Long-term observations of Uranus and Neptune at 90 GHz with the IRAM 30m telescope - (1985 -- 2005)

0.42 MB·English

by  C. Kramer

Astronomy & Astrophysics manuscript no. planets90ghz c ESO 2008
(cid:13)
February 4, 2008
Long-term observations of Uranus and Neptune at 90 GHz with
the IRAM 30m telescope
8
0
0 (1985 – 2005)
2

n
a C. Kramer1,2, R. Moreno3,2, and A. Greve4
J

9
1 I. Physikalisches Institut,Universit¨at zu K¨oln, Zu¨lpicher Strasse 77, D-50937 K¨oln, Germany
2
2 IRAM,Nucleo Central, Avda.DivinaPastora 7, E-18012 Granada, Spain
] 3 LESIA (LAM- bat.18), 5 Place Jules Janssen, 92195 Meudon, France
h 4 IRAM,300 Ruedela Piscine, Domaine Universitaire, F-38406 St.Martin d‘H`eres, France
p
-
o received date; accepted date: 23/01/2008
r
t
s
a ABSTRACT
[

1 Context. The planets Uranusand Neptunewith small apparent diameters are primary calibration standards.
v Aims. We investigate their variability at ∼ 90GHz using archived data taken at the IRAM 30m telescope during the 20years
2 period 1985 to 2005.
5 Methods. We calibrate the planetary observations against non-variable secondary standards (NGC7027, NGC7538, W3OH,
4 K3-50A) observed almost simultaneously.
4 Results. Between 1985 and 2005, the viewing angle of Uranus changed from south-pole to equatorial. We find that the disk
.
1 brightnesstemperaturedeclinesbyalmost 10% (∼2σ)overthistimespan indicatingthatthesouth-poleregion issignificantly
0 brighterthanaverage.Ourfindingisconsistentwithrecentlong-termradioobservationsat8.6GHzbyKlein&Hofstadter(2006).
8 Both data sets do moreover show a rapid decrease of the Uranus brightness temperature during the year 1993, indicating a
0 temporal, planetary scale change. We do not find indications for a variation of Neptune’s brightness temperature at the 8%
: level.
v
i Conclusions. IfUranusis tobeused ascalibration source, andif accuracies betterthan10% arerequired,theUranussub-earth
X
point latitude needs to betaken into account.
r
a
Key words.Planets - Uranus- Neptune
1. Introduction submillimeter regime. However, recent microwave as well
as observations at visible and near-infrared wavelengths
At mm-wavelengths, the planets Uranus and Neptune
indicate that Uranus is variable on time scales of several
with small apparent diameter are frequently used for cal-
years (see e.g. Klein & Hofstadter 2006, KH06 in the fol-
ibration of astronomical sources and telescope parame- ◦
lowing). Due to Uranus’ large obliquity of 82 , measure-
ters. In this context it is often tacitly assumed that they
ments from the earth alternate between observations of
are constant radiators, at least at short term intervals.
the poles and the equator, i.e. the sub-earth point (SEP)
Observations over a decade or a longer period, preferably
latitude varies. KH06 argue that the variations they ob-
with the same telescope andreceiversand traceablemod-
served at 3.5cm (8.6GHz) are partly caused by the geo-
ifications, may reveal a long–term variability of Uranus
metricaleffect,butpartlyalsobytemporalvariationsdeep
and Neptune.
inside the Uranus troposphere. However, this variability
For a long time, Uranus and Neptune have been sep-
has not yet been studied at millimeter wavelengths.
arated by a distance of 22o or less in the sky and thus
We investigate whether these long-term variations de-
∼
allowprecisecomparativemeasurements.Griffin & Orton
scribed above are noticeable in 20 years pointing obser-
(1993) observedUranusandNeptune in1990and1992to vations 1 made with the IRAM 30m telescope at 90GHz.
derive their brightness temperature in the millimeter and
1 Thiscollectionofpointingmeasurementsprovidedalsothe
Send offprint requests to: C. Kramer basisforseveralcompilationsofquasarfluxdensitiespublished
2 C. Kramer, R.Moreno, and A. Greve: Long-term 90GHz observations of Uranusand Neptune
By relating the observations of the planets to nearly si- ble. Due to the flat spectrum of the planetary nebula
multaneous observations of the constant secondary cali- NGC7027 (Sanchez Contreras et al. 1998) the reported
brators NGC7027, NGC7538, W3OH and K3–50A, the flux density variation at 1.4GHz of 0.24% per year
measurements of the planets are free from changes of the (Perley et al. 2006) is expected to occur, approximately,
telescopeperformance(reflectoradjustments,receiverup- also at mm-wavelengths. This amounts to a change of
grades,etc.) but contain, on the other hand, the errorsof 5%in 20 years.We note that we usually observedsev-
∼
the secondary measurements. The secondaries are small eral secondaries per day, using their average to calculate
′′
relative to the half power beam width (HPBW) of 27 at the planetary fluxes, thereby reducing this slight effect.
