Generic quark model. More...

Detailed Description

Referred to as Model D in Steiner13tn.

This model uses o2scl::eos_had_schematic near saturation, a polytrope (with a uniform prior in the exponent like alt_polytropes) and then a generic quark matter EOS at high densities.

Alford et al. 2005 parameterizes quark matter with

$P = \frac{3 b_4}{4 \pi^2} \mu^4 - \frac{3 b_2}{4 \pi^2} \mu^2 -B$

where $\mu$ is the quark chemical potential. QCD corrections can be parameterized by expressing $b_4 \equiv 1-c$ , and values of $ c $ up to 0.4 (or maybe even larger) are reasonable (see discussion after Eq. 4 in Alford et al. (2005)). Note that, in charge-neutral matter in beta equilibrium, $\sum_{i=u,d,s,e} n_i \mu_i = \mu_B n_B = \mu n_Q$ . where $\mu_B$ and $ n_B $ are the baryon chemical potential and baryon density and $ n_Q $ is the number density of quarks.

The parameter $b_2 = m_s^2 - 4 \Delta^2$ for CFL quark matter, and can thus be positive or negative. A largest possible range might be somewhere between $(400~\mathrm{MeV})^2$ , which corresponds to the situation where the gap is zero and the strange quarks receive significant contributions from chiral symmetry breaking, to $(150~\mathrm{MeV})^2-4 (200~\mathrm{MeV})^2$ which corresponds to a bare strange quark with a large gap. In units of $\mathrm{fm}^{-1}$ , this corresponds to a range of about $ -3.5 $ to $4~\mathrm{fm}^{-2}$ . In Alford et al. (2010), they choose a significantly smaller range, from $ -1 $ to $1~\mathrm{fm}^{-2}$ .

Simplifying the parameterization to

$P = a_4 \mu^4 +a_2 \mu^2 - B$

gives the following ranges

$a_4 = 0.045~\mathrm{to}~0.08$

and

$a_2 = -0.3~\mathrm{to}~0.3~\mathrm{fm}^{-2}$

for the "largest possible range" described above or

$a_2 = -0.08~\mathrm{to}~0.08~\mathrm{fm}^{-2}$

for the range used by Alford et al. (2010).

The energy density is

$\varepsilon = B + a_2 \mu^2 + 3 a_4 \mu^4$

Note that

$\begin{eqnarray*} \frac{dP}{d \mu} &=& 2 a_2 \mu + 4 a_4 \mu^3 = n_Q \nonumber \\ \frac{d\varepsilon}{d \mu} &=& 2 a_2 \mu + 12 a_4 \mu^3 \end{eqnarray*}$

Definition at line 403 of file models.h.

#include <models.h>

Inheritance diagram for bamr::generic_quarks:

Public Member Functions
virtual void	low_limits (entry &e)
	Set the lower boundaries for all the parameters, masses, and radii.

virtual void	high_limits (entry &e)
	Set the upper boundaries for all the parameters, masses, and radii.

virtual std::string	param_name (size_t i)
	Return the name of parameter with index `i`.

virtual std::string	param_unit (size_t i)
	Return the unit of parameter with index `i`.

virtual void	compute_eos (entry &e, int &success, std::ofstream &scr_out)
	Compute the EOS corresponding to parameters in `e` and put output in `tab_eos`.

virtual void	first_point (entry &e)
	Function to compute the initial guess.

Public Member Functions inherited from bamr::two_polytropes
virtual void	setup_params (o2scl::cli &cl)
	Setup new model parameters.

virtual void	remove_params (o2scl::cli &cl)
	Remove model-specific parameters.

virtual void	baryon_density_point (double &n1, double &e1)
	A point to calibrate the baryon density with. More...

	two_polytropes ()
	Create a model object.

Public Member Functions inherited from bamr::model
virtual void	compute_mr (entry &e, std::ofstream &scr_out, o2scl::o2_shared_ptr< o2scl::table_units<> >::type tab_mvsr, int &success)
	Compute the M-R curve directly.

Additional Inherited Members
Data Fields inherited from bamr::model
nstar_cold2	cns
	TOV solver and storage for the EOS table.

Protected Attributes inherited from bamr::two_polytropes
o2scl::cli::parameter_double	p_kin_sym
	Parameter for kinetic part of symmetry energy.

o2scl::eos_had_schematic	se
	Low-density EOS.

o2scl::fermion	neut
	Neutron for se.

o2scl::fermion	prot
	Proton for se.

double	nb_n1
	The fiducial baryon density.

double	nb_e1
	The fiducial energy density.

The documentation for this class was generated from the following file:

models.h

Detailed Description

Public Member Functions

Additional Inherited Members