Twind¶
Twind is a Python prototype of TIGRESS Multiphase Wind Launching Model. The model is built on the TIGRESS simulation suite developed as part of the SMAUG project.
Basic Usage¶
If you want to obtain scaling relations between wind (mass, momentum, energy, and metal) loading factors and star formation rate surface density at different escape velocity cuts, you would construct PDFs with Twind:
import twind
tw = twind.TigressWindModel(z0='H',verbose=True)
tw.set_axes(verbose=True)
pdf = tw.build_model(renormalize=True,energy_bias=True)
This will return 3D PDFs in the \((v_{\rm out}, c_s, \Sigma_{\rm SFR})\) space. A more complete example is available in the Quickstart tutorial.
pdf stores all information using xarray.
Then, additional manipulations are easy.
If you want to apply velocity cuts to get loading factors with a selected condition,
you would do something like:
dbinsq = pdf.attrs['dlogcs']*pdf.attrs['dlogvout']
cdf_over_vB100 = pdf['Mpdf'].where(pdf['vBz']>100).sum(dim=['logcs','logvout'])*dbinsq
etaM_over_vB100 = pdf['etaM']*cdf_over_vB100
You can get a quick and dirty plot for the mass loading factor:
etaM_over_vB100.plot()
A more complete example is available in the Loading Factors from 3D PDFs tutorial.
Installation¶
Since Twind is a pure Python module, it should be pretty easy to install. In addition to widely used packages like scipy, numpy, matplotlib, you’ll need xarray and astropy. Also, paper-figures needs seaborn, CMasher, and cmocean.
Github sources¶
pip or conda can be used to install xarray
(see their installation instruction) and astropy.
Simply, the following command would work.
conda install -c conda-forge xarray astropy
Then, you are ready to clone the repository.
git clone https://github.com/changgoo/Twind.git your-twind-path
Add path to the source directory using sys.path; e.g.,
import sys
sys.path.insert('your-twind-path')
Joint PDF Model¶
Note
See Kim et al. (2020b) for details.
Cool outflow model¶
The cool outflow (\(T<2\times10^4{\rm K}\)) in the TIGRESS suite is well described by a model combining log-normal and generalized gamma distribution:
where \(A_c=(\ln 10)^2/(2\pi\sigma^2)^{1/2}=2.12/\sigma\).
At \(|z|=H\), we adopt \(v0=25\), \(c_{s,0}=6.7{\rm km/s}\), and \(\sigma=0.1\). We found the same function form with \((v0,c_{s,0})=(45,7.5)\), (45,8.5), and (60,10) works reasonably well at \(|z|=2H\), 500pc, and 1kpc.
Hot outflow model¶
The hot outflow (\(T>5\times10^5{\rm K}\)) in the TIGRESS suite is well described by a model combining two generalized gamma distributions:
where \(A_h\equiv 2(\ln 10)^2/\Gamma(1/2)=5.98\), \(v_{\mathcal{B},z}\equiv(v_{\rm out}^2+c_s^2)^{1/2}\), and \(\mathcal{M}=v_{\rm out}/c_s\).
where \(\Sigma_{\rm SFR,0}\equiv \Sigma_{\rm SFR}/(M_{\odot}{\rm kpc^{-2}yr^{-1}})\)
We adopt \(\mathcal{M}_0=0.5\) irrespective of \(z\).
None Note: This tutorial was generated from an IPython notebook that can be downloaded here.
Quickstart¶
Step 1: initialize Twind class¶
We are initilizing the TigressWindModel class with default
parameters set to match the TIGRESS simulation suite results at
\(|z|=H\) (see Simulation PDFs). Possible options are
z0=['H', '2H', '500', '1000'].
import twind
tw=twind.TigressWindModel(z0='H',verbose=True)
number of wind phase = 2
galactic parameter = sfr
reference height = H
cool_params
A_v = 2.302585092994046
p_v = 1
d_v = 2
A_cs = 9.185985478173896
cs0 = 6.7
sigma = 0.1
vout0 = 25.0
hot_params
A_vB = 5.196378098798331
p_vB = 4
d_vB = 2
A_M = 1.151292546497023
Mach0 = 0.5
p_M = 1
d_M = 3
params
Esn = 1e+51 erg
mstar = 95.5 solMass
vcool = 200.0 km / s
Mej = 10.0 solMass
ZSN = 0.2
ZISM0 = 0.02
vej = 3171.4804794827423 km / s
ref_params
Mref = 95.5 solMass
pref = 2.5e+48 erg s / km
Eref = 1e+51 erg
Zref = 2.0 solMass
scaling_params
a = [-0.067 -1.216 -0.857 0.013 -1.426 -2.151 -1.013 -0.879 -2.228 -2.627
-0.698 -0.695 0.171 -0.942 -0.375 0.281]
b = [-0.441 -0.227 -0.069 -0.418 -0.287 -0.149 0.016 -0.157 -0.117 -0.076
0.136 0.108 -0.364 -0.146 0.04 -0.335]
A = [0.86 0.06 0.14 1.03 0.04 0.01 0.1 0.13 0.01 0. 0.2 0.2 1.48 0.11
0.42 1.91]
p = [0.559 0.773 0.931 0.582 0.713 0.851 1.016 0.843 0.883 0.924 1.136 1.108
0.636 0.854 1.04 0.665]
With the verbose=True option, key attributes are printed.
cool_params: parameters for cool mass loading PDF. See Joint PDF Modelhot_params: parameters for hot mass loading PDF. See Joint PDF Modelparams: other physical parameters related to the particular choices of the TIGRESS simulation suite (see Kim et al. (2020a))ref_params: outflow rates are normalized by \(\Sigma_{\rm SFR}q_{\rm ref}/m_*\) to obtain loading factorsscaling_params: fitting results for velocity-integrated loading factors as a function of SFR surface density (in log-log space) presented in Kim et al. (2020a). Each array contains the results for four loading factors (mass, momentum, energy, metal) of four phases (cool, intermediate, hot, whole). E.g., first four values are the results for the mass loading factor of cool, intermediate, hot, and whole gas.ais the interceptbis the slopeAis \(10^a\)pis \(b+1\) for flux scalings.
Note
\(\Sigma_{\rm SFR}\) is in \(M_\odot{\rm kpc^{-2} yr^{-1}}\) everywhere in this document.
Note
\(u \equiv \log v_{\rm out}\) and \(w \equiv \log c_s\) as defined in Kim et al. (2020b).
Step 2: setup axes¶
We use xarray extensibly for easier manipulation with broadcasting, indexing, slicing, and interpolation.
The TigressWindModel.set_axes() method accept either the
simulated PDF (in the form of xarray.Dataset) or list of ranges (in
log) and number of bins for vout and cs axes (sfr can either
be a scalar or an array). Default is
vout= (0,4,500)cs= (0,4,500)sfr= (-6,2,100)
This function will set attributes u=logvout and w=logcs as 1D
DataArray as well as vBz and Mach as 2D DataArray for
future use. If a range of sfr is passed, it will also set a member
logsfr as 1D DataArray with different coordinates so that the
final PDFs would be 3D DataArray.
