Testing Modified Newtonian Dynamics with LISA Pathfinder · Testing MOND with LISA Pathfinder...

Testing Modified Newtonian Dynamics with LISA Pathfinder

Christian TrenkelAstrium Ltd, Stevenage, UK

On behalf of the “LPF and MOND” team

2nd Iberian Gravitational Wave Meeting – Barcelona 15-17 February 2012

Overview

Dark Matter and Modified Gravity

Modified Newtonian Dynamics (MOND)

LISA Pathfinder

Testing MOND with LISA Pathfinder

Summary and Discussion



If we simply apply the gravitational laws to the matter that we can observe outside the Solar System, things don’t make sense…

This may be for the following reasons: there are other constituents that we cannot see (Dark

Matter, Dark Energy) our laws of Gravity are incomplete and require

modifications

Of course these are not mutually exclusive…



This problem is not new – in fact we used to have it within the Solar System:

Le Verrier predicted Neptune from Uranus orbital anomalies using Newtonian gravity (1846) – first example of Dark Matter!

Attempts to explain anomalous precession of Mercury with “Vulcan”, which was never found – eventually explained through General Relativity (1915)

So we have already had precedents for both –Dark Matter and Modified Gravity!


Dark Matter and Modified Gravity Now the problem has moved to galactic and extragalactic scales Already 80 years ago (~1934) Zwicky noticed that we have a

“missing mass” problem at galactic scales:

Expect – not flat rotation curves!r

vrv

rGM 12

2


Dark Matter and Modified Gravity What is the correct explanation this time – Dark Matter, Modified

Gravity, a combination of both…?

Direct search for Dark Matter particles underway (dedicated underground searches, LHC and predecessors) for decades now – so far largely fruitless

Problem with most proposed Gravity modifications: almost by definition they predict significant deviations from GR only outside the Solar System – and are therefore hard to test directly!

Direct experimental evidence (for Dark Matter or Modified Gravity) would clearly be of great value!


Overview



LISA Pathfinder




Modified Newtonian Dynamics Newtonian dynamics are modified when total gravitational acceleration

approaches a0 ≈ 10-10ms-2 (Milgrom 1983):

Newtonianwith

“MONDian”

Many forms possible for :

Automatically describes flat rotation curves – on the outskirts of galaxies we have:

Can also be seen as modification of Newton’s law of Gravity:

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4

20

2

aGMv

rav

rGM

aamF

aaamF

0

000

00 1

aa

aaaa

aaaa

Ngrav aar

GMaa 020 0aaN

)/( 0aa

2/120

00

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/1

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Purely phenomenological, non-relativistic formula with no underlying theory

Extremely successful in describing many (MANY!) galactic rotation curves without Dark Matter:

Less successful on extragalactic scales Bullet cluster still needs Dark Matter – but less Gravitational lensing still needs Dark Matter – just as much

Modified Newtonian Dynamics


Modified Newtonian Dynamics Much more recently: a relativistic theory (TeVeS) was developed

with MOND as non-relativistic limit (Bekenstein 2004) In the non-relativistic limit, the total potential is sum of Newtonian

potential and new scalar field:

This scalar field is solution of modified Poisson equation

TeVeS gave MOND some “respectability” and generated renewed interest

Other theories with MONDian non-relativistic behaviour have been proposed: bimetric theories, Einstein-Aether theory…

)( Na

Ga

04



A priori, prospects of MONDian tests within Solar System poor:

At 1AU, Sun’s gravitational pull is almost 108a0!

1.E-11

1.E-10

1.E-09

1.E-08

1.E-07

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

0.1 1 10 100 1000 10000

Distance from Sun [AU]

a [m

s-2]

Earth Saturn Neptune

PioneerMercury

108



Bekenstein & Magueijo (2006): gravitational Saddle Points provide MONDian “habitats” within the Solar System

Anomalous gravitational accelerations also result in anomalous gravity gradients

TeVeS predicts MOND gravity gradients ≥10-13s-2 within elliptical bubble around SP – for standard interpolation function

766km259000km

1532km

Sun

Earth


Overview



LISA Pathfinder




LISA Pathfinder LISA Pathfinder (LPF) is a technology

demonstrator for Laser Interferometer Space Antenna (LISA) – a low-frequency gravitational wave detector in space

Will demonstrate two key requirements for gravitational wave detection:

Reduction of acceleration noise on macroscopic Test Masses in Space at ~1mHz

Positional read-out of Test Masses in Space with sufficiently low displacement noise at ~1mHz


Acceleration Noise Displacement Noise

LISA Pathfinder Quantitative Science Requirements:

Differential Acceleration Noise between 2 Test Masses* Displacement Noise

*Simply divide by separation 0.4m to obtain gradiometer performance

3x10-14ms-2/√Hz @ 1mHz


LISA Pathfinder LPF performance compared to other missions (not quite fair)


LISA Pathfinder Mission Profile:

LPF launches into parking orbit 200x1600km on VEGA 9 apogee raising manoeuvres required to deliver LPF to L1 Propulsion Module separates during transfer phase Final orbit is 500000km x 800000km Lissajous orbit around L1 Very quiet and stable environment


LISA Pathfinder

Instrument at the core of LISA Pathfinder:

Two Au/Pt Test Masses of ~2kgs, housed in separate vacuum enclosures – baseline ~ 0.4m

Relative position of Test Masses read-out by: Heterodyne laser interferometry

on sensitive axis joining the two Test Masses

Capacitive sensing on all axes


LISA Pathfinder

Drag-free control crucial to eliminate Solar Radiation Pressure fluctuations as significant noise source

Now we “only” need to worry about the following noise sources: Electrostatics Magnetism Thermal Effects Charging Residual Gas Damping Self-Gravity …


LISA Pathfinder

The main purpose of LPF is to understand the noise sources that limit its performance

A detailed noise budget has been created with over 120 entries

Where possible, relevant parameters have been verified by test on the ground

A suite of experiments will be run during the mission to investigate specific couplings and noise sources


LISA Pathfinder

Spacecraft Integration is almost fully complete

All Spacecraft and Payload Electronic boxes are on-board

Only parts of Central Payload and Micropropulsion System are missing

Propulsion Module is “done”

Spacecraft has (successfully) completed On-Station Thermal Test at IABG


LISA Pathfinder

Current Schedule:

Spacecraft and Propulsion Module go into Hibernation (March/April 2012)

Missing elements (Payload parts and Micropropulsion system) completed by end 2012 / early 2013

End of Hibernation phase early 2013 –working towards launch!

Launch on VEGA Summer 2014


Overview



LISA Pathfinder


Summary and Conclusions


Testing MOND with LISA Pathfinder In MOND (TeVeS) we have a theory of modified gravity that

predicts potentially measureable anomalous gravity gradients in macroscopic regions around gravitational Saddle Points

In LISA Pathfinder we have a spacecraft that will be launched just a few years from now, with the most sensitive gravity gradiometer ever on-board, at least in the mHz frequency band.

→ Obvious question:Can we use LISA Pathfinder to test MOND?


Testing MOND with LISA Pathfinder Need to:

(1)Understand dynamic location of gravitational Saddle Points (SPs) in the Sun-Earth-Moon System

(2)Establish that LPF can be made to fly through the region around a SP following its nominal mission

(3)Calculate the anomalous MONDian gravity gradients that LPF will experience, including temporal behaviour

(4)Confirm that the gravity gradiometer on-board LPF is sensitive enough to detect the anomalous gradients

… using LPF “as built”, and no interference with nominal mission allowed



Saddle Points are defined by zero total gravitational field – not to be confused with Lagrange points L1, L2, etc

SPs are not a stable location for spacecraft In the Sun-Earth-Moon system, there are two SPs:


The Sun-Earth SP offers much more stability than the lunar SP, and also lower background gradients → will focus on Sun-Earth SP as target

The Sun-Earth SP position is shifted from its nominal two-body position due to the influence of other gravitating bodies: Moon: ≤ 6000km Jupiter: ≤ 20km Venus: ≤ 10km …

Eccentricity of Earths orbit around Sun results in shifts of order ±4000km (annual modulation)

All these shifts are well-known and predictable. The “true”gravitational SP can be pinpointed as a function of time to better than 1km – more than enough



Testing MOND with LISA Pathfinder Need to:

(1)Understand dynamic location of Saddle Points (SPs) in the Sun-Earth-Moon System





LPF will lie nominally on a stable manifold whilst orbiting the Earth-Sun L1 point

Only a small manoeuvre is needed to reach an unstable manifold

This allows an option to return towards Earth and access the gravitational saddle point between Sun and Earth


Saddle Point

Sun

Earth

1.5mio km

Sun

Earth

1.5mio km

Nominal Orbit around L1


Search for suitable trajectories - assumptions and constraints:

Single dV manoeuvres up to 2m/s have been considered: compatible with estimated residual FEEP control authority (≈

6m/s) and also cold gas control authority (≈4m/s) following nominal mission reasonable timescales for manoeuvres, including single thruster

failure

Consider both Rockot and VEGA launch options

Proof of Principle sought at this stage – exact trajectory can only be chosen once nominal mission is underway

