Commit fcd7d1ec authored by Gernot Maier's avatar Gernot Maier
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notebooks updates

parent 62a9e9d5
%% Cell type:markdown id:72a0298f-11fd-41cd-9858-525a442f5e67 tags:
# Shock powered transients
- [Fang, K. et al (2021)](https://arxiv.org/abs/2007.15742)
Step throught this paper to capture the relevant points.
%% Cell type:code id:a6513a2f-9f82-4b77-827f-53562ce2e8ab tags:
``` python
import astropy.units as u
import astropy.constants as const
import math
import matplotlib.pyplot as plt
import numpy as np
```
%% Cell type:markdown id:cf2f37ef-18ab-4277-bca3-ab9962d49387 tags:
#### Fang et al (2021) - Figure 1
<img src="./figures/Fang2021-Figure1.png" alt=drawing width=500/>
%% Cell type:markdown id:ec76c7bb-9616-46c9-9409-27841def1373 tags:
## Section 2.1: Shock Dynamics and Thermal Expansion
- spherical expanding homologoues ejecta of average velicity $\bar v_{ej}$
- inner layers slower than other layers: $v_{ej}\propto r$ (homologoues velocity profile)
### External medium
Density of external medium
$
n \equiv \rho / m_p
$
($\rho$ = mass densitiy)
with a radial profile of
$
n \propto r^{-k}
$
with $k\geq 2$
The external medium is concentrated in a fractional solid angle $f_{\Omega}\leq 1$.
For a thin equatorial disk, $f_{\Omega} \sim h/r$.
%% Cell type:code id:d2ad8e34-3dfe-465b-8478-b1f0d0ace7ee tags:
``` python
# assumed f_omega in the following
f_omega = 1.
```
%% Cell type:markdown id:80cb7f5e-cd0a-4a9c-ab44-a086d60c5167 tags:
### Steady wind approximation
Assume a steady wind with
- mass-loss rate $\dot M$
- wind velocity $v_w$
the density becomes
$
n \simeq \dot M/(4\pi f_{\Omega}r^2 v_w m_p) = A / (m_p r^2)
$
with
$
A \equiv \dot M/(4\pi f_{\Omega} v_w)
$
Assume here $k=2$, otherwise A(r) is a function of radius.
%% Cell type:markdown id:07d923a2-dc40-4312-840a-1e519521c55a tags:
#### Typical values
From modeling interacting supernovae Smith (2014):
- $\dot M \sim 10^{-4} - 1$ M$_{\odot}$ yr$^{-1}$
- $v_w \sim 100 - 1000$ km s$^{-1}$
(note the typo units in the Fang et al paper: A$_*$ should be in g/cm and not g/cm$^2$)
%% Cell type:code id:7f62e216-cd5d-49f5-b270-f23a50dd4ff7 tags:
``` python
# canonical value
A_star = 5.e11 *u.g/u.cm**2
def steady_wind_A(mdot, vw, fomega=1):
"mass loss A"
return mdot/(4.*math.pi*fomega*vw)
v_w = (np.linspace( 100, 1000, 5))*u.km/u.s
M_dot = np.logspace( -5., 0., 100)*u.M_sun/u.year
plt.gcf().clear()
plt.figure(figsize=(6,6))
for z in v_w:
A = steady_wind_A(M_dot, z, f_omega)
label_vw = ("v$_w=$%.0f km s$^{-1}$" % z.value)
plt.plot(
M_dot,
A.to(u.g/u.cm),
label=label_vw)
plt.xlabel("mass loss rate $\dot M$ (M$_{\odot}$/yr)",fontsize=14)
plt.ylabel("A (g/cm)",fontsize=14)
plt.yscale('log')
plt.xscale('log')
plt.legend()
plt.title("steady wind loss parameter A ($f_{\Omega}=%.2f$)" % f_omega)
plt.show()
```
%%%% Output: display_data
%%%% Output: display_data
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)
%% Cell type:markdown id:d0515d5b-23be-49b1-8c0e-2b4c488035d2 tags:
## Shocks
Collision drives two shocks
- forward shock into external medium
- reverse shock into ejecta
Shocks are radiative with rapid cooling of the gas behind both shocks --> gas accumulate in a thin shell which propagates outwards into the external medium.
%% Cell type:markdown id:7cb403f5-0ee5-44a8-b5b7-012f5276a297 tags:
Shocks reach radius $R_{sh}\approx v_{sh}t$ by the time $t$ after the explosion.
Shock speed $v_{sh}$ will reach ejecta speed $v_{ej}$ ([Metzer & Pejach (2017)](https://ui.adsabs.harvard.edu/abs/2017MNRAS.471.3200M/abstract) **READ**), which reduces the power of the reverse shock with relation to the forward shock (**???**)
$\rightarrow$ emission dominated by forward shock
%% Cell type:markdown id:8f2425bf-f1fa-41cc-9c28-7338393c2473 tags:
**Kinetic power of the forward shock**:
$
L_{sh} = \frac{9\pi}{8} f_{\Omega} m_p n_{sh} v_{sh}^3 R_{sh}^2 = \frac{9}{32} \dot M \frac{v_{sh}^3}{v_w} = \frac{9\pi}{8} A f_{\Omega} v_{sh}^3 \ \ (1)
$
with $n_{sh}(R_{sh})$: upstream density ahead of shock
%% Cell type:code id:efb1b6df-322e-4318-9d4e-9bf2abd3f4c2 tags:
``` python
def kinetic_power(A, v_sh, fomega=1):
"kinetic power of forward shock"
return 9.*math.pi/8*A*fomega*v_sh**3
v_sh = (np.logspace( 3, 5, 3))*u.km/u.s
A = np.logspace( 11., 18., 100)*u.g/u.cm
plt.gcf().clear()
plt.figure(figsize=(8,8))
for z in v_sh:
l_kin = kinetic_power(A, z, f_omega)
label_vw = ("v$_{sh}=$%.0f km s$^{-1}$" % z.value)
plt.plot(
A,
l_kin.to(u.erg/u.s),
label=label_vw)
plt.xlabel("steady wind loss parameter A ($g/cm$)",fontsize=14)
plt.ylabel("$L_{sh} (erg/s)$",fontsize=14)
plt.yscale('log')
plt.xscale('log')
plt.legend()
plt.title("Kinetic power of forward shock ($f_{\Omega}=%.2f$)" % f_omega)
plt.show()
```
%%%% Output: display_data
%%%% Output: display_data
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)
%% Cell type:markdown id:cc8be452-fc11-4d1c-b7e9-96a757a148d7 tags:
**Shock heating:**
Gas immediatly behind the shock is heated to: $kT \simeq \frac{3}{16} \mu m_p v_{sh}^2 \approx 11 v_{8.5}^2$ keV.
with $v_{sh}=v_{sh}/(3000 km s^{-1}$.
%% Cell type:markdown id:4dee965b-6662-455f-9d45-a1a4c995e49e tags:
Mean molecular weight of the fully ionized gas (solar composition): $\mu=0.62$
(would be $\mu=2$ if it would be hydrogen-poor gas)
%% Cell type:code id:2d9f096c-8a77-47a1-bacb-be7611c663c8 tags:
``` python
mu=0.62
```
%% Cell type:code id:b5b45a48-2f41-4283-ba70-6d4e7a98d055 tags:
``` python
def shock_temperature(v_sh,mu):
"gas temperature behind the shock"
return 3./16.*mu*const.m_p*v_sh**2
v_sh = (np.logspace( 3, 5, 100))*u.km/u.s
T_sh = shock_temperature(v_sh, mu)
plt.gcf().clear()
plt.figure(figsize=(6,6))
plt.plot(
v_sh,
T_sh.to(u.keV))
plt.xlabel("shock speed ($km/s$)",fontsize=14)
plt.xlabel("shock velocity ($km/s$)",fontsize=14)
plt.ylabel("shock temperature ($keV$)",fontsize=14)
plt.yscale('log')
plt.xscale('log')
plt.title("Temperature of gas behind shock ($\mu=%.2f$)" % mu)
plt.show()
```
%%%% Output: display_data
%%%% Output: display_data
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)
%% Cell type:markdown id:a8217979-9529-4c67-9524-8d39456b540f tags:
Large photoelectric opacity of the external medium: most of $L_{sh}$ is absorped and reprocessed via continuum and line emission into the optical wavelengths.
