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advanced_calc.py
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advanced_calc.py
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# entry point for the input form to pass values back to this script
def setValues(tH0,tWM,tWV,tz,tmnue,tmnumu,tmnutau,tw,twp,tT0):
H0 = tH0
h = H0/100
WM = tWM
WV = tWV
z = tz
WR = 2.477E-5/(h*h) # does not include neutrinos, T0 = 2.72528
WK = 1-WM-WR-WV
mnue = tmnue
mnumu = tmnumu
mnutau = tmnutau
w = tw
wp = twp
T0 = tT0
compute()
# tangential comoving distance
def DCMT(WK,DCMR):
import math
ratio = 1.00
x = math.sqrt(abs(WK))*DCMR
# document.writeln("DCMR = " + DCMR + "<BR>")
# document.writeln("x = " + x + "<BR>")
if (x > 0.1):
if (WK > 0) : ratio = 0.5*(math.exp(x)-math.exp(-x))/x
else: ratio = math.sin(x)/x
# document.writeln("ratio = " + ratio + "<BR>")
y = ratio*DCMR
return y
y = x*x
# statement below fixed 13-Aug-03 to correct sign error in expansion
if (WK < 0): y = -y
ratio = 1 + y/6 + y*y/120
# document.writeln("ratio = " + ratio + "<BR>")
y= ratio*DCMR
return y
# comoving volume computation
def VCM(WK,DCMR):
import math
ratio = 1.00
x = math.sqrt(abs(WK))*DCMR
if (x > 0.1) :
if (WK > 0) : ratio = (0.125*(math.exp(2*x)-math.exp(-2*x))-x/2)/(x*x*x/3)
else: ratio =(x/2 - math.sin(2*x)/4)/(x*x*x/3)
y = ratio*DCMR*DCMR*DCMR/3
return y
y = x*x
# statement below fixed 13-Aug-03 to correct sign error in expansion
if (WK < 0): y = -y
ratio = 1 + y/5 + (2/105)*y*y
y = ratio*DCMR*DCMR*DCMR/3
return y
# function to give neutrino density over rest mass density
def nurho(mnurel,mnu):
import math
y = math.pow(1+math.pow(mnurel/mnu,1.842),1.0/1.842)
return y
# calculate the actual results
def compute(z,w,WM=0.27,WV=0.73):
i=0 # index
n=1000 # number of points in integrals
nda = 1 # number of digits in angular size distance
H0 = 71. # Hubble constant
#WM = 0.27 # Omega(matter)
#WV = 0.73 # Omega(vacuum) or lambda
WR = 0. # Omega(radiation)
WK = 0. # Omega curvaturve = 1-Omega(total)
Wnu = 0. # Omega from massive neutrinos
#z = 3.0 # redshift of the object
h = 0.71 # H0/100
mnue = 0.001 # mass of electron neutrino in eV
mnumu = 0.009 # mass of muon neutrino in eV
mnutau = 0.049 # mass of tau neutrino in eV
we = mnue/93. # Omega(nu(e))h^2
wmu = mnumu/93. # Omega(nu(mu))h^2
wtau = mnutau/93. # Omega(nu(tau))h^2
mnurel = 0.0005 # mass of neutrino that is just now relativistic in eV
T0 = 2.72528 # CMB temperature in K
c = 299792.458 # velocity of light in km/sec
Tyr = 977.8 # coefficent for converting 1/H into Gyr
DTT = 0.5 # time from z to now in units of 1/H0
DTT_Gyr = 0.0 # value of DTT in Gyr
age = 0.5 # age of Universe in units of 1/H0
age_Gyr = 0.0 # value of age in Gyr
zage = 0.1 # age of Universe at redshift z in units of 1/H0
zage_Gyr = 0.0 # value of zage in Gyr
DCMR = 0.0 # comoving radial distance in units of c/H0
DCMR_Mpc = 0.0
DCMR_Gyr = 0.0
DA = 0.0 # angular size distance
DA_Mpc = 0.0
DA_Gyr = 0.0
kpc_DA = 0.0
DL = 0.0 # luminosity distance
DL_Mpc = 0.0
DL_Gyr = 0.0 # DL in units of billions of light years
V_Gpc = 0.0
a = 1.0 # 1/(1+z), the scale factor of the Universe
az = 0.5 # 1/(1+z(object))
#w = -1. # equation of state, w = P/(rno*c^2)
wp = 0. # rate of change of equation of state, w(a) = w+2*wp*(1-a)
# following Linder, astro-ph/040250
import math
h = H0/100.
