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A&A
Volume 709, May 2026
Article Number A136
Number of page(s) 6
Section Interstellar and circumstellar matter
DOI https://doi.org/10.1051/0004-6361/202658878
Published online 08 May 2026

© The Authors 2026

Licence Creative CommonsOpen Access article, published by EDP Sciences, under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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1 Introduction

Understanding the chemical pathways of sulfur in the interstellar medium (ISM) remains a puzzle (Mifsud et al. 2021). Whereas in diffuse low-density interstellar environments the abundance of atomic sulfur roughly corresponds to the known cosmic value (Goicoechea et al. 2006; Fuente et al. 2024), in dense molecular clouds, star-forming regions, and planet-forming disks there is a major depletion of gas phase atomic sulfur, by up to two orders of magnitude (Le Gal et al. 2021; Laas & Caselli 2019). Gasphase sulfur-bearing molecules, such as HCS, OCS, and SO2 have been detected (Agúndez et al. 2018; Van Gelder et al. 2024), but at concentrations far too low to account for the missing sulfur. Sulfur can also be present in volatile ices, salts, or in the more refractory species FeS. Recently, OCS (tentatively detected using Akari; Aikawa et al. 2012) and potentially SO2 ice were detected in lines of sight towards cold molecular clouds using the James Webb Space Telescope. However, H2S ice, expected to be abundant, was not detected (McClure et al. 2023). Moreover, evidence has been presented that ammonium salts may contain a significant amount of sulfur in the form of NH4SH, possibly accounting for 17-18 percent of the sulfur budget (Slavicinska et al. 2025). Refractory FeS is abundant in solar system interplanetary dust (IDP) grains of cometary origin, suggesting that a significant but difficult to quantify fraction of sulfur may be in the form of FeS in planet-forming disks (Keller & Messenger 2011).

Another class of molecules proposed as a possible sink for the missing sulfur is composed by sulfur allotropes (Jiménez-Escobar & Caro 2011; Carrascosa et al. 2024) formed in interstellar ices, of which S8 stands out as a prominent candidate. Indeed, density functional theory (DFT) calculations predict octasulfur to be the most stable SN allotrope (Fedyaeva et al. 2023). Sulfur allotropes were identified in trace abundances in the coma of comet 67 P/Churyumov-Gerasimenko12, in particular S2, S3, and S4 (Calmonte et al. 2016), while S8 was detected in Ryugu samples (Aponte et al. 2023). Astrochemical models describing the chemical pathways of sulfur-bearing molecules have been proposed, showing that among the different SN allotropes, S8 is the most abundant (Shingledecker et al. 2020; Taillard et al. 2025), given its higher fragmentation energy. However, these models lack fundamental experimental information about absorption cross sections, dissociation energies, fragmentation channels, and de-excitation mechanisms, in general. Recently, infrared absorption cross sections of S8, S4+, and S4− were quantified, based on a combination of infrared spectroscopy and DFT calculations (Ferrari et al. 2024). In addition, the work revealed a relatively low dissociation energy for S8 (1.4 eV), as well as for its cationic counterpart, S8+, with a competition of two fragmentation channels: the formation of pentamers and hexamers. These results highlight a more complex chemical network of sulfur allotropes than anticipated, in which the formation and destruction of octasulfur can occur in energetic environments. An open question remains about the survival probability of octasulfur in these interstellar environments, which can guide a targeted search in the ISM via astronomical observations, as well as providing key pieces of information to improve astrochemical models. Given that not only neutrals but also charged molecules have been found in space (McGuire 2022), such information is relevant for both S8 and S8+, which may behave differently.

In isolated conditions, where excess energy cannot be dissipated through an external heat bath, the survival probability of a thermally hot molecule is determined by three processes: fragmentation, electron emission, and radiative cooling. Here, a system is considered hot if it has a total excitation energy, equilibrated throughout its degrees of freedom, higher than its lowest dissociation energy (Hansen 2013). Under thermally hot conditions, one of the possible cooling channels typically dominates, but depending on the internal energy and molecule-specific parameters, competition can occur. Radiative cooling, which can stabilize a molecule against fragmentation if active, can proceed through two distinct mechanisms, namely direct vibrational cooling (VC) or recurrent fluorescence (RF; Zhu et al. 2022; Ito et al. 2014; Andersen et al. 2001). The latter process is also called Poincaré fluorescence, as initially suggested in the pioneering work of Léger and coworkers (Léger et al. 1988). In conventional VC, excess energy is dissipated through the emission of infrared photons through a cascade of vibrational transitions (Hansen et al. 2023). Given that in VC multiple low-energy photons are emitted through transitions with low oscillator strength, for a fixed molecular size, cooling is slow and only competitive with dissociation or electron emission at internal energies close to the threshold energies for these processes (Stockett et al. 2020). Instead, in RF, photons are emitted via electronic transitions, therefore having larger oscillator strengths and requiring only a single photon to quench any further fragmentation (Kono et al. 2015). However, for RF to be competitive to fragmentation, a molecule must possess electronic states low enough in energy to allow inverse internal conversion (IIC) to take place (Kaw et al. 2024).

