<p>You can't estimate Hubble's constant using the method you propose, for two reasons.</p>
<p>(1) Redshift and luminosity distance are only linearly related by the Hubble parameter at small redshifts.</p>
<p>(2) You need an independent estimate of the redshift (e.g. from a spectrum of a host galaxy or something - see <a href="https://astronomy.stackexchange.com/questions/36411/how-is-the-hubble-constant-determined-from-gravitational-waves?rq=1">here for example</a> or <a href="https://dspace.mit.edu/handle/1721.1/121237" rel="nofollow noreferrer">Abbott et al. 2017</a>) to get the Hubble parameter from individual gravitational wave sources. That is because the inspiralling gravitational wave signature looks the same whatever the redshift of the source but does depend on the chirp mass, binary orientation and luminosity distance. For the vast majority of gravitational wave events an optical counterpart isn't available and so the redshift is actually estimated from the luminosity distance!</p>

CC BY-SA 4.0
2021-11-18T09:51:16.470Z
This answer could be improved by explaining why redshift cannot be determined directly from a gravitational wave event.
TimRias
CC BY-SA 4.0
2021-11-18T08:29:36.343Z
2021-11-18T11:25:09.213Z
2021-11-18T11:25:09.213Z
ProfRob
<p>The comoving radial distance goes into Hubble's law,</p>
<p>A redshift of 0.71 and a Luminosity distance of 4450 Mpc corresponds to a comoving distance of about 2590 Mpc (according to Ned Smiths cosmology calculator, and assuming a flat cosmology). Which should give you something closer to H₀=0.7</p>

CC BY-SA 4.0
2021-11-18T06:35:52.813Z
2021-11-18T06:35:52.813Z
James K
<p>I am trying to get the Hubble constant from gravitational wave events. On the GWOSC website, for all events, redshift and Luminosity distances are mentioned. Now, by this information, I can get my Hubble constant by the equation <span class="math-container">$cz=H_0 D_l$</span>. By the above logic, I applied it to some events, but I am getting <span class="math-container">$H_0$</span> to be around <span class="math-container">$47$</span> km/s Mpc, which is very far away from around its actual predicted value. For example taking the GW190413_134308 event, on GWOSC, the redshift for this event is given as <span class="math-container">$0.71$</span> and the luminosity distance is given as <span class="math-container">$4450$</span>. By the above equation, I am getting the <span class="math-container">$H_0$</span> value to be <span class="math-container">$47.86$</span> km/s Mpc.</p>
<p>GWOSC website: <a href="https://www.gw-openscience.org/eventapi/html/GWTC-2/GW190413_134308/v1/" rel="nofollow noreferrer">https://www.gw-openscience.org/eventapi/html/GWTC-2/GW190413_134308/v1/</a></p>
<p>I know I am doing something horribly wrong, can anyone please point this out to to me?</p>

CC BY-SA 4.0
2021-11-18T15:09:38.587Z
Are you aware of the new paper https://arxiv.org/abs/2111.03604 where they do this calculation?
Xerxes
<gravitational-waves><hubble-constant>
Hubble constant from GW events
Ashley Chraya
# Hubble constant from GW events

(Asked by: username_0 on 2021-11-18)

I am trying to get the Hubble constant from gravitational wave events. On the GWOSC website, for all events, redshift and Luminosity distances are mentioned. Now, by this information, I can get my Hubble constant by the equation $cz=H\_0 D\_l$. By the above logic, I applied it to some events, but I am getting $H\_0$ to be around $47$ km/s Mpc, which is very far away from around its actual predicted value. For example taking the GW190413\_134308 event, on GWOSC, the redshift for this event is given as $0.71$ and the luminosity distance is given as $4450$. By the above equation, I am getting the $H\_0$ value to be $47.86$ km/s Mpc.

GWOSC website: <https://www.gw-openscience.org/eventapi/html/GWTC-2/GW190413_134308/v1/>

I know I am doing something horribly wrong, can anyone please point this out to to me?

**Tags:** gravitational-waves, hubble-constant

> **Comments:**
> **username_1**: Are you aware of the new paper https://arxiv.org/abs/2111.03604 where they do this calculation?  

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## 2 answers

### Answer by username_2 on 2021-11-18. Score: 6

You can't estimate Hubble's constant using the method you propose, for two reasons.

(1) Redshift and luminosity distance are only linearly related by the Hubble parameter at small redshifts.

(2) You need an independent estimate of the redshift (e.g. from a spectrum of a host galaxy or something - see [here for example](https://astronomy.stackexchange.com/questions/36411/how-is-the-hubble-constant-determined-from-gravitational-waves?rq=1) or [Abbott et al. 2017](https://dspace.mit.edu/handle/1721.1/121237)) to get the Hubble parameter from individual gravitational wave sources. That is because the inspiralling gravitational wave signature looks the same whatever the redshift of the source but does depend on the chirp mass, binary orientation and luminosity distance. For the vast majority of gravitational wave events an optical counterpart isn't available and so the redshift is actually estimated from the luminosity distance!

> **Comments:**
> **username_3**: This answer could be improved by explaining why redshift cannot be determined directly from a gravitational wave event.  

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### Answer by username_4 on 2021-11-18. Score: 2

The comoving radial distance goes into Hubble's law,

A redshift of 0.71 and a Luminosity distance of 4450 Mpc corresponds to a comoving distance of about 2590 Mpc (according to Ned Smiths cosmology calculator, and assuming a flat cosmology). Which should give you something closer to H₀=0.7


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