A. P. Hatzes1 - D. E. Mkrtichian2,3
1 - Thüringer Landessternwarte Tautenburg, 07778 Tautenburg, Germany
2 - Astrophysical Research Center for the Structure and Evolution of
the Cosmos, Sejong University, Seoul 143-747, Korea
3 -
Astronomical Observatory, Odessa National University, Schevchenko Park,
Odessa 65014, Ukraine
Received 8 August 2003 / Accepted 5 August 2004
Abstract
We have used precise stellar radial velocities to study the pulsational
motion of the rapidly
oscillating Ap star 10 Aql. Observations were made on three separate nights using the high
resolution spectrograph of the Harlan J. Smith 2.7 m telescope at McDonald Observatory. A high radial
velocity precision was achieved by using an iodine gas absorption cell.
The integrated radial
velocity measurements using the full wavelength region
covered by iodine absorption lines (5000-6300 Å)
failed to detect any coherent pulsational velocity variations to a level
of 2.5-5 m s-1.
An analysis over a much narrower wavelength range revealed that pulsational
radial velocity variations are indeed present in 10 Aql, but only in 5 spectral lines.
The amplitude of these variations ranged from about 100 m s-1 to
as high as 398 m s-1for an unidentified feature at 5471.40 Å. Other spectral features showing
pulsational radial velocity variations are tentatively identified as
Sm II and Tm II.
Key words: stars: chemically peculiar - stars: oscillations - stars: individual: 10 Aql
The rapidly oscillating Ap (roAp) stars are a pulsating subclass of the chemically peculiar Ap stars that exhibit p-mode oscillations with periods of 5 to 16 min. The multi-mode nature of the roAp oscillations make these objects highly amenable to asteroseismic studies. Many roAp stars, like their non-oscillating Ap counterparts, exhibit strong dipole magnetic fields and it is largely accepted that the pulsational axis is aligned with the magnetic axis rather than the rotation axis of the star. This oblique rotator model, first proposed by Kurtz (1982) has been able to explain most of the observed photometric variations of roAp stars. The asteroseismic study of roAp stars offers us a unique opportunity to study how large magnetic fields can affect both the internal structure and outer atmosphere of stars.
In the past the study of pulsations in roAp
stars largely relied on photometric measurements. In recent
years radial velocity (RV) measurements have been applied to these objects
with surprising results.
Baldry et al. (1998) made RV measurements for
Cir using narrow
wavelength bands (width
10 Å) and found that the
pulsational amplitude in individual bands could range from 100-1000
m s-1. At the same time Kanaan & Hatzes (1998) showed that individual spectral lines in
Equ could show such large
differences in amplitudes. Subsequent time resolved studies established
that the largest pulsational amplitudes seemed to come from spectral
lines of rare earth elements (REE) such as Nd and Pr (Savanov et al.
1999; Khochukhov & Ryabchikova #Khochukhov01a<#251ab; Balona & Zima 2002). However,
most of these studies were based on data covering a small wavelength
range or without techniques for precise (
m s-1) stellar RV
measurements. RV studies of roAp stars using a broad wavelength range
and precise radial velocity measurements using a simultaneous
wavelength calibration have only been done for a few roAp stars.
Phase variations have also been observed in roAp stars.
Baldry et al. (1998) found that
approximately 15-20% of the spectral bands in
Cir were almost 180 degrees out-of-phase. Khochukhov &
Ryabchikova (#Khochukhov01a<#256a) found pulsational phase shifts
between the singly and doubly ionized REE in
Equ.
More recently,
Kurtz et al. (2003) found that the
pulsational phases were constant in H
for HD 166473, yet
were variable in Pr II and III lines which presumably are formed in
the upper atmosphere. The pulsational
phase for Pr varied linearly with the fraction of the central intensity
at which the RV was measured. This was interpreted as evidence for a
standing wave in the atmosphere where H
was formed, and
a running wave in the upper atmosphere where Pr was formed.
Mkrtichian et al. (2003) found that lines of Nd III in 33 Lib
oscillate approximately
180
out of phase with Nd II lines that are formed in a
different layer of the atmosphere. This was interpreted as
a standing wave in the stellar
atmosphere with a radial node situated in the upper layers.
