Gravitational-wave standard candles and Cosmology

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

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.) thatthe 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: (wide separation) dimensionless strain luminosity distance accumulated GW phase GW frequency position and orientation dependence (redshifted) chirp mass 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. Is there an optical counterpart? 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 to much better than 1% Ultimate standard candle! Luminosity distance determination

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

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. 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 • 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

20. Gravitational LensingMagnification 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 Every source at high redshift has been gravitationally lensed Markovic 1993, PRD, 48, 4783; Wang, Stebbins, & Turner 1996, PRL 77, 2875 DH & Wald 1998, PRD 58, 063501

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 + lensing 3,000 SNe + 2 GWs 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