To date, RF has been indirectly shown to be a competitive cooling channel in a variety of carbon-bearing molecules, including polycyclic aromatic hydrocarbons (PAHs; Martin et al. 2013; Lee et al. 2023), fullerenes (Hansen & Campbell 1996; Sundén et al. 2009; Navarrete et al. 2025), and small carbon clusters (Iida et al. 2022; Chandrasekaran et al. 2014), as well as different metal clusters (Peeters et al. 2021; Ferrari et al. 2018; Hansen et al. 2017a). To date, direct detection of RF photons has only been achieved for four systems: C4− (Yoshida et al. 2017), C6− (Ebara et al. 2016), C10H6− (Saito et al. 2020), and C14H10+ (Kusuda et al. 2024). Interestingly, detailed experiments on cationic 1-cyanonaphthalene have shown an enhanced survival probability for these molecules when RF is an effective cooling channel (Stockett et al. 2023). Indeed, small PAHs have been detected in the ISM (Wenzel et al. 2024; Cernicharo et al. 2026; Cabezas et al. 2025), in environments conventionally assumed to be too harsh for such small species to survive (Andrews et al. 2015). Instead, observations show abundances of orders of magnitude higher than predicted by astrochemical models, for example, cyanonaphthalene and cyanopyrene (McGuire et al. 2021; Wenzel et al. 2024), suggesting that stabilization by RF is an important factor for evaluating astrophysical survival.

Here, using an electrostatic storage ring setup, we show that radiative cooling is an active cooling channel in S8+ cations. Employing inputs from quantum chemical calculations, the rate coefficients of fragmentation, VC, and RF are calculated as a function of the internal energy, revealing that radiative cooling proceeds via RF in this all-sulfur molecule. Based on the simulated rates, the energy-dependent survival probability of S8+ is calculated, highlighting the effect of RF on the survival of S8+ at high internal energies. The analysis is also extended to neutral S8, in which RF is not an active process. This allows us to place limits on the interstellar environments in which octasulfur could be detected.

2 Methods

2.1 Experimental details

The experiments were performed at the DESIREE facility (Double ElectroStatic Ion Ring ExpEriment) of Stockholm University (Thomas et al. 2011; Schmidt et al. 2013; Schmidt 2021). DESIREE consists of two coupled electrostatic ion-beam storage rings, but in these experiments only one ring was used, as shown schematically in Fig. 1. The circumference of the ion orbit in this ring is about 8.7 m. The cryogenic ring is cooled to ≈13 K, which results in low residual gas densities and consequently very long storage times (Gatchell et al. 2014; Bäckström et al. 2015; Gatchell et al. 2014). The α-sulfur powder was sublimed in a resistively heated oven coupled to an electron cyclotron resonance (ECR) ion source, using He as the carrier gas. The S8+ cations generated (m/z = 256) were extracted from the source and accelerated to 34 keV, followed by mass selection using a bending magnet before injection into the storage ring.

The ionization process leaves the ions with internal energies sufficiently high to induce fragmentation, a process that occurs continuously along their travel in the ring. Neutrals formed by fragmentation in the observation arm of the ring, depicted at the bottom in Fig. 1, were counted by a position-sensitive imaging detector (neutral detector), placed after a deflection unit in the ring. If multiple fragmentation channels exist in S8+, this detector counts the total fragmentation yield. In addition, a second position-sensitive detector was mounted next to the stored beam after deflection (fragment detector), as depicted in the figure. This detector collects charged fragmentation products formed by fragmentation, which can be identified through m/z-specific deflection angles. An example of a measurement with the fragment detector is shown in the top-left corner of Fig. 1, revealing the competing generation of S5+ and 6+ ions - in both cases in correlation with a neutral reaction product. This implies the fragmentation channels S8+→S5++S3Mathematical equation: S$_8^+$ $\rightarrow$ S$_5^+$ + S$_3$ and S8+→S6++S2Mathematical equation: S$_8^+$ $\rightarrow$ S$_6^+$ + S$_2$. The position of the fragment detector was optimized for the detection of S5+. Charged fragments, S5+ and S6+, and neutral fragments were continuously recorded for 1.2 seconds, after which the remaining current was measured with a Faraday cup. This measurement cycle was repeated a large number of times.

Thumbnail: Fig. 1 Refer to the following caption and surrounding text. Fig. 1

Schematic view of the storage ring DESIREE. A 34 keV beam of S8+ ions is mass selected by a bending magnet and is injected into the cold ring. The circulation direction of the ions is depicted by arrows. A detector for neutrals formed upon fragmentation is placed after the straight section opposite to injection. In addition, a second detector is placed on the side of the stored S8+ beam, after a 10° deflection, to measure the charged species created by fragmentation. Both detectors are position-sensitive. In the top-left corner, an image of the fragment detector is shown, depicting ions corresponding to SS5+ and SS6+.

