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Cosmology with 300,000 standard sirens C.Cutler & D.Holz, PRD 80, 104009 (2009) Big Bang Observer (BBO) and DECIGO: 4 very sensitive mini-LISAs BBO Noise Curve NS/NS gw 1015 10 5 for a 3-yr observation w/ BBO’s angular resolution ~ (500s)(2 0.3Hz)/SNR ~ 1 arc sec --consistent with earlier results by Cornish&Crowder(2005) BBO’s distance error (from noise) D/D ~ 1/SNR ~ 0.01 Actually, BBO’s distance error is dominated by Weak Lensing WLD 0.044 z D Holz&Linder (2005) Number of Galaxies in Error Cylinder Hubble Ultra Deep Field: dN 2 1,000/arc min d Cosmological Parameter Extraction What goes in: Assume have measured 250,000 NS-NS binaries out to z=3, with perfectly determined redshifts, z. Fit for 5 parameters: H 0 , m , X , w 0 , w a wher e w(z) p/ & Following standard convention, also assume forecasted 2 Planck prior: constrains m h to ~1%, plus a constraint on DA of Hubble scale at decoupling. 2.5e5 NSs up to z=3 H0 to 0.1% For CDM H0 to 0.025% 2.5e5 NSs up to z=3 w0 to ~0.01 wa to ~0.1 With more accurate analysis of lensing effects, and including priors from next-generation ground-base DE projects (Stage III): 20,000 --- Hirata, Holz & Cutler (2010) Of course, BBO is far in the future , and by the time it flies, DE FoM of 20,000 may be no big deal. On the other hand, this method of measuring D(z) is highly independent of others, and potentially has far better systematics. Caveat re a Selection Effect Hirata pointed out: the probability of correctly identifying the host galaxy has a small but non-negligible dependence on its magnification: higher means higher SNR, so a smaller error box and a brighter galaxy. If not accounted for, would lead to systematic bias in DL (z). Possible ways of “correcting” for this effect: 1) Use thegamma-ray burst sources to calibrate it out. I.e., using those same ~1000 galaxies to create a new synthetic data set, giving the “calibration” binaries random orientations and coalescence times. Analyze the data 2 different ways: with and without the benefit of the exact sky location. The difference is an estimate of the systematic bias. 2) Include this effect in a proper Bayesian analysis. Would need to include more parameters, especially a parametrized model of the NS-NS merger rate as a function of z, galaxy type, etc. Other Astrophysics from BBO/Decigo (1) 1. Early Warning System for ALL short/hard gamma-ray bursts (assuming they are due to mergers) BBO will predict time and location of ALL NS-NS and BHNS mergers, months in advance. Because of beaming, probably only a small fraction, will lead to observable gammaray bursts. We will learn which kinds of mergers (components, masses, orientations) lead to observable bursts, and which do not. In particular, BBO will tell us binary’s orientation, so we can study beaming. Can still look for afterglows, even when there are no observed gamma rays (so-called “orphan afterglows”). Other Astrophysics from BBO/Decigo (2) 2. Detect mergers of Intermediate Mass BHs to z>20 Estimated rate ~30/yr, with ~20/yr at z > 10, based on merger-tree simulations by Volonteri, assuming MBHs do grow from stellar BH remnants. (By comparison, for same model, Einstein Telescope would detect ~2/yr, almost all at z<8.) Summary: When we eventually build a deci-Hz space-based GW mission approaching the target sensitivities of BBO or Decigo, then Catalogue of Inspiraling Compact Binaries will be a Goldmine Offer cosmological measurements with very high accuracy , and potentially far better systematics. Plus: A complete catalogue of all NS and BH binary mergers in the universe. an All-sky gamma-ray burst monitor, high-z IMBHs, weak lensing, strong lensing, ….. extras BBO/Decigo as WL mission 1Gpci i E.g., BBO’s measurement of lensing convergence power spectrum would be more accurate than the most ambitious other proposed WL missions. Other Astrophysics from BBO/Decigo Early Warning System for ALL short/hard gamma-ray bursts. Detect mergers of Intermediate Mass BHs to z>20 (estimated rate: ~30/yr, with ~20/yr at z > 10). Strong Lensing: expect hundreds of “multiplyimaged” (in GWs) binaries, with time-delays of order a year, and measured to <0.1 sec. Can probe structure of lensing galaxies/clusters. BBO: Pie in the Sky? One idea: 6-satellite BBO/Decigo +ET Example of possible plan: Step 1. One mini-LISA +ET : rates, gamma ray bursts, high-z IMBHs Step 2. Two mini-LISAs + ET: high – precision cosmology Step 3. Full BBO: Inflationary GW background. Caveat re Calibration BBO interferometry in BBO Mission Concept Study (Phinney et al., 2003) is very “LISA-like”: no applied forces along sensitive direction. Later it was realized that this design would greatly oversaturate current UV photodiodes. Harry et al.