// EWTemperature computes the emission-wieghted temperature of a halo
// integrated out to the specified radius. Here, the emission-weighted
// temperature is:
//
// int dr r**2 rhoG**2 * Lambda * T / int dr r**2 * rhoG**2 * Lambda
//
// Here, Lambda is a cooling coefficient taken to be proportional to
// sqrt(T) and the temperature is calculated from the pressure profile which
// is specified by pbt and ppt. bt is necceary because we're using PV = nRT
// and thus need ot figure out the
//
// Return value is in keV.
func (h *Halo) EWTemperature(bt BiasType, pbt PressureBiasType, ppt PressureProfileType, rMax float64) float64 {
rMin := h.MinR()
scale := math.Log10(rMax) - math.Log10(rMin)
numFunc := createNumFunc(h, pbt, ppt, bt)
numInt := num.Integral(numFunc, rMin, scale, num.Log, num.Spherical)
denFunc := createDenFunc(h, pbt, ppt, bt)
denInt := num.Integral(denFunc, rMin, scale, num.Log, num.Spherical)
return numInt(rMax) / denInt(rMax)
}
// ThomsonY calculates the spherical Thompson Y out to the specified radius.
func (h *Halo) ThompsonY(pbt PressureBiasType, ppt PressureProfileType, r float64) float64 {
P := func(r float64) float64 {
return h.Pressure(pbt, ppt, ElectronPressure, r)
}
intTerm := num.Integral(P, h.MinR(), h.Rs, num.Log, num.Spherical)(r)
constTerm := cosmo.SigmaTMks / (cosmo.MeMks * cosmo.CMks * cosmo.CMks)
return intTerm * constTerm * cosmo.MpcMks
}
// DFluctuaction gives the linear growth rate of density fluctuations at
// a = 1 / (1 + z).
func DFluctuation(a float64) float64 {
x := pradaX(a)
term1 := (5.0 / 2.0) * math.Pow(OmegaM/OmegaL, 1.0/3.0)
term2 := math.Sqrt((1.0 + x*x*x) / (x * x * x))
dimlessIntegral := num.Integral(func(xp float64) float64 {
return xp / math.Pow(1.0+xp*xp*xp, 1.5)
}, 0, x, num.Linear, num.Flat)
return term1 * term2 * dimlessIntegral(x)
}
// GasEnclosed returns the mass of all the gas in a halo enclosed within the
// given radius. The returned value is given in MSolar.
func (h *Halo) GasEnclosed(bt BiasType, pbt PressureBiasType, ppt PressureProfileType, r float64) float64 {
rho := func(r float64) float64 { return h.RhoGas(bt, pbt, ppt, r) }
return num.Integral(rho, h.MinR(), 0.1, num.Log, num.Spherical)(r)
}