重力波について - tohoku university official english website · 2011-05-12 · – amplitudes...

Yousuke Itoh @GCOE seminar, Tohoku Univ., 2009 June 3

重力波について

“Gravitational wave detectors are already operating at interesting sensitivity levels, and they have an upgrade path that

should result in secure detections by 2014.”B.S. Sathyaprakash and B. F. Schutz (2009)

伊藤洋介

東北大天文


Plan of my talk

1.Review on LIGO results.2.Gravitational wave astronomy.3.興味4. ???


What is gravitational wave (GW)?

• Is a propagating gravitational tidal field.• Propagates at (less than) the velocity of light.• Can be generated due to temporal change of quadrupole (or

higher) moments of the system.• Can carry energy-momentum and angular momentum.

• The Earth crashes into the Sun due to GW emssion in about 10^23 years.

62250

5 1.0/

1.0/

1.0serg104~ˆˆ cvRcGMII

cGL ijijGW%%%%%%


Hulse-Taylor Pulsar PSR B1913+16 (orbital separation decreases in a consistent manner with GR prediction to

0.2% level.).

Gravitational wave

Binary Pulsar

Nobelprize.org “The Nobel Prize in Physics 1993”

C. M. Will Liv. Rev. Rel (2006)

GW is known to exist by El. Mag Astronomy.


LIGO Hanford 2Km & 4Km, Ligvingston 4kmGEO Hannover 600mTAMA 300mCLIO 100m

http://www.ligo-wa.caltech.edu/

Gravitational Wave Detectorsmeasure time variation of spatial distance


How LIGO sensitivity gets better.

http://einstein.phys.uwm.edu/FinalS3Results/


Cost

• LIGO is the largest single enterprise undertaken by NSF, with capital investments of nearly $300 million and operating costs of more than $30 million/year. (NSF Fact sheet Feb. 2008.)

• Japanese planned GW detector LCGT: 14 billion yen (Communication with TAMA people.) has not yet been approved by the Government.

• Expenditure for the Aso cabinet’s 2-trillion yen cash handout (定額給付金事務経費)：~90 billion yen. (Mainichi Shinbun 2008 Feb. 2.)

• Debt of Yubari city (夕張市借金)： ~60 billion yen (Yomiuri shinbun2006 June. 8).


LIGO Scientific Collaboration (LSC)

～400人、～４０大学・研究所


n1, n2: the detector arms vectors

H(t): Gravitational wave in the detector frameM(t): Detector relative motion in the celestial sphere coordinateh: Gravitational wave in the source frame

F: the detector response functions

(1)Detector motion in the celestial sphere coordinate(2)Detector longitude, latitude,anglebetween the two arms

Source Sky location in the celestial coordinate

Gravitational waves


Matched filtering technique for a priori known waveform

信号Ｓと雑音Ｎ

検出器雑音のPower spectral density

相関関数C。検出器ノイズがあるのでこれ自体はrandom variable.

検出器出力ｘ（ｔ）は信号h(t)と検出器雑音n(t)の重ね合わせとする。



内積の定義

信号雑音比（ＳＮＲ）

ＳＮＲを最大化するフィルタはdetector outputに含まれている予信号に比例する。

予想が完全に当たると、ＳＮＲはアンサンブル平均で最大になる。



Matched filtering:

検出器出力x(f)に対して、ρが最大になるようなテンプレート波形h(f,p)を探しだす。最大のρを与えるような波形パラメータλが天体の物理量（質量、スピンなど）を与える。


LIGOの結果の（不完全な）まとめ

• Continuous GW:

– pulsars know to exist. Early S5(8month) LIGO sees less than 500pc. Adv. LIGO would see ~ 5kpc.

• Binary GW:

– known to exist, 1 NS/NS event /1kyr for LIGO (S5 to 20Mpc). 1 NS/NS event/yr for Adv. LIGO, which would see to 200 Mpc.

• Stochastic GW:

– Amplitudes unknown. 1e-4 for S4 (1month), could be 1e-6 for 1 yr obs by LIGO, could be 1e-9 for 1yr obs by Adv. LIGO.

• Burst GW: Blind search, GRB triger search.• Ring-down of BHs:


There may be no direct measurements on ellipticity of a pulsar.GW offers one of possible direct way of measuring ellipticities of pulsars.Theoretical expectations: Crust, Magnetic field…., for normal NSs

or

Quark stars: ε ~ 1e-06 ?

Continuous GW: pulsars


Continuous GW from non-axisymetric pulsar

Doppler effect

Inclination

PSR rotation

PSR Spin down

Detector response function

Earth

PSR

PSR

Sun

(1) Non-Axisymmetric Pulsar but zero wobble angle fgw = 2 frot(2) Almost monochromatic wave


Continuous GW: waveform

h(t) =X

k=3=4;1;2;:::

X

p=+;£Fp(t)hk;p(t)

h2;+(t) =1

2h0(1 + cos2(¶)) cos(2ª(t))

h2;£(t) = h0 cos(¶) sin(2ª(t))

h0 =16¼2G

c4²If2

r

= 4 £ 10¡25µ1kpc

r

¶ µ²

10¡5

¶ ÃI

1045gcm2

! µf

100Hz

¶2

ª(t) = ©0 + 2¼X

k=0

f(k)0

tk+1

(k +1)!+

X

k

Ãk(t)

Ãk(t): Doppler by Earth orbiting about Sun: Doppler

by pulsar motion: Roemer, Shapiro, Einstein time

delay from SSB to detector:

基本的に我々の銀河内のでこぼこしたパルサー


Continuous GW: Simple Fourier Transform is inefficient

Simple Fourier transform of possible Crab pulsar GW (theoretical expectation). Assuming 24 days long observation.

