Main

TYC 8998-760-1 b (hereafter TYC 8998 b)10 is a widely separated planetary mass companion around a young solar analogue TYC 8998-760-1 (also known as 2MASS J13251211−6456207) with an age of about 17 Myr (ref. 11). With the recent detection of a second planet12, it is part of the first directly imaged multiplanet system around a solar-type star. TYC 8998 b is located at a projected separation of 160 au, with an estimated mass of 14 ± 3 MJ. We observed the planet on two nights, 5 and 19 June 2019, using Spectrograph for Integral Field Observations in the Near Infrared (SINFONI)13,14 installed at the Cassegrain focus of Unit Telescope 3 (UT3) of the Very Large Telescope of the European Southern Observatory at Cerro Paranal, Chile. The observations were performed in the K-band (1.95–2.45 μm), providing a spectral resolving power of about R = 4,500. We extracted the spectrum of TYC 8998 b from 2.10 μm to 2.45 μm, as detailed in Methods.

As shown in Fig. 1, the planet spectrum is dominated by molecular features from water (H2O) and carbon monoxide (CO). The 12CO bandheads of the vibrational transitions v = 2–0, v = 3–1 and v = 4–2 bandheads are visible at 2.2935 μm, 2.3227 μm and 2.3535 μm, respectively. When we compare the observed spectrum with the best-fit model obtained by atmospheric retrieval, an extra emission signature at 2.166 μm is seen in Fig. 1c, which is identified as the hydrogen Brackett γ (Brγ) recombination line. This is probably an indication of ongoing accretion of circumplanetary material onto the planet. We estimated a mass accretion rate of 10−9.4±1.3 M☉ yr−1 using the Brγ line luminosity (Methods). Future observations at longer wavelengths and polarimetric data can provide further insights into the circumplanetary disk and accretion process15.

Fig. 1: Observed SINFONI spectrum of exoplanet TYC 8998 b and cross-correlation signal of 13CO.
figure 1

a, The observed spectrum (flux density, Fλ) is shown in black, the best-fit model including all carbon isotopes is shown in cyan and the best-fit reduced model, without 13CO, is shown in red. The typical uncertainty per pixel in the observed spectrum is denoted by the error bar (1σ) on the upper left. b, A zoom-in over the 2.34–2.40 μm spectral region, centred on the 13CO bandhead. Specific opacity from 13CO is located where the reduced model without 13CO (in red) is higher than the observed spectrum. c, The residuals (spectrum minus best-fit models, with the residuals of the reduced model in red) revealing the Brγ emission feature at 2.166 μm and Na I absorption lines. d, Observational residuals in red are compared with the 13CO absorption model in black (the difference between the best-fit full model minus the same model with the 13CO opacity removed), revealing the similarity between the observations and models. e, CCFs between observational residuals and the 13CO model, as shown in black. The dashed line shows the autocorrelation of the 13CO model, scaled to the peak of the CCF.

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To characterize the atmosphere of the planet, we performed a Bayesian retrieval analysis on the spectrum using the radiative transfer tool petitRADTRANS (pRT)16, connected to the nested sampling tool PyMultiNest17. We focus on revealing the presence of 13CO, which is expected to be the most detectable isotopologue in the atmospheres of gas giants18, and measuring the isotopologue abundance ratio 12CO/13CO. In addition, we aim to constrain atmospheric properties of the planet, such as the carbon-to-oxygen ratio C/O, which may shed light on the conditions during the formation of the planet19.

We set up the retrieval model in a similar way as used in previous work on HR 8799 e (ref. 20; Methods). The model consists of nine free parameters: the planet radius RP, surface gravity log g, metallicity [Fe/H], the carbon-to-oxygen ratio C/O, the isotopologue abundance ratio 12CO/13CO, three parameters for the temperature–pressure (T–P) profile and a spectral slope correction factor fslope, arising from uncertainties in the calibration of the observed spectrum. We ran retrievals on the spectrum of TYC 8998 b using two sets of models: the full model including 13CO and the reduced model excluding 13CO. The setups of the two models are identical, except that we removed 13CO from the opacity sources (and therefore the 12CO/13CO parameter) in the reduced model. The best-fit model spectra are compared with the observed spectrum shown in Fig. 1. The difference between the two models is visible at the 13CO bandheads around 2.345 μm (Fig. 1b). The full model provides a substantially better fit in terms of χ2 (Extended Data Fig. 1c) as a result of the additional 13CO opacity.