WR = 2.477E-5*math.pow(T0/2.72528,4)/(h*h) # no neutrinos
# avoid dividing by zero neutrino mass
if (mnue < 0.00001): mnue = 0.00001
if (mnumu < 0.00001): mnumu = 0.00001
if (mnutau < 0.00001): mnutau = 0.00001
# rest mass omega*h^2 for the three neutrino types
we = (mnue/93.64)*math.pow(T0/2.72528,3)
wmu = (mnumu/93.90)*math.pow(T0/2.72528,3)
wtau = (mnutau/93.90)*math.pow(T0/2.72528,3)
# mass of nu that is just now relativistic
# evaluates at 3.151*kT with T = (4/11)^(1/3)*To and To=2.72528
# This is 6.13 K, and 1 eV is 11604.5 K
mnurel = 6.13*(T0/2.72528)/11604.5
Wnu = (we*nurho(mnurel,mnue)+wmu*nurho(mnurel,mnumu)+wtau*nurho(mnurel,mnutau))/(h*h)
WK = 1-WM-WR-WV
WM = WM-Wnu
az = 1.0/(1+1.0*z)
age = 0
# do integral over a=1/(1+z) from 0 to az in n steps, midpoint rule
for i in range(n): #(i = 0 i != n i++) {
a = az*(i+0.5)/n
# rho(DE) = a^{-3-3*w_o-6*w'}*exp(6*w'*(a-1))*rho_o(DE)
# based on w = w_o+w_a*(1-a) with w_a = 2*w': Linder astro-ph/0402503
rhoV = WV*math.pow(a,-3-3*w-6*wp)*math.exp(6*wp*(a-1))
# get neutrino density corrected for kT/mc^2 by using lower mass
# instead of higher T:
Wnu = (we*nurho(mnurel,mnue*a)+wmu*nurho(mnurel,mnumu*a)+wtau*nurho(mnurel,mnutau*a))/(h*h)
adot = math.sqrt(WK+((WM+Wnu)/a)+(WR/(a*a))+(rhoV*a*a))
age = age + 1/adot
zage = az*age/n
# correction for annihilations of particles not present now like e+/e-
# added 13-Aug-03 based on T_vs_t.f
lpz = math.log((1+1.0*z))/math.log(10.0)
dzage = 0
if (lpz > 7.500): dzage = 0.002 * (lpz - 7.500)
if (lpz > 8.000): dzage = 0.014 * (lpz - 8.000) + 0.001
if (lpz > 8.500): dzage = 0.040 * (lpz - 8.500) + 0.008
if (lpz > 9.000): dzage = 0.020 * (lpz - 9.000) + 0.028
if (lpz > 9.500): dzage = 0.019 * (lpz - 9.500) + 0.039
if (lpz > 10.000): dzage = 0.048
if (lpz > 10.775): dzage = 0.035 * (lpz - 10.775) + 0.048
if (lpz > 11.851): dzage = 0.069 * (lpz - 11.851) + 0.086
if (lpz > 12.258): dzage = 0.461 * (lpz - 12.258) + 0.114
if (lpz > 12.382): dzage = 0.024 * (lpz - 12.382) + 0.171
if (lpz > 13.055): dzage = 0.013 * (lpz - 13.055) + 0.188
if (lpz > 14.081): dzage = 0.013 * (lpz - 14.081) + 0.201
if (lpz > 15.107): dzage = 0.214
zage = zage*10.0**dzage
#
zage_Gyr = (Tyr/H0)*zage
DTT = 0.0
DCMR = 0.0
# do integral over a=1/(1+z) from az to 1 in n steps, midpoint rule
for i in range(n):
a = az+(1-az)*(i+0.5)/n
rhoV = WV*math.pow(a,-3-3*w-6*wp)*math.exp(6*wp*(a-1))
Wnu = (we*nurho(mnurel,mnue*a)+wmu*nurho(mnurel,mnumu*a)+wtau*nurho(mnurel,mnutau*a))/(h*h)
adot = math.sqrt(WK+((WM+Wnu)/a)+(WR/(a*a))+(rhoV*a*a))
DTT = DTT + 1/adot
DCMR = DCMR + 1/(a*adot)
#print az
DTT = (1-az)*DTT/n
DCMR = (1-az)*DCMR/n
age = DTT+zage
