Comparing radial velocities of atmospheric lines with radiosonde measurements

Abstract

The precision of radial velocity (RV) measurements depends on the precision
attained on the wavelength calibration. One of the available options is using
atmospheric lines as a natural, freely available wavelength reference. Figueira
et al. (2010) measured the RV of O2 lines using HARPS and showed that the
scatter was only of ~10 m/s over a timescale of 6 yr. Using a simple but
physically motivated empirical model, they demonstrated a precision of 2 m/s,
roughly twice the average photon noise contribution. In this paper we take
advantage of a unique opportunity to confirm the sensitivity of the telluric
absorption lines RV to different atmospheric and observing conditions: by means
of contemporaneous in-situ wind measurements by radiosondes.
The RV model fitting yielded similar results to that of Figueira et al.
(2010), with lower wind magnitude values and varied wind direction. The probes
confirmed the average low wind magnitude and suggested that the average wind
direction is a function of time as well. The two approaches deliver the same
results in what concerns wind magnitude and agree on wind direction when
fitting is done in segments of a couple of hours. Statistical tests show that
the model provides a good description of the data on all timescales, being
always preferable to not fitting any atmospheric variation. The smaller the
timescale on which the fitting can be performed (down to a couple of hours),
the better the description of the real physical parameters. We conclude then
that the two methods deliver compatible results, down to better than 5 m/s and
less than twice the estimated photon noise contribution on O2 lines RV
measurement. However, we cannot rule out that parameters alpha and gamma
(dependence on airmass and zero-point, respectively) have a dependence on time
or exhibit some cross-talk with other parameters (abridged).

Full text

Page 1

Mon. Not. R. Astron. Soc. 000, 1–11 (2011)Printed 19 October 2011(MN LATEX style file v2.2)
Comparing radial velocities of atmospheric lines with
radiosonde measurements
P. Figueira1?, F. Kerber2, A Chacon3, C. Lovis4, N.C. Santos1, G. Lo Curto2,
M. Sarazin2and F. Pepe4
1Centro de Astrof´ ısica, Universidade do Porto, Rua das Estrelas, 4150-762 Porto, Portugal
2European Southern Observatory, Karl-Schwarzschild-Strasse 2, D-85748 Garching bei M¨ unchen, Germany
3Universidad de Valpara´ ıso, Av. Gran Breta˜ na 1111, Valpara´ ıso, Chile
4Observatoire Astronomique de l’Universit´ e de Gen` eve, 51 Ch. des Maillettes, - Sauverny - CH1290, Versoix, Suisse
Accepted 2011 October 14. Received 2011 October 10; in original form 2011 August 29
ABSTRACT
The precision of radial velocity (RV) measurements depends on the precision attained
on the wavelength calibration. One of the available options is using atmospheric lines
as a natural, freely available wavelength reference. Figueira et al. (2010) measured
the RV of O2lines using HARPS and showed that the scatter was only of ∼10m/s
over a timescale of 6yr. Using a simple but physically motivated empirical model,
they demonstrated a precision of 2m/s, roughly twice the average photon noise con-
tribution. In this paper we take advantage of a unique opportunity to confirm the
sensitivity of the telluric absorption lines RV to different atmospheric and observing
conditions: by means of contemporaneous in-situ wind measurements. This oppor-
tunity is a result of the work done during site testing and characterization for the
European Extremely Large Telescope (E-ELT). The HARPS spectrograph was used
to monitor telluric standards while contemporaneous atmospheric data was collected
using radiosondes. We quantitatively compare the information recovered by the two
independent approaches.
The RV model fitting yielded similar results to that of Figueira et al. (2010),
with lower wind magnitude values and varied wind direction. The probes confirmed
the average low wind magnitude and suggested that the average wind direction is a
function of time as well. However, these results are affected by large uncertainty bars
that probably result from a complex wind structure as a function of height. The two
approaches deliver the same results in what concerns wind magnitude and agree on
wind direction when fitting is done in segments of a couple of hours. Statistical tests
show that the model provides a good description of the data on all timescales, being
always preferable to not fitting any atmospheric variation. The smaller the timescale
on which the fitting can be performed (down to a couple of hours), the better the
description of the real physical parameters. We conclude then that the two methods
deliver compatible results, down to better than 5m/s and less than twice the estimated
photon noise contribution on O2lines RV measurement. However, we cannot rule out
that parameters α and γ (dependence on airmass and zero-point, respectively) have
a dependence on time or exhibit some cross-talk with other parameters, an issue
suggested by some of the results.
Key words: Atmospheric effects, Instrumentation: spectrographs, Methods: obser-
vational, Techniques: radial velocities
?E-mail: pedro.figueira@astro.up.pt
1 INTRODUCTION
The research on extrasolar planets is currently one of the
fastest-growing in Astrophysics. Triggered by the pioneering
work of Mayor & Queloz (1995) on 51Peg, it evolved into a
arXiv:1110.3820v1 [astro-ph.IM] 17 Oct 2011

