The role of carbon in red giant spectro-seismology^††thanks: Based on observations collected with the high-resolution ($R\sim 80,000$) Veloce spectrograph at the Anglo-Australian Telescope.

Red clump (RC) stars are effective standard candles. The RC represents a stage of stellar evolution experienced by all low mass ($0.8-2.0\,M_{\odot}$) stars. Following the red giant branch (RGB) stage of evolution, where an inert helium core is surrounded by a shell of hydrogen fusion, during the RC phase both core helium burning and shell hydrogen burning are active. The ignition of this core helium fusion happens at the same core mass ($0.47\,M_{\odot}$; Girardi, 2016) regardless of the original mass of the star. As a result, RC stars possess well-confined luminosities, with $\log(L_{\rm{RC}}/L_{\odot})=1.95$, and have a mean dispersion of $\sim 0.17\pm 0.03$ mag in all colour bands (Hawkins et al., 2017).

One limitation of RC stars as standard candles is that they have very similar surface features, i.e. T${}_{\text{eff}}$, log $g$, [Fe/H], and luminosity, to lower RGB stars, which are not standard candles. This makes RC stars difficult to classify accurately using photometry and stellar parameters. However, the disambiguation of the RC from the RGB can be achieved effectively using asteroseismology (Montalbán et al., 2010; Bedding et al., 2011; Chaplin & Miglio, 2013; Stello et al., 2013; Mosser et al., 2014).

RC and RGB stars exhibit distinct asteroseismic oscillations due to their different internal structures. At the onset of helium fusion, convection is present in the helium core accompanied by an increase in the size of the core. This decreases the density contrast between the core and the surrounding hydrogen-burning shell (Montalbán et al., 2010, 2013), resulting in significant differences in the Brunt–Väisälä frequency. Therefore, RC and RGB stars exhibit different ranges of large frequency separations, $\Delta\nu$, and period spacing, $\Delta P$, and are as a result easily distinguishable in $\Delta\nu-\Delta P$ space (Chaplin & Miglio, 2013).

The oscillations present in red giants are measurable with sufficiently long time-series observations of photometry or radial velocity (e.g. 82 days for K2; Hon et al., 2018). However, it has been shown recently that this asteroseismic information is imprinted into the spectra of RC and RGB stars, beyond the radial velocity signal driven by Solar-like oscillations (e.g., Hawkins et al., 2018; Casey et al., 2019; Banks et al., 2023). This allows for the efficient classification of many more RC stars due to the existence of spectroscopic survey data capturing more stars across a larger volume of the Galaxy (e.g. APOGEE, GALAH; Majewski et al., 2017; Buder et al., 2021, respectively) compared to asteroseismic surveys (e.g. CoRoT, Kepler, K2, TESS; Baglin et al., 2006; Gilliland et al., 2010; Howell et al., 2014; Ricker et al., 2015, respectively)

Hawkins et al. (2018) used the data-driven algorithm The Cannon (Ness et al., 2015; Casey et al., 2016) to determine whether red giant spectra could effectively predict asteroseismic parameters such as the large frequency separation and period spacing (i.e. $\Delta\nu$ and $\Delta P$), or classify RC and RGB stars. They trained The Cannon on 1,676 red giants with single epoch infrared spectra from the APOGEE survey ($1.5-1.7\,\mu$; Majewski et al., 2017). They found that the spectra of RC and RGB stars of similar temperatures, surface gravities and metalicities are overall quite similar except around molecular CN and CO line features. Hawkins et al. (2018) suggest that the differences in these molecular features are to be expected from mixing along the RGB causing RC stars to have a lower [C/N] ratio compared to RGB stars with similar T${}_{\text{eff}}$, log $g$, and [Fe/H].

