LABORATORY MEASUREMENTS COMPELLINGLY SUPPORT A CHARGE-EXCHANGE MECHANISM FOR THE "DARK MATTER" ∼3.5 keV X-Ray LINE

Recently reported observations of a feature like a weak X-ray emission line at an energy of approximately ∼3.5 keV from the Perseus galaxy cluster, the galaxy M31 (Boyarsky et al. 2014), and in stacked spectra of 73 galaxy clusters (Bulbul et al. 2014) with the X-ray cameras of the XMM-Newton telescope have attracted enormous attention. The reason for this is the lack of an immediate identification of the feature in standard wavelength tables. Although the existence of a very large number of unidentified transitions in all spectral ranges is a well-known fact, it has been widely assumed that our knowledge of the X-ray emission spectra from atomic sources was sufficiently well modeled to pinpoint this transition as an exceptional phenomenon. In particular, speculations about a possible dark matter origin of this observed X-ray line feature from galaxy clusters have sparked an incredible interest in the scientific community and given rise to a tide of publications attempting to explain the possible reason for the observed unidentified line feature (ULF). Among other possibilities, the origin of this line has been hypothesized as the result of decaying, long-sought dark matter particle candidates—sterile neutrinos, presumably based on the fact that this X-ray line is not available in the present atomic databases for thermal plasmas (Foster et al. 2012; Bulbul et al. 2014).

Similar signals were later detected from the Galactic center (Boyarsky et al. 2015) and from the Perseus cluster core with the help of the Suzaku telescope (Urban et al. 2015). While these studies were able to establish upper flux limits for the ULF, they could not provide conclusive evidence for it due to statistical and model uncertainties. A very recent study on the dwarf spheroidal galaxy Draco from observations with XMM-Newton rules out a possible origin of the ULF in dark matter decay (Jeltema & Profumo 2016) based on an incompatibility with the expected dark matter distribution of that system. A comprehensive search for the ULF in stacked galaxy spectra by Anderson et al. (2015) reached a similar conclusion with no significant evidence of any emission line at 3.5 keV.

Given the importance of the matter, a very careful spectral analysis should be carried out in order to first exclude all possible known causes of X-ray emission in this spectral range. Unfortunately, the standard spectral databases used for comparison and the models based upon them have in part to rely on atomic structure calculations, since the body of laboratory data on X-ray emission lines is far from complete (Beiersdorfer 2003). In this work, we show experimental data that strongly support the cautious explanation of the ULF recently given by Gu et al. (2015): this intriguing X-ray line feature arises from charge exchange between fully stripped sulfur ions and atomic hydrogen, populating states in high principal quantum numbers of the subsequently formed hydrogen-like sulfur ions. In this model, it is compelling that X-rays should be emitted at ∼3.5 keV by a set of S¹⁵⁺ transitions from n ≥ 9 to the ground state, where n is the principal quantum number. This scenario has to be considered since the highly ionized plasma present in galaxy clusters certainly contains S¹⁶⁺ and S¹⁵⁺ ions (Mushotzky et al. 1981).

Charge exchange (hereafter CX) occurs when a neutral atom collides with a sufficiently charged ion, which becomes typically an excited product species. For a highly charged ion (HCI) moving at thermal velocities, the electron transfer takes place at—atomically speaking—large distances, since the potential well of the neutral donor is strongly distorted by the approaching HCI at internuclear separations of several atomic units. The lowering of the potential barrier between the two charged centers leads to the formation of a short-lived quasi-molecular state for the outermost electrons of the donor, with the electronic wavefunction extending between the two centers—the projectile HCI and the donor. In a classical picture of a collision at thermal energies, the electron repeatedly visits both centers during the approaching and receding phases of the collision and is likely captured by the center with the higher charge after the passage. This process is usually be modeled using, e.g., the so-called over-the-barrier method (OBM) of Ryufuku et al. (1980), and more advanced models such as the extended OBM of Niehaus (1986), multichannel Landau–Zener (MCLZ) methods (Cumbee et al. 2016), and various others. CX between HCIs and neutral donors leads to the formation of a high Rydberg state in the down-charged HCI projectile for the range of thermal collision energies. The cross sections for populating such states are rather large (10⁻¹⁵ cm² and higher for HCIs with charges 10–20). Thereafter, radiative decay of those excited states with high principal quantum number n = n_cx to the ground state n = 1 produces X-ray line emission. If the colliding HCI has K-shell vacancies, it will fill each of them through emission of an X-ray photon. In the case of multiple electron capture from a many-electron neutral donor, various non-radiative Auger processes can also lead to relaxation of the system (Fischer et al. 2002; Knoop et al. 2008; Xue et al. 2014).