2.2 Quantum chemical calculations and modeling

To model the rate coefficients of fragmentation kD, vibrational cooling kyc, and recurrent fluorescence kRF as a function of internal energy E, inputs from DFT calculations are required. For this purpose, DFT calculations were performed using the ORCA 6.0.1 software package (Neese 2022, 2023). The B3LYP exchange-correlation functional was employed (Becke 1992), together with the Def2-TZVPP basis set (Becke 1992), including dispersion corrections via the D3BJ method (Grimme et al. 2010). This combination was recently used to compute the vibrational spectra of S8, S4+, and S4−, showing a very close agreement with measurements of their gas-phase infrared spectra (Ferrari et al. 2024). Calculations were performed with the non-default “verytight” convergence criterium for the SCF procedure and geometry optimization, as previously done. Based on the measured fragmentation channels of S8+, the calculation of kD, kVC, and kRF requires the harmonic vibrational frequencies of the allotropes S8+, S6+, S5+, S3, and S2, as discussed below. The starting geometries for optimization of the allotropes were extracted from a previous work (Jin et al. 2015). No scaling factor was applied to the computed frequencies (Ferrari et al. 2024). Moreover, for the modeling of kD, the dissociation energies of the pathways S8+→S6++S2Mathematical equation: S$_8^+$ $\rightarrow$ S$_6^+$ + S$_2$ and S8+→S5++S3Mathematical equation: S$_8^+$ $\rightarrow$ S$_5^+$ + S$_3$ were required. These were taken from previous work, reported to be 1.4 and 1.8 eV for the emission of dimers and trimers, respectively (Ferrari et al. 2024). Finally, crucial factors in the calculation of kRF are the optically active electronic transitions of S8+, which we computed using time-dependent DFT (TD-DFT) at the same theoretical level as the vibrational calculations.

The fragmentation rate coefficient of S8+ dissociating via the channel S8+→S8−i++SiMathematical equation: S$_8^+$ $\rightarrow$ S$_{8-i}^+$ + S$_i$ is expressed as (Hansen 2013) kD(E)i=ωiρ8−i(E−Di)ρ8(E).Mathematical equation: k_D(E)^i=\omega_i\frac{\rho_{8-i}(E-D_i)}{\rho_8(E)}.(1)

Here, ρ8 and ρ8-i are the densities of the vibrational levels of S8+ and S8−i+Mathematical equation: S$_{8-i}^+$, respectively, which were calculated by the BeyerSwinehart algorithm (Beyer & Swinehart 1973). In addition, Di is the dissociation energy of the channel and ωi the corresponding frequency factor. The latter was estimated based on sulfur vapor pressures, as previously discussed (Veldeman et al. 2008; Hansen et al. 2014; Chen et al. 2019).

For kVC, the simple harmonic cascade (SHC) approximation was used, which leads to the expression in Eq. (2) (Chandrasekaran et al. 2014). Here, νs and AsIRMathematical equation: $A_s^{IR}$ are the frequency and Einstein A-coefficient of vibrational mode s, respectively, and n is the vibrational quantum number kVC(E)=∑sksVC=∑sAsIR∑n=1n≤E/hνsρ8(E−nhνs)ρ8(E).Mathematical equation: k_{VC}(E)=\sum_{s}k_s^{VC}=\sum_{s}A_s^{IR}\sum_{n=1}^{n\le E/h\nu_s}\frac{\rho_8(E-nh\nu_s)}{\rho_8(E)}.(2)

The recurrent fluorescence rate coefficient is (Ferrari et al. 2019) kRF(E)=∑ekeRF=∑eAeRFρ8(E−hνe)ρ8(E),Mathematical equation: k_{RF}(E)=\sum_{e}k_e^{RF}=\sum_{e}A_e^{RF}\frac{\rho_8(E-h\nu_e)}{\rho_8(E)},(3)

where AeRFMathematical equation: $A_e^{RF}$ is the Einstein A-coefficient of the electric transition at energy hνe, while e runs over the electronic transitions of S8+. The first ten electronic transitions are considered, although numerically only the first state contributes to RF (see details later).

Finally, the dynamics of the population of excited states was modeled using a master equation formalism (Lee et al. 2023), describing the survival probability of the excited S8+. For this, the population distribution of hot S8+ molecules, g(E, t), was propagated through Eq. (4), which describes the change in g in energy E due to fragmentation and radiation ddtg(E,t)=−∑ckDc(E)g(E,t)+∑s[ksVC(E+hνs)g(E+hνs,t)−ksVC(E)g(E,t)]+∑e[keRF(E+hνe)g(E+hνe,t)−ke(E)RFg(E,t)].Mathematical equation: \frac{\rm d}{{\rm d}t}g(E,t)&=-\sum_{c}k_D^c(E)g(E,t)\nonumber\\ &\quad+\sum_{s}\left[k_s^{VC}(E+h\nu_s)g(E+h\nu_s,t)-k_s^{VC}(E)g(E,t)\right]\nonumber\\ &\quad+\sum_{e}\left[k_e^{RF}(E+h\nu_e)g(E+h\nu_e,t)-k_e(E)^{RF}g(E,t)\right].(4)

The three terms describe the change in population at energy E due to fragmentation, vibrational cooling, and recurrent fluorescence, respectively. In Eq. (4), c runs over the two possible dissociation channels of S8+. We note that in this model approach, internal vibrational redistribution (IVR) is assumed to be efficient at all times (or internal energies).

