The atmosphere at mm wavelengths

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The atmosphere at mm wavelengths

• Jan Martin Winters
• IRAM, Grenoble

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Why bother about the atmosphere?Because the
atmosphere...

• emits thermally and therefore adds noise
• attenuates the incoming radiation
• introduces a phase delay, i.e. it retards the
  incoming wave fronts
• is turbulent, i.e. the phase errors are time
  dependent (seeing) and lead to a decorrelation
  of the visibilities measured by an
  interferometer, i.e. the measured amplitudes are
  degraded

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Constituents

• Species molec. weight Volume abundance
• amu
  
• N2 28
  0.78084
• O2 32
  0.20948
• Ar 40
  0.00934 99.966
• CO2 44
  3.33 10-4
• Ne 20.2 1.82
  10-5
• He 4 5.24
  10-6
• CH4 16 2.0
  10-6
• Kr 83.8 1.14
  10-6
• H2 2
  5 10-7 gt evaporated
• O3 48 4
  10-7
• N2O 44 2.7
  10-7
• H2O 18 a few
  10-6 variable!

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Simplistic Approach

• The atmosphere is a highly complex and nonlinear
  system
• (weather forecast)
• For our purpose we describe it as being
• Static d
  / dt 0 and v 0
• 1-dimensional
  f(r,f,q) -gt f(z)
• Plane-parallel
  Dz / R ltlt 1
• In Local Thermodynamic
  Equilibrium (LTE)
• at
  temperature T(z)
• Equation of state
  ideal gas

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Atmospheric model

• Equation of state
• p (r/M) RT S pi
• Hydrostatic equilibrium
• dp / dz -rg - pM / (RT) g gt dp / p
  -gM / (RT) dz gt
• p p0 exp(-z/H)
• with the pressure scale height
• H RT/gM ( 6 ... 8.5km for T210 ... 290K)
• Temperature structure (tropospheric)
• dT/dz -b ( 6.5 K/km) for z lt 11 km
• T T0 b (z-z0)

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Standard atmosphere
Midlatitude winter
Midlatitude summer
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Atmospheric structure Temperature

• Greenhouse effect
• Energy balance
• 4 pr2sT4 pr2
  (1-A) Lsun/(4pR2) (Albedo A 0.33)
• BB emission absorbed solar radiation
• gt T 252 K ( -21C)
• However, the average temperature near
  the ground is 288 K ( 15C)
• Reason
• H2O, CO2, CH4 , N2O absorb infrared radiation
• gt energy is trapped in the atmosphere

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Atmospheric transmission
Radio cm mm sub-mm
infrared optical UV
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Atmospheric structure Stability (I)

• Ground a) heats up faster than air during the day
• b) cools off faster than air
  during the night
• gt Temperature gradient near the ground
  (lt 2km) can be
  
  steeper or shallower than in
  the standard atmosphere
• Temperature inversion
• e.g. if ground cools faster than the air,
  dT/dz gt 0
• usually stops abruptly at 1-2km altitude,
  normal gradient resumes

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Atmospheric structure Stability (II)

• Stability against convection A rising air bubble
  will cool adiabatically
• Temperature structure (adiabatic)
• dq cv dT pdV 0,
• EOS gt pdVVdp (R/M)dT (cp-cv)dT
• gt dT/dz -g / cp -Gad ( adiabatic
  lapse rate 9.8 K/km)
• If b gt Gad, a rising bubble will become warmer
  than the surroundings (and less dense) gt
  unstable (upward convection, e.g. if ground heats
  up faster than air)

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Radiative transfer (I)
optical depth dtn knds, source function Sn
en/kn
gt formal solution
s
In(s) In(0) e-tn(0,s) ? Sn(s) e-tn(s,s)
kn(s) ds
0
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Radiative transfer (II)
Brightness temperature Motivation
2hn3 1 2n2
c2 exp(hn/kT) 1 c2
In TE In Bn(T) ______ ________________
____ kTR
hn/kTltlt1 Rayleigh-Jeans
Define a brightness temperature
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Radiative transfer (III)
dTb(s) dtn
_____ _ Tb(s) T(s)
gt formal solution
Isothermal medium (equivalent effective
atmospheric temperature TAtm)
Tb(s) Tb(0) e-tn(0,s) TAtm (1 - e-tn(0,s))
source attenuation atmospheric emission
(additional noise,
increases system
temperature)
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Radiative transfer (IV)

• Plane wave, travelling in x direction
• E(x,t) E0 exp i (kx - ?t)
• complex wave vector k 2p/l N
• with complex refractive index
• N n i k
• gt
• Imaginary part k determines attenuation (?4pk/l)
  (absorption)
• Real part n determines phase velocity (nc/vp)
  (refraction)
• Relation to radiation intensity
• I0 cE02/8p ( ltSgtT)
• where S is the Pointing vector

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Line profile (I)

• Absorption coefficient
• k0(n) nl s(n) cm-1
• s0 F0(n)
• (nl -gt nl (1-exp-hn0/kT), stimulated emission)
• e.g., collision broadening profile (complex van
  Vleck Weisskopf)
• F0(n) n / (pn0) 1/(n0-n - i Dn) 1/(n0n i
  Dn)
• F0(n) _____
  ___________________ ___________________
• i
  ___________________ ___________________

Dn 1/(2pt) 1/(2p) n scoll vrel p
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Line profile (II)
Collision broadening profile (van Vleck
Weisskopf) Dn 0.1n0
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Water vapor (I)

• The amount of water vapor is highly variable in
  time (evaporation/condensation process)
• gt separate description in terms of dry and
  wet component (no clouds!)
• Partial pressures
• dry wet
  total
• pd rd RT/Md, pV rV RT/MV, p rT
  RT/MT
• with
• p pd pV, rT rd rV, MT (___ ___
  ____ ___)-1

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Water vapor (II)
Precipitable water vapor column pwv (usually
given in mm) (pwv ) w __ ? rV dz __
rV,0 hV
hV water
vapor scale height The amount of pwv can be
estimated from the temperature and the relative
humidity RH rVg/m3 pV MV / RT 216.5
pVmbar / TK RH pV / psat 100,
psatmbar 6 ( TK / 273 )18 rw 106 g/m3,
hV 2000 m gt wmm 0.0952 RH ( TK /
273 )17 e.g. T 280K, RH 30 gt w 4.4mm
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Water vapor (III)
H2O
368GHz
22GHz
O2
H2O
O2
60GHz
118GHz
183GHz
325GHz
380GHz
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Water vapor (IV)

• Phase delay excess path
• Real part n of complex refractive index
• kn 2p/l n 2pnn/c 2pn/vp , vpc/n
• Extra time Dt 1/c ? (n-1) ds
• Excess path length L cDt 10-6 ? N(s) ds
• with refractivity N 106 (n-1)
• Exact determination compute n throughout the
  atmosphere
• Approximate treatment empirical Smith-Weintraub
  equation
• N 77.6 ___ 64.8 ___ 3.776 105 ___ f(n)
• L Ld LV 231cm 6.52 wcm

Sea level, isothermal atmosphere at 280K
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Water vapor (V)

• Atmosphere is turbulent
• Water vapor is poorly mixed in dry air gt
  bubbles
• These are blown by the wind across the
  interferometer array
• gt time dependent (fluctuating) amount of pwv
  along the line of sight in front of each
  telescope
• gt time variable phase variation, timescales
  seconds to hours

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Water vapor (VI)
PhD Thesis Martina Wiedner (1998)
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To be continued ...

• tomorrow morning in the session about
• Atmospheric phase correction