To qualitatively reveal the signature, we compare the observational residuals (that is, the observed spectrum with the best-fit reduced model subtracted off) to the noise-free template of the 13CO signal (that is, the best-fit full model subtracted by the same full model with the 13CO abundance set to zero). The observational residuals follow the expected 13CO signal, especially the dip caused by the 13CO bandheads and well aligned individual lines (Fig. 1d), which indicates the presence of 13CO in the data. We also cross-correlated the residuals with the 13CO model (Fig. 1e). The cross-correlation function (CCF) between the observation and model follows the autocorrelation function (ACF) of the model well. The broad feature in the CCF (and ACF) reflects the effect of 13CO bandheads, and the peak at zero radial velocity co-adds the individual lines of the 13CO signal.

In terms of the significance of the 13CO detection, comparing the Bayesian evidence (Z) of the reduced model with the full model allows us to assess the extent to which the model including 13CO is favoured by the observations. In the Bayesian model comparison, the Bayes factor Bm (calculated by the ratio of Z) is used as a proxy for the posterior odds ratio between two alternative models21. As a result, the Bayes factor between two models is ln(Bm) = ∆ln(Z) = 18, meaning that the observation favours the full model (including 13CO) at a significance level of >6σ.

The central values of the inferred parameters and their 90% uncertainties from the atmospheric retrieval are RP = 1.82 ± 0.08 RJ, log g = \({4.51}_{-0.29}^{+0.34}\), [Fe/H] = \({0.07}_{-0.18}^{+0.31}\), C/O = \({0.52}_{-0.03}^{+0.04}\) and 12CO/13CO = \({31}_{-10}^{+17}\) (Fig. 2b, c). Hence, while the C/O ratio is measured to be near the solar value, the atmosphere of the planet is observed to be rich in 13CO. The inferred T–P profile and posterior distribution of parameters for both models are shown in Extended Data Fig. 2.

Fig. 2: Spectral retrieval results.
figure 2

a, The retrieved temperature–pressure profile. The shaded regions with decreasing grey scale show 1σ, 2σ and 3σ temperature uncertainty envelopes, respectively. The grey dotted lines represent the condensation curves of three potential cloud species. The black dashed line shows the flux average of the emission contribution function. b, Posterior distribution of CO isotopologue abundance ratio 12CO/13CO. The vertical dashed lines denote the 5%, 50% and 95% quantiles (90% uncertainties) of the distribution. c, Posterior distribution of carbon-to-oxygen ratio C/O. The central values and their 90% uncertainties are given in the top right corner.

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The 12CO/ 13CO ratio of \({31}_{-10}^{+17}\) we infer for TYC 8998 b is lower (2.5σ) than that measured in the local interstellar medium (about 68; refs. 4,5), with the latter also lower than the ratio of about 89 observed in the Solar System1, which is partly thought to be the consequence of galactic chemical evolution, and reflects the relative degree of primary to secondary processing in stars4,5,6. Young systems formed in the local environment are expected to inherit the 12C/13C ratio of about 68. However, the measurements of complex carbon-bearing molecules (which formed at low temperature from CO on grains) towards protostars result in a low 12C/13C ratio of about 30, indicating an enhancement of 13CO or 13C in the ice22,23. This may be attributed to carbon fractionation processes, including isotopic ion-exchange reactions8, isotope-selective photodissociation9 and ice/gas isotopologue partitioning7. The isotopic ion-exchange reactions enhance the 13CO abundance in the gas at low temperatures, followed by the freeze-out of CO gas onto the grains to increase the 13CO abundance in the ice22. The ice/gas isotopologue partitioning, owing to the slightly different binding energies of the two isotopologues, may contribute to the enrichment of 13CO in the ice, but only in very narrow temperature ranges as shown by laboratory experiments24. The isotope-selective photodissociation alters the 12CO/13CO ratios at different layers in circumstellar disks because the self-shielding of the rarer isotopologues kicks in at a deeper layer into the disk25. The preferential photodissociation of 13CO generates more atomic 13C, which freezes out onto the ices in the midplane to enrich the 13C in other complex carbon-bearing molecules. Detailed modelling incorporating these fractionation processes in protoplanetary disks suggests that the 13CO in the gas could also be enhanced at intermediate layers25. Planets may be able to accrete the 13CO-rich gas from these intermediate layers through vertical accretion26. Alternatively, with the warm gas cycling to cold regions through vertical mixing and then freezing out onto grains, the enrichment may be inherited by pebbles and planetesimals forming there.

