Main

During its formation, Venus was similar to Earth in many ways, including the existence of substantial amounts of liquid water1,2. However, Venus eventually evolved in a divergent way, leading to substantial differences between the two planets. Unlike Earth, Venus is now an extremely dry planet that lacks an intrinsic magnetic field. The continuous impact of the solar wind on the atmospheres of both planets results in important atmospheric losses3,4,5. The atmosphere of Venus, predominantly composed of carbon dioxide with smaller amounts of nitrogen and other minor species, is affected by interactions with the solar wind, leading to important ion outflows6,7,8,9. Therefore, studying and characterizing the present escape of ions from Venus is important for understanding the evolution of its atmosphere, and in particular, the evolution of water on the surface of the planet. Such studies may also provide insights into the general climate and habitability evolution of terrestrial planets and exoplanetary systems10.

Our current understanding of the plasma environment around Venus is rooted in several pioneering missions. Mariner 2 (1962–1963)11 was the first successful mission to establish the absence of an internal magnetic field in Venus. Venera 4 (1967) provided further information by conducting the first measurements of the planet’s ionosphere during its descent into the atmosphere. Subsequently, Pioneer Venus Orbiter (PVO, 1978–1992) systematically mapped the various regions of interaction between the Sun and Venus and their boundaries7. These regions include the bow shock and magnetosheath generated by the interaction of the supersonic solar wind and the magnetic barrier region separating the shocked solar wind plasma and planetary ions12. The upstream boundary of the magnetic barrier is commonly referred to as the magnetic pileup boundary (MPB)13,14,15. Despite the restricted energy range of the Orbiter Plasma Analyzer16 on board PVO, H+ and O+ were revealed to be the dominant ion species above 200 km altitude and were shown to escape tailward17,18,19,20. More complete ion composition measurements date from the Venus Express spacecraft (VEx, 2006–2014). Its highly polar orbits and comprehensive plasma package, Analyser of Space Plasmas and Energetic Atoms (ASPERA-4)21, allowed detailed investigations of the low-altitude terminator and the mid-magnetotail regions up to a distance of about four planetary radii, which were not covered by the PVO mission (Fig. 1). One of its major findings was the absolute number of escaping hydrogen, helium and oxygen ions. In particular, it was shown that the ratio of escaping hydrogen to oxygen is about 2.6, which indicates that water is a major source of these ions22,23. Moreover, the flux of the escaping heavy ions with mass-to-charge ratio m/q ≥ 16, which includes O+, O\({}_{2}^{+}\) and CO\({}_{2}^{+}\), were observed during the solar minimum to be about three orders of magnitude larger in the mid-magnetotail region (~108 cm−2 s−1) than in the magnetosheath flank (~105 cm−2 s−1) with a total average escape rate of about 5.2 ± 1.0 × 1024 s−1 (ref. 24). Even though extensive statistical studies and reliable ion measurements were conducted, it was not possible to differentiate heavy species such as C+, N+, O\({}_{2}^{+}\) and CO\({}_{2}^{+}\) from O+ because of the limited mass resolution of the ion mass analyser of the ASPERA-4 instrument suite. So far, no evidence of C+ in the near Venus environment has been reported, except during a rare crossing of the planet’s ionotail by the Solar and Heliospheric Observatory (SOHO) spacecraft in 1996 at the first Lagrangian point in the Earth–Sun system, which was as far as 45 million km from the planet25. The flux of escaping 15 keV (15 eV with respect to the mean proton energy) O+ and C+ ions was reported to be of the order of 2 × 103 cm−2 s−1, with an abundance of C+ to O+ of ~10%.

