A Multiwavelength Look at the GJ 9827 System: No Evidence of Extended Atmospheres in GJ 9827b and d from HST and CARMENES Data

A four-orbit HST pointing on GJ 9827 was carried out with the Space Telescope Imaging Spectrograph (STIS) during the 2018 August 28 transit of planet b as part of the Cycle 25 program GO-15434 (PI: S. Redfield). The first-order FUV grating G140M was used, with its 1222 Å setting, covering the wavelength interval 1194–1250 Å, at a resolution of R ≡ λ/Δλ ∼ 10⁴. The chromospheric H i 1215 Å Lyα line is formed in the range 1-3 × 10⁴ K. Other important emission lines in this region are the Si iii 1206 Å resonance transition (T ∼ 5 × 10⁴ K) and the N v 1240 Å doublet (T ∼ 2 × 10⁵ K), although both of these were expected to be too faint to be significantly detected in the relatively brief FUV exposures of this faint, 10th-magnitude mid-K-type star. Nevertheless, the peak signal-to-noise ratio (S/N) per 2 pixel resolution element (resel) in the combined spectrum at Lyα was about 35. The 52'' × 01 narrow long slit was chosen to minimize geocoronal Lyα contamination from the upper atmosphere of Earth. After the guide stars were acquired, a peak-up was performed to center GJ 9827, using the 31'' × 05 NDC long slit in the visible at low resolution with the STIS CCD. The rest of the initial orbit was occupied by the first G140M exposure, of 1.8 ks. The remaining three orbits had single G140M exposures, of 2.9 ks each. A summary of the four FUV observations is provided in Table 2. In relation to the planetary transit, the first two exposures were pre-ingress, the third was in-transit, while the final was post-egress.

Three months later, a single-orbit out-of-transit near-ultraviolet (NUV) spectrum of the Mg ii 2800 Å region of GJ 9827 was taken, again with STIS, but now using the high-resolution echelle E230H with its setting 2713 Å (2574–2851 Å) and the "spectroscopic" slit 02 × 009 to achieve optimum resolution (R ∼ 110,000) for the narrow Mg ii absorptions. The 2713 Å setting also captures an important Fe ii multiplet near 2600 Å, although unfortunately the NUV continuum of the mid-K star was too weak for the Fe ii interstellar absorption to be detected (the peak S/N per resel at Mg ii 2796 Å in the 1.8 ks exposure is 8). A visible-light peak-up was performed with the same slit prior to the E230H echelle exposure. The NUV observation is also described in Table 2.

We performed reductions of the FUV G140M exposures utilizing the pipeline-processed (CALSTIS) X2D files, which are wavelength- and flux-calibrated spatial/spectral images derived from rectified versions of the original long-slit stigmatic spectrograms. The image x-direction is along the dispersion, with 0.053 Å pixel⁻¹. The image y-direction is the spatial (cross-dispersion) dimension, with 003 pixel⁻¹. The image pixel flux densities tabulated in the X2D files, and associated photometric errors, are provided per Å and per 00293 (the latter is the cross-dispersion angular pixel size), so the extracted spectrum (and photometric error) must be multiplied by that angular factor to yield flux densities (erg cm⁻² s⁻¹ Å⁻¹).

The upper panel of Figure 1 illustrates a co-added version of the 2D spatial/spectral image of the four G140M exposures. The vertical extent of the image represents a ±40 pixel slice in the detector y-direction (∼ ±12) centered on the apparent stellar Lyα feature. The horizontal extent is 1200 pixels along the dispersion. The narrow geocoronal stripe is conspicuous in the y-direction, bisecting the broader stellar Lyα feature. The red band outlines a 9 pixel flux extraction region (∼03) for the stellar spectrum, while the blue dashed bands highlight flanking regions where the background was sampled. The two background bands are 25 pixels wide, beginning at ±15 pixels from the center. The wide bands increase the S/N for the background subtraction. In practice, we eliminated the top three of the background values at each wavelength, in an effort to mitigate hot pixels.