Page 2

2P. Figueira, F. Kerber , A. Chacon, et al.
domain of its own, with more than 500 planets confirmed up
to date. Most of these planets (∼90%) were detected using
the radial velocity (RV) induced on the star by the orbital
motion of the planet around it. The measurement of precise
RVs can only be done against a precise wavelength reference,
and two different approaches were pursued extensively. The
first was the usage of a Th-Ar emission lamp with the cross-
correlation function (CCF) method (Baranne et al. 1996),
and the second the I2 cell along with the deconvolution pro-
cedure (Butler et al. 1996). In order to measure precise RV
in the IR with CRIRES (Kaeufl et al. 2004), Figueira et al.
(2010) recovered a method known for a long time: the usage
of atmospheric features as a wavelength anchor. Using CO2
lines present in the H band, the authors reached a precision
of ∼5m/s over a timescale of one week. While a similar pre-
cision had been attained in the past in the optical domain
using O2 lines, the studies on the stability of atmospheric
lines were limited to a timescale of up to a couple of weeks.
In order to assess the RV stability of atmospheric lines
over longer timescales, Figueira et al. (2010) used HARPS
(High Accuracy Radial velocity Planet Searcher) archival
data, spanning more than six years. Three stars – Tau Ceti,
µ Arae, and e Eri – were selected because they provided a
strong luminous background against which the atmospheric
lines could be measured, and were observed not only over a
long timespan but with high temporal frequency (in astere-
oseismology campaigns). The spectra were cross-correlated
against an O2 mask using HARPS pipeline, which delivered
the RV, bisector span (BIS) and associated uncertainties.
The high intrinsic stability of HARPS allowed one to mea-
sure these effects down to 1m/s of precision, roughly the
photon noise attained on the atmospheric lines.
The r.m.s. of the velocities turned out to be of only
∼10m/s, and yet well in excess of the attained photon noise.
An inspection of the RV pattern on one star over one night
revealed not white noise but a well-defined shape on RV,
BIS, contrast and FWHM. A component of the RV signal
was associated with BIS variation, which in turn was lin-
early correlated with the airmass at which the observation
was performed. A second component of the signal was in-
terpreted as being the translation of the atmospheric lines’
center created by the projection of an average horizontal
wind vector along the line of sight. These two effects were
described by the formula
?
where α is the proportionality constant associated with
the variation in airmass, β and δ the average wind speed
magnitude and direction, and θ and φ the telescope elevation
and azimuth, respectively. The γ represents the zero-point
of the RV, which can differ from zero. The fitting of the vari-
ables α, β, γ, and δ allowed a good description of the telluric
RV signal, with the scatter around the fit being of around
2m/s, or twice the photon noise. The fitting was performed
in two ways: first, allowing all parameters to vary freely and
second, imposing the same α and γ for the different datasets.
For details the interested reader is referred to the original
paper. However, the model represented by Eq.1, while being
physically motivated, was not fully validated due to the ab-