90GHz. One pointing measurement consists of 2 Az and 2 El
scans. The error of a pointing measurement, used in the
following, is the rms-value of the four scans. Almost all
2. Observations, selection criteria ◦
observations were made in the elevation range 20 –
◦ ∼
70 .Inthis range,thegain-elevationcorrectionat90GHz
We use heterodyne observations (0.5 and 1GHz band-
islessthan2%(cf.Table2inGreve et al.1998b).Wedid
width) made between1985and2005with the IRAM30m
not correct for this minor effect.
telescope (Pico Veleta, Spain) at 86–90GHz (3.4mm).
This procedure does not allow the derivation of abso-
Most of the data were obtained during pointing measure-
lute flux densities of the planets since their flux densities
ments, or extended pointing sessions during the earlier
were used to derive the flux densities of the standards. In
years (see Greve et al. 1996). The data are scans across
the following we therefore study relative changes of the
theplanets,andothersources,includingthefittedGauss-
planet’s flux densities and disk-averaged brightness tem-
ian profiles, their halfwidths, their pointing offsets, and
∗ peratures.
their peak antenna temperature T , separately deter-
A
We show in Fig.1 the measurements of the four sec-
mined for the azimuth (Az) and elevation (El) directions.
ondary calibrators over the entire observing period and
An archived measurement is accepted for this analysis if
the Az and El pointing offsets do not exceed 3 – 5′′, i.e. list their mean temperatures in Table1. An accuracy of
betterthan10%isachievedforallsecondariesillustrating
beingsmallcomparedtotheHPBW,andiftheAzandEl
′′ the precisionofrepeatedpointing measurementsmadeby
full width at half maximum (FWHM) are within 3 – 5
many visiting observers usually for their own programs.
of the source convolvedvalue. Under these conditions the
The observed scatter of antenna temperatures includes
antenna temperatures obtained from the Az and El scans
possible changes of the telescope efficiencies from day to
agree within 10%, and their average value is used.
∼ day and over the years. Such changes are calibrated out
The hot-cold-sky calibration method used at the 30m
when studying relative temperature variations measured
telescope corrects for atmospheric attenuation and gives
∗ on the same day.
the antenna temperature T [K] of the beam convolved
A
From the relation between the observed flux density
source.
S , the Planck function B at temperature T(θ,ψ), the
The aperture efficiency ǫ and forward efficiency F b
ap eff
beam patternP(θ,ψ), andthe solidangleΩ ofthe planet
(seeDownes1989;Greve et al.1998a)areregularlydeter-
subtended at the time of observation
mined (F to within 5%, ǫ to within 10%) and
eff ap
± ±
the flux density of a point source per beam is S = Ω
b ′ ′ ′ ′ ′
2(k/A)TA∗Feff/ǫap = 3.904TA∗Feff/ǫap [Jy] (with A the Sb = B[T(θ−θ ,ψ−ψ )]P(θ ,ψ )dΩ (1)
geometricalareaofthe30mreflector,andktheBoltzmann Z0
constant). It is impossible to recover the actual value we obtain when assuming a constant brightness tem-
Feff/ǫapforacertaindayinordertoderivethefluxdensity perature T(θ,ψ) = TBΠ(θ,ψ) across the disk (Π) of the
S from the archived antenna temperature T∗. However, planet
b A
from simultaneous observations of the constant sources
Ω
NGC7027, NGC7538, W3OH and K3–50A (see for in- S =(2k/λ2)T Π(θ θ′,ψ ψ′)P(θ′,ψ′)dΩ′ (2)
b RJ
stanceSteppe et al.1993;Reuter & Kramer1998;Sandell Z0 − −
1994), withflux densities giveninTable 1,we derivedthe
and with the Rayleigh-Jeans temperature
∗
gain Sb,sec/TA,sec = 3.904Feff/ǫap which we applied to T =hν/k(exp(hν/(kT )) 1)−1
∗ ∗ RJ B
the measurements of the planets Sb,pla = TA,pla/TA,sec× − −1
S .ThederivedfluxdensitiesoftheplanetsS con- Ω
b,sec b,pla T = (λ2/2k)S ΠP dΩ′ (3)
tain also the errors of the measurements of the standard RJ b
sources. Z 0 !
