Supersymmetric Partially Interacting Dark Matter
SSupersymmetric Partially Interacting Dark Matter
Willy Fischler, ∗ Dustin Lorshbough, † and Walter Tangarife ‡ Department of Physics and Texas Cosmology CenterThe University of Texas at Austin, TX 78712.
We present a model of partially interacting dark matter (PIDM) within the framework of su-persymmetry with gauge mediated symmetry breaking. Dark sector atoms are produced throughAffleck-Dine baryogenesis in the dark sector while avoiding the production of Q-ball relics. Wediscuss the astrophysical constraints relevant for this model and the possibility of dark galactic diskformation. In addition, jet emission from rotating black holes is discussed in the context of thisclass of models.
I. INTRODUCTION
Measurements within the standard model of cosmologyindicate that 27% of the energy in our universe today cor-responds to dark matter (DM) [1, 2]. In the context ofΛCDM, this matter is assumed to be cold, stable, andweakly interacting with “visible” matter. Current exper-imental evidence for such a form of matter relies exclu-sively on its gravitational properties.Models of interacting dark matter are favored by cur-rent galactic halo mass distribution models [3, 4]. In-deed, simulations containing only collisionless dark mat-ter show that the halo distribution is a Navarro-Frenk-White (NFW) profile with a cusp at the center. Itis, then, a challenge for theorists to describe a micro-scopic theory of dark matter that is both interactingand in agreement with all known constraints from as-trophysics, cosmology, direct/indirect detection, and col-lider physics.We present an elementary model for the composition ofdark matter in our universe within the framework of su-persymmetry. Our construction is inspired by the modelstudied in [5]. That model contains an additional un-broken gauge U D (1). We show that this scenario canhave a sub-dominant “interacting” dark matter compo-nent and still be consistent with astrophysical and cosmo-logical constraints. For the sake of simplicity, we considerthe limiting case where the dark matter couples negligi-bly to the standard model. This trivially satisfies con-straints coming from direct/indirect detection and col-lider physics.Models where a sub-dominant component of dark mat-ter is interacting and may form bound states, while thedominant component is collisionless, are referred to asPartially Interacting Dark Matter (PIDM) and were firstconsidered in [6, 7]. It has been shown that in thesemodels it is possible to form galactic disks composed en-tirely of sub-dominant dark matter particles [6, 7]. Thesemodels also account for the decrease of black hole angularmomentum through the emission of dark sector jets [8], ∗ fi[email protected] † [email protected] ‡ [email protected] as well as other phenomenological consequences [9, 10].Previous studies of a dark sector U D (1) gauge groupand its corresponding phenomology have been carried out[6–23]. The purpose of this study is to present a con-crete microscopic framework from which one may obtainPIDM models. We additionally discuss how astrophysicaland cosmological phenomenology constrains this modeland yields observables in the limiting case of a negligiblecoupling between the dark sector and the visible standardmodel.The structure of this article is the following: In sec-tion II, we present the description of our model includ-ing the calculation of the photino thermal relic density.In section III, the asymmetry generation is studied usingthe Affleck-Dine mechanism. In section IV, we apply as-trophysical constraints to our model, and, in section V,we analyze some consequences of PIDM for gamma raybursts. We end this work with concluding remarks. II. HIDDEN SUPERSYMMETRIC SECTOR
In this study, we want to explore an example of a hid-den sector containing stable neutral particles and parti-cles that are charged under some “dark” gauge interac-tion. The main goal is to provide a working model wherethe dominant constituent of dark matter (DM) is a sta-ble, light, neutral fermion ( collisionless DM ), while thereis a small fraction of DM that is composed by chargedstable particles (
PIDM ). In subsequent sections, we willconnect these types of models with astrophysical con-sequences and some of the features presented in [6–8].In this section, we describe the specifics of our modelwhich is motivated by a similar construction introducedin [5]. We consider a set of superfields that are mul-tiplets of a dark SU D (2) gauge group in a hidden sec-tor that is decoupled from the visible sector (MSSM).One of the chiral superfields, H , is a triplet of the gaugesymmetry and develops a vacuum expectation value thatbreaks the symmetry down to a dark U D (1). In addi-tion, we assume that the soft masses of this sector aremuch smaller than the soft parameters of the MSSM. Ata high energy scale, there is a set of chiral superfields(messengers) that are charged the MSSM gauge symme-try group, SU (3) C × SU (2) W × U (1) Y , and there are some a r X i v : . [ h e p - ph ] S e p messengers that are multiplets of SU D (2). Supersymme-try breaking is therefore communicated to both sectorsthrough gauge mediation [24–27]. In addition, we allowa Yukawa coupling between the SU D (2) messengers andsome of the fields in the hidden sector .The chiral field content in the hidden sector is dis-played in Table I. Besides the SU D (2) triplet, there arefour chiral doublets, X i =1 , , Y i =1 , , which carry a global U global X,Y (1) quantum number. The superpotential in thishidden sector is given by W hidden = Z Tr[ λ h H − v h ] + m X X X + m Y Y Y , (1)where, H ≡ τ a H a , λ h is a coupling and v h is a parameterwith units of