Gravitational-wave standard candles and

Cosmology

Gravitational-wave standard candles and

Cosmology

Daniel HolzCenter for Cosmological Physics

University of Chicago

Gravitation: A Decennial PerspectiveJune 10, 2003

OutlineOutline

• 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 Hughesastro-ph/0212218

Cosmology 101Cosmology 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)

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t = d /c

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1+ z = anow athen

Measuring the distance-redshift relationMeasuring 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?

Gravitational-wave standard candlesGravitational-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:

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h(t) =M z

5 3 f (t)2 3

DLF (angles)cos[Φ(t)]

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h(t)

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M z = (1+ z)(m1m2 )3 5 (m1 +m2 )1 5

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Φ(t)

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f (t) = 1 2π( )dΦ dt

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DL

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F (angles)

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/0111095Chernoff & Finn 1993, ApJ 411, L5; Finn 1996, PRD 53, 2878

Wang & Turner 1997, PRD 56, 724

Supermassive black-hole binaries and LISA

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%)

Luminosity-distance determination from LISA

Luminosity-distance determination from LISA

Sky position determination

Luminosity distance determination

Distance, but not redshift!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 massesm1/(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

Distance, but not redshift!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 massesm1/(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 redshiftElectromagnetic Counterpart!

Can we identify the host galaxy?

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)

Can we identify the host galaxy?

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

Is there an optical counterpart?

Is there an optical counterpart?

Is there an optical counterpart?

Is there an optical counterpart?

We don’t know

Is there an optical counterpart?

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

What good is a counterpart?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

Distance determination with optical counterpart

Distance determination with optical counterpart

Luminosity distance determination

• Luminosity distance to much better than 1%

Ultimate standard candle!

Cosmology with GW standard candles

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

Cosmology with GW standard candles

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

• 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 LensingGravitational 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

Gravitational LensingMagnification Distributions

Gravitational LensingMagnification Distributions

Probability distribution, , of magnification, , at high redshiftdue to gravitational lensing

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P(μ )

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μ

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P(μ )

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μ

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€

μ <1

Markovic 1993, PRD, 48, 4783; Wang, Stebbins, & Turner 1996, PRL 77, 2875DH & Wald 1998, PRD 58, 063501

Every source at high redshift has been gravitationally lensed

Cosmology with GW standard candles

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!

Cosmology with GW standard candles

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 ofgravitational-wave standard candles!

ConclusionsConclusions• 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