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 l.jpg

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


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Plan pulsar timing and astrometry

  • Pulsars as GW detectors

  • Observational constraints on massive graviton CDM

  • “Surfing effect” of massive gravitons and limits on their propagation speed


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Pulsars as GW detectors pulsar timing and astrometry

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)


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Pulsars as GW detectors pulsar timing and astrometry

Gravitational waves (1/2)

  • GW energy density (monochromatic plane):

  • Stochastic isotropic background:

Is the critical density

  • Or:


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Pulsars as monochromatic GW detectors pulsar timing and astrometry

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


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Pulsars as GW detectors pulsar timing and astrometry

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


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Pulsars as GW detectors pulsar timing and astrometry

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)


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Pulsars as GW detectors pulsar timing and astrometry

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


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Pulsars as GW detectors pulsar timing and astrometry

Stochastic GWB (2/3)

  • For arbitrary GWB («red noise»):

Kaspi, Taylor, Ryba, 1994


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Pulsars as GW detectors pulsar timing and astrometry

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 )


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Pulsars as GW detectors pulsar timing and astrometry

Present limits and prospects

(Manchester, 2007 – arXiv:0710.5026v2)


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Tests in Solar systems pulsar timing and astrometry

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)


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Solar system tests pulsar timing and astrometry

Doppler tracking (2/2)

  • Future projects: Search for Anomalous Gravity usingAtomic Sensors, SAGAS

Reynaud et al. 2008


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Astrometric constraints pulsar timing and astrometry

  • 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


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Theories with massive gravitons pulsar timing and astrometry

  • 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


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Observational constraints: PTP08 pulsar timing and astrometry

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:


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Observational constraints: PTP08 pulsar timing and astrometry

Pulsar timing (2/2)

Constraints using existing rms TOA residuals (Manchester, 2007), PSR B1937+21


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Observational constraints pulsar timing and astrometry: 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::


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Observational constraints pulsar timing and astrometry: 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:


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Observational constraints: BPPP08 pulsar timing and astrometry

«Surfing effect» (3/4)

  • Response to any harmonics is known:

  • The observed TOA residuals will be expressed through this «transfer function»:


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Observational constraints: BPPP08 pulsar timing and astrometry

«Surfing effect» (4/4)

  • R(k) depends onε(term )

  • For example, power-law spectrum:

I.

II.


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Observational constraints pulsar timing and astrometry: 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:


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Observational constraints pulsar timing and astrometry: BPPP08

«Surfing effect»: limits (2/5)

  • For known GW amplitude, the parameter ε can be constrained:

  • For theoretically motivated GWB from SMBH:

or


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Observational constraints pulsar timing and astrometry: BPPP08

«Surfing effect»: limits (3/5)


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Observational constraints pulsar timing and astrometry: 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.


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CONCLUSIONS pulsar timing and astrometry

  • Precise astronomical observations, especially pulsar timing,put strong bounds on massive graviton parameters:

  • Cold massive gravitons cannot constitute all of the galactic dark matter


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Спасибо за внимание! pulsar timing and astrometry


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Теории с массивным гравитоном pulsar timing and astrometry

Наблюдаемые проявления (1/4)

(Тиняков 2007)


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Теории с массивным гравитоном pulsar timing and astrometry

Наблюдаемые проявления (2/4)

(Hi – параметр Хаббла в инфл. эпоху)

(Тиняков 2007)


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Теории с массивным гравитоном pulsar timing and astrometry

Наблюдаемые проявления (3/4)

(Тиняков 2007)


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Принципы тайминга pulsar timing and astrometry

Одиночные пульсары(1/4)

J 1022+ 10

J 1640+22

B1937+21

J2145- 07

Stairs, 2003


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Принципы тайминга pulsar timing and astrometry

Одиночные пульсары(2/4)

Радиотелескоп РТ-64 КРАО (ТНА-1500 ОКБ МЭИ)


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Принципы тайминга pulsar timing and astrometry

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:


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Принципы тайминга pulsar timing and astrometry

Одиночные пульсары(4/4)

  • Уточнение параметров происходит по МНК. Минимизируются остаточные уклонения:

-поправки к принятым значениям


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Принципы тайминга pulsar timing and astrometry

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)


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Принципы тайминга pulsar timing and astrometry

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)


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Принципы тайминга pulsar timing and astrometry

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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