Download Detection of the Rossiter–McLaughlin effect in

MNRASL 429, L79–L83 (2013)
doi:10.1093/mnrasl/sls027
Detection of the Rossiter–McLaughlin effect in the 2012 June 6
Venus transit
P. Molaro,1† L. Monaco,2 M. Barbieri3 and S. Zaggia4
1 INAF
– OAT, Via GB Tiepolo 11, I-34143 Trieste, Italy
Vitacura, Alonso de Córdova 3107, Casilla 19001, Santiago 19, Chile
3 Dipartimento di Fisica e Astronomia, Universitá degli Studi di Padova, Vicolo dell’Osservatorio 3, I-35122 Padova, Italy
4 INAF – OAPD, Vicolo dell’Osservatorio 5, I-35122 Padova, Italy
2 ESO
Accepted 2012 November 1. Received 2012 October 23; in original form 2012 August 29
ABSTRACT
Eclipsing bodies on stars produce radial velocity variations on the photospheric stellar lines
known as the Rossiter–McLaughlin (RM) effect. The body occults a small area of the stellar
disc and, due to the rotation of the star, the stellar line profiles are distorted according to the
projected location of the body on to the stellar disc. The effect originally observed in eclipsing
binaries was also shown to be produced by extrasolar planets transits. Here we report the
detection of the RM effect in the Sun due to the Venus transit of 2012 June 6. We used the
integrated sunlight as reflected by the Moon at night time to record part of the transit by
means of the high-precision HARPS spectrograph at the 3.6-m La Silla European Southern
Observatory (ESO) telescope. The observations show that the partial Venus eclipse of the
solar disc in correspondence of the passage in front of the receding hemisphere produced a
modulation in the radial velocity with a negative amplitude of ≈−1 m s−1 , in agreement with
the theoretical model. The radial velocity change is comparable to the solar jitter and more
than a factor of 2 smaller than previously detected in extrasolar hot Neptunes. This detection,
facilitated by an amplification factor of 3.5 of the Venus radius due to proximity, anticipates
the study of transits of Earth-size bodies in solar-type stars by means of a high-resolution
spectrograph attached to a 40-m class telescope.
Key words: planets and satellites: general – techniques: radial velocities – planets and satellites: general – planets and satellites: individual: Venus – Sun: general – Sun: oscillations.
1 I N T RO D U C T I O N
The crossing of a body in front of a star and the consequent occultation of a small area of the rotating stellar disc produce a distortion in the stellar line profiles according to its projected size.
This phenomenon first predicted by Holt (1893) was discovered by
Schlesinger (1911) and later confirmed in the eclipsing binaries β
Lyrae and Algol by Rossiter (1924) and McLaughlin (1924), respectively. Schneider (2000) suggested that the transit by a planet
could also be detected in the line profile of high signal-to-noise ratio
stellar spectra of rotating stars, and a Jupiter-like planet was in fact
observed in HD 209458 by Queloz et al. (2000). Since then about
60 extrasolar planets have been observed (Fabrycky & Winn 2009;
Triaud et al. 2010; Albrecht et al. 2012; Brown et al. 2012). By
observing the Rossiter–McLaughlin (RM) effect, one can measure
Based on observations collected at the European Southern Observatory,
Chile. Programme ESO N. 289.D-5015.
† E-mail: [email protected]
the angle λ between the sky projections of the orbital axis and the
stellar rotational axis. The amplitude of the radial velocity anomaly
stemming from the transit is strongly dependent on the projected
radius of the eclipsing body and on v sin I, i.e. the component of
the star’s rotational velocity along the line of sight (Ohta et al.
2005; Gimenez 2006; Gaudi & Winn 2007). A transit across a star
with high v sin I produces a larger radial velocity signature than that
across a slow rotator. The radial velocity anomaly Vs is given by
Vs =
k2
s δp sin Is ,
1 − k2
(1)
where s is the stellar angular velocity, δ p is the position of the
planet, Is is the inclination between the stellar spin and the y-axis
and k = Rp /Rs , the ratio between the planet and stellar radii (Ohta
et al. 2005).
