20th Lomonosov Conference
on Elementary Particle Physics
August 19-25, 2021

Background for gravitational wave signal at LISA
from refractive index of solar wind plasma
F R A N T I Š E K N Ě M E C b ) , Z D E N Ě K N Ě M E Č E K b ) , A D A M S M E TA N A a ) , J A N A Š A F R Á N KO VÁ b )a ) I N S T I T U T E O F E X P E R I M E N TA L A N D A P P L I E D P H Y S I C S ,CZECH TECHNICAL UNIVERSITY I N PRAGUE, CZECH REPUBLICb ) D E PA R T M E N T O F S U R FA C E A N D P L A S M A S C I E N C E ,F A C U LT Y O F M AT H E M AT I C S A N D P H Y S I C S ,C H A R L E S U N I V E R S I T Y, P R A G U E , C Z E C H R E P U B L I C

Mon Not R Astron Soc Lett (2020) slaa155 1745-39254

Gravitational wave antennas

Ground-based GW antennas (LIGO, VIRGO)▪ Size limitation▪ Seismic noise▪ Vacuum technology▪ Ultra-high vacuum (∼ 107 molecules/cm3)▪ Vacuum (im)purity under control
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Space-based GW antennas (LISA)▪ Free of size limitation▪ No seismic noise▪ Vacuum for free
▪ Better vacuum (∼ 10 particles/cm3)▪ Vacuum (im)purity NOT under control

20TH LOMONOSOV CONFERENCE ON ELEMENTARY PARTICLE PHYSICS

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Amaro-Seoane P., et al., 2017, Laser Interferometer Space
Antenna (arXiv:1702.00786)

LISA – Laser Interferometer Space Antenna

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20TH LOMONOSOV CONFERENCE ON ELEMENTARY PARTICLE PHYSICS

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LISA challengesAmaro-Seoane P., et al., 2017, Laser Interferometer Space
Antenna (arXiv:1702.00786)

Interferometry with
▪ Variable arm length (Δl ≈ 50.000 km) during the orbit▪ Single laser path (no coherent beams)▪ Overwhelming laser wavelength noise due to unequal arm length -> Time delayedinterferometry▪ Doppler shifted laser beam (±5 m/s)
▪ Mechanical, Thermal, Electronic, Optical noise▪ Test mass charging▪ High energy cosmic rays
▪ Solar wind jitter▪ Timing and Clock Synchronisation▪ Laser stability
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20TH LOMONOSOV CONFERENCE ON ELEMENTARY PARTICLE PHYSICS

4LISA parameters▪ 6 laser links operating on the wavelength▪ Variable arm length with average▪ Displacement noise linear spectral density

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20TH LOMONOSOV CONFERENCE ON ELEMENTARY PARTICLE PHYSICS

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Refractive index of solar wind plasma
Solar wind (SW)▪ Composition: electrons ∼ protons > alpha > heavier ions▪ at 1 AU from the Sun (LISA‘s and Earth‘s orbit)▪ average particle density ∼ 10 cm−3 and quasi-neutrality → ne ≈ np ≈ 5 cm−3
▪ at scales of optical wavelengths range ∼ 1 µm, SW is practically a collision-less ideal plasma▪ electron component is characterized by plasma frequency▪ Which dominates the Sellmeier equation for refractive index n for elmag wave of frequency ωFor optical elmag wave Δn ∼ 10-21

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20TH LOMONOSOV CONFERENCE ON ELEMENTARY PARTICLE PHYSICS

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Estimation of the background for LISA
from the solar wind plasma effect▪ Effective displacement:▪ Effective strain:▪ Linear spectral density:

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hSW / Lto be compared with LISA‘s required

20TH LOMONOSOV CONFERENCE ON ELEMENTARY PARTICLE PHYSICS

7Solar wind data

WINDData:▪ Sampling frequency
6 s – 12 s
▪ Duration ≥ 24 h
≥ 10*(0.1 mHz)-1▪ No interference withEarth‘s magnetosphere

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20TH LOMONOSOV CONFERENCE ON ELEMENTARY PARTICLE PHYSICS

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Preliminary results
ERRATUM to be done:
Mon Not R Astron Soc Lett (2020) slaa155 1745-39254

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20TH LOMONOSOV CONFERENCE ON ELEMENTARY PARTICLE PHYSICS

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More detailed results• WIND data
• 2004 – 2019• 24h window• shifted by 1h→ 76210 spectra

to be published• interpolated data
resampled to 10 Hz

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20TH LOMONOSOV CONFERENCE ON ELEMENTARY PARTICLE PHYSICS

10Discussion of the result▪ The result is applicable to any space-based intereferometer of the LISA‘s type▪ The effect will be observable only at the full scale LISA, no „Pathfinder“ mission would discover it▪ Averaging-out effect▪ After all the situation does not need to be so severe

SOLAR WIND
500 km/s

LISA‘s ARM
2.5 Mkm
5000 sshall we take the risk? - subject of future modelling

SOLAR WIND
500 km/s

OUR ANALYSIS

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20TH LOMONOSOV CONFERENCE ON ELEMENTARY PARTICLE PHYSICS

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Hint from STEREO - trajectories

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20TH LOMONOSOV CONFERENCE ON ELEMENTARY PARTICLE PHYSICS

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Hint from STEREO - correlations
Correlation length:
L = 24 mil. km

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20TH LOMONOSOV CONFERENCE ON ELEMENTARY PARTICLE PHYSICS

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Proposed solutions
1.

Measure the solar wind density along the LISA‘s arms

Solar wind detector◦ What accuracy is needed?
◦ How many detectors?

2.

?

Deploy second laser system of different wavelengthand subtract their signals◦ What is a systematic bias introduced?
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J. W. Armstrong,"Low-Frequency Gravitational Wave Searches
Using Spacecraft Doppler Tracking",
Living Rev. Relativity, 9 (2006)

20TH LOMONOSOV CONFERENCE ON ELEMENTARY PARTICLE PHYSICS

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Current status
Cross check with LISA collaboration – has been made▪ Sept 1-3 2020, LISA Symposium▪ Conclusion from 90‘s was that the effect is not significant for LISA – not published▪ The effect was described in the context of the Doppler mission▪

J. W. Armstrong, "Low-Frequency Gravitational Wave Searches Using Spacecraft Doppler Tracking", Living Rev. Relativity, 9 (2006)▪ The error of factor ~3 in the LSD was detected and removed▪

ERRATUM to be done to Mon Not R Astron Soc Lett (2020) slaa155 1745-39254

Collaboration with Charles University – has been established▪ Correlation length estimates based on real data (STEREO, L1 missions)▪ More complex analysis of WIND data has been performed▪ 3D modelling (average conditions, events)▪ Simulation of the 3-arm LISA response is needed – further suppression of the effect is expected
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