For this example, we use a single value of SFR surface density and reduced number of bins for velocity axes.
tw.set_axes(vout=(0,4,200),cs=(0,4,200),sfr=0.01,verbose=True)
sfr=0.01
cs: min=0, max=4, N=200
vout: min=0, max=4, N=200
We make sure that vBz and Mach are 2D while u=logvout and
w=logcs are 1D.
print('u shpae:',tw.u.shape)
print('w shape:',tw.w.shape)
print('vBz shpae:',tw.vBz.shape)
print('Mach shape:',tw.Mach.shape)
g=tw.vBz.plot(norm=LogNorm())
u shpae: (200,)
w shape: (200,)
vBz shpae: (200, 200)
Mach shape: (200, 200)
Step 3: build mass loading PDFs¶
We have a method TigressWindModel.build_Mpdf() that
automatically builds model PDFs for mass loading factor and return a
xarray.Dataset. Note that if the range of (u,w) is not large
enough, the mass PDF may not integrate to 1 (use verbose=True to
check this).
Depending on the choice of the sfr axis, the resulting PDF can
either be 2D or 3D. The returned Dataset have variables for PDFs
(Mpdf, Mpdf-cool, Mpdf-hot) for total, cool, and
hot outflow components. This also contains vBz and Mach as
2D arrays for convenience. In addition, the integrated loading factor
(etaM and their phase-separated values, i.e., etaM-cool and
etaM-hot) as a function of sfr are saved. If sfr is a
scalar, these are also scalars.
pdf = tw.build_Mpdf(verbose=True)
Mass PDFs are integrated to: cool=0.997 hot=1
pdf[['Mpdf','Mpdf-cool','Mpdf-hot']].to_array().plot(col='variable',
norm=LogNorm(vmin=1.e-3,vmax=10),
cmap=plt.cm.cubehelix_r
)
<xarray.plot.facetgrid.FacetGrid at 0x7f88b069a400>
Step 4: build all PDFs¶
We have a method TigressWindModel.build_model() that
automatically builds model PDFs for mass, momentum, energy, and metal
loading factors and return a xarray.Dataset containing all. The last
three PDFs are reconstructed from the mass PDF as outlined in Kim et
al. (2020b). By default, they are renormalized to ensure the
integration over the entire (u,w) gives 1. Note that the metal PDF
is not normalized for the input ZISM but for ZISM0.
Again, depending on the choice of the sfr axis, the resulting PDFs
can either be 2D or 3D. The returned Dataset have variables for PDFs
(Mpdf, ppdf, Epdf, Zpdf) and their phase-separated
counterparts (e.g., Mpdf-cool, Mpdf-hot). The
velocity-integrated loading factors (etaM, etap, etaE,
etaZ) and their phase-separated counterparts (e.g., etaM-cool
and etaM-hot) as a function of sfr are also stored. Finally, if
renormalize=True (default), it also stores the renormalization
factors (p_renorm, E_renorm, Z_renorm), which are also a
function of sfr.
The Dataset has attributes for the choice of ZISM for the metal
loading PDF as well as the bin sizes dlogcs and dlogvout for
convenience.
pdf=tw.build_model(renormalize=True,energy_bias=True)
As it builds a model PDF, it automatically checks whether the mass PDFs are integrated to 1. I.e., both cool and hot PDFs should satisfy
individually. Again, this may depend on the (u,w) range. We then
apply loading factor ratios to combine the mass loading PDF as
Note that Mpdf-cool and Mpdf-hot (and corresponding other PDFs)
in the returned Dataset are not \(\tilde{f}_M^{\rm ph}\) but
\(\frac{\eta_M^{\rm ph}}{\eta_M}\tilde{f}_M^{\rm ph}\).
dudw=pdf.attrs['dlogvout']*pdf.attrs['dlogcs']
print('contribution to')
print('mass outflow rate from cool is {:.3f} and hot is {:.3f}'.format(
pdf['Mpdf-cool'].sum().data*dudw,pdf['Mpdf-hot'].sum().data*dudw))
print('energy outflow rate from cool is {:.3f} and hot is {:.3f}'.format(
pdf['Epdf-cool'].sum().data*dudw,pdf['Epdf-hot'].sum().data*dudw))
contribution to
mass outflow rate from cool is 0.968 and hot is 0.029
energy outflow rate from cool is 0.081 and hot is 0.919
Finally, 2D PDFs for mass, momentum, energy, and metal loadings at \(\Sigma_{\rm SFR}=10^{-2}\) look as follows.
pdf[['Mpdf','ppdf','Epdf','Zpdf']].to_array().plot(col='variable',col_wrap=2,
norm=LogNorm(vmin=1.e-3,vmax=10),
cmap=plt.cm.cubehelix_r
)
<xarray.plot.facetgrid.FacetGrid at 0x7f8870725898>
None Note: This tutorial was generated from an IPython notebook that can be downloaded here.
Loading Factors from 3D PDFs¶
See Quickstart for details of the first step. For this tutorial, we use the default ranges for axes setup.
import twind
tw=twind.TigressWindModel(z0='H',verbose=False)
tw.set_axes(verbose=True)
cs: min=0, max=4, N=500
vout: min=0, max=4, N=500
sfr: min=-6, max=2, N=100
Now we build joint PDFs as a function of SFR surface density, which gives a 3D PDF model.
pdf=tw.build_model(renormalize=True,energy_bias=True,verbose=False)
Note
After building the 3D PDF model, all subsequent manipulations heavily rely on the functionalities of xarray. We only show a few examples here.
Slicing back to 2D PDF¶
xarray.Dataset provides very useful functionality for slicing and
interpolating through a method sel. Since we build a 3D PDF on the
decretized sfr array, to get a PDF with a particular choice of
sfr using the current 3D PDF, we would want either get the PDF with
the closet value of sfr or interpolate to the chosen sfr. This
can be done very easily with xarray.
# find the nearest one
pdf_nearest=pdf.sel(logsfr=-2, method='nearest')
# intepolate; this takes longer
pdf_interp=pdf.interp(logsfr=-2)
print('log sfr:{} {}'.format(pdf_nearest.logsfr.data,pdf_interp.logsfr.data))
log sfr:-2.04040404040404 -2
Interpolation (or slicing) within the range of sfr would be useful
to compare pdfs at different SFRs quickly.
g=pdf['Mpdf'].interp(logsfr=[-4,-3,-2,-1,0,1]).plot(col='logsfr',col_wrap=3,
norm=LogNorm(vmin=1.e-3,vmax=10),
cmap=plt.cm.cubehelix_r
)
Selecting escapable outflows: constant velocity cut¶
For a practical use, we may want to select outflows with a certain velocity (or Bernoulli velocity) cut given a halo escape velocity. Here’s how to do this.
