MUSIC/cosmology.hh

/*
 
 cosmology.hh - This file is part of MUSIC -
 a code to generate multi-scale initial conditions 
 for cosmological simulations 
 
 Copyright (C) 2010  Oliver Hahn
 
 This program is free software: you can redistribute it and/or modify
 it under the terms of the GNU General Public License as published by
 the Free Software Foundation, either version 3 of the License, or
 (at your option) any later version.
 
 This program is distributed in the hope that it will be useful,
 but WITHOUT ANY WARRANTY; without even the implied warranty of
 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 GNU General Public License for more details.
 
 You should have received a copy of the GNU General Public License
 along with this program.  If not, see <http://www.gnu.org/licenses/>.
 
 */

#ifndef _COSMOLOGY_HH
#define _COSMOLOGY_HH

#include "mesh.hh"
#include "general.hh"
#include "transfer_function.hh"

/*!
 * @class CosmoCalc
 * @brief provides functions to compute cosmological quantities
 *
 * This class provides member functions to compute cosmological quantities
 * related to the Friedmann equations and linear perturbation theory
 */
class CosmoCalc
{
public:
	//! data structure to store cosmological parameters
	Cosmology m_Cosmology;
	
	//! pointer to an instance of a transfer function plugin
	transfer_function_plugin *m_pTransferFunction;
	
	
	//! constructor for a cosmology calculator object
	/*!
	 * @params acosmo a cosmological parameters structure
	 * @params pTransferFunction pointer to an instance of a transfer function object
	 */
	 
	CosmoCalc( const Cosmology acosmo, transfer_function_plugin *pTransferFunction )
	{
		m_Cosmology = acosmo;
		m_pTransferFunction = pTransferFunction;
	}
	
	//! returns the amplitude of amplitude of the power spectrum
	/*!
	 * @params k the wave number in h/Mpc
	 * @params a the expansion factor of the universe
	 * @return power spectrum amplitude for wave number k at time a
	 */
	inline real_t Power( real_t k, real_t a ){
		real_t m_Dplus    = CalcGrowthFactor( a );
		real_t m_DplusOne = CalcGrowthFactor( 1.0 );
		real_t m_pNorm = ComputePNorm( 1e4 );
		m_Dplus    /= m_DplusOne;
		m_DplusOne = 1.0;
		real_t scale = m_Dplus/m_DplusOne;
		return m_pNorm*scale*scale*TransferSq(k)*pow((double)k,(double)m_Cosmology.nspect);
	}
	
	//! integrand function for Calc_fPeebles
	/*!
	 * @sa Calc_fPeebles
	 */
	inline static double fy( double a, void *Params )
	{
		Cosmology *cosm = (Cosmology*)Params;
		double y = cosm->Omega_m*(1.0/a-1.0) + cosm->Omega_L*(a*a-1.0) + 1.0;
		return 1.0/pow(y,1.5);
	}
	
	//! calculates d log D+/d log a
	/*! this version follows the Peebles (TBD: add citation)
	 *  formula to compute Bertschinger's vfact
	 */
	inline real_t Calc_fPeebles( real_t a )
	{
		real_t y = m_Cosmology.Omega_m*(1.0/a-1.0) + m_Cosmology.Omega_L*(a*a-1.0) + 1.0;
		real_t fact = integrate( &fy, 1e-6, a, (void*)&m_Cosmology );
		return (m_Cosmology.Omega_L*a*a-0.5*m_Cosmology.Omega_m/a)/y - 1.0 + a*fy(a,(void*)&m_Cosmology)/fact;
	}
	
	//! Computes the linear theory growth factor D+
	/*! Function integrates over member function GrowthIntegrand */
	inline real_t CalcGrowthFactor( real_t a )
	{ 
		real_t eta =  sqrt((double)(m_Cosmology.Omega_m/a+m_Cosmology.Omega_L*a*a
								  +1.0-m_Cosmology.Omega_m-m_Cosmology.Omega_L));
		
		real_t integral = integrate( &GrowthIntegrand, 0.0, a, (void*)&m_Cosmology );
		return eta/a*integral;
	}
    
	//! Integrand used by function CalcGrowthFactor to determine the linear growth factor D+
	inline static double GrowthIntegrand( double a, void *Params )
	{
		Cosmology *cosm = (Cosmology*)Params;
		double eta = sqrt((double)(cosm->Omega_m/a+cosm->Omega_L*a*a
								   +1.0-cosm->Omega_m-cosm->Omega_L));
		return 2.5/(eta*eta*eta);
	}
	