Fig. 1: Trajectory of BepiColombo through the Venusian system on 10 August 2021 in VSO coordinates.
figure 1

The trajectory is shown in (a) \(\text{X}_{VSO}\text{Z}_{VSO}\) (b) \(\text{X}_{VSO}\text{Y}_{VSO}\) and (c) \(\text{X}_{VSO}\sqrt{\text{Y}_{VSO}^2 + \text{Z}_{VSO}^2}\) planes. The VSO system is analogous to geocentric solar ecliptic coordinates. XVSO is directed from the centre of the planet towards the Sun, ZVSO is normal to the Venus orbital plane and positive towards the north celestial pole, and YVSO is positive in the direction opposite to the orbital motion. All dimensions are expressed in terms of Venus radii (RV = 6,051 km). An empirically derived estimate of the bow-shock location48 is shown as black solid lines. An estimate of the induced magnetospheric boundary (sometimes referred to as the upper mantle boundary)49 is shown as black dashed lines for reference. The portion of the orbit highlighted in blue corresponds to the trajectory of BepiColombo during which MSA was operating (12:28–13:49 ut). The segment in red (12:47–13:04 ut) corresponds to the time interval during which low-energy planetary ions were observed. The black and grey arrows indicate the viewing direction of MSA and the magnetic field direction during the fly-by, respectively. The light grey and dark grey curves represent PVO (1984–1988) and VEx (2006-2010) trajectories during the solar minimum, respectively.

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Most of the heavy ions in Venus’s ionosphere are cold (and slow moving). However, some of them are accelerated up to the escape velocity (10 km s−1) or above (refs. 26,27 and references therein). The forces at work here involve: (1) the electric fields acting on ions, including the convective field of the solar wind (pickup process), (2) fields resulting from pressure gradients (‘polar’ wind), (3) an induced electric field (J × B force) and (4) fields of electromagnetic waves (wave–plasma interactions).

Results

Here we report the first in situ observations made by BepiColombo’s Mass Spectrum Analyzer (MSA) and Mercury Ion Analyzer (MIA) during the spacecraft’s second Venus fly-by on 10 August 2021. The two sensors are part of the Mercury Plasma Particle Experiment (MPPE)28,29. Although MIA is a toroidal top-hat electrostatic energy analyser that measures ions without mass distinction, MSA combines a spherical top-hat electrostatic energy analyser with a polarized time-of-flight (TOF) chamber (‘reflectron’ type) to allow for ion measurements with enhanced mass resolution. The combined observations of MSA and MIA provide insights into the flow of cold planetary ions and the underlying escape process in the distant flank of Venus’s magnetosphere.

During this second fly-by, BepiColombo travelled into Venus’s induced magnetosphere from dawn to dusk in the nightside northern hemisphere, with an inbound bow-shock crossing around 12:00 ut. It had its closest approach at 13:52 ut at an altitude of 552 km. It then crossed the bow-shock outbound at 14:01 ut and continued upstream in the solar wind (Fig. 1). Importantly, due to the ‘stacked configuration’ of BepiColombo during the cruise, the Magnetospheric Orbiter Sunshield and Interface Structure significantly obstructed the field of view (FOV) of all the particle sensors. In fact, only two entrance windows of MSA, which point along the +Z axis of BepiColombo, recorded the ion flux (see Fig. 4 in ref. 28). The MSA observation sequence started at 12:28 ut and lasted until 13:49 ut, at which point a ‘safe mode’ automatic procedure turned the instrument off due to the detection of an exceedingly large ion flux by MIA (ref. 29), as shown in Fig. 2e. During this 91 min observation interval (red line in Fig. 1), the count rate matrices (H+, He2+ as well as heavy ions, m/q ≥ 4) were acquired at a cadence of 66 s, whereas the TOF spectra of straight-through particles in low mode (referred hereafter as TSTL) were accumulated during 1,024 s (ref. 28). Note that because of the limited telemetry rate, some data packets were lost during this observation sequence and only three TSTL products were effectively acquired inside the magnetosphere of Venus between 12:28 ut and 13:49 ut.

