1 / 16

3 building models I

3 building models I. solving the system. In time-independent form, the interior of a star can be described by a set of four ordinary differential equations, together with four boundary conditions.

candace-hanson
Télécharger la présentation

3 building models I

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 3 building models I Stellar Structure: TCD 2006: 3.1

  2. solving the system • In time-independent form, the interior of a star can be described by a set of four ordinary differential equations, together with four boundary conditions. • If all four boundary conditions were given, say, at the centre, this would require a straightforward numerical integration from the the centre to the surface. Since they are not, some clever techniques are required. • In general, there is no analytic solution and it is necessary to find a numerical solution. • However, by making certain approximations, we can obtain some restricted but very informative solutions. • First, we look at how families of solutions might behave. • Second, we introduce methods for computing full solutions. • Subsequently, we will look at some approximate solutions. Stellar Structure: TCD 2006: 3.2

  3. homologous stars Stellar Structure: TCD 2006: 3.3

  4. homologous stars (2) Stellar Structure: TCD 2006: 3.4

  5. homologous stars (3) Stellar Structure: TCD 2006: 3.5

  6. homology relations: radiative stars Stellar Structure: TCD 2006: 3.6

  7. homology relations: radiative stars (2) Stellar Structure: TCD 2006: 3.7

  8. homology relations: convective stars Stellar Structure: TCD 2006: 3.8

  9. homology relations: upper main-sequence stars Stellar Structure: TCD 2006: 3.9

  10. solving ode’s: shooting • This method divides the star into an inner and outer part.Separate solutions are obtained by estimating a set of additional boundary conditions. These are adjusted until thee two solutions match. • Inward solution.At m=M we have Ps=0, Ts=Teff. Estimate R and L. Integrate inwards to a point mf, to obtain Pif, Tif, lif, and rif. • Outward solution.At m=0 we have rc=0, lc=0. Estimate Pc and Tc. Integrate outwards to mf, to obtain Pof, Tof, lof and rof. • In general: Pf=Pif–Pof0, Tf=Tif–Tof0, lf=lif–lof0, rf=rif–rof0. • Repeat the inward solution with R+R, L and with R, L+L. • Repeat the outward solution with Pc+Pc, Tc, and with Pc, Tc+Tc. Stellar Structure: TCD 2006: 3.10

  11. solving ode’s: shooting (2) Stellar Structure: TCD 2006: 3.11

  12. solving ode’s: difference methods (1) Stellar Structure: TCD 2006: 3.12

  13. solving ode’s: difference methods (2) Stellar Structure: TCD 2006: 3.13

  14. solving ode’s: difference methods (3) Stellar Structure: TCD 2006: 3.14

  15. solving ode’s: difference methods (4) Stellar Structure: TCD 2006: 3.15

  16. 3 building models -- review • We have obtained simple relations for properties of main sequence stars, and looked at methods for solving the full system of stellar structure equations • Homologous stars - families of models • Radiative stars • Convective stars • Solving the full system of 4 odes + 4bcs • Shooting method • Difference Equations • Henyey method • These provide an accurate numerical solution, but not much insight into how stars work. Stellar Structure: TCD 2006: 3.16

More Related