mass. For simplicity, henceforth λ h will betaken to be of order 1.On the other hand, the messenger sector is describedby the superpotential W Mess = S (cid:0) λ A AA (cid:48) + λ C C − F (cid:1) + M A AB + M C CD + κY DX , (2)where S is the spurion field whose F − term breaks SUSYspontaneously, A, A (cid:48) and B are multiplets of the MSSMgauge group and C, D are triplets of SU D (2). Sincewe wish to have small soft parameters in the hidden sector, compared to the MSSM soft terms, we assume M C (cid:29) M A . The mixing term that connects the low en-ergy degrees of freedom in the hidden sector with themessenger fields in the secluded sector will yield a CP-odd term in the low energy effective theory that otherwisewould be zero in a minimal GMSB scenario. Superfield SU D (2) U global X (1) U global Y (1) H X X ¯ − Y ¯ Y − Z The SU D (2) symmetry is broken down to a U D (1) bythe Higgs mechanism, in which the scalar triple H takesthe expectation value (cid:104) (cid:126)H (cid:105) = (0 , , v h / (cid:112) λ h ) . (3)The resulting supersymmetric mass Lagrangian in termsof component fields − L ⊃ πα D v h λ h W (cid:48) + µ W (cid:48) µ − + ( √ πα D v h √ λ h ψ + λ − + h . c . ) + (cid:112) λ h v h ψ H ψ Z (4)+ ( m X ψ X ψ X + m Y ψ Y ψ Y + h . c . ) + λ h v h | φ H | + 2 v h | φ Z | + m X ( | φ X | + | φ X | ) + m Y ( | φ Y | + | φ Y | ) , where α D is the “dark” fine structure constant. ψ ± arethe charged fermionic components of H and λ ± corre-spond to the charged gaugini. These charged fermionscombine to form two chargino mass eigenstates ˜ C ± . Thespectrum also contains a massless vector boson W µ,h ≡ γ h .The spontaneous breaking of SUSY generates softmasses for the particle spectrum via the gauge media-tion mechanism. For the scalar fields, the contributionto their masses are˜ m φ X,Y ≈ α D π (cid:18) λ C FM C (cid:19) , ˜ m φ H ≈ α D π (cid:18) λ C FM C (cid:19) , (5)at the messenger scale, whereas the gaugini λ i obtain a Direct couplings between the messengers and the low energy de-grees of freedom have been studied before in the literature, al-though not in the context of hidden sectors [28–39]. mass M λ ≈ α D π (cid:18) λ C FM C (cid:19) . (6)The lightest supersymmetric particle of this sector isthe “dark photino”, χ ≡ λ , the superpartner of the darkphoton, and has a mass m χ ≡ M λ , which is paramet-rically much smaller than the soft masses in the visiblesector. This provides a very light stable particle thatmight be of interest as a candidate for dark matter. TheLagrangian contains the photino interactions with the X, Y fields
L ⊃ · · · − i √ πα D φ X i ,Y i ψ † X i ,Y i χ + h . c . .The dark photino can decay to a gravitino and a darkphoton through the coupling of the gravitino to the su-percurrent [40]. Since we want the photino to be stable,we constrain its mass so that its lifetime is longer thanthe age of the universe. Figure 1 shows different photinomasses in the √ F − M C plane and it also depicts theregion that are is discarded by requiring the photino tobe cosmologically stable. m Χ (cid:61) m Χ (cid:61) m Χ (cid:61) m Χ (cid:61) Excluded bydecaytogravitino Α D (cid:61) (cid:180) (cid:180) (cid:180) (cid:180) (cid:180) (cid:180) (cid:180) (cid:180) (cid:180) (cid:180) (cid:180) (cid:180) (cid:180) F (cid:72) GeV (cid:76) M C (cid:72) G e V (cid:76) FIG. 1. Different values for the photino mass in GeV as afunction of √ F and M C . The area under the blue line showsthe region that is disallowed by requiring τ χ > s. When SUSY is broken and the messenger superfieldsare integrated out, the diagram shown in Figure 2 gen-erates the effective term in the scalar potential V ⊃ AM ( φ X φ Y ) + h . c ., (7)where AM ≈ κ λ C FM C , M ≈ M C , (8)which is CP-odd. This term will be used in Section III togenerate an asymmetry in the number densities n X , n Y ,via the Affleck-Dine mechanism [41], since it breaks theglobal symmetries U global X,Y (1). Figure 3 shows differentvalues of AM in terms of µ ≡ √ F and for different valuesof m χ ; we also have used κ = 1 for simplicity. The regionabove the blue line corresponds to the values of µ and m χ that are discarded by the stability of the photino. FIG. 2. Feynman diagram used to generate the effective cou-pling AM in Equation (8). m Χ (cid:61) m Χ (cid:61) m Χ (cid:61) Excluded (cid:180) (cid:180) (cid:180) (cid:180) (cid:180) (cid:180) (cid:180) (cid:45) (cid:180) (cid:45) (cid:180) (cid:45) (cid:180) (cid:45) (cid:180) (cid:45) (cid:180) (cid:45) (cid:180) (cid:45) Μ (cid:72) GeV (cid:76) A M FIG. 3. Values for the effective coupling AM as function of µ and for different values of m χ given in GeV. A. Symmetric dark relics
In this section, we now study the relic density of thelightest supersymmetric particle of the hidden sector de-scribed above, the dark photino. At early times, theparticles are very close to thermal equilibrium, with atemperature T D . We assume that the hidden and thevisible sectors are decoupled and, thus, they have dif-ferent temperatures. It is standard to define the ratiobetween the temperatures, ξ ( t ) ≡ T D ( t ) T ( t ) . (9)This ratio is constrained by BBN physics since the darkphotons and, possibly, the lightest massive particles inthe hidden sector contribute to the number of relativisticdegrees of freedom of the universe. The constraint on theeffective number of light relativistic species, ∆ N ν < . g D, ∗ ( t BBN ) (cid:18) T D ( t BBN ) T ( t BBN ) (cid:19) ≤ .
75 (95% C . L . ) . (11)In our case, this bound will be obeyed as long as ξ ( t BBN ) < . n v, γ ≈ T ≈ . ρ / γ ≈ . (cid:18) H √ G N (cid:19) / , (12) A less constrained experimental bound previous to the Planckcollaboration findings is [13] g D, ∗ ( t BBN ) ξ ( t BBN ) ≤ .