We assume that any time variance of the four sec- TRJ (λ2/2k)Sb(ΩK)−1. (4)
≡
ondary calibrators is negligible. NGC7538, K3-50A, and
W3OH are ultra-compact Hii regions which are sta- The first-order Planck correction at 90GHz is
T T hν/(2k)=T 2.1K.
RJ B B
≈ − −
by Steppeet al. (1988, 1992, 1993) and Reuteret al. (1997). In the above equations, we use for the beam pattern
′′
Unfortunately,most of the data of 1988 and 1989 are lost, for P(θ,ψ) a Gaussian profile of 27 HPBW (Greve et al.
unknownreason. 1998a), as it remained constant throughout the years by
C. Kramer, R.Moreno, and A. Greve: Long-term 90GHz observations of Uranusand Neptune 3
Table 1. Observations of the secondary calibrators at
90GHz for the years 1985 to 2005 and the adopted flux
densities and sizes at this frequency. N is the number of
observations.
Source hT∗i rms N S(1) θ(4)
A b S
[K] [%] [Jy] [′′]
W3OH(2,3) 0.63 8.2 517 3.77 14×10
NGC7538 0.41 10.1 351 2.37 20×18
K3–50A(3) 1.06 8.7 451 6.00 10×5
NGC 7027(2) 0.77 7.9 455 4.58 ∼10
References: (1) Steppeet al. (1993), for comparison: (2)
W3OH:4.08±0.12Jy, NGC7027:5.27±0.15Jy(Ulich
1981); (3) W3OH:3.93Jy, K3–50A:6.31Jy(Table3 in
Reuter& Kramer 1998); (4) approximate dimensions at
mm-wavelengths from Sandell (1994), for comparison:
′′
Reuter& Kramer (1998) give at 90GHz, W3OH: 6 and
K3–50A: 2′′.
Fig.1. Observations of the secondary calibrators at
90GHz. Dashed lines show their rms scatter (cf.Table1).
using receivers of similar illumination taper. Using the
Fig.2. Ratio of Uranus and Neptune brightness temper-
IRAM in-house programplanetswe derive fromthe flux
aturesat86-90GHznormalizedtotheaverageratio1.075.
densities the correspondingdisk-averagedbrightnesstem-
Thesolidlineistheresultofalinearfittothe81observed
perature T [K]. This program takes into account the
RJ
data(smalldots).Largedotsarethecorrespondingyearly
apparent diameter of the planets θ and the HBPW. In
s
averages.
Eq.4, the correction factor K for a non-pointlike plane-
tary disk is (cf. Eq.12 in Baars 1973):
1 exp( x2) 1/f θ the past20years(distance < 22o)andarethereforeideal
K = − − with x= s√ln2 (5) for comparative measureme∼nts.
x2 ≡ x2 θ
b
Griffin & Orton (1993) determined Uranus and
where f is called beam dilution factor. Neptune brightness temperatures in the 0.35 to 3.3mm
The apparentsurface areaofUranus changedby 2.5% region, using Mars as the primary standard. From mea-
over the 20 years observing period discussed here. This is surements made in 1990 and 1992 they derive brightness
due to its oblateness, coupled with its high obliquity. We temperatures of Uranus and Neptune at 90GHz of
take this geometrical effect into account when discussing T (Uranus) = 136K and T (Neptune) = 131K.
B B
possible temporal changes of its disk averaged tempera- Since Uranus and Neptune are close together on the
ture in Sec.3.1. The variations due to Neptune’s oblate- sky, a plot of the ratio of their brightness temperatures
ness are much smaller and ignored. derived from simultaneous measurements made with the
same telescope, may reveal also a relative change of their
brightness temperatures. Such measurements of Uranus
3. Uranus and Neptune
andNeptune made atfrequencies between86 and90GHz
′′
Becauseoftheirsmallapparentdiametersof 2 ,Uranus during 1986 and 2005, are shown in Fig.2. These data
∼
and Neptune are good calibration standards, at least for werepartlyobservedwithoutcomplementaryobservations
the larger and more sensitive mm–wavelength telescopes. of the secondaries. However, only their relative ratios are
In addition, they were never far apart in the sky during discussed in this paragraph.
