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The atmosphere at mm wavelengths

The atmosphere at mm wavelengths. Jan Martin Winters IRAM, Grenoble. 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

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The atmosphere at mm wavelengths

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  1. The atmosphere at mm wavelengths Jan Martin Winters IRAM, Grenoble Fourth IRAM Millimeter Interferometry School 2004: The atmosphere

  2. 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 Fourth IRAM Millimeter Interferometry School 2004: The atmosphere

  3. 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 => evaporated O3 48 4 10-7 N2O 44 2.7 10-7 H2O 18 a few 10-6variable! Fourth IRAM Millimeter Interferometry School 2004: The atmosphere

  4. Simplistic Approach The atmosphere is a highly complex and nonlinear system (weather forecast) For our purpose we describe it as being Static d / dt = 0and v = 0 1-dimensional f(r,f,q) -> f(z) Plane-parallel Dz / R << 1 In LocalThermodynamic Equilibrium (LTE) at temperatureT(z) Equation of state ideal gas Fourth IRAM Millimeter Interferometry School 2004: The atmosphere

  5. Atmospheric model Equation of state p = (r/M) RT = S pi Hydrostatic equilibrium dp / dz = -rg = - pM / (RT) g => dp / p = -gM / (RT) dz => p = p0 exp(-z/H) with the pressure scale height H = RT/gM (= 6 ... 8.5km for T=210 ... 290K) Temperature structure (tropospheric) dT/dz = -b (= 6.5 K/km) for z < 11 km T = T0 – b (z-z0) Fourth IRAM Millimeter Interferometry School 2004: The atmosphere

  6. US standard Standard atmosphere Midlatitude winter Midlatitude summer Fourth IRAM Millimeter Interferometry School 2004: The atmosphere

  7. Atmospheric structure: Stability (I) • Ground a) heats up faster than air during the day b) cools off faster than air during the night => Temperature gradient near the ground (< 2km) can be steeper or shallower than in the „standard atmosphere“ • Temperature inversion: e.g. if ground cools faster than the air, dT/dz > 0 usually stops abruptly at 1-2km altitude, normal gradient resumes Fourth IRAM Millimeter Interferometry School 2004: The atmosphere

  8. Atmospheric structure: Stability (II) • Stability against convection: A rising air bubble will cool adiabatically Temperature structure (adiabatic): dq = cv dT + pdV = 0, EOS => pdV+Vdp = (R/M)dT = (cp-cv)dT => dT/dz = -g / cp = -Gad(= adiabatic lapse rate = 9.8 K/km) If b > Gad, a rising bubble will become warmer than the surroundings (and less dense) => unstable (upward convection, e.g. if ground heats up faster than air) Fourth IRAM Millimeter Interferometry School 2004: The atmosphere

  9. dIn(r,n) ds dIn(s´) dtn _________ = en – knIn(r,n) _________ = – In(s´) + Sn(s´) Radiative transfer (I) optical depth: dtn = knds, source function Sn = en/kn => formal solution: s In(s) = In(0) e-tn(0,s) +  Sn(s´) e-tn(s´,s) kn(s´) ds´ 0 Fourth IRAM Millimeter Interferometry School 2004: The atmosphere

  10. c2 1 2k n2 Tb= ___ __ In Radiative transfer (II) Brightness temperature Motivation: 2hn3 1 2n2 c2 exp(hn/kT) –1 c2 In TE: In = Bn(T) = ______________________ = ____ kT hn/kT<<1 Define a brightness temperature: Fourth IRAM Millimeter Interferometry School 2004: The atmosphere

  11. s Tb(s) = Tb(0) e-tn(0,s) +  T(s´) e-tn(s´,s) kn(s´) ds´ 0 Radiative transfer (III) dTb(s) dtn _____= _Tb(s) + T(s) => 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) Fourth IRAM Millimeter Interferometry School 2004: The atmosphere

  12. 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 => Imaginary partkdetermines attenuation (=4pk/l) (absorption) Real part n determines phase velocity (n=c/vp) (refraction) Relation to radiation intensity: I0 = cE02/8p (= |<S>T|) where S is the Pointing vector Fourth IRAM Millimeter Interferometry School 2004: The atmosphere

  13. n n0-nn0+n [ pn0(n0-n) 2 + Dn 2 (n0+n) 2 + Dn 2 Dn Dn ] ) ( (n0-n) 2 + Dn 2 (n0+n) 2 + Dn 2 Line profile (I) Absorption coefficient k0(n) = nℓ s(n) [cm-1] s0F0(n) (nℓ -> nℓ (1-{hn0/kT}), stimulated emission) e.g., collision broadening profile (complex van Vleck & Weisskopf) F0(n) = n / (pn0)[1/(n0-n- i Dn) + 1/(n0+n –i Dn)] F0(n) = ________________________ + ___________________ + i ___________________ + ___________________ Dn = 1/(2pt) = 1/(2p) n scollvrel ~ p Fourth IRAM Millimeter Interferometry School 2004: The atmosphere

  14. Line profile (II) Collision broadening profile (van Vleck & Weisskopf) Dn = 0.1n0 Fourth IRAM Millimeter Interferometry School 2004: The atmosphere

  15. 1 rd 1 rV Md rT MV rT Water vapor (I) • The amount of water vapor is highly variable in time (evaporation/condensation process) • => 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 Fourth IRAM Millimeter Interferometry School 2004: The atmosphere

  16. 1 1 rw rw 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: rV[g/m3] = pV MV / RT = 216.5 pV[mbar] / T[K] RH[%]=pV /psat * 100, psat[mbar] ≈ 6 ( T[K] / 273 )18 rw=106 g/m3, hV =2000 m => w[mm] = 0.0952 * RH[%] *( T[K] / 273 )17 e.g.: T = 280K, RH = 30% => w = 4.4mm Fourth IRAM Millimeter Interferometry School 2004: The atmosphere

  17. 3 mm 2 mm 1 mm Water vapor (III) H2O 368GHz 22GHz O2 H2O O2 60GHz 118GHz 183GHz 325GHz 380GHz Fourth IRAM Millimeter Interferometry School 2004: The atmosphere

  18. pd pV pV induced dipole permanent dipole O2,N2 H2O H2O T T T2 Water vapor (IV) Phase delay – excess path Real part n of complex refractive index: kn = 2p/l n = 2pnn/c = 2pn/vp , vp=c/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 w[cm] Sea level, isothermal atmosphere at 280K Fourth IRAM Millimeter Interferometry School 2004: The atmosphere

  19. Water vapor (V) • Atmosphere is turbulent • Water vapor is poorly mixed in dry air => „bubbles“ • These are blown by the wind across the interferometer array • => time dependent (fluctuating) amount of pwv along the line of sight in front of each telescope • => time variable phase variation, timescales seconds to hours Fourth IRAM Millimeter Interferometry School 2004: The atmosphere

  20. Water vapor (V) PhD Thesis Martina Wiedner (1998) Fourth IRAM Millimeter Interferometry School 2004: The atmosphere

  21. To be continued ... …tomorrow morning in the session about Atmospheric phase correction Fourth IRAM Millimeter Interferometry School 2004: The atmosphere

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