In Banks et al. (2023) we performed a broader investigation into this spectro-seismic connection. We used moderate-resolution X-Shooter (Vernet et al., 2011) spectra of 49 red giant stars covering a tenfold larger wavelength range (i.e. $0.33-2.5\mu$) compared to Hawkins et al. (2018). We followed a similar strategy to that used by Hawkins et al. (2018), and used The Cannon to generate a model trained on the spectra of the 49 stars. This model predicts the flux at each wavelength pixel as a quadratic function of stellar and asteroseismic labels, specifically T${}_{\text{eff}}$, log $g$, [Fe/H], $\Delta\nu$, and RC_Prob (the seismic probability class prediction determined through the neural network classifier detailed in Hon et al. 2018). From this investigation, similarly to Hawkins et al. (2018), we also found that molecular features, particularly CN and CO, are the most useful in classifying RC stars from RGB stars.

In addition to the CN, CO and CH features, we found that some atomic features also hold some significance, including iron, titanium and the iron peak elements vanadium and nickel. However, there are covariances in these features with other stellar labels, namely log $g$ and T${}_{\text{eff}}$ in particular. Therefore, those atomic features may not be as important as The Cannon model suggests in predicting the evolutionary state of red giants compared to other stellar parameters.

In this study we investigate these features further, utilising a larger sample of red giant stars with known classifications from TESS asteroseismology ($N=123$) and high-resolution spectra obtained with the Veloce Rosso spectrograph at the Anglo-Australian Telescope (AAT) (Gilbert et al., 2018). Utilising a higher spectral resolution allows us to explore in more detail the spectral features identified in Banks et al. (2023), and potentially identify additional classification features not resolved in the moderate-resolution ($R\sim 10,000$) spectra of the previous study. We discuss this in Section 3.2.

In addition, we analyse the spectral features that hold the most significance in predicting RC/RGB evolutionary state, thus providing insight into the astrophysical processes that drive the spectro-seismic connection of red giants. In particular, we focus on the photospheric abundances of carbon-bearing molecules and the ¹²C/¹³C isotopic ratio, which are influenced by the first dredge-up, deep mixing along the RGB, and the helium flash. This is explored in Section 4.

We made an initial collection of stars selected from a list of red giants collated from the K2- and TESS-HERMES surveys (Sharma et al., 2019, 2018, respectively) with effective temperatures $4300<T_{\text{eff}}<5100$ K, surface gravity $2.2<\log g<2.5$, and metallicity $-0.7<\rm{[Fe/H]}<0.3$. These stars have also been explored with asteroseismology data from both the K2 mission (Howell et al., 2014) and the TESS mission (Ricker et al., 2015) and their evolutionary states have been determined by Hon et al. (2018, 2022). We made observations for a total of 301 stars (see Fig. 1) with the Rosso camera of the Veloce spectrograph ($5800-9500$ Å, $R\sim 80,000$; Gilbert et al., 2018) in conjunction with the 4 m Anglo-Australian Telescope (AAT) at Siding Spring Observatory over the course of two observing semesters, 2020B and 2021B. Table 1 is a representative list of Gaia IDs, on-sky coordinates, observation date, exposure time, $W_{2}$ apparent magnitude, stellar parameters (T${}_{\text{eff}}$, log $g$, [Fe/H]) and asteroseismic labels ($\Delta\nu$ and evolutionary state, $0=\rm{RGB}$ and $1=\rm{RC}$) for the stars in our data set. A complete table detailing all red giants observed in our sample is included in the supplementary online material of this paper.

Veloce collects light from a 2.5″ diameter aperture, using a 19-element hexagonal integral field unit (IFU), and uses optical fibres to reformat that in a 19-fibre linear pseudo-slit at the entrance of the echelle spectrograph. These 19 “star” fibres are supplemented by a ThXe simultaneous calibration exposure at one end of the pseudo-slit, a single-mode laser comb simultaneous calibration fibre at the other end of the slit, and 5 “sky” fibres offset significantly on-sky from the target star fibres.