Following the discovery of X-rays from comets (Lisse et al. 1996, 2001; Dennerl et al. 1997) and its explanation as being caused by the interaction of solar-wind HCIs and neutral coma gas (Cravens 1997), very clear observations of CX-induced X-ray emission have provided insights into the interaction between cold and hot astrophysical plasmas. The pioneering reproduction in the laboratory by Beiersdorfer et al. (2003) of the low-resolution spectra observed in comets showed how CX-induced X-ray emission can be used to diagnose the properties of the solar wind dynamics. Absolute CX cross sections were also obtained in the laboratory for solar-wind HCIs interacting with the neutrals present in comets (Greenwood et al. 2000a, 2000b; Mawhorter et al. 2007). Due to the HCI abundance, CX is a ubiquitous process that should always be considered wherever hot plasma interacts with a neutral medium. This is obviously the case in galaxy clusters where hot intracluster medium interacts with cold clouds dwelling around the central galaxies (Gu et al. 2015).

Laboratory studies have been carried out by several groups with various methods (see, e.g., Janev et al. 1983; Dijkkamp et al. 1985; Hoekstra et al. 1990; Bodewits et al. 2004, 2006; Trassinelli et al. 2012). Moreover, CX has been recognized as essential for understanding the ionization equilibrium of laboratory plasmas, and it also affects the storage time in ion traps and the energy transport mechanism in the edge region of tokamak fusion plasmas (Beiersdorfer et al. 2000; Leutenegger et al. 2010). This has motivated a number of CX studies by the electron beam ion trap (EBIT) group at the Lawrence Livermore National Laboratory (LLNL) (Beiersdorfer et al. 2000, 2003; Wargelin et al. 2005; Leutenegger et al. 2010; Betancourt-Martinez et al. 2014) and by other laboratories (Fischer et al. 2002; Allen et al. 2008; Knoop et al. 2008; Xue et al. 2014), with X-ray spectral analysis carried out at both low and high resolution. Various theoretical models have been invoked for data analysis. While confirming the role of CX, those experiments have nonetheless pointed out discrepancies in the quantitative modeling of the relative intensity of CX-fed transitions that are still a matter of active research in both theory and experiment.

A common feature of most X-ray observations is the lack of sufficient resolution capable of distinguishing the principal quantum number n and angular momentum quantum numbers l of the state in which the electron is captured. This leads to the use of various definitions of "hardness" for the observed spectra, which are basically intensity ratios (${ \mathcal R }$ and ${ \mathcal H }$ respectively for hydrogen-like and helium-like lines) between the unresolved transitions from $n\geqslant 3\to 1$ to the better separated transition $n=2\to 1$. A few high-resolution experiments using X-ray microcalorimeters (Leutenegger et al. 2010) or crystal spectrometers (Rosmej et al. 2006) do not suffer from these limitations, which greatly hinder astrophysical studies. Strong expectations of the performance of Astro-H, which among other things would have provided novel means to understand the contributions of this process, have been frustrated by the untimely demise of that critical mission.

Among other findings, the studies have revealed some intricacies in the dependence of the range of nl distribution on the donor neutral that are still not fully understood (Beiersdorfer et al. 2000, 2001) and can lead to an uncertainty in the modeling of the spectral hardness. One particularly striking example (Leutenegger et al. 2010) showed how simultaneously prepared Ar¹⁷⁺ and P¹⁵⁺ ions, in spite of the similarity of their electronic structure, produced X-ray spectra that allowed one to infer rather disparate nl populations in the capture process. Furthermore, studies have shown effects of simultaneous and sequential multiple electron capture processes in collisions (Otranto & Olson 2011; Otranto et al. 2014). These are particularly relevant for HCI interactions with a comet, where many-electron donor species are present (Ali et al. 2005, 2010, 2016), while single capture is the only possible process in interaction with atomic hydrogen.

