We have decided to analyze the accretion onto a neutron star just up until the hydrogen burning begins. We'll first attempt this as an adaptation to the Bondi accretion problem with a solid sphere near the origin (also relevant to the problem of infall onto the proto-neutron star during core collapse). If we're successful, we'll try an accretion disk in 2D with polar geometry.

• [X] X-ray bursts
  • [X] Accretion rate ~ 10^-8 Solar Mass / yr
  • [X] Radius ~ 10-15 km
  • [X] Mass ~ 1 Solar Mass
• [X] Novae
  • [X] Accretion rate ~ 10^-9 Solar Mass / yr
  • [X] Radius ~ 10^4 km
  • [X] Mass ~ 1 Solar Mass
• [ ] Density of in falling material
• [X] Alpha parameter = 0<alpha<1

Link to Code on GitHub

• 2D
  • [X] Get the VH-1 polar model working.
    • Set ngeomx = 1 (radial cylindrical), ngeomy = 3 (theta), nlefty = 3, nrighty = 3 (periodic)
  • [X] Set up accretion
    • Set nrightx = 2 (constant inflow), uotflo * rotflo * outer area of simulation (2 * pi * xmas) = 1
    • Set votflo to be the desired velocity at the boundary edge
  • [X] Implement gravity
    • In forces, set grav (n) under sweep “x”, cylindrical to be -GM/xao(n)**2
  • [X] Implement a viscosity model.
    • We're choosing to use the derivative in the radial direction of only the tangential coordinate
      • alpha*1/r(dv/dr)+alpha*d2v/dr2
    • In forces, set grav (n) under sweep “y”, cylindrical angle to the above expression
  • [X] Run Models
    • [X] Non-dimensionalize
      • The length unit is the radius of the neutron star, R_ns
      • The time unit is sqrt (R_ns^3/GM_ns)
      • The mass unit is M'sqrt (R_ns^3/GM_ns), where M' is the mass infall rate
    • [X] Determine free parameters
      • Outer radius of simulation, xmax
      • Infall velocity, uotflo
      • Viscosity, alpha
      • Tangential initial velocity, votflo
    • [X] Run models with uotflo = -0.1, votflo = 0.2, xmax = 10.0
      • [X] Viscid (alpha = 1.0)
      • [X] Semi-Viscid (alpha = 0.1)
      • [X] Inviscid (alpha = 0.0)
    • [] Run models with uotflo = -1.0, votflo = 0.2, xmax = 10.0

• [x] Get visualization working
  • [x] Install NetCDF
    • visit on ubuntu/linux was a quagmire, went with windows virtualbox installation :(
• [x] Gathering the initial conditions for novae and X-ray bursts
  • have average values for NS and WD, time permitting will constrain to single case and derive
• [x] PRESENTATION
• [x] Outline concepts and highlight theory for presentation
• [x] Encode .cdf data to video for presentation
• [x] Compile references for presentation
• [x] Compile images for presentation

Determined to be outside scope of project. * [ ] Determine the input abundances * [ ] Build the nuclear network for the problem * [ ] Take output from the codes * [ ]determine when hydrogen burning begins * [ ]analyze data values to optimize scale(linear vs log) and ranges(0-?) for visualization

1D on a solid surface was successful so the 2D case was the bulk of the project work. The solid case was unstable and resulted in an non-physical explosion. Both the infall and reflective cases were attempted, we found the [] to be optimal. We were able to model a non-viscous and viscous case using hydronamic force and energy equation. Terms for the extremely large B field (10^7-8 T) were not included. Both accreted around the central mass with a large high pressure/empty barrier for the non-viscous case, as the angular momentum is not dissipated. The viscous case correctly accreted on to the surface.

Presentation PDF

video of non viscous accretion

video of viscous accretion

video of accidental zero pressure accretion

References:

• Accretion Power in Astrophysics - Frank, King, Raine
• Accretion Disk for Beginners : External Link (Notes PDF)

(further resources in presentation)