Thumbnail: Fig. 2 Refer to the following caption and surrounding text. Fig. 2

Time-dependent neutral yield of S8+ ions. A quenched power law (Eq. (6)) is fitted to the experimental data, shown in the continuous red line. In addition, a simple power law (Eq. (5)) is included in the dashed blue line for comparison, showing the presence of radiative cooling.

3 Results and discussion

3.1 Fragmentation channels

The use of the fragment detector, as shown in Fig. 1, allowed us to obtain information about the fragmentation pathways of vibrationally hot S8+ ions. As already mentioned, only the formation of two charged products, S5+ and S6+, was observed, implying that two fragmentation pathways compete: S8+→S5++S3Mathematical equation: S$_8^+$ $\rightarrow$ S$_5^+$ + S$_3$ and S8+→S6++S2Mathematical equation: S$_8^+$ $\rightarrow$ S$_6^+$ + S$_2$. This observation agrees with previous experiments in which collision-induced dissociation (CID) was used to infer the fragmentation channels of S8+ and the competition between the formation of S5+ and S6+ (Ferrari et al. 2024). This reinforces that atom-by-atom evaporation is not an energetically favorable dissociation pathway for S8+, which instead emits neutral dimers and trimers. Previous work on neutral S has shown the same fragmentation pathways, i.e., S8 → S5 + S3 and S8 → S6 + S2 (Ferrari et al. 2024), albeit using a third excitation mechanism to induce fragmentation, infrared multiple photon excitation. Hence, it seems clear that irrespective of the excitation mechanism and its charge state, octasulfur fragments by emitting neutral S2 and S3 units, a behavior currently not included in astrochemical models of sulfur allotropes (Laas & Caselli 2019; Shingledecker et al. 2020). DFT calculations show that among the possible octasulfur fragmentation channels, the emissions of neutral S2 and S3 fragments have the lowest threshold energies.

3.2 Fragmentation time-dependence

The neutral yield (count rate) R(t) of S8+ ions, accounting for S2 and S3 fragments, is measured using the neutral detector as a function of storage time, as shown by the black trace in Fig. 2. At early times, when the S8+ ensemble is hot, a high neutral yield is recorded, implying a high fragmentation rate. In time, however, the state population of S8+ shifts to lower energies, leading to a much lower fragmentation rate. This is clearly observed in the figure, with a decrease in the detected neutral yield up to ≈300 ms. From this time on, fragmentation occurs only at a very low rate, most likely dominated by collisions with the residual gas in the storage ring.

As shown by many studies of storage rings and ion traps, given the broad energy distribution of the ensemble, the overall decay dynamics follows a power law in time, with an exponent shown to be close to −1. However, this is under the assumption that only fragmentation is responsible for the cooling of the stored ensemble of ions (Hansen et al. 2001, 2017b). This is known as the 1/t decay law, which is a consequence of the fact that the ensemble decays at different rates simultaneously for different internal ion energies, if the internal energy distribution is broad (Andersen et al. 2003). Hence, when only fragmentation occurs in the ensemble of hot S8+ ions, the measured neutral yield R(t) follows Eq. (5), with R0, δ, and C1 constants R(t)=R0t(−1+δ)+C1.Mathematical equation: R(t)=R_0t^{(-1+\delta)}+C_1.(5)

Deviations from the 1/t law, i.e., δ ≠ 0 have been tentatively assigned to effects of heat capacity, competing channels, and the shape of the internal energy distribution (Hansen 2021). An attempt to fit Eq. (5) to the data in Fig. 2 (dashed blue line) reveals a good agreement at short times, but clearly cannot grasp the full time-dependence of R(t), especially not for longer storage times. Hence, the power law decay works only at higher internal energies. Instead, if radiative cooling competes with fragmentation, the power law is exponentially quenched (Ferrari et al. 2019) R(t)=R0e−t/τct(−1+δ)+C2,Mathematical equation: R(t)=R_0e^{-t/\tau_c}t^{(-1+\delta)}+C_2,(6)

with τc the critical radiative cooling time, where the dissociation and radiative rate coefficients are roughly equal. As presented in Fig. 2, a fit of Eq. (6) reproduces the time-dependence of the observed signal well, yielding a value of τc = 95 ± 1 ms. From the fit, we further extract R0 = (1127 ± 1) ∙ 103 and δ = 0.106 ± 0.001, and a background of 4 · 103. Hence, the analysis shows that radiation is an effective cooling channel for S8+ ions. However, knowledge of τc alone cannot distinguish between vibrational cooling and recurrent fluorescence, for which modeling of the different rate coefficients is necessary.

