2.1.1. Target selection for GALAH Phase 1 and 2

For GALAH Phase 1 (DR1-DR3) and in the absence of a precise and volume-complete survey in the optical, we used the 2MASS photometric survey (Skrutskie et al. Reference Skrutskie2006) with its J and Ks filters as a precise and nearly volume-complete parent sample from which we selected stars based on approximated (De Silva et al. 2015) visual magnitudes

(1) \begin{equation}V_{JK_S} = K_S+2(J-K_S+0.14)+0.382e^{((J-K_S-0.2)/0.5)}.\end{equation}

For GALAH Phase 1, a tiling pattern (with unique field_id entries) with $2\,\mathrm{deg}$ fields of view below declination $\delta \leq +10\,\mathrm{deg}$ was created for regions with Galactic latitude $\vert b \vert \geq 10\,\mathrm{deg}$ to avoid crowding and strong extinction. For each tile, a selection of 400 stars within magnitudes $9 \leq V_{JK_S} \leq 12$ for a bright magnitude cut and $12 \leq V_{JK_S} \leq 14$ for the nominal magnitude cut is randomly selected from the complete parent sample of 2MASS. Of those, typically 350 stars are actually observed with around 2/3 main-sequence and turn-off stars and 1/3 evolved stars.

For GALAH Phase 2, a stronger focus on turn-off stars was implemented with the photometric and astrometric information of Gaia data release 2 as a parent sample. For each field, we therefore first allocate fibres to stars with absolute Gaia magnitude in the range of $2 \leq M_G \leq 4$ , where

(2) \begin{equation}M_G = G + 5 \cdot \log_{10} \left( \frac{\varpi}{100\,\mathrm{mas}} \right)\end{equation}

with apparent magnitude ( $G\;/\;\mathrm{mag} \equiv {phot\_g\_mean\_mag}$ ) and parallax measurements ( $\varpi\;/\;\mathrm{mas} \equiv {parallax}$ ) from Gaia DR2 (Gaia Collaboration et al. 2018; Evans et al. Reference Evans2018; Lindegren et al. Reference Lindegren2018). Remaining fibres are filled with targets as done with the Phase 1 selection function. This leads to a different selection function for each phase. For science cases in which selection functions matter, we thus recommend to use the survey_name (Table 1) for a clean selection of phase and selection function.

2.1.2. Observational setup

We list the observations under various sub-programs in Table 1. Except for 2 935 spectroscopic observations with the high-resolution mode of HERMES ( $R \sim 42\,000$ ) on 7, 8, 10, 11 and 12 February 2014, all observations were made in the low-resolution mode ( $R \sim 28\,000$ ) with different total exposure times chosen for different programs, but typically between 60 and 90 min. Under sufficient conditions (no clouds and seeing below $2\,\mathrm{arcsec}$ ), GALAH Phase 1 and TESS-HERMES observed 3 exposures for 6 min for bright targets ( $9 \leq V_{JK_S} \leq 12$ ) and 3 exposures for 20 min for the majority of targets ( $12 \leq V_{JK_S} \leq 14$ ).

GALAH Phase 2 extended these times to 3 exposures of 10 or 30 min, respectively, and included repeat observations of GALAH Phase 1 main targets with another 3 exposures for 15 min. K2-HERMES observations targeted stars with $13 \leq V_{JK_S}\;/\;\mathrm{mag} \leq 15$ or even $13 \leq V_{JK_S}\;/\;\mathrm{mag} \leq 15.8$ to complement the K2 Galactic Archaeology Program (Stello et al. Reference Stello2015). These fields were observed for 2 h, similar to most globular and open cluster stars. Worse seeing conditions leading to increasing full-width at half maxima or thin clouds triggered between one ( $2 \,{\lt}\, \mathrm{seeing} \leq 2.5\,\mathrm{arcsec}$ ) and 3 ( $2.5 \,{\lt}\, \mathrm{seeing} \leq 3\,\mathrm{arcsec}$ ) additional exposures. In addition to the science frames, quartz fibre flat and ThXe arc observations were taken directly before or after each set of science exposures, and bias frames were taken at the beginning or end of each observing night.

Table 1. Overview of stars observed for the programs included in GALAH DR4. Numbers of open and globular cluster observations were estimated after observations as described in Section 2.3.3. We have observed 30 globular clusters (23 with $\geq$ 5 stars) and 361 open clusters (109 with $\geq$ 5 stars).

2.3.1. Gaia DR3

We crossmatch our observations to the Gaia DR3 catalogue (Gaia Collaboration et al. 2021a, 2023) using the 2MASS ID, via the nearest neighbour crossmatches provided as part of Gaia DR3 (Torra et al. Reference Torra2021). 911 754 (99.0 %) also have astrometric information (Lindegren et al. Reference Lindegren2021b) and 849 867 (93.0 %) have radial velocity estimates (Katz et al. Reference Katz2023). We apply the corrections to both photometric (Riello et al. Reference Riello2021) and astrometric (Lindegren et al. Reference Lindegren2021a) information. Where possible we prefer the photo-geometric distances over the geometric distances from Bailer-Jones et al. (Reference Bailer-Jones, Rybizki, Fouesneau, Demleitner and Andrae2021). Where neither are available, we further try to find parallaxes from van Leeuwen (Reference van Leeuwen2007). The average parallax uncertainty of the GALAH stars is $\sigma_{\varpi} / \varpi = 1.6_{-0.9}^{+2.6}\,\mathrm{\%}$ . Only $2.3\,\%$ of GALAH stars have no parallax measurementsFootnote ^b or parallax measurements beyond 20% uncertainty, for which the priors adopted by Bailer-Jones et al. (Reference Bailer-Jones, Rybizki, Fouesneau, Demleitner and Andrae2021) start to dominate distance estimates.

2.3.2. 2MASS, WISE, and extinction

In addition to the excellent infrared photometry for 99.9 % of our sources from the 2MASS survey (Skrutskie et al. Reference Skrutskie2006), 98.7 % of them have far-infrared measurements from the WISE mission (Cutri et al. Reference Cutri2014). We therefore can estimate the extinction in the $K_S$ band via the Rayleigh-Jeans colour excess (RJCE) method (Majewski, Zasowski, & Nidever Reference Majewski, Zasowski and Nidever2011) $A_{K_S} = 0.917 \cdot \left( H - W2 - 0.08 \right)$ for most stars. We confirm this estimate by estimating the extinction in $K_S$ via the extrapolation of the colour extinction of $B-V$ , that is, $A_{K_S} \sim 0.36 \cdot E(B-V)$ (Cardelli, Clayton, & Mathis Reference Cardelli, Clayton and Mathis1989). We revert to this value if it is less than half the value of the RJCE estimate, or if either of the H and W2 bands does not have an excellent quality flag ‘A’. For negative estimates by the RJCE method and very nearby stars ( $\,{\lt}\,100\,\mathrm{pc}$ ) we null the value.

2.3.3. Open and globular cluster members and distances

We identify open cluster members using the membership catalogue from Cantat-Gaudin & Anders (Reference Cantat-Gaudin and Anders2020) via crossmatch with the Gaia source_id and adjust their parallaxes and distance estimates to the average cluster values if the latter are more precise. We identify globular cluster members (with more than 70% probability) via the membership catalogue from Vasiliev & Baumgardt (Reference Vasiliev and Baumgardt2021) by crossmatching with the Gaia source_id. We then adjust the parallaxes and distances for the member stars to the mean values listed by Baumgardt & Vasiliev (Reference Baumgardt and Vasiliev2021).

4.2.1. Downgrading synthetic spectra to observed resolution

Because dedicated line-spread-function measurements are available for every spectrum (see Section 2.2), we use this information to downgrade our synthetic spectrum with Gaussian kernels on an equidistant velocity grid to the measured resolution of each observation. We then interpolate the oversampled synthetic spectrum onto the observed wavelength grid.

4.2.2. On-the-fly re-normalisation of observed spectra

Measurements of the GALAH flux and flux uncertainty are reported in counts by the reduction pipeline. To compare with our synthetic spectra, which are normalised to the continuum, we fit an outlier-robust polynomial function to the ratio of observed and synthetic spectra and re-normalise our observed spectra and their uncertainties via this normalisation function.

This specific approach is similar to the internal routine of sme and has the important advantage that no continuum points have to be defined. This is advantageous because we try to cover the full parameter range of FGKM stars for which positions of continuum points – corresponding to 1 on a (pseudo-)continuum-normalised spectrum – differ significantly or for which continuum points may not even be present, or will be a strong function of $T_\mathrm{eff}$ and [Fe/H] (as is the case for M stars).

We make two additional adjustments to the reduced spectra, which come in the form of counts and uncertainty per wavelength, $f_\lambda$ and $\sigma_{f,\lambda}$ .

As we compare the observation to model spectra, we do not have to restrict ourselves to an a priori normalisation, but can take into account the residual information on the continuum in parts of the spectrum. For each model spectrum that we compare to, we therefore perform a normalisation by fitting a fourth order Chebyshev polynomial with outlier clipping to the ratio of model and observation (see Fig. 8). This allows us to both overcome previous shortcomings of the synthetic analysis in GALAH+ DR3 (Buder et al. Reference Buder2021), which had to be restricted to small wavelength segments and assumed a linear relation for those. Our new approach allows us to properly assess the structure of deep and steep molecular features that can dominate spectra of cool stars and carry significant information on $T_\mathrm{eff}$ , $v_\mathrm{rad}$ , as well as abundances (Mann et al. Reference Mann, Gaidos, Lépine and Hilton2012).

Figure 8. Example of normalisation for GALAH DR4 for a model spectrum ( $T_\mathrm{eff} = 3\,400\,\mathrm{K}$ , $\log g = 1.5$ , $\mathrm{[Fe/H]} = -1.0\,\mathrm{dexbest-fitting }$ ) that is selected during the label optimisation. Panel (a): Observed spectrum (counts). Panel (b): Ratio (blue) of observed spectrum and model spectrum as well as Chebyshev polynomial fit (orange). Panel (c): Normalised observed spectrum (black) compared to the model spectrum (blue). Residuals (red) can then be used as input for the likelihood function.

