Can the periodic spectral modulations of the 236 SETI candidate Sloan Survey stars be due to Dark Matter effects?
aa r X i v : . [ a s t r o - ph . S R ] J u l Can the periodic spectral modulations of the 236 SETI candidate from Sloan Sky Survey stars bedue to Dark Matter effects?
Fabrizio Tamburini
1, 2 and Ignazio Licata
3, 4, 5 ZKM – Zentrum f¨ur Kunst und Medientechnologie, Lorentzstr. 19, D-76135, Karlsruhe, Germany. MSC – bw, Stuttgart, Nobelstr. 19, 70569 Stuttgart, Germany. Institute for Scientific Methodology (ISEM) Palermo Italy. School of Advanced International Studies on Theoretical and Nonlinear Methodologies of Physics, Bari, I-70124, Italy. International Institute for Applicable Mathematics and Information Sciences (IIAMIS),B.M. Birla Science Centre, Adarsh Nagar, Hyderabad – 500 463, India.
The search for dark matter (DM) is one of the most active and challenging areas of current research. PossibleDM candidates are ultralight fields such as axions and weak interacting massive particles (WIMPs). Axions piledup in the center of stars are supposed to generate matter/DM configurations with oscillating geometries at a veryrapid frequency, which is a multiple of the axion mass m B [Brito et al. (2015); Brito et al. (2016)]. Borra andTrottier (2016) recently found peculiar ultrafast periodic spectral modulations in 236 main sequence stars in thesample of 2 . ∼
1% of main sequence starsin the F–K spectral range) that were interpreted as optical signals from extraterrestrial civilizations, suggestingthem as possible candidates for the search for extraterrestrial intelligence (SETI) program. We argue, instead,that this could be the first indirect evidence of bosonic axion-like DM fields inside main sequence stars, with astable radiative nucleus, where a stable DM core can be hosted. These oscillations were not observed in earlierstellar spectral classes probably because of the impossibility of starting a stable oscillatory regime due to thepresence of chaotic motions in their convective nuclei. The axion mass values, ( < m B < . × ) µ eV,obtained from the frequency range observed by Borra and Trottier, ( . < f < . et al. (2016);Borsanyi et al. (2016b)]. PACS numbers:
INTRODUCTION
Since Zwicky (1933) pointed out the discrepancy betweenthe dynamical and luminous matter in the Coma cluster ofgalaxies stressing the need for some form of Dark Matter, theprogress in our knowledge both in data collecting, analysisand theory (especially in the last 40 years) has been tremen-dous. Dark Matter (DM) in the realm of General Relativityand conventional cosmology is nowadays a fact even if thecommunity remains open to fundamental changes in the the-ory (MOND or emergent theories of gravity for instance) [7–11]. The most compelling evidence for the existence of DMis that the gravitational and luminous matter signatures areclearly separated in many cases, like in galaxy rotation curvesand gravitational lensing. DM is supposed to play a mainrole in galaxy formation through the gravitational effects ofDM halos and in galaxy evolution, in the formation of theanisotropies of the cosmic microwave background and alsoexplain the formation of the large scale structures observed inthe Universe. Perhaps one of the best evidence of its realityis the Bullet cluster [12, 13] and the clusters alike. Here weare witnessing the collision of two clusters of galaxies wherethe collisionless DM, as evidenced by the weak lensing obser-vations, remains unperturbed, while the gas (detected in theXray), is highly shocked.Concordance Cosmology following the latest optical andcosmic microwave background observations call for the fol-lowing parameters: DM is responsible for the 26 .
8% of thetotal mass-energy of the Universe, whilst ordinary matter is only 4 .
9% [14]. Clearly gravitation in the Universe is domi-nated by DM so that the formation and evolution of cosmicobjects and large structures is guided by DM. It is thereforeof paramount importance, for our knowledge of physics andcosmology to understand what we are dealing with and to col-lect all those hints that may lead us to a good understanding.This will lead us to know the characteristics of the particlesand eventually lead to detection.From Big Bang nucleosynthesis [15, 16], DM is thoughtto be made up of exotic invisible baryonic and non-baryonicmatter, such as axion-like light fields [17–20], neutralinos andother particles from SUSY theories. Other candidates are ster-ile or massive neutrinos and weakly interacting massive par-ticles (WIMPs) [21]. More stringent limits to WIMP’s massand cross section in spin-independent elastic WIMP-nucleoninteractions were recently set after their non-detection in LUXand PandaX-II [22, 23] experiments. For a review on DM, seeRef. [24].If DM were made mostly of ultralight fields, they are ex-pected to be axions or axion-like candidates, cold and weaklyinteracting particles - either scalars or vectors - with a verysmall rest mass [25]. Axions are pseudo-Goldstone bosonsthat were introduced in the Peccei–Quinn [18, 26] symme-try to resolve the strong charge–parity (CP) problem of quan-tum chromodynamics. In this theory the expected mass ofthe axion m B is a free parameter, 10 − µ eV < m B < et al. obtained a more stringent mass range 50 − µ eV / c from numerical simulations of lattice quantumchromodynamics (QCD) by calculating the equation of stateof QCD and the topological susceptibility for low up to veryhigh temperatures including also Standard Model particles inan Euclidean space-time lattice [4, 5]. DARK MATTER EFFECTS ON STARS.