Time delay of optical emission, as reprocessed emission from nearby the shock must propagate through the column of external medium: $\Sigma = \int_{R_sh}^{\infty} ndr \sim n_{sh} R_{sh}$.
Optical diffussion time scale:
$t_{diff} \approx \tau_{opt} \cdot (R_{sh}/c)$
with the optical depth $\tau_{opt} \equiv \sum \sigma_{opt}$ ($\sigma_{opt}$ is the effective cross section at visual wavelengths).
Adiabatic losses can be neglected as long as $t_{diff} \leq t_{dyn}$ with the expansion time scale of the shocked gas $t_{dyn} = R_{sh}/v_{sh}$:
$
\tau_{opt} \lesssim c/v_{sh} \ \ \ (3)
$
%% Cell type:markdown id:d0b6eb97-21f5-40df-95f2-e221fd2d34c1 tags:
This condition is satisfied at the critical time
This condition is satisfied at times later than $t$:
$
t \gtrsim t_{pk} \approx \frac{c}{v_{sh}^2 n_{sh}} \sigma_{opt} = \frac{\dot M \kappa_{opt}}{4\pi f_{\Omega}c v_w} = \frac{A \kappa_{opt}}{c} \ \ (4)
$
with the optical opacity $\kappa_{opt}\equiv \sigma_{opt}/m_p$ (opacity: cross section for absorbing photons per units mass material; units [m$^2$/kg]).
Label $t_{pk}$ is introduced here, as the critical time often corresponds to the peak of the light curve.
Any diffusion through the eject is ignored in this step.
Any diffusion through the ejecta and corrections to $t_{diff}$ due its non-spherical geometry are ignored in this step.
%% Cell type:code id:2d131588-2352-426c-b8a6-cba2aeead980 tags:
``` python
def peak_time(a,kappa):
"peak time"
return a*kappa/const.c
kappa_es = 0.38 *u.cm**2/u.g
t_pk = peak_time(A, kappa_es)
plt.gcf().clear()
plt.figure(figsize=(6,6))
plt.plot(
A,
t_pk.to(u.s))
plt.xlabel("steady wind loss parameter A ($g/cm$)",fontsize=14)
plt.ylabel("peak time $t_{pk}$ ($s$)",fontsize=14)
plt.yscale('log')
plt.xscale('log')
plt.title("Peak time ($\kappa=%.2f$ cm$^2$/g )" % kappa_es.value)
plt.show()
```
%%%% Output: display_data
%%%% Output: display_data
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mmfk0mDsmk2ZEqGockReFw9ynAlkLNXYFl7r7C3Q8AEwj2NnKBrZHn5Be1PDMbbGY5ZpazcePGRMUWkTT10dJN9Bs1naYNazNhcCbHNagddqSkkhSFoxhNgdVRj3MjbS8Bl5jZ48CUomZ096HunuHuGY0bN058UhFJGx8s2cCAZ2bQslFdxg/O5JgjaoUdKekk8+C4FdHm7r4HGFjqzGZXAleefPLJcQ8mIunpvUXrueW5WZxybD3GDOjGkXVrhB0pKSXzHkcuEH2T3mbAmrLOrKvjikgs3pq/lpvHzuTU44/guUGZKholSObCMQNobWatzKwG0BN4rawz634cIlJWr875ktvGz6ZT84aMHdiVBrWrhx0pqSVF4TCz8cBUoI2Z5ZrZQHfPA24F3gUWA5PcfWFZl6k9DhEpixdm5nL7xDlknHAkzwzoSv1aKhqlSYoxDnfvVUz7W8BbFRxHRCqJ8dO/4J6X53POSUcz7IYMateoGnaklJAUexyJoK4qESnJs1NX8uuX5nP+KY0ZfqOKRizStnCoq0pEijP8wxX8/tWFXNSuCU/37UKt6ioasUiKrioRkYry5ORlPPDOEi47/Vge7dmZ6lXT9vtzwqTtFlNXlYhEc3ce/c9SHnhnCT/oeDyPqWgctrTdauqqEpFD3J2H/r2ER/7zGdec0YxHenSimorGYVNXlYikNXfn/97+lKFTVtCra3Pu++HpVKlS1IUppKzStuSqq0pE3J0/vb6IoVNWcONZJ/DXH6loxEPaFg51VYlUbgUFzm9eWcDoT1Yy6Dut+OMPTsNMRSMe1FUlImknv8C5+8V5PD8zl59ccBJ3XtJGRSOOVDhEJK3k5Rfwy+fn8sqcNdz+/db87HutVTTiLG27qjTGIVL5HMwv4GcT5vDKnDXceUkbbv/+KSoaCZC2hUNjHCKVy4G8Am55bhZvzl/Lby47lVsu1L14EkVdVSKS8vYdzOcnz83iv59u4I9XtqPfOa3CjpTWVDhEJKXtPZDP4DE5fLh0E/f9qD3Xdzsh7EhpT4VDRFLWngN5DBydQ/bnm3ng2g5cl9G89Jmk3FQ4RCQl7dqfx4BRM8hZtYW/X9eRH3VuFnakSiNtB8d1VJVI+tq+9yB9R0xj5hdbeaxXZxWNCpa2hUNHVYmkp217DtBn+DQWfLmdJ68/gys6HB92pEpHXVUikjI279pPnxHTWb5xF0/37cJ32zYJO1KlpMIhIilhw8599Bk+jVWb9zD8hgzOO6Vx2JEqLRUOEUl663fso9ewbNZu28eo/mdy9klHhx2pUlPhEJGktmbbXnoPy2bjzv08M6ArXVsdFXakSk+FQ0SS1uote+g1LJvtew8yZlA3zmhxZNiRhDQ+qkqH44qktpWbdtPj6ans3JfHcyoaSSVtC4cOxxVJXcs27KLH0KnsyytgXFY3OjRrGHYkiaKuKhFJKkvW7eT64dMAZ3xWJm2OrR92JClEhUNEksaiNTvoM2Ia1aoY47LO4uRj6oUdSYqQtl1VIpJa5uVuo9ewbGpWq8LEISoayUx7HCISullfbOXGEdNpUKc647MyaX5UnbAjSQlUOEQkVDNWbqHfyOkcXb8m47IyadqwdtiRpBQqHCISmk+Wb2Lg6ByOa1iL8VmZNDmiVtiRpAw0xiEioZjy2Ub6j5pB86NqM2GwikYqSbnCYWYXmNmHZvaUmV0Qdh4Rid1/P13PoGdyOLFxPcZnZXJMfRWNVJIUhcPMRprZBjNbUKi9u5ktMbNlZnZ3pNmBXUAtILeis4pI+by7cB1DxsykzbH1GZ/VjUb1aoYdSWKUFIUDGA10j24ws6rAE8ClQDugl5m1Az5090uBXwF/quCcIlIOb85byy3PzaJ90waMHdSNhnVqhB1JDkNSFA53nwJsKdTcFVjm7ivc/QAwAbjK3Qsi07cC+qoikiJemf0lt42fRecWDXl2QFca1K4ediQ5TMl8VFVTYHXU41ygm5ldDVwCNAT+WdSMZjYYGAzQokWLxKYUkVI9n7Oau16cR2arRgy/MYO6NZP5o0dKk8yvnhXR5u7+EvBSSTO6+1BgKEBGRoYnIJuIlNG4aV9wz8vzObf10Qztm0HtGlXDjiTllBRdVcXIBZpHPW4GrCnrzLqsukj4nvlkJfe8PJ8L2zRm2A0qGukipsJhZjXNrJWZtTOzRN/wdwbQOrK+GkBP4LWyzqzLqouEa/iHK/jDawu5uF0Tnu6bQa3qKhrpotTCYWb1zexmM5sCbAeWAQuAdWa22syGmdmZ5QlhZuOBqUAbM8s1s4HungfcCrwLLAYmufvCGJapPQ6RkDw5eRl/eXMxl3c4jieuP4Ma1ZK5c0NiZe7FDwGY2R3Ab4EVBN/2pxN0F+0FjgLaA+cCPwKygdvcfWmCM8ckIyPDc3Jywo4hUim4O4++v5R//GcpP+x0PA/9uCPVqqpopCIzm+nuGUVNK21w/GzgfHdfUMz06cBIM7sJGAicDyRF4TCzK4ErTz755LCjiFQK7s5D/17CEx8s59ouzbj/mg5UrVLUMS6S6krc40gH2uMQSTx3569vLWbYh5/Tu1sL/nJVe6qoaKS0kvY4yrwPaWbPR86POPS4jZn9uAIGyUUkibk7f3xtIcM+/Jx+Z7fkvh+qaKS7WDofzwPmAJhZI2AaMBxYaGanxz9a+WhwXCTxCgqce15ewDNTV5F1biv+cGU7zFQ00l0shaM+sDby+zXASqARMAy4L76xyk+H44okVn6Bc9eL8xg//Qt+csFJ3HPZqSoalUQsheML4KTI79cCz0YOmR0NZMY5l4gksbz8An4+aQ4vzMzlju+fwp2XtFHRqERiueTISOAJM3sLuBC4KWoZSXeDYB1VJZIYB/MLuH3CHN6cv5Y7L2nDLRfq/1hlU+Y9Dnd/AHgGOAP4pbuviEzqCqxKQLZyUVeVSPztz8vnJ8/N4s35a/nNZaeqaFRSMV3kMFI8HijU3ITgkuciksb2Hczn5rEz+WDJRv70g9O48eyWYUeSkJT76riRYiIiaWzvgXwGj8nho2Wb+OuPTqd3N92uoDIrsavKzFqVdUEWaF76M0Uklezen0f/0dP5aNkmHrimg4qGlDrGMdXMRpjZWcU9wcyONLObgUXAVXFNVw46j0Ok/HbuO8iNI6czY+VW/tGjEz/O0HdDKb2rqi3wG+BNM8sHZhKcy7EPOJLgXuCnElyz6nZ3fzeBWWPi7q8Dr2dkZGSFnUUkFW3fGxSNBV9u57Genbm8w3FhR5IkUeIeh7tvc/c7CW7jejPwKcEtW1sBeQRHWXV293OSqWiISPls3X2A64dns3DNdp68/gwVDfmGMg2Ou/te4IXIj4iksU279tNn+DRWbNrN0L4ZXNj2mLAjSZJJ5nuOi0gF27BjH9cPn8bqrXsYcWMG57bWNUzl29L2DisaHBeJzbrt++g5NJsvt+1lVL+uKhpSrLQtHDpzXKTscrfu4bqnp7Jh536eHdCVs05qFHYkSWLqqhKp5L7YvIdew7LZse8gYwZ2pXOLI8OOJEnusPc4zOyWeAYRkYr3+abd9Bg6ld0H8hg3KFNFQ8qkPF1V3zWzSw49MLN6ZvZSHDKJSAVYtmEXPZ6eyv68AsYNyuT0ZurWlbIpT1fVDcC7ZpYLFADjgL/HJZWIJNSSdTu5fng2YEwYnMkpTeqHHUlSSMyFw8weI7iF7BxgIDA+MukGd58ft2QikhAL12ynz/Bp1KhWhXFZmZzUuF7YkSTFHE5X1bsEl1K/C3geaAmsAy43syviF618dDiuyLfNy91G72HTqF29KhMHn6WiIYfF3L18CzCrCbQHOgId3P32OOSKm4yMDM/JyQk7hkjoZq7aSr+R02lQpzrjszJpflTS3bhTkoiZzXT3jKKmHfYYh5llAHcSXOxwHvB3dx95uMsTkcSZ/vkW+o+aTuP6NRmXlcnxDWuHHUlSWHmOqpoAvAz8gqBwvGRm3eOSSkTi5pPlm7hx5HSObVCLiUPOUtGQcivPUVVb3P3QLWPnm9nrwP+Ad8ofS0Ti4X+fbWTwszmc0KgOzw3KpHH9mmFHkjRQnj2OFWb2KzM7tIwdwJ44ZBKROHh/8XqynsnhxMb1GJ+loiHxU57CURMYDKwys3eAhcD7ZnZCXJKJyGF7d+E6bho7k7bH1Wd8Vjca1VPRkPg57K4qd/8RgJnVBTpE/Yw1s+bu3jIuCUUkJm/MW8PPJsyhQ7MGPDOgK0fUqh52JEkzZS4cZjYf+I67f+PECHffDUyN/IhIiF6encsvJs0l44SjGNn/TOrV1HVMJf5i6ao6jaB76hvMrIGZPRG/SKUzs7pmNjOZTjgUCduknNX8fNJcMk9sxOgBKhqSOKUWDjN7y8z+CDjQvIin1AGGlCeEmY00sw1mtqBQe3czW2Jmy8zs7qhJvwImlWedIulkbPYq7nphHue2bszIfmdSp4aKhiROWd5dC4ELAAOmm9lOYC4wm+D8jbbA2nLmGA38E3j2UIOZVQWeAC4CcoEZZvYacDywCKhVznWKpIVRH3/On15fxPfaHsMT159BrepVw44kaa7UwuHudwKY2X7gLIIP7k6Rn8sjy7irPCHcfYqZtSzU3BVY5u4rIuufAFwF1APqAu2AvWb2lrsXlGf9Iqlq6JTl/PWtT+l+2rE81qszNaql7U09JYnEsj9b193zgFnAGwnKE60psDrqcS7Qzd1vBTCzfsCmooqGmQ0mOFSYFi1aJD6pSAj++d+lPPTvz7iiw3E80qMT1auqaEjFKHPhiBSNimRFxfjqF/fRxc3o7kOBoRBc5DDuyURC5O488p+lPPb+Uq7u3JQHru1ANRUNqUDJ/G7L5ZuD8c2ANWWdWZdVl3Tk7tz/zhIee38p12U048Efd1TRkAqXzO+4GUBrM2tlZjWAnsBrZZ3Z3V9398ENGuh2mJIe3J1731jMU/9bzvXdWvC3qztQtUpRO+YiiZUUhcPMxhOcQNjGzHLNbGCka+xWghtHLQYmufvCGJapPQ5JGwUFzu9fXcjIjz+n/zkt+csP21NFRUNCUu4bOSU73chJUl1BgXPPy/OZMGM1Q84/kbu7t8VMRUMSq6QbOcW0x2Fml5rZG2a2yMyaR9oGmdn34hFURL4pv8D55QtzmTBjNbd992QVDUkKZS4cZnY9wdnaS4FWwKErp1WlnOdxJIK6qiTVHcwv4PaJc3hp1pf8/KJT+MXFbVQ0JCnEssdxF5Dl7ncA0YfmZhOcDJhUNDguqexAXgE/HT+b1+eu4e5L2/LT77UOO5LIV2IpHK0p+gq4u4Aj4hMnfrTHIalqf14+P3luJm8vWMfvrmjHTeefFHYkkW+IpXCsAU4pov08YHl84sSP9jgkFe07mM/gZ2fyn8UbuPeq0xj4nVZhRxL5llgKx1DgMTM7J/K4uZndCDwA/CvuyUQqmb0H8hn4zAymLN3I364+nb5ntQw7kkiRYrnkyANm1gB4j+DKtB8A+4GH3L1C78chkm52789jwOgZzFi5hYeu7cg1XZqFHUmkWDFdtN/df2Nm9xFcmbYKsMjddyUkWTmZ2ZXAlSeffHLYUURKtGPfQfqPmsGc1dt4pEcnrurUNOxIIiWK6QRAMzsWOBs4hkLdXO7+ZHyjxYdOAJRktn3PQW4YNZ2FX27n8V6dufT048KOJAKUfAJgLPcc7wMMJ7hq7VairlQb+T0pC4dIstq6+wB9Rkzjs/U7+VefLlzUrknYkUTKJJauqvsIBsL/HMIl1kXSyqZd++kzfBorNu1m2A0ZXNDmmLAjiZRZLEdVHQGMTpWiofM4JFlt2LGPnkOzWbl5N6P6namiISknlsLxHMGtYlOCzuOQZLR2+156DM1mzba9jO7flXNOPjrsSCIxi6Wr6ufAK5ELGs4HDkZPdPc/xzOYSLrJ3bqH3sOmsWX3AcYM7EqXE44KO5LIYYmlcAwBugObgJP59uC4CodIMb7YvIdew7LZue8gYwd1o1PzhmFHEjlssRSO3wG/cPdHEhVGJB2t2LiL3sOmsS8vn3FZmbRvqu5TSW2xjHFUJYZbt4ZNg+OSDJau30mPodkczC9gwmAVDUkPsRSOUcD1iQoSbxocl7B9um4HPYdmAzBhcCZtj026i0iLHJZYuqrqAIPM7BJgHt8eHP9pPIOJpLIFX26n74hp1KxWlXFZ3Tixcb2wI4nETSyF41RgduT3toWmpfeNy0ViMGf1Nm4YMY36taozLqsbJzSqG3YkkbiK5eq4FyYyiEg6mLlqC/1GzqBh3eqMz8qk2ZF1wo4kEncxXR1XRIo3bcVm+o+eQZMjajEuqxvHNagddiSRhCixcJjZa0Afd98R+b1Y7v6DuCYTSSEfL9vEwGdm0OzIOowb1I1jjqgVdiSRhCltj2MzX49fbE5wFpGUNHnJBoaMmUmro+sydlA3jq5XM+xIIglVYuFw9/5F/Z4KdCMnqQj/WbSenzw3i9ZN6jF2YDeOrFsj7EgiCVfm8zjMrIWZWXHT4hcpPnQehyTa2/PXctPYmZx6/BGMG5SpoiGVRiwnAH4ONC7caGaNItNEKo3X5q7h1vGz6di8IWMGdqVBnephRxKpMLEcVWUUfb5GPWBffOKIJL8XZ+Zy5wtzyWh5FCP7nUm9mjo4USqXUt/xZvZY5FcH/s/M9kRNrgp0BebEP5pI8pk44wvufmk+Z5/UiGE3ZFCnhoqGVD5ledefHvnXCM4ePxA17QAwC3gozrlEks6Y7FX87pUFnH9KY57u24Va1auGHUkkFKUWjkNnjJvZKOBn7r4j4alEksyIjz7n3jcW8f1Tj+GJ68+gZjUVDam8YrnkSEodjisSL/+avJz73/mUS9sfy6M9O1OjWizHlIikH3XQipTgsfeX8vf3PuPKjsfzyHUdqVZVRUMk5QqHmZ0K/Aw4Gnjf3f8VciRJQ+7O39/7jMf/u4yrOzflgWs7qGiIRCTF/wQzG2lmG8xsQaH27ma2xMyWmdndAO6+2N1vAq4DMsLIK+nN3fnb25/y+H+X0SOjOQ/+WHsaItFiOXM8q4RpT5Uzx2ige6FlVgWeAC4F2gG9zKxdZNoPgI+A98u5XpFvcHf+/MYinp6ygj6ZLfi/q0+napUiL5ggUmnF8jXqATO7pnCjmQ0l+HA/bO4+BdhSqLkrsMzdV7j7AWACcFXk+a+5+9kUcytbMxtsZjlmlrNx48byRJNKpKDA+d2rCxj18UoGnNOKe69qTxUVDZFviWWM41rgJTPb5u7vw1dFoztwQQKyNQVWRz3OBbqZ2QXA1UBN4K2iZnT3ocBQgIyMDN2dUEqVX+Dc89J8Juas5qbzT+JX3dtQzKXZRCq9WA7Hfd/MBgAvmFl3YBBwMXCBu69IQLai/te6u08GJpc6s66OK2WUl1/AXS/M46XZX/LT757MHRedoqIhUoKYRvzc/UXgLmAKcBFwfoKKBgR7GM2jHjcD1pR1Zl0dV8riYH4Bd0yay0uzv+QXF53Czy/WnoZIaUq7A+BjxUxaD8wHfn7oP5m7/zS+0ZgBtDazVsCXQE+gd5zXIZXYgbwCfjp+Nu8sXMevL23LkPNPCjuSSEooravq9GLalxNcFffQ9HKNI5jZeIJxkqPNLBf4g7uPMLNbgXcJLqY40t0XxrBMdVVJsfbn5XPLc7P4z+IN/P6Kdgz4TquwI4mkDHNP77HjjIwMz8nJCTuGJJF9B/MZPGYmUz7byL1XnUbfs1qGHUkk6ZjZTHcv8ly5tD2rycyuNLOh27dvDzuKJJE9B/IYMHoGHy7dyP3XnK6iIXIYYrrkiJlVIzi/ogXwjftkuvuzccxVbu7+OvB6RkZGsScuSuWya38eA0bNIGfVFh7+cUeuPqNZ2JFEUlKZC4eZtQVeB1oRHCqbH5n/ILAfSKrCIRJtx76D9Bs5nbm523m0Z2eu7Hh82JFEUlYsXVX/AGYCDYA9BDd1yiC4+9+3zigPm7qq5JDtew7Sd/g05n+5nSd6q2iIlFcsheNM4C/uvhsoAKq5+yyC8zoeTkS48tB5HAKwZfcBeg3LZvHanTzVpwvd2x8XdiSRlBdL4TCCPQ2AjQSXBIHgRD0d8ypJZ9Ou/fQams3yjbsYdmMG3zu1SdiRRNJCLIPjC4COwApgOvArM8sHsoBlCchWLjqPo3LbsGMfvYdPI3frHkb2O5NzTj467EgiaSOWPY77+Pr6Ub8luBzIBwTXq4r3WePlpq6qymvt9r30GJrN2m17eaZ/VxUNkTiL5SKH70b9vgJoZ2ZHAVs93c8ilJSxesseeg/PZtvugzw7sCtdTjgq7Egiaadct45198L30BAJzarNu+k9bBo79x1k7KBudGzeMOxIImkppjPHzexSM3vDzBaZWfNI2yAz+15i4h0+HY5buazYuIseT2ez50Ae47IyVTREEiiWW8deD0wClhKcBFg9MqkqwSG5SUVjHJXH0vU7ue7pbA7mFzB+cCbtm+o1F0mkWPY47gKy3P0OIC+qPRvoFM9QImW1eO0Oeg7NxgwmDM6k7bFHhB1JJO3FUjhaA1OLaN8F6H+rVLgFX26n17BsqletwsTBmbRuUj/sSCKVQiyFYw1wShHt5xHcn0Okwsz+Yiu9hmVTt0Y1Jg05ixMb1ws7kkilEUvhGAo8ZmbnRB43N7MbgQeAf8U9mUgxclZuoe+I6RxZpwYTh2TSolGdsCOJVCqxnMfxgJk1AN