Fig. 2: Ion energy–time spectrograms and magnetic field data in Venus’s magnetosheath during the inbound part of BepiColombo’s second fly-by.
figure 2

a–h, MSA protons (a), MSA alphas (b), MSA heavies (c), MSA total ions (d), MIA ions (e), magnetic field components and magnitude in the VSO coordinate system (f), cone angle θc (g) and clock angle ϕc (h). The red segment between d and e shows the MSA TOF observation sequence between 12:47 ut and 13:04 ut during which the composition of the heavy ions was identified (Fig. 3). Note the good agreement between the total MSA and MIA DDEF spectra after 13:40 ut (d and e). The vertical dashed lines in f represent the MPBs encountered by BepiColombo in the vicinity of the distant magnetosheath (MS).

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MSA and MIA ion observations and magnetic field data

The observation sequence for MSA before the closest approach is displayed in Fig. 2. An increase of the H+ differential directional energy flux (DDEF) can be seen at ~13:08 ut and ~13:40 ut (Fig. 2a) and signatures of He2+ ions around 400 eV can be noticed between 13:45 ut and 13:49 ut (Fig. 2b) as BepiColombo was approaching the planet. These H+ and He2+ ion populations, which probably originated from the solar wind, are confirmed by the MIA instrument, which also revealed a maximum DDEF intensity near closest approach (Fig. 2e). Moreover, an increase of the heavy-ion flux is observed in the 12:30–13:08 ut time interval (also confirmed by MIA near 20 eV) and closer to the planet around 13:49 ut (Fig. 2c). Note that the vertical spread of the DDEF with respect to energy in Fig. 2a–d is an artefact from the software version used by MSA at the time of the fly-by. To support these ion measurements, magnetic field data from the magnetometer on board the Mercury Planetary Orbiter (MPO-MAG)30,31 is included in Fig. 2f. It is apparent from this latter panel that the sharp increase of the proton DDEF in the magnetosheath flank at ~13:08 ut (Fig. 2a) coincided with a change in the magnetic field orientation and magnitude. More specifically, after ~13:08 ut, the magnetic field magnitude decreased, the cone (θc, Fig. 2g) and the clock angle (ϕc, Fig. 2h) changed from ~147° (anti-sunward) and approximately −70° (southward) to ~96° (perpendicular to the Venus–Sun line) and approximately −2° (eastward), respectively. Keeping in mind that the nominal Parker spiral angle at Venus is ~144°/36°, this implies that until ~13:08 ut, the magnetic field was nearly along the Parker direction. The sharp changes of the magnetic field orientation and the ion DDEF suggest that there was a crossing of different regions in the plasma environment of Venus. The consecutive increase in the field components around 12:40 ut and 13:00 ut (consistent with an increase in draping32) and the suppression of the magnetosheath wave activity strongly indicate that BepiColombo moved across the MPB, where it subsequently observed the cold ion outflow. From 13:08 ut until 13:40 ut, along with the appearance of kilo-electronvolt ions, the spacecraft was in the dayside magnetosheath flank and got closer to the induced magnetospheric boundary after 13:40 ut (Fig. 1).