4.3.1. Which stellar labels are optimised?

As part of the synthetic grid computations, we have sampled each label of stellar parameters and elemental abundances individually between our chosen maximum and minimum ranges (see Section 3.1). This allows us to also judge which stellar labels to fit for each given star. We choose to fit a stellar label if either of these two cases applies to said label for the GALAH wavelength range when neglecting the cores of the Balmer lines: (i) The normalised spectrum between minimum and maximum label value at any pixel exceeds the threshold of 0.007 or (ii) The normalised spectrum between the minimum and maximum value changes by more than 0.005 for at least 25% of the pixels. While the first case is constructed for atomic lines, such as Li i 6 708 Å, the second case addresses in particular molecular lines like the C_2 and CN lines. The pipeline can handle missing arms, for example in the case of readout issues of a CCD, and will fix abundances to the scaled-Solar values for elements with absorption features solely in the missing arm, for example N, O, K, and Rb for CCD4.

Figure 10. Examples of masks applied to unreliable pixels for the spectrum fitting, which is done by the minimisation of residuals (red) between observation (black) and synthesis (blue). Panel (a) shows a strong synthetic line, where no line is observed in the data. Panel (b) shows an observed line without any line being synthesised. Panel (c) shows significant disagreement between the two observed lines and the synthesis.

Initial tests of the pipeline have revealed that in cases where the initial parameter estimates deviate significantly from the final values, several elemental abundance estimates were shifted towards their boundaries, leading to a masking of their elemental abundance lines by the masking module (Section 4.3.2) at the beginning of each optimisation loop. To minimise this effect, we therefore shift the interim abundance values towards the narrow label boundaries. In practice, we limit the initial and interim abundances to 1.05.3.26 for A(Li), $\mathrm{[X/Fe]} = -0.5..1.0$ for C, N, O, Y, Ba, La, Ce, and Nd, and $\mathrm{[X/Fe]} = -0.5..0.5$ for all other elements before optimising them again. For warm and hot stars ( $T_{\text{eff}} \,{\gt}\, 6\,000\,\mathrm{K}$ ), this effect was seen to affect multiple abundances, such that we needed to implement a reset of all abundances except Li to their initial values for stars above $6\,000\,\mathrm{K}$ , which would on average be expected to be young and have a Solar-like composition.

4.3.2. Masking of unreliable wavelength regions

Not all pixels of the observed or synthetic spectra might prove useful for estimating reliable stellar labels. Observations can include bad pixels/patterns and incorrect corrections (for example of telluric or sky lines). Flux predictions of synthetic spectra are only as good as the input physics (limited for example for specific lines via uncertain oscillator strengths).

To minimise the influence of inaccurate synthetic pixel predictions, we have compared a 2dF-HERMES observation of the asteroid 4 Vesta and a high-quality Solar spectrum from Hinkle et al. (Reference Hinkle, Wallace, Valenti and Harmer2000) with the flux that would be predicted by our pipeline for a star with Solar labels ( $T_{\text{eff}} = 5\,772\,\,\mathrm{K}$ , $\log g = 4.438\,\mathrm{dex}$ , $\mathrm{[Fe/H]} = 0.00\,\mathrm{dex}$ , $v_{\text{mic}} = 1.06\,\,\mathrm{km\,s^{-1}}$ , $v \sin i = 1.6\,\,\mathrm{km\,s^{-1}}$ , $v_{\text{mac}} = 4.2\,\,\mathrm{km\,s^{-1}}$ Prša et al. Reference Prša2016; Jofré et al. Reference Jofré2017, and $\mathrm{[X/Fe]} = 0.00\,\mathrm{dex}$ for the default Solar abundance pattern for marcs by Grevesse, Asplund, & Sauval Reference Grevesse, Asplund and Sauval2007).

We have identified all lines that showed differences of the normalised flux of more than $0.1$ , lines where either a synthetic line or an observed one was completely missing, or lines that were significantly misaligned. Examples of masksFootnote ^g are shown in Fig. 10. To avoid the influence of bad spectrum regions with an observational origin, we mask pixels where the synthetic and re-normalised observed spectra differ by more than $5\sigma$ or a flux of 0.3 (0.4 before the initial optimisation). To avoid the masking of lines that are vital for our spectroscopic analysis, we have created a listFootnote ^h with segments of such lines that is mainly based on the previous element masks from GALAH DR3 (Buder et al. Reference Buder2021). The final mask of pixels to use for the optimisation then includes all vital line regions, as well as those wavelengths that do not show a too strong disagreement between observation and synthesis and are not deemed unreliable in their synthesis.

In addition to this default masking, we exclude pixels for each major iteration, for which the flux of observation and synthesis differ by more than $5 \sigma$ and 30% of the normalised flux and by more than 100% of the normalised flux for the vital line regions.

We further indirectly take into account the currently less constrained molecular data for cool stars in optical spectra, in particular towards the blue (e.g. Rains et al. Reference Rains2021; Rains et al. Reference Rains2024). For presumably cool stars (with initial $T_{\text{eff}} \,{\lt}\, 4\,100\,\mathrm{K}$ ), we therefore double the observational uncertainty of the blue arm.

6.1.1. Binary signatures

The residual spectrum of our best-fitting single star analysis can help us to identify a second flux contributor to the observed spectrum. In our case, there are two points in the analysis where we can identify such an influence. Firstly, the residuals are visible in the $\chi^2$ distribution as a function of radial velocity shifts (see Fig. 9). While a single star would only show one peak (saved as rv_comp_1), a binary system like 2MASS J06084657-7815235 shows a second peak ( $-70\,\mathrm{km\,s^{-1}}$ in addition to $74\,\mathrm{km\,s^{-1}}$ ) that is saved as rv_comp_2. Secondly, we perform an automatic search for reoccuring residuals as a function of radial velocity for a few selected lines. We chose the combination of strong lines in the spectra (Balmer lines, Fe lines at 4 890 and $4\,891\,$ Å, Ni at $6\,644\,$ Å) as well as those with the largest expected wavelength shift in the infrared detector (O triplet at 7 772–7 775 Å as well as Mg at 7 692 Å). If we find several peaks with a reasonably similar radial velocity, the likely $X \in {16,50,84}\text{th}$ percentiles of this radial velocity are saved in sb2_rv_X.

Figure 12. Comparison of spectroscopic and photometric $\log g$ estimates in the allspec analysis. Panel (a) shows the distribution of spectroscopic $\log g$ and $T_\mathrm{eff}$ from the allspec module. Panel (b) shows the distribution of the same $T_\mathrm{eff}$ and photometric $\log g$ . Panel (c) shows the difference of photometric $\log g$ and spectroscopic $\log g$ as a function of photometric $\log g$ . Red error bars indicate the $1\sigma$ percentiles of this difference in $0.5\,\mathrm{dex}$ bins.

Because radial velocities from the Gaia radial velocity spectrometer (Katz et al. Reference Katz2023) are reported in Gaia DR3 for 94% (774 914) of the stars observed for GALAH DR4, we can also compare against those radial velocity estimates. For 6% (50 577) of our stars, we find a difference with respect to Gaia DR3 larger than $10\,\mathrm{km\,s^{-1}}$ . For these stars, we often noticed unrealistically high $v_\mathrm{mic}$ and $v \sin i$ or negative velocities in our allspec analysis. We note that the allspec analysis was run without boundary conditions for global parameters and thus also resulted in negative velocities, which are later flagged and might indicate binarity (Section 6.3). allstar, however, was run with $v_\mathrm{mic}$ and $v \sin i$ forced to be above $0\,\mathrm{km\,s^{-1}}$ .

6.1.2. Post-correction of logg for allspec results

While we estimate logarithmic surface gravities $\log g$ solely from spectra in the allspec results, we also perform a post-processing estimate where we employ the methodology of Section 5 while fixing all other stellar parameters. The approach of only using spectroscopic information confirmed the previous conclusions of GALAH DR1-DR3 that the spectroscopic information in HERMES spectra to estimate $\log g$ is not sufficient for the majority of the parameter space for the given SNR. We show the spectroscopic $\log g$ in Fig. 12a and the photometric $\log g$ and their difference in Fig. 12b and c, respectively.

Figure 13. Example of three diffuse interstellar bands (DIBs) and interstellar K absorption for 2MASS J06453479-0102137 with an $E(B-V) = 0.84\,\mathrm{mag}$ value from Schlegel et al. (Reference Schlegel, Finkbeiner and Davis1998). Shown are the observation (black) and stellar fit (blue) as well as a Gaussian fit (red) to the residual (orange), resulting in an estimate of the equivalent width (EW) as well as radial velocity.

Figure 14. All-sky map (l,b) of GALAH DR4 equivalent width measurements of the diffuse interstellar band around 5 780 Å, with the GSPhot extinction by Andrae et al. (Reference Andrae2023) in the background.

We see an overall good agreement of both $\log g$ estimates for stars between $4\,250 \,{\lt}\, T_{\text{eff}} \,{\lt}\, 6\,500\,\mathrm{K}$ . Hotter stars show a strong dispersion of spectroscopic $\log g$ due to limited information from fewer and shallower lines. Cooler stars show a significant trend towards much lower $\log g$ for main-sequence stars and much higher $\log g$ for cool evolved stars up to an order of $\Delta \log g$ of $1\,\mathrm{dex}$ . This trend was previously seen in GALAH DR2 (Buder et al. 2018) and is believed to be caused by the onset of molecular absorption features which suppress the continuum for almost the entire HERMES wavelength range (see for example Fig. 8), thus introducing several degeneracies. In addition, we can notice a significantly lower precision of the spectroscopic $\log g$ in comparison to the excellent precision of photometric $\log g$ , for example in the red clump stars.

