GRAVITATIONAL WAVE
DETECTORS AND GALACTIC
BINARIES
M. Benacquista
Center for Gravitational Wave Astronomy
University of Texas at Brownsville
3rd AM CVn Workshop, Warwick
1
April 17, 2012
• The
gravitational wave Galaxy
• Detector
• Baseline
description
and alternative configurations
2
• The
gravitational wave signal from the Galactic
population of white dwarf binaries will consist of
individually resolvable sources and a confusion-limited
foreground.
3
• Individually
resolvable means that the parameters
describing the binary can be obtained with reasonable
precision through data analysis (usually some kind of
matched filtering.
4
• The confusion-limited foreground is a result of signals from thousands of
binaries in each resolvable frequency bin.
5
• If
the “chirp” of resolvable systems can be measured
and the system is driven by gravitational radiation
alone, then the distance can be measured and the
chirp mass can be obtained.
• Sky
location and
distance can be used
to determine the
spatial distribution of
white dwarf binaries.
6
• The
confusion-limited signal is dominant at low
frequencies (f<~3mHz).
7
The foreground is based mostly on the disk
population and so it is anisotropic.
SNR = 5
4
p
Strain spectral density at 1 mHz 1/ Hz (⇥10
4
SNR = 1
2
Strain h (⇥10
20
)
2
0
0
-2
-2
-4
-4
0
0.5
1
)
Scientific Objectives
16
18
•
1.5
2
t (yr)
• The
spectrum of the foreground may provide
probe different star formation rates and different
evolutionary scenarios.
Figure 2.7.: Level of the Galactic gravitational wave signal as a function of time. Black is the total signal, the red after
removal of the resolved binaries. The yearly variation of the Galactic foreground can clearly be seen. The dashed lines give
the associated SNR for the contribution of the foreground signal to the total signal. For most of the time, the SNR varies
between 1 and 5. The scale on the right y-axis indicates the approximate level of the galactic foreground “noise” at 1 mHz.
Based on the R
.(
) Galactic model.
The vast majority will form an unresolved foreground signal in the detector, which is quite different from and
much stronger than any diffuse extragalactic background (F
&P
,
).
This foreground is often described as an additional noise component, which is misleading for two reasons.
The first is that there is a lot of astrophysical information in the foreground. The overall level of the foreground is
a measure of the total number of ultra-compact binaries, which gives valuable information given the current
8 The spectral shape of the foreground also
uncertainty levels in the normalisation of the population models.
• Assuming
space-based interferometric gravitational
wave detectors, different configurations have
different consequences on the ability to extract
information from both resolvable sources and the
confusion foreground.
• Noises:
• Acceleration
noise: Stray forces on the proof mass.
• Shot noise: Quantum fluctuations in light intensity.
• Position noise: Measurement and control noise.
9
• Motion
of the detector influences sensitivity to
direction of the sources.
• Rotation
of the detector
within its plane.
• Precession of the plane.
• Motion of the guiding
center of the detector
plane relative to the
stars.
The “Peanut”
10
• Sensitivity
curves are usually plots combining the
instrument noise and the transfer function along
with some sort of angle/orientation/polarization
averaging.
• This
allows one to plot the absolute strain
amplitude of a suspected source and compare it
with the expected noise level.
• Can
be misleading due to averaging.
• Require
2 years.)