In this light, we postulate a framework to explain the 13CO-rich atmosphere of TYC 8998 b, and the near-constant 13C abundance in Solar System objects. It is generally accepted that in the inner parts of a protoplanetary disk, carbon is mostly present in the gas phase as CO, but locked into ices at larger distances, in particular in the disk midplane (Fig. 3). The CO snowline—the transition region between the gaseous and solid phase—is governed by the level of stellar irradiation and is expected to be at around 20 au for young solar-mass stars27 such as TYC 8998. The current location of TYC 8998 b at >160 au is so far out that it has probably formed outside the CO snowline. This implies that it has accreted the bulk of its carbon from ices, which is generally enhanced in 13CO and 13C, as is discussed above, resulting in the observed 13CO-rich atmosphere. Our spectral analysis also points to an atmospheric C/O ratio of \({0.52}_{-0.03}^{+0.04}\), further suggesting that the planet was indeed formed beyond the CO snowline19. Similarly, for other widely separated exoplanets formed outside the CO snowline with substantial ice accretion, we would also expect 13CO-rich atmospheres.

Fig. 3: Cartoon of the birth environments of planets in a protoplanetary disk.
figure 3

The two planets inside the CO snowline denote Jupiter and Neptune at their current locations, whereas TYC 8998 b is formed far outside this regime, where most carbon is expected to have been locked up in CO ice and formed the main reservoir of carbon in the planet. We postulate that this far outside the CO snowline, the ice was 13CO-rich or 13C-rich through carbon fractionation, resulting in the observed 13CO-rich atmosphere of the planet. A similar mechanism has been invoked to explain the trend in D/H within the Solar System. Future isotopologue measurements in exoplanet atmospheres can provide unique constraints on where, when and how planets are formed.

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As, in contrast, the Solar System planets are thought to be formed within the CO snowline, we argue that the lack of any substantial enrichment in 13C in their atmospheres is because the bulk of their carbon reservoirs originate from CO gas, not ices. Although Oort cloud comets now reside in the outer Solar System far beyond the snowline, they may have also formed in the inner disk and later been scattered out through the interaction with giant planets28, therefore exhibiting the same 13C ratios as other objects in the Solar System.

As an analogy of 13CO enrichment through ice accretion, the deuterium-to-hydrogen ratios (D/H) of Uranus and Neptune are found to be enhanced compared with Jupiter, attributed to an increasing contribution from accretion of HDO-rich ices beyond the water snowline29. With the caveat that carbon fractionation is orders of magnitude smaller than deuterium fractionation, it could still result in a 13C enrichment of a factor of two. For a further understanding of the role of carbon fractionation in planet formation, it will be important to obtain a quantitative assessment of the effects through detailed disk modelling. Future measurements of exoplanet 12C/13C (and D/H) ratios18,30 can provide an exciting way to constrain when, where and how planets are formed.

