Mon. Not. R. Astron. Soc. 333, 360–364 (2002)

Rydberg in space: low-density condensed

Shahriar Badiei and Leif HolmlidP Reaction Dynamics Group, Department of Chemistry, Go¨teborg University, SE-412 96 Go¨teborg, Sweden

Accepted 2002 February 4. Received 2002 January 10; in original form 2001 August 10 Downloaded from https://academic.oup.com/mnras/article/333/2/360/1019164 by guest on 28 September 2021 ABSTRACT Here Rydberg matter is proposed as a candidate for the missing dark matter or dark baryonic matter in the Universe. Spectroscopic and other experimental studies give valuable informa- tion on the properties of Rydberg matter, especially its very weak interaction with light caused by the very small overlap with low states, and because of the necessary two-electron transitions even for disturbed matter. Recently, the unidentified infrared (UIR) bands have been shown to agree well with calculations and experiments on Rydberg matter. This is the reason for the present, somewhat speculative, proposal that dark matter has, at least partially, the form of Rydberg matter. The UIR bands have also been observed directly in emission from Rydberg matter in the laboratory. The unique space-filling properties of Rydberg matter are described: a atom in this matter occupies a volume 5 £ 1012 times larger than in its ground state or in a hydrogen molecule. Key words: ISM: general – ISM: molecules – dark matter.

observations and theory. Another interesting proposal concerning 1 INTRODUCTION the part of dark matter is the existence of cold dense clouds Dark matter is a kind of matter that accounts for the missing mass, of hydrogen molecules (Lequex, Allen & Guilloteau 1993; that is the mass that is non-luminous but must exist in the galaxies Kalberla, Kerp & Haud 2000). Here we present a type of matter and the clusters of galaxies. The evidence for this dark mass comes that has many of the properties expected for dark matter. This form from several types of studies. For example, a large dark mass is of matter is the condensed low-density material called Rydberg required to keep clusters of galaxies together, since the velocities of matter (RM) (Manykin, Ozhovan & Polue´ktov 1992a; Holmlid galaxies often are so high that the clusters would break up without 1998b; Wang & Holmlid 1998). This matter was recently proposed this dark mass. X-ray images also show that galaxy clusters contain to be the source of the unidentified infrared (UIR) bands (Holmlid large amounts of glowing hot . Gravitational lensing 2000) that are observed from all parts of the Universe. RM is observations show that the foreground galaxies are heavy. Finally, neither a mathematical device in a theoretical calculation, such as the velocity of rotational motion of the outer parts of spiral galaxies the vacuum energy, nor does it require large accelerators for its is constant (,100 km s21) and independent of the distance from study such as WIMPs and other hard-to-observe particles. Instead, the centre of the galaxy. This means that a halo of dimensions it can be studied rather easily in the laboratory. It may at least be several times the visible parts of the galaxy normally also rotates the answer to the question concerning dark baryon matter (Turner with almost the same velocity as the outer luminous part of the 1999) (amounting to 5 per cent of the mass) that is believed to exist, galaxy [the argument of the velocity profile or rotation curves even if some of the more elusive particles are responsible for the (Bergstro¨m 2000)]. Recent studies of rotation curves of several assumed 20–40 per cent non-baryonic fraction of dark matter (cold galaxies have demonstrated this important fact (Burkert & Silk dark matter) (Bergstro¨m 2000). The proposal made here that at 1997; Borriello & Salucci 2001). Estimates give the amount of the least part of the dark matter is RM is of course speculative, but it is dark matter as 99.5 per cent of the mass in the Universe, with only based on the good agreement between the UIR bands and the 0.5 per cent ordinary visible matter. theoretical predictions of the spectra based on RM theory. To understand the nature of dark matter in the Universe, several proposals have been studied extensively during recent years, such 2 RYDBERG MATTER as weakly interacting massive particles (WIMPs, Bergstro¨m 2000), massive compact halo objects (MACHOs, Lasserre et al. 2000) and The main property that a dark matter candidate should have is of vacuum energy [which is not a mass at all but is presently course that it is dark, not radiating or absorbing light. RM is formed considered to correspond to 75 per cent of the total mass (Ozer by circular Rydberg states, i.e. electronically highly excited atoms 1999)]. None of them has, however, yet been firmly supported by or small molecules, which interact and form a condensed . Most Rydberg states are almost ‘dark’, since they are metastable PE-mail: [email protected] with long radiative lifetimes (103 satn ¼ 250Þ and since they