On closer inspection, we notice several trends in Fig. 12a. Most notably, we see noding patterns along the $T_\mathrm{eff}$ and $\log g$ grids where the allspec module switches between different neural network models. Our investigation of these noding effects is addressed in Section 8. In comparison to Fig. 12b, where a clear equal-mass binary sequence is visible just above the cool main-sequence, we do not see such a sequence in Fig. 12a. The difference between spectroscopic and photometric $\log g$ will therefore be useful to identify photometric binaries with high quality spectra with $\log g$ precisions below the single to binary system offset of up to $\Delta \log g = 0.3\,\mathrm{dex}$ , as discussed in Section 6.3. We caution, however, that the use of stellar structure models for the estimation of surface gravities can introduce systematic trends, as we discuss in Section 8.4.

6.1.3. Interstellar absorption

Because we can create synthetic stellar spectra for the full wavelength range, we can now also trace interstellar absorption in the residuals of observed spectra. By default, we try to calculate the equivalent width via Gaussian fits to the three strongest diffuse interstellar bands (DIBs; 5 780.59, 5 797.19, 6 613.66 Å) with central wavelengths identified by Vogrinčič et al. (2023) as well as for interstellar K ( $7\,698.9643\,$ Å), see Fig. 13. We report the equivalent widths eq_x, standard deviations sigma_x and radial velocities rv_x Footnote ^k for x in k_is for interstellar K and x in DIB_5780, DIB_5797, and DIB_6613 for the DIBs. The coverage of interstellar material, estimated from DIB_5780, within $D_\varpi \,{\lt}\, 5\,\mathrm{kpc}$ is shown in an all-sky map in Fig. 14, with the GSPhot extinction by Andrae et al. (Reference Andrae2023) in the background.

6.1.4. Emission estimates for the Balmer lines

The shape of the Balmer absorption lines holds valuable information on active stars as well as masses for evolved stars (Bergemann et al. Reference Bergemann2016) and possibly even information on unresolved binary systems (Sayeed et al. Reference Sayeed2024). Although the cores of these lines suffer from inaccuracies in the synthesis, the residuals of synthetic and observed lines can be used in relative analyses. We therefore perform a trapezoidal integration around the Balmer lines of each normalised spectrum at $4\,861.3230$ and $6\,562.7970\,$ Å whose values we report in ew_h_beta and ew_h_alpha. By default we integrate in a window of $\pm 0.75$ and $1.25\,$ Å for $\text{H} {\unicode{x03B2}}$ and $\text{H} {\unicode{x03B1}}$ , respectively, and increase this window to $5\,$ Å if the average observed, normalised flux within $\pm 0.5\,$ Å of the Balmer line core exceeds 1. An example of such a star is shown in Fig. 15, for which we measure a residual EW of $-1.09\,$ Å. Most emission line stars in the GALAH sample are found in the region of pre-main-sequence and hot stars (see Fig. AC6a). We conservatively only flag stars with a median normalised flux above 1 in $\text{H} {\unicode{x03B2}}$ or $\text{H} {\unicode{x03B1}}$ as emission line stars.

Figure 15. Example of a flagged emission star with clear emission in the Balmer lines (here H ${\unicode{x03B1}}$ ).

6.2.1. Accuracy estimation and validation

Estimating the accuracy of spectroscopic measurements has always been a complicated endeavour, because there are no universal benchmark sets for all parameters across all stellar types. Subsequently, we describe the numerous comparisons that we have performed for both stellar parameters ( $T_\mathrm{eff}$ , $\log g$ , [Fe/H], $v_\mathrm{mic}$ , $v \sin i$ , and $v_\mathrm{rad}$ ) as well as the elemental abundance measurements. Consistent with GALAH DR3 (Buder et al. Reference Buder2021), and caused by the limited coverage of benchmark literature, we continue to use a single accuracy estimate for each stellar parameter and ignore the possibly large accuracy uncertainties for the individual elemental abundances. In all cases, we estimate an overall bias with respect to literature values and then combine these estimates to a globally applied zero-point correction. Where not explicitly stated otherwise, we assume that the spread of stellar parameters residuals is indicative of the accuracy of either method and estimate our accuracy by dividing the parameter spread by $\sqrt{2}$ . The applied shifts are listed in Table C1. We estimate the accuracy and bias correction for stellar parameters (including the iron abundance as a global parameter) and abundances separately.

Our primary reference source for parameter accuracy remains the Gaia FGK benchmark stars (Jofré et al. Reference Jofré2014; Jofré et al. Reference Jofré2015; Jofré et al. Reference Jofré2018; Heiter et al. Reference Heiter2015). Additionally, we use asteroseismic estimates from the K2 and TESS photometry (Zinn et al. Reference Zinn2020; Hon et al. Reference Hon2021) to compare our surface gravities and perform a validation to higher quality observations of globular cluster stars with typically lower metallicities (Carretta et al. Reference Carretta, Bragaglia, Gratton and Lucatello2009a; Carretta et al. Reference Carretta2009b; Johnson & Pilachowski Reference Johnson and Pilachowski2010). Because the overlap with APOGEE DR17 (Abdurro’uf et al. Reference Abdurro’uf2022) has increased from 41 941 stars in GALAH DR3 to 60 046 stars with 92 368 repeat observation matches in GALAH DR4, we also can assess systematic trends for a larger parameter space. For clarity, we discuss the stellar parameters separately, but show most accuracy estimates in a combined Fig. 16.

Table 4. List of accuracy and representative precision uncertainties for stellar parameters in GALAH DR4. Accuracy values are estimated from comparisons with literature references (see Section 6.2.1), whereas precision estimates are estimated from covariance uncertainties and repeat observations (Section 6.2.2). Here, we list the median precision uncertainties for stars with $SNR = 50 \pm 10$ on CCD2 (see Fig. 20).

Figure 16. Accuracy of the main stellar parameters $T_\mathrm{eff}$ , $\log g$ , [Fe/H], $v_\mathrm{mic}$ , $v \sin i$ , and $v_\mathrm{rad}$ for GALAH DR4. Each panel shows the comparison to literature (DR4 – literature) with median values as lines and contours between 16th and 84th percentiles. Comparisons are performed for the Gaia FGK Benchmark stars (red), APOGEE DR17 (blue), $\log g$ inferred from asteroseismic measurements (orange) and Gaia DR3 radial velocities (purple).

$T_\mathrm{eff}$ : The effective temperature estimates from GALAH DR4 show good agreement with the Gaia FGK benchmark stars (Fig. 16a). Specifically, we find a mean difference of $\Delta T_\mathrm{eff} = 21 \pm 92\,\mathrm{K}$ , indicating no significant bias between our temperatures and the benchmark values. Comparisons with APOGEE DR17 show an equally robust agreement, with $\Delta T_\mathrm{eff} = -8 \pm 78\,\mathrm{K}$ . This small offset and uncertainty suggest that the GALAH DR4 $T_\mathrm{eff}$ estimates are highly reliable across a wide range of at least G- and K-, but possibly also F- and M-type stars. Here, we use $1/\sqrt{2}$ of the residual spread with respect to Gaia benchmark stars as our accuracy estimate.

$\log g$ : For surface gravity, we compared our $\log g$ estimates to both the Gaia FGK benchmark stars, asteroseismic measurements from Zinn et al. (Reference Zinn2020) and Hon et al. (Reference Hon2021), and APOGEE DR17. The asteroseismic $\log g$ values are derived from $\nu_\mathrm{max}$ measurements for giant stars, and they show excellent agreement with our results, with a mean difference of $\Delta \log g = 0.026 \pm 0.078$ . Both the asteroseismic comparison as well as the Gaia benchmark star comparison ( $\Delta \log g = -0.011 \pm 0.059$ ) and APOGEE DR17 ( $\Delta \log g = 0.00 \pm 0.10$ ) agree well and show no trends across the $\log g$ range. For the low metallicity regime, we compare GALAH $\log g$ values with asteroseismically derived values from Howell et al. (Reference Howell, Campbell, Stello and De Silva2022) for the globular cluster M 4 (NGC 6121). Stars from this cluster were observed as part of a dedicated survey (PI M. Howell) aimed at spectroscopically characterising their sample of stars observed by the K2 mission (Howell et al. Reference Howell2014). Across the 75 overlapping targets, we find a $\Delta \log g = 0.056 \pm 0.128$ . The comparison between independently derived light element abundance variations and asteroseismic masses will be presented in an upcoming paper (Howell et al., in preparation.). This is a significant improvement over GALAH DR3, where significant deviations were found for luminous giant stars – whose parameter estimates in GALAH DR3 suffered from less precise and systematically biased distance and thus $\log g$ estimates. We find significant outliers, however, particularly for primary red clump stars, which were mistaken as secondary red clump stars, leading to larger deviations. We discuss this issue later in Section 8.4. Because this single group is driving the scatter in our disagreement with the asteroseismic estimates, we revert to the Gaia benchmark stars to estimate the accuracy.

