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model.py
445 lines (399 loc) · 16.6 KB
/
model.py
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import numpy as np
from scipy import integrate
from scipy import interpolate
import cosmology
import nfw as NFW
from astropy.io import ascii
import sedov
import pylab as plt
import cPickle as pickle
#from pylab import *
#import seaborn as sns
def ufunclike(f,x):
return np.array(map(f, np.array(np.ravel(x))))
def _zero(t):
return 0
def L(t):
return ufunclike(_zero,t)
class MFR01(object):
def __init__(self,Mvir,zvir,c=None,h=0.7,Om=0.3,Ol=0.7,Ob=0.05,
L=L,n_flat=0.1,useiso=True,useflat=False,usechampagne=False,T0 = 10**4):
self.R_SN = {}
self.t_SN = {}
self.Mvir = Mvir; self.zvir = zvir; self.c = c
self.h = h; self.Om = Om; self.Ol = Ol; self.Ob = Ob
fb = Ob/Om; self.fb = fb
self.L = L
# Set up cooling table
coolingtable = 'cooling/m-30.cie'
tab = ascii.read(coolingtable,header_start=1)
_CoolingInt = interpolate.interp1d(np.concatenate(([3.93],tab['log(T)'])),np.concatenate(([-28],tab['log(lambda norm)'])))
def _Cooling(logT):
if logT<=(3.93+.146128): return -28 # extrapolate at flat
if logT>(8.5+.146128): return -22.47 # extrapolate at flat
return _CoolingInt(logT-.146128)
def Cooling(T):
# Tbar = 5/7 T_c
logT = np.log10(np.ravel(T))
logT[~np.isfinite(logT)] = 3.
return 10**ufunclike(_Cooling,logT)
self._CoolingInt=_CoolingInt; self._Cooling = _Cooling; self.Cooling = Cooling
# Set up ambient gas density/pressure
cosm = cosmology.cosmology(Om=Om,Ol=Ol,h=h); self.cosm = cosm
nfw = NFW.NFW(Mvir,zvir,c,cosm); self.nfw = nfw
self.c = nfw.c
Rvir = nfw.Rvir * nfw.kpc
Tion = T0 #K
rho_flat = n_flat*nfw.mbar
if useiso:
def n_iso(r): #r in cm
return 10.**(-2*np.log10(r/nfw.kpc) - 3) * nfw.Tvir/1211. #scale by CM14 Tvir
r_iso = 10**(-(np.log10(n_flat*1211./nfw.Tvir)+3)/2.)*nfw.kpc #cm
def _rho0(r): #r in cm
if r < r_iso: return rho_flat
return n_iso(r)*nfw.mbar
self.r_iso = r_iso; self.n_iso = n_iso
elif useflat:
def _rho0(r):
return rho_flat
elif usechampagne:
import champagne
tau_1Myr = 1.e6 * 3.16e7
kB = 1.38e-16
cion = np.sqrt(kB*Tion/(0.59 * nfw.mp))
cdat = np.load('champagne.npy')
c_x = cdat[:,0]; c_a = cdat[:,1]
c_narr = champagne.n_(c_a,tau_1Myr)
tau_flat = np.sqrt(c_narr[0]/n_flat) * tau_1Myr
print n_flat,tau_flat/tau_1Myr
c_rarr = c_x * cion * tau_flat
c_narr = champagne.n_(c_a,tau_flat)
# extend down to r=0 at nflat
c_rarr = np.concatenate([[0],c_rarr])
c_narr = np.concatenate([[c_narr[0]],c_narr])
c_interp = interpolate.interp1d(c_rarr,c_narr)
c_rmax = c_rarr[-1]
rhoIGM = cosm.rho_m(zvir)/6.
nIGM = rhoIGM/nfw.mbar
rIGM = 10**((np.log10(nIGM*1211./nfw.Tvir)+3.)/-2.)*nfw.kpc
self.rhoIGM = rhoIGM; self.nIGM = nIGM; self.rIGM = rIGM
def n_iso(r): #r in cm
return 10.**(-2*np.log10(r/nfw.kpc) - 3) * nfw.Tvir/1211. #scale by CM14 Tvir
def _rho0(r):
if r < c_rmax: return c_interp(r)*0.59*nfw.mp
if r > rIGM: return rhoIGM
return n_iso(r)*0.59*nfw.mp
self.c_interp = c_interp; self.c_rmax = c_rmax
self.n_iso = n_iso
else:
rhoIGM = cosm.rho_m(zvir)/6.