Each star was observed in a similar manner to observations collected in Palumbo et al. (2022) in a series of multiple 600s exposures, such that the total exposure time (given the conditions) delivered an S/N per pixel of $>$50 at $\sim 6670\,$Å. For example, a star with an apparent $G$-band magnitude of 9.5 mag in typical AAT 1.5" seeing required 3$\times$600s exposures, while a $G=11$ star required 6$\times$600s exposures. At the middle of each 600s exposure, a 0.5s laser comb exposure was exposed as part of the standard Veloce calibration process. The laser comb inserts $\sim 10,000$ diffraction-limited calibration lines into a single-mode fibre at the end of the Veloce pseudo-slit. Periodic ThXe exposures are obtained as well, and the observed ‘distance’ on the detector between the laser comb and ThXe spots that result is used to calibrate the (slow) time-variation of the apparent length of the pseudo-slit.

The extraction of spectra from the Veloce Rosso echellogram uses a parametric spectrograph model, the parameters of which (the effective echelle grating spacing, the effective cross-disperser grating spacing, the pseudo-slit linear plate-scale, the detector X,Y zero-point position and detector rotation) are determined from each laser comb exposure, by doing astrometry using DAOPHOT on the individual laser comb lines and treating them as “point sources”. These X,Y positions determine the spectrograph parameters for each exposure. Those parameters are then smoothed and interpolated as a function of time, to enable a spectrograph model to be derived for any intervening exposure (even if a laser comb was not obtained, as – unfortunately – does sometimes happen).

The spectrograph model for each observation then predicts the fibre tracks on the detector for each pseudo-slit fibre in each echellogram order, driving an optimal extraction for all the fibres in all the orders. The optimal extraction requires model fibre profiles for each fibre in each order as a function of Y (i.e. the high-resolution dispersion direction) position, and these are obtained by fits to flat-field observations in 60x100 pixel chunks. The environmental stabilisation of the spectrograph ensures that these profiles do not change with time. This final spectrograph model is then used to extract the spectra from the CCD images and write them into 3D data cubes (Y $\times$ fibre number $\times$ echelle order). The spectrograph model also provides a wavelength of each pixel in each order and in each fibre, and these are used to calibrate the wavelength of the optimally extracted spectra.

Because the spectrograph model is based on grating equations and a model for the relevant angles within the spectrograph, a first-order blaze function can be constructed based on the sinc² function for the relevant echelle grating diffraction angle. A polynomial correction to this “ideal” sinc² blaze function was constructed from hundreds of nights of flat-field data, to produce a single “master blaze” that can be applied to all data.

Following this, the data is then scrunched to a common constant-velocity-spacing grid and pixels associated with telluric absorption (using the telluric map from NASA Planetary Spectrum Generator for a typical AAT exposure) deeper than 2 per cent are masked as bad.

These processing steps result in extracted exposure files with individual spectra from the 19 star fibres, five sky fibres, one ThXe calibration lamp fibre and one laser comb fibre, for each of the 40 spectral orders covering the wavelength range $5800-9500$ Å.

Following data extraction, each fibre is normalised by relative fibre throughput. Then an average sky spectrum is determined for each order by averaging the flux from the sky fibres and subtracted from the flux in each star fibre. The sky-subtracted star flux in each fibre is then normalised and combined into an average stellar spectrum for each order followed by merging each subsequent order. Merging the orders of echelle spectra often results in a distinct ripple shape in the merged spectra (e.g., Cretignier et al., 2020; Różański et al., 2022). Estimating a pseudo-continuum using a low-order polynomial to normalise the flux is non-trivial. Therefore, we made use of the neural network normalisation tool SUPPNet (Różański et al., 2022). This tool filters through the domain of spectrum measurement to the domain of possible pseudo-continua using a fully convolutional neural network based on the semantic segmentation problem. Utilising this tool in our data reduction process successfully removed the distinct ripple shape and resulted in normalised continua $\sim 1$.

