2.1.1 Overscan and bias corrections

2dFdr applies bias subtraction and corrects for pixel-to-pixel sensitivity. The bias level is computed by fitting the overscan region of CCD1 with a combined exponential and polynomial function, and those of CCD2, CCD3, and CCD4 with a polynomial function, which is then subtracted from the image. The image is then trimmed to remove the overscan region. We have verified that applying additional bias correction frames alongside the overscan correction results in negligible differences, and therefore, no further bias correction is applied.

2.1.2 Read noise and gain

For Spector CCDs (CCD3 and CCD4), we assessed the consistency of the nominal read noise and gain across the fast, medium, and slow readout modes of the new Spector spectrograph by comparing them to manufacturer specifications. All three readout modes produced results consistent with the specifications. We selected the medium readout mode for the Hector survey to achieve an optimal balance between readout time and noise performance. For CCD3 medium read-out mode, the measured read noise and gain are 2.96 e $^-$ and 1.42 e $^-$ /ADU, respectively, compared to the manufacturer specifications of 3.17 e $^-$ and 1.49 e $^-$ /ADU. For CCD4, the measured read noise and gain are 3.84 e $^-$ and 1.18 e $^-$ /ADU, respectively, compared to the manufacturer specifications of 3.93 e $^-$ and 1.12 e $^-$ /ADU. Given the small discrepancies between the measured and manufacturer-specified values, we adopt the manufacturer specifications for calculating the variance arrays.

Observations with the AAOmega CCDs were conducted in normal read-out mode, using the same setup as that employed for the SAMI survey (Croom et al. Reference Croom2021).

2.1.3 Bad pixel mask and cosmic ray rejection

Bad pixel masks are built by identifying pixels with non-linear flux or any residual bias structure. We take the ratio of defocussed flat fields taken on different nights with different exposure times to test for linearity. Pixels consistently deviating more than 3 $\sigma$ from the normalised flat median flux across different exposure times and dates are flagged as bad to avoid occasional cosmic rays or saturated pixels. Three columns (x = 2 046, 2 047 and 2 048) close to the edge of CCD2 show $\sim$ 95% of pixels as bad, so we have masked these entire columns. Due to the camera reading setup, CCD4 previously had an extra line of overscan at x = 2 049, which appeared as an extra bias column in the middle of the detector, shifting all the data by one pixel towards the end of the detector from that column onwards. As of May 2024, the camera reading setup has been corrected, resolving this issue. For data taken before this correction, we do not flag this column as bad, but we apply a correction to relocate it to the end of the detector. The total number of bad pixels for CCDs 1 through 4 are 2 398 (0.028%), 14 339 (0.169%), 4 095 (0.024%), and 8 208 (0.048%), respectively. Even accounting for gradients in our flat-field normalisation via using per-column medians instead of a single median value, the bad pixels exhibit persistent non-linearity and significant deviations ( $\gt\! 3\sigma$ ) across multiple exposure times and dates.

With 30-min exposure times for individual object frames, many are significantly affected by cosmic rays. Cosmic ray detection is performed using the Laplacian edge detection algorithm (L.A.Cosmic; van Dokkum Reference van Dokkum2001). Saturated pixels are also flagged for each frame. All pixels flagged for non-linearity, saturation, or cosmic ray effects are excluded from further processing and assigned NaN values. Remaining bad pixels, including broadened cosmic rays, are further removed just before cube reconstruction, as described in Section 2.5.

2.1.4 Extraction of spectra and removal of scattered light

Central to the data reduction of fibre-fed spectroscopy is extracting individual spectra from the 2D CCD image. This part of the data reduction is done using 2dFdr and closely follows the approach used for the SAMI Galaxy Survey (Croom et al. Reference Croom2021). Here, we briefly outline the key steps and note some minor changes compared to the SAMI pipeline.

First, the locations of the fibre paths across the CCD (commonly called tramline maps) are approximately traced by identifying each fibre in a flat field frame. Next, a higher-precision estimate of the tramline maps is made, by fitting Gaussian profiles to the fibre flat field. The centre of the Gaussian defines the tramline map, while the width is an estimate of the width of the fibre profile, used as part of the extraction process. Scattered light is estimated by averaging the counts in the gaps between slitlets (see Figure 5 of Croom et al. Reference Croom2021), then fitting smooth cubic splines along the gaps. Next, a second cubic spline is fit across the slitlet gaps to build a 2D model of the scattered light across the full detector. The spline uses 8 knots that are approximately equally spaced, depending on the gaps between slitlets. There are more gaps between slitlets for Spector (20) compared to AAOmega (12); see Bryant et al. (in preparation) for details. For the AAOmega blue arm only, we also model extra scattered light around the bright 5 577 Å line. This is not required for Spector, as the scattered light performance of the Spector optics is considerably better than that of AAOmega. The overall level of scattered light can be estimated by taking the ratio of the average flux across the image in the scattered-light model and the average extracted flux in the fibres. For a flat field image this ratio $f_\textrm{sl}/f_\textrm{ex}\simeq0.072$ , 0.068, 0.040, and 0.024 for CCDs 1 through 4, respectively. Once the scattered light is fit and subtracted, the flux in the fibres is calculated by fitting the previously defined Gaussian profiles of the fibres, allowing only the amplitude to change. This fit is done per CCD column, fitting for the amplitude of all fibres at the same time.

2.1.5 Wavelength calibration

The new Spector spectrograph has higher spectral resolution than previous large-scale IFS surveys (AAOmega is used in the same format and resolution as in the SAMI Galaxy Survey). The higher resolution is most significant in the blue part of the spectrum, which is particularly valuable for stellar kinematics and stellar population analysis. The blue arm of Spector has a resolution of $R\simeq3\,400$ at 4 800 Å, (see Table 1) compared to $R\simeq1\,800$ for SAMI (Scott et al. Reference Scott2018), $R\simeq1\,650$ for CALIFA (Sánchez et al. Reference Sánchez2012) and $R\simeq2\,000$ for MaNGA (Law et al. Reference Law2021). The higher resolution enables unique science, such as stellar kinematics of dwarf galaxies or detailed kinematic decomposition of emission lines in wind galaxies. To make the most of this advantage, it is particularly valuable to have a robust and high-quality wavelength calibration.