Methods

Observations and data analysis

We observed TYC 8998 b on two nights, 5 and 19 June 2019, using SINFONI13,14 installed at the Cassegrain focus of UT3 of the Very Large Telescope of the European Southern Observatory (ESO) at Cerro Paranal in Chile, under the ESO programme 2103.C-5012(C) (principal investigator, A.J.B.). The observations were performed in the K-band (1.95–2.45 μm), providing a spectral resolving power of about 4,500. The spatial pixel scale is 0.025″ per image slice; therefore, 32 slices in total amount to a field of view (FOV) of 0.8″. Both the primary star and the planet c are outside the FOV (Extended Data Fig. 1). As a result of the large planet–star separation (about 1.7″) and the planet-to-star contrast (magnitude difference of about 6.4)10, the starlight contamination is small. We obtained 2 × 24 science frames with a number of detector integrations of 2 and an exposure time of 150 s each. The observations were performed in pupil-stabilized mode. During the first night, the airmass ranged from 1.31 to 1.34, the seeing varied from 0.81″ to 2.63″, and the atmospheric coherence time reached 12 ms with the intervention by clouds. Given the unstable atmospheric conditions on the first night, a second night of observation was performed, delivering a seeing ranging from 0.51″ to 1.07″ at an airmass between 1.31 and 1.41 and a coherence time between 2.4 ms and 9.1 ms. During each night, we took three frames of the sky before, during and after the science frames with the same exposure setup. In addition to the science target, one featureless B-type standard star was observed each night, HIP 57861 and HIP 72332, respectively, serving for telluric and spectrophotometric calibration.

The raw data were first reduced using the SINFONI pipeline to correct for bias, flat fielding, sky background and bad pixels. Then we obtained the intermediate two-dimensional data products, which are composed of 32 vertical strips, each representing the spectra taken over an individual slitlet with its own wavelength solution. The target spectrum shows as vertical trails on slitlet images. For each science exposure, we extract the target spectrum from the intermediate two-dimensional frame. We focus our analysis on the brightest four slitlet images, where the spectrum was extracted using the optimal extraction algorithm31. This algorithm accounts for background (including the starlight contamination) and automatically rejects outliers caused by bad pixels and cosmic rays, and delivers an optimal signal-to-noise ratio (SNR). We subsequently obtained four target spectra for every science exposure. All the spectra were then linearly interpolated to a common wavelength grid and optimally combined to form a combined spectrum for each night. During the process, we discarded two frames taken on the first night, the data quality of which was too low to clearly identify the target in the data (using a threshold of three times the background noise level) as a result of the poor atmospheric conditions.

The broad-band shapes of the final spectra per night obtained above require cautious calibration. First, the efficiency of the instrument + telescope varies with wavelength. This effect can be corrected by comparing the observed spectral shape of the standard star to its theoretical spectrum. For the standard stars on the first and second nights, we used PHOENIX stellar models32 with an effective temperature of 13,500 K and 10,800 K, respectively33,34. As the observed standard star spectra are firmly in the Rayleigh–Jeans regime, potential uncertainties in effective temperature have only marginal effects on the spectral slope. Second, atmospheric dispersion affects the overall spectral shape differently for different slitlets. The optimal extraction method we adopted can further aggravate this bias as different weights were assigned to slitlets when combining the spectra. To determine the most accurate spectral shape, we extracted spectra again while avoiding weighting. We started from the data cubes reconstructed by the SINFONI pipeline, and took a circular aperture of about five times the full-width at half-maximum to sum up the flux at each wavelength, ensuring that all the flux from the object was included. This plain extraction method was performed on the target as well as standard stars on both nights. In this way, we derived spectra for the target that have a lower SNR but a more accurate spectral shape. The broad-band shape of this spectrum for each night was then applied to the optimally extracted spectrum by fitting a second-order polynomial to the division between both spectra. After the spectrophotometric correction, the shape of the combined spectra for the two nights differs by about 2% between 2.1 μm and 2.4 μm.

We used the ESO sky software tool Molecfit35 v3.0.1 to perform telluric corrections on the final spectra of each night. The tool uses a line-by-line radiative transfer model to derive telluric atmospheric transmission spectra that can be fitted to observations. For telluric model fitting, we removed a preliminary planetary model from the observed spectrum to minimize effects from the planetary spectrum on the telluric features. The fitting wavelength region is 2.19–2.43 μm, which contains the majority of strong telluric lines caused by methane (CH4) and H2O in Earth’s atmosphere. Molecfit accounted for the molecular abundances, instrument resolution, continuum level and wavelength solution that best fit the observations. The atmospheric transmission model for the entire wavelength range was then derived based on the best-fit parameters. Subsequently, the telluric model was removed from the combined spectrum to obtain the telluric-corrected spectrum. However, the correction is not perfect, resulting in artefacts at the red end of the spectra. The wavelength region beyond 2.4 μm, not important for our goals, is therefore masked in further analysis.

