PoS(CORFU2016)031 † ∗ [email protected] Speaker. This work is supported in part by STFC (UK) under the research grant ST/L000326/1. In the talk, I(SIDM), review paying some particular recent attention touse developments of restrictions on novel on observables the in the merging topic galactic SIDMway structures, of halo (total) as self-interacting and well cross as its Dark section the central from rôle spired region. of SIDM the SIDM models on involving In self-interacting the this right-handed milky (Majorana) latterof neutrino a context, DM few (with tens I mass of discuss keV), that interestingbriefly may particle-physics the exist in in- phenomenology minimal of extensions these of models, thethe and Standard “small-scale Model. argue Cosmology that I crisis”. also they describe can tackle the basic problems of ∗ † Corfu Summer Institute 2016 "School and31 Workshops August on - Elementary 23 Particle September, Physics 2016 andCorfu, Gravity" Greece Nick E. Mavromatos Self-Interacting Right-Handed Neutrinos as Warm and Small-Scale Cosmology “Crisis" King’s College London, Physics Department, TheoreticalGroup, Particle Strand, Physics London and WC2R Cosmology 2LS, UK E-mail: PoS(CORFU2016)031 ]. 2 Dark ]. On the 5 ]. Complemen- http://pos.sissa.it/ 7 Nick E. Mavromatos . In fact the current cos- etc ], on the amount of allowed 4 ]. Unknown forms of Matter ( ]. The lower bound on the mass of 1 5 [ ]. 100 GeV, decouple at non-relativistic 9 - 71%) have to be included in order to