The usual approach to wavelength calibration is to fit a polynomial to the relationship between pixel coordinates and wavelength for arc frames taken using hollow cathode lamps. This is typically done independently per fibre. The per-fibre approach has some drawbacks. First, some part of the arc lamp spectrum may have only weak lines, making the calibration less secure at those wavelengths. Second, small differences between solutions of adjacent fibres can lead to unphysical differences in calibration between fibres that contribute to the same spaxels in the final data cubes. Third, as line identification is automated in massively multiplexed surveys, occasional failures to identify the correct lines can lead to poor solutions for individual fibres, particularly near the ends of a spectrum.

All the above problems can be addressed by using an approach that finds the wavelength solution across the entire detector at once. Childress et al. (Reference Childress, Vogt, Nielsen and Sharp2014) use this approach for wavelength calibration of the Wide Field Spectrograph on the Siding Spring 2.3 m Telescope. Inspired by this approach, we implement a similar method for reduction of Hector data. The Childress et al. (Reference Childress, Vogt, Nielsen and Sharp2014) approach fits a physically motivated optical model to the arc solutions. The one drawback of this is that it is typically slow to fit (being a non-linear model). Instead, we use a model that is linear, allowing fast and reliable solutions to be derived (typically $\sim 1$ min to generate the solution for an entire arc frame on a standard laptop) but retaining some of the general physical characteristics expected of the system.

The estimated wavelength for a given x,y coordinate on the detector and fibre f is given by

(1) \begin{equation}\lambda(x,y,f) = \sum_{i=0}^{N_x} \sum_{j=0}^{N_y} a_{ij} T_i(x) T_j(y) + b_f,\end{equation}

where $a_{i,j}$ are the polynomial coefficients that parameterise the effect of the grating and optical distortion across the detector. The $b_f$ parameter is a single constant per fibre that captures features such as small misalignments between fibres as part of the construction of the spectrograph slit. The $T_i(x)$ and $T_j(y)$ are orthogonal Chebyshev polynomials of order i and j that we use as the basis functions of the polynomial part of the model. The polynomial order required depends on the spectrographs, with CCD1 and CCD2 needing $N_x=N_y = 4$ , while CCD3 and CCD4 have a higher-order optical distortion and need $N_x=N_y = 6$ .

This 2D arc fitting approach is implemented in Python as a post-processing of the arc frames after 2dFdr, using ridge regression within the scikit-learn package Pedregosa et al. (Reference Pedregosa2011). It makes use of 2dFdr’s identification of arc lines, together with the tramline maps generated during the fibre extraction process.

In Figure 1, we show example results from the 2D wavelength calibration for CCD3 (other spectrograph arms are qualitatively similar). Figure 1(a) shows a histogram of the residuals from the 2D fit that in this case has a dispersion of 0.079 Å, which is relatively large ( $\simeq0.14$ pixels), reflecting the low S/N ratio of some blue arc lines. The distribution of residuals across the detector is seen in Figure 1(b); while there is scatter and individual lines may have small shifts, globally the residuals are flat and close to zero. Based on Figure 1(b), a small number of lines are removed from the fit because they are consistently offset from the global solution. In Figure 1(c) and (d), we show the residuals projected onto the x and y axes of the detector. The coloured crosses show the mean residual from the 2D model in 10 $\times$ 10 bins across the detector. The mean residuals are consistently below $\simeq0.05$ pix and usually better than this.

Figure 1. The result of 2D wavelength calibration for an example arc frame from CCD3 (frame 19, 28 October 2024). (a) Histogram of residuals from the model fit, defined as (measured arc line wavelength) – (model wavelength). The dotted lines mark $\pm0.1$ pixels on the detector. (b) Residuals across the detector. (c) Residuals as a function of detector x pixel (i.e. the vertical collapse of panel (b)). Small red points are individual line measurements, various coloured connected points are locally averaged residuals in a 10 $\times$ 10 grid across the detector. (d) Small red points are residuals as a function of y detector pixel (i.e. the horizontal collapse of panel (b)). Coloured points are average residuals, as for (c).

One further step is applied in the wavelength calibration to allow for slow drifts in the slit position relative to the camera through the night (see Sharp et al. Reference Sharp2015). The maximum absolute shift is typically $\simeq$ 0.04 Å per hour in AAOmega (largely caused by flexure changes as liquid nitrogen boils off in the camera dewars). For Spector the change is significantly smaller ( $\simeq0.006$ Å per hour), as the cameras are more compact and thermally controlled, and is related to low-level residual thermal changes.

In each object frame the sky lines are used to derive a relative shift compared to the nominal arc frame calibration. A robust linear fit is used, so that the adjustment varies smoothly as a function of CCD x and y pixel, using the same approach as discussed by Croom et al. (Reference Croom2021). However, the fibre-to-fibre adjustment to the wavelength calibration based on twilights that was used for SAMI is not required for Hector.