[Fe/H]: The comparison of GALAH DR4 metallicities to the Gaia FGK benchmark stars initially showed the similar bias of GALAH towards more metal-poor values at the $0.049\,\mathrm{dex}$ level. The application of a zero-point correction (see Table C1) yields an excellent agreement, with $\Delta \mathrm{[Fe/H]} = 0.004 \pm 0.067$ for the benchmark stars and $\Delta \mathrm{[Fe/H]} = -0.022 \pm 0.061$ for APOGEE DR17, confirming the reliability of the GALAH DR4 metallicity estimates across a large range of metallicities. For the metal-poor regime, benchmark estimates are still rare. Luckily, a dedicated observing program – whose results are included in this data release – was performed and an overview of globular cluster Kiel diagrams is appended in Fig. AC5. We therefore only perform a comparison with globular cluster stars – often measured in 1D LTE – to get a quantitative impression of the agreement. We restrict ourselves to a few studies, namely those by Carretta et al. (Reference Carretta, Bragaglia, Gratton and Lucatello2009a,b) for NGC 104, 6121, 288, 6397, and 7099 as well as Johnson & Pilachowski (Reference Johnson and Pilachowski2010) for NGC 5139. In all cases, we find a good agreement of the metallicity distribution function for overlapping stars within the uncertainties (see Fig. 17). While this does not necessarily confirm our accuracy, it shows consistency within this uncertain parameter regime. We note however, a specific region in NGC 104, where the metallicity of the most luminous giants ( $T_\mathrm{eff} \,{\lt}\, 3\,750\,\mathrm{K}$ and $\log g \,{\lt}\, 0.5$ ) is incorrectly estimated near the Solar value. We discuss this problem in detail as a caveat in Section 8.7, since we have not been able to systematically flag these stars. More generally, we note that the strong and unexpected abundance trends with $T_\mathrm{eff}$ or $\log g$ in globular clusters from GALAH DR3 have decreased for most elements. However, we still urge users to take caution when using globular cluster abundances, and we discuss this further in Section 8.6. A custom, by hand analysis of globular cluster abundances beyond [Fe/H] will be performed in a separate study (McKenzie et al., in preparation), as these observations have been part of a dedicated observing program (PIs M. McKenzie and M. Howell). Similarly, a dedicated verification of open cluster observations (PIs J. Kos and G. De Silva) will be performed in a separate study (Kos et al. Reference Kos2025).

Figure 17. Comparison of iron abundances (16th, 50th and 84th percentiles) and overview of spectroscopic and photometric properties of globular cluster stars in GALAH DR4. Left panels show histograms of iron abundances from GALAH DR4 (blue) as well as literature estimates for the globular clusters from Giraffe (orange) and UVES (red) observations by Carretta et al. (Reference Carretta, Bragaglia, Gratton and Lucatello2009a, b) as well as observations from Johnson & Pilachowski (Reference Johnson and Pilachowski2010). Middle panels show the spectroscopic $T_\mathrm{eff}$ - $\log g$ diagrams coloured by iron abundance [Fe/H]. Right panels show the trend of GALAH DR4 [Fe/H] along the different $\log g$ values.

$v_\mathrm{mic}$ : Microturbulence velocities show a more complex pattern when compared to APOGEE DR17. We find a mean difference of $\Delta v_\mathrm{mic} = 0.23 \pm 0.39\,\mathrm{km\,s^{-1}}$ . However, the comparison reveals a linear mismatch: APOGEE DR17 tends to measure lower $v_\mathrm{mic}$ values for stars with low microturbulence and larger $v_\mathrm{mic}$ values for stars with higher microturbulence compared to GALAH DR4. This systematic trend suggests that the $v_\mathrm{mic}$ calibration between the two surveys may differ slightly, particularly at the extremes of the parameter range. We note, however, that the surveys agree much better than for GALAH DR3, where a fixed quadratic relation was used that did not allow for deviations, for example for red clump stars. Adding $v_\mathrm{mic}$ as free parameter returned a similar pattern as the empirical relation by Dutra-Ferreira et al. (Reference Dutra-Ferreira, Pasquini, Smiljanic, Porto de Mello and Steffen2016) and shows a significantly different behaviour of $v_\mathrm{mic}$ for the hottest, coolest, and red clump stars (see Fig. AA1). This mismatch of $v_\mathrm{mic}$ could have indeed driven the metallicity mismatch of metal-rich red clump stars in GALAH DR2 and DR3 (Buder et al. 2018, Reference Buder2021), since their metallicities are in agreement with other estimates now (e.g. APOGEE DR17).

$v \sin i$ : The rotational velocity estimates agree well with APOGEE DR17, with a mean difference of $\Delta v \sin i = 1.6 \pm 2.0\,\mathrm{km\,s^{-1}}$ . However, at higher rotational velocities (above approximately $24\,\mathrm{km\,s^{-1}}$ ), our neural networks start to extrapolate, leading to an upper limit in the estimates and returning significantly lower $v \sin i$ values compared to APOGEE DR17. This issue highlights the limitations of the GALAH DR4 $v \sin i$ estimates for rapidly rotating stars.

$v_\mathrm{rad}$ : For radial velocity we compared our results to both APOGEE DR17 and Gaia DR3. The comparison with APOGEE DR17 yields a small offset of $\Delta v_\mathrm{rad} = -0.09 \pm 0.39\,\mathrm{km\,s^{-1}}$ , indicating excellent agreement between the two surveys. Accounting for the much lower SNR for faint Gaia targets and unidentified binaries, we fit two Gaussian distributions to the overall difference of GALAH and Gaia radial velocities (see Fig. 18). The comparison with Gaia DR3 shows a slightly larger offset of $\Delta v_\mathrm{rad} = 0.15 \pm 0.44 \pm 1.54\,\mathrm{km\,s^{-1}}$ , which is expected due to the lower precision of the Gaia DR3 radial velocities (Katz et al. Reference Katz2023). We use the median residual of $0.15\,\mathrm{km\,s^{-1}}$ with respect to Gaia DR3 rather than the spread as our accuracy estimate.

Figure 18. Comparison of radial velocities between GALAH DR4 allspec and Gaia DR3. Panel (a) shows the difference of radial velocities as function of Gaia G magnitude. Panel (b) shows a histogram of the difference with two Gaussian distributions (with same mean) fitted to them to estimate a more robust, binary independent, radial velocity difference. Panel (c) shows the difference of radial velocities as function of radial velocity, showing the systematic scatter introduced by binaries.

Elemental abundances [X/Fe]: While there is no model-independent benchmark for absolute abundance accuracy, we continually perform comparisons with literature values to assess the consistency of our results with other studies. In GALAH DR4, we evaluate the abundance zero-points using up to five different reference estimates (see Fig. AC1): (1) the spectroscopic analysis of a Solar-composition spectrum of the asteroid Vesta (sobject_id 210115002201239), (2) abundance estimates for Solar twins corresponding to a Solar age of 4.5 Gyr (see Fig. 19), (3) abundances of Gaia FGK benchmark stars (Jofré et al. Reference Jofré2015, Reference Jofré2018), (4) stars with Solar-like metallicity $-0.1 \,{\lt}\, \mathrm{[Fe/H]} \,{\lt}\, 0.1$ within $500\,\mathrm{pc}$ of the Sun (a method introduced by Jönsson et al. Reference Jönsson2020), and (5) differences in abundance estimates for stars overlapping with the high-resolution, large-scale spectroscopic APOGEE DR17 survey (Abdurro’uf et al. Reference Abdurro’uf2022).

Figure 19. Chemical abundances [X/Fe] of Solar twin stars as a function of ages that were estimated as part of the mass and age estimation of the allstar spectrum analysis. We overplot linear fits to our age-abundance relations for Solar twins in orange and literature values from Bedell et al. (Reference Bedell2018) in red. Panels also indicate the median and standard deviation with respect to Bedell et al. (Reference Bedell2018) when assuming a correct age.

It is important to note that our abundance corrections, and consequently the Solar abundances presented in Table AC1, are determined within the framework of 1D LTE or 1D NLTE models and are not intended to represent the most accurate Solar abundances. Instead, they reflect our best effort to minimise discrepancies across different comparison cases. Given the differences in line modelling, such as those between Grevesse et al. (Reference Grevesse, Asplund and Sauval2007) (who used 3D atmospheres) and our 1D models, and possible deviations in the reference abundance from our Vesta spectrum, we refer to these adjusted values as zero-points. For certain scientific applications, adjusting these abundance zero-points might be necessary to ensure consistency with other datasets.

While we are not able to include all of our validation plots, we refer the interested reader to the publicly available code in our code repository.Footnote ^l Generally speaking, we have found that a large number of systematic trends of abundances with temperature and surface gravity has decreased with respect to GALAH DR3, as can be appreciated from dedicated validation plots (online here) – with a similar appearance as the right hand panels of Fig. 17.

Figure 20. Precision monitoring (with a median line and standard deviation shading) of stellar parameters as a function of SNR for the green CCD2 across GALAH DR4. Each panel shows the behaviour for bins of width 10 for the scatter of repeat observations of the allspec runs (blue), covariance uncertainties of allspec (orange) and allstar (red) setups as well as scatter of photometric $\log g$ from repeat observations (purple).

6.2.2. Precision estimation and validation

In addition to the accuracy uncertainty, we estimate the total uncertainty through the additional precision uncertainty (Equation 12). For this purpose, we mainly rely on the fitting uncertainties of the curve_fit function, which we rescale based on repeat observations.

While we report the raw fitting covariance matrix for each spectrum and module (see Fig. AB2 for the covariance matrices of Vesta and Arcturus), their entries are not validated for reliability and have not been adjusted to incorporate a rescaling towards the final uncertainties. For the purposes of reporting stellar parameter and abundance fitting uncertainties, we restrict ourselves to the standard deviations of each feature, that is, the square root values of the diagonal covariance matrix entries.

Figure 21. Comparison of stars with available measurements in GALAH DR4 and APOGEE DR17 for [C/Fe] and [N/Fe].

Figure 22. Comparison of stars with available measurements in GALAH DR3 (left), GALAH DR4 (middle) as well as APOGEE DR17 (right) for [Mg/Fe] (top row) and [Ni/Fe] (bottom row).

Similar to GALAH DR3, we apply a precision adjustment of the fitting uncertainty towards consistency with the scatter of repeat observations only as a function of SNR of CCD2. Contrary to GALAH DR3, we have extended this rescaling function to be fitted in bins of SNR with both a constant, linear, and exponential term with snr_px_ccd2 as the independent variable, that is, $c_1 + c2 \cdot SNR + c_3 \cdot \exp(c_4 \cdot SNR)$ . We report the fitted constants for both allspec and allstar in the online repositoryFootnote ^m for each stellar parameter and abundance.

In Figs. 20 and AC2, we then confirm that the overall trends of fitting uncertainties for allspec and allstar are consistent with the repeat observation scatter of the allspec. The latter has to be used as reference, because the allstar module uses co-added spectra of repeat observations rather than the repeat observations themselves. While this might actually overestimate the precision uncertainty of stellar parameters, we do not expect a too strong overprediction for abundances.

