[Users] GRHydro_InitData - magnetic fields - neutron stars

Fri Jan 13 18:18:12 CST 2017

Hello all,

there's a version of adding a magnetic field that was used for the
original GRHydroMHD paper (implemented most likely by Bruno Mundim,
Josh Faber or Philipp Moesta) that is in GRHydro_InitData (the
parameters for "For Poloidal Magnetic field test" ie poloidal_XXX) and
you can find a description of them in section 5.8 (page 38) of
https://arxiv.org/pdf/1304.5544.

Note though that I have not used them myself so your mileage may vary.

Yours,
Roland

> Hi Daniel,
> 
> first of all, please be aware that the option for setting an initial
> magnetic field for stars in a binary system is not yet part of the
> GRHydro_InitData thorn in the official toolkit release.
> It was implemented in the companion material for the paper you cited, but
> it hasn't been tested in production runs yet.
> 
> The initial magnetic field is imposed setting its potential. It is set as
> a poloidal field inside each star, with an expression similar to the one
> used also in the official thorn for a single star.
> 
> From the parameter files, the initial position of the star centers is taken:
> 
> >> GRHydro_InitData::Xc_1 = -13.5
> >> GRHydro_InitData::Xc_2 = 13.5
> >> GRHydro_InitData::Yc_1 = 0.0
> >> GRHydro_InitData::Yc_2 = 0.0
> >> GRHydro_InitData::Zc_1 = 0.0
> >> GRHydro_InitData::Zc_2 = 0.0  
> 
> 
> To set the magnetic potential in a grid point, the following rule is
> employed:
> 
> If the distance of the point from a star center is less than the star
> distance from the origin, the vector potential is set as:
> 
> Ax = -(y -
> Yc_{1/2})*poloidal_A_b_{1/2}*rhofac**poloidal_n_p*maxP_Pcut_1**poloidal_P_p
> 
> Ay = (x - Xc_{1/2})*
> poloidal_A_b_{1/2}*rhofac**poloidal_n_p*maxP_Pcut_{1/2}**poloidal_P_p
> 
> Az = 0
> 
> where rhofac = 1-rho/poloidal_rho_max and maxP_Pcut = max(P -
> Poloidal_P_cut_{1/2}, 0)
> 
> Else it is set to zero.
> 
> Therefore, GRHydro_InitData::Poloidal_P_cut_{1/2} sets a threshold, based
> on the pressure, to confine the B field inside the star. A common value is
> to set it to 4% of the maximum pressure, following, for example, Franci et
> al., Phys.Rev.D 88, 104028 (2013).
> 
> Instead, GRHydro_InitData::poloidal_n_p is the exponent of the rho term in
> the vector potential, which can be used to "move" the maximum of the
> magnetic field to star regions with higher or lower density and
> GRHydro_InitData::poloidal_P_p the exponent of the pressure term. Setting
> poloidal_P_p = 2 tries to accomplish a vector potential which has
> continuous first derivative at the star surface, but it is by no means a
> mandatory choice.
> 
> This initial field definition is taken from Liu et al., Phys. Rev. D 78,
> 024012 (2008).
> 
> Given this definition for the vector potential, the maximum value of the
> resulting magnetic field is given also by the pressure and density terms
> (and their spacial derivatives, when computing the curl of A), and not
> only by setting poloidal_A_b.
> 
> Hope this can be helpful,
> 
> Francesco
> 
> 
> 
> 
> 
> > Hi!
> >
> > I have a question regarding the initial data thorn of GRHydro.
> > The documentation and ccl files didn't really help me.
> >
> > The following was taken from paper [1] and now I am trying to add
> > magnetic fields to the stars.
> >
> > My questions are:
> >
> > 1) What are the units of (A) and (B) below? Is the following conversion
> > factor correct?
> > The star should have a field strength of 10^16 Gauss.
> > Using the following conversion would give "0.00011973228161339154" for
> > (A) and (B).
> >
> > 2) What are reasonable values for (C..F)? Can I just use the default
> > ones given in param.ccl?
> > Is there a reason not to use the default ones?
> > My plan is to analyse the structure of the field after the collapse and
> > the influence on the wave signal.
> >  
> >> # constants, in SI
> >> G     = 6.673e-11       # m^3/(kg s^2)
> >> c     = 299792458       # m/s
> >> M_sun = 1.98892e30      # kg
> >> mu0   = 1.2566370614e-6 # Newton/Ampere^2
> >> Kb    = 1.3806488e-23   # Joule/K
> >> Mparsec = 3.08567758e19 # km
> >> CU_to_Tesla = c**4 / M_sun / G**(1.5)* mu0**(0.5)
> >> CU_to_Gauss = c**4 / M_sun / G**(1.5)* mu0**(0.5) * 10000
> >> #-------------------------------------------------
> >> # Magentic Fields:
> >> #-------------------------------------------------
> >> (A) GRHydro_InitData::poloidal_A_b_1      = 0.00011973228161339154
> >> (B) GRHydro_InitData::poloidal_A_b_2      = 0.00011973228161339154
> >> (C) GRHydro_InitData::poloidal_P_cut_1    = 3.72e-6 #Non è in
> >> percentuale!!
> >> (D) GRHydro_InitData::poloidal_P_cut_2    = 3.72e-6 #Non è in
> >> percentuale!!
> >> (E) GRHydro_InitData::poloidal_n_p = 1 #Esponente di
> >> max((rho-rho_cut),0)
> >> (F) GRHydro_InitData::poloidal_P_p = 2 #Esponente di max((P-P_cut),0)
> >> GRHydro_InitData::Xc_1 = -13.5
> >> GRHydro_InitData::Xc_2 = 13.5
> >> GRHydro_InitData::Yc_1 = 0.0
> >> GRHydro_InitData::Yc_2 = 0.0
> >> GRHydro_InitData::Zc_1 = 0.0
> >> GRHydro_InitData::Zc_2 = 0.0  
> >
> > 3) These should be fine, right?
> >  
> >> GRHydro::transport_constraints     = "yes"
> >> GRHydro::track_divB                = "yes"
> >> GRHydro::calculate_bcom            = "yes"
> >> #GRHydro::clean_divergence            = "no"
> >> GRHydro::Grhydro_MaxNumConstrainedVars = 33
> >> GRHydro::GRHydro_MaxNumEvolvedVars     = 10
> >>
> >> HydroBase::initial_Bvec       = "bin_ns_poloidalmagfield"  
> >
> > The field is evolved and everything seems okay, I am just not sure about
> > the units and (C..F).
> >
> > 4) Is there a good method to visualize the B-field?
> > Visit + Carpet hdf5 reader + Streamlines? (seems to be "buggy")
> >
> > Thank you!
> >
> > Best regards,
> > Daniel
> >
> > References:
> > [1] "R. De Pietri, A. Feo, F. Maione, and F. Löffler, “Modeling Equal
> > and Unequal Mass Binary Neutron Star Mergers Using Public Codes,” Phys.
> > Rev., vol. D93, no. 6, p. 064047, 2016."
> >
> > _______________________________________________
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> >  
> 
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