As an independent check of the wavelength calibration we fit a high-resolution solar template to twilight frames, dividing each fibre into between 10 and 30 smaller chunks as a function of wavelength. We do this using the penalised pixel-fitting (pPXF; Cappellari & Emsellem Reference Cappellari and Emsellem2004; Cappellari Reference Cappellari2017) code in a process that is also used to test the line-spread-function (see Tuntipong et al. in preparation). We then measure the scatter in velocities measured across all the chunks for a frame. Histograms of the residual velocity for each CCD with 1D and 2D arc fitting can be seen in Figure 2. Here, we show the residuals in km s $^{-1}$ rather than Å as this is the direct output of the pPXF fits and is more relevant for science analysis (e.g. kinematic fitting of galaxy spectra). We note that at 4 800 Å, 1 km s $^{-1}$ is equivalent to 0.016 Å (or 0.015 pix for CCD1 and 0.029 pix for CCD3). At 6 800 Å, 1 km s $^{-1}$ is equivalent to 0.023 Å (or 0.040 pix for CCD2 and 0.044 pix for CCD4). The standard deviations of the distributions for the 1D and 2D fitting approaches are shown in the legends in Figure 2. We consistently see improvements moving to the 2D method. To further quantify the level of improvement, we subtract the median statistical uncertainty from pPXF (related to the S/N and number of spectral features in the twilight spectra) from the standard deviations in Figure 2, to provide an estimate of scatter due to only wavelength calibration. For CCD1, the root-mean-square (RMS) scatter in velocity changes from 4.3 to 2.5 km s $^{-1}$ (an improvement of a factor of 1.7). For CCD2, the improvement was more modest, from 1.6 to 1.3 km s $^{-1}$ (a factor of 1.2). For CCD3, the improvement is from 2.2 to 1.2 km s $^{-1}$ (a factor of 1.9). For CCD4, the improvement is large, from 5.7 to 2.0 km s $^{-1}$ (a ratio of 2.9). The large improvement in CCD4 is in part due to the high-order optical distortion in that camera, which is hard to robustly fit on an individual fibre basis. It is worth noting that the scatter in the velocity residuals in CCD2 and CCD4 are likely somewhat overestimated, as telluric absorption impacts the twilight spectrum. Wavelength ranges with obvious telluric absorption have been removed, but some weak effects may remain. Together with the above improvements, the 2D fitting completely removes catastrophic failures.

Figure 2. Comparison of twilight sky velocity residuals from 1D (blue) and 2D (red) arc fitting. We show CCDs 1 through 4 in panels (a), (b), (c), and (d), respectively. The broader distribution for 1D fitting in CCD4 is in part due to the difficulty of fitting the high-order distortion on single fibres (see text for details). The standard deviations shown in the legends are before correcting for statistical velocity measurement uncertainty. Vertical dotted lines indicate the velocity corresponding to 0.1 pixels at 4 800 Å (for CCD1 and CCD3) and 6 800 Å (for CCD2 and CCD4).

Future development of wavelength calibration will aim to look at the long-term stability of the 2D fitted parameters and where possible constrain these to physically motivated constant values. For example, the coefficients related to shifts between fibres in the slit should not change, given the physical construction of the slit. Averaging over many datasets should provide an even more accurate estimate for fibre-to-fibre positions. We will also monitor for temporal drifts in the coefficients and check that the solution remains appropriate for the data by comparing residuals.

2.1.6 Flat fielding

Using the wavelength solutions, we extract and process dome flat frames for each tile. Additionally, twilight flat frames, obtained whenever possible during observations to enhance various calibration aspects, are processed. In the SAMI Galaxy Survey, the dome flat frames had extremely faint signals at the blue end of the spectrum in AAOmega blue, so twilight flat frames were used for flat fielding in the blue arm. Since the SAMI observations concluded in 2018, several updates have been made to the AAT dome flat lighting system, including the installation of more blue lights. These improvements have led us to re-examine the spectral uniformity of the dome flat frames for calibration.

Figure 3 presents reduced and normalised spectra from the dome flat and twilight flat frames. The spectra were extracted from the fibre in the middle of each CCD, and normalised for detector gain, photon energy, collecting area, and spectral resolution. We observe several peaks at blue wavelengths ( $\lesssim 4\,500$ Å) in the dome flat spectra of the blue arm, caused by the installation of an array of different LEDs to boost blue light levels. The strong signals at the blue end greatly help reduce uncertainties in light extraction, but the presence of narrow and strong peaks combined with non-uniform illumination across the focal plane leads to residuals in the reduced dome flat frames. These persist even after normalising the flat spectra from each fibre by the median spectrum across all fibres. We find that the reduced dome flat frames exhibit residual gradients, resulting in up to 3% discrepancies compared to the reduced twilight flat frames in the blue arm, which can also introduce artificial colour gradients across the spectrum. In contrast, the red arm dome flat spectra exhibit much smoother spectral uniformity, without the residuals or colour gradient observed in the blue arm.

Figure 3. Flux density derived from dome flat (top) and twilight flat (bottom) frames, extracted from the fibre in the middle of each CCD. The flux density is normalised for gain, photon energy, collecting area, and spectral resolution. The dark and light blue spectra originate from the blue arms of AAOmega and Spector, respectively, while the red and orange spectra are from their red arms. The flat spectra, converted to a flux density scale, illustrate the shape of the flat-field frames and only indirectly reflect relative throughput. For absolute throughput measurements for Hector, refer to Section 2.3.2.

We therefore adopt the SAMI convention for flat fielding by using twilight flat frames for the blue arms, after carrying out a spline fit to the twilight generated flat field to remove the residual impact of solar absorption features in the twilight spectrum. The majority of object frames (68%) were flat-fielded using twilight flats from the same tile configuration, while the remaining 32% used twilight flats from different tiles within the same observing run. For the red arm, we use dome flat frames for flat fielding.

While twilight flats remain the default for blue-arm calibration, we will explore the feasibility of using dome flats alone in future releases. Recent upgrades to the dome flat lighting system have improved the blue-light signal, but further work is needed to address spectral non-uniformities. Ongoing development will focus on characterising and correcting these effects, for example, through empirical illumination corrections.