4 C. Kramer, R.Moreno, and A. Greve: Long-term 90GHz observations of Uranusand Neptune
Fig.3.RelativechangeofUranus’brightnesstemperature Fig.4.RelativechangeofUranus’brightnesstemperature
at 90GHz and at 8.6GHz. The solid line is the result of at 90GHz and at 8.6GHz as function of SEP latitude.
a linear fit to the 286 observed 90GHz data (small dots). Small filled dots show the individual 90GHz measure-
Their rms is 6%. Large solid dots are the yearly averages ments, large filled dots show the 90GHz data binned into
(cf.Table2). TB istheaveragebrightnesstemperatureat intervals of 15◦. Errorbarsare calculatedfrom the scatter
h i
90GHzdataof134K.Opencirclesshowthe8.6GHzdata oftheindividualdata.Opencirclesshowthe8.6GHzdata
of KH06 normalized to Tlit = 218K which was extracted of KH06.
from Fig.3 of KH06 for the period shown.
◦
obliquity of82 . In1985,Uranusshowedits southpole to
Calculating the brightness temperature ratio fromthe the earth-boundobserver,the sub-earthpoint(SEP)lati-
ratio of antenna temperatures, we took into account the tude was 82◦, the apparent radius was nearly the equa-
−
Uranus (U) and Neptune (N) apparent diameters at the torialradius.It showedits equatorin 2005when the SEP
time of the observation: TB(U)/TB(N)=TA∗(U)/TA∗(N)× latitude was −6◦ (cf. Fig.4). Insummary,Uranus showed
f(U)/f(N), with the beam dilution factor f(θs,θb) (cf. differentregionsandthediskareachangedby 2.5%over
∼
Eq.5). The average planetary diameter θs was calculated the past 20years.The change of disk area has been taken
from the equatorial and polar radii (JPL’s HORIZONS sys- into account in the following.
tem). In the case of Uranus, we took into account that The secularchange in normalizedbrightness tempera-
the effective polar diameter changes with viewing geome- tureofUranusbetween1985and2005at90GHzisshown
try (see below). in Fig.3. These data show an overall scatter (rms) of,
The ratio is expected to be constant at 1.04 again, 6%. A linear least-squares fit to the data results
(Griffin & Orton 1993). The average ratio derived from in a slope of s = 0.4810−2 per year, i.e. a drop by 9%
−
the IRAM observations is 1.07, only slightly larger. We between 1985and 2005.Again, the statistical errorof the
are, however, interested in the relative changes. The rms slopeislargeandthelinear-correlationcoefficientissmall
of the observed ratios is only 6%. (r = 0.35). The yearly averages vary between +8% in
−
A linear least-squares fit to the data 1991 and 5% in 2005 (cf. also Table3). Note that this
−
(Bevington & Robinson 1992) shown in Figure2 re- dropisconsistentwithintheerrorswiththechangefound
sults in a slope of s = 0.410−2 per year, i.e. a drop whenstudyingtheratioofUranusandNeptunebrightness
−
by 8% between 1985 and 2005. However, the statistical temperatures(Fig.2),howeverwithmuchfewerdata.This
error of the slope is very large and the linear-correlation indicates that Neptune temperatures are constant.
coefficient is small (r = 0.37). In order to study where Figure3 also shows the results of Klein & Hofstadter
−
this variationmay come from,we presentin the following (2006) who studied Uranus at 8.6GHz (3.5cm) (see also
the Uranus and Neptune data independently. These data Hofstadter & Butler 2003) over the last 36years and find
were observed near simultaneously with the secondary significant variability. In late 1993, they find a strong
calibrators to derive their brightness temperatures. temperature decrease, indicating a rapid, planetary-scale
change. And indeed, the 90GHz data also show a
temperature-drop at this time. Here, the decrease is by
3.1. Uranus
7%.