On June 5–6 one of the rarest astronomical events took place: the
transit of Venus, during which the black disc of Venus passed across
the disc of the Sun. Since its first observation by Jeremiah Horrocks
in 1639, only seven such events have taken place, and there will not
be another until 2117 December. The projected size of Venus is 1/33
C 2012 The Authors
Published by Oxford University Press on behalf of the Royal Astronomical Society
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P. Molaro et al.
of the solar disc, and therefore the RM effect is expected to be of
the order of ±1.5 m s−1 , taking a solar v sin I = 1.6 ± 0.3 km s−1
(Pavlenko et al. 2012). This is a challenging small quantity, particularly in the Sun where the possibility to obtain a high-resolution
spectrum of the integrated sunlight is paradoxically quite complicated (Gray 1992). Considerable efforts have been made to overcome the obstacle posed by the extended disc of the Sun. Asteroids
were shown to be a convenient way to get the integrated solar
spectrum since they reflect almost unaltered sunlight as point-like
sources besides being also good radial velocity standards (Zwitter
et al. 2007). The whole solar spectrum provides absolute reference
of radial velocity at sub-m s−1 level (Molaro & Monai 2012). We applied this technique to search for the RM effect through a sequence
of observations of the sunlight as reflected by the Moon in correspondence to the Venus transit. A theoretical transmission spectrum
of Venus as a transiting exoplanet was computed by Ehrenreich
et al. (2012).
The Venus transit as seen from the Moon has a slightly different
timing and projection on the solar disc from what is seen from the
Earth. The Moon was 95 per cent illuminated and about 8◦ ahead
the Earth, and Venus reached the Sun–Moon alignment with a delay
of about 2 h. As seen from the Moon centre the transit was slightly
longer than from the Earth since the Moon was above the Earth–
Sun rotation plane. The leading edge of Venus contacted the Sun
at 23h :46m UT (GMT, or 245 6084.490 278 JD) on June 5 and the
second contact was at 00h :03m UT on June 6. In egress the first
contact was at 06h :59m UT and the second at 07h :14m UT on June 6.
Our observations began at 2h :44m UT (or 245 6084.6139 JD)
on June 6 when the Moon reached about 40◦ on the horizon and
became observable and continued during the whole second phase
of the transit and after. They comprise a series of 245 spectra taken
with HARPS covering the range from 380 to 690 nm, with a small
gap at 530–539 nm. The observations have an integration time of
60 s followed by 22 s of read out at a resolving power of R =
λ/λ ≈ 115 000 and deliver a signal-to-noise ratio of ≈400 each
at 550 nm. The spectrograph is in vacuum, thermally isolated, is
stable and equipped with an image scrambler which provides a
uniform spectrograph-pupil illumination and allows very precise
observations. HARPS was able to deliver a sequence of observations
with a dispersion of 0.64 m s−1 for an extrasolar planetary system
composed by three Neptune-mass planets over a 500-d baseline
(Lovis et al. 2006).
The first 227 observations cover the transit phases between about
mid-transit to the end and for about 2 h after passage. At twilight, few
hours after the passage, 18 additional observations were also taken
for reference. A second fibre supplied ThAr spectra simultaneous
to all the 245 observations and were used to correct for instrumental
drifts along the night. The radial velocity differences with respect
to the previous calibration provide the instrumental drifts and are
shown in Fig. 1. The dispersion of radial velocity corrections on the
small scale is of about 0.2 m s−1 and is consistent with the photon
noise associated with each measurement. The binned data points
show the instrumental drift which is ≈0.5 m s−1 at the beginning of
the night and decreases rapidly to the immeasurable level of less of
0.2 m s−1 after about 2 h.