The final step of data reduction, before the spectra are in a suitable state for use and analysis in The Cannon, is performing velocity corrections. First is a heliocentric correction followed by correcting for the stars’ radial velocity via a Doppler correction. We achieve this with cross-correlation via the crosscorrRV function from the PyAstronomy python package (Czesla et al., 2019). We choose one star in the data set with an estimated relative velocity close to zero from the GALAH DR3 catalogue (star_id: 05185082-5707494, $\rm{RV}=0.0187\,\rm{km/s}$) to be the template spectrum. The remaining spectra, i.e. the observation spectra, are masked to a spectral window between $8480$ Å and $8680$ Å where there are numerous strong features present in all spectra such as the Ca II infrared triplet. The template spectrum is then Doppler shifted across a range of possible relative velocities ($-150<\rm{RV}<250\,\rm{km/s}$ in steps of $0.1\,\rm{km/s}$) and linearly interpolated to the wavelength points of each observation spectrum to calculate the cross-correlation function:

for $N$ data points $f_{i}$ at wavelengths $w_{i}$ depending on the velocity $v_{j}$ and weights $\alpha_{i}$, where $\Delta_{i,j}=w_{i}(v_{j}/c)$. The weights used in this calculation are simply the inverse square of the flux uncertainties.

The relative velocity between the template spectrum and an observation spectrum is the relative velocity where the cross-correlation is at a global maximum. We then Doppler shift the unmasked observation spectra with respect to the determined relative velocity, which results in different wavelength arrays for each spectrum. The Cannon requires all spectra to be on the same wavelength grid, so we perform a linear interpolation of all spectra onto a common wavelength grid. Following Doppler correction, we mask common regions across all spectra that exhibit telluric features.

Following these steps, the spectra are then in a suitable state for use and analysis in The Cannon as well as for direct comparison of spectral features for the investigation explored in Section 4.

In addition to normalised spectra on a common wavelength grid, The Cannon also requires a precise estimate of the flux variance for each pixel of the spectra. We assume the flux uncertainty to be Gaussian and hence use it to weight the influence of certain pixels when computing the best set of labels via minimum $\chi^{2}$ estimation. For computational speed, The Cannon is fed with the inverse variance or inverse of the squared flux uncertainty. Another necessary input to establish a spectral model with The Cannon are labels that describe the spectra to train the model, for example, stellar parameters such as T${}_{\text{eff}}$, log $g$, and [Fe/H]. In this investigation, we utilise those stellar parameters from GALAH DR3 (Buder et al., 2021). GALAH T${}_{\text{eff}}$ is estimated from the spectra rather than via photometry with precision to 49 K and log $g$ is estimated via bolometric relations. Buder et al. (2021) find excellent agreement with the values of log $g$ for Gaia Benchmark Stars as well as those that are cross-validated with asteroseismology. Finally, the [Fe/H] abundances reported in GALAH DR3 are determined from a global abundance of [Fe/H] from all Fe lines in the GALAH DR3 line list, resulting in a precision of 0.055 dex.

We also incorporate asteroseismic information derived from TESS asteroseismology. A total of 123 stars in our data set (shown in Figure 2) have reliable asteroseismic parameters available for our analysis. These include the large frequency separation, $\Delta\nu$, and their evolutionary state classification. We use the $\Delta\nu$ values presented in Reyes et al. (2022). These values are determined for red giants with at least six months of TESS observations via the SYD asteroseismic pipeline (Huber et al., 2009, 2011; Yu et al., 2018). Reyes et al. (2022) vet those values and determine a reliability score using a neural network classifier. This ensures that $\Delta\nu$ estimates are reliable regardless of the method used for their estimation. The evolutionary states of these red giants have been identified in Hon et al. (2018) and Hon et al. (2022).

The Cannon¹¹1The Cannon is named after Havard Computer Annie Jump Cannon as a recognition for her pivotal work in classifying stars without the need for stellar spectral models. (Ness et al., 2015; Ho et al., 2016; Casey et al., 2016) is a powerful tool that allows for the prediction of stellar parameters from observed stellar spectra. It is a data-driven algorithm that predicts stellar parameters without relying on a grid of synthetic spectra, unlike other tools that employ a physics-based approach by fitting an observed spectrum to a synthetic spectrum. One particular advantage of The Cannon is its ability to predict stellar labels from lower signal-to-noise data with comparable accuracy to current physics-based approaches.