4DahGc/LcfeMjdn0hQvsOmM8fTU/aKzQwYPYNjj6jFuKxMjm1QK+xIIpVOzHcANLM6BFfFdWBW5KKHSUt3AEwfHy3dxKBnZ9DsyDqMy+rGMfVVNEQSJW53ADSz24FPCfY2JgOfmtkdZmYlzSdSXh8s2cCAZ2bQslFdJgzOVNEQCVEsN3J6ABgMPMjXR1edBfweOI4kPJdD0sN7i9Zzy3OzOOXYeowZ0I0j69YofSYRSZhYLjkyCBjk7i9Etf3XzJYAT6PCIQnw1vy1/HT8bE5r2oBnB3SlQe3qpc8kIgkV67Wq5hXTFlOXl0hZvDrnS34+aS6dmjdkdP8zqV9LRUMkGcTygf8scEsR7TcDY+ITRyTw4sxc7pg4h4wTjuTZAV1VNESSSCx7HDWB3mZ2CcFlRgC6AccDz5nZY4ee6O6h359Dh+OmrgnTv+DXL8/nnJOOZtgNGdSuUTXsSCISpcyH45rZB2Vcprv7dw8/UnzpcNzU8uzUlfz+1YVc0KYxT/XpQq3qKhoiYSjpcNxYTgC8MH6RRL5t+Icr+Mubi7moXRP+2bszNaupaIgko3LdyEkkXp74YBkPvruEy04/lkd7dqZ6VR1vIZKsVDgkVO7Oo+8v5R//WcpVnY7n4R93pJqKhkhSU+GQ0Lg7D/17CU98sJxruzTj/ms6ULWKLkIgkuxUOCQU7s5f31rMsA8/p1fX5tz3w9OpoqIhkhJUOKTCuTt/en0Roz9ZyQ1nncAfrzxNRUMkhahwSIUqKHB+9+oCnpv2BYO+04rfXH4qukamSGpJucJhZj8ELgeOAZ5w93+Hm0jKKr/AufvFeTw/M5ebLziJuy5po6IhkoKS4vAVMxtpZhvMbEGh9u5mtsTMlpnZ3QDu/oq7ZwH9gB4hxJXDkJdfwC+fn8vzM3P52fdaq2iIpLCkKBzAaKB7dIOZVQWeAC4F2gG9zKxd1FN+G5kuSe5gfgE/mziHl2d/yZ2XtOGOi05R0RBJYUlRONx9CrClUHNXYJm7r3D3A8AE4CoL3A+87e6zKjqrxOZAXgG3jpvFm/PW8pvLTuWWC3XtMJFUlxSFoxhNgdVRj3MjbbcB3weuNbObiprRzAabWY6Z5WzcuDHxSaVI+w7mc/PYmby7cD1/vLIdWeedGHYkEYmDZB4cL6ovw939MeCxIqZFP2koMBSCixwmIJuUYt/BfLKezeHDpZu470ftub7bCWFHEpE4SeY9jlygedTjZsCass5sZlea2dDt27fHPZiUbM+BPPqPmsFHyzbxwLUdVDRE0kwyF44ZQGsza2VmNYCewGtlndndX3f3wQ0aNEhYQPm2Xfvz6DdyBtM+38zfr+vIdRnNS59JRFJKUhQOMxsPTAXamFmumQ109zzgVuBdYDEwyd0XxrBM7XFUsO17D9J3xDRmfrGVR3t25kedm4UdSUQSoMw3ckpVupFTxdi25wB9R0zn03U7eLzXGXRvf2zYkUSkHEq6kVNS7HEkgvY4Ks7mXfvpNWwaS9bt5Om+XVQ0RNJc2hYOjXFUjI0799NrWDYrNu5i+I0ZfLdtk7AjiUiCJfPhuJLk1u/YR+9h2azZto9R/c7k7JOPDjuSiFSAtN3jUFdVYq3ZtpceT09l3fZ9PDOgq4qGSCWStoVDXVWJs3rLHnoMncrm3QcYM6gbXVsdFXYkEalA6qqSmKzctJvew7LZfSCf5wZ1o0OzhmFHEpEKpsIhZbZswy6uH57NgbwCxmV147TjtTcnUhmlbVeVxjji67P1O+k5NJv8Apgw+CwVDZFKLG0Lh8Y44mfRmh30HJpNFYMJgzNpc2z9sCOJSIjStnBIfMzL3UavYdnUqlaFSUPO4uRj6oUdSURCpjEOKdasL7Zy44jpNKhTnfFZmTQ/qk7YkUQkCaTtHofGOMpnxsot9B0+jaPq1WDikLNUNETkK2lbODTGcfimLt/MDSOm06RBLSYNOYumDWuHHUlEkkjaFg45PB8u3Uj/0dNpflRtJgzOpMkRtcKOJCJJRmMc8pUPPt3AkLEzOalxPcYO7EqjejXDjiQiSUiFQwB4d+E6bh03i7bHHsGYgV1pWKdG2JFEJEmlbVeVBsfL7s15a7nluVmcdnwDxg7qpqIhIiVK28KhwfGyeWX2l9w2fhadWzRkzMCuNKhdPexIIpLk1FVViU3KWc2vXpxHZqtGDL8xg7o19XYQkdLpk6KSGjftC+55eT7ntj6aoX0zqF2jatiRRCRFqHBUQs98spI/vLaQC9s05l99ulCruoqGiJSdCkclM2zKCu57azEXt2vCP3ufQY1qaTvMJSIJosJRiTzxwTIefHcJl3c4jn/06ET1qioaIhK7tP3k0OG4X3N3HnnvMx58dwk/7HQ8j6poiEg5pO2nhw7HDbg7D767hEffX8q1XZrx8HWdqKaiISLloK6qNObu3PfmYoZ/9Dm9u7XgL1e1p0oVCzuWiKQ4FY40VVDg/On1hTwzdRX9zm7JH65sh5mKhoiUnwpHGioocH7zygLGT/+CrHNbcc9lp6poiEjcqHCkmfwC564X5vHirFxuufAkfnlxGxUNEYkrFY40kpdfwC+en8urc9Zwx/dP4affO1lFQ0TiToUjTRzML+D2CXN4c/5a7rykDbdceHLYkUQkTalwpIH9efncNm42/160nt9efiqDzj0x7EgiksZS7oB+MzvRzEaY2QthZ0kG+w7mc9OYmfx70Xr+9IPTVDREJOGSonCY2Ugz22BmCwq1dzezJWa2zMzuBnD3Fe4+MJykyWXvgXyyns1h8mcb+euPTufGs1uGHUlEKoGkKBzAaKB7dIOZVQWeAC4F2gG9zKxdxUdLTrv359F/9HQ+WraJB67pQO9uLcKOJCKVRFIUDnefAmwp1NwVWBbZwzgATACuqvBwSWjnvoPcOHI6M1Zu5R89OvHjjOZhRxKRSiQpCkcxmgKrox7nAk3NrJGZPQV0NrNfFzWjmQ02sxwzy9m4cWNFZK0w2/cepM+I6cxZvY3He3Xmqk5Nw44kIpVMMh9VVdQJCO7um4GbSprR3YcCQwEyMjI8AdlCsXX3AfqOnMaSdTt58vozuPi0Y8OOJCKVUDLvceQC0X0wzYA1ZZ053S6rvnnXfnoNy+az9bsY2jdDRUNEQpPMhWMG0NrMWplZDaAn8FpZZ06ny6pv2LmPnkOzWbl5NyNuzODCtseEHUlEKrGkKBxmNh6YCrQxs1wzG+juecCtwLvAYmCSuy+MYZlpscexbvs+ej6dzZfb9jKqX1fObd047EgiUsmZe9oMARQpIyPDc3Jywo5xWL7ctpfew7LZvOsAo/ufSUbLo8KOJCKVhJnNdPeMoqYl8+B4pbZ6yx56Ds1mx76DjBnYlc4tjgw7kogIkCRdVYmQyl1Vn2/azXVPT2XX/jzGDcpU0RCRpJK2hSNVB8eXbdhFj6ensj+vgPFZmZzeLLXyi0j6U1dVElmybifXD88GjAmDMzmlSf2wI4mIfEva7nGkWlfVwjXb6Tl0KlWrGBOHqGiISPJK28KRSl1V83K30XvYNGpXr8rEwWdxUuN6YUcSESmWuqpCNnPVVvqNnE6DOtUZn5VJ86PqhB1JRKREabvHkQpdVdM/38INI6bRqF4NJg05S0VDRFJC2haOZO+q+mTZJm4cOZ0mDWoxcchZHN+wdtiRRETKJG0LRzL732cb6T96Bi2OqsPEwWfR5IhaYUcSESkzjXFUsPcXr+fmsbM4+Zh6jB3UjaPq1gg7kohITNJ2jyMZxzjeWbCOm8bOpO1x9RmXpaIhIqkpbQtHso1xvDFvDbeMm8XpTRswdlA3GtZR0RCR1KSuqgrw8uxcfjFpLhknHMXI/mdSr6Y2u4ikLn2CJdiknNX86sV5nHViI4bfmEGdGtrkIpLa9CmWQGOzV/HbVxZw3imNGdq3C7WqVw07kohIuaXtGEfYg+OjPv6c376ygO+1PUZFQ0TSStoWjjAHx4dOWc6fXl/EJac14V99VDREJL2oqyrOHn9/KQ+/9xlXdDiOR3p0onrVtK3NIlJJqXDEibvzyHuf8dh/l/Gjzk158NoOVFPREJE0pMIRB+7O/e8s4an/LefHXZrxt2s6ULWKhR1LRCQhVDjKyd25943FjPz4c67v1oJ7r2pPFRUNEUljKhzlUFDg/OG1hYzJXkW/s1vyhyvbYaaiISLpTYXjMBUUOPe8PJ8JM1Yz+LwT+fWlbVU0RKRSSNvR20Sex5Ff4Nz5wjwmzFjNbd89WUVDRCqVtC0ciTqPIy+/gDsmzuHFWbn8/KJT+MXFbVQ0RKRSUVdVDA7kFfCzCbN5e8E6ftW9LTdfcFLYkUREKpwKRxntz8vnludm8Z/FG/jt5acy6NwTw44kIhIKFY4y2HcwnyFjZvK/zzZy71Wn0feslmFHEhEJjQpHKfYeyCfr2Rw+Xr6Jv119Oj27tgg7kohIqFQ4SrB7fx4DRs9gxsotPHhtR67t0izsSCIioVPhKMbOfQfpN2oGc1Zv45EenbiqU9OwI4mIJAUVjmKs2ryH5Rt38Xivzlx2+nFhxxERSRopVzjMrC7wJHAAmOzuzyViPe2bNmDKXRdyRK3qiVi8iEjKSooTAM1spJltMLMFhdq7m9kSM1tmZndHmq8GXnD3LOAHicyloiEi8m1JUTiA0UD36AYzqwo8AVwKtAN6mVk7oBmwOvK0/ArMKCIiJEnhcPcpwJZCzV2BZe6+wt0PABOAq4BcguIBSZJfRKQySeYP3qZ8vWcBQcFoCrwEXGNm/wJeL2pGMxtsZjlmlrNx48bEJxURqUSSeXC8qCsHurvvBvqXNKO7DzWztcCVNWrU6JKQdCIilVQy73HkAs2jHjcD1pR15kRdHVdEpLJL5sIxA2htZq3MrAbQE3gt5EwiIpVeUhQOMxsPTAXamFmumQ109zzgVuBdYDEwyd0XxrDMhN3ISUSkMjN3DztDQmVkZHhOTk7YMUREUoqZzXT3jKKmJcUeRyJoj0NEJDHStnBocFxEJDHStnCIiEhipG3hUFeViEhipP3guJltBFYBDYDoKhL9+NDvRbUdDWyKcbWF11WWaWXJV1rueGctbnpJWUvLGN2mbRvfbVuerKXl1batfNv2BHdvXOQz3L1S/ABDi3t86Pdi2nLKu66yTCtLvtJyxztrcdNLyqptG962LU9WbVtt27JuW3dP366qIhS+rtXrRfxeVFs81lWWaWXJV9zvicpa3PSSshZ+rG0b2/TybNvyZC1tfm3b8kmnbZv+XVXlZWY5XsyxzMkmlbJCauVV1sRJpbyplBUSl7cy7XEcrqFhB4hBKmWF1MqrrImTSnlTKSskKK/2OEREJCba4xARkZiocIiISExUOEREJCYqHGVgZiea2Qgze6GktmRRTN4fmtkwM3vVzC4OM1+0YrKeamZPmdkLZnZzmPmiFfeam1ldM5tpZleEla0oxWzbC8zsw8j2vSC8dN9UTNYqZnafmT1uZjeGma+wYvKeG9muw83skzDzRSsmawsze83MRprZ3bEus9IWjsgG22BmCwq1dzezJWa27NAGdfcV7j4w+nlFtSV53lfcPQvoB/RI8qyL3f0m4DogoYc+ljdrxK+ASYnMGce8DuwCahHcZTOZs14FNAUOJjprPPK6+4eR9+0bwDPJnBU4BXjT3QcA7WIOcDhnQabDD3AecAawIKqtKrAcOBGoAcwF2kVNf6GI5XyrLcnzPgyckexZgR8AnwC9kzkr8H2Cu1P2A65I9vcBUCXybxPguSTPejcwpLj3crLljWqbBByRzFmBRsAHwH+B/rGuv9Lucbj7FGBLoeauwDIPKvQBYALBt57QlTevBe4H3nb3WcmcNbKM19z9bOD6xCWNS9YLgUygN5BlZgn9P1XevO5eEPl1K1AzYUGJy7bNJcgJkJ+YlF+Lx/vWzFoA2919R+KSxiVrf+AP7v5d4PJY119pC0cxmgKrox7nAk3NrJGZPQV0NrNfAxTVFoIy5wVuI/h2fK2Z3VTBOSG2bXuBmT1mZk8DbyVzVnf/jbvfDowDhkV9MFekWLbt1ZHtOgb4Z8VHjek9+xJwiZk9Dkyp4JyHxJIXYCAwqiIDRokl6zvATyPtK2NdUbXyJk0zVkSbu/tm4KZCjd9qC0EseR8DHquQVEWLJetkYHIFZCpOmbNGTRyd0EQli2XbvkTwgRyWWLLuIfggDlNM7wV3/0PiIxUrlm27ALj2cFekPY5vygWaRz1uBqwJKUtZpFJeZU2cVMqbSlkhtfJWWFYVjm+aAbQ2s1ZmVoNg0PO1kDOVJJXyKmvipFLeVMoKqZW34rImcuQ/mX+A8cBavj7Ub2Ck/TLgM4KjE34Tds5UzKusyptqWVMtb9hZdZFDERGJibqqREQkJiocIiISExUOERGJiQqHiIjERIVDRERiosIhIiIxUeEQEZGYqHCIiEhMVDgEADN7w8xGV/A6R5vZG+VcRqm547EeSS1mdqSZrTezk8LOUpgFd7b8edg5ykOFI4mZ2WQzC+PS1xXlZ0CfsENI7CryvWlmnc0s38w+jmG2e4C33H35YazvKTN7JNb5YvAn4Ldm1iCB60goFQ4Jjbtvd/dtYedIRZGL2KW8Mv4dWcCTQHszO7UMy6wDDAJGHEYeA64EXo113rJy9/nAClL4S5MKR8jM7DwzyzazXWa23cymmVn7SPfL+cAtZuaRn5aRO/ndZWbLzWyvmc03sz6FltndzD40s61mtsXM3o3+D2dmdSLdN7siu/P3FJr/BjPbbGY1C7U/Z2ZFXm3TzC41s51mVi3yuHUk87+innOfmb0X9firLqTIN9gnzeyvZrbJgvspP2RRd9QrLXdZmVlNM/tHZBn7Itv/O1HTi3xNSptWzLomR77BPhp5Pbaa2YOF/q4SX6+o5fwrsk02Ah/HON/DkedsNLOfRbbBE2a2zcy+MLO+heYr9n1W3HuztPmK+ztKea1qE9xdcRjwAmW7P8dlQEHhZZtZWzP7ICrX2WZ20MzOj3ramQT3Y/8oar5GkczrIu+XBWZ2sZk1i/ztPczsv2a2x8zmRtaTYWZTIm3TLbgzYLTXgF5l+FuSU9hXeazMPwQ30toKPAScBLQl+E9