52 (95% C . L . ) . (10) n D, γ = 14 T D = ξ n v, γ = 0 . ξ (cid:18) H √ G N (cid:19) / . (13)For approximation in section IV, we will assume ξ ≈ . ξ ≈ − . However, as discussed previously, thisvalue may be as large as 0.75.As the temperature drops below the mass of thephotino, the annihilation and production rates decrease.As a consequence, the interactions of the “dark particles”freeze out of equilibrium. The evolution of the particlenumber density of χ is described by the Boltzmann equa-tion [42] dn χ dt + 3 H n χ = −(cid:104) σ χχ v DM (cid:105) (cid:0) n χ − n χ eq (cid:1) , (14)where H is the Hubble rate and v is the relative veloc-ity of the annihilating particles. (cid:104) σ χ ¯ χ v (cid:105) is the thermallyaverage annihilation cross section.Numerical solutions to Equation (14) show thatthe“dark” temperature at which the dark photinos de-part from equilibrium is given by x F O ≡ m χ T D,F O ≈ ξ ( t F O ) ln (cid:32) . m χ G − / N (cid:104) σ χχ v (cid:105) ξ / ( g tot, ∗ ) / x / F O (cid:33) , (15)where g tot, ∗ ( T ) ≡ g ∗ ( T ) + g D, ∗ ( T D ) (cid:18) T D T (cid:19) (16)is the effective number of relativistic degrees of freedom. The relic abundance at the present is found to beΩ χ h ≡ ρ χ ρ c h ≈ . × x F O
GeV − g / tot, ∗ M Pl ( a + 3 b/x F O ) , (17)with (cid:104) σ χ ¯ χ v (cid:105) ≈ a + b v . Where h is the Hubble parameterin units of 100 km s − Mpc − and ρ c is the critical density. Ψ Y Φ Y Χ W Μ h , C (cid:142) ih Ψ X , Φ X (cid:45) (cid:45) G e V FIG. 4. Spectrum exemplifying the scenario considered in thisstudy.
In this work, we want to focus on the region of pa-rameter space where m ψ X ≥ m χ > m ψ Y . In fact, wetake ψ i to have a mass under 1 MeV. As it will be shownin section IV, this regime is interesting since it leads to“dark” structure formation when there is an asymmetryin the X, Y fields and this charged matter constitutes asmall portion of the dark matter content of the universe.The process that is most relevant for the annihilation ofthe photini is χ ¯ χ → ψ Y i ¯ ψ Y i . The thermal averaged crosssection is given by (cid:104) σ χ ¯ χ v (cid:105) ≈ a + b v , where a = 3 πα D m Y (cid:114) − m Y m χ (cid:16) ˜ m φ Y + m χ (cid:16) − m Y m χ (cid:17)(cid:17) , (18) b = πα D m χ (cid:114) − m Y m χ (cid:16) ˜ m φ Y + m χ (cid:16) − m Y m χ (cid:17)(cid:17) × (cid:20) ˜ m φ Y (cid:18) m Y m χ − m Y m χ + 16 (cid:19) − m φ Y m Y (cid:18) m Y m χ − m Y m χ + 22 (cid:19) + m χ (cid:18) m Y m χ − (cid:19) (cid:18) m Y m χ − m Y m χ + 16 (cid:19)(cid:35) , which, in the limit where m Y (cid:28) m χ depends mainly onthe values of the coupling constant g D and the photinomass m χ . It is noteworthy that, since the photinoparticles form a Majorana fermion, the s − wave contri-bution to the thermally averaged cross section is sup-pressed respect to the p − wave contribution [43]. Thenumerical solution to Equation (15) for m χ ≈ . ξ ( t F O ) ≈ . x F O ≈
10 which is con-sistent with the known fact that thermal relics freezeout earlier in hidden sectors with a temperature than T visible [13]. The parameter values that yield a photinorelic abundance Ω h ≈ .
119 are shown in Figure 5.For the specific ranges 10 − ≤ α D ≤ × − and0 .
01 GeV ≤ χ ≤ . α D ≈ − and m Y ≈ × − GeV, in which case aphotino with a mass χ ≈ .
06 GeV provides the DM relicdensity and will be used when discussing the astrophysi-cal constraints in section IV. (cid:87) h (cid:62) (cid:87) h (cid:60) F (cid:61) GeV m WD (cid:61) GeV m Ψ Y (cid:61) (cid:180) (cid:45) GeV m Ψ X (cid:61) (cid:45) GeV m Χ (cid:72) GeV (cid:76) Α D FIG. 5. Range of values of α D and m χ for which Ω h ≈ . m Y , F and v h in the regime where m Y (cid:28) m χ (cid:28) m X . The X particles can annihilate into a pair of dark pho-tini or into a pair of dark photons. In the case of annihi-lation into photini, the cross section is of the same orderas the annihilation cross section of photini into Y fields(Equation 18). However, the annihilation into photons isgiven by a cross section (cid:104) σ ψ X ¯ ψ X v X (cid:105) ≈ α D π m X (cid:18) − v X (cid:19) , (19)which, for the values mentioned in the previous para-graph, turns about to be about 3 orders of magnitudelarger than the photino annihilation cross section. Thus,unless there is an asymmetry of these particles, the X fields annihilate and there are no thermal relics of thistype.Note that if we did not require the photino to be thedominant dark matter component and instead had a dif-ferent field which is completely decoupled from X and Y , we could manipulate the values of the couplings andmasses more freely and consider the regimes of param-eter space discussed in [6, 7]. We do not expand uponthis case here since the primary motivation of this studyis to present a self-consistent supersymmetric embeddingof the PIDM scenario with minimal additional degreesof freedom. Allowing an additional degree of freedom,such as an axion, to be the dominant dark matter whileretaining the field content studied here would allow foradditional freedom and potentially new phenomenologywhich we do not explore here. III. ASYMMETRIC CHARGED DARKMATTERA. Asymmetry generation