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The middle panel of Figure 1 depicts the extracted 1D spectrum from the co-added image, zoomed into the Lyα feature. The green tracing is the gross spectrum; blue with gray shadow is the background including the geocoronal H i emission feature; and black is the net flux (gross–background). The wavelength scale was set to place the geocoronal Lyα feature at its laboratory wavelength (1215.670 Å). The thin red dashed curve represents the 10σ photometric error level (per resel), derived from the spatial/spectral values provided in the original X2D files, smoothed, for display, by a double pass of a rectangular filter 15 pixels wide. The bottom panel shows the extracted Lyα features for the four exposures separately, where the geocoronal feature has been subtracted from the stellar profile. There are small differences between the Lyα peaks of the four profiles, and the difference in the wing of the red profile (that corresponds to ODRL01010 of Table 2, the first observation of the sequence) around 1215 Å is close to 3σ in significance.

We reduced the single NUV exposure directly from the CALSTIS pipeline X1D file, which is a tabulation of extracted flux densities and associated photometric errors for 27 of the echelle orders contained in the original E230H-2713 spectral image. We merged the individual orders together, tapering the overlapping zones to preserve the optimum S/N. GJ 9827 is a relatively faint star for STIS high-resolution echelle spectroscopy, so the main features visible are the Mg ii 2803 Å ("h") and 2796 Å ("k") resonance doublet, the most important spectral signatures of the stellar chromosphere below the temperatures where the higher-excitation Lyα emission forms. The peak S/N at the k line is about 8, and interstellar absorption is apparent in both emission cores.

The observed Lyα feature is the combination of the intrinsic stellar emission profile and the interstellar medium (ISM) attenuation profile (Wood et al. 2005). The core of the stellar emission line originates in the lower transition region and upper chromosphere (T ∼ (2–3) × 10⁴ K), while the outer wings form deeper in the stellar chromosphere. The Lyα emission core is strongly attenuated by neutral hydrogen (H i) and deuterium (D i) gas over the 29.7 pc sight line to GJ 9827. The star's + 31.9 km s⁻¹ RV (Prieto-Arranz et al. 2018) shifts the stellar emission lines away from much of the ISM attenuation centered near 0 km s⁻¹ (Redfield & Linsky 2008), giving the observed Lyα feature its asymmetric appearance. The Mg ii cores are less affected than Lyα owing to the much smaller cosmic abundance of magnesium.

We observed one transit of GJ 9827b and one transit of GJ 9827d with the CARMENES spectrograph (Calar Alto high-Resolution search for M dwarfs with Exo-earths with Near-infrared and optical Echelle Spectrographs; Quirrenbach et al. 2014, 2018) located at Calar Alto Observatory, in 2018 August 13 and November 6, respectively. CARMENES simultaneously covers the optical (VIS; 520–960 nm) and near-infrared (NIR; 960–1710 nm) range, giving access to two important traces of planetary evaporation processes: the NIR He i triplet at 10830 Å and the visible Hα line at 6562.81 Å. GJ 9827 is sufficiently bright (V = 10.1 mag, J = 7.98 mag) to be observed with both arms simultaneously. Both observations were performed in stare mode, taking continuous exposures before, during, and after the transit. The exposure times were set to be nearly the same for both arms, so that, accounting for the different readout overheads of the VIS and NIR arms, the central time of each exposure was coincident in both. Resetting of the Atmospheric Dispersion Corrector took place between two exposures (i.e., during readout) and approximately every 30 minutes.

For the planet b observations, the exposure time at the beginning was 190 s but was then increased to 198 s, and the averaged S/N achieved is 44 in the He i order and 30 in the Hα order. On the other hand, for the planet d observations, the exposure times were 200 and 197 s, with an S/N of 47 and 35 around He i and Hα orders, respectively. Due to a cloud crossing, the exposures taken at 19:22, 19:26, and 19:30 UT presented S/N below 30 in the He i order and below 20 in the Hα order. These exposures are discarded from the atmospheric analysis. In addition, for technical reasons, the observations were stopped from 19:59 to 20:16 UT. We note strong telluric contamination of the He i region in both nights. A log table of the CARMENES observations is given in Table 3.