We may first want to calculate the cumulative distribution functions
(CDF) with vBz > vBzcut. We then obtain the loading factors of
selected gas by multiplying the total loading factors, which are stored
as etaM, etap, etaE, etaZ in the original Dataset.
dbinsq=pdf.attrs['dlogcs']*pdf.attrs['dlogvout']
pdfs=['Mpdf','Mpdf-cool','Mpdf-hot',
'ppdf','ppdf-cool','ppdf-hot',
'Epdf','Epdf-cool','Epdf-hot',
'Zpdf','Zpdf-cool','Zpdf-hot',]
sfr=10.**pdf['logsfr']
# For a constant velocity cut
fig, axes = plt.subplots(1,4,figsize=(10,3))
for vBzcut0 in [30,100,300]:
cdf=pdf[pdfs].where(pdf['vBz']>vBzcut0).sum(dim=['logcs','logvout'])*dbinsq
for ax,q in zip(axes.flat,['M','p','E','Z']):
plt.sca(ax)
eta=pdf['eta'+q]
l,=plt.plot(sfr,cdf[q+'pdf']*eta,label=r'$v_{{\rm esc}}={}{{\rm km/s}}$'.format(vBzcut0))
plt.plot(sfr,cdf[q+'pdf-cool']*eta,ls='--',color=l.get_color())
plt.plot(sfr,cdf[q+'pdf-hot']*eta,ls=':',color=l.get_color())
plt.ylabel(r'$\eta_{}$'.format(q))
plt.xlabel(r'$\Sigma_{\rm SFR}$')
axes[2].legend()
plt.setp(axes,'xscale','log')
plt.setp(axes,'yscale','log')
plt.setp(axes,'ylim',(1.e-2,1.e1))
plt.tight_layout()
Note
\(\Sigma_{\rm SFR}\) is in \(M_\odot{\rm kpc^{-2} yr^{-1}}\) everywhere in this document.
The mass (and metal) loading factor \(\eta_M\) changes dramatically as different velocity cuts are applied. This is because the cool outflow carries most of mass (shown as dashed lines), which has typical outflow velocities insufficient to escape for \(v_{\rm esc}>100 {\rm km/s}\). However, at very high \(\Sigma_{\rm SFR}\), cold outflow may contribute to the mass outflow rate significantly again, while one should take this with a grain of salt since those are outside our original parameter space \(10^{-4}<\Sigma_{\rm SFR}<1\) over which the model is calibrated. On the other hand, the energy loading factor \(\eta_E\) is unchaged since it is dominated by the hot outflow whose Bernoulli velocity is already larger than 300km/s even at low \(\Sigma_{\rm SFR}\).
Selecting escapable outflows: SFR-dependent velocity cut¶
For some reasons, if the escape velocity is a function of SFR surface
density, we get loading factors with a varying vBzcut easily using
xarray.Dataset.where as it correctly broadcasts the information.
Let’s assume a particular form of the escape velocity:
vBzcut = 300.*sfr**0.5/(sfr**0.5+1)+30
plt.loglog(sfr,vBzcut)
plt.xlabel(r'$\Sigma_{\rm SFR}$');
plt.ylabel(r'$v_{\rm esc} [{\rm km/s}]$');
fig, axes = plt.subplots(1,4,figsize=(10,3))
for vBzcut0 in [30,100,300]:
cdf=pdf[pdfs].where(pdf['vBz']>vBzcut0).sum(dim=['logcs','logvout'])*dbinsq
for ax,q in zip(axes.flat,['M','p','E','Z']):
plt.sca(ax)
eta=pdf['eta'+q]
l,=plt.plot(sfr,cdf[q+'pdf']*eta,lw=1)
plt.plot(sfr,cdf[q+'pdf-cool']*eta,ls='--',color=l.get_color(),lw=1)
plt.plot(sfr,cdf[q+'pdf-hot']*eta,ls=':',color=l.get_color(),lw=1)
plt.ylabel(r'$\eta_{}$'.format(q))
plt.xlabel(r'$\Sigma_{\rm SFR}$')
cdf=pdf[pdfs].where(pdf['vBz']>vBzcut).sum(dim=['logcs','logvout'])*dbinsq
for ax,q in zip(axes.flat,['M','p','E','Z']):
plt.sca(ax)
eta=pdf['eta'+q]
l,=plt.plot(sfr,cdf[q+'pdf']*eta,label='total',lw=2)
plt.plot(sfr,cdf[q+'pdf-cool']*eta,ls='--',color=l.get_color(),label='cool',lw=2)
plt.plot(sfr,cdf[q+'pdf-hot']*eta,ls=':',color=l.get_color(),label='hot',lw=2)
plt.ylabel(r'$\eta_{}$'.format(q))
plt.xlabel(r'$\Sigma_{\rm SFR}$')
axes[2].legend()
plt.setp(axes,'xscale','log')
plt.setp(axes,'yscale','log')
plt.setp(axes,'ylim',(1.e-2,1.e1))
plt.tight_layout()
Obviously, the result (red) falls between vBzcut0=30 (blue) and
vBzcut0=300 (green) cases.
None Note: This tutorial was generated from an IPython notebook that can be downloaded here.
Particle Sampling¶
The TigressWindSampler class is a child class of the
TigressWindModel class. For sampling, it won’t build pdf
models, but use the scaling relations and parameters of the model.
import twind
sampler=twind.TigressWindSampler()
Sampling at a single epoch¶
For this example, we use
- \(\Sigma_{\rm SFR} = 10^{-2} M_\odot{\rm kpc^{-2} yr^{-1}}\),
- area = \(1 {\rm kpc}^2\)
- dt = 1 Myr
and
- \(m^{\rm cool} = m^{\rm hot} \in (10^2, 10^3)M_\odot\)
def draw_particle_dist(sfr0,area,dt,masses=[1.e2,1.e3,1.e4]):
Nm=len(masses)
fig, axes = plt.subplots(1,Nm,figsize=(3*Nm,3))
for ax, m in zip(axes,masses):
cool,hot=sampler.draw_mass(sfr0,m,m,area=area,dt=dt)
plt.sca(ax)
plt.plot(cool['vz'],cool['cs'],marker='o',ls='',ms=5,alpha=0.5,mew=0)
plt.plot(hot['vz'],hot['cs'],marker='o',ls='',ms=5,alpha=0.5,mew=0)
plt.xscale('log')
plt.yscale('log')
plt.title(r'$m = 10^{:.0f} M_\odot$'.format(np.log10(m)))
ax.grid('on')
ax.set_aspect('equal')
plt.xlim(1.,5.e3)
plt.ylim(1.,5.e3)
plt.xlabel(r'$u=\log v_{\rm out}$')
plt.ylabel(r'$w=\log c_s$')
plt.tight_layout()
return fig
sfr0 = 1.e-2
area = 1
dt = 1.e6
f = draw_particle_dist(sfr0,area,dt,masses=[1.e2,1.e3])
The mass in the outflow can be obatined by
For a chosen \(\Sigma_{\rm SFR}\), the total, cool, and hot mass loading factors are
etaM=sampler._eta_sfr_scaling(sfr0,'M_total')
etaMc=sampler._eta_sfr_scaling(sfr0,'M_cool')
etaMh=sampler._eta_sfr_scaling(sfr0,'M_hot')
print('eta_M={:.2f} eta_M^cool={:.2f} eta_M^hot={:.2f}'.format(etaM, etaMc, etaMh))
eta_M=7.07 eta_M^cool=6.54 eta_M^hot=0.19
which give the outflowing mass in each phase
print('M_out={:.3g} M_out^cool={:.3g} M_out^hot={:.3g}'.format(etaM*sfr0*area*dt,etaMc*sfr0*area*dt,etaMh*sfr0*area*dt))
M_out=7.07e+04 M_out^cool=6.54e+04 M_out^hot=1.93e+03
Therefore, even for \(m^{\rm hot}=10^3 M_\odot\), we expect to sample a few particles as shown in the right panel of the above figure.