∼ ), which is supplemented by the effect of M k 4 − ], when combined with the evidence from the 7 ]. In this way, re-ionization studies based on N-body 20 [ 6 ∼ z forest constraints [ ], and its predecessor WMAP [ α 3 90% of its total energy budget still remains a mystery. Only 5% of the ] and the Ly- ∼ ], exclude any Warm DM (WDM) with mass less than 10 keV as being the 8 4 C(old)DM framework. Λ (DM) - 27%) and Vacuum Energy ( 5 keV). This is so because the suppression of formation of such low mass objects in this In this talk, we shall concentrate on the self interaction (SI) aspects of dark matter (DM) [ Although the simple Friedmann-Lemaître-Robertson-Walker (FLRW) cosmological model for ' Copyright owned by the author(s) under the terms of the Creative Commons X c Attribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND 4.0). dominant DM component in them (thereby excluding lightearly gravitino epoch models makes of the formation DM of with primordialthus molecular inconsistent hydrogen with gas clouds the very large inefficient, and optical depth observed by the WMAP satellite [ acoustic oscillations owing to the coupling of the radiation field with the CDM particles [ simulations of the Universe at redshifts tary constraints, confirming such exclusion regions, areMilky those Way due satellites, to which observations on is thenumerical about number simulations,[ an of order of magnitude greater than that predicted by WDM explain the plethora of cosmologicalwell observations. by the At large scales the current data are explained WMAP observations [ Matter From a particle physics point ofModel view, (SM), DM such has as many supersymmetric candidates partners, from ,mological physics sterile data neutrinos, beyond from the Planck Standard satellite [ dark matter abundance imply stringent constraintsimplied on collider by searches supersymmetry for new (SUSY). particles, Fromas e.g. an those the “missing” astrophysical amount point of ofFLRW cosmology. matter view, It in DM has the is been Universe studied viewedsimulations as mostly simply of in compared non-interacting a with Newtonian model expectations massive independent bodies. from way,the by Such large standard performing scale simulations N-body structure aimed of at the reproducing depend (observable) universe, explicitly and on) are the intimately particle linkedthe mass with (though primordial range, do plasma. nature, not and These physics propertiescandidate of lead at the to particle the a decoupling time characteristic from interacting of free-streaming formation cold length of of massive the the leptons, dark energy gravitationally with scales, bounded masses implying DM of a seeds. order ies, very Typically, with small weakly the free-streaming corresponding length, ‘Jeans’such far mass dark below of matter the is order associated scale 10 free-streaming with of length a dwarf cutoff (i.e. galax- in largest the wavelength matter number power spectrum at thecontrary, lowest warmer end (i.e. of of the keV mass)non-relativistic DM already particles at that decouple the while radiationwiping still era, relativistic, out can with all become possible free-streaming structure scales belowof typically such DM of a halos scale. a (and Consequently, the this size, pressing will within), the affect by number the lowering of building-up the small satellite inner halos halo [ mass concentration and by sup- a homogeneous and isotropic Universe worksof very it, well nevertheless in about describing several evolutionary aspects Self-interacting Right-handed Neutrino Dark Matter 1. Introduction energy budget of the Cosmos,neutrons, consisting electrons, of as ordinary matter well and as radiation photons), (that is is well mainly understood protons, [ PoS(CORFU2016)031 , χ m (1.1) , in a standard ]. 1 . 12 − s 3 Nick E. Mavromatos 0025 cm . 0 26 CDM and observations. − 20 (in natural units, with ≤ Λ / i 10 χ m · ), with no evidence for the 1 0eV m 3 . ], namely Cosmic Microwave = 3 i 3 1.1 ∑ 94 ' ' 23 eV. ) . T = i 0 B v 2 ]. One of the main reasons for the k 22 for a neutral particle of mass h . ≤ ] to the Universe energy density, which ν i 10 0 SM ν 10 Ω m ∼ 1 Ω → ]. This is associated with the fact that the χ = 3 i Ω 11 ∑ χ χ ], ( 3 σ ]. (due to the three active left- CDM paradigm that call urgently for explanations. 6 Λ ], combined with Lensing, Acoustic oscillation 3 22 for . 0 ' i v c SM · having a freeze-out temperature [ → 1 1pb . 0 χ χ 100 keV becomes indistinguishable from (CDM), as far as ( ]. CDM paradigm for DM, on which the aforementioned WIMP miracle is based, σ & 10 h Λ of order of those of the weak interactions X data, are bounded from above as follows: ' ) m α χ SM Ω denote the light neutrino masses. From this, one also obtains a cosmological bound on the → the relative velocity. A plethora of modern particle physics models, with DM masses ranging i v Although, it should be noted that non-thermal WIMP Miracle models do exist in the literature [ In fact the It should be noted at this stage that such arguments can only place a lower The exclusion of HDM and (few keV) WDM from being the dominant source of DM at the m 1 the Boltzmann constant), which is either stable or it has at least a proper life time longer than the χ χ ( B k age of the Universe, canσ be achieved by particles with annihilation cross sections to SM particles existence of such particles. Thisbe may due not come to as axions a oreven surprise. other face DM non a may thermal situation not particles, where be suchthe thermal, more as latter e.g. than case, sterile one it some neutrinos, may dominant of and the darkmay in stringent matter be general constraints species relaxed obtained one [ exist by may in comparing collider the data universe. to cosmology In Background (CMB), Baryon Acoustic