Motivated by this, we tested the hypothesis of the CX scenario proposed by Gu et al. (2015) by investigating in the laboratory the X-ray emission spectra of fully stripped sulfur ions after interaction with neutral gas. In the following sections, we will discuss the experimental setup, data analysis, and results that corroborate the theoretical predictions of Gu and astrophysical observations.

For the measurements, we use the magnetic trapping mode of an EBIT (Beiersdorfer et al. 2000). The experimental principle is as follows. Bare S¹⁶⁺ and H-like S¹⁵⁺ ions are produced in an EBIT by interaction with an intense electron beam; recombination with a gaseous neutral species is observed after turning off the electron beam while keeping the HCIs magnetically confined (Beiersdorfer et al. 2000). By differentially varying the production conditions of the two ions, we distinguished their respective CX contributions to the recorded X-ray spectra with a photon energy resolution close to that of the X-ray cameras on board XMM-Newton. Under a broad range of conditions, a 3.5 keV transition clearly shows up in the spectra, which could well explain the aforementioned astrophysical observations.

We carried out the experiment with FLASH-EBIT (Epp et al. 2007, 2010), a device used primarily for soft and hard X-ray excitation of HCIs (Bernitt et al. 2012) with free-electron lasers and synchrotron radiation at its base location in the Max-Planck-Institute for Nuclear Physics, Heidelberg. The setup is sketched in Figure 1. An intense, magnetically compressed electron beam ionizes neutrals in its path and subsequently traps the ions in tight orbits around its own propagation axis by means of its negative space charge potential. Successive electron impact ionization is caused by the monoenergetic electron beam, which is focused to approximately 25 μm radius by a coaxial 6 T field generated by a superconducting Helmholtz coil setup. The ions are trapped along the beam axis inside a potential well (∼q × 100 V, where q is the ionic charge) produced by a set of drift tubes. Radial confinement is primarily due to the negative space charge potential of the electron beam (with a depth similar in magnitude to the axial one), but also to the axial magnetic field. In this way, an ion cloud containing millions of HCIs, with an extent that is 50 mm in length and less than 1 mm in diameter, forms in a fraction of a second. It is crucial for this experiment that, even after turning off the electron beam, the magnetic field efficiently confines the beam-generated HCIs within a cylindrical volume of larger diameter than under electron beam trapping—the so-called magnetic trapping mode (Beiersdorfer et al. 2000).

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Sulfur atoms were continuously brought into the interaction and trapping region using a volatile molecular compound, carbon disulfide (CS₂), forming an extremely tenuous molecular beam intersecting the electron beam. This molecular beam conveniently serves both for the production of sulfur HCIs and as a donor species for CX. For the production of sulfur HCIs in the charge states of interest, the electron beam energy has to exceed the ionization potential of helium-like S¹⁴⁺. The stability of closed-shell ions of this type makes it necessary to raise the collision energy well above that threshold value. While this is advantageous in terms of the yield of S¹⁵⁺ and S¹⁶⁺ ions, it also implies that the three charge states can be simultaneously present in the trap. In order to distinguish the contributions of the two species giving rise to transitions to n = 1, we perform a differential measurement by changing the beam energy below and above the threshold for production of bare S¹⁶⁺ ions.

The technique requires cyclic, rapid switching of the electron beam: beam-on mode to produce and trap HCIs, and beam-off mode, which confines the ions only by the magnetic field in the absence of electron impact excitation. With this technique, X-ray emission from CX can be distinguished from the copious production of X-rays while the beam is on. The electron beam carries a current of 150 mA during the production subcycle, which lasts for 9.4 s, after which the electron beam is turned off for 6.6 s; see Figure 2. Switching is performed by controlling the electron gun with a fast high-voltage amplifier driven by a periodic rectangular signal, leading to an overall duty cycle of ∼40%. A synchronous linear time ramp allows timing of the detected X-ray photons within the cycle. These are recorded with a commercial windowless silicon drift detector with an energy resolution of FWHM ∼ 150 eV. While this detector does not offer the excellent photon energy resolution afforded by an X-ray microcalorimeter as used in CX experiments at LLNL (Beiersdorfer et al. 2003; Leutenegger et al. 2010), it provides a conveniently large detection solid angle and reduces our measuring time.