Sampling from a time series¶
For this example, we use a sinusoidal function for SFR surface density time series for 200 Myr with
- mean \(\Sigma_{\rm SFR} = 10^{-3} M_\odot{\rm kpc^{-2} yr^{-1}}\),
- period of 50 Myr
tmax = 2.e8
dt = 1.e6
time = np.arange(0,tmax,dt)
tp = 5.e7
sfr0 = 2.e-3
area = 1
sfr=sfr0*0.5*(np.sin(2*np.pi/tp*time)+2)
For a given time series of \(\Sigma_{\rm SFR}\), we get reference values of outflow rates using the scaling relations of outflow loading factors (of each outflow phase) presented in Kim et al. (2020a).
The TigressWindSampler.get_refs() method returns four lists
containing time series of reference outflow rates and loading factors
for total, cool, and hot outflows. Each list contains mass,
momemtum, energy, and metal in order.
refs,eta,etac,etah = sampler.get_refs(sfr)
mout = [eta[0]*refs[0]*area*dt, etac[0]*refs[0]*area*dt, etah[0]*refs[0]*area*dt]
Eout = [eta[2]*refs[2]*area*dt, etac[2]*refs[2]*area*dt, etah[2]*refs[2]*area*dt]
print('mean outflowing mass = {:.3g} (total) {:.3g} (cool) {:.3g} (hot) Msun'.format(mout[0].mean(),mout[1].mean(),mout[2].mean()))
print('mean outflowing energy = {:.3g} (total) {:.3g} (cool) {:.3g} (hot) erg'.format(Eout[0].mean(),Eout[1].mean(),Eout[2].mean()))
mean outflowing mass = 2.73e+04 (total) 2.62e+04 (cool) 429 (hot) Msun
mean outflowing energy = 2.16e+51 (total) 4.3e+50 (cool) 1.82e+51 (hot) erg
For the area of 1 kpc\(^2\) and time interval 1 Myr considered here, we expect the mean mass and energy in outflow are \(2.7\times10^4 M_\odot\) and \(2.2\times10^{51}\) erg, respectively. The mass ratio between cool and hot outflows is about 50, therefore, for a fair sampling, we might need \(m^{\rm cool}/m^{\rm hot}\sim50\) with \(m^{\rm cool}<10^4 M_\odot\).
Frist, as a well sampled example, we use
- \(m^{\rm cool} = 10^3 M_\odot\)
- \(m^{\rm hot} = 10^1 M_\odot\)
def draw_particle_time_series(time, sfr, mc, mh, area, dt):
refs,eta,etac,etah = sampler.get_refs(sfr)
cool,hot=sampler.draw_mass(sfr,mc,mh,area=area,dt=dt)
fig,axes = plt.subplots(4,1,sharex=True,figsize=(5,8))
for p, etas_ in zip([cool,hot],[etac,etah]):
outs=twind.to_time_series(p,time)
for ax, q, qref, eta in zip(axes,outs,refs,etas_):
plt.sca(ax)
l,=plt.plot(time,q)
plt.plot(time,eta*qref*area*dt,color=l.get_color(),ls='--')
plt.yscale('log')
axes[0].set_title(r'$m^{{\rm cool}} = 10^{}, m^{{\rm hot}} = 10^{}$'.format(int(np.log10(mc)),int(np.log10(mh))))
axes[0].set_ylabel(r'Mass $[M_\odot/{\rm yr}]$')
axes[1].set_ylabel(r'Momentum $[(M_\odot {\rm km/s})/{\rm yr}]$')
axes[2].set_ylabel(r'Energy $[{\rm erg/yr}]$')
axes[3].set_ylabel(r'Metal Mass $[M_\odot/{\rm yr}]$')
return fig
Here, a utility function to_time_series() is used to convert
particle data into time series of rates.
f = draw_particle_time_series(time, sfr, 1.e3, 1.e1, area, dt)
The second example is for well sampled cool phase but poorly sampled hot phase.
- \(m^{\rm cool} = 10^3 M_\odot\)
- \(m^{\rm hot} = 10^3 M_\odot\)
f = draw_particle_time_series(time, sfr, 1.e3, 1.e3, area, dt)
None Note: This tutorial was generated from an IPython notebook that can be downloaded here.
Simulation Model Tables¶
We construct model PDFs based on the results from the TIGRESS simulation suite presented in Paper I. We summarize model parameters and some integrated outflow propertes here using table files made available at zenodo or github. Mainly, the results are phase separated (three large bins in temperature or \(c_s\)) but outflow velocity integrated (\(v_{\rm out}>0\)).
You can download the original notebook to reproduce tables and figures in Paper I.
Download and Prepare Tables¶
# Download Tables
import urllib.request
import os
repo_url='https://changgoo.github.io/tigress-wind-figureset'
tbl_files=['table-mean.ecsv','table-mean-err.ecsv']
if not os.path.isdir('tables/'): os.mkdir('tables/')
for f in tbl_files:
if not os.path.isfile(f):
urllib.request.urlretrieve('{}/tables/{}'.format(repo_url,f),'tables/'+f)
# Read Tables with astropy:
from astropy.table import QTable,Table
tmean=Table.read('tables/table-mean.ecsv')
terr=Table.read('tables/table-mean-err.ecsv')
# add additional time scales for Table 2 in Paper I
import astropy.constants as ac
import astropy.units as au
tmean['torb']=(2*np.pi/tmean['Omega_0'].quantity).to('Myr')
tmean['tosca']=(2*np.pi/np.sqrt(4*np.pi*ac.G*tmean['rho_tot'].quantity)).to('Myr')
tmean['toscn']=(2.0*np.pi*tmean['H'].quantity/tmean['sigma_eff'].quantity).to('Myr')
# set format for more compact display
for k in tmean.keys():
if tmean[k].info.dtype == 'float64':
tmean[k].info.format = '15.2g'
if k in terr: terr[k].info.format = '15.2g'
Table 1: Model Parameters¶
table1_varlist=['model','Sigma_gas0','Sigma_star','rho_dm','Omega_0','z_star','R_0']
for k in table1_varlist:
if tmean[k].info.dtype == 'float64':
tmean[k].info.format = '15.3g'
tbl1=tmean[(tmean['z']=='H') & (tmean['phase']=='whole') ][table1_varlist]
tbl1.pprint_all()
model Sigma_gas0 Sigma_star rho_dm Omega_0 z_star R_0
solMass / pc2 solMass / pc2 solMass / pc3 km / (kpc s) pc kpc
----- --------------- --------------- --------------- --------------- --------------- ---------------
R2 150 450 0.08 100 245 2
R4 50 208 0.024 53.7 245 4
R8 12 42 0.0064 28 245 8
R16 2.49 1.71 0.00143 11.9 245 16