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seem to have any vibrational transitions in the IR range. Since the bond force constant is so small, with quantum size of the order of 1024 cm21, the motion is practically classical. Then probabilities of transition will also be small. In an experimental study of the interaction of RM with IR laser light by stimulated Raman scattering (Holmlid 2001a), it was shown that the time for the electronic excitation to dissipate into other degrees of freedom is at least of the order of milliseconds. (Here, electronic excitation means excitation above the ground state of RM.) If ordinary vibrational motion existed in RM, the coupling would take place in much less than a nanosecond. This study also shows no other sign of vibrational transitions. Figure 1. A perspective view of a 19-atom (or molecule) Rydberg matter The vibrational and rotational motion of polar molecular core Downloaded from https://academic.oup.com/mnras/article/333/2/360/1019164 by guest on 28 September 2021 . The distances between the core ions are more than 500 nm at an excitation level of n ¼ 80. ions in RM could possibly be observed, if large enough concentrations of such ions exist in interstellar matter. However, it may be difficult to distinguish the signal of the core ions from interact only weakly with light otherwise. Such circular Rydberg other ions in ionized regions in space. The spectral lines from the states condense to form planar RM clusters with all the Rydberg core ions will also be broadened because of the interactions with electrons interacting and becoming delocalized in a plane (Holmlid the delocalized electrons in the RM. The metallic character of the 1998b), as in Fig. 1. According to theory, the radiative lifetime of delocalized electrons also means that it is difficult for the core ions RM is many orders of magnitude longer than the radiative lifetimes to emit or absorb photons with a wavelength longer than the typical of the separate Rydberg states forming it. The planar clusters electron orbit diameter. At the most probable excitation level n ¼ consist of certain numbers of atoms or molecules, so-called magic 80 in RM (Holmlid 2000), this distance is of the order of 500 nm, numbers N ¼ 7, 10, 14, 19, 37, 61, etc. Laser methods are well corresponding to visible light. Thus, the spectroscopic signatures suited to the study of such clusters by two-electron processes such corresponding to vibration and rotation of the core ions, which as Coulomb explosions (Wang & Holmlid 1998, 2000a,b). mostly lie in the IR range, will be strongly attenuated. Formation of the RM metallic phase (Svensson, Holmlid & Lundgren 1991) stabilizes the metastable Rydberg states strongly, 3 RYDBERG MATTER IN SPACE and extrapolation of the theoretical results at small n (Manykin, Ozhovan & Polue´ktov 1992b) gives a radiative lifetime of the order In a recent publication (Holmlid 2000) it was shown that the so- of the age of the Universe. called unidentified infrared bands are well described by spectral RM interacts very weakly with light. From the early quantum bands from two-electron de-excitation processes in RM. In mechanical calculations, it was concluded that RM is transparent experiments using Raman scattering (Holmlid 2001c) and IR from the visible out to very far infrared or radio frequencies emission (Holmlid 2001d) these band are also observed directly (Manykin et al. 1992a). It is likely that the interaction with from RM in the laboratory. The UIR bands have been observed electromagnetic radiation is also weak in other spectral ranges, at almost everywhere in interstellar space during the previous 30 least when RM is undisturbed and in a well-ordered form. All the years, and there are approximately ten broad bands in the infrared, available experimental information in the infrared (IR) and visible from 3.3 to 13 mm. These bands are very intense, and they show ranges shows that ordinary one-electron dipole-type transitions are structures in the bands that vary strongly depending on in which not possible in RM, even when it is disturbed. The extremely small direction or in which astronomical object they are seen. They are overlap in space of the wavefunctions for the condensed RM phase observed in the galactic plane, from other galaxies and especially delocalized electron states and for the low atomic states means that from old stars that emit carbon and other heavy atoms. If RM is the transitions down to atomic states are forbidden. Since the energy source of the UIR bands, it is reasonable to conclude that state of the RM is lower than for separate Rydberg atoms, the RM interstellar space is filled with RM. This phase will be composed state is also energetically stable. In fact, experiments show that mainly of hydrogen atoms and molecules, with heavier atoms and only two-electron processes exist (Svensson & Holmlid 1999), other small molecules as impurities in the RM. The excitation level partly since it is difficult to conserve the angular momentum in in RM is n ¼ 40–120, with the most probable value n < 80 being one-electron de-excitation processes with changes in principal determined from the UIR band spectra. The UIR bands are emitted quantum number Dn . 1 from a circular state (at maximum since the RM is disturbed and heated in the vicinity of stars. Further angular quantum number l). Transitions observed in space follow out in the galaxy haloes where RM is less disturbed by impacts of the same pattern with two-electron transitions (Holmlid 2000). In particles and quanta, such processes will probably not take place at recent experiments with disturbed RM (Holmlid 2001d), the IR all. emission spectrum has been observed for the first time, and shown The formation processes for RM in space have been treated at to agree well with the UIR bands. We conclude that the transition length in Holmlid (2000) and will not be described in detail here. It rates are extremely small for ordinary dipole processes, and thus is sufficient to state that starlight energy is proposed to be that RM is dark. It is not known whether two-electron processes converted to electronic excitation in Rydberg states, which then will work in the radio-frequency (RF) range at all. Higher-order form RM. This process will take place continuously at a slow rate mixing and stimulated Raman processes are useful for laser by radiation that is sufficiently energetic to give or spectroscopic studies of RM (Svensson & Holmlid 1999; Holmlid desorption from particle surfaces. In the laboratory, desorption 2001a–c) despite the complex processes involved. from non-metal surfaces has been found to give clusters of RM in One important fact that makes RM non-interacting with light is a the surface boundary layer (Wang, Engvall & Holmlid 1999). property that may be unique for this type of matter: RM does not Alkali atoms have a catalytic role and transfer the excitation energy q 2002 RAS, MNRAS 333, 360–364 362 S. Badiei and L. Holmlid Downloaded from https://academic.oup.com/mnras/article/333/2/360/1019164 by guest on 28 September 2021