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A typical X-ray spectrum is shown in Figure 2. During the beam-on mode, electron impact excitation into various n-states of S¹⁵⁺ and S¹⁴⁺ and subsequent decay to the ground state leads to the emission of K-shell X-rays. Furthermore, monoenergetic electrons from the beam also radiatively recombine, predominantly into the n = 1 and n = 2 states, giving rise to the ∼8 keV and ∼5 keV transitions, respectively. Their photon energy is the sum of the electron beam energy and the ionization potential of the respective shell and ion. In contrast, during the magnetic trapping mode the emission of X-rays is much weaker. After turning off the electron beam, metastable states populated by electron impact relax very quickly. In this regime, this happens typically within microseconds for sulfur ions, which is unresolvable on the present timescale. Some impurity HCIs from barium emanating from the cathode are co-trapped and appear as weak features at 4.5 keV. The dominant emission during the beam-off period is due to the radiative relaxation of high Rydberg states that are populated by CX, resulting in X-ray transitions starting from principal quantum numbers ${n}_{\mathrm{cx}}=15,\ldots ,3\to n=1$. Various radiative cascades also feed the n = 2 state, producing a strong Lyα X-ray line at ∼2.4 keV.

We measured spectra at electron beam energies in the range from 3.4 to 7 keV and with CS₂ injection pressures in the first stage of the differential pumping system used to form the molecular beam varying from 10⁻⁸ to 10⁻⁵ mbar. The scan of the electron beam energy shown in Figure 3 was performed at an injection pressure of ∼10⁻⁸ mbar. Pressure scans were carried out with a fixed electron beam energy of 5 keV. A minimum electron beam energy of 3494 eV is required for bare sulfur production. Accordingly, the experiment shows a clear appearance and evolution of the ${n}_{\mathrm{cx}}\leqslant 15\to n=1$ transitions at energies of 3.30–3.48 keV for an electron beam energy above 4000 eV.

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4.1. X-Ray Energy Calibration

4.2. Spectral Fitting

In Figure 4 we display the total number of photons detected within the magnetic trapping mode as a function of photon energy. To ensure that the spectra are completely free of photons emitted due to the electron beam–ion interaction, only those counts are considered that are detected 1 s (well above the ramp-down time of the beam) after the electron beam was switched off in each measurement cycle. We extract results for S¹⁶⁺ and S¹⁵⁺ ions by varying the production conditions and thus changing the relative populations of the types of ions in order to distinguish their respective contributions. A pure spectrum of S¹⁵⁺ ions can be produced by choosing an electron beam energy below the ionization potential of this ion. For the reason mentioned above, the emission spectrum above the ionization potential of bare sulfur is an admixture of S¹⁶⁺ and S¹⁵⁺ ions, see Figures 4(a) and (b). We remove the contribution of S¹⁵⁺ ions to this mixed spectrum by subtracting the emission components due to the presence of S¹⁵⁺ ions, and obtain in this way the spectrum of S¹⁶⁺ ions, as shown in Figure 4(c).