sence of wind measurements against which the fitted values
could be compared.
Ω = α ×
1
sin(θ)− 1
?
+ β × cos(θ).cos(φ − δ) + γ(1)
Among the atmospheric parameters studied for E-ELT
site testing is precipitable water vapor (PWV), the ma-
jor contributor to the opacity of Earth’s atmosphere in
the infrared. Hence the mean PWV established over long
timescales determines how well a site is suited for IR as-
tronomy. For the E-ELT site characterisation a combination
of remote sensing (satellite data) and on-site data was used
to derive the mean PWV for several potential sites, taking
La Silla and Paranal as reference (Kerber et al. 2010). In
order to better understand the systematics in the archival
data and to obtain data at higher time resolution, a total of
three campaigns were conducted at La Silla Paranal obser-
vatory in 2009. During each campaign all available facility
instruments as well as dedicated IR radiometers were used
to measure PWV from the ground (Kerber et al. in prep.
Querel et al. 2011). In addition, radiosondes were launched
to measure the vertical profile of atmospheric parameters
in situ, with the goal of calculating the real PWV in the
atmosphere. Radiosondes are an established standard in at-
mospheric research and all other methods were validated
with respect to the radiosonde results with very high fidelity
(Kerber et al. 2010; Querel et al. 2010; Chac´ on et al. 2010).
In the current paper we present the results of exploiting
data from the above campaigns: since HARPS observations
and radiosonde measurements were done in parallel we are
in a position to make a direct and quantitative compari-
son of the wind speed parameters (β and δ). The paper is
structured as follows. In Sect.2 we describe the data acquisi-
tion and reduction of both observing campaigns. Section3 is
dedicated to the description of the analysis of data and sub-
sequent results. In Sect.4 we discuss the implications of our
results and we conclude in Sect.5 with the lessons learned
from this campaign.
2OBSERVATIONS & DATA REDUCTION
2.1HARPS measurements
HARPS (Mayor et al. 2003) is a high-resolution fiber-fed
cross-dispersed echelle spectrograph installed at the 3.6m
telescope at La Silla Observatory. It is characterized by a
spectral resolution of 110 000 and its 72 orders cover the
the whole optical range, from 380 to 690nm. Its extremely
high stability allows one to measure RV to a precision of bet-
ter than 60cm/s when a simultaneous Th-Ar lamp is used,
and of around 1m/s without the lamp. A dedicated pipeline
(nicknamed DRS for Data Reduction Software) was created
to allow for on-the-fly data reduction and RV calculation.
This pipeline delivers the RV by cross-correlating the ob-
tained spectra with a weighted binary mask. To calculate
the atmospheric lines RV variation one needs then only to
construct a template mask representing the lines to moni-
tor. This weighted binary mask (Pepe et al. 2002) was built
using HITRAN database (Rothman et al. 2005) to select
the O2 lines present in HARPS wavelength domain. For the
details on HARPS, the data reduction procedure and the
mask construction, the reader is referred to Figueira et al.
(2010). The procedure is identical, with the exception that
the observations used in the current paper were performed
without simultaneous Th-Ar.
For this program, 9 stars were observed: HR3090,