def _rho0(r): #r in cm
if r < Rvir: return rho_flat
return (rho_flat-rhoIGM)*np.exp(-(r-Rvir)/(1.2*Rvir))+rhoIGM
self.rhoIGM = rhoIGM
def rho0(r):
return ufunclike(_rho0,r)
self.Rvir = Rvir; self.Tion = Tion
self.rho_flat = rho_flat; self.n_flat = n_flat
self.useiso = useiso
self.usechampagne = usechampagne
_rarr = np.arange(0,300*nfw.Rvir,.001)[1:]*nfw.kpc
_rhoarr = rho0(_rarr)
_rho0interp = interpolate.UnivariateSpline(_rarr, _rhoarr, s=0)
_rho0pinterp= _rho0interp.derivative()
_rho0parr = _rho0pinterp(_rarr)
_rho0ratio = _rho0parr/_rhoarr
_rho0ratiointerp = interpolate.UnivariateSpline(_rarr, _rho0ratio, s=0)
def rho0ratio(r):
return _rho0ratiointerp(r)
#minrho0p = np.abs(np.min(np.diff(_rhoarr))/np.min(np.diff(_rarr)))
#def _rho0p(r):
# out = np.abs(_rho0pinterp(r))
# if out < minrho0p: return 0
# return out
#def rho0p(r): #derivative of rho0
# return ufunclike(_rho0p,r)
if useiso:
def _P0(r):
if r < r_iso: return rho0(r)*nfw.kB*Tion/nfw.mbar #ionized
else: return rho0(r)*nfw.kB*nfw.Tvir/(1.23 * nfw.mp) #neutral
def P0(r):
return ufunclike(_P0,r)
self.cvir = np.sqrt(nfw.kB * nfw.Tvir / (1.23 * nfw.mp)) #cm/s
self._P0 = _P0; self.P0 = P0
elif useflat:
def P0(r):
return rho0(r)*nfw.kB*Tion/nfw.mbar
self.cvir = np.sqrt(nfw.kB * Tion / (1.23 * nfw.mp)) #cm/s
self.P0 = P0
elif usechampagne:
def _P0(r):
return rho0(r)*nfw.kB*Tion/nfw.mbar
#if r < c_rmax: return rho0(r)*nfw.kB*Tion/nfw.mbar #ionized
#else: return rho0(r)*nfw.kB*nfw.Tvir/(1.23 * nfw.mp) #neutral
def P0(r):
return ufunclike(_P0,r)
self.cvir = np.sqrt(nfw.kB * nfw.Tvir / (1.23 * nfw.mp)) #cm/s
self._P0 = _P0; self.P0 = P0
else:
def P0(r): #cgs: erg/cm^3
return rho0(r)*nfw.kB*Tion/nfw.mbar
self.P0 = P0
self._rarr = _rarr; self._rhoarr = _rhoarr
self._rho0interp = _rho0interp; self._rho0pinterp = _rho0pinterp
self._rho0 = _rho0; self.rho0 = rho0
#self._rho0p = _rho0p; self.rho0p = rho0p
self._rho0parr = _rho0parr
self._rho0ratio = _rho0ratio
self._rho0ratiointerp = _rho0ratiointerp
self.rho0ratio = rho0ratio
def Pb(E,R):
return E/(2*np.pi*R**3)
def nbar(R,E,T):
return 5./3 * self.Pb(E,R)/(self.nfw.kB * T) #5/3 n_c
def vdot(y,t): #Rdotdot
v,R,E,T = y
return 3*(Pb(E,R)-P0(R))/(R*rho0(R)) - 3*v*v/R - v*v*rho0ratio(R) - nfw.Gc*nfw.Msun*nfw.Mltr(R/nfw.kpc)/(R**2)
#def vdot(y,t): #if only including gravity from uniform gas, for useflat
# v,R,E,T = y
# return 3*(Pb(E,R)-P0(R))/(R*rho0(R)) - 3*v*v/R - v*v*rho0p(R)/rho0(R) - 4*np.pi*nfw.Gc*n_flat*1.23*nfw.mp*R/3
def Rdot(y,t):
return y[0]
def Edot(y,t):
v,R,E,T = y
return -4*np.pi*R*R*Pb(E,R)*v +L(t) - (4*np.pi*R**3/3)*(nbar(R,E,T)**2)*Cooling(T)
eta=6e-7 #cgs
C1 = 16*np.pi*nfw.mbar*eta/(25.*nfw.kB)
C2 = 125*np.pi*nfw.mbar/39.
