1. Gravitational-wave standard candles and Cosmology Daniel Holz Center for Cosmological Physics University of Chicago Gravitation: A Decennial Perspective June 10, 2003

2. Outline Cosmological motivation Utility of high-redshift standard candles Gravitational-wave standard candles Cosmology with GW standard candles Gravitational lensing as a source of noise Conclusions Work done in collaboration with Scott Hughes astro-ph/0212218

3. Cosmology 101 The fundamental observable of cosmology is the distance- redshift relation: redshift: related to the size of the universe at the time of emission distance: derived from a standard candle, this tells us how long ago the light was emitted Combining these tells us the size of the universe as a function of time There is now abundant evidence (CMB, SNe, cluster surveys, etc.) that the expansion of the Universe is accelerating Understanding the cause of this acceleration is one of the outstanding challenges of fundamental physics for the coming decades (centuries?)! Best way to elucidate the nature of the dark energy is through careful study of the distance-redshift curve is it a true cosmological constant? quintessence? clues for inflation? string theory? extra dimensions? is gravity broken? Great interest, from many communities (GR, cosmo, string/HEP)

4. Measuring the distance-redshift relation We know how to measure redshift take a spectrum How does one measure distance? Use standard candles: objects of known fixed intrinsic brightness Supernovae are good standard candles intrinsic luminosity can be determined to ~15% phenomenology, not physics, underlies relation worry about evolution, systematics, etc... Can we do better?

5. Gravitational-wave standard candles Black holes are straightforward to describe: No hair Binary black hole inspirals are potentially excellent standard candles well-modeled, essentially “simple” systems strongest harmonic: dimensionless strain (redshifted) chirp mass accumulated GW phase GW frequency luminosity distance position and orientation dependence (wide separation) Schutz 1986, Nature 323, 310; Schutz 2001; gr-qc/0111095 Chernoff & Finn 1993, ApJ 411, L5; Finn 1996, PRD 53, 2878 Wang & Turner 1997, PRD 56, 724

6. Supermassive black-hole binaries and LISA Galaxies have supermassive black holes at their centers Galaxies form from hierarchical mergers expect to have supermassive binary black hole (SMBBH) mergers LISA will see all SMBBH mergers in the Universe 10^5 BH binaries fall in LISA’s “sweet spot” LISA sees these out to z~10 good mass coverage in range 10^5--10^6 LISA can observe inspiral of SMBBHs for ~ 1 year uses orbital modulation to infer position on sky can determine luminosity distance with reasonable accuracy (~10%)

7. Luminosity-distance determination from LISA Sky position determination Luminosity distance determination

8. Distance, but not redshift! Gravitational waves provide a direct measure of the luminosity distance, but they give no independent information about redshift opposite from optical astronomy Gravitation is scale-free GW signal from a binary with masses m1,m2 nearby is indistinguishable from a binary with masses m1/(1+z), m2/(1+z) at redshift z If assume cosmology, then can infer redshift Probe the SMBBH population ( Hughes 2002, MNRAS 331, 805 ) To measure cosmology, need an independent determination of redshift

9. Distance, but not redshift! Gravitational waves provide a direct measure of the luminosity distance, but they give no independent information about redshift opposite from optical astronomy Gravitation is scale-free GW signal from a binary with masses m1,m2 nearby is indistinguishable from a binary with masses m1/(1+z), m2/(1+z) at redshift z If assume cosmology, then can infer redshift Probe the SMBBH population ( Hughes 2002, MNRAS 331, 805 ) To measure cosmology, need an independent determination of redshift Electromagnetic Counterpart!