Page 3

Comparing RV of atmospheric lines with radiosonde data3
HR3476, HR4748, HR5174, HR5987, HR6141, HR6930,
HR7830, and HR8431, which are fast-rotating A-B stars,
mostly featureless in the optical domain and suitable to be
used as telluric standards. For details on the stars the reader
is referred to the website “Stars for Measuring PWV with
MIKE”1and to Thomas-Osip et al. (2007). A total of 1120
measurements were collected on 8 and 9 of May, 2009, during
the course of two nights of technical time. The stars were ob-
served in a complex pattern in such a way that both low and
high airmass and different patches of the sky were probed
throughout the night in order to sample any variations of
PWV. The main consequence is that even a fraction of the
night with a couple of hours can contain observations of sev-
eral stars at a wide range of airmass and elevation/azimuth
coordinates, covering well the independent variables of Eq.1.
and allowing a precise estimation of the parameters to be fit.
2.2 Radiosonde measurements
The radiosonde (Vaisala RS-92) is a self-contained instru-
ment package with sensors to measure e.g. temperature and
humidity combined with a GPS receiver and a radio trans-
mitter that relays all data in real-time to a receiver on the
ground. The radiosonde is tied to a helium filled balloon
and after launch ascends at a rate of a few m/s following
the prevailing winds. On its ascent trajectory the sonde will
sample the local atmospheric conditions up to an altitude
of ∼20km, when the balloon will burst. By that time it has
traveled horizontally ∼100 km from the launch site. Since
it relays its 3D location based on GPS location every two
seconds, the wind vector exerting force on the balloon can
be deduced from the change in GPS position.
A total of 17 radiosondes were launched between the 5
and the 15 of May of 2009 from La Silla site. One or two
launches were conducted every day/night. On the 13th no
data were collected due to a technical problem when radio
contact with the radiosonde was lost shortly after lunch.
From the collected physical parameters, the six of interest
for our study, as well as the nominal precision of the mea-
surements are presented in Tab. 1. As the sondes rise in
height, they measure the two horizontal wind components
on each layer with a nominal precision of 1×10−3m/s, much
higher than that of contemporaneous RV measurements.
Radiosondes form the backbone of the global net-
work coordinated by the World Meteorological Organisa-
tion (WMO) for measuring conditions at the surface and in
Earth’s atmosphere by combining the in-situ atmospheric
sounding with measurements taken onboard ships aircraft
and satellites. Coordinated radiosonde launches (one launch
at 12:00 UTC is the minimum requirement, other launch
times are 00, 06 and 18 hours UTC) provide a global snap-
shot of atmospheric conditions which are then used as basic
input for describing its current state and for modeling future
conditions.
The recommended maximum distance between stations
is 250 km but the global distribution is very uneven and bi-
ased towards heavily populated areas in the Northern hemi-
sphere. South America is sparsely covered with Chile oper-
1http://www.lco.cl/operations/gmt-site-testing/stars-for-
measuring-pwv-with-mike/stars-for-measuring-pwv