We reduced CARMENES observations with the CARMENES pipeline CARACAL (CARMENES Reduction And CALibration; Caballero et al. 2016), which performs bias, flat-relative optimal extraction (Zechmeister et al. 2014), cosmic-ray correction, and the wavelength calibration (Bauer et al. 2015). The wavelengths are given in vacuum and the reduced spectra referenced to the terrestrial rest frame.

To correct for the ISM attenuation of the Lyα and Mg ii lines and recover the intrinsic stellar emission lines, we use the approach described in Youngblood et al. (2016) and García Muñoz et al. (2020), modified to jointly fit Lyα and Mg ii. This allows for stronger constraints on the physical parameters common to the two transitions. Using a Markov Chain Monte Carlo (MCMC) method (Foreman-Mackey et al. 2013), we simultaneously fit a model of the Lyα and Mg ii intrinsic stellar emission lines and ISM absorption lines to the STIS G140M and E230H spectra.

For Lyα, we parameterized the broad, intrinsic stellar emission line as a single Voigt profile in emission with a Gaussian in absorption for the line's self-reversal. For the narrow Mg ii emission lines, we used a single Gaussian profile in emission for each line and a single Gaussian for each line's self-reversal. We required the RVs for the two Mg ii lines to be identical and also required their FWHMs to be coupled such that FWHM_k = 1.05 × FWHM_h , because high-resolution stellar spectra indicate that the k line is ∼5% broader than the h line (B. E. Wood 2021, private communication). We did not require the RV of Lyα to match the Mg ii lines in case of small wavelength offsets between the two gratings.

The ISM absorbers (H i, D i, Mg ii) are modeled as single Voigt profiles in absorption (see Section 3.2 for justification for one component), each parameterized by an RV ν (offset from their corresponding stellar emission line's RV), Doppler width b, and species column density N. We assume that the ISM absorbers are coming from the same interstellar gas with the same kinematics, so all three ISM species were required to have the same RV offset from their stellar emission line's RV, and the Doppler widths were all connected assuming pure thermal broadening by b_{Mg ii} = b_{H i} /$\sqrt{24.3}$ and b_{D i} = b_{H i} /$\sqrt{2}$. While H i and D i are dominated by thermal broadening, and thus this assumption should be fine, heavier species like Mg ii will also have a significant contribution from turbulent broadening. Therefore, our value of b_{Mg ii} will underestimate the true Doppler width of Mg ii. The D i and H i column densities were fixed to be N(D i)/N(H i) = 1.5 × 10⁻⁵ (Wood et al. 2004), and N(Mg ii) was not linked to N(D i) or N(H i). The corresponding intrinsic emission lines and ISM absorption lines were multiplied together and convolved to the corresponding instrument resolution using the STIS G140M and E230H line-spread functions.

Given the lack of an in-transit detection (see Section 4.1), we co-added all four orbits' spectra to maximize the precision of the reconstruction. Figure 2 shows the best-fit model and intrinsic profiles with 68% and 95% confidence intervals. We find an intrinsic Lyα flux with 68% confidence interval (5.42 ${}_{-0.75}^{+0.96})\times {10}^{-13}$ erg cm⁻² s⁻¹. For Mg ii, we find a best-fit integrated flux of the h line of (2.30 ±0.16) × 10⁻¹⁴ erg cm⁻² s⁻¹, and the integrated flux of the k line is (3.34 ±0.17) × 10⁻¹⁴ erg cm⁻² s⁻¹ (Figure 4). The total flux is F(Mg ii h + k) = (5.64 ±0.24) × 10⁻¹⁴ erg cm⁻² s⁻¹. These fluxes and the fitted ISM parameters (described in 3.2) are printed in Table 4.