def Tdot(y,t):
v,R,E,T = y
return 3*T*v/R + T*Pdot(y,t)/Pb(E,R) - (2.3)*(C1/C2)*T**(4.5)*nfw.kB/(R*R*Pb(E,R))
def Pdot(y,t):
v,R,E,T = y
return Edot(y,t)/(2*np.pi*R**3) - 3*E*v/(2*np.pi*R**4)
def ydot(y,t):
if y[0] <= 0: return [0,0,0,0]
return [vdot(y,t),Rdot(y,t),Edot(y,t),Tdot(y,t)]
self.eta = eta; self.C1 = C1; self.C2 = C2
self.Pb = Pb; self.nbar = nbar
self.vdot = vdot; self.Rdot = Rdot; self.Edot = Edot
self.Tdot = Tdot; self.Pdot = Pdot
self.ydot = ydot
def run_model(self,Ei,tmax=100,dt=.005):
nfw = self.nfw
st = sedov.sedov(self.rho_flat,Ei)
ti = 10000.*3e7 #10^4 years to seconds
Ri = st.Rs(ti); vi = st.us(ti)
Ti = self.Pb(Ei,Ri)/(nfw.kB * (self.rho_flat/nfw.mbar))
#if Ti > 10**8.5:
#print "WARNING: Ti = {0:.2e}, setting to 1e8.5".format(Ti)
#Ti = 10**8.5
#pass
tmin = ti/(3e7*1e6)
tarr = np.arange(tmin,tmax+dt,dt)*(3e7 * 1e6)
# setup initial conditions
y0 = [vi,Ri,Ei,Ti] #cgs units
# integration
yout,out = integrate.odeint(self.ydot, y0, tarr,full_output=True)
tarr = tarr/(3e7 * 1e6)
varr = yout[:,0]/1e5
Rarr = yout[:,1]/nfw.kpc
Earr = yout[:,2]/1e51
Tarr = yout[:,3]
if not self.useiso and not self.usechampagne:
ii = varr <= 0
else:
ii = varr <= self.cvir/ 1e5
try:
iimax = np.min(np.where(ii)[0])
except ValueError:
iimax = len(ii)
ii = np.zeros(len(ii)).astype(bool)
ii[0:iimax] = True
tarr = tarr[ii]; varr = varr[ii]; Rarr = Rarr[ii]; Earr = Earr[ii]; Tarr = Tarr[ii]
self.R_SN[Ei] = np.nanmax(Rarr); self.t_SN[Ei] = np.nanmax(tarr)
return tarr,varr,Rarr,Earr,Tarr
def plot_model(self,tarr,varr,Rarr,Earr,Tarr,fig=None,**kwargs):
if fig==None:
fig,axarr = plt.subplots(3,2,figsize=(8,8))
else:
axarr = np.reshape(fig.axes,(3,2))
l, = axarr[0,0].plot(tarr,Rarr,**kwargs)
axarr[0,0].set_xlabel('t (Myr)')
axarr[0,0].set_ylabel('R (kpc)')
axarr[0,1].plot(tarr,varr,**kwargs)
axarr[0,1].plot(tarr,[self.cvir/1.e5 for t in tarr],'k:')
axarr[0,1].set_xlabel('t (Myr)')
axarr[0,1].set_ylabel('v (km/s)')
axarr[0,1].set_yscale('log')
axarr[1,0].plot(tarr,Earr,**kwargs)
axarr[1,0].set_xlabel('t (Myr)')
axarr[1,0].set_ylabel('E_51')
axarr[1,0].set_yscale('log')
axarr[1,1].plot(tarr,Tarr,**kwargs)
axarr[1,1].set_xlabel('t (Myr)')
axarr[1,1].set_ylabel('T [k]')
axarr[1,1].set_yscale('log')
axarr[2,0].plot(tarr,self.rho0(Rarr*self.nfw.kpc),**kwargs)
axarr[2,0].set_xlabel('t (Myr)')
axarr[2,0].set_ylabel('rho0 (g/cc)')
axarr[2,0].set_yscale('log')
axarr[2,1].plot(tarr,self.Pb(Earr*1e51,Rarr*self.nfw.kpc),**kwargs)
axarr[2,1].plot(tarr,self.P0(Rarr*self.nfw.kpc),**kwargs)
axarr[2,1].set_xlabel('t (Myr)')
axarr[2,1].set_ylabel('Pb,P0 (erg/cc)')
axarr[2,1].set_yscale('log')
return l