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A radiative cascade network for the S¹⁶⁺ and S¹⁵⁺ ions was calculated with FAC. Transition energies and oscillator strengths were obtained for atomic levels up to n = 15. The transition energies for ${n}_{\mathrm{cx}}=15,\ldots ,2\to 1$ are presented in Figure 4 for both S¹⁶⁺ and S¹⁵⁺ ions. Energies were extracted by fitting Gaussian distributions to the experimental CX spectrum of bare sulfur. For the fitting, we treated centroids and amplitudes as free parameters and the widths were fixed to the known energy resolution of the detector (150 eV). Fits are represented by the red curve in Figure 4(c). In total five Gaussians were fitted to the spectrum and the typical reduced χ² value was found to be 1.06 from the fits. The exact energy positions were extracted: respectively, 2.61 ± 0.001, 3.11 ± 0.005, 3.28 ± 0.02, 3.40 ± 0.044, and 3.47 ± 0.06 keV correspond to $n=2\to 1$, $n=3\to 1$, $n=4\to 1$, $n=5,6\to 1$, and $n\geqslant 7\to 1$. These values are in full agreement with the line centroids predicted with FAC, confirming the accuracy of our photon energy calibration. Several measured spectra were analyzed with the same technique; the CX-fed transition from ${n}_{\mathrm{cx}}\geqslant 7\to n=1$ is observed in all the bare sulfur spectra at 3.47 ± 0.06 keV. Our results agree perfectly with the systematic microcalorimeter measurements of Betancourt-Martinez et al. (2014) at the LLNL EBIT, which used both He and SF₆ as donor gases. The high-resolution spectra with He as CX donor show a very strong Lyη at 3438 eV, while with SF₆ as a donor the dominance of that transition is less pronounced. Also the hardness ratios ${ \mathcal R }$ and ${ \mathcal H }$ (for the S¹⁵⁺ and S¹⁴⁺ transitions respectively) found in the present work for the CS₂ case agree very well with the SF₆ values of Betancourt-Martinez et al. (2014). Moreover, we also made a proof-of-principle CX study with Ar¹⁸⁺ and Ar¹⁷⁺ ions. The results are consistent with the previous measurements by Beiersdorfer et al. (2000) and Allen et al. (2008), and show a similar discrepancy in the relative intensity of CX-induced transitions to the corresponding model.

4.3. Comparison with CX Modeling

We now compare the CX spectra obtained for bare sulfur in the experiment with the calculations by Gu et al. (2015) as implemented in the plasma emission model in the SPEX package (Kaastra et al. 1996). As described in Gu et al. (2016), the CX model incorporates reaction rates mainly calculated by the MCLZ method assuming an atomic hydrogen target (Cumbee et al. 2016), and interpolates the rates when the actual atomic calculations are not available. Only single electron capture is considered in the model. Emission spectra are then modeled including radiative cascades based on atomic levels and transition-probability data that are complete up to n = 16. Since our donor is not atomic hydrogen but CS₂ gas, we scale the value of n for the most populated level n_p according to Equation (3) of Gu et al. (2016), ${n}_{{\rm{p}},{\mathrm{CS}}_{2}}={n}_{{\rm{p}},{\rm{H}}}\times \sqrt{{I}_{{\rm{H}}}/{I}_{{\mathrm{CS}}_{2}}}$, where ${n}_{{\rm{p}},{\rm{H}}}=10$ for the low-energy limit, and I_H = 13.6 eV and ${I}_{{\mathrm{CS}}_{2}}=$ 10.1 eV are the ionization potentials of atomic hydrogen and CS₂, respectively. This yields ${n}_{{\rm{p}},{\mathrm{CS}}_{2}}=12$.

To model the sublevel splitting, we first consider a typical low-energy weighting function ${W}_{n}^{{\rm{l}}2}(l)$ (Equation (5) of Gu et al. 2016), which favors capture into low angular momentum l = 1, 2. This function is recommended for collision energies <10–100 eV u^–1 (Krasnopolsky et al. 2004). As shown in Figure 5, the model with ${W}_{n}^{{\rm{l}}2}(l)$ predicts a pileup of high-n transitions, which slightly shifts from the data toward a higher energy value. We speculate that to get better agreement with the experimental peak, the capture cross section to l = 0, which in turn cascades to p-levels at lower Rydberg states, must be enhanced. Then, following Mullen et al. (2016), we construct an ad hoc l-distribution function ${W}_{n}^{{\rm{l}}2}({l}^{\prime })$ in which ${l}^{\prime }=l-1$. Such an s-dominant capture was reported in a few theoretical calculations, e.g., Nolte et al. (2012). As shown in Figure 5, the spectrum produced by applying ${W}_{n}^{{\rm{l}}2}({l}^{\prime })$ indeed agrees well with the experiment. Hence, by including fine-tuning on the l-distribution, the current CX model can explain the EBIT result. We emphasize that the n-scaling used for the modeling has an uncertainty that is larger than our experimental determination of the centroid of the series limit. For atomic hydrogen as a CX donor, the centroid of the observed spectra could be shifted by perhaps one unit of the principal quantum number n.

