<p>I find some clues at terms &quot;<a href="https://wikimedia.org/api/rest_v1/media/math/render/svg/b4eeb0f17b35fd11d805051e0bfe1f55366bd643" rel="nofollow noreferrer">Distance measures (cosmology)</a>&quot;:</p>
<blockquote>
<p>the redshift that would pertain in that case should be used but <span class="math-container">$d_{A}$</span> should be corrected for the motion of the solar system by a factor between 0.99867 and 1.00133, depending on the direction.</p>
</blockquote>

CC BY-SA 4.0
2022-03-18T09:06:01.343Z
2022-03-18T09:06:01.343Z
user578569
<p>The luminosity distance
<span class="math-container">$$d_l=(1+z)r(z)\ ,$$</span>
where <span class="math-container">$r(z)$</span> is given by <span class="math-container">$$r(z)=cH^{-1}_0\int_{0}^{z}\frac{dz'}{E(z')}\ .$$</span></p>
<p>When I use the SNe dataset &quot;Pantheon&quot;, I find <a href="https://github.com/dscolnic/Pantheon/blob/master/lcparam_full_long_zhel.txt" rel="nofollow noreferrer">there</a> are two redshifts: <span class="math-container">$z_{cmb}$</span> and <span class="math-container">$z_{hel}$</span>.</p>
<p>In some files, the luminosity distance is also written as <span class="math-container">$d_l=(1+z_{hel})r(z_{cmb})$</span> (For example 1912.11879 and 2202.12214).
This paper 1312.0184 said it is “Since
the time dilation part of the observed luminosity distance
depends on the total redshift zhel (special relativistic plus
cosmological)”.</p>
<p>Why is the luminosity distance related to both heliocentric redshift and CMB restframe redshift? In which situations can it be used?</p>

<distances><redshift><cosmic-microwave-background><luminosity>
Is luminosity distance related to both heliocentric redshift and CMB restframe redshift？
user578569
# Is luminosity distance related to both heliocentric redshift and CMB restframe redshift？

(Asked by: username_0 on 2022-03-11)

The luminosity distance
$$d\_l=(1+z)r(z)\ ,$$
where $r(z)$ is given by $$r(z)=cH^{-1}\_0\int\_{0}^{z}\frac{dz'}{E(z')}\ .$$

When I use the SNe dataset "Pantheon", I find [there](https://github.com/dscolnic/Pantheon/blob/master/lcparam_full_long_zhel.txt) are two redshifts: $z\_{cmb}$ and $z\_{hel}$.

In some files, the luminosity distance is also written as $d\_l=(1+z\_{hel})r(z\_{cmb})$ (For example 1912.11879 and 2202.12214).
This paper 1312.0184 said it is “Since
the time dilation part of the observed luminosity distance
depends on the total redshift zhel (special relativistic plus
cosmological)”.

Why is the luminosity distance related to both heliocentric redshift and CMB restframe redshift? In which situations can it be used?

**Tags:** distances, redshift, cosmic-microwave-background, luminosity

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## 1 answers

### Answer by username_0 on 2022-03-18. Score: 1

I find some clues at terms "[Distance measures (cosmology)](https://wikimedia.org/api/rest_v1/media/math/render/svg/b4eeb0f17b35fd11d805051e0bfe1f55366bd643)":

> the redshift that would pertain in that case should be used but $d\_{A}$ should be corrected for the motion of the solar system by a factor between 0.99867 and 1.00133, depending on the direction.


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