Evidence for a second node was inferred in
layers of the atmosphere close to continuum formation level based on
phase jumps of the RV variations for weak Fe spectral lines.
Clearly, to derive
the maximum information about the oscillations in roAp stars one needs
to study both the phase and amplitude variations of individual lines
from a variety of atomic species. This naturally requires a broad
wavelength coverage.
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Figure 1: The discrete Fourier transform of the integrated RV measurements for each of the nights of our observations. The vertical dashed lines mark the frequencies of the known photometric modes. |
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We have been using precise stellar radial velocity
measurements spanning a broad
wavelength range (5000-6300 Å)
to study the oscillations in roAp stars for the past
several years.
This program has already detected pulsational RV variations in 5 known roAp
stars:
Equ (Kanaan & Hatzes 1998),
HR 1217 and HD 134214 (Hatzes et al. 1999a),
33 Lib (Hatzes et al. 1999b; Mkrtichian et al. 2003),
and HD 122970 (Hatzes et al. 2000). These
studies has also established
CrB to be a ultra-low
amplitude roAp star (Hatzes & Mkrtichian 2004). Here we present
the results of a search for RV variations in the roAp star 10
Aql.
10 Aql (HR 7167; HD 176232) is an F0 SrEu star (Hoffleit 1982)
with a surface magnetic field strength showing reversing polarity over
timescales of years Babcock (1958). The roAp status of 10 Aql
was reported by Heller & Kramer (1988) and it has one of the lowest
photometric amplitudes for these class of objects. In a subsequent
analysis based on 26 h of photometric data Heller & Kramer (1990)
found the presence of 3 pulsation periods: a dominant mode
f1 =
1.436 mHz (=124.07 cycles d-1,
min),
mmag,
f2 = 1.385 mHz (119.66 cycles d-1,
min),
mmag, and
f3 = 1.239 mHz (107.07 cycles
d-1,
min),
mmag. These
frequencies did not appear to be equally spaced contrary to what is
expected from p-mode oscillations, but Heller & Kramer (1990)
did note that the amplitudes were very close to the noise level and this
could affect the selection of frequencies. A choice of nearby aliases
would make the frequencies more evenly spaced.
Recently, Kochukhov et al. (2002) measured radial
velocities for
10 Aql for a total of
7.7 h spanning 2 nights using the Gecko spectrograph of the
Canada-France-Hawaii Telescope. They failed
to detect RV variations in most of the spectral lines in their
wavelength interval (6105-6190 Å). They did, however, find
pulsational RV variations in 3 spectral lines:
Nd III 6145 Å, Eu II
6173 Å,
and Gd II
6180 Å. Pulsational amplitudes ranged from
35 to 135 m s-1. Most periods were consistent, to within the
errors, of the dominant mode found by Heller & Kramer (1990).
The false alarm probability (FAP) for the detections of
these signals ranged from 0.005 to 0.08.
10 Aql shows
radial velocity variations in the fewest spectral lines of all known roAp
stars. The observations of Kochukhov et al. (2002) were made
over a narrow wavelength range (85 Å), so it is not
known how many more spectral lines show RV variations. Furthermore,
these RV measurements were made without a simultaneous
wavelength calibration. The Gecko spectrograph used for these
measurements can show short term
instrumental shifts on some nights that are as large as 300 m s-1(Walker et al. 2003). These were
based on Th-Ar calibration lamps taken every 20 or 40 min. The amplitude
of instrumental shifts on timescales of minutes (pertinent
for roAp stars) has not yet been quantified. Use of simultaneous wavelength
calibration will minimize such instrumental shifts and thus make
RV detections more certain. Here we present
rapid, precise stellar RV measurements for 10 Aql taken with a self-calibrated
iodine absorption cell.
To minimize the dead time between exposures the Tektronix
CCD detector was framed to read a subset of the full array
(normally the detector covers a
4000-10 000 Å range). The detector
was also binned by a factor of two perpendicular to the direction of
dispersion. The total deadtime, including storage of the observation, was about
15 s. Table 1 summarizes the journal of the observations.
Table 1: Journal of observations.
Precise stellar radial velocity measurements were made using
a velocity metric provided by an iodine (I2) absorption cell.