ating 4 stations only one of which (Santo Domingo, WMO
station number 85586) launches two radiosondes per day
at 00 and 12 UTC. Data from all active launch sites can be
found at http://weather.uwyo.edu/upperair/sounding.html.
The WMO also defines the requirements in terms of
equipment and procedures such as number of barometric
pressure levels, etc. A number of different radiosondes from
different manufacturers are used in the various countries. To
ensure comparability the WMO regularly conducts cross-
calibration campaigns with parallel measurements (Jauhi-
ainen & Lehmuskero, 2005)2. The Vailsala radiosonde RS-
92 used in our campaign is considered to be the most reli-
able and accurate commercial device available. Its minor bi-
ases in particular for day-time launches are well-documented
(Jauhiainen & Lehmuskero, 2005, Miloshevich et al. 2009).
The global snapshot of the state of the atmosphere,
taken at 00:00 and 12:00 UT is used as initial condi-
tions of global meteorological numerical models (GFS(1),
ECMWF(2), GME(3) among others3).
These initial conditions are employed in numerical ap-
proximations using dynamical equations, which predict the
future state of the atmospheric circulation (Holton 2005).
The models are a simplification of the atmosphere because
the horizontal resolution of the grid can be between 60 km
(GME) to 100 km (GFS) - and sometimes more - and the
vertical resolution provides only very small number of lay-
ers, but on a global scale the results are very good and
have improved considerably over the past decades. There are
other models called mesoscales models (MM5 (4), WRF(5),
MesoNH(6), among others), which provide higher spatial
resolution (horizontal and vertical) use more specific dynam-
ical equations (physics parameterization) and better resolu-
tion of the surface terrain. The initial conditions for these
models are usually the global model augmented by some
local weather stations. Details on the models are available
from the sites mentioned above.
Concerning the applicability of RS data to our purpose
it is important to note that the radiosonde is the accepted
standard in atmospheric and meteorological research. For
global weather forecasting a distance of order 250 km be-
tween radiosonde launch stations is the desired but by no
means always achieved standard, while the cadence is be-
2Performance
Vaisala DigiCORA Sounding System MW31 in the WMO
Mauritius Radiosonde Intercomparison, February 2005. webpage
http://www.vaisala.com/Vaisala%20Documents/White%20Papers/
Vaisala%20Radiosonde%20RS92%20in%20Mauritius%20Intercomparison.pdf
3(1) Global Forecast System (http://www.emc.ncep.noaa.gov/gmb/
moorthi/gam.html)
(2) European Center of Medium range Weather Forecasting
(http://www.ecmwf.int/products/data/operational system/description/
brief history.html)
(3) Global NumericalWeather
(http://journals.ametsoc.org/doi/abs/10.1175/1520-0493(2002)
130%3C0319%3ATOGIHG%3E2.0.CO%3B2)
(4) The Fifth-Generation NCAR/ Penn State Mesoscale
Model. NCAR=NationalCenterof
(http://www.mmm.ucar.edu/mm5/)
(5) Weather Research and Forecasting model (http://www.wrf-
model.org/index.php)
(6) Non-HydrostaticMesoscale
(http://mesonh.aero.obs-mip.fr/mesonh/)
of the Vaisala Radiosonde RS92-SGPand
Prediction Model
AtmosphericResearch
AtmosphericModel

