Transcript Acceleration of Coronal Mass Ejection In Long Rising Solar

CSI 662 / ASTR 769
Lect. 10
Spring 2007
April 10, 2007
Neutral Upper Atmosphere
References:
•Prolss: Chap. 2, P11-77; Chap. 3.2-3.5, P103 – 159 (main)
•Gombosi: Chap. 8, P125 – P156; Chap. 9.1-9.4, P158 – 169
(supplement)
•Tascione: Chap. 6, P. 79 – 88 (supplement)
Neutral Upper Atmosphere
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Atmospheric layers
Barospheric density distribution
Exospheric density distribution
Solar radiation energy
Radiation absorption processes
Temperature distribution
Thermospheric winds
Atmospheric waves
Atmospheric Layers
Classified by temperature
• Troposphere
• 0  10 km
• ~300 K  200 K
• Stratosphere
• 10 50 km
• ~200 K 250 K
• Mesosphere
• 50 km  80 km
• ~250 K  160 K
• Thermosphere
• > 80 km (~10000)
• 160 K  ~1000 K
Atmos. Layers
Classified by Gravitational binding
• Barosphere
• 0 km 600 km
• binding
• Exosphere
• > 600 km
• Escaping or evaporation
Classified by Composition
• Homosphere
• 0 km 100 km
• Homogeneous
• Heterosphere
• 100 km  ~2000 km
• Inhomogeneous
• Hydrogensphere (Geocorona)
• > ~2000 km
• Dominated by hydrogen
Basic Parameters
Chemical composition (ni/n):
• Height = 0 km, 78% N2, 21% O2, 1% others (trace gases)
• Height = 300 km, 78% O, 21% N2, 1% O2
Pressure:
• Height = 0 km, P = 105 pa
• Height = 300 km, P=10-5 pa
Atomic Number
Mass Number
H
He
N
O
N2
O2
1
1
2
4
7
14
8
16
28
32
f (Degree of freedom) 3
3
3
3 translation
2
T  Uf
k
3
5
5
+ 2 rotation
T: temperature
Uf: internal energy per freedom
k: Boltzmann constant

Cp
Cv

f 2
f
Some Kinetic Parameters
Flow and random velocity
• Actual gas particle velocity v
• Flow (bulk, wind) velocity u
• Random (thermal) velocity c
  
v u c
Test particle: type 1; Gas particle: type 2
• Cross section σ1,2 : probability of interaction (m2)
Ideal collision (billiard ball collision)
1,2   (r1  r2 )2
• Collision frequency:
1,2  1,2n2c1,2
l1, 2 
• Mean free length
l1,1 
c1
1, 2
1
n 1,1
Barospheric Density Distribution
Hydrostatic equilibrium or aerostatic equations
dP
  g
dz
P
  mn  m
kT
dP
P

dz
H
kT (h)
H ( h) 
Pressure Scale Height
m ( h) g ( h)
h
P (h)  p (h0 ) exp{  Hdz( z ) } Barometric Law
h0
h
n(h)  n(h0 ) TT((hh0)) exp{  Hdz( z ) }
h0
n(h)  n(h0 ) exp( 
isothermal
h  h0
H
)
Barospheric Density Distribution
In upper thermosphere (~ >200 km)
T  T
m  mo
H0 
kT
mo g
Isothermal, thermopause temperature
Dominated by atomic oxygen
 60km
In lower thermosphere (120 km -- 200 km)
T (h)  T  (T  t (h0 ) exp(s(h  h0 ))
Bates temperature profile
h0=120 km, T(h0)=350 K,
and s=0.021 km-1
Barospheric Density Distribution
• Isothermal Scale
Heights
– Hi = kT/(mig)
N2
for g(200 km)
HN2 = 0.032* T
HO2 = 0.028* T
HO = 0.0567* T
O
O2
Altitude interval where density
decreases by 10:
Homosphere to Heterosphere
In hydrostatic state, particle distribution is determined by
gravitational setting and molecular diffusion
Density scale height depends on the molecular mass
This would create a gravitationally-separated atmosphere
 D   D dn
dz
Molecular diffusion flux
kT
D1,1 
m1,1
Molecular diffusion coefficient
3
2
Homosphere to Heterosphere
In hydrostatic state, particle distribution is determined by
gravitational setting and molecular diffusion
Density scale height depends on the molecular mass. Heavy gas
has small scale height, and decreases rapidly with height
This would create a gravitationally-separated atmosphere
   D dn
dz
Molecular diffusion flux
kT
D1,1 
m1,1
Molecular diffusion coefficient
D
3
2
Homosphere to Heterosphere
However, the atmosphere remains homogeneous up to 100 km.
This mixing is caused by eddy diffusion or turbulence
• Turbopause or Homopause
– Where eddy and molecular diffusion rates are equal
– Typically ~ 105 km
• But transition is smooth over some altitude
interval
• Below is called the homosphere
• Above is the heterosphere
Heterosphere
Turbopause
Homosphere
Turbopause
Gombosi, Fig 8.3
Exosphere
• Exosphere: where the density is so small that direct escape
(evaporation) of gas particles is possible
• The lower boundary of the exosphere is called the exobase
• Exobase height: above which, a radially outward moving
particle will suffer less than one collision