an assumed observation time (usually 1 or
11
12
13
• Shorter
armlengths:
• Increase
acceleration noise
• Decrease
shot noise
• Increase
position noise
• Improve
response at high frequencies
14
Approximative sensitivity
1e-12
std : LISA
c1 : LISA1_P005c_LPF
c2 : LISA1_P2_DRS
c3 : LISA1_P07_D25_DRS
1e-13
1e-14
h
1e-15
1e-16
1e-17
1e-18
1e-19
1e-20
1e-05
0.0001
0.001
0.01
0.1
1
f (Hz)
Figure 2: Comparison of sensitivity (SNR=1, ”instantaneous”) for standard LISA
15
configurations 1c, 2 and 3
16
• LISA-like
orbits:
• Add
annual rotation of the “peanut”
• Annual variation of polarization phase
• Annual variation of Doppler phase
SNR = 1
p
2
Strain h (⇥10
20
)
2
0
0
-2
-2
-4
-4
0
0.5
1
18
4
Strain spectral density at 1 mHz 1/ Hz (⇥10
SNR = 5
4
)
Scientific Objectives
16
1.5
2
t (yr)
17
Figure 2.7.: Level of the Galactic gravitational wave signal as a function of time. Black is the total signal, the red after
picture of its excitement and promise. Over its two-year science mission, SGO
Free-fall
also impliesThis
that noconcept
station-keeping
is needed. This is not strictly true for NGO.
o different
designs.
was or formation-flying
thousands of individual GW signals from a variety of source classes. Many of th
O
Firstly it is not the satellites that are in free fall, but thebetest
masses,
the satellites
will have toratio
be actuated
detected
with so
sufficiently
high signal-to-noise
(SNR) thatto
their astrophy
(masses,
spins,control
distance,
sky location,
etc.)described
will be measured
follow the test masses, which is the task of the drag-free
attitude
system
(DFACS)
in somewith high p
detections
enable SGO
Low the
to address
a number of the
detail in chapter 5. Secondly, the satellites need to rotate
over and
the measurements
course of thewill
mission
to keep
“Mother”
questions[1,3] identified Table 1 of the RFI.
spacecraft (or “Daughter” spacecraft, respectively) in the field of view. Both manoeuvres are purely local, i.e. no
Box 1. The solid b
coordination between the satellites is needed. Other than those manoeuvres, there is no station-keeping foreseen.
shows SGO Lowʼs
The distance between the satellites as well as the angles (i.e. the shape of the constellation) is evolving freely
noise, in units of H
under the action of gravity alone, so NGO requires no formation-flying in any phase of the mission lifetime.speaking, all sour
curve are detectab
Low. The blue sta
the frequencies an
known Galactic bi
“verification binari
height above the n
NGO’s two measurement arms are defined by three spacecraft orbiting the Sun (figure 3.1) in a triangular
gives their matche
in a one-year inte
configuration. A key feature of the NGO concept is a set of three orbits that maintain a near-equilateral triangular
two dashed black
formation, without the need for station-keeping. Depending on the inital conditions of the spacecraft, the formation
dashed green cur
can be kept in an almost constant distance to the Earth or be allowed to slowly drift away to about 70 ⇥ 106 sources
km, (two SMB
and an EMRI, res
whose frequency
upward significan
Lowʼs observation
9m
The height of the source curve above the noise strain approximates the SNR contributed
Earth 1 ⇥ 10
logarithmic frequency interval. See [1, 2] for more details. For comparison, the noise curve
Sun noise and confusion noise from unresolved
is shown in red. For SGO High, instrumental
20°
binaries are both significant; the latter causes the “hump” around 1 mHz. For SGO Low, t
60°
confusion noise is almost insignificant.
3.1. NGO design concept
Figure 1: Constellation geometry for
SGO Low
ands of compact binaries in our Galaxy.
1 AU
lack hole (MBH) binaries at moderate
1 AU
SGO-Low 2/10
Sun
s with a precision that is unprecedented
ecisely measure the capture of compact
e estimates allow for some risk that no
Figure
3.1.: TheaNGO
orbits: of
Thethe
constellation
Low to
address
number
scienceis shown trailing the earth Earth by about 20° (or 5 ⇥ 107 km) and is
by 60° with respect to the ecliptic. The trailing angle will vary over the course of the mission duration from 10° to
icant inclined
loss
in
science with SGO Low as
25°. The separation between the S/C is 1 ⇥ 106 km.
in the detection of stochastic and un18
ectly results from the reduction of links
Curt Cutler1 , John Ziemer1 , Daniel A. Shaddock2 , Ruth Skoug3 , and John Steinberg3
• Other
Propulsion Laboratory, California Institute of Technology, Pasadena, California
heliocentric
orbits:
Department of Physics, The Australian National University, Canberra, Australia
1 Jet
2
3 Los
Alamos National Laboratory, Los Alamos, New Mexico
• No
precession of the
orbital
plane -> loss of
November
10, 2011
Abstract
sensitivity
pattern
variation.