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Table 4. Stellar and ISM Parameters

Parameter	Value	Units
Stellar Fluxes
Intrinsic Lyα flux F(Lyα)	(5.42${}_{-0.75}^{+0.96}$) × 10−13	erg cm−2 s−1
Intrinsic Mg ii h flux F(Mg ii h)	(2.30 ±0.16) × 10−14	erg cm−2 s−1
Intrinsic Mg ii k flux F(Mg ii k)	(3.34 ±0.17) × 10−14	erg cm−2 s−1
Intrinsic Mg ii h + k flux F(Mg ii h+k)	(5.64 ±0.24) × 10−14	erg cm−2 s−1
Surface Lyα flux FS (Lyα)	(2.81${}_{-0.39}^{+0.50}$) × 106	erg cm−2 s−1
Surface Mg ii flux FS (Mg ii)	(2.92 ±0.13) × 105	erg cm−2 s−1
ISM Absorbers' Parameters
H i RV νH I	−3.4${}_{-2.8}^{+2.8}$	km s−1
H i Doppler width bH i	${12.8}_{-4.5}^{+2.2}$	km s−1
H i column density log10 N(H i)	${18.22}_{-0.10}^{+0.08}$	cm−2
Mg ii RV νMg ii	${2.5}_{-2.3}^{+2.1}$	km s−1
Mg ii Doppler width bMg ii	${2.6}_{-0.9}^{+0.4}$	km s−1
Mg ii column density log10 N(Mg ii)	${12.11}_{-0.59}^{+0.51}$	cm−2
N(Mg ii)/N(H i)	${8.0}_{-6.0}^{+18.3}\,\times$ 10−7

Note. The stellar RV is +31.9 km s⁻¹ (Prieto-Arranz et al. 2018). The v_{H i} and v_{Mg ii} values are derived from the same free parameter in the fit, an RV offset from the stellar H i and Mg ii emission-line centroids. The v_{H i} and v_{Mg ii} values differ because of differences in the absolute wavelength solution between the two gratings (G140M and E230H). The b_{H i} and b_{Mg ii} values are also derived from the same free parameter (b_{H i} ) under the assumption of thermal line broadening (b_{Mg ii} = b_{H i} /$\sqrt{24.3}$).

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In Figure 3, we compare the line core shapes of the reconstructed Lyα and Mg ii lines, with ISM attenuation and instrument resolution effects removed. The Lyα line is >100 km s⁻¹ broader than Mg ii, as expected. Their self-reversal shapes are roughly similar, but there are significant discrepancies between the depth, width, and asymmetry of the two species. For Lyα, the self-reversal was only allowed to deviate ±10 km s⁻¹ from line center owing to significant degeneracy between the self-reversal depth and ISM absorption, but it is centered almost exactly at line center. The self-reversal in the Mg ii lines was allowed to vary more widely, and it is readily apparent from the observed spectra that the self-reversal is asymmetric (i.e., not centered exactly at the stellar velocity). The Lyα self-reversal depth also appears larger than Mg ii's; however, the uncertainties on Lyα's self-reversal parameters are extremely large, as the line core is not observed owing to severe ISM attenuation.

