GPS as a dark matter detector Andrei Derevianko University of - PowerPoint PPT Presentation

GPS as a dark matter detector Andrei Derevianko University of Nevada, Reno, USA

GPS.DM (?) collaboration G. Blewitt (GPS, Nevada-Reno) A. Derevianko (Theory/Clocks/Data analysis, Nevada-Reno) M. Pospelov (Theory, Perimeter/UBC) J. Sherman (Clocks, NIST -Boulder) Students (all Nevada-Reno) S. Alto, M. Murphy*, N. Lundholm, A. Rowling * = graduated + GNOME connections Postdoctoral position available supported by the US NSF

Outline • What do we know about DM? • “Lumpy” dark matter • Atomic clocks • GPS as a dark matter detector Andrei Derevianko - U. Nevada-Reno

What do we know about DM? Dark Matter halo Velocity distribution v 2 f H v L 0 300 650 v, km ê s Galactic orbital motion Energy density v g ~ 300km/s ρ DM ∼ 0.3 GeV/cm 3 Andrei Derevianko - U. Nevada-Reno

Candidates: from WIMPs to MACHOs ? M > 10 − 24 M ⊙ M ~10 − 56 − 10 − 54 M ⊙ M ~10 − 7 − 10 2 M ⊙ WIMPs MACHOs Weakly interacting massive particles Quantum fields Massive compact halo objects

DM as a gas of stable extended objects • Self-interacting quantum fields • Networks of topological defects (light quantum fields = monopoles, vortices, domain walls), solitons, Q-balls • Non-gravitational (dissipative) interactions in the dark sector Illustration: ferromagnets Curie point in ferromagnetic phase transitions Andrei Derevianko - U. Nevada-Reno

DM halo=“preferred” reference frame α ' ' 12 11 1 α 10 2 9 3 ' 8 4 7 5 α 300 km/s 6 ' ' Macroscopic DM objects Are there correlations with galactic velocity of moving through DM halo? Andrei Derevianko - U. Nevada-Reno

Are the clouds “natural”? Andrei Derevianko - U. Nevada-Reno

“Gas of topological defects” DM model φ a 2 A 2 d 12 11 1 10 2 9 3 8 4 7 5 6 L ! Defect size and d ~ particle mass m φ c ⎛ ⎞ A 2 ρ TDM ∼ 1 1 L 3 × d 2 d 3 ⎜ ⎟ Energy density ⎝ ⎠ ! c 1 1 n σ v ∼ T coll ~ 1/ L 3 × d 2 × v g Time b/w “collisions” M. Pospelov τ ~ d Interaction time v g

Atomic clocks - amazing listening devices • Most precise instruments ever built • Modern nuclear/atomic clocks aim at 19 significant figures of accuracy • Fraction of a second over the age of the Universe • Best limits on modern-epoch drift of fundamental constants Andrei Derevianko - U. Nevada-Reno

Clocks quantum oscillator: φ 0 ( t ) / ω 0 t ∫ φ 0 ( t ) = ω 0 d ′ phase = time = t 0 t ∫ φ ( t ) = ( ω 0 + δω ( ′ d ′ with TDM clock speeds up/slows down t )) t 0 ( ) ( ) = Δ φ TDM t ( ) = Δ t TDM t t ∫ Δ φ TDM t δ ω ( ′ t ) d ′ t ω 0 −∞ Andrei Derevianko - U. Nevada-Reno

Basic idea Lump of dark matter ~300 km/s atomic frequencies are shifted 12 v g 11 1 10 2 by the lump 9 3 8 4 7 5 6 “New physics” interaction time reading - linear bias ! absolute time d / v g Andrei Derevianko - U. Nevada-Reno

Dark matter signature 12 12 v g 11 1 11 1 10 2 10 2 9 3 9 3 8 4 8 4 7 5 7 5 6 6 difference in clock readings l / v g time Monitor time difference b/w two spatially-separated clocks 
 ⇒ persistent clock discrepancy for over time l/v g GPS aperture =50,000 km => l/v g ~ 150 sec Details in Derevianko and Pospelov, Nature Phys. 10, 933 (2014) Andrei Derevianko - U. Nevada-Reno

Tomography of a monopole 2 12 11 1 10 2 9 3 8 4 v g 7 5 6 12 11 1 10 2 9 3 8 4 7 5 6 1 3 12 11 1 10 2 9 3 8 4 7 5 6 clock phase 1 2 3 time Andrei Derevianko - U. Nevada-Reno

Dark-matter portal ⎛ ⎞ 2 + m p pp 2 + ... ) m e ee 1 ( − L int = a 2 r , t + 2 F ⎜ ⎟ µ ν Λ e Λ p 4 Λ γ 2 ⎝ ⎠ DM field electrons protons EM field Compare to the QED Lagrangian ( ) m e c 2 → m e c 2 1 + a 2 r , t ⎛ ⎞ 1 L QED = i ! ceDe − m e c 2 ee − 2 ⎜ ⎟ F Λ e ⎝ ⎠ 2 µ ν 4 µ 0 TD lump pulls on the rest masses of electrons, quarks and EM coupling Energies and frequencies are modulated as TD sweeps through Andrei Derevianko - U. Nevada-Reno

Variation of fundamental constants ⎛ ⎞ ω clock α , m q , m e δω ( t ) δ X ( t ) δα ( t ) ∑ ⎜ ⎟ = = K α + ... K X Λ QCD ⎝ ⎠ m p ω 0 α X X = fndconsts Compare ratio of frequencies of two clocks with different sensitivities T. Rosenband, et al. Science 319, 1808 (2008)