(Jaranowski, Krolak & Schutz1998)

Demodulation をおこなうmatched filterが必要。


Spin down upper limit

B0531+21: (Crab) f=29.81 Hz, fdot = -3.74x1e-10, J0030+451: f=205.53Hz, fdot=-4.20x1e-16, r=250pcJ1939+2134 f=641.93Hz, fdot=-4.33x1e-14

Continuous GW analysis on know pulsars

ＬＳＣ２００９


Continuous GW analysis on know pulsars

Crab pulsarＬＳＣ２００９


All-Sky pulsars search


Einsetin@Home project

http://http://einstein.phys.uwm.edueinstein.phys.uwm.edu//

計算機～２３万台、参加者～１０万人、

～２１０カ国、平均15８ TeraFLOPS


Binary GW: waveform

最低次である四重極公式に対して、3.5 PN 補正(v/cの７次補正)まで求まっている。Post-Newtonian tail とtail of tailを含む。

r½r½¹h¹º + 2RB¹®º¯

¹h®¯ = (Source)


3PN EOM (Newtonian 運動方程式のv/cの6次補正)

150項ぐらい。


Inspiral binaries event rate

Cutler & Thorne (2002)


binary inspiral and merger

Simulation by Prof. Shibata of Yukawa Insititutehttp://www.esa.c.u-tokyo.ac.jp/~shibata/animation.html


Binary GW: results

LSC 2009 Gr-qc 0901.0302


Binary GW: waveform

GEO noise

NS/BH

NS/BH in GEO noise

Satyhaprakash作成

B.S. Sathyaprakash and B. F. Schutz (2009)


Burst GW: detection method.

• Waveform が事前に分からず、持続時間の短いものをburstと呼ぶ。• 既知の天体としては、超新星爆発やGRB、相対論的連星系

(NS/NS,NS/BH,BH/BH)の合体などがターゲット。• 超新星爆発やGRB、相対論的連星系の合体などは数値計算によって波形が求まっているが、パラメータ空間を網羅できるほど、したがって観測に必要な波形予測ができるほどの計算機速度は今はない。

• よってmatched filteringは近い将来は使えないと思われる。suboptimalな方法をとらざるをえず、持続時間も短いので（1ms~1s）、LIGOでは天の川銀河もしくはlocal group内のイベントしか見えない。

• 基本的にexcess noise法でcandidate eventを選別し、複数検出器間の時間に関するコンシステンシーを見る。


Bursts GW: S5 first year results.

•S5 first year results (November 2005 – November 2006).

•6e-22 /sqrt(Hz) to a few x 1e-21 /sqrt(Hz) over the frequency range of .64 – 2000Hz

•.Ott et al 2006 Super Novae model (Newtonian axi-symmetric) を考えると、600pcの距離に11 Msolarのプロジェニターが居てＳＮを起こしたなら５０パーセントの確立で検出。25Msolarの場合、24kpc.

•10Msolar -10Msolar BH/BH binaryが4Mpcで合体すると５０パーセントの確立で検出。

•50Msolar-50Msolar BH/BH binaryな180Mpcで合体すると５０パーセントの確立で検出。

LSC 2009 Gr-qc/0905-0020v3.


Ringdown GW: wave form and reach

LSC 2009

Gr-qc/0905.1654v1


Ringdown GW: characteristics

LSC 2009 Gr-qc/0905.1654v1


Stochastic GW: detection method.

• 四方八方から断続的にランダムに来る(arrival timeも方向もrandom)重力波の検出。

• 一つの検出器がもう一つの検出器に対して、matched filterになる（複数の検出器間の相互相関解析）。

• Stochastic GWの源は、Foreground (low mass x-ray binaries, pulsars, 中性子星連星、ブラックホール連星、白色矮星連星、銀河中心にあるSMBH のbinaries, cosmic stringなど)とbackground (インフレーション起源の重力波など)。

• LISA（DECIGO）では白色矮星連星（中性子星連星）がForegroundになるので、インフレーション起源重力波を見るためには、Foregroundの差っ引き方法の研究が必要（Cutler & Harms 2003）。

• ただし振幅やスペクトルについて、良く分かっているわけではない。


Stochastic background GW

LSC 2007

1 yr integration for “initial LIGO” and “Adv. LIGO”

GW h2100 = 10¡6

Ã pSh

3 £ 10¡21=p

Hz

!2 µf

10Hz

¶5=2Ã

T

3yrs

!¡1=2

Sathyaprakash & Schutz (2009)


Stochastic GW: results


Stochastic GW from Cosmic superstrings

LSC 2007, Damour & Vilenkin 2005 model.


