Example #1
0
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
Example #3
0
     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))
Example #4
0
    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
Example #5
0
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)