2.1.7 Correcting fibre-to-fibre variations in throughput

Accurately correcting fibre-to-fibre throughput variations is essential for ensuring reliable flux calibration and uniformity in spectral data. This is achieved using throughput maps derived from twilight flat observations, taken with the same fibre configuration on the same day. Twilight flats are ideal for this purpose, as they provide uniform and consistent illumination across all fibres, enabling precise calibration of their relative sensitivities. When twilight flats cannot be acquired due to challenges like poor weather, the pipeline adopts an alternative approach by generating throughput maps from dome flat frames specific to the same tile. The relative throughput values estimated from dome flats show reasonably good agreement with those derived from twilight flats. For example, in frames taken in November 2024, 90%, 92%, 91%, and 88% of fibres on CCDs 1 through 4, respectively, exhibit discrepancies of less than 1% between the two estimates. Additionally, if the residuals after sky subtraction (as described in Section 2.1.8) are large in frames where dome flats were used for throughput correction, the pipeline switches to a sky-line-based throughput correction, using the fluxes of night-sky lines averaged across multiple frames taken for a single tile.

The relative throughput for each twilight flat (or occasionally a dome flat) is calculated by determining the mean flux for each fibre while excluding bad pixels and then normalising these mean values across fibres using their median. If multiple twilight flat frames are available for a tile, the final relative throughput is obtained by averaging the throughput values from all available frames. To correct throughput variations, each fibre’s spectral data is divided by its respective throughput value, ensuring consistent normalisation across fibres. Fibres with invalid throughput values (e.g. NaN or values below zero) are flagged, and their spectra are excluded from further analysis.

2.1.8 Sky subtraction

Sky subtraction is performed following the same approach used by the SAMI Galaxy Survey (Sharp et al. Reference Sharp2015; Croom et al. Reference Croom2021). A median sky spectrum is calculated from the sky spectra per frame and subtracted from the data. The main difference between SAMI and Hector is that the sky fibres are located around the edge of the field-of-view. Hector also has a larger number of sky fibres than SAMI (at least in part to compensate for not all sky fibres being active at any one time). To assess the level of sky-subtraction accuracy, we calculate the median residual sky in sky-subtracted sky spectra. The median absolute per-fibre fractional continuum sky residual (i.e. flux in sky-subtracted spectrum divided by flux without sky subtraction) across all data from 2023 and 2024 is 0.014, 0.016, 0.012, and 0.010 for CCDs 1 through 4, respectively. The better performance for CCD3 and CCD4 reflects the overall lower level of scattered light in the Spector spectrographs (see Section 2.1.4). We also calculate the sky residuals left in night sky emission lines. The median absolute per-fibre fractional sky-line residuals are 0.011, 0.012, 0.015, and 0.010 for CCDs 1 through 4, respectively. We only calculate the sky-line fractional residuals at the location of strong night-sky emission lines.

2.2.1 Distortion dependence on field radius and wavelength

As part of the Hector instrument commissioning phase, we conducted stellar observations to map chromatic variation in distortion across the 2-degree field of view of the Hector plate. For each stellar observation, we quantified the stellar centroids shifts by fitting a Moffat profile in 100 Å wavelength intervals. Figure 4 presents these distortions as a function of both radial distance from the centre of the Hector plate and wavelength, using the coordinate system of the Hector robotic positioning system.

Figure 4. Stellar observations illustrating the effects of chromatic variations in distortion (CVD) are shown as a function of wavelength and position across the Hector plate, presented in the coordinate system used by the Hector robot. Black-filled circles mark the stellar centroid at a reference wavelength of 6 000 Å, while coloured points trace the shift in the centroids of stellar observations across wavelength, shifting from redder to bluer wavelengths (red-to-blue filled-in circles) relative to the centroid at the reference wavelength. For clarity, the centroid shifts due to CVD effects are exaggerated by a factor of 20; the maximum shift is $\sim$ 120 $\unicode{x03BC}$ m (1.17 times the fibre core diameter). For several hexabundles, we also illustrate the hexabundle orientation and cable direction (see Section 3.4 for discussion on the orientation of hexabundles and associated corrections). Grey lines connect the physical centres of each hexabundle to the centre of the Hector plate.

Each stellar observation is colour-coded from blue to red, indicating the centroid shift with increasing wavelength relative to the centroid at a reference wavelength of 6 000 Å. For clarity, the magnitude of distortion is exaggerated, with the maximum variation reaching 120 $\unicode{x03BC}$ m. The solid grey lines connect the stellar centroid at the reference wavelength to the centre of the Hector plate.

We model the distortion across the Hector plate using a polynomial function with terms $\alpha^7$ , $\alpha^5$ , $\alpha^3$ , and $\alpha^1$ , where $\alpha$ represents the field radius. The wavelength dependence of each coefficient is then parameterised using a quadratic function.

Figure 5(a) compares the modelled distortion with the values observed along a radial direction of the plate. As in Figure 4, each vertical colour-coded set of points represents the centroid offsets relative to the reference position for each stellar observation. The modelled quadratic distortion pattern is shown for the bluest (3 730 Å) and reddest (7 330 Å) wavelengths of the Hector data as solid blue and red lines, respectively.

Figure 5(b) presents the residuals between the model and the data at three different wavelengths, demonstrating that the residuals are within $\pm5\,\unicode{x03BC}$ m at $\lambda\gt 4\,600$ Å, approximately one-fifth the size of 1 fibre core (Bryant et al. Reference Bryant, Bryant, Motohara and Vernet2024). The relatively larger scatter observed at the blue points, corresponding to residuals at 3 800 Å, is largely driven by the reduced signal-to-noise at the blue end of the blue CCDs, increasing the scatter in the measured centroid positions.

The final two panels, Figure 5(c) and (d), show the RMS of the residuals. The panel (c) presents the RMS as a function of plate radius, with points colour coded from blue to red to indicate increasing wavelength, and (d) shows the RMS as a function of wavelength.