The observed radial velocities were then corrected by the motions
of the observer relative to the Moon and of the motion of the Moon
relative to the Sun (Molaro & Centurion 2011). These quantities
are computed by using the JPL horizon ephemerides and are shown
in Fig. 2 together with the radial velocities measured from the
Moon spectra already corrected by the instrumental drift. During
our observations the motions of the observer relative to the Moon
Figure 1. Trajectory of Venus transit of 2012 June 6 as seen from the centre
of the Moon. The sun image is a SDO image of the 6th June showing the
dark spot of Venus (courtesy of SDO Science team).
Figure 2. Instrumental radial velocity drift along the night of June 6 as
measured by HARPS from ThAr spectra taken with a second fibre simultaneously to the science observations. The drift is the radial velocity difference
of a ThAr frame with respect to the previous calibration. Squares show data
binned over 30 m, with the error bar showing 1σ within each bin.
is increasing from −0.260 to +0.409 km s−1 , while the Moon
relative to the Sun decreases from −0.113 to −0.191 km s−1 as
illustrated by the two dashed lines in Fig. 2. When these corrections
are applied the resulting radial velocity shows a constant offset
of 102.2 ± 0.86 m s−1 between the observed and expected radial
velocity. This offset likely originates from the HARPS procedure
to measure radial velocities. The HARPS pipeline returns a radial
Detection of RM effect in Venus transit
velocity which is obtained from a cross-correlation with a mask
of a G2 V star. This mask is the Fourier Transform Spectrometer
solar spectrum which has an uncertain zero-point of the order of
100 m s−1 (Kurucz et al. 1984; Molaro & Monai 2012). We thus
used the radial velocities measured in the observations taken after
the transit (from 10h :19m to 10h :48m UT) to fix a reference point for
the absolute radial velocity. Solar spots could also affect the radial
velocity of the solar lines and indeed solar images taken on June 6
showed the presence of several solar spots (Lagrange et al. 2010).
However, their characteristic change rate is on a time-scale of solar
rotation and are essentially frozen during the few hours of the Venus
transit. A radial velocity reference outside the transit include any
contribution originated by the presence of solar spots.
2 R E S U LT S
The whole set of solar radial velocities obtained from the 245 Moon
spectra and corrected for instrumental motions, motion of the observer towards the Moon, motion of the Moon towards the Sun
and for a constant offset computed outside the transit are shown in
Fig. 3.
The mean radial velocity of the Sun when Venus is crossing the
central part of the solar disc is the same as that at the end and out
of the transit. The radial velocity baseline differs by 10 cm s−1
at most, showing that instrumental drifts and relative motions are
well corrected. In contrast, in correspondence to Venus crossing the
semihemisphere of solar disc, the radial velocity drops smoothly
and reaches a peak of negative variation of about −1 m s−1 when
the planet is at about the centre of the semihemisphere.
During our observations Venus was eclipsing the receding solar
hemisphere and the small blue shift of the lines reveals the prevalence of light coming from the approaching solar hemisphere. The
behaviour would have been symmetrically positive for the passage
Figure 3. Radial velocities of the 245 Moon spectra of June 6 (crosses).
The two red dotted lines show the motion of the observer towards the Moon,
line close to measurements and of the Moon with respect to the Sun. The
continuous blue line shows the resulting apparent motion which follows the
observed radial velocity but with a constant radial velocity offset originated
by the reference solar spectrum used by the HARPS pipeline
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of the planet in front of the approaching solar hemisphere which
we could not track since the first half of transit was not observable
from Chile. The details of the RM effect depend on several orbital
parameters of the system, which are all well known for Venus, thus
allowing a unique test of the whole theory.
We compute the theoretical variation of the solar radial velocity
due to the Venus transit as it was seen from the Moon (see Fig. 4)
using the algorithm presented by Gimenez (2007). This algorithm
was presented for the modelling of the RM effects on extrasolar
planets. The parameters needed as input are the following:
(i) angular separation δ(t) between the centre of Venus and the
centre of the Sun as a function of time;
(ii) relative ratio of the radii k = rV /R and relative sum of the
radii Sr = (rV + R )/aV , where rV is the apparent radius of Venus
as calculated below;1
(iii) inclination iV of the Venus orbit relative to the line of sight
of the observer;
(iv) angle λV between the projected axis of Sun rotation and the
direction of pole of the orbit of Venus, projected to the celestial
sphere;
(v) inclination I of the rotation axis of the Sun on the plane of
the sky;
(vi) rotational velocity Vrot, of the Sun;
(vii) limb-darkening coefficients of the Sun (see below).
