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I do not understand that much about the term Hubble flow. For cosmological studies with type Ia supernova, I often see the sentence like "We used 100 SNe Ia in the Hubble flow". What does the difference between "located in the Hubble flow" and "not in the Hubble flow"? Thank you.

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The apparent motions of external galaxies can be broken down into two components and the redshift observed will be due to the sum of both.

The first is an apparent recession velocity that is given by Hubble's law. $v_H = H_0 d$, where $v_H$ is the apparent recession velocity, $d$ is the proper distance and $H_0$ is the current value of the Hubble parameter.

On top of that, a galaxy will have a peculiar velocity $v_P$ with respect to the cosmological rest frame (usually taken to be coincident with the frame in which the cosmic microwave background has no dipole anisotropy). This preculiar velocity is due to the gravitational influence of nearby other galaxies or due to a galaxy's motion within a group, cluster or supercluster of galaxies.

Since the first component grows with distance, whereas the second component is fixed and of order hundreds to perhaps a thousand or so km/s, then if you look far enough away from the Earth then $v_H \gg v_P$. This is what it means to be "part of the Hubble flow" - the velocity that you measure for that object is dominated by the cosmological expansion of the universe and local peculiarities and gravitational perturbations that the galaxy is influenced by play a small enough role that they become a negligible source of uncertainty.

Since $H_0 \simeq 70$ km/s per Mpc, and $v_P \sim 1000$ km/s, then a quick bit of maths tells you that in order for $v_H \gg v_P$, then $d \gg 14$ Mpc for an object to be considered part of the Hubble flow. There is no exact definition.

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