YITP, Kyoto UniversityFebruary 12th, 2019

A standard siren measurement of the Hubble constant from

GW170817 without the electromagnetic counterpart

Ignacio Magaña Hernandez

Motivation: Hubble constant tension

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Distance, but not redshift

3

h(t) =M5/3

z f(t)2/3

DLF(angles)cos(Φ(t))

• Gravitational waves provide a direct measurement of luminosity distance, but they give no independent information about redshift, so called “standard sirens”.

• Gravitation is scale free:

• GWs from a local binary with masses are indistinguishable from masses at redshift z. (m1, m2) ( m1

1 + z,

m2

1 + z )

Mz = (1 + z)(m1m2)3/5/(m1 + m2)1/5

⟷

• To measure cosmology, need an independent measure of redshift.Credit: Daniel Holz

How to measure the redshift?

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• If the merger produces an EM counterpart (e.g. GRB).

• If one knows the neutron star (NS) equation of state.

• If the shape of the NS mass distribution is known.

• If the post-merger signal is observed.

• Even if no EM counterpart found, one can use a reliable galaxy catalog to cross correlate.

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GW170817: First standard siren measurement of H0

• LVC reported a 1-sigma uncertainty of ~14%

• Of this uncertainty:

• ~11% came from uncertainty in measuring GW luminosity distance.

• The rest came from uncertainty in the peculiar velocity of the galaxy w.r.t the Hubble flow.

H0 = 70+12−8 km/s/Mpc

Credit: Salvatore Vitale

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Cross correlating with galaxy catalogs

Credit: Chris Messenger

GW170817 statistical H0: Galaxy catalog

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• First application of the statistical method to a real GW event.

• In here we pretend we don’t know the location of the GW event (at z~0.01).

• We use the GLADE galaxy catalog for cross correlation, around 50% complete out to 120 Mpc.

0.00 0.01 0.02 0.03 0.04

z

0.0

0.2

0.4

0.6

0.8

1.0

p com

ple

te(z

)

LB > 0.25L?B

LB > 0.05L?B

LB > 0.01L?B

0.00 0.01 0.02 0.03 0.04

z

0

100

200

300

400

500

p cat

(z)/

p vol(z

)

LB > 0.626L?B

LB > 0.25L?B, LB weights

LK > 0.005L?K, LK weights

LK > 0.005L?K

205� 200� 195� 190�

-15�

-20�

-25�

Right Ascension

Dec

linat

ion NGC 4993

0.005

0.010

0.015

0.020

0.025

0.030

0.035

0.040

0.045

Red

shift

z 8

• Galaxies that contribute to the statistical cross correlation with GLADE using the 99% GW170817 localization region within the redshift range 0 < z < 0.046.

GW170817 statistical H0: Localization

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GW170817 statistical H0: Results

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GW170817 statistical H0: Results

Star formation weights

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GW170817 statistical H0: Results

Stellar mass weights

Different possible galaxies for each event

Combine inform

ation from all observed events ⇒

Independent events

⇒

⇒+

+

Joint H0 posteriorH0 posteriors

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Mock data studies

Mock data studies

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• Use LIGO’s First Two Years dataset:

• End-to-end simulation of 250 BNS events at O2 like sensitivities.

• Full parameter estimation for each event available.

• Use the MICE catalog (end-to-end mock galaxy catalog simulation from an N-body light cone simulation).

• Realistic DES-like galaxy catalog with large scale structure, incompleteness, EM selection effects and more.

40 50 60 70 80 90 100H0 (km s�1 Mpc�1)

0.00

0.05

0.10

0.15

0.20

0.25

p(H

0)(k

m�

1s

Mpc)

40 50 60 70 80 90 100H0 (km s�1 Mpc�1)

0.00

0.01

0.02

0.03

0.04

0.05

p(H

0)(k

m�

1s

Mpc

)

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How good was GW170817?

Conclusion

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• GW standard sirens provide an independent measurement of cosmological parameters

• Statistical method uncertainty due to galaxy catalog incompleteness, photometric redshift uncertainties and large number of galaxies.

• GW+EM counterparts provide the tightest constrains.

• Statistical method might be the only way to constrain cosmology using binary black holes.

Thank you for listening

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