(2006) proposed a more “LIGO-like” design,with forces on the test mass to keep photodiode operating near dark fringe. But this spoils calibration accuracy unless the force is measured very accurately. DECIGO is in same situation. We have spoken with several instrumentalists, and are optimistic that this is a solvable problem; e.g., 1) Widen beam onto array of ~1000 photodiodes 2) Use interferometry to measure applied force BBO/Decigo as WL mission i 7 ~ 10 i i 2 2 Comparable to most ambitious/optimistic other WL experiments, such as JDEM or LSST, which measure WL shear thru correlations in galaxy shape distortions. We estimate that BH-BH binaries likely contribute about as much to 2 as NS-NS binaries. Though we assume the BH-BH merger rate is ~1/20 the NS-NS rate, each 2 i is ~25 times larger. i Recent work: more careful analysis of WL error. WLD 0.044 z D for single source Cutler&Holz(2009) estimated that for N sources at same z: WLD (0.044 z) /N1/ 2 D for N sources That’s correct if you take an average, but because the distribution of magnifications is quite skew, the average is not the best estimator. The maximum likelihood estimator gives: WLD (0.030 z) /N1/ 2 D for N>4 sources see Hirata,Holz&Cutler(2010); Shang&Haiman(2010) Decigo Roadmap 2007 08 09 10 11 12 13 Mission R&D Fabrication 14 15 16 17 18 19 R&D Fabrication DECIGO Pathfinder (DPF) 20 21 22 23 24 25 R&D Fabrication Pre-DECIGO DECIGO Objectives Scope Test of key technologies Observation run of GW Detection of GW w/ minimum spec. Test FP cavity between S/C Full GW astronomy 1 S/C 1 arm 3 S/C 1 interferometer 3 S/C, 3 interferometer 3 or 4 units from Kawamura 26 Decigo: Pre-conceptual design Differential FP interferometer Arm length: 1000 km Mirror diameter: 1 m Laser wavelength:0.532 m Finesse: 10 Laser power: 10 W Mirror mass: 100 kg S/C: drag free 3 interferometers Arm cavity Arm cavity Laser Photodetector Drag-free S/C from Kawamura Mirror Optical Follow-ups Recall that BBO gives DL and a small error box on sky. Optical astronomers must still provide 300,000 redshifts. Is this realistic? • By the time BBO flies, the LSST could have determined photometric redshifts (accurate to 2-3%) for a large fraction of galaxies over 1/3 of the sky. •There are several proposed wide-field spectroscopic surveys. E.g., BigBOSS would meaure ~5 million spectroscopic redshifts per year (~4,000 at a time) for galaxies in the range 0.2 < z < 3.5, over an area of 14,000 sq. degrees. (WFMOS instrument on Subaru telescope would have been Comparable to BigBoss, but their funding was just cut.) Nominal BBO parameters (used in paper) , • , Laser power = 300 x LISA, arm length = 0.01 x LISA, mirror D ~ 10 x LISA, S1/acc2 = 0.01 x LISA Binaries as standard GW sirens (using quadrupole approximation for simplicity) I ij M A rAi rAj A D 1 d2 hij PTT 2 Iij (t D) D dt h(t) ~ D1 r 22 ~ D1 M1 M 2 2 / 3 x F(angles) f 1/ 3 M df 96 8 / 3 M1 M 2 11/ 3 f + higher order terms 1/ 3 dt 5 M Summary: If we can build a deci-Hz space-based GW mission approaching the target sensitivities of BBO or Decigo, and with excellent calibration accuracy (at ~ 104 level), then inspiraling Compact Binaries will be Goldmine a Cosmology Offer cosmological measurements, with far better accuracy than with any other proposed methods, and potentially far better systematics (modulo those 2 caveats). Plus: great WL mission, gamma-ray burst monitor, high-z IMBHs, strong lensing, ….. Copyright 2010. All rights reserved. Summary: If we can build a deci-Hz space-based GW mission approaching the target sensitivities of BBO or Decigo, and with excellent calibration accuracy (at ~ 104 level), then inspiraling Compact Binaries will be Goldmine a Cosmology Offer cosmological measurements with very hight accuracy , and potentially far better systematics. Plus: All-sky gamma-ray burst monitor, high-z IMBHs, weak lensing, strong lensing, ….. Copyright 2010. All rights reserved.