N (h)   ( H ,O ( z ) / cH )dz
h

N (h)   H ,O  no ( z )dz
Number of collisions
h

N (h)   n( z )dz
Column density (above h)
h
N ( h)   
0
dp
p ( h ) mg

N ( h)  n( h) H ( h)
p(h)
mg ( h )
Exosphere
• Exobase height:
E.g., ~ 420 km, for σH,O=2 X 1019 m2, T=1000 K, H0=60 km,
n0(250 km) =1.5X1015 m-3
• Escape flux:
• Depends on how many particles at the exobase have an
escape velocity?
• Ves ≈ 11 km/s
• At T=1000 K, CO=1.25 km/s, CHe=2.5 km/s, CH=5 km/s
f M (c )  n(
3/ 2
m
2kT
)
2
e
 mc
2 kT
Particle Maxwellian distribution function
Hydrogen: φes=1012 m-2 S-1, τes=70000 years
Other elements are well gravitationally-bound
Solar Radiation Energy
The temperature structure of the Earth’s upper atmosphere is
determined by the properties of solar radiation, the primary
source of energy
SOLAR - TERRESTRIAL
ENERGY SOURCES
Source
Energy
(Wm-2)
Solar Cycle
Change (Wm-2)
Deposition
Altitude
Solar Radiation
• total
• UV 200-300 nm
• VUV 0-200 nm
1366
15.4
0.15
1.2
0.17
0.15
Particles
• electron aurora III
• solar protons
• galactic cosmic rays
0.06
0.002
0.0000007
Peak Joule Heating (strong storm)
• E=180 mVm-1
Solar Wind
0.4
0.0006
surface
10-80 km
50-500 km
90-120 km
30-90 km
0-90 km
90-200 km
above 500 km
SPECTRUM
VARIABILITY
TOTAL
IRRADIANCE
VARIABILITY
Solar Energy
Deposition
Atmospheric
Structure
SPACE
WEATHER
EUV
FUV
MUV
RADIATION
GLOBAL
CHANGE
Atmospheric Absorption Processes
• Ionization
– O2 + h  O2+ + e*, …
• Dissociation
– N2 + h  N + N, …
• Excitation
– O + h  O*
• O* O + h ’
• O* + X  O + X
radiation
quenching or deactivation
• Dissociative ionization – excitation
– N2 + h  N+* + N + e, …
Energy Thresholds for Processes*
Species Dissociation Dissociation
(Å)
(eV)
H
He
O
O2
N2
NO
2423.7
1270.4
1910
5.11
9.76
6.49
Ionization
(Å)
Ionization
(eV)
911.75
504.27
910.44
1027.8
796
1340
13.6
24.58
13.62
12.06
15.57
9.25
* From Heubner et al., Astrophys. Space Sci., 195, 1-294, 1992
Useful relationship: E(eV) x  (Å) = 12397
Radiative Absorption
F
Change in photon
flux
dz’
dF  nF dz
n = # absorbers/cc
 = absorption cross
section
Integrating,
F+dF

F(z)  F() e

 n(z ')dz '
z
Optical Depth

• Definition
(z)   n(z')dz'
z
• For several species
– i = N 2 , O2 , O

(z)    ini (z')dz'
i
z
• Altitude of unit optical depth: F(z)= F() e-1
– Solve (z) = 1 for z
– Where solar radiation is effectively extinct
Optical Depth
• If  const.,

(z)   n(z')dz'   N(z)
z

• Vertical Column Density
N(z)   n(z')dz'
z
 number of atoms/molecules in a 1 cm2
column above altitude z
Slant path optical depth
Assume plane parallel
atmosphere
– H << earth radius
– Away from terminator
F()
0

(s)
s

s = z / cos 
and
(s) = (z) / cos 
(z)
z
  solar zenith angle
What happens at the
terminator ( = 90o)?
Large solar zenith angles
• Allowing for earth curvature and isothermal atmosphere,
then:
(s) = (z) Ch(x, )
–
–
–
–
X = (Re + z)/H
Re = earth radius
H = scale height
Ch(x, ) = Chapman function
0.5
1