3.3 Rates of fragmentation, vibrational cooling, and recurrent fluorescence

Following the procedure discussed in the Methods section, and using Eq. (1), the total fragmentation rate coefficient of S8+ is modeled as a function of internal energy. The result is presented in Fig. 3a as a solid green curve. Given the activated nature of fragmentation, the process stops below the lowest dissociation energy of S8+, computed as 1.4 eV using DFT (Ferrari et al. 2024). The region in between the horizontal dashed lines denotes the dynamical range to which the experiment is sensitive. Above the upper line, fragmentation will occur faster than the time it takes S8+ to cover half a turn in the ring, whereas the rates below the lower line correspond to time scales longer than the total storage time in the ring in the present experiment (1.2 s).

In addition, the figure shows the rate of vibrational cooling (short-dashed red line). For this, Eq. (2) is used, which needs as input the vibrational frequencies of S8+. We relied on DFT calculations for the frequencies, using a recently applied method to successfully compute the infrared spectra of S8, 4+ and S4− (Ferrari et al. 2024). The infrared spectrum presented in that reference reveals only a few infrared-active modes, all of low intensity due to the relatively high symmetry of S8+.

As a consequence, the VC rate is low, barely reaching values within the experimentally sensitive region and would give a critical time of 770 ms, much longer than the measured value of τc = 95 ± 1 ms. Hence, another process should be invoked to explain the experimental results.

Finally, Fig. 3a presents the modeled rate of recurrent fluorescence (dashed blue line). In this case, the analysis requires the optically active electronic transitions of S8+, which we computed using TD-DFT. To assess the reproducibility of such calculations, we also computed the optical spectrum of S8, which can be compared with measurements performed in methanol solution (Steudel et al. 1988). The experimental data show broad absorption features at roughly 270 (4.59) and 235 (5.28) nm (eV), in close agreement with predicted optical transitions at 270 (4.59) and 237 (5.23) nm (eV). The calculated absorption spectra of S8+ and S8 are shown in Fig. 3b. Given the closed-shell electronic configuration of neutral S8, electronic transitions are only found at high energies, above 4.42 eV. Instead, for the open-shell S8+, a low-lying electronic transition is predicted at 0.76 eV, which is the main source of RF. When comparing the rates of fragmentation and RF, a much better correspondence is found with the experiment than in the case of VC. For RF, a critical rate of 80 s−1 is predicted, slightly different from the experimental value of τc = 95 ± 1 s−1 but on the same order of magnitude. Considering a typical uncertainty of ±0.2 eV for the computation of transition energies with TD-DFT using hybrid functionals (Laurent & Jacquemin 2013), the modeled RF rates are reasonably close to the experimental value.

Thumbnail: Fig. 3 Refer to the following caption and surrounding text. Fig. 3

(a) Modeled rates of fragmentation (solid green line), vibrational cooling (dotted red line) and recurrent fluorescence (dashed blue line). The region in between the horizontal dotted lines highlights the dynamical range covered experimentally. (b) TD-DFT-computed optical absorption spectrum of S8+ (filled blue) and S8 (red). The y-axis represents oscillator strength (f). A top axis in wavelength is included.
Thumbnail: Fig. 4 Refer to the following caption and surrounding text. Fig. 4

(a) Survival probability of S8+ as a function of initial internal energy (blue circles). The situation in which RF is excluded is presented in red squares. (b) Survival probability of neutral S8.

3.4 Survival probability

Astrochemical models accounting for sulfur allotropes assume that S8 is the end of the reaction chain (Shingledecker et al. 2020), given the predicted higher stability of octasulfur with respect to other allotropes. However, recent DFT calculations of dissociation energies (Ferrari et al. 2024) showed much lower values than other species present in the ISM, such as PAHs and C60. This raises the question of the survival probability of octasulfur in energetic interstellar environments, which ultimately determines where octasulfur could be detected in space.

To address this, we used the formalism of Eq. (4) to model the survival probability of S8+ as a function of internal energy. Starting from an initial delta function distribution centered at energy E0, the rates of fragmentation, VC, and RF (Fig. 3a) were employed to track the distribution as a function of time. Equation (4) is numerically solved in steps of 0.05 μs, for a total time of 1 s. The survival probability is defined as the ratio of the integrated initial and final population distribution. The result for S8+ is presented in Fig. 4a, which also depicts the situation when RF is excluded from the analysis. As seen, without RF, the probability rapidly falls to zero at internal energies above 1.4 eV. Instead, RF helps stabilize S8+, which now has a survival probability of 50% at an energy of 1.49 eV. With RF, there is still a survival probability of 1% at an internal energy of 1.7 eV. Hence, RF provides a stabilizing pathway, but the effect is not dramatic. Assuming a heat capacity of (3N - 6)kB, this means a temperature of 1100 K as the limit for the environments in which S8+ could be detected.