We now present the specifics of generating a net num-ber density of charged X and Y particles. We follow themechanism presented by Affleck and Dine [41, 44, 45],in which baryogenesis was realized by flat directionsof quarks. Leptons are given some large expectationvalue and their subsequent evolution generates a non-zero baryon or lepton number. In this study, we use asimilar construction in order to generate non zero X and Y density numbers, n global X , n global Y . In Equation (7), an effective term was presented afterintegrating-out the heavy messenger field C . The poten-tial for the X and Y scalar fields becomes V X,Y = M X | φ X | + M Y | φ Y | + (cid:18) AM ( φ X φ Y ) + h . c . (cid:19) , (20)where M X,Y includes the contributions to the mass of φ X ,Y coming from the supersymmetric Lagrangian (5)and from SUSY breaking terms (5), M X,Y = m X,Y + ˜ m φ X,Y . (21)For the specific value m X ≈ . m Y (cid:28) M λ We have chosen the initial conditions such that the fieldbegins rolling at time t − ∗ = 2 H ∗ ∼ (cid:113) AM | ϕ | . Thisimplies the initial conditions ˙ ϕ ( t ∗ ) = 0 and ϕ ( t ∗ ) = | ϕ | e iθ .Let a n ϕ = i ( ˙ ϕ ∗ ϕ − ϕ ∗ ˙ ϕ ) be the dark baryon/leptonnumber density. The evolution in time may be easilysolved. For the case of radiation domination, a ( t ) ∼ t / ,we obtain˙ n ϕ + 3 H n ϕ = 1 a ddt (cid:0) a n ϕ (cid:1) = 2 Im [ V ,ϕ ϕ ] , (25) t / n ϕ ( t ) = 2 (cid:90) tt ∗ dt (cid:48) t (cid:48) / Im [ V ,ϕ ( t (cid:48) ) ϕ ( t (cid:48) )] . (26)The only term contributing to the imaginary part of (26)is the quartic piece,Im [ V ,ϕ ( t ) ϕ ( t )] = 4 AM Im (cid:0) ϕ (cid:1) (27)To finish computing the integral we must choose valuesfor the specific parameters. For the case of (A/M) wechoose 8 . × − based on the discussion in section II.For the mass parameter we will take m ϕ = 0 . e iθ = 1and the initial amplitude we will choose to be | ϕ | =10 . GeV. This initial amplitude results in productionof interacting dark matter comparable to what is allowedby astrophysical bounds as we will see later.With this choice of parameters we integrate (26) nu-merically until a time t final = 1700 t ∗ to ensure no furtherproduction contributes to the result and are therefore in-sensitive to t final . Choosing t final to be a larger valueresults in the integration (26) becoming numerically un-stable. The number of dark photons at the final time isgiven by (13) with ξ = 0 . H = 1 / t final . This yieldsa dark sector baryon to photon ratio of (cid:18) n ϕ n D, γ (cid:19) ≈ × − . (28)The standard model baryon to photon ratio is given by ∼ − [50], though we emphasize that the dark sectoris allowed to have a baryon to photon ratio very differ-ent from that in the visible sector. In terms of numberdensity today we find n ϕ ≈ × − n D, γ ( H = H today ) ≈ × − cm − (29)As in [6, 7], we introduce a parameter (cid:15) that measuresthe fraction of PIDM to all dark matter globally which For instance, if there is a finite temperature potential correctionof the form ∼ T ϕ that is relevant at early times, the initialfield value may be obtained by allowing for a reheat temperatureof ∼ GeV if the field value at the end of reheating is ∼ . × GeV. will also be assumed to be the ratio within galaxies. Wemay bound this parameter using the measured density ofdark matter today and (29). Namely, (cid:15) = Ω PIDM Ω DM ≈ . . (30)We summarize the result of choosing a different initialamplitude | ϕ | in Table II. | ϕ | (GeV) ( n ϕ /n D ,γ ) (cid:15) t final ( t ∗ )10 . × − . × − × − . × − . × − (cid:15) and numericallyused final integration time for each initial amplitude. Thedark sector baryon to photon ratio and density ratio (cid:15) areinsensitive to the exact value of t final used, though if t final ischosen to be too large the integration (26) becomes numeri-cally unstable. In principle, one may need to be concerned with theformation of Q-balls in the context of gauge mediationsymmetry breaking and the Affleck-Dine mechanism [51–58]. The effective scalar potential for ϕ in our model isgiven by [52, 53] V eff ( ϕ ) ≈ m ϕ Log (cid:20) (cid:18) | ϕ | M C (cid:19)(cid:21) + λ | ϕ | , (31)where the logarithmic term comes from integrating outthe messenger D in Equation (2) and λ ∼ − . StableQ-balls exist if V eff ( ϕ ) / | ϕ | has a minimum for somenon-zero value of ϕ [51, 59]. In our case, there does notexist such a minimum.Under U D (1), the excess ψ X and ψ Y have charges +1and − ψ X is not a composite particle, but the astrophysical phe-nomenology of the bound state atom is still similar tothat of visible sector Hydrogen. However, for the pa-rameters considered in this study, the interacting darkmatter never decouples from the dark photon bath. Wewill discuss how to interpret astrophysical constraints inthis context in the next section.The number density we have obtained, n ϕ , is the globalnumber density of the interacting Dark matter particles.For the remainder of this study, we will be interested inthe local number densities of the n X and n Y , which wewill take to be equal. In the next section, we will findbounds on the local number density of interacting darkmatter and compare those bounds to the bound on theglobal number density through the parameter (cid:15) . IV. ASTROPHYSICAL AND COSMOLOGICALCONSTRAINTS The model we have proposed will now be shown tobe consistent with bounds arising from astrophysical andcosmological considerations. Following [6, 7], we will con-sider halo shape analysis and the bullet cluster observa-tion. We will additionally discuss the impact of darkacoustic oscillations [60].There is a cosmological constraint arising from the ex-istence of dark acoustic oscillations [60]. Radiation pres-sure due to the interacting dark matter opposes matterinfall and results in shallower gravitational potential wellswhich impact the CMB and matter power spectrum. Forthe benchmark parameters discussed in section II with ξ = 0 . 