In respect to the case of extrasolar planets, the Venus transit has a
major difference originating from the observing perspective under
which we see Venus transiting on the Sun from the Moon (or the
Earth). As a consequence, the ratio of the apparent Venus radius, rV ,
to the Sun radius, r , is larger than the theoretical value at infinity.
We calculated the angle subtended by Venus using the ephemeris
of the transit event as seen from the centre of the Moon calculated
via the JPL Horizons On-Line Ephemeris System (Giorgini et al.
1997). In the first approximation the amplification value ϑ = rV /rV
of the Venus disc on the face of the Sun is simply given by the ratio
of the relative distances of Sun–Moon dSM and Venus–Moon dMV ;
a more precise evaluation is given by the following formula:
rV
dSM
sin atan
;
(2)
ϑ=
rV
dMV
adopting the values of the middle of the event we calculated that
Venus seen in front of the Sun from the Moon centre is ϑ = 3.5236
times bigger than as is seen at infinity. Due to the relative motion of
Venus and Moon, ϑ changes during the transit event. We verified
that the variation is less than 10 parts per million, so we kept it
fixed.
An important parameter needed for the computation of the RM
effect is the Sun’s inclination. We obtain this value from JPL Horizons; actually what is available is the Sun’s north pole position
angle ψ and its angular distance from the centre of the Sun disc.
The Sun’s north pole position angle is measured on the plane of the
sky in counterclockwise direction.
Since the solar rotation axis is at an inclination of I 7.◦ 25
with respect to the Earth’s orbital plane and is pointing towards
RA = 286.◦ 13, Dec. = 63.◦ 87, the value of sin(I ) depends on the
year time. Luckily enough, during the Venus transit on 2012 June 6
sin(I ) = 1.0. We verified that the Sun’s north pole ψ during the
event changed from the hidden hemisphere to the visible hemisphere
1R
5
= 6.963 × 10 km is the Sun radius, rV = 6051.8 km is the Venus
radius and aV = 108.2 × 106 km is the orbital semimajor axis of Venus.
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P. Molaro et al.
Figure 4. Radial velocity measurements obtained from 245 integrated solar spectra reflected by the Moon during the 2012 Venus transit. The sequence of
18 observations taken at twilight is also shown. The thin continuous line shows the theoretical RM effect for the whole Venus transit of 2012 June 6. The
decrease in RV in the second part of the transit from mid-transit to egress shows the RM effect due to the partial coverage of the solar receding hemisphere by
Venus. Note that due to a slight misalignment the point of zero radial velocity occurs with a delay of ≈10 min with respect to mid-transit. The residuals of the
observations against the model shown in the bottom panel do not present any systematic effect. Their power spectra in the inset clearly show the power excess
around the frequency of the solar oscillations of 3.032 27 mHz with an amplitude of 0.40 m s−1 .
on June 6 at UT 02:56. On average the inclination is equal to 90◦ ,
while the variation during the transit is less than 0.◦ 0067. The north
pole position angle varies very little during the transit and has an
average value of ψ = 354.◦ 243 ± 0.◦ 003.
The adopted value for the quadratic limb-darkening coefficients
were taken from the tables of Claret (2004); for the g filter and an
Atlas model with the following characteristics [Fe/H] = 0, Teff =
5750 K, log g = 4.5, ξ = 1 km s−1 and the limb-darkening coefficients are ua = 0.5524 and ub = 0.3637.
From the JPL Horizons ephemeris in Cartesian coordinates we
derived the value of Venus inclination as seen from the Moon. From
simple geometry, the inclination is
dSM sin δc
,
(3)
iV = acos
dSV
where dSM is the Sun–Moon distance, δ c is the angular separation
between Venus and Sun at the transit centre and dSV is the Sun–
Venus distance, and this formula gives iV = 89.◦ 8375. For the angle
λ between the sky projections of the orbital axis of Venus and the
stellar rotational axis, we adopted λV = 3.◦ 86.