The possible influence of DM in the evolution and struc-ture of stars has been widely discussed in the literature. De-pending on the type of DM particles considered, one can findslightly different effects that may alter the structure and evo-lution of a star such as the increase of energy production or,conversely, the dissipation of the internal energy at a fasterrate. To give an example, the presence of an high concentra-tion of WIMPs accumulated in the core of a star is supposedto trigger self-annihilation processes between WIMPs, becom-ing an additional source of energy [33], causing the decreasingof temperature and pressure in the stellar core and increasingthe life of all the stellar spectral classes, with a more signifi-cant contribution to lower mass stars [34]. Light DM particles,instead, can shorten the lifetime to all stars transporting awaythe energy generated by the nuclear reactions in a very effi-cient way [26]. Because of their small cross sections, axionsand ultralight Axion-like DM particles may give rise to non-standard cooling mechanisms, similar to the neutrino coolingmechanism. This axion cooling mechanism is used to explainsome discrepancies found between the observational data andthe standard theoretical models of stellar evolution [26, 35].Bosonic DM may also perturb the stability of the structureof a star. The most interesting effect induced by ultralightbosonic DM fields is the onset of ultrafast oscillations of stel-lar configurations described by a perfect fluid and a bosoniccondensate. In fact, real scalar massive bosonic fields mini-mally coupled to gravity can have a non-trivial time dependentstress-energy tensor that gives rise to long-term stable oscillat-ing geometries: self-gravitating bosonic fields such as axionsor axion-like fields can form particular “breathing” configura-tions, where both the spacetime geometry and the field oscil-late at a frequency that depends on the mass of the boson.Stable DM cores can form inside stars. DM can accreteand cluster inside compact and non-compact stars and formoscillating DM cores when both the bosonic DM field andthe gravitationally–coupled fluid density vary periodically. Inthese oscillating configurations both the stellar material andthe field oscillate at a precise multiple of a fundamental fre-quency f m that depends on the mass m B of the boson, f m = . × m B c eV Hz . (1)These results, obtained with a simple model that describesthe star as a regular fluid sphere with an equation of stateof polytropic index n and the usual pressure-density relation-ship P ∝ ρ ( n + ) / n , remain valid also for models described bya more general equation of state, where the oscillating compo- nents in the equation of motion behave as small perturbationsof a static star [1, 2]. STAR SPECTRAL MODULATION AND AXION MASS.