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We used the LISM Kinematic Calculator ²² (Redfield & Linsky 2008), which calculates whether or not a cloud of LISM traverses any given sight line, in addition to the radial and traverse velocities of the clouds in a given direction. In the case of GJ 9827, the LISM Kinematic Calculator yields no traversing clouds along the sight line. We note that this is likely due to the boundaries of clouds not being well sampled by limited LISM data sets, and this sight line probably does traverse at least one LISM cloud. There are five clouds passing within 20° of GJ 9827's sight line, including the Local Interstellar Cloud (LIC). The RVs of these clouds range from −7 to +10 km s⁻¹ with a weighted average of −3.1 ±5.8 km s⁻¹. Given the limitations of our data (low S/N in Mg ii and low spectral resolution for H i), we fit a single ISM cloud component to our spectra. This results in fitted parameters that are likely akin to an average of the true parameters of the multiple clouds along the sight line. From our reconstructions described in the previous section, we find for interstellar H i the following parameters: ν_{H I} = −3.35${}_{-2.83}^{+2.81}$ km s⁻¹, ${\mathrm{log}}_{10}N$(H i) = ${18.22}_{-0.10}^{+0.08}$ cm⁻², and b_{H i} =${12.8}_{-4.5}^{+2.2}$ km s⁻¹. For interstellar Mg ii, we find log₁₀ N(Mg ii) = ${12.11}_{-0.59}^{+0.51}$ cm⁻². Recall that Mg ii's Doppler b parameter is defined as b_{H i} /$\sqrt{24.3}$, and the offset between the ISM RV and the intrinsic stellar RV was defined to be the same for the two species. This gives ν_{Mg ii} = ${2.45}_{-2.31}^{+2.07}$ km s⁻¹ and b_{Mg ii} = ${2.6}_{-0.9}^{+0.4}$ km s⁻¹. While we expect b_{Mg ii} to be underestimated, this is within the reasonable range for the Doppler width of LISM Mg ii absorption (Redfield & Linsky 2004). Note that the absolute uncertainty in the STIS MAMA wavelength calibration is 0.5–1 pixels, or 6–12 km s⁻¹ for G140M at Lyα and 1.5–3.0 km s⁻¹ for E230H at Mg ii.

The constraint on the Mg ii interstellar absorbers is weak because of the narrowness of the stellar emission line serving as a backlight for the interstellar Mg ii ions to absorb against. The interstellar Mg ii atoms are Doppler shifted almost −30 km s⁻¹ from an emission line with FWHM = 24 km s⁻¹, and no stellar continuum is detected around the stellar emission lines.

From our simultaneously fitted H i and Mg ii column densities, we calculate the ratio N(Mg ii)/N(H i)=${8.0}_{-6.0}^{+18.3}\times {10}^{-7}$ for GJ 9827's sight line. This value overlaps with the N(Mg ii)/N(H i) ratio from Linsky (2019) ((${3.6}_{-1.6}^{+2.8})\times {10}^{-6}$) at the 68% confidence interval (2.0 × 10⁻⁷–2.6 × 10⁻⁶).

To verify our measurement of the Mg ii ISM absorption, we also applied the ISM fitting technique described in Redfield & Linsky (2002). We assume that the interstellar absorbers have an RV equal to the LIC for this line of sight (+1.24 km s⁻¹; Redfield & Linsky 2008), and we assume the wings of the Mg ii emission line to be symmetric. Masking the blueward, ISM-affected half of the line, we mirrored the redward half of the Mg ii k profile to create the assumed intrinsic stellar profile, which clearly indicated the presence of ISM absorption in the blue wing. The low S/N in the wings of the line prevented a free fit to the column density. However, visual inspection using the mirrored profile led to a minimum column density log₁₀ N(Mg ii) ≈ 12.5. This value is 0.14 dex above the 1σ uncertainty range of the previous fitting results shown in Figure 4. Using the log₁₀ N(Mg ii) = 12.5 value from our mirrored profile fitting of the Mg ii line, we find N(Mg ii)/N(H i) = 1.9 × 10⁻⁶, which is in agreement with the ratio value from Linsky (2019). The conclusion from using two different methods is that LISM absorption is present on the blueward wing, although it does not significantly alter the Mg ii emission profile. Our assumption of a single LISM absorption component and our choice of the stellar emission profile (i.e., automated Gaussian vs. a mirrored profile) do not formally enter into our error analysis and, given the comparison to the LISM average N(Mg ii)/N(H i) ratio, indicate that our Mg ii LISM column density may be slightly underestimated.