yKtCA4J7bI4FjIz9VgfuAJUB3oFXk+buBy6OWe03kpzXQgeAeyMuAGpHpTwJfApcA7YHngR3A6Mj02pFc10UtswGwB7iqmL+lHsGVOjMjj7OAjcCnUc/5mKgrdgKjgTciv08GtgN/Bk4BrgPygF5Rzy8xdwnb+av1RB4/SnBl0csj23oYsAs4rpTXpNhpJax7MrATeDzy/Osif+fPy/p6FVrOw5HlnBrDfDuAP0ae9wvAgbcJugpPBu4F9gPHR81X7PuMYt6bpc1X3N9RymvXF5gb+f0CYANQvZR5HgX+XaitbWQ7PBDZdlcQ3C3PgSOjnvdX4Nmox80Irj77CnB2ZHv1I7hd8BWR+ScTFNLTgU+BbIJ7eX8H6Eiwd/GPQnm6AweA2mF/Dh3WZ1fYASrzD3BU5I13fjHTJwP/jHpcF9gLnFvoef8g6M8tbj11Ce7Z/B2CD/j9wPVR0+sB24j6ACa4reg7UY9vBtYB1UpYzzTg15HfnwP+EMl7HFAn8h/lnKjnj+abhWNqoeW9BwyPylhq7mJyRa+nbiTHDVHTqxJchvovJb0mpb1eJbyGn0FwJepI22+B3LK8XoWWM6+UdRU339Sox0ZQ0F+Laqse2SbXlvV9Vvi9GeN8Jf4dheb9H/DLqOwrgWtKmecV4JlCbf8GXizU9iywslDbQuDqqMdvEty+2IpYz28i778mUW2PR7Zvo6i2UcDEQvN2iLyXTirrtkimH906NkTuviWy2/+umb0PvA887+6ri5mlHcFu9DtmFn09/OpE3TfYgiNJ7gW6AY0JuiSrAC0Ivu3VAKZG5dhlZvMLrWsYMMvMmrl7LjCA4D9jXgl/0mSCb4X/R/AN7FHgu5G2TQR7JNNLmH9eocdrgGMiv59UxtylOYlge33VjeHu+WY2FWhX0mtyGK/XIdke+bSImArca2ZHuPuOUl6vaDOjH8Qw31fb1d3dzDYA86PaDprZVr7e1mV6nxWhrPN94+8ojpmdDJxDpEsnkv05gvGLF0uYtTawPmo5zYGLgE6FnrcfmFtofScC70YetyDo9jqz0Ot3SCeCLyTro9paAC95cLvW6LYZhebdG5U15WiMI2Tu3p/gP/4U4AfAZ2Z2STFPP/R6XUnwpj30cxpwcdTzXif4IBkSWXZngm6fGhR9X+Kics0FZgH9In34GQRdEyWZDJxjZu2A+gQfEJOBCwmKxyfufrCE+QtPc77+m8uUuwwOLaeoDwKHkl+TGF+vsirp9Yq2+zDnK2q7lrSty/o+K6ys8xX+O4oziGBv8AszyzOzPOBu4OJIMSjOJuDIqMdnEGyXwl9MTgXmRD3+IfC+ux/Kd2h7FlfoOhJ0S0XrTNSXm6jnzS7UdlTk343FLDupqXAkAXef6+73u/sFBB+0N0YmHSD4j3PIIoJvSSe4+7JCP6sgGMgj+A/xV3f/j7svJvgQP7R3uYzIWMShhZpZXYIxg8KGEfTnDgI+dvclpfwpHwI1gbuAj9w9n28WjsmlzF+SWHKXtpwDBN12h5ZTFTiLYPsCJb4mJU4rRjcziy58mcCayN5Gaa9XkQ53vjIq9X3Gt9+bZZ2vTCw4yOJG4Nd8swh1JCgA/UuYfTbB3s8h+ZGsdaKW34Vgb2Zu1POuIujmOuQgwfasX0S+ugR7r7Oj2o4iuOd3dFtzoBHfLhztCd4D60lB6qoKkZm1Ivi2+BrBoO+JBH2fh45EWgl0jRyxsgvYQjAw+1Dkg2gKQT9/JlDg7kMJBm83AVlmthpoCjxI8M3pUPfOCOD+yFEta4Df8+0PAQhuT/l3gvGNm0r7eyLLnkVwmOHdkeapBP+ZWhEUlMMSY+6SlrPbgiO9/mZmm4DPgTuAJsCTJb0mZXi9inM88A8ze5JgAPVOgvEUKOX1KsHhzlcqd99pZqW9z1ZS6L1ZxvnK6nLgaGBYoW4fzGwCcLOZ/cXdC4qY912C90mjyLw5BAXtQTN7mOAggUPnacyJLLNxJOe1UcuZRrCdnzKz+/h6nHAGXxeh6MLTObKeRVFtnQi2z7JCGc8F3inh709uYQ+yVOYfgg+rlwg+hPYDXxAc9VE9Mv0Ugg/ePQRdCS0Julpu4+tvdxsJBpEvilrud4EFwL7Iv5cQvHn7RabXJRgY3EVwlMrvgDcoYpCZoHtqJ1C3jH/T3yJZM6LaJhN0T1Qv9NzRfHNwvPBg61fTY81dynJqEgzYro9sw2wiA8olvSalvV7FrHsy8BTBwQbbCD6IHiZyFFJZXq8Sts/hzrcA+GOhtnXArVGPS3yfUcR7s4zzfStPMdvtNQodGRU17cTIOi8uYf6pwC1Rj68jKHa7I++ZXwEboqYPIOhKLbyccwjGw3ZGXr/3CI4iu4moIwYjz/0lkFOo7bcEe9/RbbUIjqzLrOjPnHj96J7jUiIze5vgCKCssLOkIjObDCxw91vDzlKZmFl3goMz2nnQZRo9zQi+7S93959E2l4l6I59oAKy3UJwWHtJ40VJTV1VUqRIf+33CQY1O4YcRyQm7v6OmT0BNIuMMxxLcLBHI4KuyU58c5zkY4Ku2YpwkGCvLGWpcEhxZhEc+XGPuy8IO4xIrNz9MQAzOxO4n2AcaCNBd1kXd18T9dyE72lErSuWsZ6kpK4qERGJiQ7HFRGRmKhwiIhITFQ4REQkJiocIiISExUOERGJiQqHiIjERIVDRERiosIhIiIx+X/KnsVKmjhMbQAAAABJRU5ErkJggg==)
%% Cell type:markdown id:f1ef373f-bf29-4aa1-8920-b064924d13ca tags:
**Shock velocity is function of peak luminosity and peak time**:
$
v_{sh} = \left( \frac{8}{9\pi} \frac{L_{pk} \kappa_{opt}}{ct_{pk}f_{\Omega}} \right)^{1/3}
$
(derived from combining (1) and (4))
Assume here that $L_{pk} \approx L_{sh}$ (all optical emission is shock powered, without any contribution from e.g. radiactive decay).
%% Cell type:markdown id:a7d2c5e2-7398-4254-a28d-b14bf19efa1b tags:
## Calorimetric Technique
Conditions on the optical depth are very similar to the required conditions for particle acceleration and that the shock discontinuity is mediated by collisionless plasma. At times earlier than $t_{pk}$, the trapped radiations thickens the shock transition to macroscopic scale and does not allow any particle injection.
