Image 1 Caption: "The color and shape of a galaxy is largely controlled by gas (usually ∼ 72--75 % hydrogen (He) 25 % helium (He), 0 to 2--3 % metals by mass fraction) flowing through an extended galactic halo around it. All modern simulations of galaxy formation and evolution find that they CANNOT explain the observed properties of galaxies without modeling the complex accretion and "feedback" processes by which galaxies acquire gas (usually of primordial cosmic composition maybe sometimes somewhat enriched by metals from stellar nucleosynthesis and supernova nucleosynthesis from past outflows from galaxies) and then later expel it after stellar nucleosynthesis and supernova nucleosynthesis. Hubble Space Telescope (HST) spectroscopic observations show that galaxies like the Milky Way recycle gas while starburst galaxies will lose gas to intergalactic space and become "red and dead" (i.e., quenched galaxies). Credit: NASA; ESA; A. Feild, STScI." (Somewhat edited.)
Features:
But we can say here that galaxy mergers often cause starbursts by strongly compressing the colliding interstellar medium (ISM) which induces a high star formation rate (SFR). After a starburst has exhausted the ISM, the SFR falls steeply and will usually go to near zero permanently if the merged galaxy mass (including dark matter mass) exceeds the golden mass 10**12 M_☉ after order 1--3 Gyr???? (see Dekel et al. (2019)). The golden mass 10**12 M_☉ galaxy quenching rule is NOT a law of nature, but rather a conspiracy of nature: i.e., various physical effects combine to effect it.
Note quenched galaxies (which are usually elliptical galaxies) are often referred to as red. But this actually means that their spectrum in the visible band (fiducial range 0.4--0.7 μm) is stronger in red light than unquenched galaxies. The psychophysical response to their spectrum is actually white light or yellowish white in true color.
The star formation rate (SFR) in starburst galaxies probably varies tremendously, but the typically it is thought that their rate is ∼ 30 times that of ordinary unquenched galaxies like the Milky Way (see Wikipedia: Starburst galaxy), and so the supernova rate is probably typically ∼ 30 times that of ordinary unquenched galaxies.
Image 2 Caption: The cosmichemical evolution of metallicity illustrated by the proxy of simulated oxygen (O) abundance evolution calculated for a simple model (David Weinberg 2016, On the Deuterium-to-Hydrogen Ratio of the Interstellar Medium, p. 3).
Features:
Abundance ratio is the logarithmic ratio of a metallicity proxy to hydrogen both in number of atoms per unit volume divided by the same for the Sun. The generic formula is
The fiducial curve is the green one that saturates at the solar metallicity which is zero for [O/H].
The subsequent production of
metals was in
stars
and supernovae
which ejected the
metals
into the interstellar medium (ISM).
The stars did this via
strong stellar winds
mainly in their
post-main-sequence phase.
The ISM enriched in
metals, then
contributes to ISM
would strictly increase in
metallicity
with cosmic time
as new generations of stars
contributed to its metallicity.
The increasingly enriched ISM
would then cause
new generations of stars to also be
enriched in metals
But this is NOT the case.
The ejected matter is largely
replaced by inflows from the
intergalactic medium (IGM
of mostly primordial matter
from the Big Bang: i.e.,
matter
with the
primordial cosmic composition
which is nearly pure
hydrogen,
helium,
and a small about of lithium.
Assume a 1-zone model of
galaxy of fixed size with
average density ρ.
As a simplifying assumption, we assume that no matter is permanently locked up into
compact remnants
(white dwarfs,
neutron stars,
black holes),
brown dwarfs,
planets,
or smaller astro-bodies.
We can easily dispense with this assumption if want to.
A differential equation
determining the change in ρ with time t is
ρ = (dρ/dt)_inflow*t + ρ_0            
       
       
       
      
for t << τ;
ρ = ρ_∞ = (dρ/dt)_inflow*τ
           
           
           
     
for t → ∞,
where ρ_0 is the initial density at time zero
whatever that is for the galaxy.
We see that ρ saturates at ρ_∞ = (dρ/dt)_inflow*τ.
Note that as the rate of outflow constant decreases (i.e., τ increases), the
saturation density increases:
i.e., τ
↑
ρ_∞
↑.
Now metallicity
times density Zρ obeys
the differential equation
Note the
age of the observable universe = 13.797(23) Gyr (Planck 2018)
(see Planck 2018: Age of the observable universe = 13.797(23) Gyr)
according to the Λ-CDM model
which is our current
standard model of cosmology (SMC, Λ-CDM model)
The Λ-CDM model.
might be revised or replaced sometime in the
2020s.
See
Tensions of the Λ-CDM Model Circa 2020s,
for a discussion of current problems with the
Λ-CDM model.
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(dρ/dt) = (dρ/dt)_inflow - κρ ,
where (dρ/dt) is rate of change in ρ,
(dρ/dt)_inflow is a constant inflow rate,
κ = 1/τ is the rate of outflow constant,
and τ is time parameter that is the inverse
of κ.
The solution of the differential equation
via an integrating factor is
ρ = (dρ/dt)_inflow*τ*[1-exp(-t/τ)] + ρ_0*exp(-t/τ)     in general;
[d(ρZ)/dt] = Z_IGM(dρ/dt)_inflow - κ(Zρ) + γρ ,
where Z_IGM is the constant
metallicity
of the intergalactic medium (IGM)
and γ is the rate of creation of metallicity
constant which has units of
inverse time.
For the saturation solution, we set [d(ρZ)/dt] = 0 and ρ = ρ_∞, and obtain
Z = γτ + Z_IGM .
If γτ = 0, then the metallicity
is just that of
the intergalactic medium (IGM).
Note that as
(γτ)
↑
Z
↑.