5, this corresponds to a bound of (cid:15) (cid:46) . . Thisconstraint will decrease for the case of lower ξ . This con-straint is the most restrictive for both the case in whichgalaxies form and the case in which galaxies do not form.We have shown that our benchmark parameters readilysatisfy this bound in (30).There are two regimes of parameter space given thebenchmark parameters discussed in II. One for which thePIDM does not decouple and remains a dark plasma to-day, and one for which the PIDM does decouple and darkatoms may be long lived and form galaxies. For the caseof ξ ≈ . 5, the dark photon temperature is always higherthan the binding energy of the dark atoms and thereforethe PIDM never decouples from the dark photon bath.For the case of a much colder dark sector than the vis-ible sector, ξ (cid:46) − , the binding energy is eventuallylarger than the dark photon bath temperature and wemay produce long lived dark atoms. However, the pa-rameters which allows for dark galaxy formation resultsin a large Σ DAO ( ∼ − A. The Bullet Cluster and Halo Shape Analysis There are potentially two constraining astrophysicalbounds for the case in which dark galaxies do not form,the Bullet Cluster and halo shape analysis. The con-straint on the amount of PIDM, (cid:15) , comes from obser-vations of Bullet Cluster [61, 62]. In particular, frommeasurements of the mass-to-light ratio of the clusterand subcluster one can obtain an upper bound on thefraction of dark matter lost in the galactic merger. Theparticle loss fraction is determined by the fractional de-crease of the mass to light ratio (M/L) for the subcluster We would like to thank Francis-Yan Cyr-Racine for bringing thisto our attention in a private communication. within 150 kpc, f = | ( M/L ) I,main cluster − ( M/L ) I,subcluster | ( M/L ) I,main cluster . (32)Here the subscript I denotes the Ith frequency bandchosen for determining (M/L). Lensing map analysis[63, 64] has determined ( M/L ) I,subcluster = 179 ± 11 and( M/L ) I,cluster = 214 ± 13 which results in an upper boundof the particle loss fraction of f (cid:46) . 30 [64] to 95% con-fidence.In the scenario we are considering where the dominantcomponent of dark matter is collisionless, the particle lossfraction bound becomes a bound on the amount of darkmatter that can be interacting, (cid:15) (cid:46) . ξ = 0 . 5, the strongest constraint on (cid:15) is therefore the constraint arising from dark acousticoscillation considerations previously discussed in which (cid:15) (cid:46) . V. GAMMA RAY BURST PHENOMENOLOGY In a companion paper [8], we have explored thepossibility of dark matter which is neutral under thestandard model modifying our conclusions about blackhole spin measurements during gamma ray burst emis-sion events. The main result from that study is thatthe rate of change of the dimensionless spin parameter − < a ≡ J/G N M B < +1, for the case of prograde ro-tation ( a > M B , visible infall ˙ M in,v , the visible jet emission L jet,v , the dark matter infall ˙ M in,D , the dark matter jetemission L jet,D , and the gravitational radiation emission L gr as˙ a = λ γM B (cid:16) ˙ M in,v + ˙ M in,D − L jet,v − L jet,D − L gr (cid:17) . (33)We have defined λ ≡ √ (cid:18) − a − √ − a (cid:19) / and γ ≡ √ (cid:16) (cid:112) − a (cid:17) / . In [8] we have given nu-merical estimates for these terms, but ultimately“two-sector” numerical simulations should be done todevelop a better understanding of how such a sectormay modify the expected change in spin during any suchevent. We have assumed the increase of irreducible blackhole mass during infall is negligible. In order to justifythis assumption, note that the change in irreduciblemass is proportional to the black hole temperature, T BH , which vanishes for spin parameter near unity δM irr = 14 M P T BH δA horizon = 116 π M P M B √ − a (cid:0) √ − a (cid:1) δA horizon . (34)Previous numerical studies have shown that the blackhole spin rapidly grows during the collapsing stage [68],and therefore the irreducible mass becomes approxi-mately constant after a short time.The scenario described in [8] relies upon the assump-tion that the collapsar model [68–70] is sufficient to ex-plain some of the observed long gamma ray bursts andthat the jets themselves are dominantly generated bythe Blandford-Znajek (BZ) mechanism [71–84]. The pro-posal in [8] is that by measuring the spin of the black holeover time and comparing with observed jet emission, sim-ulated visible matter infall from the progenitor star, andsimulated gravitational radiation losses, one may boundthe amount of dark matter infall and dark jet emission.In order for there to be dark matter in the imme-diate vicinity of the progenitor star and therefore non-negligible dark matter