Here we make the ansatz of extending these results also tothe inner core of lower spectral classes main sequence (MS)stars where the energy flux in the inner core is carried out byradiative transfer. This region of the star, also known as radia-tive zone, can be described in terms of a static fluid. FollowingBrito et al. [1, 2], we argue that the local density of the radia-tive stellar core, when enough DM is piled up in the center,becomes a periodic function of time with a period given bythe properties of the scalar field. The two fluids of ordinaryand dark matter oscillate together with spacetime, with the ef-fect of transmitting this ultrafast oscillatory motion outwardsto the outer layers of the star, with experimentally observableeffects. The decrease of DM density and of energy due to theflux of axions leaving the star should generate a variation inthe amplitude of the oscillations that could be likely observ-able.From the theory of stellar structure and evolution, these os-cillatory motions can occur in MS stars with masses lowerthan 1 . M ⊙ down to 0 . M ⊙ that correspond to a range ofspectral classes from F to M. Stars with masses M ≃ . − . M ⊙ are almost totally radiative and, for smaller masses,the stellar core is surrounded by a convective envelope thatbecomes larger and larger the smaller is the mass of the star.Main sequence stars with less than 0 . M ⊙ are instead totallyconvective. Conversely, for masses larger than 1 . M ⊙ thecore region starts becoming convective and is surrounded bya radiative envelope, an environment that does not favor theonset of DM-induced ultrafast oscillatory motions. In fact,the onset of a stable oscillatory regime, in these conditions,can occur only if its frequency is much lower than that of thechaotic rapid variations induced by the convective motions inthe stellar core, namely, when the chaotic flows become uni-formly indistinguishable from white noise and can modeledin terms of a stochastic flow coupled to a slowly-evolving de-terministic flow that should describe our ultrafast oscillations[36–38], and it is clearly not our case.DM-induced oscillations could be actually the possible ex-planation of the spectral modulations, with periods varyingfrom 1 . × − up to 1 . × − seconds, foundby Borra & Trottier [3] in 236 MS halo stars obtained fromthe Fourier transform analysis of 2 . ∼
1% of the sub-set of metal-poor population II MSstars in the halo [40] with a radiative nucleus, in the spectralinterval mainly from F to K, for which SDSS instrumentationcould reveal this type of signal.The observational data were taken in the spectral regions ofblue (380 nm – 600 nm) and red (600 nm – 9200 nm) and theSDSS spectra were obtained from two different spectrographs,one in the blue region ( nm < λ < nm ) and one in thered region ( nm < λ < nm ) , while the signals extendover the entire spectral range. This excludes the presence of asystematic instrumental error.These spectral modulations could be caused by the ultrafastoscillations induced by the pulsating matter/DM cores hostedin these stars. In fact, objects that emit light and oscillateat those frequencies generate periodic spectral modulationsdetectable in their astronomical spectra, similarly to a set ofhigh-intensity light pulses separated by constant time intervalsshorter than 10 − seconds [39].As shown in Fig 1, we remark that all these stars belong toa narrow spectral range centered near the spectral type of theSun, a number of 234 stars that have spectral classes mostly inthe F–K spectral range with some exceptions like very smallsamples of A and M class stars. The distribution is peakedon the F class with a smooth decay towards the lower spec-tral regions where the outer convective region becomes largerand larger and would not contribute actively to the ultrafastoscillations of the radiative nucleus. The inset of Fig 1 showsthat F9 is the dominating spectral class of this sample, whileG0, F2 and K3 stars represent about the 1% of the signal andthere are very few samples of A0, K3, K5 and M5 stars. Apossible explanation to the fact that the majority of the signalshave been found in spectral types ranging from F to G mightbe also due to a selection effect: the SEGUE survey targetedstars are mostly F to K-type stars and, in addition to that, F-Gstars are the dominant populations in our galaxy. Noteworthy,we point out that the dominant stellar spectral type in whichthe distribution is peaked is the F9 spectral class that has amass of M ∼ . M ⊙ for which the energy transfer is almosttotally radiative, in agreement with our idea: at a first approxi-mation, in the equations of motion of the fluid, the whole starcould be described as a fluid sphere, the optimal conditionsfor the onset of star/DM oscillations.Stellar rotation, population type, metallicity, dark mattereffects and stellar evolution processes may influence the en-ergy transport in the inner core, with the result of modifyingor even extending the mass range to higher mass values forwhich a star can host a stable inner core that could explainthe presence, in that sample, of a four A-spectral type starswhere convection in the inner core is expected and one M5star [40–43].Our interpretation could be an alternative to the fascinat-ing possibility that the spectral modulations are caused byhigh-intensity and rapidly variating pulses of light generatedby extraterrestrial civilizations [44], sharing a sort of com-mon protocol based on almost identical sets of ultrafast lightpulses: this ultrafast oscillatory behavior can be due to effectsof axion-like dark matter.Applying the experimental results presented in Ref. [3] toEq. 1, one can easily obtain the mass m B of the axion that de-pends on a precise multiple of the main frequency f m dictatedby the axionic field. For the frequency range ( . < f < . ) THz derived from the spectral modulations, we findthis mass range for the axion ( < m B < . × ) µ eV.Interestingly, as reported in Table 1, this mass value over- A F G K M050100150