LGR2 150 110 0.015 50 500 2
LGR4 60 50 0.005 30 500 4
LGR8 12 10 0.0016 15 500 8
- Sigma_gas0: initial gas surface density, \(\Sigma_\text{gas,0}\)
- Sigma_star: stellar surface density, \(\Sigma_{*}\)
- rho_dm: midplane dark matter density, \(\rho_\text{dm}\)
- Omega: angular velocity of galactic rotation, \(\Omega\)
- R_0: galactocentric radius, \(R_0\)
- z_star: scale height of stellar disk, \(z_*\)
Table 2: Time Scales¶
table2_varlist=['model','torb','toscn','tosca','tdep40','surf','sfr40']
tbl2=tmean[(tmean['z']=='H') & (tmean['phase']=='whole') ][table2_varlist]
tbl2.pprint_all()
model torb toscn tosca tdep40 surf sfr40
Myr Myr Myr Myr solMass / pc2 solMass / (kpc2 yr)
----- --------------- --------------- --------------- --------------- --------------- -------------------
R2 61 32 23 66 74 1.1
R4 1.1e+02 51 38 2.4e+02 29 0.12
R8 2.2e+02 1.2e+02 75 2.1e+03 11 0.0051
R16 5.2e+02 4.6e+02 3.1e+02 3.1e+04 2.5 8e-05
LGR2 1.2e+02 52 48 1.5e+02 74 0.49
LGR4 2e+02 87 80 4.2e+02 38 0.09
LGR8 4.1e+02 2.2e+02 1.7e+02 3.3e+03 10 0.0032
- torb: orbit time, \(t_\text{orb}=2\pi/\Omega\)
- toscn: vertical oscillation time derived from numerical measures, \(t_\text{osc,n}=2\pi H/\sigma_{\rm z,eff}\)
- tosca: vertical oscillation time derived from input parameters, \(t_\text{osc,a}=2\pi/(4\pi G\rho_{\rm tot})^{1/2}\)
- tdep40: gas depletion time with SFR surface density in 40 Myr, \(t_\text{dep,40}=\Sigma_\text{gas}/\Sigma_\text{SFR,40}\)
- surf: mean gas surface density, \(\Sigma_\text{gas}\)
- sfr40: mean SFR surface density from star particles young than 40 Myr, \(\Sigma_\text{SFR,40}\)
mean and error are determined from bootstrap resampling with a sample size of 10 for time series over \(0.5<t/t_{\rm orb}<1.5\)
Table 3-1: Fluxes¶
z0='H' # height can be ('H','2H','500','1000')
table3_varlist1=['model','phase','mass','mom','energy','metal','metal_sn']
tbl3=tmean[tmean['z']==z0][table3_varlist1]
tbl3.pprint_all()
model phase mass mom energy metal metal_sn
solMass / (kpc2 yr) km solMass / (kpc2 s yr) erg / (kpc2 yr) solMass / (kpc2 yr) solMass / (kpc2 yr)
----- ----- ------------------- ------------------------ --------------- ------------------- -------------------
R2 cool 0.74 50 7.2e+46 0.029 0.0032
R2 int 0.063 10 2.8e+46 0.0026 0.00056
R2 hot 0.13 1.4e+02 2.8e+48 0.0096 0.0062
R2 whole 0.94 2e+02 2.9e+48 0.041 0.01
R4 cool 0.26 12 1e+46 0.0081 0.00042
R4 int 0.014 1.8 4.1e+45 0.00047 7.1e-05
R4 hot 0.026 18 2.2e+47 0.0013 0.00058
R4 whole 0.3 32 2.3e+47 0.0098 0.001
R8 cool 0.032 0.78 4.4e+44 0.00071 2.1e-05
R8 int 0.0012 0.12 2.3e+44 2.9e-05 2.9e-06
R8 hot 0.0013 0.67 5.5e+45 4.1e-05 1.5e-05
R8 whole 0.035 1.6 6.2e+45 0.00078 3.8e-05
R16 cool 0.0055 0.085 2.3e+43 0.00011 2.5e-09
R16 int 3.6e-05 0.0028 3.7e+42 7.7e-07 5.2e-08
R16 hot 1.4e-05 0.0093 6.1e+43 4.4e-07 1.8e-07
R16 whole 0.0055 0.097 8.8e+43 0.00011 8.4e-08
LGR2 cool 0.55 26 2.8e+46 0.018 0.0015
LGR2 int 0.026 3.6 8.8e+45 0.00097 0.00019
LGR2 hot 0.055 48 6.8e+47 0.0033 0.0018
LGR2 whole 0.63 78 7.1e+47 0.023 0.0034
LGR4 cool 0.45 14 8.3e+45 0.012 0.00021
LGR4 int 0.01 1.2 2.5e+45 0.0003 3.7e-05
LGR4 hot 0.015 10 1.1e+47 0.00065 0.00028
LGR4 whole 0.47 25 1.2e+47 0.013 0.00048
LGR8 cool 0.04 0.86 3.6e+44 0.00087 7.9e-06
LGR8 int 0.00074 0.073 1.3e+44 1.7e-05 1.5e-06
LGR8 hot 0.00089 0.44 3.3e+45 2.7e-05 8.6e-06
LGR8 whole 0.042 1.4 3.8e+45 0.00092 1.8e-05
- mass: mass flux, \(\overline{\mathcal{F}}_M\)
- mom: momentum flux, \(\overline{\mathcal{F}}_p\)
- energy: energy flux, \(\overline{\mathcal{F}}_E\)
- metal: metal flux, \(\overline{\mathcal{F}}_Z\)
- metal_sn: SN-origin metal flux, \(\overline{\mathcal{F}}_Z^{SN}\)
mean and error are determined from bootstrap resampling with a sample size of 10 for time series over \(0.5<t/t_{\rm orb}<1.5\)
Table 3-2: Loading Factors¶
z0='H' # height can be ('H','2H','500','1000')
table3_varlist2=['model','phase','mass_loading','mom_loading',
'energy_loading','metal_loading','metal_sn_loading',]
tbl3=tmean[tmean['z']==z0][table3_varlist2]
tbl3.pprint_all()
model phase mass_loading mom_loading energy_loading metal_loading metal_sn_loading
----- ----- --------------- --------------- --------------- --------------- ----------------
R2 cool 0.68 0.035 0.0064 1.3 0.14
R2 int 0.058 0.0071 0.0025 0.11 0.025
R2 hot 0.12 0.1 0.24 0.42 0.27
R2 whole 0.86 0.14 0.25 1.8 0.44
R4 cool 2.2 0.075 0.008 3.2 0.17
R4 int 0.12 0.012 0.0032 0.19 0.028
R4 hot 0.22 0.12 0.17 0.5 0.23
R4 whole 2.5 0.2 0.18 3.9 0.4
R8 cool 6.3 0.12 0.0081 6.6 0.19
R8 int 0.24 0.018 0.0043 0.27 0.027
R8 hot 0.25 0.099 0.1 0.38 0.14
R8 whole 6.8 0.23 0.11 7.3 0.36
R16 cool 56 0.66 0.022 54 0.0012
R16 int 0.37 0.022 0.0036 0.38 0.025
R16 hot 0.14 0.072 0.06 0.22 0.087
R16 whole 56 0.75 0.086 55 0.041
LGR2 cool 1.2 0.042 0.0056 1.9 0.15
LGR2 int 0.054 0.0058 0.0018 0.098 0.02
LGR2 hot 0.12 0.077 0.14 0.33 0.18
LGR2 whole 1.3 0.13 0.14 2.3 0.35
LGR4 cool 5 0.12 0.0088 6.2 0.11
LGR4 int 0.11 0.01 0.0027 0.16 0.02
LGR4 hot 0.17 0.085 0.11 0.35 0.15
LGR4 whole 5.3 0.21 0.12 6.8 0.26
LGR8 cool 12 0.2 0.011 13 0.12
LGR8 int 0.23 0.017 0.004 0.26 0.022
LGR8 hot 0.28 0.1 0.099 0.4 0.13
LGR8 whole 13 0.32 0.11 14 0.27
- mass_loading: mass loading factor, \(\eta_M\)
- mom_loading: mom loading factor, \(\eta_p\)