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We also searched for other ISM-affected spectral lines in the spectral range of STIS/E230H (2576–2823 Å), such as the iron lines at 2586 and 2600 Å, but the S/N is too low and the spectrum does not present any other spectral features.

We compare GJ 9827's Lyα and Mg ii fluxes to other K dwarfs with measured fluxes for both lines (Figure 5). To compare to data from Wood et al. (2005) and Youngblood et al. (2016), we convert our fluxes into surface fluxes using the 0.579 ±0.018 R_⊙ radius from Kosiarek et al. (2020) and the 29.69 pc distance from Gaia DR2 to obtain F_S (Lyα) = (2.81${}_{-0.39}^{+0.50}$) × 10⁶ erg cm⁻² s⁻¹ and F_S (Mg ii) = (2.92 ±0.13) × 10⁵ erg cm⁻² s⁻¹. GJ 9827's rotation period is poorly constrained but appears to be between 15 and 30 days, with a most likely value of 28.72 days (Rice et al. 2019).

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Compared to other K dwarfs of similar rotation period, ²³ GJ 9827 has approximately 3.0 times less Mg ii surface flux and 2.8 times more Lyα surface flux. Mg ii is commonly used as an estimator for the difficult-to-observe Lyα line (Wood et al. 2005), and if we relied on the Mg ii observation to estimate GJ 9827's Lyα emission, we would have underpredicted it by almost a factor of 5. Figure 2 shows how this Mg ii-derived Lyα profile (both intrinsic and observed) would appear and how the Lyα spectrum strongly rules out this flux level at the >3σ level. This underestimation could have significant consequences for the atmospheres of GJ 9827's planets, because Lyα has a strong effect on photochemistry and, as a proxy for the EUV (Linsky et al. 2014), could have implications for the atmospheric escape from the planets.

We estimate that there is a 0.001% probability that GJ 9827's Lyα flux is consistent with the other K dwarfs in Figure 5 and a 16% probability that its Mg ii flux is consistent with other K dwarfs. To calculate this, we drew 10⁶ random samples from GJ 9827's Lyα and Mg ii flux posterior distributions, as well as 10⁶ random samples from a normal distribution describing the red best-fit lines in the middle and right panels of Figure 5, and determined what percentage of the posterior samples overlapped with samples from the best-fit lines. The normal distributions describing the best-fit lines had means equal to zero and standard deviations equal to the standard deviations of all data points about the best-fit line, normalized by the best-fit line. For Lyα the standard deviation is 0.29, and for Mg ii it is 0.46. The samples from the Lyα and Mg ii posterior distributions were also cast as differences from the best-fit line and then normalized by the best-fit line.

What is causing the apparently significant discrepancy in the Mg ii–Lyα flux ratio for this star? It is possible that this ratio is within the expected scatter of K dwarf UV flux–flux relations, and more UV spectroscopic observations of K dwarfs are needed to quantify that typical scatter. Mg ii and Lyα form in slightly different regions in the stellar atmospheres, and therefore their emission mechanisms are not exactly coupled, but in practice the scatter is likely dominated by the nonsimultaneity of the Mg ii and Lyα observations. For example, the GJ 9827 Mg ii and Lyα observations were taken 100 days apart, or approximately 3.5 stellar rotation periods apart. Stellar surface inhomogeneities (e.g., active regions, faculae, plage), as well as evolution of these features responsible for much of the Mg ii and Lyα emission, could cause deviations in the expected Mg ii–Lyα flux ratio.