While the precision levels of stellar parameters have on average actually remained similar to the estimates of GALAH DR3, we see notable improvement of the precision for multiple elements, such as C, Mg, V, Cr, Co, Ni, La, Ce, Nd, and Sm. The precision of Eu, however, seems to have decreased.

Separately from this work, we performed an extensive analysis of the precision and accuracy of spectroscopic parameters from the observation of star clusters, 43 open clusters of all ages and 10 globular clusters (Kos et al. Reference Kos2025). In this work, we compare $T_\mathrm{eff}$ , $\log g$ , and stellar ages with the values obtained from cluster isochrone fitting. Ages show typical uncertainties of 10 to 50%, depending on the stellar type. $T_\mathrm{eff}$ and $\log g$ match well for stars hotter than $4\,000\,\mathrm{K}$ with a bias of $\Delta T_\mathrm{eff}=-68\,\mathrm{K}$ (GALAH – Isochrones), and $\Delta \log g = -0.03$ . For stars cooler than stars $4\,000\,\mathrm{K}$ , GALAH DR4 temperatures are overestimated by up to $250\,\mathrm{K}$ at $T_\mathrm{eff} = 3\,000\,\mathrm{K}$ and we find a complicated pattern in $\Delta \log g$ , with $\log g$ being sometimes severly overestimated for the coolest dwarf stars.

Most interesting is the analysis of elemental abundances. Assuming that stellar clusters are chemically homogeneous, we can study the precision of the reported abundances over a large range of temperatures. We find that cold stars show consistent systematic trends, that can reach values of $0.5\,\mathrm{dex}$ for some elements. Dwarf stars are most affected at temperatures $T_\mathrm{eff} \,{\lt}\, 4\,600\,\mathrm{K}$ , while giants show much smaller systematics with strong trends only at $T_\mathrm{eff} \,{\lt}\, 4\,000\,\mathrm{K}$ . The results of this cluster validation (Kos et al. Reference Kos2025), including a detrended set of elemental abundances, will be published as value-added-catalogues in DR4.

6.2.3. Uncertainties in light of GALAH DR3 and APOGEE DR17

To get a better idea of the actual improvement of accuracy and precision, we have performed more elaborate comparisons than those in Fig. 16 and only showcase a few in this manuscript with reference to the online repository. We have found the comparison of GALAH DR4 with both GALAH DR3 and APOGEE DR17 highly informative.

Because GALAH DR3 did not include N measurements and only a limited amount of C measurements, our first comparison concerns the abundances of C and N between GALAH DR4 and APOGEE DR17 in Fig. 21. We attach the comparisons for the other overlapping elements O, Na, Al, Si, K, Ca, Ti, V, Cr, Mn, Co, and Ce in Figs. AC3 and AC4. While we see a generally good agreement of the shapes, we notice biases of $-0.03\,\mathrm{dex}$ and $0.10\,\mathrm{dex}$ for C and N, respectively. These can be, however, explained by the lower precision of GALAH and might, in part, be driven by the slightly different trends of C and N towards lower metallicities. In particular, [C/Fe] decreases to sub-Solar level in APOGEE DR17 for metal-poor stars, whereas it is Solar or even enhanced in GALAH DR4. Enhanced levels would be expected for metal-poor disk stars, whereas sub-Solar levels are expected for accreted stars (Amarsi, Nissen, & Skúladóttir Reference Amarsi, Nissen and Skúladóttir2019b), warranting a future population analysis to test the accuracy of either survey.

In addition to these novel abundances, we also showcase two previously measured abundances, namely [Mg/Fe] and [Ni/Fe] in Fig. 22. The ${\unicode{x03B1}}$ -process element Mg has significant value for Galactic studies because it is predominantly produced by core-collapse supernovae (Kobayashi, Karakas, & Lugaro Reference Kobayashi, Karakas and Lugaro2020). In GALAH DR3, only the Mg i $5\,711\,$ Å line was used, whereas we now use a combination of several lines. This has led to a significant improvement in precision, as can be appreciated from the comparison of Fig. 22a and b. Even more positive, we see an improved agreement of the [Fe/H] vs. [Mg/Fe] measurements between GALAH DR4 (Fig. 22b) and APOGEE DR17 (Fig. 22c), with no abundance bias. One of the elements with the most significant precision improvement is Ni. For this element, our move to fitting the full wavelength range has increased the number of lines from two very reliable lines to several dozen lines. Albeit less reliable in their line data and possibly blended, the sheer increase in flux information used has improved the precision almost to the level of APOGEE DR17 – with no bias and a standard deviation of only $0.05\,\mathrm{dex}$ between APOGEE DR17 and GALAH DR4 (see Fig. 22c–f).

In addition to these instructive comparisons, we also return to the precision of Solar twins from Fig. 19. Here we specifically highlight the significant improvement of precision from GALAH DR3 to GALAH DR4 with respect to the linear estimate from Bedell et al. (Reference Bedell2018) for C (from 0.09 to 0.045), Si (from 0.04 to 0.023), Ca (0.07 to 0.049), Ti (0.05 to 0.031), V (0.13 to 0.050), Cr (0.06 to 0.024), Ni (0.07 to 0.033), and Y (0.12 to 0.080). This improvement of sometimes a factor of 2 is remarkable and most of our comparisons indicate that these values are representative of a precision improvement beyond the Solar twins, as shown for example for Ni in Fig. 22.

7.2.1. VAC of crossmatches with Gaia DR3, 2MASS and WISE

The value-added catalogue of the crossmatchFootnote ⁿ with the Gaia DR3, 2MASS, and WISE catalogues as well as the distance catalogue of Bailer-Jones et al. (Reference Bailer-Jones, Rybizki, Fouesneau, Demleitner and Andrae2021) was calculated by performing an OUTER JOIN ADQL-query in the Gaia archive.

The query first performed an INNER JOIN with the 2MASS near-infrared photometry catalogueFootnote ^o via its designation and linked this match to the Gaia DR3 catalogue via the best neighbourFootnote ^p and joinedFootnote ^q catalogues of 2MASS to Gaia DR3 (Torra et al. Reference Torra2021). When cross-matching between Gaia DR3 and 2MASS, less than 1% of stars were associated with multiple possible matches. To ensure the best match, the data were sorted from brightest to faintest G-band magnitude, and only the brightest match for each sobject_id was retained.

The crossmatch to the WISE far-infrared photometry catalogueFootnote ^r (Cutri et al. Reference Cutri2014) was performed via the Gaia DR3’s best neighbour catalogueFootnote ^s (Torra et al. Reference Torra2021). The match to the distance catalogueFootnote ^t of Bailer-Jones et al. (Reference Bailer-Jones, Rybizki, Fouesneau, Demleitner and Andrae2021) via the Gaia DR3 source_id.

The catalogue also includes uncertainties in the Gaia DR3 photometric magnitudes (G, ${G_{{\rm{BP}}}}$ , ${G_{{\rm{RP}}}}$ ) that were recalculated following the recommendations from the Gaia Early Data Release 3 (EDR3) documentation (Riello et al. Reference Riello2021). The total uncertainties were computed by combining the photon flux error with an additional systematic term.

Table 6. List of elemental abundance quality flags flag_fe_h for [Fe/H] or flag_X_fe for element X.

We further corrected the Gaia DR3 parallaxes for systematic zero-point errors by applying the correction model provided by Lindegren et al. (Reference Lindegren2021a). This correction depends on several factors, including the G-band magnitude, effective wavenumber ( ${\nu _{{\rm{eff}}}}$ ) used in astrometry, pseudocolour, latitude, and the astrometric solution type. The parallax zero-points and original parallaxes are reported as plx_zpt_corr and parallax_raw, respectively.

Beyond the crossmatch with the Gaia DR3 gaia_source catalogue, multiple other crossmatches can easily be performed via the gaiadr3_source_id column. We have for example crossmatched the sources from GALAH DR4 with those from Gaia DR3’s variability catalogues (Rimoldini et al. Reference Rimoldini2023). We find 47 493 stars in GALAH DR4 that overlap with the gaiadr3.vari_classifier_result catalogue. In particular, we find 17 256 SOLAR_LIKE variables, 14 477 stars in the ${\unicode{x03B4}}$ Scuti, ${\unicode{x03B3}}$ Doradus, or SXPhoenicis category (DSCT/GDOR/SXPHE), 6 247 LPV (long-period variables), 4 074 ECL (eclipsing binaries), 3 355 RS (RS Canum Venaticorum variables), 1 096 YSO (young stellar objects), 401 RR (RR Lyrae types), and a large variety of other variables, including the white dwarf 2MASS J05005185-0930549 that was already found in GALAH data by Kawka et al. (Reference Kawka2020).

7.2.2. VAC of stellar dynamics

The value-added catalogue for stellar dynamicsFootnote ^u includes the kinematic and dynamical properties for stars in the GALAH DR4 survey. The catalogue is created with a publicly available scriptFootnote ^v as part of GALAH DR4. We define the position of the Sun in our Galactic reference frame as $R_\mathrm{GC} = 8.21\,\mathrm{kpc}$ (McMillan Reference McMillan2017), $\varphi_\mathrm{GC} = 0\,\mathrm{rad}$ , and $z_\mathrm{GC} = 25\,\mathrm{pc}$ (Bland-Hawthorn & Gerhard Reference Bland-Hawthorn and Gerhard2016). We then combine the total velocity in V of the Sun at $R_\mathrm{GC}$ based on the proper motion measurement of $6.379\pm0.024\,\mathrm{mas\,yr^{-1}}$ by (Reid & Brunthaler Reference Reid and Brunthaler2004), that is, $V_\odot = 248.27\,\mathrm{km\,s^{-1}}$ with the circular velocity of $V_\mathrm{circ} = 233.10\,\mathrm{km\,s^{-1}}$ from McMillan (Reference McMillan2017) to estimate a peculiar velocity of the Sun with respect to the local standard of rest of $15.17\,\mathrm{km\,s^{-1}}$ . For the other two components, we use the estimate by Schönrich, Binney, & Dehnen (Reference Schönrich, Binney and Dehnen2010), leading to a peculiar velocity of the Sun of $(U,V,W) = (11.1, 15.17, 7.25)\,\mathrm{km\,s^{-1}}$ .