∼
Uranus has a 84year orbital period of which we have ob- A plot of the 90GHz temperature variation against
servedapproximatelyoneseason(Fig.3),betweensolstice SEP latitude (Fig.4) shows an almost monotononic de-
in the mid 1980s and almost equinox which will take creaseofalmost10%,fromabout+5%atSEPlatitudesof
◦ ◦
place in 2007. Uranus is slightly oblate, the polar radius about 85 to 4%atSEPlatitudesofabout 10 ,indi-
− − −
of 24973km is 2.4% smaller than its equatorial radius of catingthatUranusbrightnesstemperaturedependsonthe
25559km (Lindal1987, 1992). Inaddition, Uranushas an viewing angle. This decrease is detected at the 2σ-level
∼
C. Kramer, R.Moreno, and A. Greve: Long-term 90GHz observations of Uranusand Neptune 5
Table 2. Yearly averages and rms of Uranus’ brightness
temperature (cf. Fig3). T is the yearly average, T is
B B
h i
the overallaverage of 134K. N is the number of observa-
tions.
Year T /hT i rms N
B B
[%]
1986 1.05 4.6 8
1987 1.04 6.1 5
1991 1.08 2.7 6
1992 1.06 2.6 12
1993 1.06 6.7 14
1994 0.99 3.9 10
1995 0.98 7.1 11
1996 0.99 6.6 14
Fig.5. Uranus thermal profile P(T) (Lindal 1987) and 1997 0.99 7.3 16
vertical distribution of NH3 and CH4 mixing ratios. The 1998 1.00 6.4 18
values of the NH and CH mixing ratios below their 1999 1.03 5.0 19
3 4
condensation levels are equal to 6 10−6 and 2.3 10−2, 2000 1.03 7.4 21
× ×
respectively. These have been used as input to a radia- 2001 1.00 3.7 38
tivetransfermodeltocalculatethe weightingfunctions of 2002 0.97 4.0 32
2003 0.97 4.5 19
Uranus’ continuum. The model had previously been used
2004 0.97 4.7 28
for Jupiter (Moreno et al. 2001). The weighting function
2005 0.95 7.2 14
at 8.5, 90 and 230 GHz are shown in black.
asthe binneddatahaveanaveragermsof5.4%(Table3). Table 3. Normalized Uranus brightness temperatures as
◦
2Onaverage,the8.6GHzdataofKH06showasimilarde- function of SEP latitudes binned into intervals of 15
pendencewithyearandSEPlatitude,howeverwithlarger width (see also Fig.4). N is the number of observations.
scatter.
Figure5 shows that higher frequencies probe succes-
SEP hYeari T /hT i rms N
sively higher layers of the Uranus atmosphere. The con- B B
Latitude [K] [%]
tinuum at8.5GHz stems fromthe highpressurezone,i.e.
-85.0 1986.70 1.05 5.0 13
11.0 to 5.7bar at low altitudes, where the opacity is sen-
-70.0 1991.92 1.06 3.6 13
sitive to the NH vertical distribution and the thermal
3 -55.0 1994.16 1.03 6.7 44
structure. In contrast, 90GHz emission probes the region -40.0 1998.17 1.00 6.5 57
of pressures between 6.1 and 4.7bar, higher in the at- -25.0 2001.67 0.99 5.5 108
mosphere, where the opacity is also a function of NH3, -10.0 2004.55 0.96 5.6 51
but muchmoresensitiveto the thermalstructure.Atstill
higherfrequencies,the230GHzcontinuumemissionarises
fromstillhigheratmosphericlevels(3.5-0.8bar),nearthe
A linear least-squares fit indicates a very small drop of
tropopause.Thecontinuumat230GHzismainlysensitive
only 2% between 1985 and 2005.In addition, the statisti-
tothethermalstructure,andonlyslightlytotheCH ver-
4
cal uncertainty of the fitted slope is large, 80%. We con-
tical distribution, but not to NH .
3
clude that Neptune temperatures are constant within the
It is important to note that between 8.5 and 90GHz,
8% observationalerror.
the difference ofthe opacitysensitivity toNH andtothe
3
thermal structure, may explain the differences of the rel-
ative changes of Uranus’ brightness temperature between 4. Summary
8.5 and 90GHz shown in Figures3 and 4.
By careful selection of data from the archived pointing
measurements made at the IRAM 30m telescope during
3.2. Neptune
the period 1985 to 2005, we have been able to study the
long-term behaviour of Uranus and Neptune at 90GHz.
Figure6 shows the brightness temperatures of Neptune,
The large number of selected observations allowed a sta-
normalizedtotheaveragetemperatureof T of128.3K.
B
h i tistically meaningful analysis.