Figure 3. Potential energy diagram for the interaction between two 19- member Rydberg matter clusters. The bonding distances in the clusters are 0.95 mm corresponding to an excitation level of n ¼ 80. The curve with no maximum, which is everywhere repulsive is the normal form of interaction, but for some relative (lateral) positions, the curve with a maximum of 42 K applies.

The proposal that a large part of the dark matter is in the form of cold hydrogen molecules in dense clouds in the haloes of galaxies (Lequex et al. 1993; Kalberla et al. 2000) is of interest in this connection, since the hydrogen molecules in such clouds may be in Figure 2. Time-of-flight spectra where all the different sixfold symmetric the form of RM. neutral Rydberg matter clusters of hydrogen molecules can be identified. This is caused by a pressure of hydrogen of 8 £ 1026 mbar in this case. The force between the RM clusters when they are at a long Spectra are shifted vertically to increase visibility. All clusters (and the distance from each other can be calculated as the electrostatic molecule) are fragments from a large cloud. The common excess energy for Coulomb force in the classical limit, in a way similar to the all clusters is 1.0 eV from the laser-induced fragmentation process in the classical calculation for the bonding within a cluster (Holmlid form of Coulomb explosions. 1998b). It is important to know whether the clusters are stable when they collide, or whether they de-excite and decompose in the collisions. We will discuss the interactions between two coplanar that they obtain in the desorption process (Holmlid 1998a) to other RM clusters in which the electrons move coherently and with the atoms and molecules (Wang & Holmlid 2000a). This is the most same angular phase. When two such clusters approach each other, a rapid process for forming RM, and it is likely to work better at repulsive potential energy exists, which will prevent close extremely low pressures since quenching gas phase processes will collisions (Badiei & Holmlid, in preparation). In some lateral have very low rates. The radiative lifetime of RM is expected to be positions of the two clusters, the potential is attractive at short extremely long from extrapolation of calculations at lower distances. However, there always exists a barrier in the potential excitation levels (Manykin et al. 1992b), possibly of the order of energy surface at an intermediate distance. This barrier will prevent the age of the Universe. It may be interesting to compare the close collisions of the clusters. For an excitation level n ¼ 80, the reasons for the long radiative lifetime of RM, that is caused by the barrier has a height of 42 K for two 19-atom clusters, with a turning extremely small overlap between the RM states and low atomic distance in the collisions close to 1 mm (see Fig. 3). At the cluster– states, with those for the radiative lifetime of dipole forbidden cluster distance giving the lowest barrier, the lateral variation of the transitions such as vibrational de-excitation in H2. In this latter potential energy is shown in Fig. 4 for one instantaneous position case, which is caused by the vanishing of the dipole operator in the of the coherently moving electrons in the clusters. This means that transition integrals, the lifetime is considerably shorter, of the order RM clusters will be quite stable even during cluster–cluster of a few years (Black 2000). collisions at low temperatures in space. Of special interest from an astrophysical point of view is the The large binding distances in RM makes it fill empty space production in the laboratory of clusters of hydrogen molecules with more efficiently than any other type of condensed matter. Possibly the form (H2)N,withN ¼ 7, 14, 19, 37 and 61 (Wang & Holmlid the easiest way to see this is to compare the volumes that an H atom 2000a). An example of results from a similar experiment is given in will take in an ordinary gas relative with the volume occupied by an Fig. 2. There, the signal to the detector is shown as a function of the H atom within RM. The interaction of H atoms is only repulsive at time of flight to the detector after the laser pulse passes through a distance ,74 pm, which is the bonding distance in the H2 the RM cloud in the vacuum chamber and fragments parts of it. In molecule, giving a volume of 2 £ 10231 m3 for the H atom. The the figure, monomers of H2 and clusters with N ¼ 7, 19, 37, 61 and intercluster repulsive distance was found to be 1 mm above, and the 91 are observed. These cluster peaks are observed at pressures bond distance in the clusters is of the same size. The volume for an 1000 times smaller than in Fig. 2 with no change in intensity. This H atom in RM is then 1 £ 10218 m3,i.e.5£ 1012 times larger than shows that the formation of RM is not very sensitive to the in a gas. Also the form of the RM, as large planar clusters, means surrounding pressure since the small clusters are formed in that the structure in space will be of very low density. the boundary surface layer of the emitter from adsorbed species. Clusters of RM are strong magnetic dipoles. The magnetic