The Cannon works in essentially two steps: the training step and the test step. The training step involves creating a generative spectral model from a set of input spectra and the stellar labels that describe those spectra (i.e. the training objects and training labels respectively). This model describes a probability density function (pdf) for the flux at every pixel in the spectrum as a function of input labels. Following the training step, the test step assumes this generative model holds for all other objects in the data set (i.e. the test objects). The spectra of the test objects are each compared to the generative model, which allows for the labels of the test objects to be solved providing, in effect, a label transfer from the training objects to the test objects. See Ness et al. (2015) for a more in-depth explanation.

Abundance determination for the stars in this data set is the topic of upcoming work, but there are useful indicators of abundance, isotopic ratio, and the physical mechanisms responsible for the spectro-seismic connection in the equivalent widths of significant features and The Cannon coefficients we are considering in this study. Our RGB stars were selected to have similar stellar parameters to our RC stars, which are fairly confined by nature. As a result, the relative strengths of absorption lines (as measured by their equivalent widths), which are the important factor for The Cannon, reflect abundances more directly than they would for a more heterogeneous set of stars, and we can use them as a rough proxy to compare the abundances between the RC and RGB stars. However, our data set does cover a range of 1 dex in [Fe/H], 800K in T${}_{\text{eff}}$ and 0.3 in log $g$, and this will add some scatter to the mapping from abundance to line strength. We expect that any trends found in the spectral feature analysis will become clearer when viewed as abundance trends.

Within the 66 spectral features, we find to be significant for predicting evolutionary state, we find that the linear coefficient for the ev_state label in The Cannon is negative for the majority of CN lines and positive for the majority of CH lines. This indicates that the CN lines are stronger and the CH lines are weaker in RC stars than in RGB stars, implying a higher nitrogen abundance and lower carbon abundance in the more evolved stars. This is the direction we expect for those abundances to evolve as a result of deep mixing during the RGB phase (e.g., Gratton et al., 2000; Martell et al., 2008).

The ${}^{12}\rm{C}/^{13}\rm{C}$ ratio for carbon isotopes is also known to change as a result of deep mixing during the RGB phase (e.g., Charbonnel et al., 1998). Its typical value drops from around 20 to around 8, and remains low in RC and horizontal branch stars. To test whether this effect can be seen in our data set and whether the ${}^{12}\rm{C}/^{13}\rm{C}$ ratio is meaningful for the spectro-seismic connection, we compared the ratio of line strength in ¹²C¹⁴N and ¹³C¹⁴N features in RC versus RGB stars. As a result of ¹²C¹⁴N depletion and ¹³C¹⁴N enrichment during deep mixing, a lower ${}^{12}\rm{C}/^{13}\rm{C}$ ratio in RC stars should, therefore, result in a lower line strength ratio in those stars (modulo the effects of varying temperatures and metallicity within our data set). We identified three pairs of ¹²C¹⁴N and ¹³C¹⁴N features within our spectra (that is, three transitions with a clear isotope shift) where at least one of the pair has been identified as significant in our The Cannon model for the prediction of red giant evolutionary state (see Table 2). We use the REvIEW code (Routine for Evaluating and Inspecting Equivalent Widths;²²2https://github.com/madeleine-mckenzie/REvIEW/tree/main McKenzie et al., 2022), an automated tool that fits individual absorption lines using the scipy.optimize function curve_fit, to determine equivalent widths for those lines in the 123 stars for which we have asteroseismic classifications.