Starting from the crossmatch of GALAH DR4 with the Gaia DR3 (see Section 7.2.1), we use the galpy.orbit module by Bovy (Reference Bovy2015) to estimate heliocentric Cartesian coordinates (X,Y,Z) and velocities (U,V,W) as well as Galactocentric cylindrical coordinates $(R, \varphi, Z)$ and velocities ( $v_R, v_\varphi, v_Z$ ). We approximate the orbit actions $J_R, J_\varphi = L_Z, J_Z$ and frequencies $\omega_i$ with the galpy.actionAngle.actionAngleStaeckel function with a focal length of the confocal coordinate system ${delta} = 0.45$ in the Milky Way potential by McMillan (Reference McMillan2017). We further use the Staeckel approximation (Binney Reference Binney2012) to calculate eccentricity, maximum orbit Galactocentric height, and apocentre/pericentre radii with galpy’s EccZmaxRperiRap (Mackereth & Bovy Reference Mackereth and Bovy2018). Our assumption of a time-invariant, axisymmetric potential further allows us to extract the orbit energy via galpy. Orbit.E.

In particular the dedicated observing programs of GALAH towards low angular momentum stars (PI S. Buder) and globular clusters (PI M. McKenzie and PI M. Howell) have increased the number of spectroscopic observations for stars on halo-like orbits. This is showcased by both the action-action diagram of angular momentum $L_Z$ versus radial action $\sqrt{J_R}$ (Fig. 26) and angular momentum $L_Z$ versus orbit energy E (Fig. 27) and visualises the potential of GALAH DR4 observations to complement Galactic dynamics studies and enable Galactic chemodynamic studies.

Figure 24. Overview of stellar parameters and elemental abundances for the allstar estimates of GALAH DR4. The top left panel shows the density distribution of stars in the Kiel diagram of $T_\mathrm{eff}$ and $\log g$ . All other panels show the logarithmic elemental abundances (for elements indicated in the top left of the panel) as a function of the logarithmic iron abundances [Fe/H]. Elements are coloured by different nucleosynthetic channels (black for big bang nucleosynthesis, blue for core-collapse supernovae, red for supernovae Type Ia, green for asymptotic giant branch star contributions and pink for the rapid neutron capture process with contributions from merging neutron stars) following the colour schema from Kobayashi et al. (Reference Kobayashi, Karakas and Lugaro2020). Percentages indicate the fraction of detections of stars for each element.

Figure 25. The ratio of [C/N] and isochrone masses in comparison panel (a), and as a function of $T_\mathrm{eff}$ and $\log g$ in panels (b) and (c), respectively.

Figure 26. Distribution of the dynamical properties of angular momentum $L_Z$ and radial action $J_R$ of stars in GALAH DR4 (black), with globular cluster members highlighted in colour. Cluster members were selected as those with more than 70 percent membership probability according to Vasiliev & Baumgardt (Reference Vasiliev and Baumgardt2021). The Sun is indicated with a red $\odot$ symbol.

Figure 27. Distribution of the dynamical properties of angular momentum $L_Z$ and orbital energy E of stars in GALAH DR4 (black), with globular cluster members highlighted in colour. Cluster members were selected as those with more than 70 percent membership probability according to Vasiliev & Baumgardt (Reference Vasiliev and Baumgardt2021). The Sun is indicated with a red $\odot$ symbol.

7.2.3. VAC of 3D NLTE lithium abundances

In this value-added catalogue,Footnote ^w we use spectrum fitting to infer 3D non-local thermodynamic equilibrium (NLTE) lithium abundances. For each spectrum, the Li line is modelled with a 3D NLTE breidablik line profile (Wang et al. Reference Wang2021). In cases where the Li line is blended with nearby lines such as Fe and CN, we model blending lines as Gaussian absorption profiles. From this model, we measure the equivalent width (EW) and errors in EW of the Li line using UltraNest (Buchner Reference Buchner2021), a Monte Carlo nested sampling algorithm. The Li abundance, A(Li), is then inferred from the measured EW using breidablik and the stellar parameters from GALAH DR4’s allstar. See Wang et al. (Reference Wang2024a) for a detailed description of the methodology.

Wang et al. (Reference Wang2024a) measured a local line width for the Li region and fit the width of the Li line separately from other lines. For this work, we use the GALAH instrumental profile convolved with the rotational velocity as the width of our blending lines and set the width of the Li line based on this convolved kernel, better constraining the line widths. Whilst we still measure a local radial velocity due to a lack of ThXe arc lines for CCD3 (see Section 8.1), we apply the GALAH radial velocity for poorly constrained Li depleted stars where we cannot measure the local radial velocity. In addition, the sampled EW posterior is now modelled using a first order boundary corrected kernel density estimator from Lewis (Reference Lewis2019), which has better convergence than histograms. Lastly, GALAH DR4 analyses stars down to 3 000 K, but the stagger model atmospheres only reach 4 000 K, therefore, we provide an additional column of 1D NLTEFootnote ^x A(Li) inferred through our measured EWs using a new interpolator. Similar to the existing EW interpolators in breidablik (Wang et al. Reference Wang2021), we train a feedforward neural network on NLTE Li abundances synthesised using the 1D marcs model atmospheres. We use a 2-layer architecture with the ReLU activation function and find best hyperparameters: $i = 900$ neurons, and $\alpha = 0.1$ L2 penalty. This model is included in the breidablik package. Using the updated methodology it takes $\sim$ 2 min per star in comparison to $0.5$ –2 h per star reported in Wang et al. (Reference Wang2024a), with the main speed up coming from fixing the Li line width.

EWs are measured for 892 223 stars (97% of GALAH DR4), with 3D NLTE A(Li) detections reported for 417 825 stars (46%) and upper limits for 474 398 stars (52%). Fig. 28 shows the mean EW over $T_\mathrm{eff}$ and $\log g$ . The Li-dip can be seen on the main-sequence turn-off at $T_\mathrm{eff}$ $\approx 6\,500$ K and $\log g$ $\approx 4.2$ and extends up the subgiant branch. There is a Li enhanced population of stars at $\log g$ $\approx 2.5$ in the red clump whilst the horizontal branch is depleted in Li. Although the secondary red clump appears to be depleted in Li, these stars have an overestimated $\log g$ driven by incorrectly inferred masses (see Section 8.4), and should be primary red clump stars. The increase of mean Li EW up the giant branch is due to a large proportion of stars with EW $\approx 100$ mÅ. Features of this figure will be studied in follow-up papers.

Figure 28. Mean EW binned in $T_\mathrm{eff}$ and $\log g$ . The Li-dip can be seen at $T_\mathrm{eff}$ $\approx 6\,500$ K and $\log g$ $\approx 4.2$ . At $\log g$ $\approx 2.5$ , red clump stars have a higher mean Li EW whilst horizontal branch stars have a lower mean Li EW compared to surrounding stars. The mean Li EW increases going up the red giant branch.

A quality flag (flag_ALi) is raised by 1 for upper limits, 2 or more to indicate other quality issues, such as stellar parameters falling outside of the model atmosphere grid (see Wang et al. Reference Wang2024a) for more details on the bitmask flag). We recommend flag_ALi < 2 when using the 3D NLTE A(Li), and flag_ALi < 4 when using Li EWs. A similar quality flag flag_ALi_1D is provided corresponding to the 1D NLTE A(Li) included in the VAC.

For convenience, we have included the most important columns of this catalogue in the allstar catalogue (see Table A1), as we recommend to use them instead of the less accurate 1D NLTE abundances estimated with an imperfect neural network interpolation, which we indicate with nn_li*.

7.2.4. Ages

A value-added-catalogue for stellar ages and masses from BSTEP (Sharma et al. Reference Sharma2018) is currently in preparation. In the meantime, users can rely on the on-the-fly age and mass estimates already provided in the allstar and allspec catalogues from the pipeline.

7.3.1. Reduced spectra

The reduced spectra of each night are provided in the observations directoryFootnote ^y and sorted into directories with four spectra – one for each of the four CCDs. These spectra are produced by the reduction pipeline (see Section 2.2) and include several extensions as outlined in Table 2, with wavelength information stored in the fits headers with starting wavelength CRVAL1 in Å and linear pixel scale CDELT1 in Å/px, and the number of pixels NAXIS1. The reduced spectra are only provided per exposure and not in a co-added manner, since the co-adding was performed as part of the allstar module (see Section 7.3.3 for co-added spectra). We note that not all files might be available for a given exposure due to the rare failure of CCD readouts.

7.3.2. Additional products of the allspec module

The allspec analysis product directoryFootnote ^z provides the files that were produced by the allspec module. These include the on-the-fly assessment of the radial velocity fit *rv.png (similar to Fig. 9), the raw fitting results *results.fits and their covariance matrices *covariances.npz (similar to the entries used to produce Fig. AB2). We also provide a combined *spectrum.fits file (concatenated over the four bands) that includes the wavelength, flux, and flux uncertainty of the velocity-corrected and re-normalised observed spectrum as well as the best-fitting model spectrum interpolated onto the same wavelength. Finally, we provide a *comparison.pdf (similar to Fig. AB1) which displays the fit results, comparison of observed and model spectrum, masked wavelength regions, and wavelengths of the most important element lines. If the module did not run to completion, for example because the SNR of the spectra was below the threshold of $\mathrm{SNR} = 10$ for any CCD to even attempt a fit, not all products are available for a spectrum.

7.3.3. Additional products of the allstar module

The allstar analysis product directoryFootnote ^aa also includes the radial velocity monitoring *rv.png, results files *results.fits, combined spectra *spectrum.fits and *comparison.pdf overview, similar to the ones described in Section 7.3.2. In addition, each directory also includes a *sobject_ids.txt file that lists all individual spectra that were co-added to create the observed spectrum and its uncertainty in *spectrum.fits.