将来計画

• Enhanced LIGO: 2009. 2 times better sensitivity than Initial LIGO.

• Advanced LIGO: 2014. 10times better sensitivity than Initial LIGO.

• Einstein Telescope (ET)• LISA: NASA/ESA joint space antenna mission. 2018+• BBO: One of NASA beyond LISA case studies. Cosmic

GW Background. Space antenna.• DECIGO: Japanese space antenna. Cosmic GW

Background. Acceleration of the universe. 2030?• SKA (pulsars timing)


GW sources for LIGO, Adv. LIGO.


• LIGO (US), VIRGO (Itary-France), GEO (Germany), TAMA(Japan): currently working

•Adv. LIGO (2013), Adv. VIRGO (?), LCGT (Japan), ACIGA (Australia)

•LIGO can see NS/NS at Virgo cluster, ~ 1 event/kyr.

•Adv. LIGO can see NS/NS at ~ 300 Mpc, ~ 10 events/yr.


LISA: Laser Interferometer Space Antenna


2018+ (NASA/ESA joint mission)


DECIGO/BBO

Cutler & Harms 2006

Crowder & Cornish 2005

BBO はcase studyのみ。


川村さん（NAOJ）2005年のスライドから。

DECIGO はやる気。1000億円プロジェクト

2030年ぐらい？


Einstein Telescope

“ET (Einstein Telescope) is a Design Study project supported by theEuropean Commission under the Framework Programme 7(FP7, Grant Agreement 211743). ” http://www.et-gw.eu/


Pulsar timing

A proposed MBH in 3C66B (Sudo et al 2003) was ruled out by timing observation of an existing millisecond pulsar data sets (Janet et al 2004).

hc = ¾T OA=Tobs


What can we learn from GW astronomy?

E.g.,• GWs from inspiralling NS/NS, NS/BH, BH/BH binaries

– Mass, spin, inclination angle, distance• From neutron stars mergers

– Equation of state (from tidal disruption, GW waveform)• From isolated neutron stars

– Equation of state (from r-mode, f-mode)• Black hole quasi-normal mode ringing

– Test of relativity. mass and spin of BH. • Small object orbiting around super-massive BHs.

– Mapping geometry of the SMBHs.


Grav. Wave Astronomy by LISA: example

Position and distance error distributions for sources at z = 1 (Left) and 3 (Right). The binaries masses are M1 = 10^5, and M2 = 6x10^5 in the solar unit. Figures from Holzand Hughes (2006).


GWA by LISA: example (cont’d)

Same as before but when electromagnetic counterparts are available so that positional errors are negligible. Fisgures from Holz and Hughes (2006).


GWA by LISA: example (cont’d)

Holz and Hughes (2006).


GWA: our work

Gravitational lensing of gravitational wavesYI, T. Futamase and M. Hattori

•Gravitational lensing by galaxies and clusters of galaxies:predicted by Einstein’s general relativity.

•GW propagates along null rays and should be lensed, aselectromagnetic wave is.

•Difference is that GW is coherent: chance of seeing interference.


GL of GWs (cont’d)

http://www.bottomlayer.com/bottom/reality/chap2.html

Some subtleties:

•Continuous GWs are usually not cosmological.

•Cosmological GWs are usually chirping.

•There is a time-deay of ~ months to years for galaxies and ~ kilo-years for clusters.

¢x

v= 5years

Ã200km=s

v

! µ10"

µ

¶ Ã0:1Hz

f

!

= 5years

Ã200km=s

v

! µ1mas

µ

¶ Ã1kHz

f

!


GL of GWs (cont’d)

•BBO/DECIGO

•.5.1 years of integration.

•NS/NS binary.

•5.1 years time delay

•Image separation 6.26’’

•Other parameters are the same as Q0957561.


GWA and Tohoku Univ. Science-web

• T. Futamase, S. Yoshida, M. Kajisawa, U. Lee, and YI (Astronomy)

• M. Yamaguchi (Particle theory and cosmology group)• T. Kawakatsu (Theoretical condensed matter and statistical

physics)• H. Tamura (Neuclear physics)• K. Hagino (Neuclear physics)

- GW and NS EOS, cosmic string, warm dark matter etc.- Review on NS oscillation by Yoshida on 2008/12/24.- GCOE start-up (3 million yen.)


Extreme mass ratio binaries as LISA sources

Mino, Sasaki & Tanaka (1997). Quinn & Wald (1997).

To construct waveform templates for LISA to detect extreme mass ratio binaries

•How to apply this equations to Kerr background?

•How to compute gravitational waveform at future infinity?


予期せぬ発見

• QSO (Maarten Schmidt (1962))

• CMB (Penzias & Wilson (1965) Gamov, Dicke, Peebles, …)

• Pulsars (Hewish & Bell (1968) Landau, Baade & Zwicky,…)

• GRB (Klebesadel et al. (1973))

• Holographic noise ? (GEO HF? Craig Hogan)


Stefan Hild （２００８）スライド

重力波について - tohoku university official english website · 2011-05-12 · – amplitudes...

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