Although the experiments presented here are performed only on the cationic S8+, the analysis of the rate coefficients can be extended to the neutral S8. As shown in Fig. 3b, S8 only has electronic transitions at energies above 4 eV, and therefore RF is not a possible cooling channel, leaving only fragmentation and VC. In this case, the survival probability rapidly falls to zero above 1.4 eV, making the temperature constraint lower, implying that above 900 K S8 will promptly fragment.

4 Conclusions

Experiments on hot S8+ ions were performed in the cryogenic ion-beam storage ring DESIREE, showing quenching of fragmentation by radiative cooling on a critical time scale of 95 ms. Fragmentation was seen to proceed via two competitive channels: S8+→S5++S3Mathematical equation: S$_8^+$ $\rightarrow$ S$_5^+$ + S$_3$ and S8+→S6++S2Mathematical equation: S$_8^+$ $\rightarrow$ S$_6^+$ + S$_2$, in agreement with previous collision-induced dissociation experiments (Ferrari et al. 2024). Interestingly, these channels are the same as for neutral S8. Using inputs from quantum chemical calculations, the rate coefficients of fragmentation, vibrational cooling, and recurrent fluorescence were modeled, showing good agreement with the experiment. The analysis revealed that radiative cooling in S8+ proceeds via RF from a low-lying electronic transition at 0.76 eV. Nevertheless, the stabilization provided by RF is not drastic and at internal energies greater than 1.7 eV there is a survival probability of less than 1% for S8+, which has a lowest dissociation energy of 1.4 eV. The analysis was extended to neutral S8, in which RF is not a possible cooling mechanism due to the lack of low-lying electronically excited states. For S8, destruction already occurs immediately from the dissociation-energy limit of 1.4 eV.

Acknowledgements

We acknowledge the DESIREE infrastructure for provisioning of facilities and experimental support, and thank the operators and technical staff for their invaluable assistance. The DESIREE infrastructure receives funding from the Swedish Research Council under the grant numbers 2021-00155 and 2023-00170. H.Z., H.C., and H.T.S. thank the Swedish Research Council for individual project grants (with Contracts No.2025-05087, No.2023-03833, and No.2022-02822). Furthermore, H.T.S, H.C., and H.Z. acknowledge the project grant “Making and Breaking of Molecular Bonds” funded by the Knut and Alice Wallenberg Foundation under contract 2024.0134. This article is based upon work from COST Action CA21126 - Carbon molecular nanostructures in space (NanoSpace), supported by COST (European Cooperation in Science and Technology). We further acknowledge the Dutch Research Council (NWO) for support through computational resources (grant 2024.009).

