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17-Galactic chemical evolution p2 (Instantaneous Simple model (Works well…
17-Galactic chemical evolution p2
Observations
Compared to sun Pop 2 stars are higher in oxygen wrt iron
This is because most solar iron comes from SNe 1a which have longer lifetimes that SNe 2 (which make O)
Flat distribution shows that over range ~300 in Fe content enrichment was by SNe 2 only short timescale
Galactic context
Also should consider local conditions of star life and death
Is the system isolated, well mixed, inflows and outflows of gas, does the system have inhomogeneities, or violent star formation bursts (can change yields)
Parameters to consider
Total mass is stars
total mass in gas
surface brightness
luminosity function
processes which deplete total gas content (star formation, gas accretion)
processes which enhance total gas content (ejecta from agn, SN, O-stars; inflow from IGM)
GCE equations
4 variables need to be calculated
total system mass M
Mass of gas g
mass existing in the form of stars (includes compact remnants) , s
abundance of elements of interest, A (assumes certain inital condition, laws governing SFR, flows of material in/out of system)
Maths
Specific GCE models - simple 1 zone model
Assumptions
System isolated with constant mass, no inflows or outflows
system is well mixed at all times
system stars with pure gas with primordial abundances
yields of primary elements from IMF and nucleosynthesis are unchanging
Can be applied to other systems, e.g. galactic halo, dwarf, elliptical galaxies, galactic bulges
drawbacks : failure to account for metallicity distribution function of long lived stars in the solar neighborhood
Instantaneous Simple model
Incorporates the 'instantaneous recycling approximation' whereby it is assumed all processes take place instantly on the timescale of galactic evolution
results in quantities such as alpha and p not having explicit time dependence (may be affected by other parameters e.g. chemical composition, which change with time)
Works well for products of massive star evolution as long as
SFR doesn't vary rapidly on a short timescale
return fraction R isn't dependant on long-lived low mass stars
residual gas fraction isn't small
Works less well for elements such as Fe, N, s-process, C which come from low mass stars with O (Gyr evolution timescales)
Delayed Production approximation
Introduced to address the shortcoming of the instantaneous recycling approximation, specifially the problem with element formation from stars with long evolution times
simply introduces the concept that the element is produced instantaneously at some single time delta after the start of star formation
Results
Models can be used to predict quantities such as
Abundance ratios of primary elements
Ratios as a function of gas fraction
secondary element yields
In general predictions are in good agreement with experimental observations
Problems, notably with metal-poor G and K main-sequence stars
distribution is not in agreement with predictions from closed-box models
Models over predict number of metal-poor stars
effect also seen in K dwarfs