Planet Mass and composition allocation determined entirely by AU, Stellar Mass, Stellar Rotation and Disc mass

I posted a link to my model but I didn't explain what it was, how it worked, or what it did, and I realize I left people just confused, so I will explain:

First here is my github with all of my source code: https://github.com/jamesgdahl/HYDROS-Planet-Formation-Model

All declared variables:

Z 0.014 Solar metallicity

f rock 0.22 Rocky fraction of condensables (Lodders 2003)

f ice/rock 3.5 Ice/rock ratio past full condensation

M ⊕ thresh 3.0 Core mass for gas accretion onset

ϵ pebble 0.40 Pebble capture efficiency (Lambrechts)

η rock 0.78 Rock retention (Mulders pebble drift loss)

A 0 58 H/He envelope amplification at t form = 0

k H/He 0.684 H/He decay rate (per Myr)

t disc 5 Myr Disc dispersal time at Sol disc-mass

M ⊙ / M ⊕ 332946 Solar mass in Earth masses

On formation of a stellar system like ours, the accretion disc is governed primarily by viscosity and torque being the primary drivers of mass dynamics. This disc is bounded on its inner and outer edges.

The inner edge, the Alfvén radius, is calculated:

RA=0.20⋅M⋆M⊙,prim⋅Ω4/7 AU

The outer edge is also determined by the same forces

Rdisc=30⋅M⋆M⊙,prim⋅Ω−1/2 AU

The inner edge, in a normal system, is the main backstop of mass accretion potential, providing a baseline, as the inhibition of viscous flow from the Alfvén radius backstop increases the overall accretion potential of the entire rest of the disc. In highly compressed systems, the outer edge is not a "dead zone" as it is in our system (and there is a very slight backstop at our outer edge, it is not in fact dead) which also increases the "ambient" accretion potential of the rest of the disc.

Disc compression is calculated:

C=RA/Rdisc

This can result in an inverted system if spin is extreme enough, with the outer line being pushed below the inner line, resulting in the radial mass accretion potential from all outer radii compressed into the innermost parts of the solar disc.

This establishes a linear and uniform accretion potential that scales linearly with AU:

slope=M⋆⋅Z⋅frock⋅fdisc⋅ηrockRdisc M⊕/AU

With "slope" being the AU determined rocky accretion potential at that AU for planetary formation. This "slope" calculation then determines the rock content of any planet at a precise AU:

Mrock(r)={slope⋅[(r+0.078)−RA]if RA≤r<2RAaintercept+slope⋅rif 2RA≤r≤Rdisc0otherwise (inner/outer void)

With intercept defined as:

aintercept=0.596⋅M⋆M⊙,prim⋅Ω2/7 M⊕

The Snow Line is determined as a property of the viscous heating of the disc, with scenarios ranging from "small grains" scenario (high viscous heating) to a "large grains" scenario (low viscous heating), Sol's observed Snow Line at 2.7 AU results in a moderate-to-low grains scenario of 0.82 between those ranges. (Mulders et al)

rsnow=[1.6+1.7,g2.2]⋅(M⋆M⊙,prim)!2⋅fdisc0.01 AU

Within the Snow Line, the earlier stated accretion potential is the main driver of initial planetary mass, other factors being negligible. Beyond the snow line, ice can become solid and then is available for accretion:

ηice(r)=exp![−r−rsnow0.8⋅Rdisc]

There is a pile up at the Snow Line, due to melting and re-freezing at that point

Mbump(r)=0.5⋅slope⋅rsnow⋅exp![−(r−rsnow)22⋅(0.15,rsnow)2]

So the amount of ice accretion a planet can recieve is calculated:

Mice(r)=slope⋅(r−rsnow)⋅3.5⋅ηice(r)+Mbump(r)

Pebble accretion is available to all planets but not all benefit equally. Pebbles defined as:

Mpeb,total=fdisc⋅Z⋅(1−frock)⋅M⋆⋅ϵpebble

Per planet weight:

wi=1ri−rsnow(ri>rsnow)

With only sufficiently massive planets benefitting:

Mpeb,i=Mpeb,total⋅wi∑j∈eligiblewj

H/He defined:

A(tform)=58⋅exp![−kH/He⋅tform]

Solar wind will not allow H/He accumulation at a defined distance

wwind(r)=11+(Ω/30)⋅(0.5/r)2

So the calculation for available H/He:

MH/He=Mcore⋅A(tform)⋅wwind

Is allocated to a defined H/He envelope:

kH/He=0.684⋅max![1,(Mdisc,SolMdisc,sys)2]

Taken all together, a Planetary mass potential at a given AU is:

M(r)=Mrock+Mice+Mpebble+MH/He+δM

This all factors into my simulator I linked to yesterday:

https://jamesgdahl.github.io/HYDROS-Planet-Formation-Model/

My simulator also includes "best fit" and planet location prediction mechanics which I can get into if anyone's interested.

The modelling of the Solar System then fills all predicted "slots" for the Solar system of planets (9 planets total) but has modifiers from potential to currently observed. Mercury for instance has lost approximately 30% of its mantle due to a variety of factors but the most likely culprit being matter infall luminosity bursts during disc formation when due to magnetic anomalies the Alfvén radius temporarily weakened, where L would have increased by 100x for brief periods, boiling Mercury's mantle. These short 100x L bursts also explain the thin layer of desiccated material on the surface of C type asteroids within 3.5 AU, but the lack of surface desiccation beyond 3.5 AU.

Theia, which should have been approximately 2 Earth masses following formation including 0.4 ice accretion, instead was disrupted by the incursion of Saturn (not Jupiter) which caused a loss of angular momentum of early Theia (then only 0.1 Earth masses) eventually resulting in impact with Earth. This Saturn incursion later scattered ~90% of Martian mass potential. These modifications then result in the observed current mass distribution and 7.1 fully formed planets, rather than 9.