- energy_loading: energy loading factor, \(\eta_E\)
- metal_loading: mass loading factor, \(\eta_Z\)
- metal_sn_loading: SN-origin metal loading factor, \(\eta_Z^{SN}\)
mean and error are determined from bootstrap resampling with a sample size of 10 for time series over \(0.5<t/t_{\rm orb}<1.5\)
Table 4: Velocities and Metals¶
z0='H' # height can be ('H','2H','500','1000')
table4_varlist=['model','phase','vout_flux','vB','Z','enrichment','fmass_sn','fmetal_sn']
tbl4=tmean[tmean['z']==z0][table4_varlist]
tbl4.pprint_all()
model phase vout_flux vB Z enrichment fmass_sn fmetal_sn
km / s km / s
----- ----- --------------- --------------- --------------- --------------- --------------- ---------------
R2 cool 69 1e+02 0.039 1.1 0.026 0.14
R2 int 1.4e+02 2.1e+02 0.042 1.2 0.044 0.21
R2 hot 5.8e+02 1.4e+03 0.072 2.1 0.23 0.63
R2 whole 1.6e+02 5.6e+02 0.044 1.3 0.059 0.27
R4 cool 47 67 0.032 1.1 0.011 0.068
R4 int 1.1e+02 1.6e+02 0.034 1.1 0.023 0.13
R4 hot 3.8e+02 8.2e+02 0.046 1.6 0.095 0.4
R4 whole 1e+02 3.2e+02 0.034 1.1 0.024 0.14
R8 cool 20 37 0.022 1 0.0035 0.032
R8 int 69 1.3e+02 0.024 1.1 0.012 0.1
R8 hot 2.4e+02 6e+02 0.031 1.4 0.054 0.34
R8 whole 34 1.4e+02 0.023 1.1 0.0066 0.057
R16 cool 7.9 20 0.02 1 7.3e-06 7.9e-05
R16 int 36 95 0.022 1.1 0.0063 0.071
R16 hot 1.3e+02 5.5e+02 0.032 1.6 0.051 0.37
R16 whole 8.4 32 0.02 1 6.3e-05 0.00068
LGR2 cool 44 68 0.035 1.1 0.015 0.084
LGR2 int 1.1e+02 1.8e+02 0.039 1.2 0.036 0.19
LGR2 hot 4.2e+02 1e+03 0.057 1.8 0.15 0.51
LGR2 whole 92 3.4e+02 0.038 1.2 0.031 0.16
LGR4 cool 30 45 0.028 1 0.0046 0.032
LGR4 int 92 1.5e+02 0.03 1.1 0.018 0.12
LGR4 hot 3.1e+02 7.4e+02 0.041 1.5 0.08 0.38
LGR4 whole 47 1.7e+02 0.028 1.1 0.0085 0.058
LGR8 cool 13 26 0.022 1 0.0014 0.013
LGR8 int 50 1.2e+02 0.024 1.1 0.014 0.11
LGR8 hot 1.6e+02 4.6e+02 0.029 1.4 0.039 0.29
LGR8 whole 17 72 0.022 1 0.0032 0.027
- vout_flux: characteristic outflow velocity, \(\overline{v}_\text{out}\)
- vB: Bernoulli velocity, \(\overline{v}_{\mathcal{B}}\)
- Z: outflow metallicity, \(\overline{Z}\)
- enrichment: metal enrichment factor, \(\zeta\)
- fmass_sn: fraction of SN-origin mass flux, \(f_M^{SN}\)
- fmetal_sn: fraction of SN-origin metal flux, \(f_Z^{SN}\)
mean and error are determined from bootstrap resampling with a sample size of 10 for time series over \(0.5<t/t_{\rm orb}<1.5\)
None Note: This tutorial was generated from an IPython notebook that can be downloaded here.
Simulation PDFs¶
The time averaged joint PDFs from the TIGRESS simulations suites for all
7 models (see Simulation Model Tables) at all 4 heights are available. This
tutorial demonstrates how to download, read, and handle simulation PDFs
using TigressSimLoader class. More comphrensive examples can
be found at Figures in Paper II.
import twind
# read in simulated PDF
sim = twind.TigressSimLoader('R4','H')
sim.load(download=True)
Since TigressSimLoader is a child class of
TigressWindModel, this itself can be used to build model
PDFs. If the simulation pdf is passed in
TigressWindModel.set_axes() method, it will make axes identical
to the simulation PDF.
sim.set_axes(pdf=sim.simpdf,verbose=True)
modelpdf=sim.build_model()
Setting up from simulation PDF...
u in (0.0,3.5) with du = 0.02
w in (0.0,3.5) with dw = 0.02
Sigma_SFR = 0.0917, ZISM = 0.0302
Mpdf : cool=0.867 int=0.046 hot=0.085 total=0.998
ppdf : cool=0.381 int=0.057 hot=0.560 total=0.999
Epdf : cool=0.044 int=0.018 hot=0.938 total=1.000
Zpdf : cool=0.824 int=0.047 hot=0.127 total=0.998
# show all PDFs from R4 simulation
simpdf = sim.simpdf
simpdf[['Mpdf','ppdf','Epdf','Zpdf']].to_array().plot(col='variable',
norm=LogNorm(vmin=1.e-3,vmax=10),
cmap=plt.cm.cubehelix_r)
# this can be compared with model PDF
modelpdf[['Mpdf','ppdf','Epdf','Zpdf']].to_array().plot(col='variable',
norm=LogNorm(vmin=1.e-3,vmax=10),
cmap=plt.cm.cubehelix_r)
<xarray.plot.facetgrid.FacetGrid at 0x7fa83075e048>
Looking for more comprehensive comparisons? Check Figures in Paper II
None Note: This tutorial was generated from an IPython notebook that can be downloaded here.
Figures in Paper II¶
This tutorial shows how Twind package can be used to produce figures
in Paper II. See the source code
twind/plotter.py
to know what is happening under the scean.
import twind
from twind.plotter import *
Figure 1: display simulation PDFs¶
# read in simulated PDF
sim = twind.TigressSimLoader('R4','H')
sim.load(download=True)
sim.set_axes(sim.simpdf)
with plt.style.context([{'axes.grid':False}]):
fig=plot_flux_pdfs_yZ(sim.simpdf,grid=True)
This figure shows the joint PDFs of \(u\equiv \log_{10} v_{\rm out}\) and \(w\equiv \log_{10} c_s\) for Model R4 at |z| = H. (a) Mass loading PDF, (b) energy loading PDF, and (c) enrichment factor. The red and blue dashed lines denote temperature cuts to separate cool (\(T < 2 \times 10^4\) K), intermediate (\(2\times10^4\) K \(< T < 5 \times 10^5\) K), and hot (\(5 \times 10^5\) K \(< T\)) phases. The dotted gray lines denote loci of constant Bernoulli velocity (labeled in (a))
and Mach number (labeled in (b))
Notice that both mass and energy loading PDFs are distributed widely in large range of u and w, and there is clear correlation between the enrichment factor \(\zeta(u,w)\) and Bernoulli velocity \(v_{B,z}\).
