Transcript astrod

Low-frequency sensitivity to
gravitational waves for
ASTROD
A. Pulido Patón
Purple Mountain Observatory, Chinese
Academy of Sciences, Nanjing 210008
3rd International ASTROD Symposium & 1st Sino-German Bilateral Symposium
on Laser Astrodynamics, Space Tests of Relativity and Gravitational-Wave
Astronomy
2006, July 14th
Outline
• ASTROD concept.
• Gravitational Reference Sensor (GRS)
concept and drag-free goal.
• Acceleration noise requirements.
• Gravitational wave strain sensitivity.
ASTROD concept
S/C 2
S/C 1
Laser Ranging
Launch Position
Inner Orbit
Sun
Outer Orbit
Earth Orbit
point
.EarthL1(800
days after launch)
ASTROD mission concept is to use three drag-free spacecraft. Two of the
spacecraft are to be in an inner (outer) solar orbit employing laser
interferometric ranging techniques with the spacecraft near the Earth-Sun
L1 Lagrange point. Spacecraft payload: a proof mass, two telescopes, two
1 W lasers, a clock and a drag-free system.
Gravitational wave detection
ASTROD 3rd objective: Detecting and observing gravitational waves from
massive black holes and galactic binary stars in the frequency range 5
µHz≤ƒ≤5 mHz. Background GW will also be explored.
SC 1
SC 2
l2
θ2
l1
θ1
ERS
Gravitational detection topology. Path 1: ERS-SC1-ERS-SC2-ERS. Path 2: ERSSC2-ERS-SC1-ERS. To minimize the arm-length difference.
For example if a monochromatic gravitational wave with + polarization arrives
orthogonal to the plane formed by SC1, 2 and ERS, then the optical path difference
for laser light traveling through path 1 and 2 and returning simultaneously at the
same time t, is given by
l  4h (c fG )(cos 21  cos 22 ) cos 2 fG (1  2 )  cos 2 fG (1   2 ) cos 2 f (t  0 )
With 1=2l1c and 2=2l2c.
ASTROD drag-free performance
goal
•To achieve such objectives the ASTROD proof masses
inside the spacecraft, acting as references for the
interferometer mirrors, must follow geodesic paths.
•ASTROD aims to a drag-free performance goal of:
(0.3-1)10-15 m s-2 Hz-1/2 at 0.1 mHz.
ASTROD Gravitational Reference
Sensor (GRS) preliminary concept
Move towards true drag-free conditions and improving LISA drag-free
performance.
1.
2.
3.
4.
GRS provide reference positioning only. Laser beam does not illuminate directly
the proof mass (avoiding cross coupling effects and pointing ahead problem)
surface but the GRS housing surface. Separate interferometry.
Only one reference proof mass. GRS measures the center of mass position of
the proof mass.
Optical sensing could replace capacitive sensing. Capacitance could still be used
for control purposes.
Absolute laser metrology to measure structural changes due to thermal effects and
slow relaxations.
LISA has adopted condition 1. Both conditions 1 and 2 avoid cross coupling
due to control forces aimed to keep the right orientation of the proof mass
used as a mirror.
ASTROD will employ separate interferometry to measure the GW signal and
the proof mass-spacecraft relative displacement independently.
ASTROD GRS
b)
a)
Outgoing Laser beam
Telescope
Optical readout
beam
Anchoring
Proof mass
Dummy telescope
Dummy telescope
Proof mass
Housing
LASER Metrology
Large gap
Incoming
Laser beam
Telescope
Schematic of possible GRS designs for ASTROD: a) a cubical proof
mass free floating inside a housing anchored to the spacecraft,
capacitive control of position and orientation b) a spherical (cylindrical)
proof mass is also considered, light pressure for control purposes.
Detecting Gravitational Waves
• To estimate gravitational wave strength sensitivity
1/ 2
3/ 2