MSA TOF analysis

Due to the low signal-to-noise ratio of MSA data during this encounter and the low mass resolution of the count rate matrices during the cruise, heavy ions cannot be clearly identified from the corresponding energy–time spectrograms (Fig. 2). However, identifying these ions is possible from the acquired TOF spectra. During this fly-by, only two TOF spectra were acquired inside Venus’s induced magnetosheath, in the time intervals 12:47–13:04 ut and 13:04–13:22 ut. The first TOF spectrum (in the distant magnetosheath) is shown in Fig. 3. The ion TOFs were measured for 2,000 TOF channels of 0.78125 ns each. The histogram in Fig. 3 shows the data between 12:47 and 13:04 ut as groups of 24 TOF channels and are compared with MSA calibration profiles for O+ and C+ (green and orange curves, respectively). Note that the MSA raw data were obtained by integrating counts up to 1 keV, although most of these ions have an energy of only ~18 eV (described in more details in Methods), consistent with MIA observations (Fig. 2e). The histogram shown in this figure exhibits several peaks of particular interest. Indeed, although the peaks near 423 and 557 ns reflect the presence of O+ (with a 95% confidence level, confidence intervals are [417, 462] ns and [532, 587] ns, respectively), the additional peak in the 460–530 ns interval denotes the presence of C+ (confidence interval of [486, 513] ns). Note the slight deviation between the calibrated carbon peak and the observed one. At the time of writing, the reason for this deviation is unclear (possibly due to instrumentation, calibration methodology or counts statistics). These well-defined peaks provide clear evidence of planetary heavy ions in the distant magnetosheath flank, a region that has never been explored before. For comparison, the leftmost and rightmost panels in Fig. 4 show histograms before and after the time interval shown in Fig. 3. It is clear from the left-hand (Fig. 4a) and right-hand (Fig. 4c) panels that there is no clear evidence of heavy-ion species in contrast to the centre panel (Fig. 4b). Note that no changes in the spacecraft attitude were observed during this observation period. This confirms that most of the ions observed between 12:47 ut and 13:04 ut were not due to the spacecraft outgassing or sputtering. Furthermore, in the centre panel of Fig. 4, the second peak associated with O+ appears broadened by another peak between 610 and 700 ns. This additional peak corresponds to a mass-to-charge ratio of approximately 28 atomic mass units (AMU) per electron charge (for singly charged ion species), which could be due to the presence of molecular ions like CO+ and N\({}_{2}^{+}\). However, the densities of these molecular ions are noticeably lower than that of O+ above 200 km, and their molecular form was unlikely to be observed by MSA at ~6RV due to dissociative recombination33. Note that these signatures could be caused as well by Si+ or other complex ions emitted from the spacecraft, for example, due to Mio’s optical specular reflector outgassing or sputtering34. The peak in the 300–380 ns interval is probably due to a combination of two contributions: (1) a minor contribution of negative carbon ions (see caption of Fig. 3) and (2) a substantial contribution of multiply charged heavy ions that experience a post-acceleration higher than that of C+ before entering the MSA TOF chamber; hence, they have shorter TOFs than those of C+. Precise identification of these multiply charged ions species will require further investigation based on both experimental datasets and numerical modelling, which is out of the scope of the present study. By fitting the peaks of the TOF spectra with Lorentzian distributions (dashed lines in Fig. 3; see Methods for more details), we can integrate the total counts and get an estimate of the density fraction of C+ with respect to O+. Overall, the abundance of carbon relative to oxygen is at most 31% ± 21%, which is higher than the previously reported abundance of C+ to O+ of about 10% (ref. 25). This suggests that the observed oxygen ions are due to a combination of (1) atomic O+ released from the ionosphere, (2) the dissociation of CO or water group ions and (3) the dissociation of molecular O\({}_{2}^{+}\) ions that broke up when crossing the MSA carbon foil. Note that closer to the planet, the composition of the intense ion flux observed by MSA near 20 eV (Fig. 2d) cannot be investigated due to the lack of TSTL data.

Fig. 3: Total counts versus ion TOFs.
figure 3

Counts were recorded for Venus’s induced magnetosheath during the second gravity-assist manoeuvre of BepiColombo on 10 August 2021 in the time interval 12:47–13:04 ut. The grey profiles show the data obtained using the full TOF resolution of MSA (namely, 2,000 TOF channels of 0.78125 ns each). The blue histogram represents a binning of these data summed within bins of 24 TOF channels. The error bars along the blue profiles depict the 1σ deviation of the measurements assuming a Poisson-like distribution. Each point and relative error bar refer to the sum and plus or minus the standard deviation. The green and orange curves represent the MSA calibration of O+ and C+, respectively, for a voltage of ±8 kV applied inside the TOF chamber. The peaks highlighted in the grey area at TOF >600 ns represents ions with m/q ≥ 28 AMU e−1, which may be due to Si+ or other complex ions emitted from the spacecraft.