Molecular iodine has useful absorption
lines in the wavelength interval 5000-6300 Å (14 spectral orders), although redward of 6000 Å these lines become
weak and this degrades the RV precision.
The sub-framing of the CCD was chosen so as to cover
the full wavelength region spanned by I2 absorption lines, as well as
the hydrogen H
and H
lines.
The radial velocity reduction procedure requires a high signal-to-noise spectrum
of the star taken without the cell in the light path. For this an
exposure of several minutes was taken.
Each spectral order was divided into 30 spectral chunks and the RV calculated in each chunk. The achieve the highest RV precision the spatial and temporal variations of the instrumental profile must also be modeled as determined using the iodine absorption lines. This was done largely following the procedure outlined in Valenti et al. (1995) and Butler et al. (1996). The individual RV from all spectral chunks were then combined to form a mean RV value for that observation. This measurement of the RV is consistent with those obtained by cross-correlation techniques. This is well established procedure that has demonstrated an RV precision of better than 3 m s-1 on narrow-lined solar-type stars. Table 2 shows the rms scatter of the integrated RV measurements for 10 Aql for each of the nights. The higher rms scatter for the night of 26 July 1997 is due to the lower signal-to-noise of that data because of poorer observing conditions.
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Figure 2: The spectral region of 10 Aql near the high amplitude RV lines which are marked by vertical lines. |
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Table 2: The rms scatter for the integrated RV measurements and detection limit of an 11.6 min input sine-wave at a false alarm probability of 0.01.
Figure 1 shows the discrete Fourier transform of the integrated RV measurements for each night. The are no pulsation modes present with amplitudes greater than about 2-3 m s-1. Monte Carlo simulations were performed to determine the detection limit of coherent pulsational RV variations in these integrated RV measurements. An input sine wave with the frequency of the primary pulsation mode ( f1 = 124.07 c d -1 = 1.43 mHz) was sampled in the same manner as the data. Random noise was added with a standard deviation consistent with the rms scatter of the RV variations. The amplitude of the input sine wave was then varied until a Lomb-Scargle periodogram (Lomb 1976; Scargle 1982) yielded power at the input frequency at a false alarm probability of 1%. These simulations show that we would have detected a known pulsation mode at an amplitude as small as 5 m s-1 on 26 July 1997 and an amplitude as small as 2.5 m s-1 on 11 and 13 Aug. 1998.
Kanaan & Hatzes (1998) first demonstrated that the pulsational RV
amplitude in roAp stars can differ by factors of ten or more between
different spectral lines. Furthermore, Kochukhov et al. (2002)
reported RV variations in 10 Aql in only a few spectral features.
If this is the case then some spectral
lines 10 Aql could have a
measurable pulsational amplitude that would be averaged below
detection limits when computing the radial velocity over the full wavelength
region that includes many lines.
To expedite the analysis the RV was first determined on the individual chunks
that spanned about 4 Å and which included just a few spectral lines.
If a periodogram of the RV measurements produced significant power at a
pulsational frequency (FAP
0.02), then the wavelength window
was reduced to include only one spectral line.
This was repeated for every spectral line in the window so that
the spectral feature(s) responsible for the
RV variations was (were) isolated. This procedure ensured that we would
find lines with statistically significant variations which minimizes the
risk of trying to interpret signals that are due to noise.
Table 3: Spectral line identifications.
Our analysis yielded only five spectral lines
which exhibited significant
evidence for RV variations at one of the photometric
frequencies.
These lines are listed in Table 3 along with
the measured wavelength (corrected for the Earth's barycentric
motion and the absolute RV of 10 Aql)
and the tentative identification of the feature.
The identifications were based on the coincidence of the
wavelengths of our spectral
features to
wavelengths and intensity of those calculated using the
VALD (Piskunov et al. 1995) "extract stellar'' option and the
,
model atmosphere. This provided the
closest match to the stellar parameters for 10 Aql
(Ryabchikova et al. 2000).
The wavelengths of the DREAM (Biemont et al. 2003) database and
the line-list of Przybylski's star (Cowley et al. 1998) were also used.