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Figure 4. Potential energy surface for the interaction of two RM clusters with size N ¼ 19 for one position of the coherent electrons at an excitation level of n ¼ 80. The lateral position of the two clusters is varied in the x and y directions, with the cluster–cluster distance fixed to 0.66 mm. This is the distance where the potential barrier is a minimum, i.e. at the maximum of Figure 5. The form of packing of undisturbed sixfold symmetric Rydberg the peak in Fig. 3. Dx ¼ Dy ¼ 0 corresponds to the case when each ion in matter clusters that is believed to exist in space. The magnetic momenta of one of the clusters is centred between three ions in the second cluster: see the clusters are directed along the filaments, all in the same direction. the inset for the positions of the electrons in this calculation. polarized in one direction (this does not mean there will be any dipole strength increases both with excitation state n and with the absorption of the light). This may, for example, explain the number of atoms or molecules in the clusters. This means that the observation (Bailey et al. 1998) of circularly polarized light from clusters will easily line up in an external magnetic field in space, reflecting clouds in the constellation Orion. That the effect was due to the small energy of rotation at low temperatures. RM observed in the infrared is reasonable, since the rotational clusters will thus tend to aggregate into filaments as shown in Fig. 5. frequency of the RM electrons is of the order of 1 cm21. A relation Such filaments will form RM clouds with a low filling factor. between the circularly polarized light and biological homo- The density in space of ordinary luminous matter is on average chirality, as suggested by Bailey et al., is of course of great interest. 2 106 m 3, and if a dark mass 10 times larger than this mass is As a final corollary, it should be noted that interstellar space 2 included the density is 107 m 3. If we assume a density of RM in flight will be extremely difficult or impossible if dense RM clouds 2 the filaments of 1015 m 3 as observed in the laboratory, such exist in the path of the spaceship. At a velocity of only 10 per cent 2 filaments of RM only have to occupy 10 8 of the total volume to of the speed of light, the heating of the spaceship passing through account for all the missing dark mass. In the vicinity of stars, large such a cloud with a rather low density of 1015 m23 (density 1023 of voids in the RM will certainly exist since the material has been a dense RM phase) will be enormous, equal to 20 GW m22,giving attracted into the star, but further away from stars space is believed a temperature of 25 000 K for a surface in radiative equilibrium. to be filled with this type of low-density matter. Owing to the Since the clouds are almost invisible, they will be difficult to space-filling repulsive properties of RM, an internal pressure will observe and map beforehand or during the journey. Of course, in exist in clouds of RM that may give a certain rigidity to the clouds the close vicinity of stars large voids in the RM will be formed in motion, for example in the outer parts of galaxies. caused by gravitation. At large RM densities in clouds, the stacked clusters as in Fig. 5 will also give rise to a considerable magnetic field themselves. Thus, large RM regions in space may be ordered by a magnetic 4CONCLUSIONS field. This ordering means that all electrons in the clusters or sheaths of RM rotate in the same direction. If light is reflected from It is shown that Rydberg matter has many of the properties required a dense RM region, which will behave as an almost metallic and for dark matter in the Universe, especially concerning the polarized cloud, the reflected light will be preferentially circularly necessary very weak interaction with radiation. The excellent q 2002 RAS, MNRAS 333, 360–364 364 S. Badiei and L. Holmlid space-filling properties caused by its Rydberg nature, planar cluster Holmlid L., 2000, A&A, 358, 276 structure and cluster–cluster repulsive interaction even at long Holmlid L., 2001a, Phys. Rev. A, 63, 013817 distances mean that Rydberg matter has qualities as dark matter Holmlid L., 2001b, Langmuir, 17, 268 that have never been thought to exist for any type of matter. The Holmlid L., 2001c, ApJ, 548, L249 spectroscopic signatures of Rydberg matter observed in the form of Holmlid L., 2001d, Chem. Phys. Lett., submitted Kalberla P. M. 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