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Fig. 4: Three consecutive TOF spectra recorded during the second gravity-assist manoeuvre of BepiColombo on 10 August 2021.
figure 4

a, In the solar wind upon approach to Venus’s induced magnetosphere. b,c, In Venus’s induced magnetosheath in the time intervals 12:47–13:04 ut (b) and 13:04 ut–13:22 ut (c). The grey profiles show the data obtained using the full TOF resolution of MSA (namely, 2,000 TOF channels each of 0.78125 ns). The blue histograms represent a binning of these data summed within bins of 24 TOF channels. The error bars along the blue profiles depict the 1σ deviation of the measurements assuming a Poisson-like distribution. Each point and relative error bar refer to the sum and plus or minus the standard deviation. The format is identical to that of Fig. 3.

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Discussion

Although previous measurements of cold planetary oxygen were mostly obtained in the ionotail close to Venus, the MSA data presented here provide evidence of cold heavy ions of planetary origin (O+ and C+) in the flank of Venus’s induced magnetosphere, in the vicinity of the upstream MPB. To obtain the total flux, the DDEF was integrated between 12:40 ut and 13:04 ut over the various energy steps of MSA and solid angle. To do so, the measured flux was considered to be obtained from only two MSA entrance windows looking along the spacecraft’s Z axis (see above) and an isotropic ion distribution was assumed. This yielded an average flux of ~4 ± 1 × 104 cm−2 s−1. As noted earlier, previous studies could not distinguish the heavy ions. Nevertheless, a higher flux was reported in the magnetosheath flank closer to Venus ~3RV (~1 × 105 cm−2 s−1)24, and a lower one was reported in the ionotail further away from the planet ~7,500RV (~2.4–4.4 × 103 cm−2 s−1)25.

The lack of high-resolution field and particle measurements during this fly-by hinders a thorough analysis of the escape process for the planetary ions. However, the estimate of the pitch angle of approximately 140° made using the MSA FOV (Fig. 5) suggests that the ions predominantly flow outwards and parallel to the magnetic field, rather than perpendicular to it. Therefore, it is unlikely that these ions are pickup ions. Furthermore, considering the low energy of these observed ions (~18 eV), a plausible explanation for their escape is a process similar to the ‘polar-wind’, in which the thermal pressure gradient and the gravitational separation of ions and electrons along the magnetic field lines set up an ambipolar electrostatic field that accelerates ions towards electrons. As a result, there is an upward flow of ionospheric material35,36,37. Note that measurements made by VEx indicate the formation of an electric field in the Venusian upper ionosphere with a strength of approximately 9.9 V. This electric field can accelerate any ion lighter than 18 AMU to escape velocities38,39. Note that C+ and O+ ions would have escape energies of 6.3 and 8.4 eV, respectively, if they were released in the vicinity of the planet’s surface. Furthermore, it has been estimated that the spacecraft potential was approximately 9 V during this fly-by40. Consequently, these ions would have undergone an energization of no more than 30 eV before reaching MSA. This indicates that the spacecraft potential plays an insignificant role in accelerating the ions compared to the ambipolar electrostatic field. An alternative explanation to ion acceleration by the ambipolar electric field could be the centrifugal energization (a few tens of electronvolts) experienced by ions as they flow away from the planet due to the E × B convection of the magnetic field lines, as described, for example, in ref. 41.

Fig. 5: Schematic view of planetary material escaping through Venus’s magnetosheath flank.
figure 5

The illustration is of the X–YVSO plane with a cut at ZVSO = 0. The red segment shows the MSA observation sequence between 12:47 ut and 13:04 ut. The black arrows represent the FOV of MSA, and the blue arrow reflects the ions escaping at an angle of ~140° with the magnetic field lines (the angle is calculated using the FOV of MSA). Unlike other observation sequences, during this time window the incoming ions were moving in the same direction as the MSA FOV. The open magnetic field lines were obtained using the global hybrid model LatHyS (Latmos Hybrid Simulation50), with input parameters (for example, density, velocity, proton temperature and clock angle) constrained by Solar Orbiter observations in the upstream solar wind51. The polar view of Venus was taken from the Venus Monitoring Camera (VMC) onboard Venus Express (credits: ESA/MPS).