1. no efficient particle acceleration before $t_{pk}$
2. fixed fraction $\epsilon_{rel}$ of the shock power $L_{sh}$ is placed into relatistic particles
Total energy of relativistic particles $E_{rel}$ is proportional to the fraction of radiated optical fluence $f_{sh}$:
$
E_{rel} \approx f_{sh} \epsilon_{rel} E_{opt}
$
$\epsilon_{rel} E_{opt}$ is an upper limit to the energy of accelerated particles, as $f_{sh}<1$.
The total optical energy of shock-powered transients places an upper bound on the total gamma-ray and neutrino emission, as the relativistic particles cool quickly (**calorimetric method**).
%% Cell type:markdown id:1244bc13-2c94-4ece-a430-a2af2b5f6de0 tags:
## Coooling time scales
(skip discussions on cooling time scales, **revisit later**)
Shocks are generally radiative ($t_{cool} \ll t_{dyn}$) for $v_{sh} \lesssim 10,000-30,000$ km s$^{-1}$.
%% Cell type:markdown id:39e2b1d9-50e3-476a-89d6-6e26dec8b21a tags:
For Novae: $\epsilon_{rel} \sim 0.003 - 0.01$
%% Cell type:markdown id:0b6c4b04-bc1e-440a-bf55-855aad526789 tags:
**Dynamical tooling time scale:**
$t_{dyn} \sim R_{sh} / v_{sh}$
%% Cell type:markdown id:c5d4d50b-450c-4b4b-abeb-5b4e7e2e1b4c tags:
**Cooling times scale for radiatively cooled thermal gas**:
$
t_{cool} = \frac{9}{128} \frac{m_p v_{sh}^2}{\Lambda n_{sh}}
$
at $T = T_{sh}$ and with cooling function $\Lambda$.
At high temperatures $T \gtrsim 10^{7.3}$ K with dominating free-free cooling:
$\Lambda \approx \Lambda_{ff} \approx 2.3 \times 10^{-27} (T_{sh}/$K$)^{1/2}$ erg cm$^3$ s$^{-1}$
Line emission cooling contributing at $10^5 < T < 10^{7.3}$:
$\Lambda_{line} \approx 1.1 \times 10^{-22} (T_{sh}/$K$)^{-0.7}$ erg cm$^3$ s$^{-1}$
(see discussion in Draine, B. T. 2011, Physics of the Interstellar and Intergalactic Medium (Princeton University Press, 2011)
%% Cell type:code id:a3aaa2aa-1a46-44bf-a320-27917e0500f4 tags:
``` python
def t_cool(n, v_sh, T_sh):
"thermal cooling time scale"
lambda_ff=2.3e-27*math.sqrt(T_sh.to(u.k))
return 9.128*const.m_p*v_sh**2/lambda_ff/n_sh
```
%% Cell type:markdown id:a7220e62-9fbf-4845-873d-a973a99b8994 tags:
**Cooling time scale PP interactions**:
$
t_{pp} \approx \left( n \sigma_{pp} c \right)^{-1}
$
($\sigma_{pp} = 5 \times 10^{-26}$ cm$^2$ at 1 PeV)
%% Cell type:code id:90740c71-67bf-466e-bfdc-cd417f25bc01 tags:
``` python
def t_pp(n, sigma_pp=5.e-25*u.cm**2):
"cooling time scale pp interactions"
return 1./n/sigma_pp/const.c
```
%% Cell type:code id:4ab678c7-fb7f-4b45-a640-e58f83f9922d tags:
``` python
```
......
......@@ -198,7 +198,7 @@ plt.plot(
v_sh,
T_sh.to(u.keV))
plt.xlabel("shock speed ($km/s$)",fontsize=14)
plt.xlabel("shock velocity ($km/s$)",fontsize=14)
plt.ylabel("shock temperature ($keV$)",fontsize=14)
plt.yscale('log')
plt.xscale('log')
......@@ -224,7 +224,7 @@ plt.show()
# \tau_{opt} \lesssim c/v_{sh} \ \ \ (3)
# $
# This condition is satisfied at the critical time
# This condition is satisfied at times later than $t$:
#
# $
# t \gtrsim t_{pk} \approx \frac{c}{v_{sh}^2 n_{sh}} \sigma_{opt} = \frac{\dot M \kappa_{opt}}{4\pi f_{\Omega}c v_w} = \frac{A \kappa_{opt}}{c} \ \ (4)
......@@ -234,7 +234,7 @@ plt.show()
#
# Label $t_{pk}$ is introduced here, as the critical time often corresponds to the peak of the light curve.
#
# Any diffusion through the eject is ignored in this step.
# Any diffusion through the ejecta and corrections to $t_{diff}$ due its non-spherical geometry are ignored in this step.
# +
def peak_time(a,kappa):
......@@ -258,6 +258,8 @@ plt.xscale('log')
plt.title("Peak time ($\kappa=%.2f$ cm$^2$/g )" % kappa_es.value)
plt.show()
# -
# **Shock velocity is function of peak luminosity and peak time**:
......@@ -271,5 +273,72 @@ plt.show()
# ## Calorimetric Technique
#
# Conditions on the optical depth are very similar to the required conditions for particle acceleration and that the shock discontinuity is mediated by collisionless plasma. At times earlier than $t_{pk}$, the trapped radiations thickens the shock transition to macroscopic scale and does not allow any particle injection.
#
# 1. no efficient particle acceleration before $t_{pk}$
# 2. fixed fraction $\epsilon_{rel}$ of the shock power $L_{sh}$ is placed into relatistic particles
#
# Total energy of relativistic particles $E_{rel}$ is proportional to the fraction of radiated optical fluence $f_{sh}$:
#
# $
# E_{rel} \approx f_{sh} \epsilon_{rel} E_{opt}
# $
#
# $\epsilon_{rel} E_{opt}$ is an upper limit to the energy of accelerated particles, as $f_{sh}<1$.
#
# The total optical energy of shock-powered transients places an upper bound on the total gamma-ray and neutrino emission, as the relativistic particles cool quickly (**calorimetric method**).
#
# ## Coooling time scales
#
# (skip discussions on cooling time scales, **revisit later**)
#
# Shocks are generally radiative ($t_{cool} \ll t_{dyn}$) for $v_{sh} \lesssim 10,000-30,000$ km s$^{-1}$.
#
#
#
# For Novae: $\epsilon_{rel} \sim 0.003 - 0.01$
# **Dynamical tooling time scale:**
#
# $t_{dyn} \sim R_{sh} / v_{sh}$
# **Cooling times scale for radiatively cooled thermal gas**:
#
# $
# t_{cool} = \frac{9}{128} \frac{m_p v_{sh}^2}{\Lambda n_{sh}}
# $
#
# at $T = T_{sh}$ and with cooling function $\Lambda$.
#
# At high temperatures $T \gtrsim 10^{7.3}$ K with dominating free-free cooling:
#
# $\Lambda \approx \Lambda_{ff} \approx 2.3 \times 10^{-27} (T_{sh}/$K$)^{1/2}$ erg cm$^3$ s$^{-1}$
#
# Line emission cooling contributing at $10^5 < T < 10^{7.3}$:
#
# $\Lambda_{line} \approx 1.1 \times 10^{-22} (T_{sh}/$K$)^{-0.7}$ erg cm$^3$ s$^{-1}$
#
# (see discussion in Draine, B. T. 2011, Physics of the Interstellar and Intergalactic Medium (Princeton University Press, 2011)
def t_cool(n, v_sh, T_sh):
"thermal cooling time scale"
lambda_ff=2.3e-27*math.sqrt(T_sh.to(u.k))
return 9.128*const.m_p*v_sh**2/lambda_ff/n_sh
# **Cooling time scale PP interactions**:
#
# $
# t_{pp} \approx \left( n \sigma_{pp} c \right)^{-1}
# $
#
# ($\sigma_{pp} = 5 \times 10^{-26}$ cm$^2$ at 1 PeV)
def t_pp(n, sigma_pp=5.e-25*u.cm**2):
"cooling time scale pp interactions"
return 1./n/sigma_pp/const.c
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