Figure 2: reconstruct PDFs from mass loading PDF¶
As the joint PDF we are after is a function of the outflow velocity \(v_{\rm out}\) and sound speed \(c_s\), the momentum, energy, and metal loading PDFs can be reconstructed from the mass loading PDF. We present a reconstruction procedure in Section 3 of the paper. How good is this reconstruction procedure? See below.
sims=twind.TigressSimContainer(z0='H')
fig=flux_reconstruction(sims.sims)
(a) Examples of PDFs for loading factors projected onto \(\log v_{B,z}\) for model R4 at \(|z|=H\). Thick lines show direct measurements of all PDFs, while thin lines with the same color (overlying the thick lines almost everywhere) show reconstructions from the mass PDF of momentum, energy, and metal PDFs.
(b) The ratios of reconstructed PDFs to the original PDFs for all models at \(|z|=H\). The mean ratio at a given \(\log v_{B,z}\) is obtained by a massflux weighted average. (Thick lines correspond to model R4, shown to left.
Figure 3: comparison between model and simulation PDFs¶
Joint PDF Model gives a mass loading PDF model for cool and hot outflows
separately. The model PDF is entirely determined with two parameters:
\(\Sigma_{\rm SFR}\) and \(Z_{\rm ISM}\). How good are the
simple Twind model PDFs in comparison with the complex simulation
PDFs? Here, we show multi-axes projection to give a quantitative view.
figM=comparison_pdfs(sims.sims['R4'],q='M')
figE=comparison_pdfs(sims.sims['R4'],q='E')
Comparison between simulated and model PDFs for R4: (a) mass loading and (b) energy loading. In each row, the first column shows full joint PDFs in logarithmic color scale (\(\log\, f_{M,E}\,[\rm dex^{-2}]\)) from the simulation (color) and model (contour). The remaining four panels are histograms showing projections onto (from left to right) outflow velocity \(v_{\rm out}\), sound speed \(c_s\), Bernoulli velocity \(v_{B,z}\), and Mach number \(\mathcal{M}\) axes. Model PDFs are separated into cool (blue) and hot (orange) components. The sum of the two (yellow) matches simulated PDFs (black lines) well (especially for dominating components).
Figure 4: Loading factor scalings¶
What is the model prediction for outflow properties as a function of \(\Sigma_{\rm SFR}\)? How much mass, momentum, energy, and metals can travel far from the launching position in a given galactic halo? Beyond the velocity-integrated loading factor scalings presented in Paper I, it is important to ask how much of outflows have specific energy \(v_{B}^2/2\) large enough to climb up the potential well:
Depending on specific questions, one can use \(v_{\rm esc} \equiv \sqrt{2\Delta\Phi}\) for gravitational potential difference between any distance, e.g., \(\Delta \Phi= \Phi(R_{\rm vir}) - \Phi(H)\).
tw=twind.TigressWindModel(z0=sims.z0,verbose=False)
tw.set_axes(verbose=False)
modelpdf=tw.build_model(renormalize=True,energy_bias=True,verbose=False)
fig = show_loading(modelpdf,sims=sims.sims)
Loading factors for outflows with \(v_{B,z}>v_{\rm esc}\). Filled circles are directly calculated from the simulation PDFs, while solid lines are from the model PDFs. Solid and dashed lines in (d) denote the model loading factors for \(Z_{\rm ISM}=0.02\) and 0, respectively.
Overall, the model tracks the general behavior of the simulation results.
Beyond the result at \(|z|=H\) presented in Paper II, Twind
includes model and simulation PDFs at \(|z|=2H\), 500 pc, and 1 kpc.
Given its simplicity, the agreement with the simulation PDFs is
stunning!
Figure 4 at z=2H¶
sims=twind.TigressSimContainer(z0='2H')
tw=twind.TigressWindModel(z0=sims.z0,verbose=False)
tw.set_axes(verbose=False)
modelpdf=tw.build_model(renormalize=True,energy_bias=True,verbose=False)
fig = show_loading(modelpdf,sims=sims.sims)
plt.setp(fig.axes,'ylim',(1.e-3,1.e2))
[0.001, 100.0, 0.001, 100.0, 0.001, 100.0, 0.001, 100.0]
Figure 4 at z=500pc¶
sims=twind.TigressSimContainer(z0='500')
tw=twind.TigressWindModel(z0=sims.z0,verbose=False)
tw.set_axes(verbose=False)
modelpdf=tw.build_model(renormalize=True,energy_bias=True,verbose=False)
fig = show_loading(modelpdf,sims=sims.sims)
plt.setp(fig.axes,'ylim',(1.e-3,1.e2))
[0.001, 100.0, 0.001, 100.0, 0.001, 100.0, 0.001, 100.0]
Figure 4 at z=1kpc¶
sims=twind.TigressSimContainer(z0='1000')
tw=twind.TigressWindModel(z0=sims.z0,verbose=False)
tw.set_axes(verbose=False)
modelpdf=tw.build_model(renormalize=True,energy_bias=True,verbose=False)
fig = show_loading(modelpdf,sims=sims.sims)
plt.setp(fig.axes,'ylim',(1.e-3,1.e2))
[0.001, 100.0, 0.001, 100.0, 0.001, 100.0, 0.001, 100.0]
Figure 5: sampling example¶
Can we use Twind in cosmological simulations? Yes! We are working
hard on developing subgrid model based on Twind in the SMAUG
collaboration.
Here’s a quick demonstration of wind particle sampling. (See Appendix B
of Paper II or the source
code
for the procedure in detail.)
# read in time series
sim = twind.TigressSimLoader('R8','H')
sim.load(download=True,time_series=True)
sim.set_axes(sim.simpdf)
fig = sampling_from_simulation_sfr(sim)
Model sampling demonstration for (a) mass outflow rate of cool gas and (b) energy outflow rate of hot gas. The simulation result (black solid) is compared to the model for three different particle mass choices (colored lines; see keys). The input to the model is \(\Sigma_{\rm SFR}(t)\) from TIGRESS simulation R8, where SFR\(=\Sigma_{\rm SFR} L_x L_y\) is shown as the grey shaded region in (a) and the corresponding SN energy injection rate is shown as the grey region in (b). (c) Distributions of cool (circles) and hot (squares) outflow particles sampled over \(t =220\) - \(440\)Myr from the different mass sampling cases (number of particles drawn is shown in the legend). The simulation PDF over the same time interval is shown in the background.