8.1.1. Wavelength solutions

For each CCD, the reduction pipeline estimates the most suitable wavelength solution, linking pixels with actual wavelengths based on the ThXe arc lines. In GALAH DR3 (Buder et al. Reference Buder2021) we identified several issues for spectra where not enough ThXe lines could be used to constrain the wavelength solution. Improvements have been made for the new reduction version to improve the number of useful ThXe lines and restrict the flexibility of wavelength solutions to move them closer to previous results. This has helped us to decrease the number of problematic wavelength solutions towards the red end of CCD3 which includes the used absorption features of Li and Eu. We have decreased bad wavelength solutions for this CCD from initially 7.9% of the spectra to roughly 1% bad solutions, that is, similar to the other CCDs.

8.1.2. Holistic spectrum extraction

Although much work has been spent on improving telluric and sky lines in the reduction step, most reduction steps are currently run sequentially rather than in parallel. Using the information of stellar spectra when modelling the wavelength solution would certainly help to overcome the limited information in ThXe calibration spectra in the absence of laser combs (Kos et al. Reference Kos2018). Multiple steps in this direction have been taken (Saydjari et al. Reference Saydjari, Uzsoy, Zucker, Peek and Finkbeiner2023) and should be rolled out in future spectrum analysis. This would especially help to mitigate imperfect telluric and sky line removal while simultaneously improving the wavelength solution – among many other effects.

8.2.1. Spectrum synthesis

The GALAH survey’s success relies heavily on the ability to accurately model stellar spectra to infer accurate stellar properties. The survey has seen significant improvements in moving from the approximation of 1D LTE towards 1D NLTE (Amarsi et al. Reference Amarsi2020b). This includes the use of 1D NLTE synthesis for atomic lines using the 3D NLTE code balder (Amarsi et al. Reference Amarsi2018b), a custom version of Multi3D (Botnen & Carlsson Reference Botnen, Carlsson, Miyama, Tomisaka and Hanawa1999; Leenaarts & Carlsson Reference Leenaarts and Carlsson2009). The code employs model atoms for H (Amarsi et al. Reference Amarsi2018b), Li (Lind, Asplund, & Barklem Reference Lind, Asplund and Barklem2009a; Wang et al. Reference Wang2021), C (Amarsi et al. Reference Amarsi, Barklem, Collet, Grevesse and Asplund2019a), N (Amarsi et al. Reference Amarsi2020a), O (Amarsi et al. Reference Amarsi, Barklem, Asplund, Collet and Zatsarinny2018a), Na (Lind et al. Reference Lind, Asplund, Barklem and Belyaev2011), Mg (Osorio et al. Reference Osorio2015), Al (Nordlander & Lind Reference Nordlander and Lind2017), Si (Amarsi & Asplund Reference Amarsi and Asplund2017), K (Reggiani et al. Reference Reggiani2019), Ca (Osorio et al. Reference Osorio, Lind, Barklem, Allende Prieto and Zatsarinny2019), Mn (Bergemann et al. Reference Bergemann2019), Fe (Amarsi et al. Reference Amarsi2018b; Amarsi et al. Reference Amarsi, Liljegren and Nissen2022), and Ba (Gallagher et al. Reference Gallagher2020) over the marcs model atmosphere grid. The work by Wang et al. (Reference Wang2024a) also enables us to present measurements of Li in 3D NLTE as part of this release.

All of these advances contrast with the lack of a proper way of modelling molecular features appropriately. This could explain the significant mismatch of oxygen abundances between the optical and infrared (compare e.g. Bensby, Feltzing, & Oey Reference Bensby, Feltzing and Oey2014; Abdurro’uf et al. Reference Abdurro’uf2022). It can, however, also lead to mismatches in the GALAH wavelength range, where atomic features, such as C I, can be modelled in 1D NLTE, whereas much stronger molecular features of $\mathrm{C}_2$ and CN have to be modelled in 1D LTE and linelists of molecules, such as TiO, might be incomplete (Hoeijmakers et al. Reference Hoeijmakers2015; McKemmish et al. Reference McKemmish2019).

For our synthesis, we have employed version 580 of the IDL-based code Spectroscopy Made Easy (Valenti & Piskunov Reference Valenti and Piskunov1996; Piskunov & Valenti Reference Piskunov and Valenti2017). As part of the continuing improvement of this code, several bugs have been identified and fixed. We also note that a Python-based version of SME, pySME (Wehrhahn et al. Reference Wehrhahn, Piskunov and Ryabchikova2023), has become available. In addition, the spectrum synthesis code KORG (Wheeler et al. Reference Wheeler, Abruzzo, Casey and Ness2023; Wheeler, Casey, & Abruzzo Reference Wheeler, Casey and Abruzzo2024) has been published in Julia with a Python interface. It offers a faster alternative to SME once 1D NLTE synthesis is implemented, which is essential for applying to many NLTE-sensitive lines, such as O and K, in the GALAH wavelength range. KORG already internally adjusts the metallicity that is used to interpolate atmospheres based on the overall chemical abundances, whereas this would need to be adjusted in SME by hand, since atmospheres are interpolated with the sme.feh entry that is independent of the chemical composition sme.abund. Because we have not performed said adjustment, we note that the spectrum synthesis for chemical compositions far from scaled-Solar may have used an mismatched atmosphere in the synthesis in SME for GALAH DR4.

8.2.2. Mismatch of atmosphere and spectrum chemistry

For several of our synthetic spectra, the chosen chemical composition deviates significantly from the scaled-Solar pattern of the marcs model atmospheres, particularly for ${\unicode{x03B1}}$ -process elements such as O and Mg, as well as C and N. These elements can substantially affect opacity and energy transport, and therefore, their abundances must be adjusted to match observed spectra more accurately. For instance, ${\unicode{x03B1}}$ -enhancements in stars with non-Solar abundance patterns can shift line strengths and depths significantly (Asplund Reference Asplund2005; VandenBerg et al. 2012). Likewise, variations in C and N abundances, particularly in cooler stars, can impact molecular equilibrium, altering CO and CN molecular line strengths significantly (Tsuji Reference Tsuji1976; Smith et al. Reference Smith2013). Dedicated marcs atmospheres with modified ${\unicode{x03B1}}$ and C abundances (Mészáros et al. Reference Mészáros, Allende Prieto and Edvardsson2012; Jönsson et al. Reference Jönsson2020), such as those used in modelling APOGEE spectra (Abdurro’uf et al. Reference Abdurro’uf2022), or more flexible interpolation schemes by Westendorp Plaza, Asensio Ramos, & Allende Prieto (Reference Westendorp Plaza, Asensio Ramos and Allende Prieto2023), address this mismatch. However, the NLTE grids would also need to be expanded to cover all grid points of the extended marcs models to ensure consistency.

8.3.1. Training set selection

Before the neural networks are computed, it should actually be tested what the abundance zero-points are. In the case of several elements like Na and Al they are significant, on the order of $0.2\,\mathrm{dex}$ . When this occurs, stars with actual high abundances of $0.7-0.8\,\mathrm{dex}$ , for example in old stars and especially in globular clusters (see e.g. Carretta et al. Reference Carretta2009b), are not sufficiently covered.

One of the primary challenges in creating an optimal training set for spectrum interpolation lies in the choice of parameter sampling. A common caveat is the use of randomised, uncorrelated parameter sampling, which can lead to unrealistic combinations of elemental abundances. Elements that share a similar nucleosynthesis channel often exhibit correlated behaviour, for instance, stars with high abundances of Mg are typically also enhanced in Si, Ca, and Ti, while Na and Al tend to be elevated together. Similarly, neutron-capture elements like Y and Ba often follow similar trends (e.g. Ting et al. Reference Ting, Freeman, Kobayashi, De Silva and Bland-Hawthorn2012; Kobayashi et al. Reference Kobayashi, Karakas and Lugaro2020; Buder et al. Reference Buder2021). To better capture this behaviour in the training set, the use of scaled linear functions or normalising flows could be advantageous. These approaches would help minimise the occurrence of unlikely parameter combinations and yield a more representative sample.

For stars of the thin disk population, one could for example consider sampling from a noisy age-[X/Fe] relation to model chemical evolution (see Fig. 19, Nissen Reference Nissen2015; Spina et al. Reference Spina2016; Bedell et al. Reference Bedell2018). This approach becomes more complicated when considering the thick disk, halo, and peculiar stars, where distinct nucleosynthesis histories introduce greater variability in elemental abundance trends.

8.3.2. Masking of spectra

Because the correlation between spectral features, stellar parameters, and abundances is often complex, degeneracies can arise when two stellar properties influence similar pixels of a spectrum (e.g. C and N for CN, or $T_\mathrm{eff}$ and [Fe/H] for cool dwarfs) or two stellar properties tend to act in lockstep in actual stars (e.g. Mg, Si, and Ti as ${\unicode{x03B1}}$ -process elements). In GALAH DR2 (Buder et al. 2018), we attempted to overcome these issues by specifically masking the coefficients of spectrum interpolation, that is, effectively restricting the interpolation to only change smaller parts of the spectrum for a given stellar property.

In GALAH DR4, we have relaxed this restriction again, since we have trained on random abundance combinations in the hope of being able to break correlation degeneracies. We note, however, that too little information in spectra can again cause by-chance correlations (e.g. if neutron-capture lines are always very weak and the training set is not sufficiently large). We believe that this is the cause of the decrease in precision for Eu measurements from GALAH DR3 to GALAH DR4. The Eu abundance was mainly measured only from the weak Eu $6\,645\,$ Å line in DR3, whereas the neural networks of DR4 are not restricted to this region.