To test for a difference in the ${}^{12}\rm{C}/^{13}\rm{C}$ ratio between RC and RGB stars in our data set, we consider $\Delta\log\frac{\textrm{EW}}{\lambda}$ (¹²C¹⁴N$-$¹³C¹⁴N), the difference between the reduced equivalent width for these isotopic line pairs, in the sense of ¹²C¹⁴N minus ¹³C¹⁴N. Due to the depletion of ¹²C¹⁴N and the enrichment of ¹³C¹⁴N along the RGB, we expect the population of RC stars to be slightly less negative than the RGB population. Figure 7 shows this difference for the ${}^{12}\rm{C}/^{13}\rm{C}$ line pair near 8043Å  across all 123 stars with asteroseismic classifications. There is a slight deviation in the distributions of the RC and RGB samples, suggesting a potential difference in the ${}^{12}\rm{C}/^{13}\rm{C}$ between the two populations due to carbon depletion from deep mixing along the RGB. We performed a two-sample Kolmogorov–Smirnov (KS) test to investigate whether the distributions of the difference in reduced EW for each line for RC and RGB stars are consistent with being drawn from the same parent distribution. This test returned a $p$-value of $2.3\times 10^{-25}$, indicating that the two distributions are more likely to have been drawn from different source populations. However, additional abundance analysis is necessary to confirm whether the ${}^{12}\rm{C}/^{13}\rm{C}$ follows the anticipated trends resulting from carbon depletion along the RGB.

Star-to-star differences in stellar parameters will add scatter to the line strengths even at fixed abundance, broadening both the RC and RGB distributions of reduced equivalent width difference. While this look at reduced equivalent widths is suggestive of a difference in the ${}^{12}\rm{C}/^{13}\rm{C}$ ratio between our RC and RGB stars, isotopic abundances determined through spectrum synthesis are needed to be sure.

This investigation is the first high-resolution study of the spectro-seismic connection of red giant stars. Here we have used Veloce Rosso spectra of 123 red giants to train a generative model with the data-driven algorithm The Cannon. We trained a model with 95 RC and 28 RGB stars with known asteroseismic classifications from TESS asteroseismology (Hon et al., 2018, 2022). With this The Cannon model, we were able to investigate which spectral features hold the most significance in predicting the evolutionary state of red giant stars, as well as probe these spectral features further to reveal more detail about the astrophysical processes that drive this spectro-seismic connection.

We followed a similar method for identifying significant spectral features for the prediction of red giant evolutionary state to that introduced in Banks et al. (2023). A spectral feature was determined to be significant in the prediction of red giant evolutionary state if the model coefficient pertaining to both the linear and quadratic terms for the evolutionary state label were greater than the 90th percentile of the distribution of those coefficients across all pixels. Following this same method as Banks et al. (2023) we found 504 such features that are significant in the prediction of red giant evolutionary state.

However, as noted in Banks et al. (2023), many of these significant features also hold some significance in the prediction of the other stellar labels (T${}_{\text{eff}}$, log $g$, and [Fe/H). To be as certain as possible that we are focusing on features that are truly influenced by the evolutionary state of red giants, we refine our list of 504 significant features to exclude those that are also found to be significant in the prediction of other stellar labels. This reduces our list of significant features to 66, which are dominated by CN molecular features ($\sim 53$ per cent). This is in agreement with previous studies (e.g., Hawkins et al., 2018; Banks et al., 2023) that also find CN molecular features to be the dominant tracer of the spectro-seismic connection of red giant stars. In this process, we found that 42 of the significant features were also significant in the X-Shooter data we used for analysis in Banks et al. (2023). With the higher spectral resolution of Veloce Rosso we found that 18 of those were actually blended lines, and for 13 of the 18 the feature with the most significance for evolutionary state was not the one we originally identified. In Appendix B we have compiled a list of the 66 significant features that are only significant for predicting the evolutionary state of red giants, and we have noted the features for which our identification has changed since the previous study.

Focusing on the features we find to be significant in the prediction of red giant evolutionary state, we found that a stronger absorption in CN features and a weaker absorption in CH features was associated with The Cannon coefficient for ev_state for the majority of significant CN and CH features, suggesting that the typically higher [N/Fe] and lower [C/Fe] abundance in RC stars relative to RGB stars is an important contributor to the spectro-seismic connection.