References

  1. Agúndez, M., Marcelino, N., Cernicharo, J., & Tafalla, M. 2018, A&A, 611, L1 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  2. Aikawa, Y., Kamuro, D., Sakon, I., et al. 2012, A&A, 538, A57 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  3. Andersen, J. U., Gottrup, C., Hansen, K., Hvelplund, P., & Larsson, M. 2001, Eur. Phys. J. D, 17, 189 [Google Scholar]
  4. Andersen, J. U., Bonderup, E., Hansen, K., et al. 2003, Eur. Phys. J. D., 24, 191 [Google Scholar]
  5. Andrews, H., Boersma, C., Werner, M., et al. 2015, ApJ, 807, 99 [NASA ADS] [CrossRef] [Google Scholar]
  6. Aponte, J. C., Dworkin, J. P., Glavin, D. P., et al. 2023, EPS, 75, 28 [Google Scholar]
  7. Bäckström, E., Hanstorp, D., Hole, O. M., et al. 2015, Phys. Rev. Lett., 114, 143003 [Google Scholar]
  8. Becke, A. D. 1992, J. Chem. Phys., 96, 2155 [NASA ADS] [CrossRef] [Google Scholar]
  9. Beyer, T., & Swinehart, D. 1973, CACM, 16, 379 [Google Scholar]
  10. Cabezas, C., Agúndez, M., Pérez, C., et al. 2025, A&A, 701, L8 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  11. Calmonte, U., Altwegg, K., Balsiger, H., et al. 2016, MNRAS, 462, S253 [NASA ADS] [CrossRef] [Google Scholar]
  12. Carrascosa, H., Muñoz Caro, G., Martín-Doménech, R., et al. 2024, MNRAS, 533, 967 [Google Scholar]
  13. Cernicharo, J., Tercero, B., Marcelino, N., et al. 2026, A&A, 705, L7 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  14. Chandrasekaran, V., Kafle, B., Prabhakaran, A., et al. 2014, J. Phys. Chem. Lett., 5, 4078 [Google Scholar]
  15. Chen, F.-Q., Kono, N., Suzuki, R., et al. 2019, Phys. Chem. Chem. Phys., 21, 1587 [Google Scholar]
  16. Ebara, Y., Furukawa, T., Matsumoto, J., et al. 2016, Phys. Rev. Lett., 117, 133004 [NASA ADS] [CrossRef] [Google Scholar]
  17. Fedyaeva, M., Lepeshkin, S., & Oganov, A. R. 2023, Phys. Chem. Chem. Phys., 25, 9294 [Google Scholar]
  18. Ferrari, P., Vanbuel, J., Hansen, K., et al. 2018, Phys. Rev. A, 98, 012501 [Google Scholar]
  19. Ferrari, P., Janssens, E., Lievens, P., & Hansen, K. 2019, Int. Rev. Phys. Chem., 38, 405 [Google Scholar]
  20. Ferrari, P., Berden, G., Redlich, B., Waters, L. B., & Bakker, J. M. 2024, Nat. Commun., 15, 5928 [Google Scholar]
  21. Fuente, A., Roueff, E., Le Petit, F., et al. 2024, A&A, 687, A87 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  22. Gatchell, M., Schmidt, H. T., Thomas, R. D., et al. 2014, J. Phys. Conf. Ser. 488, 012040 [Google Scholar]
  23. Goicoechea, J., Pety, J., Gerin, M., et al. 2006, A&A, 456, 565 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  24. Grimme, S., Antony, J., Ehrlich, S., & Krieg, H. 2010, J. Chem. Phys., 132, 154104 [Google Scholar]
  25. Hansen, K. 2013, Statistical Physics of Nanoparticles in the Gas Phase (Berlin: Springer), 73 [Google Scholar]
  26. Hansen, K. 2021, Mass Spectrom. Rev., 40, 725 [Google Scholar]
  27. Hansen, K., & Campbell, E. 1996, J. Chem. Phys., 104, 5012 [Google Scholar]
  28. Hansen, K., Andersen, J. U., Hvelplund, P., et al. 2001, Phys. Rev. Lett., 87, 123401 [Google Scholar]
  29. Hansen, K., Li, Y., Kaydashev, V., & Janssens, E. 2014, J. Chem. Phys., 141, 024302 [Google Scholar]
  30. Hansen, K., Ferrari, P., Janssens, E., & Lievens, P. 2017a, Phys. Rev. A, 96, 022511 [Google Scholar]
  31. Hansen, K., Stockett, M. H., Kaminska, M., et al. 2017b, Phys. Rev. A, 95, 022511 [Google Scholar]
  32. Hansen, K., Licht, O., Kurbanov, A., & Toker, Y. 2023, J. Phys. Chem. A, 127, 2889 [Google Scholar]
  33. Iida, S., Hu, W., Zhang, R., et al. 2022, MNRAS, 514, 844 [NASA ADS] [CrossRef] [Google Scholar]
  34. Ito, G., Furukawa, T., Tanuma, H., et al. 2014, Phys. Rev. Lett., 112, 183001 [NASA ADS] [CrossRef] [Google Scholar]
  35. Jiménez-Escobar, A., & Caro, G. M. 2011, A&A, 536, A91 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  36. Jin, Y., Maroulis, G., Kuang, X., et al. 2015, Phys. Chem. Chem. Phys., 17, 13590 [Google Scholar]
  37. Kaw, K. A., Louwerse, R. J., Bakker, J. M., et al. 2024, Commun. Chem., 7, 124 [Google Scholar]
  38. Keller, L. P., & Messenger, S. 2011, Geochim. Cosmochim. Acta, 75, 5336 [NASA ADS] [CrossRef] [Google Scholar]
  39. Kono, N., Furukawa, T., Tanuma, H., et al. 2015, Phys. Chem. Chem. Phys., 17, 24732 [Google Scholar]
  40. Kusuda, J., Fukuzaki, R., Majima, T., Tsuchida, H., & Saito, M. 2024, Nucl. Instrum. Methods Phys. Res. B, 553, 165387 [Google Scholar]
  41. Laas, J. C., & Caselli, P. 2019, A&A, 624, A108 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  42. Laurent, A. D., & Jacquemin, D. 2013, Int. J. Quantum Chem., 113, 2019 [Google Scholar]
  43. Le Gal, R., Öberg, K. I., Teague, R., et al. 2021, ApJS, 257, 12 [NASA ADS] [CrossRef] [Google Scholar]
  44. Lee, J. W., Stockett, M. H., Ashworth, E. K., et al. 2023, J. Chem. Phys., 158 [Google Scholar]
  45. Léger, A., Boissel, P., & d’Hendecourt, L. 1988, Phys. Rev. Lett., 60, 921 [Google Scholar]
  46. Martin, S., Bernard, J., Brédy, R., et al. 2013, Phys. Rev. Lett., 110, 063003 [NASA ADS] [CrossRef] [Google Scholar]
  47. McClure, M. K., Rocha, W., Pontoppidan, K., et al. 2023, Nat. Astron., 7, 431 [NASA ADS] [CrossRef] [Google Scholar]
  48. McGuire, B. A. 2022, ApJS, 259, 30 [NASA ADS] [CrossRef] [Google Scholar]
  49. McGuire, B. A., Loomis, R. A., Burkhardt, A. M., et al. 2021, Science, 371, 1265 [Google Scholar]
  50. Mifsud, D. V., Kanuchová, Z., Herczku, P., et al. 2021, Space Sci. Rev., 217, 14 [CrossRef] [Google Scholar]
  51. Navarrete, J. N., Martini, P., Rosén, S., et al. 2025, Phys. Rev. Lett., 135, 213001 [Google Scholar]
  52. Neese, F. 2022, Wiley Interdiscip. Rev. Comput. Mol. Sci., 12, e1606 [Google Scholar]
  53. Neese, F. 2023, J. Comput. Chem., 44, 381 [Google Scholar]
  54. Peeters, K., Janssens, E., Hansen, K., Lievens, P., & Ferrari, P. 2021, Phys. Rev. Research., 3, 033225 [Google Scholar]
  55. Saito, M., Kubota, H., Yamasa, K., et al. 2020, Phys. Rev. A, 102, 012820 [NASA ADS] [CrossRef] [Google Scholar]
  56. Schmidt, H. T. 2021, in ECLA (Berlin: Springer), 183 [Google Scholar]
  57. Schmidt, H. T., Thomas, R. D., Gatchell, M., et al. 2013, Rev. Sci. Instrum., 84, 055115 [Google Scholar]
  58. Shingledecker, C. N., Lamberts, T., Laas, J. C., et al. 2020, ApJ, 888, 52 [Google Scholar]
  59. Slavicinska, K., Boogert, A., van Dishoeck, E., et al. 2025, A&A, 693, A146 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  60. Steudel, R., Jensen, D., Göbel, P., & Hugo, P. 1988, Ber. Bunsenges. Phys. Chem., 92, 118 [Google Scholar]
  61. Stockett, M. H., Bull, J. N., Buntine, J. T., et al. 2020, Eur. Phys. J. D, 74, 150 [Google Scholar]
  62. Stockett, M. H., Bull, J. N., Cederquist, H., et al. 2023, Nat. Commun., 14, 395 [CrossRef] [Google Scholar]
  63. Sundén, A., Goto, M., Matsumoto, J., et al. 2009, Phys. Rev. Lett., 103, 143001 [Google Scholar]
  64. Taillard, A., Martín-Doménech, R., Carrascosa, H., et al. 2025, A&A, 694, A263 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  65. Thomas, R. D., Schmidt, H. T., Andler, G., et al. 2011, Rev. Sci. Instrum., 82, 065112 [Google Scholar]
  66. Van Gelder, M., Ressler, M., Van Dishoeck, E., et al. 2024, A&A, 682, A78 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  67. Veldeman, N., Janssens, E., Hansen, K., et al. 2008, Faraday Discuss., 138, 147 [Google Scholar]
  68. Wenzel, G., Cooke, I. R., Changala, P. B., et al. 2024, Science, 386, 810 [NASA ADS] [CrossRef] [Google Scholar]
  69. Yoshida, M., Furukawa, T., Matsumoto, J., et al. 2017, J. Phys. Conf. Ser., 875, 102016 [Google Scholar]
  70. Zhu, B., Bull, J. N., Ji, M., Zettergren, H., & Stockett, M. H. 2022, J. Chem. Phys., 157, 044303 [NASA ADS] [CrossRef] [Google Scholar]