Figures of merit for trajectories: transfer time from L1 to SP SP miss distance



Search Space Analysis First step: understand structure of search space Initial dV from 0 to 2 m/s Initial Time of manoeuvre from 0 to 60 days Chaotic search space



Further Optimisation – zoom into the search space After several iterations: Parameter Space finally well behaved

at the 10-4m/s, 10min scale – characteristic “valleys” emerge

Optimisation tools have been developed to search within valleys

10min

10-4

m/s



Example trajectories – Rockot

First example: direct low-miss distance Manoeuvre: 0.4237 m/s Miss Distance: 1407 km after 577 days

Saddle point Saddle point



Example trajectories – Rockot

Second example: LGA low-miss distance Manoeuvre: 0.8673 m/s Miss Distance: 396 km after 464 days




Best trajectories – VEGA


• Second example:

• Manoeuvre: -1.232 m/s

• Miss Distance: 130 km after 512 days

• First example:

• Manoeuvre 0.2301m/s

• Miss Distance: 2333 km after 348 days



Typical total DV budget: ~2 m/s Very substantial improvement due to second manoeuvre

Rockot 1635

Rockot LGA

VEGA LGA fast VEGA 130

One manoeuvre

strategy

Total DV 0.3225 m/s 0.8673 m/s 0.2301 m/s -1.232 m/s

Miss distance 1635 km 396 km 2333 km 130 km

Two manoeuvres

strategy

DV1 0.3225 m/s 0.8673 m/s 0.2301 m/s -1.232 m/s

DV2 1.4 m/s 1.8 m/s 1.87 m/s 0.05 m/s

Total DV 1.7225 m/s 2.6673 m/s 2.1001 m/s 1.282 m/s

Miss distance 242 km 253 km 355 km 72 km

Obvious strategy to reduce further the miss distance: additionalmanoeuvres

Add second manoeuvre only at the apogees, starting with the best solutions from the single-manoeuvre search



Third Iteration: can we find solutions with multiple SP crossings?

Impossible to find (with reasonable effort) by “forward propagation”. Instead:

Start at SP at certain date & time, with initial SC velocity vector

Find trajectories that cross SP for at least one more time (“exactly”)

Identify those that, propagated backwards, originate from a suitable LPF orbit around L1 – including single dV manoeuvre

Further backpropagation back to Earth, to ensure compatibility with LPF launcher



Results so far:

Trajectories with >2 SP crossings are too stable – they cannot be reached from L1!

Numerous candidate solutions for double crossings found, even for single dV manoeuvres – again multiple manoeuvres will improve chances further

However at the moment we cannot say for sure whether a suitable double crossing solution exists for every launch date – more work required



Example of solution found (Rockot):


a: Launch, 24/2/2013.inclination = 57.6°perigee altitude: 322 km

b: Libration orbit, 73 days after launch

c: Exiting libration orbit, 258 days after launch. The spacecraft has spent 185 days around L1.

d: Reaching the SP for the first time, 543 days after launch (285 days after escaping from L1).

e: Reaching the SP for the second time, 582 days after launch (39 days after the first passage).

Major/minor axes of libration orbit:out of ecliptic: 417,000 kmin plane: 775,000 km


The issue of navigation – just as critical: Assume that you have identified the trajectory that you want

LPF to follow Can you in practice navigate the spacecraft along this nominal

trajectory, given the limitations of the micropropulsion system and non-zero tracking errors?

Not obvious at all because: Earth and Moon perturbations may be too high to be corrected –

the real trajectory may diverge from the nominal one despite your best efforts!

Total dV requirements may exceed available propellant Application of required trajectory correction manoeuvre may

take too long



Earth / Moon fly-by

Results so far: the navigation issue should be manageable – in 6 out of 7 cases, a chosen trajectory could be successfully followed

During transfer, contact to SC will be required every few days for navigation purposes



Many possible trajectories exist to take LPF from L1 to the SP – many “needles in the haystack”

Transfer time to reach the SP from L1 is typically 1 - 1.5 years with Rockot, and around 1 year with VEGA

Using multiple manoeuvres, the miss distance for a single SP crossing will be limited by SC tracking – conservatively estimated at 10km

Navigation issue seems under control – but should be taken into account when selecting trajectory

Some simple candidate solutions with double SP crossings found –but jury is still out on abundance / practicality of these

Large computational overheads due to chaotic nature of search space – but proof of principle obtained!