Two lines at
5471.40 Å and
5730.34 Å are unidentified in the
spectrum of 10 Aql. The same lines were also found unidentified in the
spectrum of Przybylski's star. Figure 2 shows the spectral
regions of these high amplitude spectral lines.
Figure 3 shows the discrete Fourier transform (amplitude is in m s-1) for these five spectral features. The Fourier transform for a single spectral line on each night is shown horizontally. Vertical dashed lines indicate the location of the published photometric frequencies.
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Figure 3: The discrete Fourier transform for the spectral lines showing evidence for pulsational RV variations for the three nights of our observations. Each night is shown in vertical panels. The number in the upper right corner of each panel is the wavelength of the spectral line in Å. |
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Table 4: Pulsational amplitude and phases for spectral lines in 10 Aql. False alarm probabilities (FAP) were computed assuming no a priori knowledge of the presence of possible frequencies. The FAP values in parentheses are for a pre-selected (photometric) frequency.
The dominant photometric mode, f1 (=124.07 c d
-1 = 1.436 mHz)
is the one found in nearly all of the RV variations for individual spectral lines.
There is only one instance where another mode (f3 = 107 c d
-1
= 1.239 mHz) may be present and that is for 5069 Å on the night of 26 Jul 1997.
Table 4 lists the detected period, amplitude, and
phase for the 5 spectral lines for each of the nights.
The period was taken as the highest peak in the periodogram nearest
a photometric frequency. In most instances this peak also
coincided with the highest peak in the frequency interval that was
examined. The amplitudes listed in Table 4 result from a least squares
sine fit to the data using the period found in our Fourier analysis.
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Figure 4: The radial velocity variations for the 5471.40 Å feature on the night of 11 Aug. 1998. |
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There are large amplitude variations between the different spectral lines and
for the same line, but on different nights.
The largest amplitude is found in an unidentified spectral
feature at 5471.40 Å. The highest amplitude for this line occurred
on 11 Aug. 1998 with a semi-amplitude (
m s-1, but this dropped to
m s-1 on
the successive night. Figure 4 shows the RV variations
of
5471.40 Å feature for the night where it had the highest amplitude
and Fig. 5 shows the same RV variations phased to a
period of 11.6 min.
For consistency, the phases in Table 4 were reckoned using
the same frequency, f1,
derived from the photometry. Most of the
frequencies in Table 3 differ slightly to that of the photometric mode
f1 and these may introduce
artificial phase shifts. (The only exception
was the 13.39 min period (
c d-1) of the
5069 Å feature.) Using a single frequency minimizes this.
Because the data span such a large time difference and the
pulsation periods are not known to a high enough accuracy to
use the same zero point,
the phases in Table 3 were reckoned using a different starting time.
Comparisons
of the pulsational phases between different lines should only be made
between phases on a given night. The zero points used were
T0 =
2 450 655.7629 (26 July 1997), 2 451 036.6357 (11 August 1998), and 2451038.632
(13 August 1998).
The phases listed in Table 4 correspond to the phase of minimum
radial velocity.
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Figure 5:
The radial velocity variations for the ![]() |
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In Table 4 one can note phase differences between different lines on different nights, but we will not comment on this further as it was done in our previous paper on 33 Lib (Mkrtichian et al. 2003). The relatively small amount of spectral lines showing RV variations and the multiperiodicity of 10 Aql may introduce significant phase errors that are larger than the formal errors of the least-square solutions. A careful study of the phase variations in multiperiodic stars would require considerably more data.
Kochukhov et al. (2002) reported RV variability in 10 Aql in
3 spectral lines. Unfortunately,
the spectral region used by Kochukhov et al. is in a region where the iodine
absorption lines are too weak to give a good measurement precision
(
150 m s-1) for an individual line.
A periodogram analysis was performed on the wavelength chunks containing
Nd III
6145 Å, Eu II
6173 Å,
and Gd II
6180 Å. No significant RV variations were found
to a level of about 100 m s-1.
