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Searching for ultra-light new particles with black holes Robert Lasenby, Perimeter Institute 0905.4720 1004.3558 1411.2263 1604.03958 16xx.xxxxx … A. Arvanitaki, S. Dimopoulos, S. Dubovsky, N. Kaloper, J. March-Russell A. Arvanitaki, S. Dubovsky A. Arvanitaki, M. Baryakhtar, X. Huang A. Arvanitaki, M. Baryakhtar, S. Dimopoulos, S. Dubovsky, RL M. Baryakhtar, RL Outline • Light, weakly-coupled new particles — motivation & constraints • Black hole superradiance — particle production by energy extraction • Observational signatures • Spin-down of black holes • Coherent gravitational wave emission Light, weakly-coupled new particles Coupling to SM Standard Model SUSY? Grand Unification? Experimentally excluded New long Axions? range forces? Mass Light, weakly-coupled new particles Coupling to SM Standard Model LHC Experimentally excluded Black hole superradiance Mass Gravitational production of light particles • New particles must couple to SM through gravity • Problem: astrophysically, spacetime curvature scale & km => effective source density very low • • e.g. BH Hawking temperature, TH = 1/(8⇡GM ) ⇠ 10 Take advantage of coherence enhancement: classical energy extraction from spinning BHs 8 K Extracting energy and angular momentum from black holes • Spinning BHs have ergosphere - region where particles can have negative energy (as viewed from infinity) Ergosphere • Event horizon Mechanical Penrose process: throwing negative-energy particle into horizon Extracting energy and angular momentum from black holes • Spinning BHs have ergosphere - region where particles can have negative energy (as viewed from infinity) Ergosphere • Event horizon Mechanical Penrose process: throwing negative-energy particle into horizon Extracting energy and angular momentum from black holes • Spinning BHs have ergosphere - region where particles can have negative energy (as viewed from infinity) Ergosphere • Event horizon Mechanical Penrose process: throwing negative-energy particle into horizon Extracting energy and angular momentum from black holes • Spinning BHs have ergosphere - region where particles can have negative energy (as viewed from infinity) Ergosphere • Event horizon Mechanical Penrose process: throwing negative-energy particle into horizon Extracting energy and angular momentum from black holes • Spinning BHs have ergosphere - region where particles can have negative energy (as viewed from infinity) Ergosphere • Event horizon Mechanical Penrose process: throwing negative-energy particle into horizon Extracting energy and angular momentum from black holes • Spinning BHs have ergosphere - region where particles can have negative energy (as viewed from infinity) Ergosphere • Event horizon Wave Penrose process: transmitted wave has negative energy, reflected wave carries extra energy away Extracting energy and angular momentum from black holes • Spinning BHs have ergosphere - region where particles can have negative energy (as viewed from infinity) Ergosphere • Event horizon Wave Penrose process: transmitted wave has negative energy, reflected wave carries extra energy away Wave superradiance • Ingoing flux at horizon can correspond to negative E1 flux • For wave with angular quantum number m, ' ⇠ ei!t 1 2 P = '0 AH !(! 2 • im m⌦H ) Incoming waves can be scattered with amplification (max 4.4% for spin-1, 138% for spin-2) [Teukolsky & Press, 1974] Wave superradiance • Ingoing flux at horizon can correspond to negative E1 flux • For wave with angular quantum number m, ' ⇠ ei!t 1 2 P = '0 AH !(! 