2.3.1 Primary flux calibration

We derive the transfer function for flux calibration, $\mathcal{T}(\lambda)$ , using primary standard stars, selected from A- or F-type stars listed in the high-resolution, telluric-corrected spectra provided by the Supernovae Factory projectFootnote ^b Aldering et al. (Reference Aldering, Tyson and Wolff2002). These stars were typically observed three times per night for each instrument, whenever conditions allowed.

Since we use telluric-corrected spectra as our reference, the first step involves applying telluric corrections to the reduced primary standard star frames. See Section 2.4 for details on the telluric correction process for Hector. After applying CVD corrections, we extract the standard star spectrum from each calibration frame using 2D Moffat fitting to better account for the PSF wings. Atmospheric extinction is corrected by scaling the standard extinction curve for Siding Spring Observatory to the effective airmass of each observation and adjusting both the flux and variance. Figure 6(a) and (b) demonstrate that the Moffat fitting method efficiently extracts stellar spectra with fluxes that are approximately 1–1.2 times higher than those obtained by summing the flux over the entire bundle, minimising noise contamination and recovering flux lost in the gaps between fibres. Even though we use high-resolution standard spectra (often with 1–4.2 Å bins) as a reference, the observed spectra exhibit even finer spectral resolution and binning. Consequently, we re-bin the observed spectra to match the coarser scale of the reference spectrum, a step also employed in SAMI DR3. Additionally, we introduce a new step: convolving the observed spectra to match the resolution of the reference spectra. This convolution helps prevent overestimation of the transfer function, particularly in the presence of strong absorption lines. For example, without convolution, the transfer functions are typically overestimated by 0.5–2% below 4 000 Å, with larger discrepancies in the presence of strong absorption lines.

Figure 5. Modelling the Chromatic Variation in Distortion across the Hector plate. (a) Distortion as a function of position along the Plate y-coordinate across the Hector plate, from left-to-right, as shown in Figure 4. Also, as in Figure 4, the colour gradient from blue to red represents measured centroid offsets as a function of wavelength. The modelled distortion at wavelengths of 3 730 and 7 330 Å is shown as solid blue and red lines, respectively. (b) Residuals between the model and observed distortions at 3 800, 5 000, and 7 200 Å, demonstrating that the model effectively reproduces the measured distortions across the Hector plate to approximately within $\pm 10 \unicode{x03BC}$ m. (c) RMS of the residuals as a function of radius on the Hector plate, with colours indicating increasing wavelength from blue to red. (d) RMS of the residuals as a function of wavelength, illustrating that RMS progressively becomes larger towards bluer wavelengths.

Figure 6. Example of deriving the transfer function $\mathcal{T}(\lambda)$ from a primary standard star, LTT 3218, observed on 8 December 2023 using Hexabundle O from Spector blue. (a) Extracted standard star spectrum using Moffat fitting and integrated spectrum over the bundle. (b) Comparison between the extracted and summed spectra. (c) Ratio between the reference and unconvolved observed (extracted) spectra (grey). The transfer function (red dashed line), derived after convolving the observed spectrum to match the reference resolution, does not show local peaks at the positions of absorption lines. (d) Observed, reference, and flux-calibrated spectra. The flux-calibrated spectrum matches the reference well, while retaining sharper absorption features due to its higher spectral resolution.

We then apply a cubic spline fit to the flux ratios between the reference and modified observed spectra to derive the transfer function for each standard star frame (Figure 6(c)). To better address the characteristics of the Spector CCDs, which exhibit a sharp turn at the edge of the transfer function due to the dichroic, we increase the number of knots compared to the SAMI approach. For the AAOmega red CCD, which has a smooth and relatively consistent flux ratio, we use 6 knots for the fitting. For the AAOmega blue CCD, we use 8 evenly distributed knots and introduce an additional knot at each end of the wavelength range to more accurately capture any edge variations. The Spector blue CCD, with its sharper changes at the red end, requires additional knots in that region, while the Spector red CCD needs extra knots at the blue end. Specifically, we add 8 extra knots above 5 600 Å for Spector blue and below 6 000 Å for Spector red to ensure the fitting process accurately captures these edge effects. Figure 6(d) presents an example for the Spector blue CCD, comparing the reference, observed, and calibrated spectra. The transfer functions are median combined for each CCD within each observing run and applied to the reduced object frames for primary flux calibrations.

2.3.2 Sky to detector throughput estimation

After deriving the standard star transfer function, $\mathcal{T}(\lambda)$ , for each primary standard star frame, as described in Section 2.3.1, we convert it into a fractional throughput, $\eta(\lambda)$ , via

(2) \begin{equation}\eta(\lambda)\;=\;\frac{1}{\mathcal{T}(\lambda)}\;\times\;\frac{h\,c}{\lambda\,A\,\Delta\lambda}\;\times\;\texttt{gain}\end{equation}

where h is Planck’s constant, c is the speed of light, A is the telescope’s collecting area, and $\Delta\lambda$ is the wavelength bin size.

We then combine $\eta(\lambda)$ from each standard-star exposure to form a ‘best’ and ‘mean’ throughput reference for each spectrograph arm. To determine the best throughput, we first exclude outlier throughput curves that are greater than $\pm20\%$ of the median of all curves. The best curve is the remaining curve with the highest throughput at specific wavelengths for each spectrograph arm. For the blue arms, we select the throughput with the highest value at 4 500 Å and for the red arms, we select the highest value at 6 500 Å. The best throughputs from our observations are shown in Figure 7. The best throughput represents the sky to detector throughput in the best conditions. Lower throughputs are in poorer conditions, typically due to weather. Notably, Spector demonstrates higher throughput across its entire wavelength range, exceeding AAOmega by more than 35% on the blue arm and 20% in the red arm near their respective peaks.

Figure 7. Sky to detector throughput achievable by Hector in the best conditions. Spector shows significantly higher throughput in both the blue and red arms relative to AAOmega.