Oscillationstheless (BAO), it weak fails and to strong accountare lensing for serious unresolved data, observations problems, at never- related mainly smallerinner to scales. discrepancies halo in regions In the of particular, distribution of galaxies atThese matter between galaxy issues in numerical the present scales, simulations serious there challenges based to on the in spite of offering a convincing explanation for the observed data [ and Lyman notation, where the energy densitiesand are expressed in unitssum of of the the critical masses density of the of three the light universe, neutrino species observed relic abundance of DM inassumed the to be universe [ thermal with from a few hundreds of GeV to acosmological few especially TeV, data supersymmetric ones, at have been current tested against colliders, such as the LHC, using ( bound on the mass of thewith WDM candidate. masses The reader should bearlarge-scale in mind structure that formation Warm Dark is Matter concerned [ large scale Universe has promptedon a the plethora CDM of model, works, which bothonly depending in by on particle astrophysical its observations physics but thermal and also history astrophysics, (LHC) at may particle at be colliders, CERN, such constrained as assuming significantly the that not Large DM Hadron Collider is particle in origin [ Self-interacting Right-handed Neutrino Dark Matter handed neutrino species of the SM)by is the also upper excluded as limits the for dominantaccording the source to corresponding of the contributions DM recent in Planck the 2015 universe data [ particle physicists taking a great interestMassive in Particle the (WIMP) DM coincidence problem or was ‘miracle’ the [ so called Weakly Interacting PoS(CORFU2016)031 ], ], 15 16 , CDM Λ 14 , 13 CDM simulations Nick E. Mavromatos Λ CDM-based (DM only) Λ ]. 20 , we present our conclusions. 4 ]. ”), which we shall identify here: 18 , we outline the problems/challenges 2 CDM model at galactic scales (which we ). In other words, the 1 Λ problems or the luminosity of the Sun [ 5 CDM model as regards the observed distribution of matter Λ ]. On the contrary, the rotation curves of most of the observed (or, as is also known, the problem), arises from a , we present a particle physics model of self-interacting WDM 3 , at small radii. This is, e.g., evidenced in the standard Navarro- 17 1 − , that is a discrepancy arising between the most massive subhaloes ]. CDM simulations and the observed dynamics of the brightest dwarf r Λ 19 ∝ (or, as is also known, the cuspy-halo problem), refers to a discrepancy ρ CDM-based numerical cosmological simulations that predict the evolution small-scale cosmology crisis Λ CDM paradigm, including either self interactions among the dark matter particles [ In this review we shall concentrate on SIDM models and their galactic phenomenology. The There are three major problems/challenges to the All three problems have their root in the fact that the cold DM particles, which the Understanding the shape and depth of the gravitational potential in dSph may have an impor- The too big to fail problem The “missing satellite problem” Λ The Core-Cusp problem Frenk-White (NFW) DM profile [ (i) between the observed dark matterpredicted by density cosmological N-body profiles simulations. of Characteristically, all low-masssimulations the form galaxies dark and matter the halos which densityincreasing have steeply, profiles “cuspy" i.e. dark as matter distributions, with the density predict that the most massivesatellites, subhaloes with luminosity of higher the than Milky 10 way are too dense to host any of its bright (iii) predicted in (dissipationless) spheroidal (dSph) galaxies in the (see Fig. structure of the article is the following: in the next section of the distribution of(where matter smaller in halos the merge universe toenough - form observed normal-sized larger pointing galaxies halos) to towards - account a fordwarf and such galaxies hierarchical observations. is a clustering orders numerical Although of distribution, of the magnitude there number lower DM example, seem than of we to that mention expected be that from there the were simulations.and observed As only to a around be concrete 11 around 38 orbiting dwarfMilky the galaxies Way Milky dwarf in Way, satellites the yet [ Local one Group, dark matter simulation predicted around 500 due to novel kind of forceswhich exclusive to have important the dark back sector, reaction or effects studying on viscous the properties standard of cosmological DM equations. [ 2. Small-Scale Cosmology Crisis and Self-interacting Dark Matter can collectively call “ dwarf galaxies indicate flat central density(ii) profiles ("cores") [ discrepancy between provided by right-handed Majorana neutrinos,way which consistent addresses with observations. successfully The these model is challengesparticle also in consistent physics with a data the for rest of right the handed cosmological neutrinos. and Finally, in section tant bearing in the understanding of these fundamental questions. In this respect we mention a new Self-interacting Right-handed Neutrino Dark Matter Various proposals for a resolution of thesethe problems have been proposed, some of which go beyond faced by the simulations based on the simulations rely upon, have too shortand free therefore streaming they length form during too the clumped epochs and of too galaxy many formation, structures compared to those observed. at galactic scales and discuss potential resolutions,place among our which emphasis self on. interactions of In DM, section which we PoS(CORFU2016)031 (2.1) ) is the 2 φ , respec- σ ν 2 = and 2 , θ r , σ 2 dr Nick E. Mavromatos dr 5 = ] performed an illus- r 3 r 2 t Φ 21 ) carry more or less the σ d r Φ d ( d r d i 2 2.1 r 2 r i σ v 2 r CDM model. The