2
A
1
4
hc

1/ 2
0

ShM 0 ( f ) 
rss  2 
,
Hz

2
2
sin cu0


P
D
L
(2

f
)
  t 

Shot noise with u0   L Acceleration noise
c
Lasing power (Pt): LISA 1W, ASTROD 10 W
Shot noise level (ASTROD)≈ 1.2×10-21
Acceleration noise (A0) is the dominant source
of noise at low frequencies.
Proof mass acceleration
disturbances (A0)
Spacecraft acceleration
disturbances (ns)
Proof mass (PM)
Thrusters
Thrusters
SC-PM
Stiffness (K) Direct PM acceleration
disturbances (np)
Spacecraft (SC)
PM acceleration disturbance:
p  -KXnr + np + (ns + TNt)Ku-1-2
Acceleration noise units ms^(-2)^Hz^(-1/2)
ASTROD acceleration
noise goal
1.00E-10
LISA
LISA Bender
1.00E-11
ASTROD
1.00E-12
1.00E-13
1.00E-14
1.00E-15
1.00E-16
1.00E-06
1.00E-05
1.00E-04
1.00E-03
Frequency (Hz)
ASTROD acceleration noise goal compared to LISA and LISA extended
version at low frequencies proposed by P. Bender [11].
Acceleration disturbances
•
Environmental disturbances
1.
2.
Impacts: residual gas and cosmic rays,
Magnetic disturbances due to susceptibility and permanent
moment.
Lorentz forces due to proof mass charging.
Thermal: radiometer effect, out-gassing effect, thermal radiation
pressure and thermally induced gravity gradients.
3.
4.
•
Sensor back action disturbances
1.
Capacitive sensing: dielectric losses, patch fields and
disturbances due to applied voltages and charge.
Optical sensing: fluctuating laser power.
2.
Environmental disturbances
• We have assumed improvements with respect to
LISA, in housing pressure, magnetic shielding
and thermal isolation proof mass-optical bench:
P = 10-6 Pa versus 3×10-6 Pa of LISA, m = 10
versus no magnetic shielding for LISA, and TS =
150 versus 30-100 considered in LISA budget.
• With these assumptions the dominant
contribution to acceleration disturbance at 0.1
mHz is due to residual gas:
2 PAP
1/ 4
16
2
1/ 2
f rg 
3
k
Tm

1.6

10
m
s
Hz
 B N
mP
Environmental disturbances at
0.1 mHz
Capacitive sensing (CS)
V2
Cx2
Cx1
V1
Cg
d-Δd
d+Δd
Vg
• The capacitive sensor is used to measure the displacement of the
proof mass relative to the spacecraft.
• The capacitive sensor exerts a back action force (due to voltage and
geometric offsets, charge and disturbances associated). Also patch
fields and dielectric losses.
Back-action disturbances (CS)
• In the case of capacitive sensing the dominant
disturbances at 0.1 mHz are: patch fields and
Vd×q.
f pe 
1 Cx
Vpe q  2.0 (290) 1016 m s 2 Hz 1/ 2
mp d C
Compensating patch fields of 0.1 V to 0.7 mV
f q ,1 
1 Cx
Vd  q  1.4 1016 m s 2 Hz 1/ 2
mp d C
Voltage difference across capacitors 0.5 mV. A
factor 10 improvement respect to LISA
Back action disturbances at 0.1
mHz (CS)
Dominant acceleration
disturbances at low frequencies
1.
fm2 
Magnetic interaction between the proof mass susceptibility
and the interplanetary field.
2 1
0   m
1.
Bsc Bip  0.20 10
16
 10      0.1 mHz 
 

6  

3

10
f


 m 
2/3
m s 2 Hz 1/ 2
Capacitive sensing back action
Vd   0.1 mHz 
1 Cx
16 
2
1/ 2
f q ,1 
Vd  q   2   0.72 10 
m
s
Hz

4  
mP d C
5

10
f



Dominant acceleration
disturbances at low frequencies II
TOB is Optical bench temperature fluctuations
1/ 2
f  104 Hz,  TOB
1/ 2
 1 mHz 
 3.0 105 

f


f  3 10 5 Hz ,  TOB
1  0.1 mHz 
K Hz 1/ 2 , fTR  1.2 1015

 ;
TS 
f

1
 32 105 K Hz 1/ 2 , fTR  1.2 1014
;
f  105 Hz,  TOB  12 103 K Hz 1/ 2 ,
TS
fTR  4.6 1013
f  3 106 Hz,  TOB  13 102 K Hz 1/ 2 ,
1
TS
fTR  4.9 1012
;
1
TS
;
ƒTR (Thermal Radiation Pressure) in units m s-2 Hz-1/2
Coherent Charging Signals
• Arise due to steady build up of charge on the test mass
Q(t)
Protons
Q(t) = 17.012t
140
120
 t  Qt 
Qt   Q
net charge(e+)
100
80
60
40
Coherent
terms
20
0
0
2
4
Time(s)
Coulomb:
6
t
8
Q VT t C T
Q t N 1 C iN
e k (t)   k t 