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In conclusion, the science opportunity offered by the second Venus fly-by of BepiColombo allowed us to investigate to some extent the ion composition of Venus’s magnetospheric flank. The present study demonstrates the presence of cold (~18 eV) heavy planetary ions (C+ and O+) with an average total flux of ~4 ± 1 × 104 cm−2 s−1. Although O+ ions have been observed to outflow from Venus by previous spacecraft, this study provides the first evidence of escaping C+ ions around six planetary radii. Modelling efforts are underway to further investigate the presence of cold heavy ions in the distant magnetosheath flank close to the MPB. Characterizing the loss of heavy ions and understanding the escape mechanisms for Venus are crucial for improving our knowledge regarding the water evolution on the surface of the planet, for determining the history of volatiles in our Solar System and for better constraining models of terrestrial exoplanets.

Methods

MSA instruments

The MSA is a high-mass-resolution ion spectrometer on board Mio, BepiColombo’s magnetospheric orbiter. Being part of the MPPE, which is dedicated to particle measurements29, MSA is designed to provide three-dimensional mass-resolved ion-phase space densities in Mercury’s magnetosphere. This ion spectrometer combines a spherical top-hat analyser for energy analysis with a TOF chamber for mass analysis. At the entrance of the TOF analyser, the ions interact with carbon foils and, as a result of charge exchange, may exit as neutrals or positive or negative ions. Unlike most spectrometers on board spacecraft, such as the Fast Imaging Plasma Spectrometer on board MESSENGER42,43, which has an equipotential TOF chamber, a prominent characteristic of MSA (from which derives its complexity) is that the TOF chamber is linearly polarized, which allows us to correct the energy and angular scattering upon entry of the positive ions into the TOF chamber28. This original ‘reflectron’ concept44 leads to isochronous TOFs, hence, with an enhanced mass resolution (m/Δm > 40). Such performance has seldom been achieved with onboard mass spectrometers and will be particularly useful at Mercury because of the large variety of ions of planetary origin that circulate in its magnetosphere after ejection by different processes (for example, solar wind sputtering, thermal desorption or meteorite impact). On the other hand, most of the incoming ions measured by MSA exit the carbon foils as neutrals or negative ions. These ions have ‘straight-through’ trajectories towards the bottom end of the MSA TOF chamber (see Fig. 2 in ref. 28). Throughout the cruise phase, because of the limited telemetry rate, MPO and Mio data are produced at low resolution and only straight-through data produced by MSA are transmitted. It should be stressed here that not all ions entering the MSA TOF chamber display two peaks in straight-through spectra. Although one of these two peaks (the most prominent one) is due to ions that are neutralized upon crossing the carbon foil, the second peak (at shorter TOFs) is due to ions that exit the carbon foil negatively charged in substantial numbers, such as carbon or oxygen but not helium or argon. Because of the linear electric field applied inside the TOF chamber, these latter ions are rapidly accelerated towards the straight-through detector and, thus, have shorter TOFs than those of neutrals28; hence, two distinct peaks are present (as for the O+ and C+ ions), in contrast with the single peak obtained by an ion spectrometer with an equipotential TOF chamber45.