8.3.3. Flexibility of neural networks in general

The decision to use a large set of neural networks, each covering a restricted region in the $T_\mathrm{eff}$ , $\log g$ , and [Fe/H] space, was motivated by the goal of reducing the complexity required of any single model. By dividing the parameter space into smaller subsets, each neural network can be specialised and therefore less flexible, which allows for more precise modelling within its specific region. This approach avoids the trade-off faced by a single, monolithic neural network, which would either lack sufficient flexibility across the entire parameter space or be computationally more expensive to train and evaluate. For this data release, we have fixed the chosen network architecture of a 2-layer perceptron with 300 neurons and specific learning rate. While we have tested other activation functions than leaky rectified linear units, namely sigmoid, tanh and exponential linear unit functions, we found the lowest root mean square errors for our chosen activation function. Given the found issues with model fluxes above 1, we also would recommend to test a sigmoid as last activation layer of the neural network to ensure that the neural network always predicts fluxes between 0 and 1, as is expected from modelled stellar spectra. We have further tested a larger number of neurons, but found the root mean square errors to stabilise around 300 neurons for our test cases. It has to be acknowledged that due to the limit of human power to properly train and test the neural networks, we have not been able to properly test all neural networks and explore more flexible architectures. For this data release, we have decided not to rerun these steps, but make the current results available to the community. In the future, the restriction to one or only a few network models is recommended. The latter could cover regions of cool dwarfs, main-sequence turn-off stars, hot stars, and giant stars with individual models – and possibly explore the split in metal-poor and solar-like regimes. This would also decrease overhead, in particular for training and loading different models as well as possible noding effects between different models.

8.3.4. Flexibility of neural networks for extreme abundances

While this approach has proved to be powerful for all elements across their abundance ranges, we have noticed sinusoidal shapes for weak Li lines (see also Wang et al. Reference Wang2021). This is likely caused by the large dynamical range of $0 \,{\lt}\, \mathrm{A(Li)} \,{\lt}\, 4$ that has to be covered by the neural network. For Li, the more sophisticated approach is to fit Gaussian lines to multiple components in the wavelength range around $6\,708\,$ Å, measure EW(Li), which are then used to infer 3D-NLTE based A(Li) abundances. This inference is preferable to our 1D-NLTE based neural network estimates, as it is independent of the network flexibility and superior to our less accurate spectrum synthesis in 1D.

While several studies have identified that the abundances of stars in the Galactic disk are often very similar (e.g. Ness et al. Reference Ness2019), the Galactic halo offers a more diverse picture. An example is 2MASS J22353100-6658174 (140707003601047), a turn-off star with extremely high s-process abundances and actually visible lines of La and Nd in addition to the usually visible Y and Ba. In this case, the fits to the La and Nd lines are significantly weaker than the observations. GALAH DR3 actually produced reasonable fits to this star with high abundances in [Y/Fe]=1.2, [Ba/Fe]=1.5, [La/Fe]=1.5, [Ce/Fe]=1.1, [Nd/Fe]=1.9, and [Sm/Fe]=1.2. A neural network that is not trained on such high abundances is likely to improperly extrapolate stellar spectra.

While we have tried to extract abundances of chemically peculiar stars, such as carbon-enhanced metal-poor stars, the significant effect of their molecular features onto the whole stellar spectrum is not to be underestimated and can in-itself pose a problem to the flexibility of neural networks.

8.3.5. Over- and underdensities at neural network edges

While the use of one neural network to interpolate the high-dimensional spectrum space is preferable, in practice, different science cases may drive the decision to use several networks. If the science case is to reach maximum precision, one neural network that is trained on the typical spectrum could be used at the expense of properly modelling peculiar spectra. If the science case is to reach maximum accuracy, only the regions with reliable line data and spectrum synthesis might be preferable. If the science case is to find peculiar stars, a larger coverage is needed to avoid the inaccurate extrapolation of stars with extreme abundances. In practice, large collaborations likely unite all of these goals, and a compromise has to be struck among the different approaches. For future analyses, a possible solution could therefore be to follow a two-step approach of first running one generic neural network for all spectra and then using optimised neural networks – or full spectrum synthesis – on smaller target samples of specific science cases.

8.3.6. Quantitative performance of neural networks

Throughout the training of our neural networks, we optimised model parameters using a mean absolute error (MAE) loss function across the spectrum pixels. The MAE remains consistently below 0.01 for all neural networks, indicating high accuracy in model predictions, particularly for turn-off and most metal-poor stars where errors are typically below 0.001 (see Figs. 29 and 30).

Figure 29. Neural network performance shown as a function of $T_\mathrm{eff}$ vs. $\log g$ with each panel showing a different range of [Fe/H]. Colours indicate the mean absolute errors of the training (large circles) and validation (small circles) for the neural networks.

Despite these low average error rates, the performance of neural networks can vary significantly across different spectral regions. Errors are minimal in continuum areas but tend to increase around strong or strongly changing absorption features, such as those of lithium, which are discussed in Section 8.3.4. The neural network architecture does not track uncertainty for each weight and bias, limiting our ability to generate perturbed models for assessing the impact of interpolation uncertainties on derived parameters and abundances. Additionally, retraining networks with varied initial conditions to evaluate prediction stability is computationally intensive.

Figure 30. Histogram of the mean absolute errors for the neural networks. These were used as loss function during the training (blue) and validation (red) on seen and unseen spectra, respectively.

To gauge the practical impact of these uncertainties, we compared the MAE against the noise levels in the GALAH spectra. Errors significantly lower than the noise levels for stars above $T_\mathrm{eff} \,{\gt}\, 5\,000\,\mathrm{K}$ suggest that the interpolation inaccuracies minimally impact our analysis. However, for cooler stars with MAE around 0.01, interpolation inaccuracies could potentially influence precise chemical abundance studies more substantially.

Despite the high degree of accuracy achieved, the limitations outlined necessitate careful interpretation of derived parameters, especially in regions with significant absorption features (see Figs. 29 and 30).

8.4.1. Incorrect masses driving incorrect stellar parameters

We estimate masses and ages through isochrone matching, where stellar parameters (validated against photometric estimates) are known for not being fully consistent with spectroscopic values. We believe this leads to significant mismatches especially for stars close to the red clump. In this region, a small change in spectroscopic and photometric information can imply a significant change in inferred mass (e.g. from primary to secondary red clump, with the latter being 2 or more solar masses and thus significantly more than the usual $\sim$ 1 solar mass). This issue has only become noticeable after the production runs and we have therefore decided not to rerun this particular region of the parameter space for this data release. We have extensively tested the possible reasons and identified the mismatch of isochrones and actual stellar spectroscopic parameters as the cause. We have not been able to fully resolve this issue by either including a prior based on the initial mass function to weigh against massive stars (see e.g. Sharma et al. Reference Sharma2018) and move from likelihood-weighted to posterior mass estimates. Similarly, we have not been able to resolve these effects by artificially upscaling the spectroscopic uncertainties when calculating the likelihood-weighted masses. More work needs to be done to mitigate the current inconsistencies of theoretical isochrones and spectroscopic estimates.

Another solution for this particular region of the parameter space could be the use of chemical stellar evolution through the correlation of core and thus total mass with the ratio of [C/N] after the first dredge-up (Masseron & Gilmore Reference Masseron and Gilmore2015; Martig et al. Reference Martig2016), given that GALAH spectra also contain information on both elements. This could thus be used to better constrain high masses and counteract the information from isochrone-inferred masses. For this data release, the [C/N] information could at least serve as an indicator of how trustworthy high masses for giant stars are.

8.4.2. To use or not to use non-spectroscopic information?

The implementation of non-spectroscopic information, as done in our allstar module, has the advantage of overcoming spectroscopic degeneracies (as proven for the limited information on $\log g$ in the HERMES wavelength range) as well as improving accuracy and precision also for the lowest quality spectra (because $\log g$ is no longer solely dependent on the spectrum information).

However, this approach is only useful if the non-spectroscopic information is not biased (as it would be for astrometric and photometric information in the case of unresolved binarity). While the astrometric information for almost all GALAH targets is exquisite, this may not be the case for other surveys. The significant improvement from GALAH DR3 to GALAH DR4 has most definitely benefited from the improved astrometric information of Gaia EDR3 (Gaia Collaboration et al. 2021a; Lindegren et al. Reference Lindegren2021b) and Gaia DR3 (Gaia Collaboration et al. 2023) with respect to Gaia DR2 (Gaia Collaboration et al. 2018; Lindegren et al. Reference Lindegren2018). Further improvement could be expected when also taking Gaia’s photometric information into account, in addition to our use of 2MASS photometry.

8.8.1. Bug in flag_fe_h">Bug in flag_fe_h

The quality flag for iron abundance, flag_fe_h, was computed similarly to the elemental abundances, that is, by comparing the best-fitting spectrum with a spectrum with the lowest grid value of the neural network subgrids. In the case of [Fe/H], however, this is not the appropriate reference value. For example, for a star with $\mathrm{[Fe/H]} = -0.74\,\mathrm{dex}$ , the spectrum will be compared to a reference with $\mathrm{[Fe/H]} = -0.75\,\mathrm{dex}$ , which will appear essentially identical within the spectrum uncertainties, and the code concludes there are no spectral features that are significantly different. This has affected up to 34% of stars – most with detectable iron lines – and we therefore do not recommend the use of this flag at all. In the future, such a test should be performed with respect to an actually low (undetectable) amount of iron, such as $\mathrm{[Fe/H]} = -4\,\mathrm{dex}$ .

8.8.2. Fitting machinery stuck in local minimum

As laid out in Section 8.7, we have not been able to automatically flag all estimates for which our fitting machinery has become stuck in local minima, most notably at the initial value.

8.8.3. Binary or fast rotating star?

With the increasing number of turn-off stars as part of ongoing GALAH observations, we have tried to implement a more sensitive approach to identify binaries in this region. This may, however, mean that we have also introduced more false-positive detections of stars that are only fast rotating with higher $v \sin i$ , rather than being a binary system. We therefore suggest carefully considering using or neglecting the accompanying flag in GALAH DR4 (see Table 5).