We introduce a new non-drag-free concept for space-based gravitational wave detection in which the spacecraft constellation geometry is chosen so the largest spacecraft disturbances are weakly coupled into the
• Annual
polarization
remains.
science measurement,
and existing instruments phase
are used to calibrate
these effects. A three spacecraft constellation is presented with significant hardware simplifications and reductions in spacecraft mass, power,
and size compared with the Laser Interferometer Space Antenna (LISA) mission, while preserving much of
• Annual
Doppler
phase
the LISA science (see
Figure 1). The cost
is estimated toremains.
be $ 1.1 Billion (FY12 dollars).
Lagrange Pt 2
ec
el
er
at
io
n
n
io
Strain [1/rtHz]
cc
s
re
pp
−17
n
io
−18
10
Calibration
−19
10
16o
−20
10
Sun
Geometric
Suppresion
at
r
ib
al
1AU
A
su
c
st
−16
10
10
Earth’s orbital
path
ft
−15
10
Po
Earth
ric
et
3
om
ge
10
1
ra
−14
ith
L
ac
10
W
L
2φ
2
Sp
−13
L = 21 million km
Not to scale
−4
10
−3
10
e)
op
c
s
le
e
E
mT
NG
c
A
0
4
GR
E(
LA
NG
A
GR
LA
A
LIS
−2
10
Frequency [Hz]
−1
10
0
10
Figure 1: Left: Geometric suppression of spacecraft noise: solar-radiation
and solar-wind pressures are orthogonal to
19
the interferometer sensitive axis. Right: While degraded from the LISA sensitivity, this mission is sensitive enough to
tal cost for the OMEGA mission, including launch vehicle, was 153M$
stimated using the on-line NASA inflation calculator). The TMCO panel
oposal concluded that
• Geocentric
orbits
le cost problem, and assuming that the drag-free technology is
such as ODIE [a University-Explorer-class mission planned to
OMEGA drag-free system], the OMEGA costs seem reasonable.”
• Slight
plane precession.
• Polarization phase variation depends on
armlength (through orbital radius).
• Doppler phase variation is still one year.
hat were made for the 1998 MIDEX opportunity that we would like to
2. OMEGA Science
ould typically increase the cost above the projected 211 $M total cost.
at a mission along the lines of the OMEGA mission can be flown for an
OMEGA Sensitivity Curves. The sky-averaged sensitivity curve for OMEGA is displayed in Figure 3. Th
dollars, that the hardware will be robust and reliable, and that the curve was generated using the Online Sensitivity Curve Generator[1]. The armlength used was the
all of the basic science goals of the LISA mission.
OMEGA baseline of L = 1 x 109 meters, which is 1/5 the LISA baseline. The noise-level inputs to the
Generator were set at (Sa)1/2 = 3 x 10-15 m/(s2Hz1/2) for acceleration noise, identical to LISA acceleratio
noise levels, and at (Sx)1/2 = 5 x 10-12 m/(Hz1/2) for position noise, which is one-fourth the LISA position
identical microprobes in a 600,000-km-high earth orbit, two probes
noise, reflecting the advantages of the stronger signals due to the shorter armlengths. The figure is
angle. These orbits are stable, allowing for 3 years of planned science
overlaid with representative tracks of the major source classes in this band. As may be seen, OMEGA
y of an extended mission if desired. Each probe is protected from be sensitive to all the source classes in the LISA science portfolio: massive black hole binaries, extrem
mass ratio inspirals, ultra-compact galactic binaries, as well as known verification binaries.