infall, we must have some local-ized overdensity of interacting dark matter. The darkmatter gas may be dense enough to cause gravitationalmicrolensing in which case constraints from MACHOsearches become relevant. Dense, compact objects gener-ically are referred to as MACHOS (Massive CompactHalo Objects). The existing constraints on MACHOS[85–88] are from gravitational microlensing experimentsand stability of wide binary star systems. Gravitationalmicrolensing occurs due to a massive compact objectmoving within the line of sight of an observer and a lightsource. The result is that the light source is temporar-ily magnified. Since present studies depend heavily onthe model of the dark matter distribution, they are notdirectly applicable to the case of dark matter disk galax-ies without further analysis [6]. We note dark mattercapture by the progenitor star will be small since wehave not allowed for non-gravitational interactions be-tween the dense progenitor core and the interacting darkmatter. Previous studies have shown that for these typesof models, even if a small interaction between nucleonsand the interacting dark matter is allowed, the amountof capture is small [10]. We emphasize that it is not unreasonable to assumethat there are local over-densities of interacting darkmatter in the immediate vicinity of a progenitor star.In the dwarf galaxy Mrk 996 there is evidence of a re-cent minor merger that has allowed for an abundance ofWolf-Rayet star formation [89]. In addition to acquir-ing baryonic matter during the merger, interacting darkmatter would be acquired as well. Dwarf galaxies tend tobe overwhelmingly dominated by dark matter, thereforewe naively expect there to be approximately four timesas much interacting dark matter in a dwarf galaxy thanbaryonic matter ( (cid:15) (cid:46) ∼ ± g/cm [68]) the Jeans mass of the gas must be M J ≈ (cid:114) π (cid:18) k B T D (0) G N m X (cid:19) / √ ρ acc ≈ . × − ± M Sun . (35)For the specific case of Mrk 996, the total amount ofall dark matter is ∼ M Sun [90] and therefore the totalamount of allowed interacting dark matter is (cid:46) M Sun .This allows for many such clouds of interacting dark mat-ter to form even if most of the interacting dark mattersinks to the center of the galaxy. Further analysis forother galaxies and an extension to the case of decoupledinteracting dark matter will be addressed in future work.The amount of visible matter infall may be calculatedusing the free-fall model [82, 91, 92]. We review thisargument here in order to comment on its applicabilityto the dark sector. In the visible sector the pressure, P v ,for the gas we consider is dominated by electrons sincenucleons are in large nuclei. The equation of state for therelativistic electrons is given by P v = K v ρ / , (36)where K v = (cid:15) F Y / e (cid:16) (cid:0) S e π (cid:1) (cid:17) ρ − / . We have in-troduced the electron to nucleon ratio Y e , the electronFermi energy (cid:15) F = (cid:0) π ρ v Y e (cid:1) / and the entropy perelectron S e = (cid:0) π T /(cid:15) F (cid:1) . The density distribution priorto collapse is given in terms of a mass dependent O (1) The Wolf-Rayet stars in Mrk 996 are ∼ . z ∼ − )[90], therefore the relevant interacting dark matter temperatureis that of the dark photon bath approximately today since theinteracting dark matter is still coupled with the dark photonbath. coefficient, C , by ρ v (∆ t = 0) ≈ C (cid:18) r (cid:19) g/cm . (37)The density and matter infall rate after an elapsed time∆ t are given as ρ v ≈ C √ G N M B M Sun (cid:18) t (cid:19) (cid:18) r (cid:19) / g/cm , (38)˙ M in,v ≈ (0 . C (cid:18) t (cid:19) M sun /s . (39)The dark sector gas infall scenario may be significantlymore complicated than the scenario for the visible sectorthat we have presented. The initial conditions for thedark sector gas are independent of the stellar propertiesof the progenitor star since it only interacts gravitation-ally with the visible stellar matter. The position of thedark sector gas is influenced by the position of the visibleprogenitor gravitational well, but the magnetohydrody-namical properties of the dark gas are not. How exactlythe dark sector cloud of gas, which may be nearly coin-cident with the progenitor star, infalls requires furtherstudy of dark sector substructure which we leave for fu-ture work.The dark U (1) D sector allows for dark electromag-netism similar to electromagnetism in the visible sector.Therefore jet production through the BZ mechanism mayproceed as is well-known for the visible sector. Sincethe microscopic properties of the interacting dark matterneed not be identical to those of the visible sector it maybe that a given collapsar event allows jet production forthe visible sector but not for the dark sector. In particu-lar, the mass-to-charge ratio and fine structure constantmust allow for the Alfven speed to exceed the local freefall speed in the ergosphere [82] and pair production tobe efficient [71].Observations of Fe K α spectral emission [93–95] haveallowed astronomers to determine spin for black holes at various redshifts. In particular, the spin has been de-termined for some supermassive blackholes at redshiftscomparable to those at which we observe long gammaray bursts. Therefore it seems to us