 Vi
mC T k mC T i 1
k
Q 2 CT 2
f k (t )   k t 
t
2
2CT m k
2


Lorentz: l x t    x t  Q t m V I  B IP  xˆ
Coherent Charging Signals II
•
•
•
•
CHS due to Coulomb forces are due to geometric (machining accuracy) and
voltage offsets (non-uniformity in the sensor surfaces, to minimise work
function differences, patch effects, etc) in the capacitive sensor.
These signal increases at low frequencies.
The magnitude of these signals have been shown to compromise the target
acceleration noise sensitivity of LISA (see D. N. A. Shaul [13])
Ways of dealing and/or suppressing these signals are also discussed in [13].
f (Hz)
1E-04
1E-03
1E-01
ASTROD I
LISA PF
LISA
1E-09
1E-10
1E-11
1E-12
1E-13
1E-14
ASTROD
Lorentz ~
t
1E-15
Acceleration spectral density
(ms-2Hz-0.5)
Coulomb
~t
Coulomb ~
t2
1E-02
Q
1E-16
1E-17
1E-18
UV discharging
Optical sensing
• Capacitive sensing presents the disadvantage of needing close
gaps between metallic surfaces to increase sensitivity, proportional
to the difference between capacitance (C1-C2), therefore
proportional to d-2.
• Larger gaps between the PM and the entire structure can be used
by replacing capacitive sensing with optical sensing.
• Optical sensing provides a way of sensing essentially stiffness free
and with improved sensitivity with respect to capacitive sensing.
• Optical sensing sensitivity is limited by shot noise. Picometer
sensitivity can be achieved with W of lasing power and 1.5 m
wavelength.
1/ 2
X nr
1  hc 
 
  2 P 
• Back action force, 2P/c, can be made negligible, with 1%
compensation ~10-17 m s-2 Hz-1/2.
LISA and ASTROD GW strain
sensitivity (S/N≈5, int. time 1yr)
1E-15
z=1
1E-16
LISA Bender extension
Gravitational Wave Strain
LISA, 1 yr int. time S/N=5
1E-17
ASTROD, 1 yr int. time, S/N=5
10^5 (6 months)
1E-18
10^6 (6 months)
z = 40
10^7 (6 months)
10^5 (10 years)
1E-19
10^6 (10 years)
10^7 (10 years)
1E-20
1E-21
1E-22
1E-23
1E-24
1E-25
1.00E-07
1.00E-06
1.00E-05
1.00E-04
1.00E-03
1.00E-02
1.00E-01
Frequency (Hz)
Gravitational wave strengths of massive black hole binaries at different red shifts
(z=1, 5, 10, 20 and 40), 6 months and 10 years before coalescence (following [14]),
compared to ASTROD and LISA GW strain sensitivities. It has been considered 1 year
integration time and S/N of 5.nal wave strain sensitivity of ASTROD and LISA
Conclusions
• ASTROD aims at improving LISA drag-free performance
by a factor 3-10, i.e., (0.3-1)×10-15 m s-2 Hz-1/2 at 0.1
mHz.
• To achieve that, ASTROD needs to reduce housing
pressure, introduce magnetic shielding and active
thermal shielding at low frequencies.
• A continuous discharging scheme is to be used to avoid
CHS.
• Having longer arm length in average ASTROD will detect
gravitational waves at lower frequencies than LISA. The
maximum sensitivity is achieved at frequencies between
0.4-0.5 mHz with a strain sensitivity (2-3)×10-24
References
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•
•
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[1] W.-T. Ni and Y. Xia, “ASTROD and ASTROD I” submitted to Nuclear
Physics B; and references therein.
[2] W.-T. Ni, “ASTROD and ASTROD I: an overview” Gen. Relat. Gravit.
Vol 38, 2006, in press.
[3] A. Pulido Patón and W.-T. Ni, “The low-frequency sensitivity to
gravitational waves for ASTROD” to be submitted to Gen. Relat. Gravit
[4] A. Pulido Patón “ASTROD Gravitational Reference Sensor (GRS): goal
and requirements” submitted to Nuclear Physics B.
[5] W.-T. Ni et al., 2004, Class. Quantum Grav. 22, S269-S277.
[6] S. Shiomi and W.-T. Ni, Class. Quantum Grav. 23, 4415-4432, 2006.
[7] W.-T. Ni et al., Journal of Physics: Conference Series 32 (2006):154-160.
[8] W.-T. Ni et al., J. Korean Phys. Soc. 45: S118-S123 (2004).
[9] X. Xu and W-T. Ni, Adv. Space Res. 32 (7), 1443 (2003).
[10] LISA, ESA System and Technology Study Report, ESA-SCI 11, 2000.
[11] P. L. Bender, Class. Quantum Grav. 20 (2003) S301-S310.
[12] W. J. Weber et al., arXiv: gr-qc/0309067 v1 13 Sep 2003.
[13] D. N. A. Shaul et al. Int. J. Mod. Phys. D, 14, p51-p71.
[14] J. Baker and J. Centrella, Class. Quantum Grav. 22 (2005) S355-S362.