Total sample of stars with ultrafast oscillation
Spectral Class
A0 F2 F5 F9 G0 G2 K1 K3 K5 M5020406080100
Spectral class
FIG. 1: Histogram of the spectral class of stars presenting ultrafastoscillations. The maximum peak is found for the F spectral-typeclass, with a peak on the F9 subclass where the energy transfer ismostly radiative and the star can be modeled as a fluid sphere. Thisis the optimal situation for the onset of stable dark matter ultrafastoscillations. In general, these stars have an inner core that can behavelike a fluid ball because convection is not present there and the upperlayers have thinner outer convective regions that may damp the signalamplitude with respect to the lower-mass classes. The presence in thesample of four A0 and one M5 stars are briefly discussed in the text. laps the mass range found with Lattice QCD simulations,50 − µ eV / c [4, 5] when 2 ≤ k ≤
48 and this range isalso compatible with the possible axion detections in Joseph-son junctions [28], m B ≃ µ eV and with the results fromsolar observations [45], when the frequency observed exper-imentally, f , is one of the multiples of the fundamental os-cillating frequency of the boson, f m , i.e. f = k f m , as dis-cussed in Refs. [1, 2]. In fact, for k = m B = µ eV for the lower bound of the detectedfrequency, f = . × Hz, and m B = . µ eV for = . × Hz. Larger values of k correspond to lowerfrequencies f m and thus to smaller values of the mass of theaxion. For more details, see Tab. I. For k =
48, the lowermass value for the axion obtained from lattice QCD simula-tions [4] is found. This range of masses agrees also with thelimits fixed by stellar evolution and the neutrino cooling ofSN1987a that precludes axions in the mass range of 10 − upto 2 eV. These axions are non-thermal, with lifetime muchlonger than the age of the Universe. In this scenario axionscan be hardly detected from their decay in two photons [26].Interestingly, the mass range we found overlaps also the massrange of the axionic DM of the Standard Model Axion SeesawHiggs (SMASH) [46].Following Ref. [3], there might be other different phenom-ena able to explain the presence of these spectral modulationssuch as rapid pulsations in small regions of the atmospheresof the stars. However, the period of the pulsation, which ison the order of 1 . × − seconds, is unrealistically smallfor a standard stellar structure. These rapid pulsations can-not even be ascribed to the effect of highly peculiar chemical Multiplication fundamental axion massfactor k frequency f m (THz) µ eV1 0 .
607 2 . × .
304 1 . × .
202 810 . .
152 607 . .
076 303 . .
038 151 . .
019 75 . .
013 50 . m B , derived from the multiples of the mainfrequency oscillations f m of the axionic field. The experimentally ob-served frequency f is considered as a multiple harmonic of a funda-mental oscillation f m due to dark matter on the star, namely, f = k f m [1, 2]. We report the range of values of k > m B overlapswith the results of Lattice QCD simulations [4]. compositions that could be present in a small fraction of galac-tic halo stars, as these peculiarities were not observed. Othercauses e.g. due to the difference in the strength of spectrallines, chemical composition, effective temperature, gravity, ro-tational velocities, turbulence or radial velocities are excluded,favoring our DM conjecture. DISCUSSION AND CONCLUSIONS
The Fourier analysis of the spectra of 2 . . ∼
1% of the sub-set of metal-poor population II main sequence stars in the halo [40] hostinga radiative nucleus (F–K spectral types) for which SDSS couldreveal this type of signal. After having excluded any possibleorigin from instrumental errors, data analysis and other stan-dard astrophysical effects, these modulations were supposedto be due to optical signals from extraterrestrial civilizations[3].We argue, instead, that these spectral modulations are of as-trophysical origin and are due to ultrafast oscillations of thestellar structure of these stars induced by the presence of ul-tralight fields such as axions or axion-like dark matter in theircores that may induce these ultrafast oscillations with frequen-cies proportional to the axion mass m B [1, 2]. Assuming thatthe frequency f derived from the observed spectral modula-tions is a multiple of the fundamental oscillating frequency f m induced by the boson, we found a range of axion masses ( < m B < . × ) µ eV that surprisingly overlaps the re-cent simulations of lattice QCD [4, 5] when the parameter k isfound in the range 2 ≤ k ≤ . M ⊙ (F-G stars) the energy transfer is totally radiative and thewhole stellar structure can be modeled as a fluid sphere. Thiscould explain why the sample of 236 stars is peaked aroundthe F9 spectral class, one of the dominating spectral classesin our galaxy. Only five stars, four A-spectral class stars, thatare supposed to start to have a convective core and one M5 starthat is supposed to be totally convective present the same spec-tral modulation. These exceptions might be caused by otherastrophysical effects or even by the presence of DM fields thatmay alter the structure of these stars.These stars have been observed to oscillate almost at thesame frequency with similar