	//! Compute the factor relating particle displacement and velocity
	real_t ComputeVFact_old( real_t a ){
		real_t fomega, dlogadt, eta;
		real_t Omega_k = 1.0 - m_Cosmology.Omega_m - m_Cosmology.Omega_L;
		
		real_t Dplus = CalcGrowthFactor( a );
		
		eta     = sqrt( (double)(m_Cosmology.Omega_m/a+ m_Cosmology.Omega_L*a*a + Omega_k ));
		fomega  = (2.5/Dplus-1.5*m_Cosmology.Omega_m/a-Omega_k)/eta/eta;
		dlogadt = a*eta;
		
		//... /100.0 since we would have to multiply by H0 to convert
		//... the displacement to velocity units. But displacement is
		//... in Mpc/h, and H0 in units of h is 100.
		return fomega * dlogadt/a *100.0;
	}
	
	real_t ComputeVFact( real_t a ){
		return Calc_fPeebles(a)*sqrt(m_Cosmology.Omega_m/a+m_Cosmology.Omega_L*a*a+1.0-m_Cosmology.Omega_m-m_Cosmology.Omega_L)*100.0;
	}
	
	real_t ComputedDdt( real_t a )
	{
		return Calc_fPeebles(a);
	}
	
	
	//! Integrand for the sigma_8 normalization of the power spectrum
	/*! Returns the value of the primordial power spectrum multiplied with 
	 the transfer function and the window function of 8 Mpc/h at wave number k */
	static double dSigma8( double k, void *Params )
	{
		if( k<=0.0 )
			return 0.0f;
		
		transfer_function *ptf = (transfer_function *)Params;
		
		double x = k*8.0;
		double w = 3.0*(sin(x)-x*cos(x))/(x*x*x);
		static double nspect = (double)ptf->cosmo_.nspect;
		
		double tf = ptf->compute(k);
		
		//... no growth factor since we compute at z=0 and normalize so that D+(z=0)=1
		return k*k * w*w * pow((double)k,(double)nspect) * tf*tf;
		
	}
	
	
	//! Computes the square of the transfer function
	/*! Function evaluates the supplied transfer function m_pTransferFunction
	 and returns the square of its value at wave number k
	 \param k wave number at which to evaluate the transfer function
	 */
	inline real_t TransferSq( real_t k ){
		//.. parameter supplied transfer function
		real_t tf1 = m_pTransferFunction->compute(k);
		return tf1*tf1;
	}
	
	
	//! Computes the normalization for the power spectrum
	/*!
	 * integrates the power spectrum to fix the normalization to that given
	 * by the sigma_8 parameter
	 */
	real_t ComputePNorm( real_t kmax )
	{
		real_t sigma0, kmin;
		kmax = m_pTransferFunction->get_kmax();//m_Cosmology.H0/8.0;
		kmin = m_pTransferFunction->get_kmin();//0.0;
		sigma0 = 4.0 * M_PI * integrate( &dSigma8, (double)kmin, (double)kmax, (void*)m_pTransferFunction );
		
		return m_Cosmology.sigma8*m_Cosmology.sigma8/sigma0;
		
	}
	
	
};


//! compute the jeans sound speed
/*! given a density in g/cm^-3 and a mass in g it gives back the sound
 *  speed in cm/s for which the input mass is equal to the jeans mass
 *  @params rho density 
 *  @params mass mass scale
 *  @return jeans sound speed
 */
inline double jeans_sound_speed( double rho, double mass )
{
	const double G = 6.67e-8;
	return pow( 6.0*mass/M_PI*sqrt(rho)*pow(G,1.5), 1.0/3.0 );
}

//! computes the density from the potential using the Laplacian
void compute_Lu_density( const grid_hierarchy& u, grid_hierarchy& fnew );

//! computes the 2nd order density perturbations using also off-diagonal terms in the potential Hessian 
void compute_LLA_density( const grid_hierarchy& u, grid_hierarchy& fnew, unsigned order=4 );

//! computes the source term for the 2nd order perturbations in the displacements
void compute_2LPT_source( const grid_hierarchy& u, grid_hierarchy& fnew, unsigned order=4 );



#endif // _COSMOLOGY_HH