Gravitational Environment during SP region crossing – a few relevant parameters:

LPF speed through SP region typically ≈1.5km/s (essentially free-fall)

Newtonian gradients around SP are ≥ 2x10-11s-2. For a miss distance of 50km, the lowest gravitational acceleration level experienced by LPF will be ag ≈ 1x10-6ms-2

Even if LPF flies through the SP exactly, it will spend, at most, ≈6s in an environment with ag ≤ 1x10-7ms-2

(-) LPF will only be able to test the intermediate MOND region

(+) Spacecraft self-gravity (< 10-8ms-2 ) is not an issue



Experiencing ag ≈ 1x10-6ms-2 to 1x10-5ms-2 at 1AU from the Sun is not bad:

Equivalent to travelling out to between 25 and 75 AU!


1.E-11

1.E-10

1.E-09

1.E-08

1.E-07

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

0.1 1 10 100 1000 10000

Distance from Sun [AU]

a [m

s-2]

Earth Saturn Neptune

PioneerMercury


Need to:







Prediction of anomalous MOND gravity gradients in TeVeS:

Numerical relaxation method has been developed (Bevis & Magueijo) to calculate anomalous gradients at grid points of cubic volume around SP

Assumes standard interpolation function between Newtonian and MONDian behaviour

Includes effects of Sun, Earth and Moon position – in principle accepts arbitrary sources outside volume

Used to investigate signal as function of lunar phase –dependence found to be insignificant



A typical LPF trajectory is propagated through the volume and the anomalous gradients are extracted at each point:

45°

45°

Earth

Sun

Typical LPF Trajectory

Sun-Earth SP



Due to sun-pointing constraints, only (one) gravity gradient orthogonal to Sun-Earth line can be measured:

LPF speed through SP region – 1.5km/s – is used to convert spatial into temporal gradient variations


Sun Earth

Test Mass

Test Mass

Sun Earth

Test Mass

Test Mass

Solar Array

or


Results Anomalous MOND gradients as a function of miss distance:

0km50km100km400km


MOND signal ≈ 500s - 1000s long → ~ mHz (!!)


Total external gravity gradient seen by LPF for 50km miss distance

Smooth Newtonian background is predictable and can be subtractedor filtered out

Newtonian onlyNewtonian + MOND



Need to:







Testing MOND with LISA Pathfinder Comparison of predicted MOND signal to LPF differential

acceleration performance requirement (divided by Test Mass separation to give gradiometer performance):

→ If LPF “only” meets its requirements, MOND gradient detection does not look good!


Testing MOND with LISA Pathfinder However, extensive test campaigns on flight hardware show that

the currently predicted LPF performance is substantially better than the requirement:


Testing MOND with LISA Pathfinder Even the above estimate can be regarded as conservative and

“worst case”. The actual LPF performance could be as good as

Of course we won’t really know until LPF flies!


Testing MOND with LISA Pathfinder Signal-to-Noise Ratio can be calculated in analogy with

gravitational wave detection. Assuming stationary instrument noise, the following SNR plot is obtained (Magueijo):

→ SNRs between 15 and 60


Testing MOND with LISA Pathfinder The LPF speed through the SP crossing is virtually optimal:

1.5km/s

This remarkable coincidence just has to be exploited!


Need to:

Understand dynamic location of Saddle Points (SPs) in the Sun-Earth-Moon System

Establish that LPF can be made to fly through the region around a SP following its nominal mission

Calculate the anomalous MONDian gravity gradients that LPF will experience, including temporal behaviour

Confirm that the gravity gradiometer on-board LPF is sensitive enough to detect the anomalous gradients


Can we use LISA Pathfinder to test MOND? If everything works as we currently expect it to, we can!


Overview



LISA Pathfinder




Summary and Discussion It seems pretty clear that a direct test of MONDian behaviour is

possible, by flying LPF through the Sun-Earth SP region once the nominal LPF mission is completed

MONDian gradients (derived from TeVeS) could not just be detected, but measured in detail, with substantial SNR, based onexpected LPF performance and standard interpolation function

LPF presents us with the rare chance to subject an alternative gravitational theory to a direct experimental test – at the relatively minor cost of extended operations

A positive detection would represent a major breakthrough in fundamental physics

Constraints on theories with MONDian behaviour from a null result are being investigated


Summary and Discussion The idea of using LPF to look for MONDian gradients near the SP

is slowly gaining traction – it is being appreciated that this really is a “once-in-a-lifetime” opportunity that should not be wasted

The “LPF and MOND team” plans to submit a proposal to ESA for a Mission Extension to LPF to test MOND – we think there is enough value for money!

Meetings / workshops so far held in July 2010 (RAL), June 2011 (ICL), December 2011 (Oxford) – next one planned June 2012 (Astrium, UK)

Testing Modified Newtonian Dynamics with LISA Pathfinder · Testing MOND with LISA Pathfinder...

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