def boost(Mh,mv=10**-2,a=10**-1,nosomm=0,gamma=1,einasto=0,mo=10**-6,bo=0.,n=-0.9,q=0.1,A=2.3*10**-2,C=2.5*10**-2,K1=10.5,K2=-.11):
"""Calculates the boost factor for a given halo mass
Input:
Mh - Halo mass
mv - force carrier mass (/mchi)
a - new force fine structure constant
gamma - GNFW gamma or Einasto gamma
einasto - if 0 GNFW, 1 Einasto
mo - free-streaming limit
bo - boost at mo
n - mass function exponent
q - mass fraction until which to integrate
A - normalization of mass function
C - normalization of sigma(m) relation
K1 - normalization of concentration-mass relation
K2 - exponent of concentration-mass relation
nosomm - DON'T include Sommerfeld enhancement
Output:
boost
"""
if nosomm == 0:
#To speed up the calculation, first find where the Sommerfeld enhancement saturates, and pass that value to the differential equation to use for smaller velocities.
vdisp_Mh= C*pow(Mh,1./3.)/(3*10**5)
vdisp_mo= C*pow(mo,1./3.)/(3*10**5)
vdisps=[vdisp_Mh,vdisp_Mh*10**-1,vdisp_Mh*10**-2,vdisp_Mh*10**-3,vdisp_Mh*10**-4,vdisp_Mh*10**-5,vdisp_Mh*10**-6,vdisp_Mh*10**-7,vdisp_Mh*10**-8,vdisp_Mh*10**-9,vdisp_Mh*10**-10]
#vdisps=[10**-2,10**-3,10**-4,10**-5,10**-6,10**-7,10**-8,10**-9,10**-10,10**-11,10**-12]
somms=zeros(11)
indx=0
for ii in range(11):
if vdisps[ii] < vdisp_mo:
break
somms[ii]= avg_enhance(mv,1.,a,vdisps[ii])
if ii > 0:
if somms[ii] <= 1.1*somms[ii-1]:
break
else:
indx+= 1
vdisp_sat= vdisps[indx]
somm_sat= somms[indx]
else:
vdisp_sat=10*Mh
somm_sat= 1
start= mo
end= Mh
y0= bo
time=[start,end]
y= integrate.odeint(deriv,y0,time,args=(mv,a,gamma,einasto,n,q,A,C,K1,K2,vdisp_sat,somm_sat),mxstep=10**8)
return y[1]
if data['nas'] != nas:
print "Warning: suppplied nas does not equal savefile nas"
sys.exit(-1)
mv= data['mv']
a= data['a']
redboostS= data['redboostS']
print 'restarting at ii= '+str(ii)+', jj= '+str(jj)+', at iteration '+str(ii*nas+jj+1)+'/'+str(nms*nas)
else:
redboostS= zeros((nms,nas))
ii= 0
jj= 0
savefile=open(savefilename,'w')
while ii < nms:
while jj < nas:
somm= avg_enhance(mv[ii],m,a[jj],vdisp)
redboostS[ii,jj]= boostS[ii,jj]-log10(somm*(1.0+subboost))
#print boostS[ii,jj], log10(somm*(1+subboost))
sys.stdout.write('\r'+str(ii*nas+jj+1)+'/'+str(nms*nas))
sys.stdout.flush()
jj= jj+1
data={'mv':mv,'a':a,'redboostS':redboostS,'nms':nms,'nas':nas,'ii':ii,'jj':jj}
savefile.seek(0,0)
pickle.dump(data,savefile)
savefile.flush()
ii= ii+1
jj= 0
sys.stdout.write('\n')
#Now plot the result
lumdata.append(VLdata[ii,8])
lumdata.append(VLdata[ii,9])
rs= VLdata[ii,4]/2.16258
if rs > VLdata[ii,6]:
print "Warning: rs outside of tidal radius"
rhos= 8.56*10**4/pow(rs,2.)*pow(VLdata[ii,3],2.)
lumdata.append(4.63*10**-24*pow(rhos,2.)*pow(rs,3.)*7.*pi/6.)