Here we consider some additional effects, including metallicity and rotation evolution. GJ 9827 has slightly subsolar metallicity ([M/H] = −0.26 to −0.5; Rice et al. 2019), which could potentially explain a low Mg ii flux relative to Lyα, as well as GJ 9827's potentially anomalously high Lyα flux. A detailed investigation into the effect of metallicity on relative Mg ii and Lyα line strengths in K dwarfs would be needed to determine that. Another possible explanation is the observed rotation evolution of Lyα luminosity compared to less optically thick chromospheric lines like C ii. Pineda et al. (under review) showed with a sample of young and field age M dwarfs that Lyα luminosity declines much more slowly with increasing stellar rotation period (a proxy for stellar age) than other FUV lines like C ii. Assuming that Mg ii behaves more similarly to lines like C ii rather than Lyα, GJ 9827 could be at a point in its rotational evolution when its Mg ii luminosity has decreased significantly but Lyα has not been impacted as much by stellar spin-down. More UV observations of low-activity K dwarfs are needed to determine whether this increasing Lyα/Mg ii flux ratio with increasing rotation period is a real effect.

We investigate the behavior of GJ 9827's observed Lyα profiles during the different phases of the transit. Starting from the four spectra obtained in Section 2.1 (one per orbit), we calculated the in-transit absorption depth as 1 − F_IN/F_OUT, where F_IN is the flux of the Lyα line during the transit and F_OUT is the out-of-transit flux. Figure 6 shows the out-of-transit (black solid line) and in-transit (red solid line) spectra for GJ 9827b, where the out-of-transit spectrum (F_OUT) is obtained by averaging the three out-of-transit spectra and the single in-transit spectrum represents F_IN. We find that the observed Lyα spectra are very similar in and out of the transit, and there is no evident planetary absorption during the transit. The largest apparent absorption depths occur in the spectral region most strongly contaminated by ISM absorption and geocoronal emission.

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Furthermore, we compare pre-ingress and post-egress spectra, as in Kulow et al. (2014), to search for a possible atmospheric comet-like tail. McCann et al. (2019) showed that the stellar wind can significantly shape the planetary outflow, creating strong absorption signatures many hours before and after the optical transit. Figure 7 shows pre-ingress and post-egress spectra in the top panel and the difference between these spectra in the bottom panel. No evident difference is found.

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We integrated the flux in the Lyα blue wing from −250 to −75 km s⁻¹ in the stellar rest frame (1214.787–1215.496 Å) to obtain the average fluxes of each of the four orbits (units 10⁻¹⁵ erg cm⁻² s⁻¹): 2.20 ±0.19, 2.28 ±0.15, 2.16 ±0.15, and 2.41 ±0.16. To obtain an upper limit of the size of the planet's H i atmosphere, we fit a transit model of an opaque sphere using an MCMC routine. We use the batman package (Kreidberg 2015) with transit ephemerides from Rice et al. (2019) and uniform limb-darkening parameters. The size of the planet at Lyα relative to the star (R_Lyα /R_⋆) was the only free parameter, and we find 1σ, 2σ, and 3σ upper limits of 0.36, 0.48, and 0.57 for R_Lyα /R_⋆ in the blue wing. We repeated this upper limit calculation for the Lyα red wing (+10 to +250 km s⁻¹ in the stellar rest frame; 1215.841–1216.813 Å) and find average fluxes of each of the four orbits (units 10⁻¹³ erg cm⁻² s⁻¹) of 1.10 ±0.04, 1.10 ±0.03, 1.09 ±0.03, and 1.13 ±0.03. The 1σ, 2σ, and 3σ upper limits on R_Lyα /R_⋆ in the red wing are 0.21, 0.27, and 0.32.

Prieto-Arranz et al. (2018) suggested that the GJ 9827 planetary system is an excellent laboratory to test atmospheric evolution and planetary mass-loss rates. We investigate the presence of evaporation traces in the atmospheres of GJ 9827b and GJ 9827d using CARMENES observations. In particular, we use the data obtained with the NIR channel to study the He i triplet lines (at 10829.09, 10830.25, and 10830.34 Å) and the visible channel data to study the Hα line (at 6562.81 Å).

As a first step, we correct the observed spectra of telluric absorption contamination using molecfit (Smette et al. 2015 and Kausch et al. 2015), assuming the parameters presented in Nagel et al. (submitted) for the CARMENES instrumental line-spread function model. In particular, the He i region is contaminated by telluric absorption of water vapor and telluric emission of OH (Nortmann et al. 2018; Salz et al. 2018). The water vapor absorption is corrected with molecfit, and the OH emission lines are masked, following the methods described in Palle et al. (2020). The telluric line removal and masked regions are illustrated for each planet/night in the top panels of Figures 8 and 9.