After telluric removal, we combined the spectra of both nights into one master spectrum. We noted that the spectrum of the first night turned out to be of lower signal to noise than that of the second night, as expected from the observational conditions. We shifted the two spectra to the planetary rest frame and weighted-combined them by SNR squared. The SNR of each spectrum was measured by the standard deviation of the residuals (that is, the observation minus the model spectrum generated by retrieval fitting) in the wavelength range from 2.35 μm to 2.4 μm. The master spectrum was finally scaled to the photometric flux of 8.8 × 10−16 W m−2 μm−1 at 2.25 μm (ref. 10). In this way, we obtained a final master spectrum of the companion shown in Fig. 1, with an SNR of about 50 near 2.2 μm and about 0 at the red end. We note that the uncertainty per wavelength step is almost constant along the wavelengths and independent of the flux of the object because the observations are read-noise limited. The red end of the spectrum, therefore, has lower SNR because of the lower object flux level and strong telluric absorption.

Atmospheric retrieval model

For our atmospheric retrieval, we performed a Bayesian analysis using the radiative transfer tool pRT16, connected to the nested sampling tool PyMultiNest17, which is a Python wrapper of the MultiNest method36. To model the temperature structure of the planet atmosphere, we consider two classes of parameterization of the T–P profile: the analytical and flexible model. The first temperature model involves analytical solutions for self-luminous atmospheres assuming a grey opacity. We set the temperature according to Eddington approximation: T(τ)4 = 0.75Tint4(2/3 + τ), where the optical depth τ is linked to the pressure by τ = δPα, with δ and α as free parameters. We defined Pphot as the pressure where τ = 1. Hence, δ = Pphot−α. This temperature model therefore has three free parameters, Tint, α and Pphot, with Tint as the effective temperature. The Eddington solution leads to an isothermal upper atmosphere. Although this seems unrealistic, the model still works well because the medium-resolution observations barely probe that high up in the atmosphere. At low altitudes, the atmosphere transitions to convective, where we force the temperature gradient onto a moist adiabat.

In the flexible temperature model, we focus on the temperature from 0.01 bar to 10 bar, where the contribution function of the observed spectrum peaks. The temperature outside this range is considered to be isothermal. We set four temperature knots spaced evenly on a log-scale pressure within 0.02 bar to 5 bar. The T–P profile is obtained by spline interpolation of the temperature knots in the log space of pressure. There is no physical reasoning behind this T–P profile, therefore imposing fewer prior constraints on the solution.

The chemistry model used in our retrievals is detailed in ref. 20. In short, the chemical abundances are determined via interpolation in a chemical equilibrium table using pressure P, temperature T, carbon-to-oxygen ratio C/O and metallicity [Fe/H] as inputs. Then pRT computes synthetic emission spectra using temperature, chemical abundances and surface gravity as inputs.

We tested the retrieval framework to ensure parameters can be correctly recovered by using synthetic spectra. Using the forward model presented above, we generated a mock spectrum at 2.1–2.45 μm, with a spectral resolution of 4,500. The flux error was set to be constant, leading to an SNR of around 50 at 2.2 μm, which is similar to that in the master spectrum. The mock spectrum was then perturbed by random noise generated according to this uncertainty in flux. We were able to recover all parameters within a 1σ interval, validating the capability of the retrieval model.