Page 4

4 P. Figueira, F. Kerber , A. Chacon, et al.
tween 6 and 24 h. Hence, the radiosonde data set that we
use for comparison with HARPS observations is well within
the accepted limits of applicability in terms of spatial and
time resolution.
It is evident that local topography and diurnal vari-
ations may limit the value of a set of radiosonde data to
smaller distances and shorter periods of time. To this end
there is a very instructive analysis by Kalthoff et al. (2002)
that is directly applicable to our case. They use the Karl-
sruhe Atmospheric mesoscale model (KAMM) and compare
with wind measurements taken at stations around 30 degrees
South in Chile, including the Cerro Tololo Interamerican
Observatory (CTIO). La Silla (70◦44’4”5 W 29◦15’15”4 S)
is located within that region only about 100 km N of CTIO.
Kalthoff et al. (2002) find that the wind patterns over this
region are stable, their diurnal variations are highly repro-
ducible and that wind conditions are mostly stable during
night time. Their main finding is that for altitudes between 2
and 4 km northerly winds prevail whereas above 4 km large
scale westerly winds dominate. The reason for the Northerly
wind is a deflection of westerly winds by the Cordillera de
los Andes which forms a barrier. They provide a physical
explanation (their section 4) in terms of the Froude number
(ratio between inertial forces and buoyancy) demonstrating
that this deflected northerly flow is a naturally stable phe-
nomenon. As mentioned La Silla is located in the same re-
gion and the wind roses of Cerro Tololo (2200 m) (their Fig.
7) and La Silla (2400m)4are very similar, clearly showing a
predominance of northerly wind.
In particular winter months (June-August) are charac-
terized by very constant daily ground wind properties (Fig
5 of the same paper). Our observations were made in May.
In addition it is a well-established fact that wind conditions
in the free atmosphere are much more stable than in the
turbulent and highly variable ground layer (see e.g. Holton
2005; Wallace & Hobbs 2006).
As a consequence of the very homogeneous overall wind
structure between 2 km and 4 km and above 4 km we have
reason to believe, that the information on the wind vectors
obtained by a radiosonde will be representative of conditions
over the time span of at least a good fraction of a night for
our campaigns.
3 ANALYSIS & RESULTS
3.1 HARPS measurements
We analyzed the data from the 9 stars as if coming from
a single data set, as there is no reason to treat them sepa-
rately. As done in Figueira et al. (2010), we discarded the
27 datapoints with photon noise precision worse than 5m/s,
which correspond to only 2.5% of the observations.
The total RV scatter and average photon noise were
5.01m/s and 2.82m/s, respectively. If one separates the set
in the two nights that constitute it, the values for the first
night are of 5.36 and 2.92m/s, and 4.60 and 2.72m/s for the
second night. We note that the photon noise contribution to
the precision from the stellar spectrum is larger than 1m/s,
4http://www.eso.org/gen-fac/pubs/astclim/lasilla/humidity/
LSO meteo stat-2002-2006.pdf
validating the choice of not using the lamp simultaneously
with the observations.
We fitted the RV variation on the two nights using Eq.1,
as described in Figueira et al. (2010). When fitting, we con-
sidered splitting the dataset in three different ways and mak-
ing two different hypothesis for the parameters variation.
On the splitting of the dataset we employed: 1) the same
parameters for all the observations, 2) an independent set
of parameters per night, and 3) a set of parameters for each
one-third of the night. After allowing all parameters to vary
freely at first, we repeated this imposing α and γ to be the
same for the the whole dataset in 2) and 3). The resulting
parameters, χ2
in Tab. 2 for each case. The error bars were estimated by
bootstrapping the residuals and repeating the fitting 10000
times. The 95% confidence intervals were drawn from the
distribution of the parameters, and the 1σ uncertainty esti-
mations are presented.
While one might be tempted to compare the χ2
data as a way of quantifying the quality of the fit, there are
several reasons not to do so. The first is that as one divides
the data into subsets that are fitted independently, there is
some ambiguity in how the χ2
combined χ2
that we are considering a problem with priors, as the reader
will realize when noting that β ∈ [0, ∞[ . The consequence
is that this corresponds to the fitting of a non-linear model,
for which the number of degrees of freedom is ill-defined,
as recently underlined by Andrae et al. (2010). In order to
compare the quality of the data description by the different
models, we follow the recommendations of the same authors.
We calculate the probability that the normalized residuals
of the fitting are drawn from a gaussian distribution with
µ=0 and σ =1, as expected if no signal is present and the
scatter is dominated by the measurement uncertainty. To do
so we use the Kolmogorov-Smirnov test (as implemented in
Press et al. 1992) and compute the probability PKS which,
loosely speaking, corresponds to the probability that the
residuals after fitting the model are drawn from a gaussian
distribution. The larger the value of PKS, the more appro-
priate the model is to describe the data-set in hands. We
also calculated the probability PKS(nofit) for normalized
RVs of each dataset without fitting the model, but to which
only the average value was subtracted (which corresponds
to fitting only a constant). The probability for each case on
each data set is presented in Tab.3.
red, and scatter around the fit are presented
redof the
redof a set is compared with the
redof the subsets. However, more important is
3.2Radiosonde measurements
The measurement of the radiosonde wind vector (u,v) as
a function of time, or height, while interesting, is hardly
insightful for our objective. We need to calculate the effect
of this wind as integrated along the line of sight, such as
it is measured by any telescope and spectrograph on the
ground. This will deliver an average wind vector which can
then be compared with the one obtained with HARPS (see
the previous section).
A way of calculating this average wind is to consider
a plane-parallel atmosphere that is composed of horizontal
layers. Every radiosonde measurement probes the properties
of a layer in its ascent. To obtain the average wind speed we
weight the wind speed of each of these layers with its ab-

