# Talent

## Goal

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.

## Log Book

#### Input: Sarah Schwartz

• [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

#### Code: Justin Brown

• 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

#### Analysis: Amber Lauer

• [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

## RESULTS

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.

References:

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

(further resources in presentation) 