Retrievals on the TYC 8998 b spectrum

We set up the retrieval model using the analytical T–P profile, with eight free parameters, RP, log g, [Fe/H], C/O, Tint, α, Pphot and 12CO/13CO. The priors of these free parameters are listed in Extended Data Table 1. In the full model, we included 12CO, H2O, CH4, ammonia (NH3) and the isotopologue 13CO as line opacity species, and the collision-induced absorption of H2–H2 and H2–He. As for the reduced model, we removed 13CO from the opacity sources. We used the line-by-line mode of pRT to calculate the emission spectra at high spectral resolution. To speed up the calculation, we took every fifth point of opacity tables with λ/Δλ ≈ 106. This sampling procedure, which has been benchmarked against the full tables, shows negligible effects on the synthetic spectra and retrieval results. The synthetic high-resolution spectra were convolved with a Gaussian kernel to match the resolving power of the instrument (R ≈ 4,500), then binned to the wavelength grid of the master spectrum, and scaled to the observed flux according to RP and distance of the target.

In addition, as we noted above, there exists up to 2% discrepancy in terms of the broad-band spectral shape between the two nights of observations. Therefore, before comparing the synthetic model spectra to the observation, we multiplied the models by a linear slope spanning from 1 − fslope to 1 + fslope in the wavelength range from 2.1 μm to 2.4 μm, where we introduced the slope correction factor fslope as a nuisance parameter to marginalize the uncertainty in the spectral shape. The retrieval process was performed by PyMultiNest, which uses 4,000 live points to sample the parameter space and derives the posterior abundances of the fit. We ran MultiNest in ‘importance nested sampling’ mode with a constant efficiency of 5%. The outcome is shown in Extended Data Fig. 2. We also used the flexible T–P profile to consolidate the retrieval results. The inferred parameters are found to be robust for different T–P model setups.

The retrieved value of log g should be treated with caution, because we note that any small changes in the wavelength coverage of the fitting or the broad-band shape of the spectrum can result in notably different values. As also indicated in other retrieval studies37, CO and H2O features in the K-band are not very sensitive to log g. Free retrievals in the K-band alone are therefore unable to place robust constraints on the surface gravity and hence the planet mass. We also run retrievals with prior constraint on the planet mass. The solution converges to a lower surface gravity and the same isotopologue ratio, suggesting that the inaccurate log g does not affect the inference of the 12CO/13CO ratio.

We compared the Bayesian evidence (Z) of the reduced model with the full model (Extended Data Fig. 1c), the difference of which is related to the Bayes factor Bm that translates to a frequentist measure21 of more than 6σ significance of the 13CO detection. Although the evidence is dependent on the prior of the 13CO abundance (Extended Data Table 1), we noted that increasing the prior range of log(13CO/12CO) from (−12, 0) to (−20, 0) did not lead to a notable change in the final evidence, and both of the priors are much broader than the ratio that one would expect in reality.

Effects of clouds

Clouds are ubiquitous in planetary atmospheres and can have an important role in the interpretation of spectra. We investigated their potential effects on the 13CO measurement by including clouds in the retrieval models. We used the cloud model detailed in ref. 19, which introduced four additional free parameters: the vertical eddy diffusion coefficient Kzz, the settling parameter fsed, the width of the log-normal particle size distribution σg and the mass fraction of the cloud species at the cloud base log X. The temperature of TYC 8998 b is too high to form magnesium- and iron-bearing condensates in the atmosphere. We therefore considered a more refractory species, aluminium oxide (Al2O3), as the source of cloud opacity38. After testing cloudy models, we found the solution converged to cloud-free atmospheres, and the inferred parameter values remained unaffected, because the atmospheric temperature (Fig. 2a) is too warm to form optically thick clouds that could make a substantial impact on the spectrum. Therefore, we did not include clouds in our nominal models.

Constraining mass accretion rate

The Brγ emission line (Fig. 1) provides constraints on the mass accretion rate of the planet. We measured a Brγ line flux of 7.6 (± 0.9) × 10−18 W m−2, and a line luminosity LBrγ compared with the solar luminosity L☉ of log(LBrγ/L☉) of −5.7 ± 0.5, from which we estimated the accretion luminosity log(Lacc/L☉) to be −2.7 ± 1.3 using the linear correlation given by ref. 39. Combining this with the retrieved values of radius and surface gravity, we derived a mass accretion rate of 10−9.4±1.3 M☉ yr−1.