We also considered the relative strengths of absorption in CN isotopic pairs, i.e., the same transitions for ¹²C¹⁴N and ¹³C¹⁴N. There are three such pairs of lines in our red giant spectra where at least one member of the pair is identified as significant only to the prediction of red giant evolutionary state. We measured the reduced equivalent widths for these lines across all our red giants with asteroseismic classifications using the automated EW estimator review. We then performed a two-sided KS test to investigate whether the distributions of the difference in reduced EWs between ¹²C¹⁴N and ¹³C¹⁴N were significantly different between the RC and RGB populations. For the line pair near 8043Å, this test returned a $p$-value of $2.3\times 10^{-25}$, indicating that we cannot reject the hypothesis that the two distributions originated from two different parent populations.

These tendencies in line strength behave as we would expect if the physical processes that change the surface abundances and isotopic ratios in red giant stars, such as deep mixing and the helium flash, are the driving forces of the spectro-seismic connection in red giants. Follow-up work including elemental and isotopic abundance determination will help to solidify this connection and quantify whether red giants with similar T${}_{\text{eff}}$ and log $g$ can be distinguished by quantifying the C and N abundances or measuring ${}^{12}\rm{C}/^{13}\rm{C}$ without data-driven analyses such as those performed with The Cannon.

This work builds on previous investigations, first by Hawkins et al. (2018) and Ting et al. (2018) using APOGEE ($1.5-1.7\,\mu$, $\rm{R}\sim 28~{}000$) and LAMOST ($3600-9000\,$Å, $\rm{R}\sim 1800$) spectra for large samples of red giants, followed by a broad wavelength investigation by Banks et al. (2023) with red giant spectra from the VLT/X-Shooter spectrograph ($0.33-2.5\,\mu$, R$\sim 10~{}000$). Molecular features involving carbon (i.e. CN, CO and CH) were found to be significant in the prediction of red giant evolutionary state in these studies; however, further investigation was required to understand which astrophysical processes could be responsible for the spectro-seismic connection.

Using the coefficients of The Cannon model for our 123 red giant stars with asteroseismic classifications, we find that the spectral features in our Veloce Rosso sample that are significant for separating RC and RGB stars are likely to correspond to the surface abundance changes caused by deep mixing on the RGB. Specifically, the depths of CN and CH absorption lines, along with the line depth ratios for the same transitions in ¹²C¹⁴N versus ¹³C¹⁴N correlate to The Cannon coefficient for ev_state. This suggests that RC stars are expected to display lower [C/Fe], higher [N/Fe], and a lower ${}^{12}\rm{C}/^{13}\rm{C}$ ratio compared to RGB stars.

The accumulated result of ongoing abundance changes caused by the first dredge-up and deep mixing on the RGB must be visible in the abundances of RC stars, which have already experienced their full RGB lifetime plus the helium flash at the tip of the RGB. However, a detailed abundance analysis based on these same spectra is necessary to be sure that the differences we find in absorption line strength between RC and RGB stars is truly representative of the expected changes in abundance during red giant evolution. A study on this topic is currently in progress.

Building from the idea that red giant evolution is the main driver of the spectro-seismic connection, we can make a number of testable predictions for the observable properties of RGB versus RC stars:

• •

  The spectroscopic differentiation of upper RGB stars from RC stars will be more difficult than for lower RGB stars due to less distinct abundances. This does not present a significant difficulty, since these stars are more easily differentiated in T${}_{\text{eff}}$ - log $g$- luminosity space.

• •

  The spectro-seismic connection should be more pronounced in metal-poor red giants because deep mixing is much more efficient in red giants with lower metallicity. For example, Martell et al. (2008) found that the carbon depletion rate from deep mixing in red giants is doubled at a metallicity of $\text{[Fe/H]}=-2.3$ as compared to $\text{Fe/H}=-1.3$.