that it is in principlepossible to determine the spin of the newly formed blackhole in a collapsar scenario that may underlie some longgamma ray bursts. Studies for future missions [96–102]are presently underway to further develop our capabilityto measure black hole spin. VI. CONCLUSIONS We have described a microscopic model of PIDMwithin the framework of supersymmetry. We have dis-cussed the astrophysical and cosmological constraints forsuch a model in the limiting case that the interactionsbetween the dark sector and visible sector are negligible.Furthermore, we have explored ways in which this classof models may be relevant for observational studies ofgamma ray bursts and explored the phenomena of darksector jets powered by the Blandford-Znajek mechanism.Our proposal to compare spin down rate with jet emis-sion luminosity potentially provides a new tool to studythe microscopic theory of dark matter.The model proposed here may be generalized to largersymmetry groups or to allow a stronger coupling betweenthe dark sector and the visible sector. These are inter-esting directions for future work. Another interestingquestion is how collapsar model physics is modified bythe existence of such a dark sector. ACKNOWLEDGMENTS D.L. and W.T. would like to thank Paul Shapiro andKathryn Zurek for helpful discussions. D.L. would liketo thank Jimmy for useful discussions. We would like tothank Francis-Yan Cyr-Racine for helpful comments onan earlier draft of this paper. This work was supportedby the National Science Foundation under Grant NumberPHY-1316033. [1] P. A. R. Ade et al. [Planck Collaboration],arXiv:1303.5062 [astro-ph.CO].[2] P. A. R. Ade et al. [Planck Collaboration],arXiv:1303.5076 [astro-ph.CO].[3] D. N. Spergel and P. J. Steinhardt, Phys. Rev. Lett. ,3760 (2000) [astro-ph/9909386].[4] R. Dave, D. N. Spergel, P. J. Steinhardt and B. D. Wan-delt, Astrophys. J. , 574 (2001) [astro-ph/0006218].[5] W. Fischler and W. Tangarife Garcia, JHEP , 025(2011) [arXiv:1011.0099 [hep-ph]].[6] J. Fan, A. Katz, L. Randall and M. Reece, Phys. DarkUniv. , 139 (2013) [arXiv:1303.1521 [astro-ph.CO]]. [7] J. Fan, A. Katz, L. Randall and M. Reece, Phys. Rev.Lett. , no. 21, 211302 (2013) [arXiv:1303.3271 [hep-ph]].[8] T. Banks, W. Fischler, D. Lorshbough and W. Tangar-ife, arXiv:1403.6844 [astro-ph.HE].[9] M. McCullough and L. Randall, JCAP , 058 (2013)[arXiv:1307.4095 [hep-ph]].[10] J. Fan, A. Katz and J. Shelton, [arXiv:1312.1336 [hep-ph]].[11] B. Holdom, Phys. Lett. B , 196 (1986).[12] D. A. Demir and H. J. Mosquera Cuesta, Phys. Rev. D , 043003 (2001) [astro-ph/9903262]. [13] J. L. Feng, H. Tu and H. -B. Yu, JCAP , 043 (2008)[arXiv:0808.2318 [hep-ph]].[14] L. Ackerman, M. R. Buckley, S. M. Carroll andM. Kamionkowski, Phys. Rev. D , 023519 (2009)[arXiv:0810.5126 [hep-ph]].[15] N. Arkani-Hamed, D. P. Finkbeiner, T. R. Slatyerand N. Weiner, Phys. Rev. D , 015014 (2009)[arXiv:0810.0713 [hep-ph]].[16] J. L. Feng, M. Kaplinghat, H. Tu and H. -B. Yu, JCAP , 004 (2009) [arXiv:0905.3039 [hep-ph]].[17] D. E. Kaplan, G. Z. Krnjaic, K. R. Rehermann andC. M. Wells, JCAP , 021 (2010) [arXiv:0909.0753[hep-ph]].[18] S. D. McDermott, H. -B. Yu and K. M. Zurek, Phys.Rev. D , 063509 (2011) [arXiv:1011.2907 [hep-ph]].[19] W. Fischler and J. Meyers, Phys. Rev. D , 063520(2011) [arXiv:1011.3501 [astro-ph.CO]].[20] D. E. Kaplan, G. Z. Krnjaic, K. R. Rehermann andC. M. Wells, JCAP , 011 (2011) [arXiv:1105.2073[hep-ph]].[21] J. M. Cline, Z. Liu and W. Xue, Phys. Rev. D ,101302 (2012) [arXiv:1201.4858 [hep-ph]].[22] K. M. Belostky, M. Y. .Khlopov and K. I. Shibaev,Grav. Cosmol. , 127 (2012).[23] F. -Y. Cyr-Racine and K. Sigurdson, Phys. Rev. D ,no. 10, 103515 (2013) [arXiv:1209.5752 [astro-ph.CO]].[24] M. Dine and W. Fischler, Phys. Lett. B , 227 (1982).[25] C. R. Nappi and B. A. Ovrut, Phys. Lett. B , 175(1982).[26] M. Dine and W. Fischler, Nucl. Phys. B , 346 (1982).[27] L. Alvarez-Gaume, M. Claudson and M. B. Wise, Nucl.Phys. B , 96 (1982).[28] M. Dine and W. Fischler, Nucl. Phys. B , 477 (1983).[29] Z. Chacko and E. Ponton, Phys. Rev. D , 095004(2002) [hep-ph/0112190].[30] Z. Komargodski and N. Seiberg, JHEP , 072 (2009)[arXiv:0812.3900 [hep-ph]].[31] P. Grajek, A. Mariotti and D. Redigolo, JHEP ,109 (2013) [arXiv:1303.0870 [hep-ph]].[32] Z. Kang, T. Li, T. Liu, C. Tong and J. M. Yang, Phys.Rev. D , 095020 (2012) [arXiv:1203.2336 [hep-ph]].[33] A. Albaid and K. S. Babu, arXiv:1207.1014 [hep-ph].[34] P. Byakti and T. S. Ray, JHEP , 055 (2013)[arXiv:1301.7605 [hep-ph]].[35] N. Craig, S. Knapen and D. Shih, arXiv:1302.2642.[36] J. A. Evans and D. Shih, arXiv:1303.0228 [hep-ph].[37] M. Abdullah, I. Galon, Y. Shadmi and Y. Shirman,JHEP , 057 (2013) [arXiv:1209.4904 [hep-ph]].[38] Z. Kang, J. Li and T. Li, JHEP , 024 (2012)[arXiv:1201.5305 [hep-ph]].[39] W. Fischler and W. Tangarife, arXiv:1310.6369 [hep-ph].[40] P. Fayet, Phys. Lett. B , 471 (1986).[41] I. Affleck and M. Dine, Nucl. Phys. B , 361 (1985).[42] E. W. Kolb and M. S. Turner, Front. Phys. , 1 (1990).[43] P. Fayet, Phys. Rev. D , 023514 (2004) [hep-ph/0403226].[44] M. Dine, L. Randall and S. D. Thomas, Nucl. Phys. B , 291 (1996) [hep-ph/9507453].[45] R. Allahverdi and A. Mazumdar, New J. Phys. ,125013 (2012).