====== Exercise #1 ======

==== Purpose ====
The main objective of this exercise is to test the behaviour of the oscillation frequencies of p-modes around nu_max with different oscillation codes. This exercise is performed on a given model for which HE (Hydrostatic Equilibrium) and BV (Brunt-Vaisala frequency). 

The actual models and information details on the HE and BV tests are given in [[data:models1|Models (exercise #1)]]


==== Procedure ====
**<color #22b14c>Step 1</color>**. Selection of the model. We decided to use the well-known modelS, computed by Jørgen for which HE and BV tests were positively passed.


**<color #22b14c>Step 2</color>**. Computation of adiabatic oscillation frequencies
  - Only p-modes (up to cut-off frequency) (L=0,1,2,3).  
  - No Richardson Extrapolation 
  - Compute both with Lagrangian and Eulerian variables
  - Limit (surface) conditions: P → 0 :?:
  - Same gravitation constant G: :!: 

:?: We need to choose the same for all the codes 
:!: We need to select a value, or decide to read it from the model)

**<color #22b14c>Step 3</color>. Comparison of 
  - Individual frequencies around nu_max (± 10 radial orders)
  - Comparison of Δν and δν


==== Discussion ====
The complete discussion and results obtained for the exercise can be found in the [[http://festelar3.ugr.es/plato-reports/ex1_report.html|this report]].

The analysis was done using [[http://example.com|this online app]] developed by the WP121.130 team.



 


==== Conclusions ====

  - Both frequency and large separation differences are around 10−3−10−2 for ℓ>0 modes and may reach 0.15-0.2 when radial modes are included. This behavior is only found for comparisons with GraCo (see complete statistics in Appendices).
  - IS(4) (or equivalent using Richardson extrapolation) is optimum (as suggested by ESTA/CoRoT exercises). We do thus suggest to freeze this parameter from now on.
  - Model 1-002 shows a better overall behavior of the frequencies and large separations, thus we encourage to promote the use of full analytic CEFF in the model computations.
  - Mode identification shows anomalies at low-n (between 1 and 15). It is not an issue for higher frequencies. This however might be a problem when solar-like stars different from the Sun (and definitely not so well tuned as modelS), and for evolved stages with the presence of mixed modes. So our recommendation is that the chosen code must be robust in mode identification.
  - Missing modes at low-frequency range (n=[1,10]) is another important issue for some codes (in this exercise: GraCo and LOSC). This might be solved when remeshing is performed on the models.