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Constraints on massive graviton dark matter from precision pulsar timing and astrometry

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Constraints on massive graviton dark matter from precision pulsar timing and astrometry

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  1. Constraints on massive graviton dark matter from precision pulsar timing and astrometry Konstantin POSTNOV (Sternberg Astronomical Institute) Collaborators: Maxim Pshirkov (PRAO Lebedev Phyical Institute), Artyom Tuntsov (SAI), Aleksandr Polnarev (QMC London UK), Deepak Baskaran (Cardiff UK) QUARKS-2008

  2. Plan • Pulsars as GW detectors • Observational constraints on massive graviton CDM • “Surfing effect” of massive gravitons and limits on their propagation speed

  3. Pulsars as GW detectors Gravitational waves (1/2) • General Relativity • GW propagation velocity in empty space isс: • Along axisz: & • Polarizatrion tensor have two non-zero components • Monochromatic transverse GW has two polarizatios (GR)

  4. Pulsars as GW detectors Gravitational waves (1/2) • GW energy density (monochromatic plane): • Stochastic isotropic background: Is the critical density • Or:

  5. Pulsars as monochromatic GW detectors Monochromatic GW (1/3) • GW changes the observed pulsar frequency(Sazhin (1978), Detweiler (1979)) x PSR z y • In GR interaction is independent of distance (if ) – no secular increase ~D. Is the GW polarization vector

  6. Pulsars as GW detectors Monochromatic GW (2/3) • Variation of the observed frequency results in time residuals in • time of arrival (TOA): h • Maximum sensitivity at frequencies ~ 1/Tobs • Longer GWs also contribute to the observed • Pulsar period and its derivative 1/Tobs 1/Tsamp 1/Tint Tobs~ 10 years Tsamp~ 10 days Tint ~1 hour

  7. Pulsars as GW detectors Monochromatic GW (3/3) h • In 2003 periodic motions in 3C66b were explained by binary SMBH (Sudou et al., 2003)-80 Mpc, 1.5x1010 M⊙ • Timing of PSRB1855+09 rejected this possibility (Jenet et al., 2004)

  8. Pulsars as GW detectors Stochastic GWB (1/3) • RMS of TOA residuals depend on GW energy density • For flat GW spectrum of width Δf~f centered atf • RMS of TOA residuals is (Detweiler, 1979): - the critical density

  9. Pulsars as GW detectors Stochastic GWB (2/3) • For arbitrary GWB («red noise»): Kaspi, Taylor, Ryba, 1994

  10. Pulsars as GW detectors Stochastic GWB (3/3) • GW noise is the same for all pulsars • It is advantageous to observe ensemble of pulsars and correlate rms of TOA residuals between each pair of pulsars Pair correlation of the TOA residuals for 20 pulsars (simulation, R,Manchester, 2007 )

  11. Pulsars as GW detectors Present limits and prospects (Manchester, 2007 – arXiv:0710.5026v2)

  12. Tests in Solar systems Doppler tracking (1/2) • Estabrook & Wahlquist, 1975, principle similar to pulsar timing • Best current limits: Cassini mission, 10-3-10-6 Hz(Armstrong et al. 2003)

  13. Solar system tests Doppler tracking (2/2) • Future projects: Search for Anomalous Gravity usingAtomic Sensors, SAGAS Reynaud et al. 2008

  14. Astrometric constraints • A GW causes «drizzling» of visual position of a source on the sky (e.g, Kaiser&Jaffe, 1997): • The observed quantity is the arc length between two sources Ψ: • In the presence of a GW sources on the sky would oscillate w.r.t. to their true position with amplitude h. Modern ICRF precision (~100 μas) constrain low-frequency GWB: h<5x10-10

  15. Theories with massive gravitons • Massive gravity ( Rubakov 2004, Dubovsky 2004) with spontaneous Lorentz braking (Rubakov & Tinyakov arXiv:0802.4379 for a review) • Healthy theory: no ghosts, no vDVZ discontinuity, no strong coupling at low scale • Interesting phenomenology: DE-like term in Fridmann equations + possibility to produce massive gravitons in the early Universe copiously enough to explain all of CDM (Dubovsky, Tinyakov & Tkachev 2005) • Taking graviton mass < (1015 cm)-1 (binary PSR constraints) and assuming all galactic CDM due to massive gravitons leads to a strong almost monochromatic (Δf/f~10-6) GW signal with amplitude

  16. Observational constraints: PTP08 Pulsar timing (1/2) , 2008arXiv0805.1519: Pshirkov, Tuntsov, Postnov • Isotropic GW background affects pulsar timing • GW amplitude can be constrained from rms residuals of TOA of even one pulsar • Strong monochromatic signal (e.g. if all of galactic DM is due to massive gravitons, as in Dubovsky et al 2005)will manifest itself at frequencies < 1/Tint(PSR integration time ~ 1-2 hrs) (PTP08): • Limit on the GW amplitude from the existing rms residuals of TOA of pulsars:

  17. Observational constraints: PTP08 Pulsar timing (2/2) Constraints using existing rms TOA residuals (Manchester, 2007), PSR B1937+21

  18. Observational constraints: BPPP08 «Surfing effect» (1/4) arXiv:0805.3103: Baskaran, Polnarev, Pshirkov, Postnov • Unlike in GR, massive gravitons propagate with velocity less than c : • Mass of the graviton is expressed through phenomenological parameterε: • Pulsar frequency change by massive GW::

  19. Observational constraints: BPPP08 «Surfing effect» (2/4) • TOA residuals: • Unlike GR, residuals seculary increase with distance to the sourceD ! • Above results for a monochromatic GW can be generalized to stochastic GWB:

  20. Observational constraints: BPPP08 «Surfing effect» (3/4) • Response to any harmonics is known: • The observed TOA residuals will be expressed through this «transfer function»:

  21. Observational constraints: BPPP08 «Surfing effect» (4/4) • R(k) depends onε(term ) • For example, power-law spectrum: I. II.

  22. Observational constraints: BPPP08 «Surfing effect»: limits (1/5) • Depending on ε, PSR timing put bounds on energy density of GWB: • Or some combination of GW energy density and ε:

  23. Observational constraints: BPPP08 «Surfing effect»: limits (2/5) • For known GW amplitude, the parameter ε can be constrained: • For theoretically motivated GWB from SMBH: or

  24. Observational constraints: BPPP08 «Surfing effect»: limits (3/5)

  25. Observational constraints: BPPP08 «Surfing effect»: limits (5/5) • In terms of the graviton mass: • From modern pulsar timing (Manchester 2007) , • which is by 3 orders of magnitude better than from Solar system bounds • can be increased by one order with increasing observational time • comparable to the future LISA constraints.

  26. CONCLUSIONS • Precise astronomical observations, especially pulsar timing,put strong bounds on massive graviton parameters: • Cold massive gravitons cannot constitute all of the galactic dark matter

  27. Спасибо за внимание!

  28. Теории с массивным гравитоном Наблюдаемые проявления (1/4) (Тиняков 2007)

  29. Теории с массивным гравитоном Наблюдаемые проявления (2/4) (Hi – параметр Хаббла в инфл. эпоху) (Тиняков 2007)

  30. Теории с массивным гравитоном Наблюдаемые проявления (3/4) (Тиняков 2007)

  31. Принципы тайминга Одиночные пульсары(1/4) J 1022+ 10 J 1640+22 B1937+21 J2145- 07 Stairs, 2003

  32. Принципы тайминга Одиночные пульсары(2/4) Радиотелескоп РТ-64 КРАО (ТНА-1500 ОКБ МЭИ)

  33. Принципы тайминга Одиночные пульсары(3/4) • N-ый импульс от пульсара приходит на РТ в момент времени tN. • Редукция в барицентр Солнечной системы. Момент прихода в барицентр СС: • Считается, что пульсар вращается по известным законам. Момент прихода N-го импульса связан с его номером, частотой вращенияи её производными и может быть предсказан. • В действительности, между наблюдаемыми моментами прихода N-го импульса и предсказанными значениями всегда существует разница-остаточные уклонения:

  34. Принципы тайминга Одиночные пульсары(4/4) • Уточнение параметров происходит по МНК. Минимизируются остаточные уклонения: -поправки к принятым значениям

  35. Принципы тайминга Остаточные уклонения • После процедуры остаются остаточные уклонения моментов прихода импульсов Остаточные уклонения пульсаров B1937+21 и B1855+09 (1985-1993, Аресибо), Kaspi, Taylor&Ryba(1994)

  36. Принципы тайминга Двойные пульсары • Движение в двойной системе описывается стандартными кеплеровскими параметрами: • Период обращения: Pb • Проекция большой полуоси: • Эксцентриситет:e • Долгота периастра:ω • Эпоха периастра: T0 • В сильных гравитационных полях появляются ПК-параметры ( и т.д. ) • Все эти параметры могут быть найдены из тайминга (аналогично, МНК-методом)

  37. Принципы тайминга Алгоритм • Наблюдения, вычисление моментов прихода импульсов пульсаров (МПИ) в барицентре Солнечной системы. • Вычисление теоретических значений МПИ с использованием модели хронометрирования. • Определение отклонения значений теоретических МПИ от наблюдаемых (расчет остаточных уклонений – ОУ МПИ). • Уточнение параметров модели хронометрирования (далее к п.3 до сходимости модели).

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