2 • im m⌦H ) Incoming waves can be scattered with amplification (max 4.4% for spin-1, 138% for spin-2) [Teukolsky & Press, 1974] Black hole bombs and bound states • “Black hole bomb” : superradiant scattering with a mirror [Teukolsky & Press, 1972] • Massive particles can form bound states around BH, enabling same exponential amplification Black hole bombs and bound states • “Black hole bomb” : superradiant scattering with a mirror [Teukolsky & Press, 1972] • Massive particles can form bound states around BH, enabling same exponential amplification Black hole bombs and bound states • “Black hole bomb” : superradiant scattering with a mirror [Teukolsky & Press, 1972] • Massive particles can form bound states around BH, enabling same exponential amplification Black hole bombs and bound states • “Black hole bomb” : superradiant scattering with a mirror [Teukolsky & Press, 1972] • Massive particles can form bound states around BH, enabling same exponential amplification (Pseudo)scalar bound states • For small mass, bound state spectrum is hydrogen-like ↵ ⌘ GM µ = rg µ ✓ !n ' µ 1 2 ↵ 2n2 n2 rn ⇠ ⇠4 µ↵ Im(!) ⇠ '20 (a⇤ m ◆ 400rg 2µr+ ) (Pseudo)scalar bound states • For small mass, bound state spectrum is hydrogen-like ↵ ⌘ GM µ = rg µ ✓ !n ' µ 1 2 ↵ 2n2 n2 rn ⇠ ⇠4 µ↵ Im(!) ⇠ '20 (a⇤ m ◆ 400rg 2µr+ ) (Pseudo)scalar bound states • For small mass, bound state spectrum is hydrogen-like ↵ ⌘ GM µ = rg µ ✓ !n ' µ 1 2 ↵ 2n2 n2 rn ⇠ ⇠4 µ↵ Im(!) ⇠ '20 (a⇤ m ◆ 400rg 2µr+ ) Superradiant growth rates Im(!) ⇠ ↵4l+4 (a⇤ m amplitude near horizon suppressed 2µr+ )µ a 0.5 1. 1.5 =1 M = 10 Mü =2 10-4 2. a* = 0.99 =3 10-6 10-8 a* = 0.9 10-2 =4 10-10 100 10-12 102 10-14 0.5 1 1.5 ma H10-11 eVL 2 2.5 Gsr rg Smaller alpha, larger l Gsr -1 HyearsL • Superradiant growth rates Smaller alpha, larger l Im(!) ⇠ ↵4l+4 (a⇤ m If ↵/l > 1/2 then angular phase -4 10 velocity faster than horizon, so mode -2 10 is decaying Gsr -1 HyearsL • • Fastest growth rate for µ ⇠ 1/(GMBH ) amplitude near horizon suppressed 2µr+ )µ a 0.5 1. 1.5 2. M = 10 Mü a* = 0.99 10-6 10-8 a* = 0.9 10-10 100 10-12 102 10-14 0.5 1 1.5 ma H10-11 eVL 2 2.5 Gsr rg • Superradiant growth rates If ↵/l > 1/2 then angular phase -4 10 velocity faster than horizon, so mode -2 10 is decaying Gsr -1 HyearsL • • Fastest growth rate for µ ⇠ 1/(GMBH ) 2µr+ )µ a 0.5 1. 1.5 2. M = 10 Mü a* = 0.99 10-6 10-8 a* = 0.9 10-10 100 10-12 102 10-14 0.5 1 1.5 ma H10-11 eVL 2 2.5 Gsr rg Im(!) ⇠ ↵4l+4 (a⇤ m amplitude near horizon suppressed 0.4 Smaller alpha, larger l 0.3 • Superradiant growth rates Smaller alpha, larger l Im(!) ⇠ ↵4l+4 (a⇤ m amplitude near horizon suppressed 2µr+ )µ a 0.5 1. 1.5 =1 For stellar BH, efolding times in plot ~100 sec 100 yr -1 Gsrsr-1 HyearsL • M = 10 Müü =2 -4 10-4 2. a**= 0.99 =3 -6 10-6 -8 10-8 a** = 0.9 -2 10-2 =4 -10 10-10 1000 -12 10-12 1022 -14 10-14 0.5 1 1.5 -11 eVL maa H10-11 2 2.5 Gsrsr rgg • Black hole spin-down a* ��� =1 ��� =2 ��� =3 ��� ��� ��� � �� �� �� �� M�� /M☉ ��� Black hole spin-down a* ��� =1 ��� ⇠ 10 yr ��� =2 =3 ��� ��� ��� � �� �� �� �� M�� /M☉ ��� Black hole spin-down a* ��� =1 ��� ⇠ 10 yr ��� =2 =3 2 ⇥ 107 yr ��� ��� ��� � �� �� �� �� M�� /M☉ ��� Black hole spin-down a* ��� =1 =3 ��� =2 ��� ⇠ 10 yr =2 =3 =1 2 ⇥ 107 yr ��� ��� ��� � �� �� �� �� M�� /M☉ ��� Exclusions from BH spin measurements • Higher BH spin => innermost stable orbit at smaller radius rISCO • • GM Accretion disk can get closer to BH 8 Detect X-rays from accretion disk, infer disk properties Contra-rotrating 6 4 Co-rotrating 2 0.2 0.4 0.6 0.8 1.0 a* Exclusions from BH spin measurements • Higher BH spin => innermost stable orbit at smaller radius • Accretion disk can get closer to BH • Detect X-rays from accretion disk, infer disk properties X-ray spin measurements Spin measurements from different black holes: 1.0 Black Hole Spin a* 0.8 0.6 0.4 0.2 ma =10-11 eV 0.0 5 10 Black Hole Mass HMüL 15 20 X-ray spin measurements Spin measurements from different black holes: 1.0 Black Hole Spin a* 0.8 0.6 0.4 0.2 ma =10-11 eV 0.0 5 10 Black Hole Mass HMüL 15 20 X-ray spin measurements Spin measurements from different black holes: 1.0 Black Hole Spin a* 0.8 0.6 0.4 0.2 ma =3x10-12 eV 0.0 5 10 Black Hole Mass HMüL 15 20 Light particle exclusion limits Large self-coupling => bosonic cloud growth cut off Self- coupling -14 -16 4 2 1 1: M33 X-7 2: LMC X-1 3: GRO J1655-40 4: Cyg X-1 5: GRS 1915+105 Log@l