Page 5

Comparing RV of atmospheric lines with radiosonde data5
Table 1. The six parameters used from the data collected by radiosondes.
ParameterUnit Precision [Unit]Comment
time
T
P
Height
u
v
s
K
0.1
0.1
0.1
1
0.01
0.01
measurements cadence of one every 2s
—
—
limited to 30km
E-W wind component, East positive
N-S wind component, North positive
hPa
m
m/s
m/s
Table 2. The fitted parameters and data properties, before and after the fitted model is subtracted from it, with all parameters kept
varying freely (top), and when α and β are imposed as the same for the datasets (bottom, marked with *).
data set#obsσ [m/s]σ(O−C)[m/s]σph[m/s]χ2
red
α[m/s]β [m/s]γ [m/s]δ [o]
08+09-05-2009 1093 5.014.14 2.82 2.207.79+0.76
−0.73
5.74+1.87
−1.81
8.20+0.83
−0.81
8.97+1.41
−1.41
10.79+21.27
−17.98
29.77+11.86
−12.13
15.50+1.70
8.47+0.76
−0.68
13.93+3.12
220.56+0.05
−0.31
126.10+4.41
−5.56
08-05-2009 (1stn.) 554 5.364.382.92 2.12
−2.61
220.32+0.31
−0.79
145.14+5.58
−13.00
09-05-2009 (2ndn.) 5394.603.68 2.721.83
6.75+0.60
−0.50
4.44+3.31
−0.89
15.99+43.88
−8.00
74.86+41.90
−31.07
15.98+4.50
219.95+0.36
−0.04
97.75+6.67
−7.91
(1stn., section1/3)1853.462.891.88 2.25 223.58+0.97
−0.75
42.17+47.29
−17.60
17.22+77.04
−96.66
4.28+63.12
−2.35
24.96+18.08
−7.08
90.87+31.05
−47.05
66.26+17.98
−27.05
(1stn., section2/3) 1854.58 4.58 3.27 1.71223.96+5.24
−4.91
(1stn., section3/3) 1846.264.513.601.53 230.09+5.25
−5.30
(2ndn., section1/3) 1804.80 3.302.521.73
−1.71
−3.19
223.51+1.28
−1.18
(2ndn., section2/3)1804.503.742.841.758.76+2.47
−2.38
-15.06+18.00
−18.04
3.61+5.17
−0.78
7.78+2.77
−1.77
220.10+0.91
−0.50
(2ndn., section3/3)1803.863.482.821.58220.61+0.74
−0.70
08-05-2009 (1stn.)*5545.364.382.922.12†
6.85+0.76
−0.77
6.85+0.76
−0.77
—
13.57+1.31
−1.25
220.19+0.13
−0.23
143.17+2.94
−3.72
09-05-2009 (2ndn.)*539 4.603.682.72 1.83†
6.95+0.69
−0.60
—
220.19+0.13
−0.23
—
102.14+6.81
−8.25
—global fit parameters10935.014.062.821.98
(1stn., section1/3)*185 3.462.971.88 2.34†
8.81+1.09
−1.09
8.81+1.09
−1.09
8.81+1.09
−1.09
8.81+1.09
−1.09
8.81+1.09
−1.09
8.81+1.09
−1.09
—
6.05+2.00
−1.41
14.38+8.65
221.39+0.42
−0.39
127.53+10.59
−23.16
(1stn., section2/3)* 1854.584.623.271.73†
−4.70
221.39+0.42
−0.39
131.27+7.37
−53.92
(1stn., section3/3)* 1846.264.553.601.55†
11.17+1.44
−0.55
221.39+0.42
−0.39
77.45+16.67
−15.42
71.89+14.36
−13.51
5.39+36.17
−7.01
95.93+8.41
(2ndn., section1/3)* 1804.803.492.521.90†
8.00+1.01
−0.73
9.23+4.15
−2.92
13.47+1.82
221.39+0.42
−0.39
(2ndn., section2/3)* 1804.503.782.841.78†
221.39+0.42
−0.39
(2ndn., section3/3)* 1803.863.532.821.62†
−1.59
—
221.39+0.42
−0.39
—
−9.63
—global fit parameters10935.013.872.821.81
Note that δ =0owhen wind direction points towards North, and positive eastwards. The error bars on each of the fitted parameters
were drawn by bootstrapping the residuals (see text for details). Note that the χ2
they are calculated assuming 4 fitting parameters for the considered subset, with the objective of allowing comparison with the
corresponding unconstrained fitting.
redmarked with†are not defined in the strict sense:
sorptivity. In doing so we are considering that the absorption
line we measure with our spectrograph is the result of the
product of the transmission of all layers, and each one of
these creates a small line shifted by its respective horizontal
wind. It is important to note that we chose doing so because
absorptivity is proportional to the depth of the line at the
central wavelength, and thus proportional to the spectral
information contribution for the CCF as described in Pepe
et al. (2002).
The absorptivity on each layer Ai is Ai = 1 - e−τ
where τ is the optical depth and calculated as τ = I(T) ×
AmplitudeLorentz× σO2(T,P) × ∆h where I is the spectral
line intensity, AmplitudeLorentz the relative amplitude of a
Lorentzian function, σO2the surface density of O2, and ∆h
the height of the layer in question.
The first component of τ is I, the spectral line in-
tensity (basically, the line area) and is given in [cm−1/
(molecule.cm−2)] in HITRAN. Since I is a function of T we
calculated a grid of HITRAN I from the minimum to the
maximum temperature measured by the radiosondes, with a
step of 0.1K for all the O2 lines within HARPS wavelength
domain. For each temperature an average I was assigned to
the overall spectrum. This gives us I(T), and to obtain val-
ues for T in between two grid points we fitted second-degree