, Stockholm, SE-106 91, Sweden

118 Astrophysics Group, Blackett Laboratory, Imperial College London, London SW7 2AZ, UK

119 Univ. Grenoble Alpes, CNRS, Grenoble INP, LPSC-IN2P3, 53, Avenue des Martyrs, 38000 Grenoble, France

120 Dipartimento di Fisica, Sapienza Università di Roma, Piazzale Aldo Moro 2, 00185 Roma, Italy

121 Institut d’Astrophysique de Paris, 98bis Boulevard Arago, 75014, Paris, France

122 ICL, Junia, Université Catholique de Lille, LITL, 59000 Lille, France

123 Center for Astrophysics and Cosmology, University of Nova Gorica, Nova Gorica, Slovenia

124 CERCA/ISO, Department of Physics, Case Western Reserve University, 10900 Euclid Avenue, Cleveland, OH 44106, USA

125 Laboratoire Univers et Théorie, Observatoire de Paris, Université PSL, Université Paris Cité, CNRS, 92190 Meudon, France

126 Departamento de Física Fundamental. Universidad de Salamanca. Plaza de la Merced s/n. 37008 Salamanca, Spain

127 Universiteit Gent, Department of Physics and Astronomy, Proeftuinsraat 86 N3, 9000 Ghent, Belgium

128 Konkoly Observatory, HUN-REN CSFK, MTA Centre of Excellence, Budapest, Konkoly Thege Miklós út 15-17. H-1121, Hungary

129 MTA-CSFK Lendület Large-Scale Structure Research Group, Konkoly-Thege Miklós út 15-17, H-1121 Budapest, Hungary

130 Université de Strasbourg, CNRS, Observatoire astronomique de Strasbourg, UMR 7550, 67000 Strasbourg, France

131 Scuola Superiore Meridionale, Via Mezzocannone 4, 80138, Napoli, Italy

132 Department of Physics, Astronomy and Mathematics, University of Hertfordshire, College Lane, Hatfield AL10 9AB, UK

133 Instituto de Astrofísica e Ciências do Espaço, Faculdade de Ciências, Universidade de Lisboa, Tapada da Ajuda, 1349-018 Lisboa, Portugal

134 Institute of Cosmology and Gravitation, University of Portsmouth, Portsmouth PO1 3FX, UK

135 Department of Physics & Astronomy, University of California Irvine, Irvine CA 92697, USA

136 Institute for Astronomy, University of Hawaii, 2680 Woodlawn Drive, Honolulu, HI 96822, USA

137 Departamento Física Aplicada, Universidad Politécnica de Cartagena, Campus Muralla del Mar, 30202 Cartagena, Murcia, Spain

138 Instituto de Física de Cantabria, Edificio Juan Jordá, Avenida de los Castros, 39005 Santander, Spain

139 CEA Saclay, DFR/IRFU, Service d’Astrophysique, Bat. 709, 91191 Gif-sur-Yvette, France

140 Department of Mathematics and Physics E. De Giorgi, University of Salento, Via per Arnesano, CP-193, 73100, Lecce, Italy

141 INFN, Sezione di Lecce, Via per Arnesano, CP-193, 73100, Lecce, Italy

142 INAF-Sezione di Lecce, c/o Dipartimento Matematica e Fisica, Via per Arnesano, 73100, Lecce, Italy

143 Department of Computer Science, Aalto University, PO Box 15400, Espoo, FI-00 076, Finland

144 Ruhr University Bochum, Faculty of Physics and Astronomy, Astronomical Institute (AIRUB), German Centre for Cosmological Lensing (GCCL), 44780 Bochum, Germany

145 DARK, Niels Bohr Institute, University of Copenhagen, Jagtvej 155, 2200 Copenhagen, Denmark

146 Department of Physics, Centre for Extragalactic Astronomy, Durham University, South Road, Durham, DH1 3LE, UK

147 Astrophysics Research Centre, University of KwaZulu-Natal, Westville Campus, Durban 4041, South Africa

148 School of Mathematics, Statistics & Computer Science, University of KwaZulu-Natal, Westville Campus, Durban 4041, South Africa

149 Department of Physics and Astronomy, Vesilinnantie 5, University of Turku, 20014 Turku, Finland

150 Finnish Centre for Astronomy with ESO (FINCA), Quantum, Vesilinnantie 5, University of Turku, 20014 Turku, Finland

151 Serco for European Space Agency (ESA), Camino bajo del Castillo, s/n, Urbanizacion Villafranca del Castillo, Villanueva de la Cañada, 28692 Madrid, Spain

152 ARC Centre of Excellence for Dark Matter Particle Physics, Melbourne, Australia

153 Centre for Astrophysics & Supercomputing, Swinburne University of Technology, Hawthorn, Victoria 3122, Australia

154 Department of Physics and Helsinki Institute of Physics, Gustaf Hällström katu 2, University of Helsinki, 00014 Helsinki, Finland

155 Ohio University, Physics & Astronomy Department,1 Ohio University, Athens, OH 45701, USA

156 Brazilian Center for Research in Physics (CBPF), Dr. Xavier Sigaud st. 150, zip 22290-180, Rio de Janeiro, RJ, Brazil

157 Institute for Theoretical Particle Physics and Cosmology (TTK), RWTH Aachen University, 52056 Aachen, Germany

158 IRFU, CEA, Université Paris-Saclay 91191 Gif-sur-Yvette Cedex, France

159 INAF-Osservatorio Astrofisico di Arcetri, Largo E. Fermi 5, 50125, Firenze, Italy

160 Centro de Astrofísica da Universidade do Porto, Rua das Estrelas, 4150-762 Porto, Portugal

161 HE Space for European Space Agency (ESA), Camino bajo del Castillo, s/n, Urbanizacion Villafranca del Castillo, Villanueva de la Cañada, 28692 Madrid, Spain

162 Dipartimento di Fisica “G. Occhialini”, Università degli Studi di Milano Bicocca, Piazza della Scienza 3, 20126 Milano, Italy

163 Department of Astrophysics, University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland

164 Space physics and astronomy research unit, University of Oulu, Pentti Kaiteran katu 1, FI-90014 Oulu, Finland

165 Theoretical astrophysics, Department of Physics and Astronomy, Uppsala University, Box 524, 751 20 Uppsala, Sweden

166 Mathematical Institute, University of Leiden, Einsteinweg 55, 2333 CA Leiden, The Netherlands

167 School of Physical Sciences, The Open University, Milton Keynes, MK7 6AA, UK

168 Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge CB3 0HA, UK

169 Univ. Lille, CNRS, Centrale Lille, UMR 9189 CRIStAL, 59000 Lille, France

170 Kobayashi-Maskawa Institute for the Origin of Particles and the Universe, Nagoya University, Chikusa-ku, Nagoya, 464-8602, Japan

171 Department of Astrophysical Sciences, Peyton Hall, Princeton University, Princeton, NJ 08544, USA

172 Fakultät für Physik, Universität Bielefeld, Postfach 100131, 33501 Bielefeld, Germany

173 School of Mathematics, Statistics and Physics, Newcastle University, Herschel Building, Newcastle-upon-Tyne, NE1 7RU, UK

174 Department of Physics and Astronomy, University of British Columbia, Vancouver, BC V6T 1Z1, Canada