To compute the mean throughput, we average $\eta(\lambda)$ across all standard-star frames and exclude any that deviate by more than 20% from this mean, thus removing cloud-affected or otherwise problematic exposures. As a further quality check during observations, we define transmission to be the ratio of the current throughput to the mean throughput. A low transmission indicates poor transparency (e.g. due to adverse weather), and such frames are flagged for possible re-observation. The overall shape of the mean throughput is similar to that of the best throughput curve, but, as expected, it exhibits a lower amplitude due to the averaging over multiple exposures.

2.3.3 Secondary flux calibration

The primary flux calibration is only approximate, as it assumes no change in the atmospheric conditions between the observations of the spectrophotometric standard stars and the galaxies. In practice, however, variations such as changes in airmass, telluric absorption, and sky conditions occur. Therefore, a more precise normalisation is achieved by observing two secondary standard stars–one feeding into AAOmega and the other into Spector–alongside the galaxies, using two dedicated hexabundles that are allocated for this purpose during each observation.

The Hector secondary standard catalogue is constructed from stars colour-selected to be of spectral type F, with an additional magnitude cut applied to ensure high signal-to-noise observations. Owing to their relative abundance in the Milky Way, and their comparatively smooth spectral energy distributions, F-type stars are commonly adopted as flux calibrators (Yan et al. Reference Yan2016). These stars are then compared to their photometric magnitudes to determine a modified transfer function. This secondary flux calibration process for Hector data follows the same approach used in the SAMI Galaxy Survey and described in Croom et al. (Reference Croom2021).

Prior to secondary flux calibration, we correct each reduced row stacked spectra (RSS) frame for atmospheric extinction, approximately flux calibrate using the primary standard, and correct for telluric absorption. The flux of the secondary standard star is then extracted from each RSS frame by fitting a Moffat profile, incorporating corrections for the CVD effects. These extracted spectra are fitted using the pPXF code, using Kurucz (Reference Kurucz1992) model atmospheres. Model atmospheres are used in preference to empirical reference spectra, as reliable observed spectra are not available for these secondary standards.

The pPXF fitting process consists of two steps: first, individual templates spanning a grid of effective temperature ( $T_{\text{eff}}$ ), metallicity ([Fe/H]), and surface gravity are fitted. Then, for the best-fitting surface gravity, the four nearest templates in $T_{\text{eff}}$ and [Fe/H] are refitted, allowing a linear combination of templates.

The fitting is performed only on the blue arm data, as it contains the prominent absorption features required to constrain the models, and includes an eighth-order multiplicative polynomial to correct residual transfer function errors. Moreover, the template weights are averaged across all observations within a field, typically encompassing seven observations of the same star, to derive a best-fitting template. This template is then normalised using the observed g- and r-band photometry of the star, applying the average normalisation from the two bands.

Although transfer functions can be derived for individual RSS frames by comparing the observed spectrum to the best-fitting template, this approach can introduce scatter. To mitigate this, we apply an averaged transfer function, computed from all observations of a standard star in a given field. Individual frame normalisation is still allowed to account for variations in transmission.

Figure 8. (a) Hector-to-SDSS flux ratio using 3-arcsec diameter aperture spectra as function of Hector PSF FWHM. (b) Distribution of Hector-to-SDSS flux ratio. Black squares denote the median and normalised median absolute deviation computed across four bins of the PSF FWHM. Blue and red horizontal lines denote the median value of AAOmega/Spector blue and red arms, respectively.

2.3.4 Flux calibration stability

Following a similar approach to Croom et al. (Reference Croom2021), here we compare 3-arcsec circular aperture spectra extracted from Hector datacubes to single-fibre SDSS spectra using a subsample of 151 galaxies. Apertures are placed in the datacubes at the sky location determined by the SDSS fibre coordinates PLUG_RA, and PLUG_DEC. Since SDSS fibre spectra are matched to PSF magnitudes, we account for this effect by scaling the fluxes by a factor $\simeq 0.72$ (i.e. 0.35 magFootnote ^c ).

Figure 8(a) shows the median Hector-to-SDSS flux ratio across both arms as function of the Hector PSF FWHM. Panel (b) shows the distribution of the flux ratios in both arms. This is equivalent to Figure 11 in Croom et al. (Reference Croom2021), where they reported a median offset and dispersion with respect to SDSS of 1.04 and 0.16, respectively. Here we report median ratio values of 0.86 and 0.87 (blue and red horizontal lines of Figure 8(b)), and dispersion 0.15 and 0.14 for the blue and red arms, respectively.

To further investigate the quality of our calibration as function of wavelength, we show in Figure 9 the 16, 50 and 84 percentiles of the ratio between Hector and SDSS spectra in bins of 100 Å for both arms. To isolate systematic trends with wavelength, each spectrum ratio has been normalised by the corresponding median value for its arm, as reported in the previous paragraph. These results can be directly compared with Figure 13 in Croom et al. (Reference Croom2021).

The calibration of the red arm shows minimal dependence with wavelength. The blue arm, on the other hand, presents a systematic decreasing offset inversely proportional to the wavelength, which is similar to the effect seen in the SAMI-SDSS comparison (Croom et al. Reference Croom2021). In contrast, Husemann et al. (Reference Husemann2013) reported a decreasing SDSS-to-CALIFA flux ratio toward the blue, which represents the opposite trend. These differences highlight that blue-end discrepancies can depend on the choice of reference dataset and calibration method, and should be taken into account when interpreting or comparing spectral shapes across surveys. Such wavelength-dependent offset can result from a combination of multiple effects in either the SDSS or Hector data sets, including a poorer signal on the blue end of the detector due to lower throughput, challenging the estimation of the transfer function, as well as problems related to atmospheric extinction. Nevertheless, the comparison of aperture fibre-like spectra is challenging as it is heavily affected by differences in the seeing conditions of both surveys as well as potential astrometric mismatches between both datasets.