H10-10 eVêmaL2D Log@GeVê fa D -12 2s exclusion -60 -65 5 3 Q -70 on i x a CD -18 -20 -13 -75 -12 -11 Log@maêeVD Mass -10 -9 Binary black hole mergers [Abbot et al, 2016] • LIGO GW150914: first direct detection of gravitational waves! • From 2.5 events so far, infer merger rate of 9-240 / Gpc yr • At design sensitivity, 70-1200 visible mergers / year! BBH spin measurements [Abbot et al, 2016] • Spin-orbit interaction => BH spin components parallel to orbital axis affect inspiral waveform • Spin components misaligned with orbital axis can cause precession, modulating inspiral waveform • Intrinsic spins contribute to spin of final BH, which is constrained by merger and ringdown waveform • GW150914: if spins are aligned, obtain a1 < 0.2 , a2 < 0.3 (90%) Spin-down 1.0 Black Hole Spin a! 0.8 0.6 0.4 0.2 Initial Spin !actual" 0.0 0 20 40 60 Black Hole Mass !M!" 80 100 Spin-down 1.0 Black Hole Spin a* 0.8 0.6 0.4 0.2 0.0 0 20 40 60 Black Hole Mass HMüL ma = 6 x 10-13 eV HactualL 80 100 Spin-down measured 1.0 Black Hole Spin a* 0.8 0.6 0.4 0.2 0.0 0 20 40 60 Black Hole Mass HMüL ma = 6 x 10-13 eV HmeasuredL 80 100 Gravitational radiation from bound states • Bosonic cloud corresponds to classical scalar field oscillations => oscillating energy-momentum • Oscillating Tµ⌫ = rµ 'r⌫ ' radiation • gµ⌫ (. . . ) sources gravitational 1 Xp Ni Decomposing into levels, ' = p 2µ i have 1 ⇣ Tij = N1 (ri 2µ 1 )(rj 1 )e “Annihilations” 2i!1 t + p N1 N2 (ri ie i!i t ⇤ 1 )(rj + h.c. 2 )e “Transitions” i(!2 !1 )t + ... ⌘ Gravitational radiation from bound states • Bosonic cloud corresponds to classical scalar field oscillations => oscillating energy-momentum • Oscillating Tµ⌫ = rµ 'r⌫ ' radiation • gµ⌫ (. . . ) sources gravitational 1 Xp Ni Decomposing into levels, ' = p 2µ i have 1 ⇣ Tij = N1 (ri 2µ 1 )(rj 1 )e “Annihilations” 2i!1 t + p N1 N2 (ri ie i!i t ⇤ 1 )(rj + h.c. 2 )e “Transitions” i(!2 !1 )t + ... ⌘ All-Sky GW search • From each BH with a cloud, expect GWs from annihilations at frequency ✓ ! ' 2µ 1 • Coherent, monochromatic signals, very slow frequency drift Signals from different black holes clustered just below ! = 2µ • • Expected signals determined by BH mass and spin distribution potentially hundreds eventually visible! Most signals from BHs in our galaxy ↵ 2n2 ◆ = 2µ (1 [0, 0.03]) 100 f HHzL 1000 10000 Explorer Voyager aLIGO Design aLIGO 2015 ANNIHILATIONS 104 Expected Events • 2 X-ray spin limits 100 1 Initial LIGO limits 0.01 10-13 ttot = 1 year tcoh =2 days 10-12 ma HeVL 10-11 10-10 Summary • Black hole superradiance is a unique probe of light, weakly-coupled bosons • Gravitational wave detectors can probe SR in multiple, complementary ways: • • Monochromatic GWs from cloud • Statistics of BH spins, measured in mergers • Signals possible in near future! Observations of supermassive black holes, via telescopes and future lowerfrequency GW detectors, can constrain lower-mass bosons • Less clean astrophysical environment - further investigation required Statistical evidence Could obtain statistical evidence for structure in mass-spin plane with 50-200 measurements ���� time to merge:107 years ��� ������� • ��� �� time to merge:1010 years �� × ��-�� �� × ��-�� �� × ��-�� μ� /�� �� × ��-�� �� × ��-�� GWs from newly formed BHs • Measure parameters of newly-formed BH => prediction for SR process, given axion mass • Axion cloud takes days/years to grow • Typical reach ~ 30 Mpc for annihilation GW signals • e.g. if GW150914 had been < 10 Mpc away, potentially observable signal GWs from newly formed BHs • • • f HHzL Measure parameters of newly-formed BH => prediction for SR process, given axion mass 100 1000 1000 Explorer Voyager aLIGO Design DIRECT SEARCHES 100 aLIGO 2015 BH-BH Expected Events • Axion cloud takes days/years to grow Typical reach ~ 30 Mpc for annihilation GW signals e.g. if GW150914 had been < 10 Mpc away, potentially observable signal 10 1 BH-NS 0.1 0.01 0.001 1 ¥ 10-13 2 ¥ 10-13 5 ¥ 10-13 1 ¥ 10-12 ma HeVL 2 ¥ 10-12 5 ¥ 10-12