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#### In-depth analysis of LISA Pathfinder performance results: time evolution, noise projection, physical models, and implications for LISA

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##### Citation

Armano, M., Audley, H., Baird, J., Binetruy, P., Born, M., Bortoluzzi, D., et al. (in preparation). In-depth analysis of LISA Pathfinder performance results: time evolution, noise projection, physical models, and implications for LISA.

Cite as: https://hdl.handle.net/21.11116/0000-000F-4D7C-1

##### Abstract

We present an analysis of the LISA Pathfinder differential acceleration

performance over the entire mission . We show that the Brownian noise level,

detected for frequencies $f\gtrsim \SI{1}{mHz}$, has been evolving consistently

with the outgassing of a single gaseous species, with an activation temperature

of $(7.0\pm 0.2)\,\text{kK}$. In excess to the Brownian noise, the acceleration

amplitude spectral density (ASD) always shows a sub-mHz tail which is

reasonably well fit, between $f=\SI{36}{\micro\hertz}$ and

$\SI{1}{\milli\hertz}$, to $\widetilde{S}_{\Delta g}^{1/2}(1\, \text{mHz}/f)$.

A Bayesian estimate of $\widetilde{S}_{\Delta g}^{1/2}$ on a partition of the

entire set of measurements in 27 data stretches, each 2.75\,d long, gives

$\widetilde{S}_{\Delta

g}^{1/2}=(1.1\pm0.3)\,\si{\femto\meter\,\second^{-2}/\rtHz}$, with no

particular time pattern over the course of the mission. The width the posterior

contains, in excess of the statistical uncertainty, a true physical fluctuation

of $\widetilde{S}_{\Delta g}^{1/2}$ from run to run, of about

$\SI{0.2}{\femto\meter\,\second^{-2}/\rtHz}$, with no correlation with specific

operating conditions. At the lowest considered frequency of

$f=\SI{18}{\micro\hertz}$, the ASD significantly deviates from the $1/f$

behavior, because of temperature fluctuations that appear to modulate a

quasi-static pressure gradient, sustained by the asymmetries of outgassing . We

also present a projection of acceleration noise on the sources for which we had

either a correlation measurement, or an estimate from dedicated

experiments.These sources account for about 40\% of the noise power the $1/f$

tail. We discuss the possible sources of the unaccounted-for fraction, present

a series of analyses that rule many of them out, and identify the possible

measures that may be taken to keep the remaining ones under control in LISA.

performance over the entire mission . We show that the Brownian noise level,

detected for frequencies $f\gtrsim \SI{1}{mHz}$, has been evolving consistently

with the outgassing of a single gaseous species, with an activation temperature

of $(7.0\pm 0.2)\,\text{kK}$. In excess to the Brownian noise, the acceleration

amplitude spectral density (ASD) always shows a sub-mHz tail which is

reasonably well fit, between $f=\SI{36}{\micro\hertz}$ and

$\SI{1}{\milli\hertz}$, to $\widetilde{S}_{\Delta g}^{1/2}(1\, \text{mHz}/f)$.

A Bayesian estimate of $\widetilde{S}_{\Delta g}^{1/2}$ on a partition of the

entire set of measurements in 27 data stretches, each 2.75\,d long, gives

$\widetilde{S}_{\Delta

g}^{1/2}=(1.1\pm0.3)\,\si{\femto\meter\,\second^{-2}/\rtHz}$, with no

particular time pattern over the course of the mission. The width the posterior

contains, in excess of the statistical uncertainty, a true physical fluctuation

of $\widetilde{S}_{\Delta g}^{1/2}$ from run to run, of about

$\SI{0.2}{\femto\meter\,\second^{-2}/\rtHz}$, with no correlation with specific

operating conditions. At the lowest considered frequency of

$f=\SI{18}{\micro\hertz}$, the ASD significantly deviates from the $1/f$

behavior, because of temperature fluctuations that appear to modulate a

quasi-static pressure gradient, sustained by the asymmetries of outgassing . We

also present a projection of acceleration noise on the sources for which we had

either a correlation measurement, or an estimate from dedicated

experiments.These sources account for about 40\% of the noise power the $1/f$

tail. We discuss the possible sources of the unaccounted-for fraction, present

a series of analyses that rule many of them out, and identify the possible

measures that may be taken to keep the remaining ones under control in LISA.