Figure 9. (a) Flux ratio of Hector 3-arcsec diameter aperture spectra to SDSS fibre spectra. The median flux ratio is estimated in bins of 100 Å. Blue and red lines illustrate the 16th, 50th (filled circles) and 84th percentiles of the flux ratio as function of wavelength for both blue and red AAOmega/Spector arms, respectively. (b) Same as (a) but re-scaling each spectra by the median offset between SDSS and Hector.

We perform an additional test by comparing synthetic DECam g-and r-band (Flaugher et al. Reference Flaugher2015) photometry with Legacy Survey (LS) DR10 imaging data (Dey et al. Reference Dey2019). Synthetic photometry is derived by convolving Hector spectra with the DECam g and r filters using the Population Synthesis Toolkit (PST Footnote ^d ; Corcho-Caballero et al. Reference Corcho-Caballero, Ascasibar and Jiménez-López2025). Then we measure the curve of growth using circular apertures with diameters ranging from 2 to 20 arcsec for both LS and Hector datasets.

Figure 10. (a) Ratio of the Hector to Legacy Survey (LS) g-band aperture flux as function of aperture diameter. The black solid line and red (blue) region denote the median and 68% (90%) confidence interval, respectively, as function of aperture diameter. (b) Hector-to-LS flux ratio distribution for a 10-arcsec diameter circular aperture. The solid and dotted lines illustrate the median and dispersion (based on the 16th and 8th percentiles) of the distribution reported on the top-right corner of the panel. (c) and (d) Same as (a) and (b), respectively, using the r band and restricted to Spector cubes. (e) Aperture-based $g/r$ colour ratio between Hector and LS as function of aperture diameter. (f) Distribution of colour ratios for a 10-arcsec diameter circular aperture.

The results are summarised in Figure 10, where panels (a) and (b) illustrate the ratio distribution between Hector and LS circular apertures as a function of aperture diameter, for the g and r bands, respectively. In panel (b) the sample is restricted to Spector data, whose spectral range fully covers the r bandpass. The best agreement between both datasets is found for an aperture of $\simeq10$ arcsec in both bands.

Panels (b) and (d) show the flux ratio distribution computed using a 10-arcsec aperture in both bands. The median flux ratio in the g and r bands is 0.97 ( $\pm 0.10/0.14$ ), and 0.94 ( $\pm 0.07/0.12$ ), respectively, consistent with an absolute spectro-photometric accuracy of $\lesssim15\%$ . Panel (e) shows the $g/r$ flux ratio between Hector (Spector data only) and LS as function of aperture diameter as an additional proxy for colour stability. The median displays an almost perfectly flat trend at all apertures. Using the same aperture diameter as in (b) and (d), we show in panel (f) the $g/r$ flux ratio distribution between Hector and LS. We find a small fraction of outliers presenting elevated colour offsets of up to 50%. These objects appear more extended in the synthetic g-band maps than in the LS imaging data, potentially due to seeing differences, requiring a more careful photometric analysis (e.g. using seeing-dependent apertures). In addition, Figure 11 shows the g band offset as function of effective airmass, where no correlation between both quantities is detected. Overall, we find that $g/r$ flux ratio between Hector and LS imaging data presents a global median and dispersion values of $1.03\pm 0.09/0.11$ , indicating a relative spectro-photometric calibration of $\simeq10\%$ ( $\sim 0.1$ mag).

Figure 11. (a) Distribution of cube effective airmass. (b) g-band Hector-to-LS flux ratio distribution using a 10-arcsec diameter circular aperture as function of effective airmass. Red symbols denote the median and NMAD computed on bins equal to the x-axis error bars.

At the $\sim$ 10% relative $g/r$ uncertainty level implied by the Hector–LS comparison, the corresponding colour scatter is of order $\Delta(g{-}r)\simeq 0.1$ mag (with a median offset of $\simeq 0.03$ mag), which translates to an upper-bound $\Delta E(B{-}V)\simeq 0.1$ mag under standard extinction/attenuation curves (e.g. Calzetti et al. Reference Calzetti2000). This should be regarded as an upper limit, and the propagated effects on broad-wavelength inferences (dust attenuation and SPS) are expected to be modest and do not affect the qualitative trends in our early-science results (e.g. Conroy Reference Conroy2013; Walcher et al. Reference Walcher, Groves, Budavári and Dale2011). We also expect strong-line metallicities and stellar kinematics to remain effectively unchanged (Kewley & Ellison Reference Kewley and Ellison2008; Cappellari & Emsellem Reference Cappellari and Emsellem2004).

2.3.5 Overlap between blue- and red-arm spectra

We test how well the spector blue- and red-arm spectra aligned with each other, which may serve as an independent check on the accuracy of the flux calibration. Since the blue- and red-arm spectra from Spector overlap within a short wavelength range, we measured the flux differences at eight wavelength points ( $\lambda$ -points) within this region. Figure 12 shows the outcome of this test for an example galaxy. The means and noises of the spectra, estimated within $\pm5$ Å at each $\lambda$ -point, are presented in Figure 12(c). Here, noise is defined as the standard deviation of the flux values, which was estimated after removing local linear trends to account for spectral slope variations. Figure 12(d) shows the percentage flux difference between the blue- and red-arm spectra relative to the red-arm flux at 5 800 Å. The flux difference mostly appears to be less than 2 per cent, which falls within a reasonable scope considering the spectrum noise and the intrinsically low throughput in the overlap region (see Figure 7).

Figure 12. Examining the overlap between blue- and red-arm spectra for an example galaxy. (a) Overall shapes of the blue- and red-arm spectra, both normalised to the red-arm flux at 5 800 Å. (b) Zoomed-in view of the overlapping region. (c) Mean (solid lines) and standard deviation (dashed lines) of the flux values at eight wavelength points in this galaxy, each within a $\pm 5$ Å interval. The standard deviation was estimated after removing local linear trends. (d) The percentage difference between the blue and red fluxes relative to the red-arm flux at 5 800 Å (solid line) with its propagated uncertainty (dashed lines).