The solar rotation is well known with respect to the approximate
knowledge of the rotation for star hosting extrasolar planets. Here
we adopted a simple formulation for the solar rotation (Cox 2001):
= a + b sin2 φV + c sin4 φV ,
(4)
where ω is the solar angular velocity measured in degrees per day,
φ V is the solar latitude and a, b, c are the coefficients derived from
the magnetic field pattern (a = 14.37, b = −2.3, c = −1.62). The
corresponding rotational velocity at latitude φ V is
Vrot, = 2πR (a + b sin2 φV + c sin4 φV );
(5)
φ V is calculated from the real trajectory of Venus on the face of the
Sun as calculated below.
The trajectory of Venus in front of the Sun (depicted in Fig. 4)
was computed for any given time of the transit on the reference
system centred on the Sun and with axis of symmetry the rotation
axis of the Sun at the position angle ψ . The coordinates were
computed from the sky observing coordinates (RA, Dec.) of Venus
relative to the centre of the Sun using the formulae
X(t) = (RAV − RA ) cos(Dec.V ),
Y (t) = (Dec.V − Dec. ),
and rotating the reference frame on the Sun’s rotation axis ψ ,
X (t) = X cos(ψ ) − Y sin(ψ ),
Y (t) = X sin(ψ ) + Y cos(ψ );
hence, the separation between the centre of Venus and the centre of
the Sun is
(6)
δ(t) = X2 + Y 2 .
The theoretical variation of the solar radial velocity during the
Venus transit computed with the above-derived parameters is overplotted to the observations in the upper panel of Fig. 3. An RM
effect of comparable magnitude, although a factor of 2 larger, was
detected through the observations of several transits in the hot Neptune HAT-P-11b by Hirano et al. (2011) and Winn et al. (2010).
The residuals of the observations against the model do not present
any systematic effects; the residuals are indeed centred on zero,
with a mean value of 0.11 m s−1 and an rms of 0.77 m s−1 . The
power spectra of the residuals, shown in Fig. 3, clearly reveal the
power excess around the frequency of the p modes of the solar
oscillations (Claverie et al. 1979). The highest peak in the power
spectra corresponds to a frequency of 3.032 27 mHz with amplitude
of 0.40 m s−1 .
The spin–orbit angle measurements provide crucial information
on the mechanisms involved in the formation of planetary systems. This information can be obtained by comparing the relative
orientation of the host-star spin axis, usually regarded as a relic
of the angular momentum of the protostellar accretion disc, and
the orbital axes of the planets, which may be largely affected by
planet–planet interactions. Tidal interaction may in some extreme
cases lead to modification of the stellar rotation rate – though any
Detection of RM effect in Venus transit
substantial transfer of angular momentum from a close-orbiting
planet to a slowly rotating star will result in the planet’s destruction
(Brown et al. 2011, and references therein). The orientation of the
orbital angular momentum of a transiting planet with respect to the
spin angular momentum of the star provides a unique observational
constraint to the actual spin–orbit misalignment. This can be studied
via the RM effect. So far, λ has been published for about 60 transiting extrasolar planets, the majority of which do show values of λ
close to zero, pretty much like the planetary bodies orbiting our Sun,
like Venus, although nearly 40 per cent show substantial misalignment (Winn 2010). Yet, the quality of these determinations largely
depends on the brightness of the star and on the instrumentation
used, besides the RM effect amplitude itself.
AC K N OW L E D G M E N T S
This project was the ESO programme DDT 289.D-5015, and we
warmly acknowledge the ESO director Tim De Zeeuw for this opportunity. Very useful discussions with Emilio Molinari and Gaspare
Lo Curto at different stages of this work are also acknowledged.
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