[Users] GRHydro_InitData - magnetic fields - neutron stars

Fri Jan 13 18:03:57 CST 2017

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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