All Figures

Thumbnail: Fig. 1 Refer to the following caption and surrounding text. Fig. 1

Schematic view of the storage ring DESIREE. A 34 keV beam of S8+ ions is mass selected by a bending magnet and is injected into the cold ring. The circulation direction of the ions is depicted by arrows. A detector for neutrals formed upon fragmentation is placed after the straight section opposite to injection. In addition, a second detector is placed on the side of the stored S8+ beam, after a 10° deflection, to measure the charged species created by fragmentation. Both detectors are position-sensitive. In the top-left corner, an image of the fragment detector is shown, depicting ions corresponding to SS5+ and SS6+.
In the text
Thumbnail: Fig. 2 Refer to the following caption and surrounding text. Fig. 2

Time-dependent neutral yield of S8+ ions. A quenched power law (Eq. (6)) is fitted to the experimental data, shown in the continuous red line. In addition, a simple power law (Eq. (5)) is included in the dashed blue line for comparison, showing the presence of radiative cooling.
In the text
Thumbnail: Fig. 3 Refer to the following caption and surrounding text. Fig. 3

(a) Modeled rates of fragmentation (solid green line), vibrational cooling (dotted red line) and recurrent fluorescence (dashed blue line). The region in between the horizontal dotted lines highlights the dynamical range covered experimentally. (b) TD-DFT-computed optical absorption spectrum of S8+ (filled blue) and S8 (red). The y-axis represents oscillator strength (f). A top axis in wavelength is included.
In the text
Thumbnail: Fig. 4 Refer to the following caption and surrounding text. Fig. 4

(a) Survival probability of S8+ as a function of initial internal energy (blue circles). The situation in which RF is excluded is presented in red squares. (b) Survival probability of neutral S8.
In the text

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