age_Gyr = age*(Tyr/H0)
DTT_Gyr = (Tyr/H0)*DTT
DCMR_Gyr = (Tyr/H0)*DCMR
DCMR_Mpc = (c/H0)*DCMR
DA = az*DCMT(WK,DCMR)
DA_Mpc = (c/H0)*DA
kpc_DA = DA_Mpc/206.264806
DA_Gyr = (Tyr/H0)*DA
DL = DA/(az*az)
DL_Mpc = (c/H0)*DL
DL_Gyr = (Tyr/H0)*DL
V_Gpc = 4*math.pi*math.pow(0.001*c/H0,3)*VCM(WK,DCMR)
#print 'z',z,'DA_Mpc',DA_Mpc
return DCMR
if __name__ == '__main__':
import pylab
cluster_z_low = 0.2
cluster_z_high = 0.6
for cluster_z in [0.2,0.3,0.55]: #,1.2]:
for w in [-1]: #.5,-1,-0.5,]:
d_cluster_low = compute(cluster_z_low,w)
d_cluster_high = compute(cluster_z_high,w)
d_cluster = compute(cluster_z,w)
refer = (compute(0.8,w) - d_cluster)/compute(0.8,w)
import scipy
ratios_save = []
zs = []
for z in scipy.arange(cluster_z,3.,0.1):
zs.append(z)
s = compute(z,w)
#ratio = (d_cluster_high/(1+cluster_z_high))/(d_cluster_low/(1+cluster_z_low))*(s - d_cluster_high)/(s - d_cluster_low)
ratio = (d_cluster_high/(1+cluster_z_high))/(d_cluster_low/(1+cluster_z_low))*(s - d_cluster_high)/(s - d_cluster_low)
#nprint ratio, s, d_cluster, z
#ratios.append(ratio)
ratios_save.append((compute(z,w) - d_cluster)/compute(z,w)/refer)
for w in [-1.5,-1,-0.5,]:
d_cluster_low = compute(cluster_z_low,w)
d_cluster_high = compute(cluster_z_high,w)
d_cluster = compute(cluster_z,w)
refer = (compute(0.8,w) - d_cluster)/compute(0.8,w)
import scipy
ratios = []
zs = []
i = 0
for z in scipy.arange(cluster_z,3.,0.1):
zs.append(z)
s = compute(z,w)
#ratio = (d_cluster_high/(1+cluster_z_high))/(d_cluster_low/(1+cluster_z_low))*(s - d_cluster_high)/(s - d_cluster_low)
ratio = (d_cluster_high/(1+cluster_z_high))/(d_cluster_low/(1+cluster_z_low))*(s - d_cluster_high)/(s - d_cluster_low)
#print ratio, s, d_cluster, z
#ratios.append(ratio)
ratios.append((compute(z,w) - d_cluster)/compute(z,w)/refer/ratios_save[i])
i += 1
pylab.plot(scipy.array(zs), scipy.array(ratios))
pylab.savefig('shearratio.pdf')
pylab.show()
def compute_cube():
import scipy
dict = {}
for w in [-1]: #scipy.arange(-2,2,0.1):
for WM in [0.3]: #scipy.arange(0,1,0.1#):
WV = 1 - WM
for z in scipy.arange(0,2.5,0.01):
d = compute(z,w,WM,WV)
dict['%.2f' % z + '_' + '%.2f' % w + '_' + '%.2f' % WM] = d #str(z) + '_' + str(w) + '_' + str(WM)] = d
print d, z, w, WM, WV
print dict.keys()
import pickle
f = open('DA.pickle','w')
m = pickle.Pickler(f)
pickle.dump(dict,m)
f.close()
def dist_ratio(zs,cluster_z=0.55,w=-1.,omega_m=0.27,omega_lambda=0.73):
import pylab
#cluster_z = 0.55
ratios = []
for z in zs:
d_cluster = compute(cluster_z,w,omega_m,omega_lambda)
ratios.append((compute(z,w) - d_cluster)/compute(z,w,omega_m,omega_lambda))
import scipy
return scipy.array(ratios)