10. Can we identify the host galaxy? LISA error box, even in the best case, contains many thousands of galaxies Use knowledge of the cosmology to narrow the potential redshift range of host galaxies Locate galaxies that are morphologically promising have clearly suffered a merger recently (multiple interacting galaxies, tidal tails/streams, etc.) Calculate distances using many potential host galaxies, and demand concordance across multiple sources ( Schutz ) Use statistical knowledge of source population ( Chernoff & Finn )

11. Can we identify the host galaxy? LISA error box, even in the best case, contains many thousands of galaxies Use knowledge of the cosmology to narrow the potential redshift range of host galaxies Locate galaxies that are morphologically promising have clearly suffered a merger recently (multiple interacting galaxies, tidal tails/streams, etc.) Calculate distances using many potential host galaxies, and demand concordance across multiple sources ( Schutz ) Use statistical knowledge of source population ( Chernoff & Finn ) Look for something that goes BANG! Can select promising potential targets Will have wide-field, deep instruments  Optical, X-ray, radio,...  fully cover the LISA error box Can predict precise time of merger

12. Is there an optical counterpart?

13. We don’t know

14. Is there an optical counterpart? Galaxy mergers are cataclysmic events Some modeling ( e.g. Begelman, Blandford, & Rees 1980, Armitage & Natarajan 2002 ) suggests likely counterpart gas within the binary is driven onto larger BH super-Eddington accretion high-velocity outflows jets OJ 287: flaring outbursts from binary + accretion-disk Much more work is warranted Regardless of theoretical situation, error box will be scrutinized for counterparts

15. What good is a counterpart? Precise location of GW source on sky drastic improvement in GW modeling, and hence distance determination Independent determination of redshift allows use of GW source to put point on distance-redshift curve

16. Distance determination with optical counterpart Luminosity distance determination Luminosity distance to much better than 1% Ultimate standard candle!

17. Cosmology with GW standard candles The equation-of-state of the dark energy: Non-evolving equation-of-state: 3,000 SNe, 0.7<z<1.7 2 GWs, z=1.5, z=3. 3,000 SNe + 2 GWs Tremendously powerful probe of the dark energy

18. Cosmology with GW standard candles Tremendously powerful probe of the dark energy Gravitation giveth, and gravitation taketh away The equation-of-state of the dark energy: Non-evolving equation-of-state: 3,000 SNe, 0.7<z<1.7 2 GWs, z=1.5, z=3. 3,000 SNe + 2 GWs

19. The Universe is mostly vacuum, with occasional areas of high density Photons do not experience experience a Robertson-Walker Universe in their travels. Gravitational lensing due to matter inhomogeneities causes a change in brightness of observed images strong lensing: tremendous increase in brightness, and multiple images weak lensing: slight increase or decrease in brightness Gravitational Lensing Data in cosmology comes almost exclusively from the observation of distant photons In interpreting this data, a uniform, isotropic Robertson- Walker universe is generally assumed Key assumption: the Universe is filled with homogeneous matter

20. Gravitational Lensing Magnification Distributions Probability distribution,, of magnification,, at high redshift due to gravitational lensing The average magnification is given by the Robertson-Walker value (normalized to 1) The distributions are peaked at, with tails to high magnification Distributions are Non-Gaussian Markovic 1993, PRD, 48, 4783; Wang, Stebbins, & Turner 1996, PRL 77, 2875 DH & Wald 1998, PRD 58, 063501 Every source at high redshift has been gravitationally lensed

21. Cosmology with GW standard candles Without the effects of gravitational lensing 3,000 SNe, 0.7<z<1.7 3,000 SNe + 2 GWs When neglecting lensing, even a few GW standard candles have a major impact on cosmology!

22. Cosmology with GW standard candles Including the effects of gravitational lensing 3,000 SNe, 0.7<z<1.7 3,000 SNe + 2 GWs 3,000 SNe + 2 GWs + lensing Lensing seriously compromises the use of gravitational-wave standard candles!

23. Conclusions One of the most promising avenues for studying the dark energy is through observations of high-redshift standard candles Supermassive binary black holes offer perhaps the best high-redshift standard candle sources Comparable to supernovae candles, but no redshift With electromagnetic counterpart, orders of magnitude better than supernovae in distance, and redshift determination of host galaxy Gravitational lensing seriously degrades utility of individual GW standard candles. Nonetheless: resulting standard candles are important sanity checks high statistics allow for powerful cosmological measures opportunity to measure distances at very high redshift