Changes between Version 22 and Version 23 of u/erica/radtimescales


Ignore:
Timestamp:
04/04/16 13:10:10 (9 years ago)
Author:
Erica Kaminski
Comment:

Legend:

Unmodified
Added
Removed
Modified
  • u/erica/radtimescales

    v22 v23  
    142142Given the radius of the box is r=.05 pc, we have,
    143143
    144 [[latex($\boxed{R\approx \frac{22}{.05} =440}$)]]
     144[[latex($\boxed{R\approx \frac{l}{h} =440}$)]]
    145145
    146146This moves us into the 'free-streaming' regime on the [[latex($\lambda(R)$)]] curve, and thus we can approximate [[latex($\lambda\approx 1/R$)]]. Thus, we have:
     
    159159[[latex($\boxed{t_{fs}=\frac{L}{c}\approx\frac{1.5e+17}{3e+10}= 57 ~days}$)]]   
    160160
    161 Given these timescales, the diffusion wave probably won't be strongly peaked, yet will be broad -- traveling close to the speed of light. If my 'assumptions' were correct about a pre-stellar core (their average size and mass), then given their 'average density' and the rosseland mean opacity, we see that they are in the optically thin limit for diffusion. Given cores are not optically thin, this means that either the density assumption is way off (they should be centrally concentrated), or setting the scale height = box radius is off (perhaps for an optically thick core the scale height should be greater than the core size (so that the energy is roughly constant throughout the core).
    162 
    163 Tackling this slightly differently could be like confining the core to a smaller dimension so that we were ensuring we would be in the optically thick limit. That is, beginning by constraining [[latex($\lambda\approx 1/3$)]]. Then, we should be able to predict the timescale over which we would see a well-defined 'diffusion wave' propagate through the grid.
    164 
    165 ''' Coupling time estimate '''
     161Given these timescales, the diffusion wave probably won't be strongly peaked, but will be broad -- traveling close to the speed of light. If my 'assumptions' were correct about a pre-stellar core (their average size and mass), then given their 'average density' and the rosseland mean opacity, we see that they are in the optically thin limit for diffusion. Given cores are not optically thin, this means that either the density assumption is way off (they should be centrally concentrated), or setting the scale height = box radius is off (perhaps for an optically thick core the scale height should be greater than the core size, so that the energy is roughly constant throughout the core).
     162
     163Tackling this slightly differently could be starting from the optically thick limit, [[latex($\lambda\approx 1/3$)]]. Then, we should be able to predict the timescale over which we would see a well-defined 'diffusion wave' propagate through the grid.
     164
     165= Diffusion estimate for optically thick 1 solar mass core =
     166
     167If we let,
     168
     169[[latex($R=1$)]], then we have
     170
     171[[latex($l=\frac{1}{\kappa_R \rho}=h$)]]
     172
     173and from before,
     174
     175[[latex($M=\rho l^3$)]]
     176
     177Solving these two equations gives:
     178
     179[[latex($h=$)]]
     180
     181[[latex($l=$)]]
     182
     183
     184= Coupling time estimate =
    166185
    167186This timescale provides an estimate for how long it should take the gas to 'heat up' (or cool down) from radiation. This is controlled by the planck opacity, [[latex($\kappa_P$)]]. For low [[latex($\kappa_P$)]], the matter and radiation are relatively decoupled. Adjusting the degree of coupling is akin to adjusting the specific heat capacity of the material.