Large structure of Venus’s induced magnetosphere

To better understand the ion observations, we calculated the clock and cone angles of the magnetic field to identify the large-scale structure of Venus’s induced magnetosphere. The cone (θc) and clock (ϕc) angles are defined as:

$${\theta }_{\mathrm{c}}={{{\mbox{tan}}}}^{-1}\left(\frac{\sqrt{{B}_{\rm{y}}^{2}+{B}_{\rm{z}}^{2}}}{{B}_{\rm{x}}}\right),$$
(1)
$${\phi }_{\mathrm{c}}={{{\mbox{tan}}}}^{-1}\left(\frac{{B}_{\mathrm{z}}}{{B}_{\mathrm{y}}}\right).$$
(2)

The Venus Solar Orbital (VSO) coordinate system is used, where XVSO is along the Venus–Sun line, YVSO is in the opposite direction of Venus’s orbital velocity and ZVSO completes the triad and is along Venus’s rotational axis. A cone angle of θc = 0° (180°) implies a sunward (anti-sunward) directed B field and θc = 90° is a field directed perpendicular to the Venus–Sun line. The clock angle ϕc is the direction of the magnetic field in the Y–Z VSO-plane with ϕc = 0° indicating an eastward pointing field and ϕc = 90° a northward one.

Histograms of the TOF spectra

Upon the entry of an ion into the MSA TOF chamber, a START pulse is produced by secondary electrons, which opens a TOF window of 1,562 ns and during which a STOP pulse is expected. Once the START and STOP pulses are acquired, the ion TOF in the chamber is computed with a time-to-digital converter resolution of 0.78125 ns (ref. 28). MSA TOF spectra were subsequently analysed by summing these different TOF channels. Supplementary Fig. 1 shows MSA TOF spectra between 250 and 750 ns and binned over 12 (light blue), 24 (medium blue) and 40 (dark blue) TOF channels. It is apparent from this figure that the C− and C peaks persist using either 12 or 24 TOF channel binning, although not surprisingly, these features are noticeably attenuated if a bin size that is too wide (40 TOF channels) is used.

Estimating the heavy-ion energy

The bulk of the heavy-ion energy was estimated from MSA TOF spectra (from 12:47:17 ut to 13:04:55 ut) by integrating the counts within each TOF boundary up to 1 keV for 12 ≤ m/q ≤ 23 (Supplementary Fig. 2). Since TOF spectra below 1 keV hardly depend upon the ion energy on entry into the instrument (due to post-acceleration up to 8 kV at the exit of the energy analyser), we have limited the analysis to 1 keV to exclude the effect of the energy spreading (Fig. 1).

Fitting the TOF spectrum

As mentioned in Main, because of limited counting statistics, we use a nonlinear least-squares method to fit the main peaks in the TOF spectra between 300 and 650 ns. The dispersion within the carbon foil is a random process that is expected to yield a velocity distribution constrained by both a maximum and a minimum28,46,47. This primarily impacted the heavy-ion species by introducing a broadening in the TOF spectra at longer TOFs. When performing the nonlinear least-squares fit to the main peaks of the TOF spectra, we considered three different types of distributions, namely, Gaussian, log-normal and Lorentzian (also known as a Cauchy–Lorentz distribution). Although the three distributions fit the MSA data relatively well, we show in Fig. 3 the results obtained using the Lorentzian distribution, which better fitted the width of the TOF peaks. This function has the following shape:

$$f(x;A,\mu ,\sigma )=\frac{A}{\pi }\left[\frac{\sigma }{{(x-\mu )}^{2}+{\sigma }^{2}}\right],$$

where the parameter amplitude corresponds to A, the centre to μ and the standard deviation to σ.

Calculation of uncertainties

The uncertainties in the binned TSTL spectra (Fig. 3) are due to counting (Poisson) statistics. Thus, the error ϵ is calculated assuming a Poisson distribution where \(\epsilon =\sqrt{N}\) and N is the number of counts in each bin. The error on the abundance calculation of C+/O+ is calculated as:

$$\sqrt{{\left(\frac{\sum \delta\mathrm{O}^{+}}{\sum \mathrm{O}^{+}}\right)}^{2}+{\left(\frac{\sum \delta\mathrm{C}^{+}}{\sum\mathrm{C}^{+}}\right)}^{2}},$$
(3)

where δX and X represent, respectively, the standard deviation and the total counts of the corresponding Lorentzian fit for each species.