Variation of fundamental constants Drift vs transients 12 v g 11 1 10 2 Transient 9 3 8 4 7 5 6 d ~100km 12 v g 11 1 10 2 Slow drift (e.g., NIST Al/Hg ion clocks) 9 3 8 4 7 5 6 d > 300km/s × 1year = 10 10 km Andrei Derevianko - U. Nevada-Reno

Networks of clocks Global Positioning System ❖ Each GPS satellite has four clocks (32 satellites) ❖ Data are sampled every second ❖ Vast terrestrial network of monitoring stations (H masers) Trans-european clock network ❖ Optical fiber connects state-of-the art clocks ❖ Elements were demonstrated 
 (PTB-MPI Munich 920 km link) (Predehl et al., Science (2012)) TAI dissemination network between national labs Andrei Derevianko - U. Nevada-Reno

Signal-to-noise ratio (thin wall) 12 11 1 12 10 2 v g 11 1 time difference 10 2 9 3 9 3 8 4 7 5 8 4 6 7 5 6 ! absolute time T m Time b/w events c ! K X ρ DM d 2 T coll ∑ S / N = Λ X T m σ y ( T m ) 2 T m v g / l 2 fundametal constantsX defect size Allan variance Dark matter 
 energy density Andrei Derevianko - U. Nevada-Reno

Projected limits (thin domain walls) 
 (if the TDM signature is not observed) Trans-continental network of Sr optical lattice clocks 10 11 , TeV 10 8 n o i t a l l e t s n o c Energy scale Plank energy scale 10^16 TeV S P G 10 5 100 Excluded by terrrestial experiments and astrophysical bounds 10 4 10 5 1 10 100 1000 m = 10 10 eV m = 10 14 eV defect size d, km Total monitoring time =1 year Andrei Derevianko - U. Nevada-Reno

GPS as a dark matter detector • GPS = max 32 satellites with Rb/Cs clocks • 50,000 km aperture - largest human-built DM detector - no extra $$$ • None of conventional effects would sweep at 300 km/s (except for solar flares) • Other navigation systems: Glonass/Galileo/BeiDou • Extensive terrestrial clock network on receiving stations Andrei Derevianko - U. Nevada-Reno

GPS clocks • Presently a mix of II-generation block sats (IIA,IIR,IIRM,IIF) • 12 hr orbits • Each satellite has 4 clocks (depends on individual satellite) • Only a single clock is operational at a time on a single satellite 
 (misbehaving clocks are swapped, swaps are documented) • Rb and Cs clocks (20+ Rb, 5 Cs) • The broadcast microwave signals are tied to the clock output Andrei Derevianko - U. Nevada-Reno

Data acquisition Downlink microwave signals: L1 = 1572.42 MHz L2 = 1227.6 MHz L5 = 1176.45 MHz λ ~20 cm Measure the carrier phase of the broadcast signal (much more precise than the navigational message) Collect data from many receivers around the world Phases are combined => clock,orbit, position solutions Errors: time ~ 0.1ns and positions ~ 1 mm

Representative GNSS ground stations (with 10 years of 1-sec carrier phase data) Quartz oscillators (black) Atomic clocks: Hydrogen Rubidium Cesium Andrei Derevianko - U. Nevada-Reno

Signature 12 12 v g 11 1 11 1 10 2 10 2 9 3 9 3 8 4 8 4 7 5 7 5 6 6 difference in clock readings l / v g time Monitor time difference b/w two spatially-separated clocks 
 ⇒ persistent clock discrepancy for over time l/v g GPS aperture =50,000 km => l/v g ~ 150 sec Andrei Derevianko - U. Nevada-Reno

GPS data (Oct 16, 2007, 7AM EST) Clock difference G02-G08 in seconds - 1.5 ¥ 10 - 9 ! ## - 2. ¥ 10 - 9 Work in progress - 2.5 ¥ 10 - 9 ≈ 40 σ " Reject b/c of x-correlation ## - 3. ¥ 10 - 9 $ - 3.5 ¥ 10 - 9 ! 830 835 840 845 850 855 GPS epoch (30s) 150seconds 40 σ signal - but this occurs for all pairs with G02 satellite - => technical glitch with the clock on the G02 satellite ? Andrei Derevianko - U. Nevada-Reno

Data analysis At the end of the day I would like to be able to say: a certain signature fits the data with such-and-such probability. Also we need to estimate parameters for a given signature Andrei Derevianko - U. Nevada-Reno

Bayesian data analysis ( ) P ( M i | D , I ) = P ( M i | I ) × P D | M i , I ( ) P D , I M 0 = “No DM signal” ⎧ ⎪ M 1 = “Thin domain wall” ⎪ Hypoteses: ⎨ M 2 = “Monopole” ⎪ … ⎪ ⎩ M X =“….” ( ) O i ,0 = P D | M i , I Relative odds (assuming equal priors): ( ) P D | M 0 , I Complex multi-parameter models are “punished” automatically: built-in Occam’s razor Andrei Derevianko - U. Nevada-Reno

( ) O i ,0 = P D | M i , I ( ) P D | M 0 , I How to assign likelihoods? Andrei Derevianko - U. Nevada-Reno

Clocks are noisy and non-stationary Deterministic: Time offset Frequency offset Frequency drift Stochastic: White noise PM Flicker noise PM White noise FM Flicker noise FM Random walk FM Andrei Derevianko - U. Nevada-Reno

Allan variances as noise characteristics E. R. Griggs, E.R. Kursinski, D.M. Alkos (Radio Science, in press) ( ) = τ ( ) σ x τ Mod σ y τ Time projection error 3 ( ) ~ 3.5 × 10 − 3 (Cs-IIF) − 5.2 × 10 − 2 (Rb-IIRM) ns σ x 30s Andrei Derevianko - U. Nevada-Reno