data points h v Λ , which is taken to be close to ) h ) ) β r is the gravitational potential and ( dr 6 β are projections of 3 2 ρ Φ r − dz − 7 ) Φ ( 5 r d r ], based on exploiting the higher order ]. Based on such novel approaches, and ( d ( ν ν ν ν ∞ 21 21 0, which provide global constraints on the 0 ∞ ∞ ∞ ∞ Z 0 0 − ), the authors of Ref. [ Z Z = R s 4 2 2 3 5 35 2.1 W ) = = = = R + ]. ( z Σ K 20 dR 3 RdR RdR ) by effectively integrating the spherical Jeans equations i i R and i and the density profile 4 z 2 z i n z 2 z v v R v ) h h v h r ) ) h ( ) R R ν ( ( R ( Σ Σ Σ ∞ ∞ 0 0 ∞ 0 Z Z Z is the stellar velocity anisotropy parameter, with ) ) r r ( ( 2 2 r t σ σ fourth order : second order : − 1 The “too-big-to-fail problem”: the continuous line denotes the rotation curve of typical largest ) = denotes the physical (three-dimensional (3D)) radius of a star from the centre of its galaxy, r r ( is the 3D number density of stars, β ) r = ( β tively, onto the plane perpendicular to the line of sight (LOS); analogues of the projected Virial Theorem 2 where ν defining appropriate Virial shape estimators from ( pertain to observed circular velocities ofdiscrepancy is the obvious. largest subhalos Picture of taken the from Ref. Milky [ Way at their half light radii. The method for estimating the dSph gravitational potential [ moments of the velocity distribution ( over all radii: variance of the radial (tangential) velocitysame distributions. information The as quantities the ( corresponding Jeans equations [ trative analysis on the DMphenomenological profile expressions of for the galaxy Sculptor,the NGC NFW. This 253, galaxy in is a the goodity Sculptor study of group, case, the given using Milky that Way, it and is isto one a several of starburst, astronomers that the it is brightest is it galaxies believed in undergoes tohundred intense the have star million vicin- been formation, years caused which ago, by according disturbing the its collisionalso disc with a and belief a started that dwarf the there galaxy currently is a a observed few supermassive starburst. black There hole is at its centre which is slightly heavier that that of Figure 1: subhalo of the Milky Way Galaxy, as simulated within the collisionless Self-interacting Right-handed Neutrino Dark Matter PoS(CORFU2016)031 ]. 25 ]. 27 ], where more ]. However, this 21 21 Nick E. Mavromatos ]. Other works have 22 to the core-cusp problem have ]. One is that the smaller halos 24 [ CDM simulations [ Λ ). The novel analysis of Ref. [ /g (right panels). The upper panels pertain to large ∗ 2 possible solutions ]. 23 = 1 cm (Sgr A potential solutions ∗ σ CDM model simulations (left panels) with Sel-interacting Dark Λ have been used, has demonstrated that one can fit the velocity dispersion ) r ( β Comparison of coillisionless CDM simulations. Although from such a single study case one cannot make generic con- Λ Adopting the standard point of view, several The missing satellite problem has two Such ultra-faint dwarfs substantially alleviate the discrepancy between the predicted and observed been proposed. Many recentfeedback from studies supernovae have and shown active that galacticmatter nuclei) including profile, can baryonic since "flatten feedback-driven feedback out" gasthat (particularly the outflows transfers core produce energy of to a a the galaxy’s time-varying orbits dark gravitational of potential the collisionless dark matter particles [ Matter (SIDM) simulations with cross section Figure 2: scale structure, where the two modelsobserves agree, that while in the SIDM lower models, panels galaxies appear refer to more cored individual and galaxies, spherical. where Pictures one taken from Ref. [ general functions of clusions, nevertheless one would becores, tempted in to which conjecture case that there thepoint should dwarf of be spheroidals view no do is discrepancy not not with shared have by the majority of the astrophysicists. do exist but only a fewenough of them baryonic end matter up becoming to visiblein create because 2007 a they have of visible not eight been dwarfalmost able newly galaxy. exclusively to composed discovered attract of In DM, ultra-faint around support Milky 99.9% of (with Way a this, dwarf mass-to-light ratio Keck satellites of observations about showed 1000) that [ six were of Sculptor using NFW profiles, leading toyses the based conclusion on that, contrary traditional to Jeans thewith equations, results of there other is anal- no extended core in the Sculptor in agreement Self-interacting Right-handed Neutrino Dark Matter the centre of the Milky Way, Sagittarius A shown that the core-cusp problemMatter can (CDM) be paradigm: solved simulations outside withduce warm of dark or the matter self-interacting most cores dark in widely matter low-mass accepted (SIDM) galaxies also Cold [ pro- Dark PoS(CORFU2016)031 . ) /g, θ 2 ( σ , θ 100 cm − CDM at large 1 Λ . 0 ), consistent with is consistent with 2 Nick E. Mavromatos 1 ∼ c − / ], the authors argued m g / 2 25 σ DM scattering. This leads to 1 cm . 0 ], motivated by updated analysis χχ = 27 1 ]. In this latter respect we mention → (up to 10 GeV − 2 13 c χχ / CDM, as mentioned above. However, con- Λ 2 barn GeV , the exchange of long-range dark photons in the . 0 ∼ m / ], observations from clusters, such as the aforementioned σ ], constitute important tools to probe self-interacting DM would generate shallower inner DM profiles, with a neces- 13 28 m Au contraire / ]. The original idea of self-interacting DM (SIDM) was imple- . σ σ 26 ]. ], new cosmological simulations within CDM were performed, with the 13 ] concluded that ], according to which self interactions can lead to both deceleration and 28 27 29 , suggesting that normalized total cross-sections of order 3 ). As emphasised in ref. [ 2 pc /