The statistical significance of the detected signals was estimated
using a bootstrap randomization technique (Murdoch et al. 1993; Kürster
et al. 1993). The measured RV values were
randomly shuffled keeping the observed times fixed. A periodogram was then computed
for each "random'' data set. The fraction of a large number of
periodograms (105 in this case) having power higher
than the data periodogram in the range 50 <
< 200 c d-1
represents the false alarm probability that noise would create the detected
signal. This is a more rigorous means of establishing the FAP
over simple use of the power in the Lomb-Scargle periodogram. The false
alarm probabilities are listed in Table 4.
We note that this is a very conservative estimate of the FAP. A more liberal (and possibly more appropriate) estimate of the FAP should be made by asking what the probability is that noise will produce a peak higher than the observed peak exactly at a certain frequency. In this instance the frequency range over which the maximum power is searched should be narrowly confined to an interval spanning this known frequency, not the broad range we have considered. In this instance the FAP will be significantly less. This FAP, also determined from the Monte Carlo simulations, is listed in parentheses in Table 3 for a few of the weaker detections.
The dominant photometric mode, f1,
is the one present in most of our spectral lines. Our mean value for
f1 determined from the periodograms showing the strongest signal
(excluding the 5069 Å feature)
is 123.31
0.5 c d-1 (= 1.440
0.0058 mHz). The
5069 Å
feature on 26 July shows a peak at a significantly higher frequency of
127.6
c d-1 = (1.477
0.05 mHz). Although this is consistent with the location of f1to within the errors, it is nearly 5
away from the mean value of
f1 determined from other spectral lines. We note that for the two
other spectral lines with strong power at f1 on this night
(
5373 Å and
5471 Å) had a
mean frequency of 128.4 c d-1 (=1.446 mHz) and these data
had the same sampling as for the
5069 Å feature. One intriguing
possibility is that
5069 Å on 26 July shows evidence of another
mode. If we assume a frequency spacing of the p-modes
defined by the difference in frequency of the first
two photometric modes, i.e.
= f1 - f2, then
a new mode could be located at a frequency of 1.487 mHz,
tantalizing close to the detected frequency.
A more detailed
investigation with longer time series is needed to confirm this.
We find no strong evidence for the presence of photometric modes f2and f3 in any of the 5 spectral features showing strong RV
variations, with the possible exception of the 5069 Å
line on the
night of 26 July 1997. The highest peak of the RV Fourier transform is
coincident with f3 and the FAP is reasonably low (0.0015, for a
pre-selected frequency). The second highest peak is at frequency
of about 121 c d-1 and could be
the unresolved blend of f1 and f2.
Again, we would be more confident of this
result with more data.
All of the features in Fig. 3 show strong variations in the amplitude from night to night. The rotation period of 10 Aql is unknown so it is not clear if these pulsation amplitude variations are due to rotational modulation.
Probable small periodic variations of equivalent widths of chromium, iron, and calcium lines with a period of 6.02 days in 10 Aql were recently reported by Kallinger et al. (2003). If this represents the rotational period then our observations on the nights 11 Aug. and 13 Aug. 1998 may show rotational modulation of the pulsational amplitude as these were separated by 0.33 of a rotation period. However, the mean integrated relative RV of 10 Aql on these two nights agree to within 2 m s-1 which at face value excludes rotational modulation with periods of several days.
A longer rotation period also seems consistent with the
magnetic field measurements of Preston (1970) which show a constant effective
field
strength of
Gauss over a 10 day span. The sparse
magnetic field measurements of Babcock (1958) showed field
reversals, but on time scales of years.
The errors of
these measurements (
30 G) were about one-tenth the
measured field strength, and as commented by Babcock: "The magnetic
field is measured with precision and shows a reversal of polarity''.
These measurements imply a rotation period much greater than 10 days,
and possibly of order years. Clearly, confirmation of the 6 day period in
10 Aql is important for the interpretation of the amplitude variations in 10 Aql.
Alternative hypotheses are that the amplitude variations result from the growth and decay of the pulsational mode or close multiperiodicity. Data of a much longer time series are needed to answer this.
What distinguishes 10 Aql from the other roAp stars for which we
have measured RV variations is the complete lack of RV variability for most
spectral lines throughout the 5000-6300 Å wavelength region of 10 Aql.