#calculate total mass within rs
mass= 4.*pi*rhos*pow(rs,3.)*massfactor
boo= boost(mass,mv,a,0,1,0,mo,bo)
mo= mass
bo= boo
lumdata.append(boo)
lumdata.append(boost(mass,mv,a,1))
vdisp= 2.5*10**-2*pow(mass,1./3.)/(3*10**5)
lumdata.append(avg_enhance(mv,1.,a,vdisp))
lumdata.append(rs)
lumdata.append(rhos)
lumdata.append(mass)
sys.stdout.write('\n')
#Now put them in a nice matrix form
print "Number of bound subhalos:"
print nlums
sublum= zeros((nlums,natt))
for ii in range(nlums):
for jj in range(natt):
sublum[ii,jj]= lumdata[ii*natt+jj]
#Calculate the actual luminosities and distances etc for different fiducial observers
#sublumobs holds: distance_from_earth, luminosity, total_boost, reduced_boost, rs, rhos, mass
natt2= 7
sublumobs= zeros((nobs,nlums,natt2))
if data['nas'] != nas:
print "Warning: suppplied nas does not equal savefile nas"
sys.exit(-1)
mv= data['mv']
a= data['a']
S= data['S']
print 'restarting at ii= '+str(ii)+', jj= '+str(jj)+', at iteration '+str(ii*nas+jj+1)+'/'+str(nms*nas)
else:
S= zeros((nms,nas))
ii= 0
jj= 0
savefile=open(savefilename,'w')
while ii < nms:
while jj < nas:
S[ii,jj]= log10(avg_enhance(mv[ii],m,a[jj],b))
sys.stdout.write('\r'+str(ii*nas+jj+1)+'/'+str(nms*nas))
sys.stdout.flush()
jj= jj+1
data={'mv':mv,'a':a,'S':S,'nms':nms,'nas':nas,'ii':ii,'jj':jj}
savefile.seek(0,0)
pickle.dump(data,savefile)
savefile.flush()
ii= ii+1
jj= 0
sys.stdout.write('\n')
#Plotting parameters
fig_width = 3.25 # width in inches
def deriv(y,t,mv,a,gamma,einasto,n,q,A,C,K1,K2,vdisp_sat,somm_sat):
"""Implements the right hand side of the boost differential equation
Input:
y - current dependent variable value
t - current independent variable
mv - force carrier mass (/mchi)
a - new force fine structure constant
gamma - GNFW gamma or Einasto gamma
einasto - if 0 GNFW, 1 Einasto
n - mass function exponent
q - mass fraction until which to integrate
A - normalization of mass function
C - normalization of sigma(m) relation
K1 - normalization of concentration-mass relation
K2 - exponent of concentratio-mass relation
vdisp_sat - velocity dispersion at which the Sommerfeld enhancement saturates
somm_sat - saturated value of the Sommerfeld enhancement
Output:
derivative
"""
#Calculate each factor/term in turn
#First calculate the concentration
conc= K1*pow(t,K2)/pow(10.,K2*12)
concq= K1*pow(q*t,K2)/pow(10,K2*12)
#First up, L(qM)/L(M)
LL= pow(q,3.*K2+1.)
if einasto == 1:
fc= special.gammainc(3./gamma,2./gamma*pow(conc,gamma))
LL*= pow(fc,2)#we don't need to add gamma(3/gamma) since this would get divided out
LL/= pow(special.gammainc(3./gamma,2./gamma*pow(concq,gamma)),2)#we don't need to add gamma(3/gamma) since this would get divided out
fc*= special.gamma(3./gamma)*1./gamma*exp((3.*log(gamma)+2.-log(8.))/gamma)
#dlnLdlnM= 1.+3.*K2+2.*conc/fc*K2*(pow(2,3./gamma)*pow(gamma,1.-3./gamma)*pow(conc,2.)*exp(-2./gamma*pow(conc,gamma)))
dlnLdlnM= 1.+3.*K2-2.*conc/fc*K2*(pow(conc,2.)*exp(2./gamma*(1.-pow(conc,gamma))))
# print -2.*conc/fc*K2*(pow(conc,2.)*exp(2./gamma*(1.-pow(conc,gamma))))
# print special.gammainc(3./gamma,2./gamma*pow(conc,gamma))
# print fc
# print (pow(conc,2.)*exp(2./gamma*(1.-pow(conc,gamma)))), (pow(conc,2.-gamma)*pow(1.+conc,gamma-3.))
# print dlnLdlnM
else:
if gamma == 1:
fc= log(1.+conc)-conc/(1.+conc)
LL*= pow(fc,2)#This is only valid for NFW
LL/= pow(log(1+concq)-concq/(1.+concq),2)#This is only valid for NFW
else:
fc= special.hyp2f1(3.-gamma,3.-gamma,4.-gamma,-conc)*pow(conc,3.-gamma)/(3.-gamma)
LL*= pow(fc,2)
LL/= pow(special.hyp2f1(3.-gamma,3.-gamma,4.-gamma,-concq)*pow(concq,3.-gamma)/(3.-gamma),2)
dlnLdlnM= 1.+3.*K2-2.*conc/fc*K2*(pow(conc,2.-gamma)*pow(1.+conc,gamma-3.))
# print (pow(conc,2.)*exp(2./gamma*(1.-pow(conc,gamma)))), (pow(conc,2.-gamma)*pow(1.+conc,gamma-3.))
# print -2.*conc/fc*K2*(pow(conc,2.-gamma)*pow(1.+conc,gamma-3.))
# print dlnLdlnM
vdisp= C*pow(t,1./3.)/(3*10**5)
if vdisp <= vdisp_sat:
somm= somm_sat
#somm= 1
else:
somm= avg_enhance(mv,1.,a,vdisp,10)
#somm= 1
#somm= enhance(mv,1.,a,vdisp)
#Now that we have everything, calculate dB/dM
return 1./(1.+(1.-q)*LL) * 1./t * (A*pow(q,n)*(somm+y)*LL - n*y-y*dlnLdlnM)