API Reference¶
-
class
twind.TigressWindModel(z0='H', verbose=False)¶ TIGRESS Wind Launching Model class
Parameters: z0 (['H','2H','500','1000']) – Examples
>>> from twind import * >>> tw = TigressWindModel(z0='H') >>> tw.set_axes() >>> pdf = tw.build_Mpdf()
-
CoolMassFluxPDF(u, w, sfr=1.0, params=None)¶ Model of mass loading/flux PDF for cool gas
This utilizes generalized gamma (vout) and log-normal (cs) distributions.
Parameters: - u (array_like (xarray.DataArray)) – log vout
- w (array_like (xarray.DataArray)) – log cs
- sfr (float, array_like) – SFR surface density
- params (array_like or None) – (p_v, d_v, cs0, sigma) if None, cool_params attribute will be used
Returns: pdf
Return type: array_like (xarray.DataArray)
Notes
see Joint PDF Model
-
HotMassFluxPDF(u, w, sfr=1.0, params=None)¶ Model of mass loading/flux PDF for hot gas
This utilizes generalized gamma distributions in vBz and Mach, where vBz = sqrt(vout^2 + 5*cs^2) and Mach = vout/cs
Parameters: - u (array_like (xarray.DataArray)) – log vout
- w (array_like (xarray.DataArray)) – log cs
- sfr (float, array_like) – SFR surface density
- params (array_like or None) – (p_v, d_v, cs0, sigma) if None, cool_params attribute will be used
Returns: pdf
Return type: array_like (xarray.DataArray)
Notes
see Joint PDF Model
-
build_Mpdf(verbose=False)¶ Build mass loading/flux PDF
This will use axes attributes (logvout, logcs, sfr) set by set_axes method
Parameters: verbose (bool) – print integrations of both cool and hot PDFs Returns: pdfs Return type: xarray.Dataset
-
build_model(ZISM=None, renormalize=True, energy_bias=True, verbose=False)¶ Build full PDFs for mass, momentum, energy, and metal PDFs
This will use axes attributes (logvout, logcs, sfr) set by set_axes method
Parameters: - ZISM (float) – set ZISM for metal PDF (if None, ZISM=0.02)
- renormalize (bool) – if True, momentum, energy, and metal PDFs are renormalized
- energy_bias (bool) – if True, apply energy bias factor in building the energy PDF
- verbose (bool) – print integrations of both cool and hot PDFs
Returns: pdfs
Return type: xarray.Dataset
-
reset_parameters(z0)¶ Reset parameters for different z0
This sets z0 attribute and calls _set_parameters() method.
Parameters: z0 (['H','2H','500','1000']) –
-
set_axes(pdf=None, sfr=(-6, 2, 100), vout=(0, 4, 500), cs=(0, 4, 500), verbose=False)¶ Set axes (vout, cs, sfr) using xarray for convenient manipulations
If a simulated pdf is an input, model axes are set to be identical to those of the input pdf otherwise, axes are set for a given (log min, log max, N bins)
Key attributes, u = logvout, w = logcs, logsfr, vBz, and Mach, will be set
Parameters: - pdf (xarray.Dataset or xarray.DataArray) – a joint pdf from simulation
- sfr (float, tuple, list) – a single value of SFR surface density, or log values of min, max, and No. of bins for SFR axis
- vout (tuple, list) – log values of min, max, and No. of bins for vout axis
- cs (tuple, list) – log values of min, max, and No. of bins for cs axis
- verbose (bool) – print input ranges
-
show_parameters()¶ Print all parameters in readable forms
-
-
class
twind.TigressWindSampler(z0='H', verbose=False)¶ Particle sampler for the TIGRESS Wind Model
Parameters: z0 (['H','2H','500','1000']) – Examples
>>> from twind import * >>> sampler = TigressWindSampler() >>> cool,hot=sampler.draw_mass(sfr0,mcool,mhot,area=area,dt=dt)
-
draw_energy(sfr, ecool, ehot, area=1.0, dt=1000.0)¶ Draw particles with fixed particle energy quanta
Parameters: - sfr (float, array_like) – SFR surface density in Msun/yr/kpc^2
- ecool (float) – energy of cool gas in 10^51 erg
- ehot (float) – energy of hot gas in 10^51 erg
- area (float) – area in kpc^2
- dt (float, array_like) – time interval over which particle is sampled
Returns: cool, hot – dicts containg particle mass, 3 component velocity, sound speed, metallicity, and index of each particle in the corresponding input SFR surface density array, which will be used for reconstuction of time series
Return type: dicts
-
draw_mass(sfr, mcool, mhot, area=1.0, dt=1000.0)¶ Draw particles with fixed particle mass quanta
Parameters: - sfr (float, array_like) – SFR surface density in Msun/yr/kpc^2
- mcool (float) – Mass of cool gas in Msun
- mhot (float) – Mass of hot gas in Msun
- area (float) – area in kpc^2
- dt (float, array_like) – time interval in yr over which particle is sampled
Returns: cool, hot – dicts containg particle mass, 3 component velocity, sound speed, metallicity, and index of each particle in the corresponding input SFR surface density array, which will be used for reconstuction of time series
Return type: dicts
-
get_refs(sfr)¶ Obtain reference rates and loading factors for a given SFR surface density using scaling relations
Parameters: sfr (array_like) – SFR surface density Returns: - refs (array_like) – reference mass, momemtum, energy, metal outflow rates
- eta (array_like) – mass, momemtum, energy, metal loading factors for total gas
- eta_cool (array_like) – mass, momemtum, energy, metal loading factors for cool gas
- eta_hot (array_like) – mass, momemtum, energy, metal loading factors for hot gas
-
-
twind.to_time_series(p, time)¶ Function to convert the particle data into time series
Parameters: - p (dict) – paticle data as returned by TigressWindSampler.draw method
- time (array_like) – time array corresponding to SFR time series used to sample particles
Returns: out – time series of mass, momemtum, energy, and metals carried by sampled particles
Return type: (m, p, E, mZ)
-
class
twind.TigressSimContainer(z0='H', modelnames=['R2', 'R4', 'R8', 'R16', 'LGR2', 'LGR4', 'LGR8'])¶ Simulation PDF container for the TIGRESS simulation suite
Load all models at a given height.
Parameters: - z0 (['H','2H','500','1000']) –
- modelnames (['R2','R4','R8','R16','LGR2','LGR4','LGR8']) – list of model names to load
Examples
>>> from twind import * >>> sim = TigressSimContainer(z0='H')
-
class
twind.TigressSimLoader(name='R4', z0='H')¶ Simulated PDF loader for the TIGRESS simulation suite
Parameters: - name (['R2','R4','R8','R16','LGR2','LGR4','LGR8']) –
- z0 (['H','2H','500','1000']) –
Examples
>>> from twind import * >>> sim = TigressSimContainer(model='R4',z0='H')
-
download(source='tigressdata', time_series=False)¶ Download simulation pdf data
Parameters: source (['tigressdata','dataverse','cca']) – Note
‘cca’ server is not yet available as a source
-
load(download=False, time_series=False)¶ Load simulation PDF
Parameters: download (bool) – automatically call download() method if file doesn’t exist
-
pdf_reconstruction()¶ PDF reconstruction from mass loading PDF
License & Attribution¶
Twind is free software made available under the MIT License.
If you make use of Twind in your work, please cite our papers: