Astrophysical constraints on dark matter Anne Green University of Nottingham Primordial Black Holes as a dark matter candidate Observational constraints on PBH abundance Applying constraints to, realistic, extended mass functions arXiv:1609.01143 Astrophysical uncertainties (on microlensing constraints) arXiv1705.10818 Primordial Black Hole Astrophysical constraints on ^ dark matter Anne Green University of Nottingham Primordial Black Holes as a dark matter candidate Observational constraints on PBH abundance Applying constraints to, realistic, extended mass functions arXiv:1609.01143 Astrophysical uncertainties (on microlensing constraints) arXiv1705.10818 Primordial Black Holes as a dark matter candidate Primordial Black Holes (PBHs) form in the early Universe (before nucleosynthesis) and are therefore non-baryonic. PBHs evaporate (Hawking radiation), lifetime longer than the age of the Universe for M > 1015 g. A DM candidate which (unlike WIMPs, axions, sterile neutrinos,…) isn’t a new particle (however their formation does usually require Beyond the Standard Model physics, e.g. inflation). LIGO has detected gravitational waves from mergers of 10 M BHs. ⇠ LIGO-Virgo, Elavsky could be formed by astrophysical processes, but such a large population possibly unexpected?? Could PBHs be the CDM? (and potentially also the source of the GW events?? Bird et al.; Sasaki et al.) Formation Most ‘popular’ mechanism is collapse of large (at horizon entry) density perturbations during radiation domination, forming PBHs with mass of order the horizon mass. Zeldovich & Novikov; Hawking; Carr & Hawking For gravity to overcome pressure forces resisting collapse, size of region at maximum expansion must be larger than Jean’s length. Simple analysis: Carr; see e.g. Harada, Yoo & Kohri and Yoo, Harada, Garriga & Kohri for refinements ⇢ ⇢¯ density contrast: δ − ⌘ ⇢¯ p 1 threshold for PBH formation: δ δ w = = ≥ c ⇠ ⇢ 3 3/2 15 t PBH mass: M w M MH 10 g H ⇠ 10 23 s ⇠ ✓ − ◆ initial PBHs mass fraction (fraction of universe in regions dense enough to form PBHs): 1 β(M) P (⇥(M )) d⇥(M ) ⇠ H H Zδc assuming a gaussian probability distribution: δ β(M)=erfc c p2σ(M ) ✓ H ◆ σ(MH) (mass variance) typical size of fluctuations PBH forming fluctuations δc but in fact β must be small, and hence σ ≪ δc PBH abundance Since PBHs are matter, during radiation domination the fraction of energy in PBHs grows a . / Relationship between PBH initial mass fraction, β, and fraction of DM in form of PBHs, f: 1/2 9 M β(M) 10− f ⇠ M ✓ ◆ i.e. initial mass fraction must be small, but non-negligible. 5 On CMB scales the primordial perturbations have amplitude σ(M ) 10− H ⇠ If the primordial perturbations are close to scale-invariant the number of PBHs formed will be completely negligible: β(M) erfc(105) 105 exp (105)2 ⇠ ⇠ − ⇥ ⇤ To form an interesting number of PBHs the primordial perturbations must be significantly larger (σ(MH)~0.01) on small scales than on cosmological scales. Constraints on the primordial power spectrum Large scale Ultracompact structure Primordial Black Holes minihalos* & the CMB 1 2 10− 10− 2 3 WIMP kinetic decoupling 10− 10− ❙ ❙ 3 4 10− 10− Allowed regions 4 5 10− 10− ) ) k k Ultracompact minihalos (gamma rays, Fermi-LAT) 5 ( ( 6 10− δ 10− R Ultracompact minihalos (reionisation, WMAP5 ⌧e) P 10 6 P 10 7 − − Primordial black holes 7 8 10− 10− CMB, Lyman-↵, LSS and other cosmological probes 8 9 10− 10− 9 10 10− 10− 3 2 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 10− 10− 10− 1 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 1 k (Mpc− ) Bringmann, Scott & Akrami * UCMH constraints only hold if most of the DM is WIMPs. Recent studies find they have shallower density profiles than previously assumed. Gosenca et al., Delos et al. Observational constraints on PBH abundance Microlensing Temporary (achromatic) brightening of background star when compact object passes close to the line of sight. EROS EROS constraints on fraction of halo in compact objects, f, assuming a delta- function mass function: f log10(M/M ) EROS MACHO constraints on fraction of halo in compact objects in the 1-30 M range: f M/M MACHO Very similar to EROS limits for M> 3 M . Ultra-faint dwarf heating Brandt Gravitational interactions transfer energy to stars, heating and cause the expansion of, i) star clusters within dwarf galaxies (e.g. star cluster at centre of Eridanus II) ii) ultra-faint dwarf galaxies increase in half-light radius with time constraint f M/M Mass segregation in dwarf galaxies Koushiappas & Loeb Mass segregation would lead to a deficit of stars in the centre of dwarf galaxies and a ring in the projected stellar surface density profile. projected stellar mass density constraint (f=0.1, M = 30 M ) log10 f M/M Wide binary disruption Chaname & Gould; Yoo, Chaname & Gould; Quinn et al.; Monroy-Rodriguez & Allen Massive compact objects perturb affect the orbits of wide binaries. Need to make assumptions about initial distribution of orbits of binaries. dist of semi-major axes constraint (1000, 100 & 10 M v. obs) 100f M/M Monroy-Rodriguez & Allen Cosmic Microwave Background distortions Ricotti et al; Ali-Haϊmoud & Kamionkowski; Horowitz; Blum, Aloni & Flauger Accretion onto PBH leads to emission of X-rays which can distort the spectrum (FIRAS) and anisotropies (WMAP/Planck) of the CMB. Significant uncertainties in constraint due to modelling of complex astrophysical processes. � wide binaries ����� micro-lensing Planckultra-faint dwarfs Planck ) ����� (collisional ionization) ��� � (photoionization) ( ����� ROM ��� ��-� ��-� ��� � �� ��� ���� ��� ����/�⊙ Ali-Hamoud & Kamionkowski X-ray and radio emission Gaggero et al; Inoue & Kusenko Accretion onto PBH leads to X-ray and radio emission. 100 DM f 1 10− DM fraction Radio constraint (2σ,3σ,5σ); λ =0.01 X-ray constraint (2σ,3σ,5σ); λ =0.01 10 2 −101 102 M [M ] But including effects of gas turbulence reduces accretion onto PBH and removes X-ray bound. Hector, Hutsi & Raidal quasar microlensing Quasar microlensing by compact objects in lens galaxy leads to variation in brightness of images in multiply lensed quasars. Chang & Refusal α= 0.2 ± 0.05 of the mass is in compact objects with 0 . 05 M <M< 0 . 45 M , consistent with abundance of stars. Mediavilla et al. However no constraint on f (fraction of mass in dark compact objects) published. OPTICAL rs=5 lt-day 100.0 10.0 • O M/M 1.0 0.1 0.05 0.1 0.4 1. supernova microlensing Compact objects affect lensing magnification distribution of type 1a SNe (most lines of sight are demagnified relative to mean, plus long-tail of high magnifications): Zumalacarregui & Seljak magnification distribution constraint f 0.9 ↵ =0 100 ↵ =0.85 0.8 101 Maximum near 0.7 SNe lensing 80 empty beam (this work) Eridanos II =1 0.6 z (95% c.l.) at 0.5 60 ) M ↵ 0 10 ⌦ 0.4 Magnification / µ 3 40 µ, z, tail ∆ − 0.3 PBH ( / EROS ⌦ L Planck (photo) Dark Matter fraction [%] P 0.2 ⌘ 20 ↵ 0.1 Planck (coll) 1 10− LIGO BHs 0.0 0 4 3 2 1 0 1 2 3 4 10− 10− 10− 10− 10 10 10 10 10 0.1 0.0 0.1 0.2 0.3 0.4 0.5 0.6 − MPBH [M ] ∆µ (relative to FRW mean) M/M gravitational waves PBH binaries can form: i) in the early Universe (from chance proximity), Nakamura, Sasaki, Tanaka & Thorne ii) via gravitational capture in present-day halos. Bird et al. If PBH binaries formed in the early Universe survive to the present day then their mergers are dominant, and orders of magnitude larger than the merger rate measured by LIGO. Nakamura et al.; Ali-Haϊmoud, Kovetz & Kamionkowski 100 DM ⌦ / 1 10− PBH ⌦ = PBH 2 f 10− LIGO EROS+MACHO 3 Eridanus II 10− Accretion - radio DM fraction Accretion - X-ray CMB - PLANCK CMB - FIRAS 4 10− 100 101 102 103 MPBH [M ] Kavanagh, Gaggero & Bertone, taking into account PBH’s dark ‘dresses’ Compilation of ~Solar mass region constraints f log10(M/M ) ________ . LMC microlensing (EROS & MACHO) - - - dwarf galaxy dynamical constraints __ _ __ _ __ - - - - - wide binary disruption (tightest) CMB constraints — — — X-ray & radio _______ SNe microlensing Doesn’t include Mediavilla et al. microlensing of quasars (no constraint on f published) or gravitational waves from mergers. microlensing of stars in M31 Same principle as MW microlensing, but sensitive to light compact objects (due to higher cadence obs.). Source stars unresolved. MM/M/M M/M 1111 11 1010-17-17 10-17 1010-7-7 10-7 10103 3 103 10101313 1013 FF WDWD F WD KK KMLML ML WBWB WB EGEG EGNSNS NS EE E 0.1000.100 0.100 mLQmLQ mLQ FIRASFIRAS FIRAS LSSLSS LSS 0.0010.001 0.001 WMAPWMAP WMAP f f f DFDF DF HSC-M31 constraint (95% C.L.) 1010-5-5 10-5 ー + one remaining candidate - - w/o one remaining candidate 1010-7-7 10-7 10101616 1016 10102626 1026 10103636 1036 10104646 10Niikura46 et al. MM/g/g M/g 1111 11 10 However analysis assumes geometric optics, however for M . 10 − M wavelength of light is larger than Schwarzschild radius of lens diffraction occurs and lowers maximum magnification. Inomata et al. neutron star destruction Capture of PBHs would lead to destruction of neutron stars in high density & low velocity dispersion environments. Constraints from observation of neutron stars in globular clusters: Capela, Pshirkov & Tinyakov; Pani & Loeb 100 r = 4 102 GeVcm 3 dm · − 3 3 DM r = 2 10 GeVcm 1 dm · − W 10− / PBH W 4 3 rdm = 10 GeVcm− 2 10− 1018 1019 1020 1021 1022 1023 1024 1025 1026 BH mass, g But do globular clusters have a high DM density? white dwarf explosions Transit of PBHs through white dwarf heats it, due to dynamical friction, causing it to explode.