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4.4. Comparison with Astrophysical Observations

Following our experimental finding of a set of transitions from highly excited states in bare sulfur ions in agreement with model predictions of Gu and earlier work on these (Betancourt-Martinez et al. 2014) and other HCIs, we compare our modeled data that consider atomic H as a CX donor with some recent astrophysical observations.

Due to the weak signal and other sources of uncertainty in the modeling of the astrophysical X-ray spectrum, there are uncertainties in the photon energy of the ULF. Its centroid energy has been variously reported: 3.46–3.53 keV in the observation of the Andromeda nebula and the Perseus galaxy cluster (Boyarsky et al. 2014), 3.51–3.57 keV in the stacked spectra of 73 galaxy clusters (Bulbul et al. 2014), 3.54 keV in the Galactic center (Boyarsky et al. 2015), and 3.51–3.59 keV in the Perseus cluster (Urban et al. 2015). We took the spectral fitting residuals reported from the observations for comparison with our CX model, see Figure 6. These spectral residuals are produced by fitting the observed data with thermal plasma models. We note that the expected $n=3\to 1$ transition in S¹⁵⁺ at 3.1 keV does not show up in the data sets taken from the papers by Bulbul, Urban, and Boyarski (Boyarsky et al. 2014; Bulbul et al. 2014; Urban et al. 2015) that are displayed in Figure 6. This contradicts our CX model, which predicts that line. An explanation for this was already given in Gu et al. (2015): basically, it rests on the fact that it would be extremely difficult to detect any excess of CX at any photon energy for which strong transitions are expected. At the position of the S¹⁵⁺ $n=3\to 1$ line there is a blend with the strong Kα transition of helium-like Ar¹⁶⁺. The spectral models used by Bulbul, Urban, and Boyarski are adjusted to yield a zero photon excess at 3.12 keV (Ar xvii $n=2\to 1$ "triplet" lines). Moreover, the models used (Boyarsky et al. 2014; Bulbul et al. 2014; Urban et al. 2015) include further strong Ar, S, and Ca lines in the 3–4 keV range that were fitted independently. These free fits explain why the sulfur transition $n=3\to 1$ is seemingly absent from the X-ray photon excess data. Furthermore, if those models slightly overestimate the contribution from hydrogen-like Ar¹⁷⁺ Lyα (Ar xviii at 3.31 keV), one would expect that the subtracted photon excess signal would experience a shift of its centroid, resulting in a ULF at an apparent energy higher than its actual value. Therefore, we conclude that even comparatively small uncertainties in the spectral models used by Bulbul, Urban, and Boyarski can certainly explain the minor shift to higher energies of the ULF in comparison with our CX modeled spectrum.

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We have presented experimental charge exchange spectra of S¹⁶⁺ and S¹⁵⁺ interacting with a CS₂ gas target in an EBIT, and found excellent agreement with analogous work by the LLNL group (Betancourt-Martinez et al. 2014). The inferred energy of a charge-exchange-induced spectral feature of 3.47 ± 0.06 keV is in full accord with both the astrophysical observations and our own FAC calculations, and confirms the prediction of Gu et al. (2015). The transitions observed appear at photon energies that are statistically consistent with the astrophysical observations at the level of mutual uncertainties. We conclude that inclusion of CX in the modeling of the astrophysically observed spectra together with uncertainties given by the lack of experimental data on charge exchange of HCIs with atomic hydrogen might well explain a large fraction, and perhaps even all, of the photon signal observed from galaxies and clusters at ∼3.5 keV. Furthermore, we cannot see a reason why this well-known process should not be active in the cases that have been purported, since the cosmic abundances of both sulfur and hydrogen compellingly point to its ubiquity in the neighborhood of galactic winds. Indeed, other explanations are possible, including some K xvii lines and low-energy satellites of KLM DR lines in Ar xvii. However, charge exchange is a proven mechanism, and its exclusion would require some additional explanation that has not yet been put forward. The absence of CX-induced X-ray transitions from high-n Rydberg states in models and databases should, therefore, be corrected, since the inclusion of this process would certainly improve the accuracy of the spectral models.