Additional assessments of the reliability of 13CO detection in TYC 8998 b

We further assess the reliability of the 13CO detection in several ways. We study the 13CO signal for the individual nights and that from the first and second bandheads separately, and investigate the impact of inaccurate telluric line removal and the effects of possible other opacity sources. In addition, we show that for an easier accessible, nearby, isolated brown dwarf, archival spectroscopy data of the same 13CO features at higher spectral resolving power show a strong signal—as expected from our TYC 8988 b observations (albeit with a more typical 12CO/13CO ratio).

Analysis on data of individual nights and bandheads

To assess whether the 13CO signal is present on both nights, we performed the retrieval and cross-correlation analyses as detailed above for each night separately. The retrieval results are shown in Extended Data Fig. 3. 13CO is detected on both nights but at a lower significance, as expected. The derived constraints on 12CO/13CO are consistent with each other. There is around 2% difference in the slope correction factor fslope on the two nights, as already noted in the spectral calibration above. This probably contributes to the slight discrepancies in the derived values for log g and C/O. The CCFs are shown in Extended Data Fig. 4, also indicating that 13CO is detected on both nights individually, albeit at lower significance.

We also investigated whether the two bands of 13CO, starting at 2.345 μm and 2.374 μm, can both be detected individually. We examined this by separating the wavelength region into two parts, 2.34–2.37 μm and 2.37–2.40 μm, then calculating the cross-correlation in each part. Before the cross-correlation, the residuals were high-pass filtered using a Gaussian kernel with a width of 3 nm to remove the low-frequency variation in residuals and enhance the signal. The low-frequency variation, especially apparent in the second part of the data, introduces broad-band shape in the CCF, which suppresses the signal. The filtered residuals are shown in Extended Data Fig. 4c, and the cross-correlation results in Extended Data Fig. 4d. The CCF for both bands show peaks at zero velocity, while the signal from the second band is less significant. We argue that although the expected absorption from the two bands is similar, the signal to noise of the spectral data at the 2.374-μm bandhead is lower due to the stronger telluric absorption in this region. This is highlighted in Extended Data Fig. 5a, showing the telluric transmission spectrum, observational residuals from the reduced model (without 13CO), and the 13CO model. We believe that it is for this reason that the 13CO signal from the second bandhead is not as significant as from the first bandhead.

Impact of telluric absorption

Extended Data Fig. 5b shows the CCF between the 13CO model and the telluric line spectrum, demonstrating no evident signal. It indicates that the observed 13CO signal is not caused by any under- or overcorrection of telluric lines.

Other potential opacity sources

In the retrieval models, we include the major molecular opacity sources (CO, H2O, CH4 and NH3) that have a role in the K-band. We inspected other potential absorbers given the expected temperature, including carbon dioxide (CO2), hydrogen cyanide (HCN) and acetylene (C2H2). None of them shows notable features at the same wavelength region as 13CO. Moreover, we performed retrieval analysis to marginalize over these absorbers. Adding these molecules to the retrieval model does not change the inferred value of any parameter. Therefore, it is not plausible that the detected 13CO feature is caused by these molecules.

Archival reference data of the young brown dwarf 2M0355

To boost confidence in the detection of 13CO in TYC 8998 b, we analysed archival data of the young brown dwarf 2M0355 (ref. 40). This object resembles in several ways a young super-Jupiter like TYC 8998 b, but as it is isolated, and located nearby at 8 parsec, it is spectroscopically much more accessible. From our 13CO detection in TYC 8988 b, it is expected that 13CO should be straightforward to see in 2 h of data41 from the near-infrared echelle spectrograph (NIRSPEC) at the Keck telescope, in particular at a spectral resolving power of λ/Δλ ≈ 27,500. Our detailed analysis will be presented in a forthcoming publication. Extended Data Fig. 6 shows the spectrum, best-fit model and the 13CO cross-correlation signal, after performing an identical analysis— targeting the same features as our SINFONI data of TYC 8998 b. We retrieve a 12CO/13CO isotopologue abundance of around 90–100, similar to the solar value. It will be intriguing to compare measurements between isolated brown dwarfs and exoplanets, revealing the role of the carbon isotopologue ratio as a tracer of planet formation.