e system. The two microprobes at each vertex exchange laser phase
cks
a
r
he
he
he
e
e
Figure 1. Artist’s conception of the OMEGA mission geometry. Figure 3. OMEGA’s root spectral amplitude sensitivity (in units of Hz
-1/2
) is plotted against the baseline LISA
sensitivity. Overlaid on the figure are expected signal strengths for the low-frequency gravitational wave source
classes.20
The height above the curve is roughly the signal-to-noise ratio to be expected for matched filtering in a
one-year observation. For the EMRI and MBH binaries, the sources evolve dramatically during the observations
SUMMARY
• Gravitational
Galaxy.
wave observations can explore the whole
• Both
individual sources and the unresolved foreground contain
useful information.
• Mission
de-scopes have a variety of consequences on the
amount of science recoverable from DWD observations.
21
GRAVITATIONAL WAVES
• Quadrupole
Formula
G5/3 M5/3
2/3
2
h+ = 2
(2⇡f )
1 + cos ◆ cos (2⇡f t)
4
c d
G5/3 M5/3
2/3
(2⇡f
)
cos ◆ sin (2⇡f t)
h⇥ = 4
4
c d
• Chirp
mass M = (M1 M2 )
• Inspiral
• Outspiral
3/5
1/5
(M1 + M2 )
5/3
5/3
96
G
M
11/3
f˙ =
f
5
c5
—?
22
= µ3/5 M 2/5
AM CVn stars
White dwarf donor
3
ES Cet
V407Vul
CR Boo
Kl Dra
AM CVn V803 Cen
HP LIb
CP Eri
SDSS J1240
2003aw
GP Com
CE 315
Helium star donor
RX 0806
Evolved donors
CV’s/LMXB’s
Figure 1. Formation paths of AM CVn stars (see text). The known systems
(including the two candidates) are shown at their orbital period.
of the accreting white dwarf (Roelofs et al. 2004), while the continuum emission
of GP Com and CE315 is also shown to come from the white dwarf (Bildsten et
al., in prep). In these cases, however, the effective temperature of the accreting
white dwarf is too low to show He absorption.
The low-state systems probably
23
have stable cool accretion discs.
Scientific Objectives
10
10
20
10
21
10
22
10
23
Strain sensitivity
SN core collapse
black hole IMR
EMRI
compact binary coalescence
compact binaries
10
24
10
5
10
4
10
3
10
2
10 1
100
Frequency (Hz)
NGO
101
102
103
104
LIGO
Figure 2.4.: Comparison between the NGO sensitivity (red curve) and the sensitivity of present ground-based detectors such
as LIGO (blue curve). While having about the same strain sensitivity, NGO covers a much lower frequency range than
LIGO and aims for different astrophysical sources. NGO is sensitive to the inspiral, merger and ringdown (IMR) of massive
black hole binaries (in red), the quasi-monochromatic signal from compact binaries (in green) and the extreme mass ratio
inspirals (EMRIs, in orange). Ground based detectors operate in the acoustic frequency range and are sensitive to the
coalescence of compact binaries (in green) and “burst” events like supernovae core collapses (in cyan). While the compact
binaries observed by NGO and ground based detectors are in principle the same systems, they are separated by millions
of years of evolution. Note that in this plot the strain sensitivities are compared, that take into acoount the differences in
intergration time.
), but predictions are very uncertain at the high-redshift end, which is beyond the reach of electromagnetic
observations. NGO will lift the veil of these cosmic “dark ages”, providing a direct record of the history of
galaxy formation and central black hole growth in the observable universe.
Smaller galactic objects can also be captured (and eventually consumed) by the central black hole. Compact
objects such as degenerate dwarfs, neutron stars, and black holes sometimes will be driven by chance encounters
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25
AM CVn stars are among the expected 'verification
binaries' for a number of proposed space-based
gravitational wave missions. I will discuss the
expected characteristics of the detectable
population of AM CVn stars and other white dwarf
binary systems in relation to several proposed
mission concepts.
26