Ch(x, χ)   π x sinχ  e
2

 xcos 2 χ 


 2 


2

 xcos χ 
1 ± erf 
 2 




0.5




*
where +   > 90o and -   < 90o
• Must do numerical integration along slant path from Sun:
– If not isothermal
– If accounting for oblate spheroid shape of Earth
* From Rishbeth and Garriott, Intro. To Iono. Phys.
Energy Deposition from Radiation
q (h)  E phn(h) (h)
E
Eph=hpc/λ : energy of
single photon
Φph(h): radiation flux at
height h
The deposition rate at
height h depends on the
combination of the
radiation flux and gas
density at h.
ph
Energy Deposition from Radiation
• Change composition through photo-dissociation
• Change the upper atmosphere into a conducting medium through
photo-ionization
• Heat is also generated, e.g., hot photoelectron through ionization
• Buoyancy
O + photon
oscillation
(λ = 30.4 nm)  O+ + e + excess energy
41 ev
14 ev
27 ev
• Hot photoelectron first transfer kinetic energy to ambient
thermal electron, leading to heating of electron gas
• Hot electron gas heats up the cooler neutral gas
Heat Loss
• Radiation cooling. Important for trace gases like NO and CO2,
whose vibration and rotational transitions are effective excited at
thermospheric temperature
• Molecular heating conduction.
 z  
W
  a T
dT
dz
Temperature Profile
• Temperature profile is determined by the heat balance equation
(or energy equation)
c
T
p t
 q l  d
W
W
W
qW: heat production by radiation absorption
lW Heat loss through radiation cooling
dW Heat gain/loss through conduction
MSIS Class Empirical Atmospheric Models
• MSIS-class Models Are the Community Standard
• Inputs: Day, Time (UT, Apparent Solar Local Time),
Location, Solar EUV Flux Proxy (F10.7 , F10.781 day
ave), Magnetic Activity (ap, Ap)
• Outputs: Composition (N2, O2, O, N, He, Ar, H, Oa),
Total Mass Density, and Temperature, 0 - 1000 km
• Empirical, Analytic, Assimilative
– Spherical Harmonics + Bates-Walker Altitude Profile
– Interpolates Among Or Extrapolates Numerous Data Sets To
User-Specified Inputs
– Nominal 1s Error 15-25 % (vs Altitude/Latitude)
• NRLMSIS 2000E supercedes MSISE-90:
Automated/Web Distribution
MSIS Accessibility
• Description and downloading:
– http://uap-www.nrl.navy.mil/models_web/msis/msis_home.htm
– http://modelweb.gsfc.nasa.gov/models/msis.html
• MSIS 90 (earlier version)
• Reference to NRLMSIS2000
– Picone, J. M., A. E. Hedin, D. P. Drob, and A. C. Aikin, J.
Geophys. Res., 107(A12), 1468 (2002)
• MSIS solar-geophysical inputs can be found
at:
– ftp://ftp.ngdc.noaa.gov/STP/GEOMAGNETIC_DATA/INDICES/KP_AP/
– http://www.sec.noaa.gov/today.html
NRLMSIS Example: March 21
F10.7 = 150, Ap = 4 , Altitude = 300 km
Thermospheric Winds
• Thermosphere is not statis
• It corotates with the Earth
• Uco=Ωrcosφ
• At h=300 km, Uco=500 m/s
• It has global circulation winds
• It has atmospheric waves
Diurnal Wind Circulation
• Caused by considerable temperature and density differences
exist in the thermosphere between the day and night
•
•
•
•
High pressure in the afternoon sector (~ 3 PM)
Low pressure shifts by 12 hours (~ 3 AM)
Pressure difference is 4 μPa
Produce airflow as high as 200 m/s (700 km/hr)
• This airflow is also called tidal wind because of its 24 hour
periodicity
Diurnal Wind Circulation

•
•
•
•
•

Du
Dt
  p  

 2u h
z 2

 
 
 g   n,i (ui  u )  2 u   E
Pressure gradient force
Viscosity force
Gravity force
Ion drag force
Coriolis force
Altitude-Latitude Variation of Thermospheric
Circulation from GCM Model
Geomagnetic
Activity
Quiet
Average
Storm
Atmospheric Waves
• Acoustic Wave
• ~ 340 m/s at h=0
• ~860 m/s at h=300 km, T= 1000K
Vs   / k  p /   kT / m
• Buoyancy oscillation
• At h=300 km, τg=2π/ωg ~13 min
 g  g / c pT
• Gravity wave
• a combination of acoustic wave and buoyancy effect
• Responsible for quasi-periodic fluctuation of electron density
and layer height
The End