Fig. M 2 cf. − Self interactions among DM particles could tackle the core-cusp and too big to fail problems by Finally, the Too-Big-to-Fail Problem may also be tackled by the combined inclusion of self At this point we stress that self interactions have been argued to play an important rôle in would imply observational effects inSIDM the regime inner with regions these values of of thesary DM reduction halos. in the It amount was ofand also sub-structures, the shown thereby that missing alleviating a satellite (or eventemporaneously, problems some solving) of tension the with collisionless core-cusp upper limitsstudies in on the galaxy DM cluster cross scales sections emerged. as In obtained a from subsequent lensing work [ reducing the central density. Stringent constraints cansections be of imposed SIDM on by the pertinent studying interaction merging cross (colliding) galaxies [ evaporation of a DM halo when the latterin moves through a a shift background of of DM particles.evaporation the This phenomenon halo’s results is centroid rare, relative and tomassive may non-Abelian the be vector collisionless dark attributed boson stars to exchange and a graph in short galaxies. range The dark force, substructure e.g. due to a of the Bullet Cluster [ refined analyses in the bulletmodels. cluster [ the works of Ref. [ aim of further scrutinizing the effectsThe of authors SIDM of on inner Ref. halo [ cores of galaxies and galaxy clusters. interactions in DM, which tendwith baryonic to feedback make [ the individual galaxies more cored and spherical, along that, if galaxy formation inthen low-mass the dark matter simulated halos circular is velocityagreement strongly function with suppressed of after the CDM re-ionization, observed subhalossolutions circular can may be velocity be brought function that into ofgalaxies dwarf approximate due Milky to galaxies complex Way interactions. tend satellite This tidal todwarf galaxies. stripping be has galaxies been in merged part Other of the into the first problemsurface or in place, brightness identifying tidally which and is are stripped an highly apart diffused, extremely so by difficult much task larger that since they these are virtually objects unnoticeable. have low the nature of the effective interactions andthinking the regarding mean self-interactions free paths was considered applied in uniquelyof that on work. 10 DM This halo way scales of with typical densities isotropic scattering cross sections above self-interaction, is frequent, leading tothe low-momentum transfer sense and that directional the scattering, cross in section is no longer isotropic but depends on the scattering angle galactic structure already in Ref. [ mented for CDM particles with rest masses above 1 MeV Self-interacting Right-handed Neutrino Dark Matter numbers of satellites around thefour Milky too Way, but few there dwarf are galaxies still over discrepancies a by significant a range factor of of masses. about In Ref. [ all the observational constraints. In general,scales, SIDM but would individual make galaxies no would difference appear from moresion ( cored and spherical, with higher velocity disper- PoS(CORFU2016)031 ). 2.2 ], as a result /g imposed by ], yields more 2 30 13 [ Nick E. Mavromatos 1cm . 0 ≥ ]. In fact, their basic point m / ] 31 σ 13 ) still remains [ [ the DM drag m 2.2 / ], the authors estimated the DM self- 30 47 (2.2) SIDM . σ 0 ≤ 1 m − / ] is based on a class of self-interacting models g 2 15 , when self interactions result in a drag force, and 1 , SIDM − cm σ g 14 2 ≤ ]. However in Ref. [ ] criticised, was the assumption that the effective DM drag 1 . 13 0 3 cm 30 ] to interpret the observations in terms of DM self interactions ' 31 m / g, which together with the lower bound / 2 SIDM ] includes in addition to gravity, other important physical ingredients, such in the case of contact interactions, in tension with the upper bounds ( σ 1 15 − , g 47cm ] is . 2 14 0 30 ≤ 5 cm . m 1 / σ ' ] which the authors of Ref. [ m / 31 The above example of Abell 3827 shows how active in research and yet inconclusive, due However, by defining new observables, taking into account A challenge, and some tension with the upper bound of ( SIDM σ the cosmology on galaxy scales, defines a new range for force was constant throughout the evolution of theif system. the Such subhalo a were feature on might a haveis been circular disfavoured expected orbit by along observations. the Moreover, trajectory thefact of constant-drag-force the that assumption Abell a also 3827 contradicts typical cluster, the wich ratethe however of cluster, DM as self well interactions asin the depends fact DM on the density rate the of of velocity DMthe the of self cluster. core the interactions of subhalo is Both negligibly relative the vary small, to alonganalysis cluster. as the of long The subhalo Ref. as trajectory, corrected the [ and subhalo estimate is for far the away from SIDM cross section per DM mass in the of massive right-handed neutrinosimportant that to exist stress in that, minimal inproposed extensions contrast in Refs. of to [ standard the N-body standard simulations, model. the semi-analytical It approach is to both theoretical and observationalgeneric astrophysical challenges, view is point. the Notice however fieldto that of analyze no self attempt microscopic is interactions interactions made that of insections. may DM the lead above from A discussions to the phenomenologically concrete acceptable example SIDM of cross SIDM [ interaction cross section needed to reproduce theAbell observed 3827 effects, has and argued been that significantly the overestimatedwas sensitivity in of that a the previous model study used [ infailed Ref. to [ take intodue account to the the initial non gravitationalseparation, independent bound as of development observed, the of one former the would tostrength need stars the to external latter. and forces the Indeed, the (such gravitational to as DMRef. attraction achieve self [ a subhalo within interactions) star-subhalo the comparable system. in Another feature of the model used in Self-interacting Right-handed Neutrino Dark Matter This leads to substructure deceleration.limited constraints on By SIDM concentrating cross on sectionsof by such galaxies, the without phenomena, (conventional) taking study one into of may account several merging DM impose clusters drag during the collision. stringent constraints on the self-interaction DM crossusing section. this In new particular, technique the study imposed ofDM a 72 mass mergers more stringent constraint on the SIDM cross section per unit to be considered in galacticcosmology studies. problems” of DM. This leads to a possible resolution ofof the observations in three the “small Abell scale and Cluster the 3827. stars The of observed separation aAbell between 3827 galaxy the in moving dark this through matter case), aprovide halo which the region is first evidence of a of characteristic large a feature SIDM dark [ of matter SIDM, density suggests (i.e. that this the cluster may core of PoS(CORFU2016)031 , 3 1, 0, γ 2 = = (3.1) (3.2) γ is the c 1 µ ] γ b V ) charge = 0 γ 1 µ ¯ γ , , together h i MSM, we − ∂ a Ψ γ ν C , [ = 1 = 5 ab = µ R γ depend only on c † ω N λ i C 8 Ψ µ e Nick E. Mavromatos γ 1 − R µ and N ∂ µ ν the spin connection. The e V = is right-handed (R), whilst , V ab 1 µ µ R g R ) ω ∇ c − N should not be viewed as gauge MSM. As we shall argue in this 1 is the unitary ( Ψ where ν = R µ , c C V I µ V ] is based on minimal (non super- ) = ( N J L c ϕ µ m ) 14 and 2 V mediator. For concreteness we assume L + 1 2 T V µ V Ψ g sin ), with important implications for the very − ( Ψ V 2 L − 1 r C R + − = = N the Ricci scalar for the static spherically sym- DM distribution in galaxies , 1 I c R 2 µ R r N & L Ψ ∇ − L µ , γ λ , + 1 e µ R − GR V N , µ i ν of three right-handed neutrino species that, e.g. appear L V e . We shall discuss this model and its rôle in resolving the = 2 V ( 1 2 = 1 R m satisfy the Majorana four-spinor condition, R ] N 1 2 N L 1 diag 14 R L + = N compact core - dilute halo denotes the polar angle. The quantity µν , µν ϕ V g G ], but this identification is not binding. However, unlike µν π R and V 33 16 4 1 r , with the + (-) sign denoting Right-(Left)handed spinors, and − − ] Ψ  32 = = 5 is left-handed (L). The definition of chirality (handedness) is the standard one, 4 Dirac matrices. The massive-vector-mesons γ , where the conjugate spinor field V L × GR ) C ∓ L c T 1 L Ψ  Ψ is the mass of the , with 1 2 the 4 MSM model [ = ν m = ( µ = γ c Ψ ) The Lagrangian of the right-handed neutrino sector, including gravity, reads (in units Similar core - halo DM density behaviour have also been obtained within modern quantum-wave dark matter 3D The right-handed neutrino model for SIDM of Ref. [ ) 2 R ( R L Ψ Ψ which we use throughout here) [ where conjugation operator, flipping the fermion chirality,( i.e. N-body simulations [ the fermions to befermions). of This Majorana is type the common (nevertheless, feature thework, our there formalism model shares is is with an readily the intriguing extendableneutrino similarity DM to in mass Dirac the between the allowed two rangeby models, quite (in despite different the reasons. the few fact tens that of these keV) bounds have of been the obtained sterile with bosons if the fermions are Majorana. As is well known, the Lorentz gauge condition symmetric) extensions of themay Standard be Model provided with by sterilein the neutrinos. the lightest Inallow such our models, right-handed the neutrinos DM trino to self-interactions be through self-interacting. a massive-vector-meson We introduce phenomenologically neu- where Self-interacting Right-handed Neutrino Dark Matter as quantum (fermionic) physics andDM thermodynamics. fermion Interestingly, (right-handed such neutrino) a has scenario,and a in novel DM which mass density the of profile a ( ordercentral a and few halo tens regions of ofaforementioned keV, implies three-problems galaxies of a small universal scale cosmology in the next section. 3. Self-interacting right-handed neutrino metric metric background gravitational covariant derivative acting on a Majorana spinor, with right-handed sterile neutrinos with the radial coordinate; PoS(CORFU2016)031 ]. ). H 34 3.2 (3.4) ( , similar I 2 L , where ]. This is due H by means of conserved in ν , is to be able to 14 µ ν V not → J I µ is V Nick E. Mavromatos N ]) J 0, in which case the µ V J 33 2 Pauli matrix. Upon = . 1 V × , with a potential enhancement α m γ F + 3 (3.3) ν the 2 , ] has been performed within a 2 2 → in the interaction term , is not discussed here. It may well τ 14 1 1 µ V are appropriate Yukawa couplings, R V J N = I m MSM in Ref. [ . In such a case α I ν F H , with , ? τ + φ , ., , i 2 c 2 V . µ τ φ i , h m h e / = + 2 = V = c c g φ φ φ α ≡ RI . , necessitated by the seesaw mechanism. However, an interesting V N I i.e C α α F ` I . The important feature for us are the self-interactions of ) implies decays of the heavy neutrinos α 3 F ) a Yukawa term, coupling the (three, in general) right-handed 3.3 MSM, the lightest of the heavy neutrinos decay time is longer = ν 3.1 Yuk (which acquires dynamics upon implementing quantum corrections). L µ ] and discussed here. A ) for fermion energies much lower than the scale 14 , given that ( 1 R 3.2 N are the lepton doublets of the SM, ] it was assumed that the self-interactions among the DM neutrinos occur only in the α is the SM conjugate Higgs field, ` c 14 The inclusion of such interactions do not affect our conclusions, as justified in detail in Ref. [ In general one may add to ( φ metric. The microscopic origin of the vector meson mass 3 ab time. However, in the context of than the age of the universe,thus hence playing the the latter rôle can of belightest DM. considered neutrino For as our and stable purposes, ignore for as such all already practical a mentioned, purposes, mixing we with concentrate the here SM on sector, this setting an auxiliary vector field Such a four-fermion-contact-interaction model isthe also detailed model the ( effective low-energy approximation of denotes the Higgs excitation field, defined via: lightest neutrino is absolutelythe stable right-handed neutrino, which willthe be used radius for and ensuring mass phenomenologically ofrelativistic correct mean the values field galactic for (RMF) core. approximation,corresponding according The to to analysis which a in the Ref. static systemstrength [ can uniform be of matter considered the distribution as self-interaction in couplingthe its mass of of ground the the state. effective vector-meson interactions mediator is of Information encoded the about in fermions the the quantity (‘inos’) and which determines the order ofbelow. magnitude of As the we corresponding haveRef. cross discussed section, [ above, as this we is shall explain important for the small-scaleto DM the distributions. very weak nature In of the Yukawa coupling The latter could find a plausibleto explanation the by one means obtained of in a Ref. DM [ particle species with a mass of order 50 keV/c This current is conserved if decaysfrom of sterile linearisation neutrinos of are a ignored. Thirring-type Such a four coupling fermion may vector also arise current interaction neutrinos to the active neutrino sector (see, e.g., the case of motivation to include coupling of the right-handed neutrinos with the SM sector (active) neutrinos Self-interacting Right-handed Neutrino Dark Matter which we assume here, emerges in that casedices as denote a pertain consequence to of flat their tangent equations space ofη and motion. hence Latin they in- are raised and loweredcome with from the an Minkowski appropriate Higgs mechanism incoupling the of dark sector. the For vector simplicity field we assume with minimal- the sterile neutrino current where obtain a possible indirect detection method through the decaying channel and due to their self-interacting nature.satellite, In providing this evidence of respect a we clear emission cannot in resist the in energy range pointing 10–25 out keV from the the recent central observations region of by the the Galaxy [ Fermi considering such a coupling, oneangle obtains and mass the of stringent X-ray and BBN constraints of the mixing PoS(CORFU2016)031 , T m B r mk h (3.5) > π 2 r √ = 6 6 B 10 10 λ 4 ) for the same ino 4 0 10 10 Nick E. Mavromatos ] The region = Cf) Cf) 2 0 2 16 16 14 10 C 1. That is, we consider 10 : The same as in previous , , =10 =10 o o > 0 1 1 0 (C (C r (pc) l r (pc) 10 1), marks the transition from 10 / < > B Milky Way (m=47 keV) l l ]. λ  5 , where core and halo Milky Way -2 / / -2 l , B B Big Elliptical (m=47 keV) 10 10 16 14 10 / profiles (vs distance r from the centre λ λ T B 10 4 θ -4 λ , is the core-halo matching point, with -4 10 = c 10 10 r 0 3 The RAR profile (in the non-interacting case C 0 10  when when =30) 0 NFW 0 r θ 8000 6000 4000 2000 500 -500 Einasto 2 10000 2000 1500 1000 3500 3000 2500

