Neutrino Propagation in Supernovae with Nonstandard Interactions

A lesson on how the Wolfram Language can be used to create a simple toy model that can efficiently guide toward understanding general features of complex systems.

June 19, 2017—Daavid Väänänen

Setting Up a System of Interacting Neutrinos and Antineutrinos with Two Distinct Types

COMMENT:
If you would like to learn more about the system, please visit the APS Journal.

First, we define a toy function to describe the shape of the background potential caused by neutrinos interacting with other non-neutrino background particles (including nonstandard interaction contributions, which are assumed to behave similarly as weak interactions):

In[]:=

potBG[yshiftBG_,xshiftBG_,widthBG_,r_]:=(yshiftBG-((r-xshiftBG)/widthBG)^2);(*yshiftBGcanbeusedtoadjustashiftalongy-axis,xshiftBGcanbeusedtoadjustashigtalongx-axis,widthBGcanbbeusedtoadjustwidthofthepotential,rdescribestheradialdistancefromtheemissionlocation*)

Next, we define a function to describe the shape of the background potential caused by neutrinos interacting with other surrounding neutrinos and antineutrinos:

In[]:=

potNu[scaleNu_,steepnessNu_,r_]:=scaleNuExp[-r/steepnessNu];potAnu[asymmetry_,scaleNu_,steepnessNu_,r_]:=-asymmetrypotNu[scaleNu,steepnessNu,r];(*potNu[scaleNu_,steepnessNu_,r_]describestheneutrinopotential,scaleNucanbeusedtoadjustintialscalingofthepotential,steepnessNucanbeusedtoadjuststeepnessofthepotential,potAnu[asymmetry_,scaleNu_,steepnessNu_,r_]describestheantineutrinopotential(whichisassumedtoscalelinearlywithrespecttotheneutrinopotential),asymmetrydescribestheinitialasymmetrybetweenneutrinosandantineutrinos,rdescribestheradialdistancefromtheemissionlocation*)

Now we can visualize the different possible extreme configurations for the potentials with some interesting input values:

In[]:=

yBG=400(*anexamplevalueforyshiftBG*);xBG=500(*anexamplevalueforxshiftBG*);wBG=8(*anexamplevalueforwidthBG*);scNu=25000(*anexamplevalueforscaleNu*);stNu=80(*anexamplevalueforsteepnessNu*);as=0.9(*anexamplevaluefortheinitialneutrino-antineutrinoasymmetry*);rmin=20(*initialradialevaluationpoint*);rmax=700(*finalradialevaluationpoint*);Plot[{potBG[xBG,yBG,wBG,r](*backgroundpotential*),-potBG[xBG,yBG,wBG,r](*inverseofbackgroundpotential*),potNu[scNu,stNu,r]+potAnu[as,scNu,stNu,r](*totalneutrinopotential,bothwithelectrontypeneutrinoandantineutrino*),-potNu[scNu,stNu,r]-potAnu[as,scNu,stNu,r](*totalneutrinopotential,bothwithnon-electrontypeneutrinoandantineutrino*),potNu[scNu,stNu,r]-potAnu[as,scNu,stNu,r](*totalneutrinopotentialwithelectrontypeneutrinoandnon-electrontypeantineutrino*),-potNu[scNu,stNu,r]+potAnu[as,scNu,stNu,r]}(*totalneutrinopotentialwithnon-electrontypeneutrinoandelectrontypeantineutrino*),{r,rmin,rmax},FrameTrue,PlotStyle{Cyan,{Cyan,Dashed},Red,{Red,Dashed},{Red,DotDashed},{Red,Dotted}},FrameLabel{"Radial Distance [a.u.]","Interaction Potential [a.u.]"},FrameTicksStyleThick,LabelStyleDirective[FontSize20],PlotLegends{"Background Potential","Inverse Background Potential","Neutrino Potential (both electron type)","Neutrino Potential (both non-electron type)","Neutrino Potential (electron neutrino, non-electron antineutrino)","Neutrino Potential (non-electron neutrino, electron antineutrino)"}]

Out[]=

	Background Potential
	Inverse Background Potential
	Neutrino Potential (both electron type)
	Neutrino Potential (both non-electron type)
	Neutrino Potential (electron neutrino, non-electron antineutrino)
	Neutrino Potential (non-electron neutrino, electron antineutrino)

Simulating the Evolution of Neutrinos and Antineutrinos

AUTHORSHIP INFORMATION

Daavid Väänänen

6/19/17