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After removing the telluric contamination, we can extract the transmission spectrum in both He i and Hα regions using the same approach, presented in different studies such as Wyttenbach et al. (2015), Casasayas-Barris et al. (2019), and Chen et al. (2020). CARMENES observations are referenced to Earth's rest frame. Thus, we shift the spectra to the stellar rest frame considering the barycentric RV information and the system velocity (31.95 km s⁻¹; Prieto-Arranz et al. 2018). After computing the ratio of each stellar spectrum to the master out-of-transit spectrum (combination of all out-of-transit spectra using the simple average), we move the residuals to the planet rest frame (see middle panels of Figures 8 and 9). To do this, we calculate the planet's RV using the RV semiamplitudes ${K}_{p}^{{\rm{b}}}=166.3$ km s⁻¹ and ${K}_{p}^{{\rm{d}}}=98.2$ km s⁻¹ for GJ 9827b and GJ 9827d, respectively. These values are calculated assuming the stellar RV semiamplitude (K_⋆) and the planet and star masses reported by Kosiarek et al. (2020) and using K_p = K_⋆ M_⋆/M_p (Birkby 2018). Finally, we combine all in-transit residuals in the planet rest frame to obtain the transmission spectrum. In the He i region, the masked intervals due to OH contamination are the same for all spectra in the stellar rest frame but change when moving the spectra to the planet rest frame. When combining the in-transit residuals to extract the transmission spectrum, we only include the nonmasked pixels in the calculation. The final transmission spectra are presented in the bottom panels of Figures 8 and 9. We note that different K_⋆ and mass values are reported in the literature, which result in different K_p values (see, e.g., Rice et al. 2019; Prieto-Arranz et al. 2018). However, these different K_p values do not have significant impact on the derived transmission spectra.

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It is important to notice, however, that, using the parameters from Kosiarek et al. (2020), the mid-transit time of GJ 9827d's observations differs from that obtained using the parameters from Prieto-Arranz et al. (2018), Rodriguez et al. (2018), and Rice et al. (2019). This difference is produced, mainly, by the differences in the derived orbital period value. The orbital period derived by Kosiarek et al. (2020) differs by more than 30 s from the ones presented in the previous studies, and this difference is propagated along the different epochs. To be on the safe side, we have repeated the analysis using the parameters from the different references, and the resulting transmission spectra do not show any significant feature in any of the cases.

In the two-dimensional residual maps presented in Figures 8 and 9, we are not able to visually distinguish absorption features during the transit that could have planetary origin, for either of He i or Hα. The overall transmission spectrum does not show significant absorption features either. The excess absorption measured in the transmission spectra of GJ 9827b using a 0.7 Å passband centered on the He i and Hα line core is −0.3% ±0.2% and −0.2% ±0.2%, respectively. On the other hand, for GJ 9827d, we measure +0.2% ±0.2% and −0.1% ±0.2% excess, respectively. The expected absorption signal ($\approx 2{{nHR}}_{p}/{R}_{\star }^{2}$) of the annular area of one (n = 1) atmospheric scale height (H) during the transit is around 3 × 10⁻⁵ for both planets, respectively, assuming an atmosphere dominated by H/He mixture and near-solar composition (μ = 2.3). However, it has been observed in several exoplanet observations that the detected He i signals are comparable to those created by an annular area of n = 100 times the scale height (see dos Santos et al. 2020). Here, with only a single transit per planet and the relatively small S/N of the observations, especially in the line core, we find no evidence for an extended H/He upper atmosphere around GJ 9827b or GJ 9827d. This is consistent with the nondetection of He i presented for GJ 9827 d by Kasper et al. (2020).