δ

10 m m

θ r θ r 1 r (pc) < > at temperature 10 r r , with and degeneracy l 6 6 r RAR model ( 0 10 10 ρ δ 10 at + 4 4 c -1 ], while the rest from Ref. [ r 10 10 10 15 = Cf) Cf) =0) 0 -2 o m 2 2 16 16 0 at C r 10 8 6 4 2 0 -2 -4 Burkert 10 10 10 ( =10 =10

in the interaction regime 10 10 10 10 10

10 10 o o

10

Logaritmic O•

ρ ) pc

(M 2 -3 : Mass density , C , C 0 0 =38.8, C c 4 3 o r (pc) r (pc) ) = / θ 10 10 ( r ( the thickness of the core-halo intermediate layer.[ V keV -2 -2 Milky Way (m=47 keV) =2.8x10 C r o =1.02x10 Big Elliptical (m=47 keV) 10 10 θ o δ 47 ( θ ( = -4 -4 10 10 5 0 0 5 -5 -5 20 15 10 15 10

10 10 10 10

10 10

10 10 10 10 10

O• O• ρ ρ ) pc (M ) pc (M

-3 -3 First two upper panels is a positive constant and ] which is in good agreement with Burkert profile. Middle two panels 0 15 C ) and its comparison with the NFW and a cored Einasto profile for a typical spiral galaxy. The picture 0 = the core radius and V c of the galaxy) forobservational m constraints are fulfilled, compared with the non-interacting case ( at the bottom panel was taken from Ref. [ Figure 3: case but for the case of a large elliptical galaxy. Lower panel: is larger than the inter-particle mean distance mass. Both the interactingprofile,[ and non-interacting cases use the Ruffini-Argüelles-Rueda (RAR) DM density Self-interacting Right-handed Neutrino Dark Matter quantum regime and thus within the core, where the thermal de-Broglie wavelength the ansatz: where the DM distribution is in a much more dilute state (i.e. the quantum degenerate state to the Boltzmann one. where r C PoS(CORFU2016)031 ] > 14 and (see m (3.6) 1 for . The 2

/ V or < )) C M r 2 ( 6 V c ) ν g / m − 10 r 0 ( ν × ( -31.8 -31.8 -31.8 -32.8 -29.3 -29.3 -29.3 -37.3 -37.3 -37.3 θ e 4 (coupling). The . 0 , by defining and 4 β 0 ]. The calculations 47 keV F 5 5 5 5 4 4 4 7 7 4 Nick E. Mavromatos C − − − − − − − − − − ≈ G = 15 < and coupling 2 10 10 10 10 10 10 10 10 10 10 m (pc) m m , and the corresponding m / 0 × × × × × × × × × × / r T C 9 8 0 8 1 2 4 7 4 0 3 δ Pl ...... is the uppermost bound set B . 3 4 7 1 2 2 2 6 9 2 k M ) 2 scattering cross-section in the c 1 ∝ ≡ / 1 5 4 4 4 4 4 4 6 6 4 R cr  − − − − − − − − − − c β N 2 - M ) 10 10 10 10 10 10 10 10 10 10 1 m ] in a perturbative regime (pc)