In fact, we can exclude the presence of integrated RV variations in 10 Aql
down to a level of 2.5 m s-1. Integrated RV measurements have always
detected RV pulsational variations, even in the new, ultra-low amplitude
roAp star
CrB (Hatzes & Mkrtichian 2004). (Interestingly,
high amplitude RV variations were only found in one spectral line of
CrB
at
6727 Å, a probable Ce II line blended with a Cr II
feature.)
Why do most spectral lines in 10 Aql show no RV variability?
The answer may lie in the results of an RV study of the roAp star
33 Lib. Mkrtichian et al. (2003) found
evidence for two radial nodes in the atmosphere of 33 Lib. RV
variations of the Nd III lines that are possibly formed higher in the stellar
atmosphere and thus
above a node oscillate approximately 180out-of-phase with respect
to Nd II lines formed below the node. In the case of 33 Lib the majority of
spectral lines are formed far from the radial node.
It may be that the radial node in 10 Aql is in the center of
the line formation region. Since the majority of
spectral lines are formed in a region where there is little atmospheric
motion due to pulsations, the RV amplitude should be very low and
undetectable. The continuum, from where the photometric variations originate,
lies in a region of the stellar atmosphere below
where the spectral lines are formed, and hence away from the
node. Thus the pulsational photometric amplitudes will have
non-zero amplitudes. The hypothesis of the presence of
a vertical atmospheric
standing wave and acoustic node in line-forming region can explain
the zero amplitudes of the majority of spectral lines and the
very low photometric amplitudes that have been measured in 10 Aql.
We can think of two explanations for the high pulsational velocities of the spectral features in Table 4. The first assumes the presence of a horizontal node in the nonradial pulsations and that the surface distributions of the elements responsible for the high RV amplitude lines are inhomogeneous. They could be concentrated in overabundant and highly localized spots on the stellar surface (say at the magnetic poles where the pulsation amplitudes are expected to be large). In this case the measured RV comes from a small region of the star and there is less cancellation effects for non-radial modes. This results in an apparent amplification of the observed disk-integrated pulsational amplitude due to spatial filtering of nonradial pulsations (Mkrtichian 1994).
For most elements, if they are evenly distributed across the surface of
10 Aql, cancellation effects would reduce the RV amplitude to below
detectable levels. This would occur in both dipole and quadropole modes
if 10 Aql is viewed from a large angle (45-90
)
with respect to the pulsational (and thus magnetic)
axis.
The variations in amplitude from
night to night could arise from rotational modulation as the spots move
out of view. However, the rotational period of 10 Aql is not known with
certainty and spectral monitoring
of 10 Aql is needed
to establish if the certain elements are indeed concentrated in spots on
the surface.
An alternative and probably more realistic explanation is within the framework of the vertical acoustic node hypothesis (Baldry et al. 1998). This assumes that the elements of the high amplitude lines are stratified and formed at a different height in the stellar atmosphere from most spectral lines in 10 Aql. Such stratification has been found in other roAp stars (Ryabchikova et al. 2002). If these regions are sufficiently far from the radial node then the RV amplitude should be higher. Vertical stratification in the atmosphere of 10 Aql may cause the lines from certain atomic species to be formed at layers far above the average line forming region. There is observational evidence for such stratification inferred from the acoustic cross sections of the atmosphere of 33 Lib using the Nd lines (Mkrtichian et al. 2003). It cannot be excluded that both horizontal and vertical node effects work in the atmospheres of roAp stars and these could be isolated and studied separately by an analysis of the RVs of individual spectral features.
Our RV analysis of the high amplitude spectral lines was able to find the dominant photometric period found by Heller & Kramer (1988), although there are strong amplitude variations from night to night. We suspect that this is due to short-term amplitude variability of modes or close multiperiodicity. A less probable explanation that this is due to rotational modulation.
Acknowledgements
D.E.M. acknowledges his work as part of research activity of the Astrophysical Research Center for the Structure and Evolution of the Cosmos (ARCSEC) which is supported by the Korean Science and Engineering Foundation. Part of this work was done under the US Civilian Research and Development Foundation (CRDF) grant UP2-317 and a grant by the German Academic Exchange Service (DAAD). APH acknowledges the support of grant 50OW0204 from the Deutsches Zentrum für Luft- und Raumfahrt e.V. (DLR).