GRAVITATIONAL WAVE DETECTORS AND GALACTIC BINARIES

Transcription

1 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

2 The gravitational wave Galaxy Detector description Baseline and alternative configurations 2

3 The gravitational wave signal from the Galactic population of white dwarf binaries will consist of individually resolvable sources and a confusion-limited foreground. 3

4 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

5 The confusion-limited foreground is a result of signals from thousands of binaries in each resolvable frequency bin. 5

6 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

7 The confusion-limited signal is dominant at low frequencies (f<~3mhz). 7

8 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 ( ) ) Scientific Objectives 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.

9 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

10 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. 10 The Peanut

11 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 an assumed observation time (usually 1 or 2 years.) 11

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14 Shorter armlengths: Increase acceleration noise Decrease shot noise Increase position noise Improve response at high frequencies 14

15 1e-12 1e-13 1e-14 Approximative sensitivity std : LISA c1 : LISA1_P005c_LPF c2 : LISA1_P2_DRS c3 : LISA1_P07_D25_DRS 1e-15 h 1e-16 1e-17 1e-18 1e-19 1e-20 1e f (Hz) 15

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17 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 ( ) Strain spectral density at 1 mhz 1/ Hz ( 10 SNR = 5 4 ) Scientific Objectives 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

18 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 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 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 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 km. in the detection of stochastic and un18 ectly results from the reduction of links

19 Other heliocentric orbits: No precession of the orbital plane -> loss of sensitivity pattern variation. Annual polarization phase remains. Annual Doppler phase remains. Lagrange Pt 2 L = 21 million km L 2 2φ L Spacecraft Acceleration Earth s orbital path Earth 1AU 16 o Sun Not to scale Strain [1/rtHz] With geometric suppresion Post calibration Geometric Suppresion Calibration LAGRANGE LAGRANGE (40cm Telescope) LISA Frequency [Hz] 19

20 Geocentric orbits Slight plane precession. Polarization phase variation depends on armlength (through orbital radius). Doppler phase variation is still one year. 20

21 SUMMARY Gravitational wave observations can explore the whole Galaxy. 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

22 GRAVITATIONAL WAVES Quadrupole Formula h + =2 G5/3 M 5/3 c 4 (2 f) 2/3 1 + cos 2 cos (2 ft) d h = 4 G5/3 M 5/3 c 4 (2 f) 2/3 cos sin (2 ft) d Chirp mass M =(M 1 M 2 ) 3/5 (M 1 + M 2 ) 1/5 = µ 3/5 M 2/5 Inspiral f = 96 5 G 5/3 M 5/3 c 5 f 11/3 Outspiral? 22

23 White dwarf donor RX 0806 ES Cet V407Vul AM CVn HP LIb CR Boo Kl Dra V803 Cen CP Eri 2003aw Helium star donor SDSS J1240 GP Com CE 315 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. 23

24 10 20 Strain sensitivity black hole IMR EMRI SN core collapse compact binary coalescence compact binaries Frequency (Hz) NGO LIGO 24

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26 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