Figure 13 presents the statistics of the blue-red flux difference in percentage. For this, we produced a pair of blue- and red-arm spectra by integrating the data cubes within a central 3-arcsec radius for each galaxy observed using Spector. For the spector galaxy spectra with S/N $\geq$ 10 in Figure 13(b), their absolute mean values of the blue-red flux difference are close to zero ( $\lesssim 0.8\%$ ). The half value of the range between 16 and 84 percentiles, which approximately corresponds to the 1 $\sigma$ range if a normal distribution is supposed, is as large as $\approx 5\%$ at $\lambda$ -points 3–6. Figure 13(c) shows the blue-red flux difference divided by the propagated noise. The 16th-to-84th percentile half-range is mostly below one, indicating statistically reasonable agreement. The data distributions for each $\lambda$ -point in Figure 13(c) follow a normal distribution reasonably well, except that the distribution at $\lambda$ -point 1 exhibits significantly larger variance. This indicates a higher level of uncertainty at the blue end of the red-arm spectrum, while the data at the remaining $\lambda$ -points appear to be stable. It is worth noting that, at the edges of the overlap range, the throughput of the blue or red arm of Spector is extremely low ( $\lesssim 0.03$ ).

3.5.1 Spectra

In Figure 21, we show a comparison between the AAOmega and Spector integrated spectra (within 1.5 kpc, corresponding to 3.1 arcsec) for a galaxy observed with both instruments (ID:W43690869503589). The small flux offset between the two spectra originates from differences in seeing conditions between the two observations: the AAOmega spectrum was taken with a PSF FWHM of 2.34 arcsec, which results in a fainter flux within a small aperture compared to the Spector spectrum, which was observed with a FWHM of 1.8 arcsec (see Figure 8).

Figure 21 shows the continuous wavelength coverage of Spector, highly desirable for full spectral fitting, that is not available for AAOmega data. In particular, Spector data covers the wavelength range 5 787–6 296 Å, a region that is not sampled by AAOmega. This part of the galaxy’s spectrum includes the NaD absorption line doublet (highlighted in the orange inset panel in Figure 21), a strong indicator of neutral gas and a useful tracer of galactic inflows and outflows.

Spectra from Spector exhibit significantly sharper emission lines than those from AAOmega, particularly in the blue arm, where the spectral resolution is higher by a factor of approximately 1.8 (compared to 1.3 in the red; see Table 1). This improvement is clearly demonstrated in the $\mathrm{H}\beta$ emission line, which appears much sharper in Spector data than in AAOmega. In contrast, the difference is less pronounced in $\mathrm{H}\alpha$ , where both instruments provide comparably high resolution. Spector data also resolve the [OII] $\lambda\lambda$ 3726, 3729 doublet, which appears blended in the AAOmega spectra. This enables more accurate flux measurements of the individual [OII] doublet lines, which is particularly important for electron density diagnostics in the H ii region. In addition, the improved resolution facilitates the study of complex emission line profiles. While such features (e.g. emission line profiles characterised by multiple Gaussian components) have been identified in AAOmega spectra taken for the SAMI survey, it was pointed out by Zovaro et al. (Reference Zovaro2024) that the lower resolution of AAOmega in the blue arm results in unreliable flux measurements for emission lines in this wavelength range (most notably, $\mathrm{H}\beta$ and [OIII]).

3.5.2 Kinematic and emission-line maps

To demonstrate the quality of the Hector data, we show three example galaxies that are kinematically interesting, one from AAOmega (Figure 22) and two from Spector (Figures 23 and 24). For each galaxy, we display maps of the continuum, $\mathrm{H}\alpha$ and $\mathrm{H}\unicode{x03B2}$ flux maps, stellar and gas kinematics, and typical diagnostic flux ratios. The stellar kinematics are fitted using pPXF with a Gaussian LOSVD and 12th-order additive Legendre polynomial, similar to the method in SAMI van de Sande et al. (Reference van de Sande2017). The stellar continuum is fitted using the kinematics and a 12th-order multiplicative polynomial, which is subtracted from the spectrum so that a multi-Gaussian component emission line fit can be performed. For simplicity, only single-component Gaussian fits are shown here. A more detailed description of the pipeline used to generate these products will be provided in Quattropani et al. (in preparation).

Figure 24. A galaxy with a kinematically decoupled core (ID: W42700250208413) observed in bundle N (diameter 15.5 arcsec) of Spector. The panels are the same as Figure 22.

C901005167309223 (Figure 22) is a massive barred galaxy observed with one of the largest AAOmega bundles, with a diameter of 25.9 arcsec. The galaxy exhibits a mild kinematic twist in both the stellar and ionised gas velocity fields, which can only be detected with such extended spatial coverage. Low [N ii]/H $\alpha$ ratios and the Balmer decrement trace a star-forming ring, while elevated central line ratios suggest the presence of a active galactic nucleus (AGN) or shock ionisation.

W183970774910266 (Figure 23) is a low-mass star-forming galaxy with a stellar mass of $\log(M_*/M_{\odot}) = 8.95$ . The high spectral resolution of Spector enables reliable kinematic measurements even in such low-mass systems. The kinematic maps reveal a clear counter-rotation between the ionised gas and stars, although the stellar velocity field appears more irregular and only weakly rotating.

W42700250208413 (Figure 24) is an intermediate-mass early-type galaxy observed with Spector. The gas velocity map shows regular rotation, while the stellar velocity field reveals a prominent kinematically decoupled core (KDC), with the inner region rotating in a direction misaligned with the outer stellar body. The stellar velocity dispersion map also displays two off-centre peaks, indicative of a complex assembly history for this galaxy.