where
S
F
R
{\textstyle SFR}
is the total star formation rate, measured in solar masses per year, and
M
∗
{\textstyle M_{*}}
is the total stellar mass, measured in solar masses. A rigid definition of quenching in the local Universe sets the quenching threshold at
s
S
F
R
<
10
−
11
{\displaystyle sSFR<10^{-11}}
.
However, in the grand scheme of cosmic history, the picture becomes more complicated. Across cosmic time, the star formation rate and stellar mass of galaxies have evolved significantly. For example, the Universe is theorized to have had elevated rates of star formation around two to three billion years after the Big Bang, a period also known as "Cosmic Noon". This is unlike our current epoch, which is called "Cosmic Twilight" as today's galaxies are forming stars at much lower rates. To accommodate for these evolving galaxy properties across different epochs, the quenching threshold has also been defined in more flexible terms. One such definition parameterizes the threshold as:
where
t
H
{\displaystyle t_{H}}
is the age of the Universe, and depends on the corresponding redshift
z
{\displaystyle z}
at that epoch. With this definition, a massive galaxy in the early Universe like GS-9209, with
s
S
F
R
=
10
−
10.3
{\displaystyle sSFR=10^{-10.3}}
, can be classified as quenched, because at its redshift, the quenching threshold is actually
s
S
F
R
<
10
−
9.8
{\textstyle sSFR<10^{-9.8}}
.
Shock heating is not possible across all ranges of galaxy halo mass, but is restricted to halos with masses above 1012 solar masses. This is because at lower masses, the gas pressure generated by the shock is curtailed by radiative cooling and cannot prevent the shock from gravitational collapse. Moreover, even in cases where the shock is supported and successfully generates a hot medium, there may still be gas filaments within the halo that are too cold and dense to be heated up. These filaments will provide critical gas supply to the post-shock galaxy, which is now dominated by the hot medium. In such scenarios, a full quenching of the galaxy will require supplementary factors, including AGN feedback.
There are additional processes within a galaxy that can contribute to its quenching in limited cases. One such process is supernovae, which can indeed heat up cold gas but is too distributed to singlehandedly quench galaxies inside massive dark matter halos. However, in the case of ultra-faint dwarf galaxy Eridanus II, whose halo is only 107 solar masses, supernova feedback alone has been shown to be capable of driving out star-forming gas, thereby quenching the system.
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