R ) / × × × × × × × × × × ) c 2 M N

14 r 9 4 0 8 2 2 3 3 9 9

350 keV p 9 ...... ( M 0) discussed in Ref. [ 7 1 3 3 6 6 6 1 5 5 M 6 10 = 8 . = 10 × m 7 7 7 7 7 7 10 m V 8 6 6 6 6 − − − − − − × . 2 C × − − − − ) that can fit the Milky Way observables. On the 1 4 0 m 10 10 10 10 10 10 3 . . θ 10 10 10 10 4 0 = 2 , × × × × × × 29 β 0 c × × × × 4 = = ) C , and the self-interaction constant 7 4 3 0 one can see that for DM mass M c . . . . ) V 065 065 065 431 104 065 cr c 0 1 1 1 3 ...... ), the degeneracy parameter at the centre (depending on 1 π M m T 3 1 1 1 1 1 1 M m / . The corresponding galaxy density profiles and degeneracy B 4 and ino mass / k 1 V 0 ( 0 g ) ) T ( / † † β , where for comparison (in the bottom panel) we also plot the 3 5 4 3 ( ( B 0 3 1 4 4 3 k 6 5 µ ≈ 10 10 10 10 , together with the the sterile neutrino mass 10 10 10 10 = 10 10 ) 0 = × × × × 0 × × × × θ 0 tot core Elliptical ( 0 × × θ Milky Way ( β 8 7 8 5 is the lower bound for the particle mass that satisfies the observed core , θ σ 02 63 27 70 ...... 0 , one can also see that the inclusion of sufficiently strong interactions 2 Large Elliptical ( 2 1 5 1 40 76 ) 1 3 1 3 3 . . β c 0 2 1 / µ , temperature 0 ] can constrain the degeneracy parameters θ 18 14 10 47 keV 0 16 14 16 14 14 16 1 2 2 C × = 10 10 10 10 10 10 at the core ( 5 there is no pair of parameters ( ) . m 4 2 T c B Set of right-handed SIDM model parameters for three different galaxy types analyzed in Ref. [ / ]). From figure k ( / 35 From the results presented in Table There are three free parameters in the approach, evaluated at the galactic centre: the DM µ 47 47 47 (keV) 350 ≡ by reaching the critical core mass for gravitational collapse, 350 keV Ref. [ constraints (within the observational errors), while θ relevant constraints are given in Table that satisfy all the appropriate core and halo conditions. other hand, in the dark sectorhigher among central the degeneracies sterile than neutrinos the can free lead case. to significantly The total more compact cores and Table 1: analysis of ref. [ were done for the maximumcentral allowed degeneracy range of the interaction constant quantum core of the Galaxythe has dimensionless been interaction coupling: calculated in Ref. [ To put things in perspective, one cansector normalize (SM) the weak interaction field interaction strength dimensionfull in coupling, terms of the the Fermi visible “constant” m the chemical potential parameters are depicted in figure corresponding results for the non interacting case ( temperature per unit mass ( Self-interacting Right-handed Neutrino Dark Matter PoS(CORFU2016)031 ∼ V keV, (3.7) (3.8) C 4 10 × 3 . V one constrains the m Nick E. Mavromatos has been obtained in e.g. V C /g (or in general to lie in the ). Another important feature 2 3 1 cm ]. Thus, if, . 0 keV. It worths noticing that for CDM cosmology, associated with the , 14 ) ) Λ , = 8 g m / 10 350 2 / , × tot cm 7 47 σ , ( 18 8 ∈ − 10 be sufficiently large so that a scattering probability m 10 × σ & 6 . 2 , as done in Ref. [ m ( 1 / would be constrained to the value − F ∈ σ G V V 2 C . C  F V V g G m 2  & ], self-interactions among WDM right-handed Neutrinos, in minimal = V 14 V C 1 as requested by the self-consistency of the perturbation scheme we have C . V ) that g 3.6 )), the coupling constant ] by requiring that the cross section 2.2 , the mass of the massive-vector meson would be constrained to values 14 CDM paradigm. We have discussed briefly how interacting dark matter models may tackle F In this work we have emphasized the rôle of self interactions in the dark matter (SIDM) sector As stressed in Ref. [ Λ G 8 is the fact that theof right-handed the neutrino WDM DM models mass available is in ‘colder’ the by literature, a which few implies keV that as the compared model does to not most suffer from in order to satisfy applied to compute theRef. cross-section. [ A conservative lower bound of extensions of the Standard Model,cosmology, and may model provide more solution accurately to thethis all galactic picture structure. three is problems not The expected inclusion ofself to of the interactions baryonic change affects small-scale matter the the core/halo in basic structure conclusion andand that in particular higher the induces introduction compactness higher of central of WDM degeneracies thenatural fermion inner resolution quantum to core the ofbased core-cusp galaxies. on problem fermionic Moreover, of phase-space the DM distributions modelin develop at provides a always small a way an scales, that extended because plateau resemble on the Burkert halo or density scales, cored profiles Einasto profiles (cf. Fig. of the universe in bridgingthe the gap between observations andthe the three numerical basic challenges simulations for based N-body on simulations based on 10 among the inos occurs at least once during the age of the galaxy: 4. Conclusions and outlook DM distribution in galaxies (“small-scaletion Cosmology at crisis"). present is We have faraforementioned also from Abell seen being 3827 how conclusive, cluster, the givenmatter which situa- that may, challenge there like even matter, are the consist alwaysat most of observed various more successful cases, scales, than of like in one models. such the dominantscale a species, structure, way Dark but which that, other co-exist species, for such harmonically instance asplaining CDM right-handed the neutrinos, may observed play provide details also a an in important good core-halomore rôle structures explanation for mundane of for ex- astrophysical a large explanations galaxy. may One be shouldin in also order operation bear to together in account with mind for DM that a self complete interactions, set of observations. estimating the quantity Self-interacting Right-handed Neutrino Dark Matter total cross-section to the N-bodyregion simulation ( value for right-handed neutrino masses in the range implying from ( PoS(CORFU2016)031 , 2 47 c , , 12 ≥ , m , 175 Nine-Year 148 Nick E. 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