[46] N. F. Bell, K. Petraki, I. M. Shoemaker andR. R. Volkas, Phys. Rev. D , 123505 (2011)[arXiv:1105.3730 [hep-ph]]. [47] C. Cheung and K. M. Zurek, Phys. Rev. D , 035007(2011) arXiv:1105.4612 [hep-ph].[48] B. von Harling, K. Petraki and R. R. Volkas, JCAP , 021 (2012) [arXiv:1201.2200 [hep-ph]].[49] J. Shelton and K. M. Zurek, Phys. Rev. D , 123512(2010) arXiv:1008.1997 [hep-ph].[50] J. Beringer et al. (Particle Data Group), Phys. Rev.D , 010001 (2012).[51] S. R. Coleman, Nucl. Phys. B , 263 (1985) [Erratum-ibid. B , 744 (1986)].[52] A. Kusenko and M. E. Shaposhnikov, Phys. Lett. B ,46 (1998) [hep-ph/9709492].[53] K. Enqvist and J. McDonald, “Q balls and baryogenesisin the MSSM,” Phys. Lett. B , 309 (1998) [hep-ph/9711514].[54] S. Kasuya and M. Kawasaki, Phys. Rev. D , 041301(2000) [hep-ph/9909509].[55] M. Laine and M. E. Shaposhnikov, Nucl. Phys. B ,376 (1998) [hep-ph/9804237].[56] S. Kasuya and M. Kawasaki, Phys. Rev. Lett. , 2677(2000) [hep-ph/0006128].[57] S. Kasuya and M. Kawasaki, Phys. Rev. D , 123515(2001) [hep-ph/0106119].[58] T. Chiba, K. Kamada and M. Yamaguchi, Phys. Rev.D , 083503 (2010) [arXiv:0912.3585 [astro-ph.CO]].[59] A. Kusenko, Phys. Lett. B , 285 (1997) [hep-th/9704073].[60] F. -Y. Cyr-Racine, R. de Putter, A. Raccanelliand K. Sigurdson, Phys. Rev. D , 063517 (2014)[arXiv:1310.3278 [astro-ph.CO]].[61] D. Clowe, A. Gonzalez and M. Markevitch, Astrophys.J. , 596 (2004) [astro-ph/0312273].[62] M. Markevitch, A. H. Gonzalez, D. Clowe, A. Vikhlinin,L. David, W. Forman, C. Jones and S. Murray et al. ,Astrophys. J. , 819 (2004) [astro-ph/0309303].[63] M. Bradac, D. Clowe, A. H. Gonzalez, P. Marshall,W. Forman, C. Jones, M. Markevitch and S. Randall etal. , Astrophys. J. , 937 (2006) [astro-ph/0608408].[64] S. W. Randall, M. Markevitch, D. Clowe, A. H. Gon-zalez and M. Bradac, Astrophys. J. , 1173 (2008)[arXiv:0704.0261 [astro-ph]].[65] D. A. Buote, T. E. Jeltema, C. R. Canizares andG. P. Garmire, Astrophys. J. , 183 (2002) [astro-ph/0205469].[66] J. Miralda-Escude, Astrophys. J. , 60 (2002) [astro-ph/0002050].[67] A. H. G. Peter, M. Rocha, J. S. Bullock and M. Kapling-hat, arXiv:1208.3026 [astro-ph.CO].[68] A. MacFadyen and S. E. Woosley, Astrophys. J. ,262 (1999) [arXiv:astro-ph/9810274].[69] S. E. Woosley, Astrophys. J. , 273 (1993).[70] B. Paczynski, Astrophys. J. , L45 (1998)[arXiv:astro-ph/9710086].[71] R. D. Blandford and R. L. Znajek, Mon. Not. Roy. As-tron. Soc. , 433 (1977).[72] Komissarov S. S., Mon. Not. Roy. Astron. Soc. , L41(2001).[73] S. S. Komissarov, [arXiv:astro-ph/0211141].[74] S. S. Komissarov, Mon. Not. Roy. Astron. Soc. ,1431 (2004) [astro-ph/0402430].[75] S. Koide, Astrophys. J. , L45 (2004).[76] J. C. McKinney and C. F. Gammie, Astrophys. J. ,977 (2004) [astro-ph/0404512]. [77] J. C. McKinney, Mon. Not. Roy. Astron. Soc. , 1561(2006) [astro-ph/0603045].[78] M. V. Barkov and S. S. Komissarov, Mon. Not. Roy.Astron. Soc. , 1 (2008) [arXiv:0710.2654 [astro-ph]].[79] S. S. Komissarov, J. Korean Phys. Soc. , 2503 (2009)[arXiv:0804.1912 [astro-ph]].[80] M. V. Barkov and S. S. Komissarov, AIP Conf. Proc. , 608 (2009) [arXiv:0809.1402 [astro-ph]].[81] S. Nagataki, Astrophys. J. , 937 (2009)[arXiv:0902.1908 [astro-ph.HE]].[82] S. S. Komissarov and M. V. Barkov, Mon. Not. R.Astron. Soc. , 3 (2009) [arXiv:0902.2881 [astro-ph.HE]].[83] A. Tchekhovskoy, R. Narayan and J. C. McKin-ney, Mon. Not. Roy. Astron. Soc. , L79 (2011)[arXiv:1108.0412 [astro-ph.HE]].[84] R. F. Penna, R. Narayan and A. Sadowski,[arXiv:1307.4752 [astro-ph.HE]].[85] G. C. Lacey and J. P. Ostriker, Astrophys. J. , 633(1985).[86] J. Yoo, J. Chaname and A. Gould, Astrophys. J. ,311 (2004) [astro-ph/0307437].[87] M. Moniez, Gen. Rel. Grav. , 2047 (2010)[arXiv:1001.2707 [astro-ph.GA]].[88] F. Iocco, M. Pato, G. Bertone and P. Jetzer, JCAP , 029 (2011) [arXiv:1107.5810 [astro-ph.GA]].[89] S. Jaiswal and A. Omar, Journal of Astrophysics andAstronomy, , 3 [arXiv:1307.4594 [astro-ph.CO]].[90] B. L. James, Y. G. Tsamis, M. J. Barlow, M. S. West-moquette, J. R. Walsh, F. Cuisinier, K. M. Exter, Mon.Not. Roy. Astron. Soc. , 2 (2009) [arXiv:0903.2280 [astro-ph.GA]].[91] J. Cooperstein, H. A. Bethe, and G. E. Brown, Nucl.Phys. A, , 527 (1984)[92] H. A. Bethe, Rev. Mod. Phys. , 801 (1990).[93] J. E. McClintock, R. Narayan, S. W. Davis, L. Gou,A. Kulkarni, J. A. Orosz, R. F. Penna and R. A. Remil-lard et al. , Class. Quant. Grav. , 114009 (2011)[arXiv:1101.0811 [astro-ph.HE]].[94] L. Brenneman, [arXiv:1309.6334 [astro-ph.HE]].[95] A. C. Fabian, E. Kara and M. L. Parker,arXiv:1405.4150 [astro-ph.HE].[96] T. Takahashi et al. [NeXT team Collaboration],[arXiv:0807.2007 [astro-ph]].[97] T. Takahashi, K. Mitsuda, R. Kelley, F. Aharonian,F. Akimoto, S. Allen, N. Anabuki and L. Angelini etal. , Proc. SPIE Int. Soc. Opt. Eng. , 77320Z (2010)[arXiv:1010.4972 [astro-ph.IM]].[98] N. E. White, A. Parmar, H. Kunieda, K. Nandra,T. Ohashi and J. Bookbinder, [arXiv:1001.2843 [astro-ph.IM]].[99] X. Barcons, D. Barret, A. Decourchelle, J. -W. d. Herder, T. Dotani, A. C. Fabian, R. Fraga-Encinas and H. Kunieda et al. , [arXiv:1207.2745 [astro-ph.HE]].[100] D. Barret, K. Nandra, X. Barcons, AFabian, J-Wd. Herder, L. Piro, M. Watson and J. Aird et al. ,[arXiv:1310.3814 [astro-ph.HE]].[101] M. Garcia, M. Elvis, J. Bookbinder, L. Brenneman,E. Bulbul, P. Nulsen, D. Patnaude and R. Smith et al.et al.