2 Using the equatorial radius for the calculation of the disk
areaatalltimes,i.e.nottakingintoaccountthechangeofdisk 1. We obtained 286 observations of Uranus. The scatter
area with viewingangle, would lead toaslightly steeperslope of the derived normalized brightness temperatures is
and a decrease of −7% at SEP latitudes of −10◦. 6%.
6 C. Kramer, R.Moreno, and A. Greve: Long-term 90GHz observations of Uranusand Neptune
Greve, A., Kramer, C., & Wild, W. 1998a, A&AS, 133,
271
Greve,A., Neri, R., & Sievers,A. 1998b,A&AS, 132,413
Greve, A., Panis, J.-F., & Thum, C. 1996, A&AS, 115,
379
Griffin, M. J. & Orton, G. S. 1993, Icarus, 105, 537
Hofstadter, M. D. & Butler, B. J. 2003, Icarus, 165, 168
Klein, M. J. & Hofstadter, M. D. 2006, Icarus, 184, 170
(KH06)
Lindal, G. 1987,JGR, 92, A13, 14987
Lindal, G. 1992,AJ, 103, 967
Fig.6. Normalized Neptune brightness temperature. Moreno, R., Marten, A., Biraud, Y., et al. 2001,
Smalldotsanderrorbarsshowtheindividualobservations Planet. Space Sci., 49, 473
andtheirrmserrors.Dashedlinesshowthe8%(10K)rms Perley,R.A.,Zijlstra,A.,&vanHoof,P.2006,inBulletin
scatter of all 86 observations. oftheAmericanAstronomicalSociety,Vol.38,Bulletin
of the American Astronomical Society, 1028
Reuter, H.-P. & Kramer, C. 1998, A&A, 339, 183
We find a systematic variation of the Uranus bright-
Reuter,H.-P.,Kramer,C.,Sievers,A.,etal.1997,A&AS,
nesstemperatureof 10%withsub-earthpoint(SEP)
∼ 122, 271
latitude when the orientation of Uranus changes from
SanchezContreras,C.,Alcolea,J.,Bujarrabal,V.,&Neri,
south-poleviewtoequatorview.Thiseffectisdetected
R. 1998, A&A, 337, 233
atthe 2σlevel,themeanscatterofthedataaveraged
◦∼ Sandell, G. 1994,MNRAS, 273, 75
in 15 bins is 5%.A similar changeis indicatedby the
Steppe, H., Liechti, S., Mauersberger, R., et al. 1992,
8.6GHz observationsof KH06.The year 1993shows a
A&AS, 96, 441
rapiddecreaseofbrightnesstemperaturesat90GHzof
Steppe, H., Paubert, G., Sievers, A., et al. 1993, A&AS,
7%,whichcorrespondstoasimilardecreaseseenby
∼ 102, 611
KH06,indicatingatemporalchangeofalargefraction
Steppe,H.,Salter,C.J.,Chini,R.,etal.1988,A&AS,75,
of the Uranus atmosphere.More observationsatother
317
frequencies and improvedmodels of the Uranus atmo-
Ulich, B. L. 1981, AJ, 86, 1619
sphere, taking into account its latitude structure, are
neededtobetterdeterminethevariationswithSEP.If
Uranus is to be used as calibration source at 90GHz,
the latitude dependence of its brightness temperature
needs to be taken into account.
2. For Neptune, we only obtained 71 observations tied
to secondary calibrators and 81 simultaneous obser-
vations with Uranus. Both show that its brightness
temperature stays constant at a level of better than
8%.
Acknowledgements. We would like to thank our referee Mark
Hofstadter for helpful comments. During the 20 years 1985
- 2005, many astronomers and operators of the 30m telescope
contributedtothepointingmeasurements.Wethankthemany
colleagues for their contribution which, unnoticed by most
of them, allowed the collection of these data. The computer
division, J.Pen˜alver (IRAM, Spain), and M.Bremer (IRAM,
Grenoble)helpedefficientlyintheretrievalandtransferofthe
data. M. Ruiz (IRAM, Spain) provided the Linux version of
theprogram planets.
References
Baars, J. 1973, IEEE Trans. Ant. Propagat.,AP-21, 461
Bevington, P. & Robinson, D. 1992, Data reduction and
error analysis for the physical sciences (McGraw-Hill,
Inc.)
Downes,D.1989,inLNPVol.333:EvolutionofGalaxies:
Astronomical Observations, ed. I. Appenzeller, H. J.
Habing, & P. Lena, 351