if __name__=="__main__":
zvir = 25
Mvir = 1e6
#zvir = 20
#Mvir = 5.e5
ESNarr = 10**np.array([50,50.5,51,51.5,52,52.5,53])
nflatarr = 10**np.array([0,-.5,-1,-1.5,-2])
#nflatarr = 10**np.array([-.5])
modelarr = [MFR01(Mvir,zvir,n_flat=n_flat,useiso=False,useflat=False,usechampagne=True) for n_flat in nflatarr]
for model in modelarr:
for Ei in ESNarr:
model.run_model(Ei,tmax=5000)
nfw = modelarr[0].nfw
fig,ax = plt.subplots()
output = []
for nflat,model in zip(nflatarr,modelarr):
Rarr = [model.R_SN[Ei] for Ei in ESNarr]
ax.plot(ESNarr,Rarr,'o-',label=r'$\log n_{flat}$='+str(round(np.log10(nflat),1)))
output.append([ESNarr,Rarr])
ax.plot([1e50,1e53],[nfw.Rvir,nfw.Rvir],'k:')
ax.set_xscale('log')
ax.set_xlabel('E (erg)'); ax.set_ylabel('R (kpc)')
ax.legend(loc='upper left')
#plt.show()
with open('MFRchampagne_ESNarr_Rarr.p','w') as f: pickle.dump(output,f)
fig,ax = plt.subplots()
output = []
for nflat,model in zip(nflatarr,modelarr):
tarr = [model.t_SN[Ei] for Ei in ESNarr]
ax.plot(ESNarr,tarr,'o-',label=r'$\log n_{flat}$='+str(round(np.log10(nflat),1)))
output.append([ESNarr,tarr])
ax.set_xscale('log')
ax.set_xlabel('E (erg)'); ax.set_ylabel('t (Myr)')
ax.legend(loc='upper left')
#plt.show()
with open('MFRchampagne_ESNarr_tarr.p','w') as f: pickle.dump(output,f)
fig,ax = plt.subplots()
output = []
for nflat,model in zip(nflatarr,modelarr):
plotR = np.logspace(-3,1.5,200)
plotn = model.rho0(plotR*model.nfw.kpc)/model.nfw.mbar
ax.plot(plotR,plotn,label=r'$\log n_{flat}$='+str(round(np.log10(nflat),1)))
output.append([plotR,plotn])
ax.set_xscale('log'); ax.set_yscale('log')
ax.set_xlabel('R (kpc)'); ax.set_ylabel(r'n (cm$^{-3}$)')
ax.set_xlim((10**-3,10**1.5)); ax.set_ylim((10**-4,10**0.5))
ax.legend(loc='upper right')
with open('MFRchampagne_Rarr_narr.p','w') as f: pickle.dump(output,f)
plt.show()
def plot_flat_stuff():
zvir = 10
Mvir = 1e8
ESN = 10.**51
T0arr = [1e3, 1e4]
nflatarr = 10**np.array([0,-.5,-1,-1.5,-2])
modelarr = [[MFR01(Mvir,zvir,n_flat=n_flat,T0=T0,useiso=False,useflat=True) for n_flat in nflatarr] for T0 in T0arr]
for nmodel in modelarr:
for model in nmodel:
tarr,varr,Rarr,Earr,Tarr = model.run_model(ESN)
allR = [[model.R_SN[ESN] for model in nmodel] for nmodel in modelarr]
tauarr = np.array([10,70,100])
Dttauarr = 8.1e-4 * tauarr
fig,axarr = plt.subplots(2,1,figsize=(8,10))
ax = axarr[0]
for i,thisR in enumerate(allR):
ax.plot(nflatarr,thisR,'o-',label='T={0:.0f}K'.format(T0arr[i]))
ax.set_xscale('log')
ax.set_xlabel(r'n (cm$^{-3}$)')
ax.set_ylabel('R (kpc)')
ax.legend(loc='upper right')
ax = axarr[1]
colorarr = ['b','g']
stylearr = ['--',':','-.']