• •

  Oxygen may also be a spectro-seismic indicator because it is also slightly depleted during phases of deep mixing (Weiss et al., 2000; Johnson & Pilachowski, 2012). We do not find a significant correlation between atomic oxygen spectral features and the evolutionary state of red giants in our data. In addition, there are no CO lines present in the wavelength coverage of Veloce Rosso. Other moderate- to high-resolution spectroscopic surveys that derive oxygen abundance, e.g. APOGEE (Majewski et al., 2017), may be able to investigate this further.

• •

  Lithium is often of high interest in studies of red giants; however, it will not be useful for this kind of study. Lithium is almost completely depleted by the first dredge-up and the strong mixing at the RGB bump (Lind et al., 2009), leaving little behind to allow for the detection of a significant difference between the lower RGB and RC.

• •

  Previous studies (e.g., Hawkins et al., 2018; Ting et al., 2018; Banks et al., 2023) have discussed whether the helium flash may also be a driver of the spectro-seismic connection seen in red giants. Comparing the abundances of secondary RC stars to primary RC stars with the same metallicity might be a way to test this, since the secondary RC stars ignite helium fusion smoothly, without a flash.

In the pursuit of spectroscopically identifying RC stars, we have found that stars falling within the specific ranges of T${}_{\text{eff}}$, log $g$ and [Fe/H] explored in this study ($4330<T_{\text{eff}}<5030$ K, $2.2<\log g<2.5$, and $-0.95<\text{[Fe/H]}<0.31$) have spectral features identifiable with high-resolution spectra that are effective for RC classification. Leveraging these features is particularly valuable for Galactic archaeology, as RC stars serve as standard candles. While the limiting magnitude of Veloce Rosso, $T\sim 12\,$mag, confines observations to a relatively limited volume of the Galaxy compared to those of TESS and Kepler ($\sim 14\,$mag; Hekker et al., 2011; Stello et al., 2022), several other spectroscopic instruments such as VLT/UVES, Magellan/MIKE, Keck/HIRES, and Gemini/GHOST (Dekker et al., 2000; Bernstein et al., 2003; Vogt et al., 1994; Rantakyro et al., 2024, respectively) provide comparable high-resolution capabilities to Veloce Rosso while offering the advantage of fainter limiting magnitudes, $\sim 19\,$mag. This enables the accurate mapping of stellar population and abundance trends over a significantly larger volume of the Galaxy than Gaia parallax. The reach of RC star samples in spectroscopic surveys will expand from the 6 kpc covered by current-generation surveys like GALAH (Buder et al., 2021) and APOGEE (Majewski et al., 2017) to 16 kpc in upcoming projects such as 4MOST (de Jong et al., 2019) and WEAVE (Dalton et al., 2012), and potentially up to 100 kpc in proposed future projects like WST (Pasquini et al., 2018) and MSE (The MSE Science Team et al., 2019).

The authors would like to thank the anonymous reviewer for their insightful comments on the contents of this paper.

The authors would also like to thank A. R. Casey for providing an updated version of The Cannon and guidance during the use and analysis of the program.

KAB and SLM acknowledge funding support from the UNSW Scientia program. SLM is supported by the Australian Research Council through Discovery Project grant DP180101791. DS is supported by the Australian Research Council through Discovery Project grant DP190100666.

The authors acknowledge the Traditional Custodians of the land on which the analysis for this investigation was conducted, the Bedegal people of the Eora nation. The authors also acknowledge the Traditional Custodians of the land on which the Anglo-Australian Telescope is situated, the Gamilaraay people. The authors pay respect to elders both past and present and extend that respect to other Aboriginal and Torres Strait Islander peoples reading this paper.

The data in this work were obtained with the Veloce spectrograph at the Anglo-Australian Telescope through programs A/2020B/18 and A/2021B/07. Raw data are available from the AAT archive through AAO Data Central (archives.datacentral.org.au). TESS asteroseismic classifications from Reyes et al. (2022) can be searched and downloaded via the VizieR astronomical catalogue service.