oscillation amplitudes that wouldfavor the the DM hypothesis, as the amplitude depends on theDM characteristics. The energy of these oscillations is about10 − the energy emitted in the SDSS spectral range [3]. For aSun-like star, this corresponds to a power of 10 W.Following Refs. [1, 2], the results from observations mayconfirm the DM scenario where is expected a dependence ofthe amplitude on the mass coupling of the scalar field andon the energy density of the scalar field and fluid. The for-mation of these composite stars occurs though two differentchannels: through gravitational collapse in a DM-rich environ-ment, forming a star with a DM core inside, or, in the secondcase, from capture and accretion of DM through the so-calledgravitational cooling mechanism that prevents stars growingto the collapse through the ejection of mass, even when DMis composed of light massive fields.To give an order of magnitude estimate of the mass cou-pling parameter µ s that characterizes the oscillatory motion,let us consider an averaged value of the axion mass inthe range overlapping lattice QCD simulations, m B ≃ × µ eV, and in the mass range of the radiative nuclei of Fto K spectral type stars, one obtains 0 . < µ s M < et al. indicate that the time averaged energy densityof the scalar field, ρ φ , can be very peaked at the center of thestar with the same order of magnitude of the fermion fluid en-ergy density, ρ F ∼ − . Moving far away from the centerof the star, ρ φ rapidly falls down, assuming values that canbe orders of magnitude smaller than ρ F . On the other hand,smaller values of m B , compatible with lattice QCD simula-tions, give a completely different scenario where stars presentan extended scalar condensate that protrudes away from theirstructure, with a negligible influence on the fluid distribution.In this case stars are expected to present broad and light oscil-latory regimes where the energy density of the scalar field ρ φ at the center of the star can differ by two orders of magnitudewith respect to ρ F .To explain why only 1 over about one hundred of MS halostars with a radiative nucleus oscillate, energy considerationsderived from the experimental results by Borra and Trottierseem to favor at a first glance scenarios with small values of m B unless invoking a damping effect due to the viscosity ofthe stellar matter. In fact, the oscillations are supposed to bedamped by the viscosity of the stellar material that will lead toa depletion of the scalar field core and the damping in the outerlayers of the star; in any case, the exact effect of viscosityand the local thermalization of the scalar field with the stellarmaterial together with the effects of the stellar magnetic fieldin the outer regions of the stellar structure that are thought tomodify the viscosity of the outer layers of the star is still notwell determined.Moreover, according to the first and second DM stellar for-mation channels, a non-uniform distribution of DM-rich re-gions in the galactic halo may act as further selection effect,when considering scenarios where axions may cluster in densesmall-scale substructures such as axion miniclusters, that cantidally interact with stars, captured and disrupted forming tidalstreams with densities that are one order of magnitude largerthan the average value [47, 48].One can also argue that the small sample of stars observedcould be due to an oscillatory motion with a transient behaviordue to axion loss because of interaction with matter and fieldsor because axions may actually leave the gravitational poten-tial well of star. For example, axions may be influenced bygravity in a process of condensing cold axion particles and/orevaporating the axionic field; instead, axion DM appears tobe stable with respect to gravity behaving as a classical field,remaining coherent and gravitationally confined by the star[49]. In fact, under certain conditions, axions in the range ofmasses µ B found here can cluster even down to clumpy con-figurations such as axionic star-like structures [50] suggestingthat the evaporation of the axionic field from an isolated starcan be negligible as these particle mainly interact gravitation-ally. Other additional effects that can decrease the number ofaxions in the core is the interaction of axions with matter andphotons [51] or with the stellar magnetic fields that perme-ate down to the radiative zone producing photons [52] that arealmost negligible with respect to the effects of viscosity damp-ing but that can be revealed as an extra production of energyfrom the star. In MS stars, this hypothetical axion loss canbe easily counterbalanced by DM accretion onto the radiativezone. In any case, a much deeper theoretical investigation isneeded to understand this point.At our knowledge, the search of such ultrafast periodic mod-ulations in the stars of our galactic plane has not been madesystematically as in the work by Borra and Trottier [3]. Thestudy of the modulations in the spectrum of the Sun, eventhough not trivial because it is an extended object, may helpthe current investigation of the presence of DM in our star[45]. What we need actually to support or discard our DM conjecture is an extensive analysis of the spectra of other starsin globular clusters [53], in the galactic plane and where highconcentrations of DM are expected taking into account alsothe effects of different metal composition of stars [54] wherethe presence of a forest of metallic spectral lines would makethe detection of the oscillatory motion experimentally diffi-cult. 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