for i,thisR in enumerate(allR):
thisR = np.array(thisR)
Vmixarr = 4*np.pi/3 * (thisR*model.nfw.kpc)**3
massarr = Vmixarr * nflatarr * model.nfw.mp/(model.nfw.Msun)
ax.plot(nflatarr,massarr,color=colorarr[i])
turbmixVlist = [4*np.pi/3 * ((thisR*model.nfw.kpc)**2 + 6*Dttau*(model.nfw.kpc)**2)**1.5 for Dttau in Dttauarr]
for j,turbmixV in enumerate(turbmixVlist):
massarr = np.array(turbmixV) * nflatarr * model.nfw.mp/(model.nfw.Msun)
if i==0:
ax.plot(nflatarr,massarr,stylearr[j],color=colorarr[i],label=r'$\tau={0}\ Myr$'.format(tauarr[j]))
else:
ax.plot(nflatarr,massarr,stylearr[j],color=colorarr[i])
ax.legend(loc='upper left')
ax.set_xscale('log'); ax.set_yscale('log')
ax.set_xlabel(r'n (cm$^{-3}$)')
ax.set_ylabel(r'$M_{mix}$ ($M_\odot$)')
plt.show()
def old_main_model():
zvir = 25
Mvir = 1e6
ESNarr = 10**np.array([50,50.5,51,51.5,52,52.5,53])
nflatarr = 10**np.array([0,-.5,-1,-1.5,-2])
modelarr = [MFR01(Mvir,zvir,n_flat=n_flat,useiso=True) for n_flat in nflatarr]
for model in modelarr:
for Ei in ESNarr:
model.run_model(Ei,tmax=200)
nfw = modelarr[0].nfw
fig,ax = plt.subplots()
for nflat,model in zip(nflatarr,modelarr):
Rarr = [model.R_SN[Ei] for Ei in ESNarr]
ax.plot(ESNarr,Rarr,'o-',label=r'$\log n_{flat}$='+str(round(np.log10(nflat),1)))
ax.plot([1e50,1e53],[nfw.Rvir,nfw.Rvir],'k:')
ax.set_xscale('log')
ax.set_xlabel('E (erg)'); ax.set_ylabel('R (kpc)')
ax.legend(loc='upper left')
plt.show()
fig,ax = plt.subplots()
for nflat,model in zip(nflatarr,modelarr):
tarr = [model.t_SN[Ei] for Ei in ESNarr]
ax.plot(ESNarr,tarr,'o-',label=r'$\log n_{flat}$='+str(round(np.log10(nflat),1)))
ax.set_xscale('log')
ax.set_xlabel('E (erg)'); ax.set_ylabel('t (Myr)')
ax.legend(loc='upper left')
plt.show()
fig,ax = plt.subplots()
for nflat,model in zip(nflatarr,modelarr):
plotR = np.logspace(-3,1.5,200)
plotn = model.rho0(plotR*model.nfw.kpc)/model.nfw.mbar
ax.plot(plotR,plotn,label=r'$\log n_{flat}$='+str(round(np.log10(nflat),1)))
ax.set_xscale('log'); ax.set_yscale('log')
ax.set_xlabel('R (kpc)'); ax.set_ylabel(r'n (cm$^{-3}$)')
ax.set_xlim((10**-3,10**1.5)); ax.set_ylim((10**-4,10**0.5))
ax.legend(loc='upper right')
plt.show()
def old2():
zvirarr = [30,25,20,15]
Mvir = 1e6
Earr = 10**np.array([50,50.5,51,51.5,52,52.5])
modelarr = [MFR01(Mvir,zvir) for zvir in zvirarr]
for model in modelarr:
for Ei in Earr:
model.run_model(Ei,tmax=150)
fig,ax = plt.subplots()
for zvir,model in zip(zvirarr,modelarr):
Rarr = [model.R_SN[Ei] for Ei in Earr]
ax.plot(Earr,Rarr,'o-',label='z='+str(zvir))
ax.set_xscale('log')
ax.set_xlabel('E (erg)'); ax.set_ylabel('R (kpc)')
ax.legend(loc='upper left')
plt.show()
def old():
fig,axes = plt.subplots(2,2,figsize=(10,10))
fig.subplots_adjust(wspace=.25)
model = MFR01(1e6, 25)
tarr,varr,Rarr,Earr,Tarr = model.run_model(1e51)
model.plot_model(tarr,varr,Rarr,Earr,Tarr,fig=fig)
tarr,varr,Rarr,Earr,Tarr = model.run_model(1e52)
model.plot_model(tarr,varr,Rarr,Earr,Tarr,fig=fig)
ax = axes[1,1]; ax.legend(['1e51','1e52'],loc='upper right')
plt.show()