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Constraining a Thin Dark Matter Disk with Gaia

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Constraining a Thin Dark Matter Disk with Gaia LCTP 17-03, MIT-CTP 4957 Constraining a Thin Dark Matter Disk with Gaia Katelin Schutz,1, ∗ Tongyan Lin,1, 2, 3 Benjamin R. Safdi,4 and Chih-Liang Wu5 1Berkeley Center for Theoretical Physics, University of California, Berkeley, CA 94720, USA 2Theoretical Physics Group, Lawrence Berkeley National Laboratory, Berkeley, CA 94720 3Department of Physics, University of California, San Diego, CA 92093, USA 4Leinweber Center for Theoretical Physics, Department of Physics, University of Michigan, Ann Arbor, MI 48109 5Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA 02139 If a component of the dark matter has dissipative interactions, it could collapse to form a thin dark disk in our Galaxy that is coplanar with the baryonic disk. It has been suggested that dark disks could explain a variety of observed phenomena, including periodic comet impacts. Using the first data release from the Gaia space observatory, we search for a dark disk via its effect on stellar kinematics in the Milky Way. Our new limits disfavor the presence of a thin dark matter disk, and we present updated measurements on the total matter density in the Solar neighborhood. Introduction.| The particle nature of dark matter height of hDD 10 pc are required to meaningfully im- (DM) remains a mystery in spite of its large abundance pact the above∼ phenomena.1 in our Universe. Moreover, some of the simplest DM Here we present a comprehensive search for a local DD, models are becoming increasingly untenable. Taken to- using tracer stars as a probe of the local gravitational po- gether, the wide variety of null searches for particle DM tential. Specifically, we use the Tycho-Gaia Astrometric strongly motivates taking a broader view of potential Solution (TGAS) [47, 48] catalog, which provides mea- models. Many recently-proposed models posit that DM sured distances and proper motions for 2 million stars is part of a dark sector, containing interactions or par- in common with the Tycho-2 catalog [49].∼ Previous work ticles that lead to non-trivial dynamics on astrophysical searching for a DD with stellar kinematics used data from scales [1{16]. Meanwhile, the Gaia satellite [17] has been the Hipparcos astrometric catalog [50] and excluded lo- 2 observing one billion stars in the local Milky Way (MW) cal surface densities ΣDD & 14 M /pc for dark disks with high precision astrometry, which will allow for a vast with thickness hDD 10 pc [51]. As compared with improvement in our understanding of DM substructure Hipparcos, TGAS contains∼ 20 times more stars with in our Galaxy and its possible origins from dark sectors. three dimensional positions∼ and proper motions within In this Letter, we apply the first Gaia data release [18] a larger observed volume, which allows for a significant to constrain the possibility that DM can dissipate en- increase in sensitivity. Our analysis also improves on ergy through interactions in a dark sector. Existing con- previous work by including a comprehensive set of con- straints imply that the entire dark sector cannot have founding factors that were previously not all accounted strong self interactions, since this would lead to devia- for, such as uncertainties on the local density of bary- tions from the predictions of cold DM that are inconsis- onic matter and the tracer star velocity distribution. We 2 tent with cosmological observations [19{22]. However, it exclude ΣDD 6 M /pc for hDD 10 pc, and our re- & ∼ is possible that only a subset of the dark sector inter- sults put tension on the DD parameter space of interest acts strongly or that DM interactions are only strong in for explaining astrophysical anomalies [36{42]. low-velocity environments [23{25]. In these cases, there Vertical kinematic modeling.| We use the framework is leeway in cosmological bounds and one must make use developed in Ref. [52] (and extended in Ref. [51]) to de- of smaller scale observables [26, 27]. If the DM compo- scribe the kinematics of TGAS tracer stars in the pres- nent can dissipate energy through emission or upscatter- ence of a DD. This formalism improves upon previous ing (see e.g. [16, 28{35] for examples of mechanisms), constraints on a DD that did not self-consistently model then it can cool and collapse to form DM substructure. the profiles of the baryonic components in the presence arXiv:1711.03103v2 [astro-ph.GA] 30 Aug 2018 These interactions could result in a striking feature in our of a DD [53{57]. These bounds typically compared the Galaxy: a thin DM disk (DD) [14, 15] that is coplanar total surface density of the Galactic disk, measured from with the baryonic disk. the dynamics of a tracer population above the disk, to A thin DD may be accompanied by a range of observa- a model of the surface density of the baryons based on tional signatures. For instance, DDs may be responsible extrapolating measurements from the Galactic midplane. for the 30 million year periodicity of comet impacts [36], However, the models did not include the pinching effect the co-rotation∼ of Andromeda's satellites [37, 38], the of the DD on the distribution of the baryons, which would point-like nature of the inner Galaxy GeV excess [39, 40], the orbital evolution of binary pulsars [41], and the for- 1 mation of massive black holes [42], in addition to having A thicker DD with hDD & 30 pc can cause periodic cratering 2 implications for DM direct detection [43, 44]. Typically, [45], however a larger surface density ΣDD ∼ 15-20 M /pc is 2 required to be consistent with paleoclimactic constraints [46]. a DD surface density of ΣDD 10 M /pc and a scale ∼ 2 3 lower the inferred baryon surface density for fixed mid- Baryonic Component ρ(0) [M /pc ] σ [km/s] Molecular Gas (H2) 0.0104 0.00312 3.7 0.2 plane density. Instead, Refs. [51, 52] consider the dy- ± ± Cold Atomic Gas (HI(1)) 0.0277 0.00554 7.1 0.5 namics close to the disk and self-consistently model the ± ± Warm Atomic Gas (HI(2)) 0.0073 0.0007 22.1 2.4 baryonic components for fixed DD surface density and ± ± Hot Ionized Gas (HII) 0.0005 0.00003 39.0 4.0 scale heights. We summarize the key components below. Giant Stars 0.0006 ± 0.00006 15.5 ± 1.6 ± ± The phase-space distribution function of stars f(x; v) MV < 3 0.0018 0.00018 7.5 2.0 ± ± in the local MW obeys the collisionless Boltzmann equa- 3 < MV < 4 0.0018 0.00018 12.0 2.4 ± ± 4 < MV < 5 0.0029 0.00029 18.0 1.8 tion. Assuming that the disk is axisymmetric and in ± ± 5 < MV < 8 0.0072 0.00072 18.5 1.9 equilibrium, the first non-vanishing moment of the Boltz- ± ± mann equation in cylindrical coordinates is the Jeans MV > 8 (M Dwarfs) 0.0216 0.0028 18.5 4.0 White Dwarfs 0.0056± 0.001 20.0 ± 5.0 equation for population A, Brown Dwarfs 0.0015 ±0.0005 20.0 ± 5.0 ± ± 1 2 1 2 Total 0.0889 0.0071 | @r(rνAσA;rz) + @z(νAσA;zz) + @zΦ = 0 ; (1) ± rνA νA TABLE I. The baryonic mass model that informs our priors. where Φ is the total gravitational potential, νA is the 2 stellar number density, and σA;ij is the velocity dis- persion tensor. The first term in Eq. (1), commonly vertical component of the equilibrium Boltzmann equa- tion is vz@zfi @zΦ@v fi = 0, which is satisfied by known as the tilt term, can be ignored near the disk − z midplane where radial derivatives are much smaller than Z p 2 vertical ones [58]. We assume populations are isother- νi(z) = νi;0 dvzfi;0 vz + 2Φ(z) ; (5) 2 mal (constant σA;zz) near the Galactic plane [59]. With these simplifying assumptions, the solution to the verti- where fi;0 is the vertical velocity distribution at height −Φ(z)/σ2 z = 0, normalized to unity. Given Φ(z), we can then cal Jeans equation is νA(z) = νA;0 e A , where we predict the vertical number density profile for a tracer impose Φ(0) = 0 and define σA σA;zz. For populations composed of roughly equal mass≡ constituents (including population. In our analysis we determine fi;0 empirically gaseous populations), we then make the assumption that and do not assume that our tracer population is neces- the number density and mass density are proportional, sarily isothermal. −Φ(z)/σ2 Mass Model.| In order to solve for the gravita- i.e. ρA(z) = ρA;0 e A . We connect the gravitational potential to the mass tional potential, we must have an independent model density of the system with the Poisson equation for the baryons. In TableI, we compile some of the most up-to-date measurements of ρA;0 and σA for the 2 2 1 local stars and gas, primarily drawing from the results Φ = @ Φ + @r(r@rΦ) = 4πGρ ; (2) r z r of Ref. [57] and supplementing with velocity dispersions where ρ is the total mass density of the system. The from Refs. [62, 63]. The velocity dispersions for gas radial term is related to Oort's constants, with re- components are effective dispersions that account for ad- 1 ditional pressure terms in the Poisson-Jeans equation. cent measurements showing r @r(r@rΦ) = (3:4 0:6) −3 3 ± × We include uncertainties (measured when available, esti- 10 M /pc [60], which can be included in the anal- ysis as a constant effective contribution to the density mated otherwise) and profile over these nuisance param- [61].
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