Free Access
Volume 534, October 2011
Article Number L6
Number of page(s) 5
Section Letters
DOI https://doi.org/10.1051/0004-6361/201117713
Published online 12 October 2011

© ESO, 2011

1. Introduction

For transiting planets, the Rossiter-McLaughlin effect (Holt 1893; Rossiter 1924; McLaughlin 1924; Queloz et al. 2000; Gaudi & Winn 2007) allows the measure of β (also called λ in the literature), which is the projection on the sky of the angle ψ between the stellar spin axis and the orbital spin axis.

Until recently, planets had been thought to be mostly on coplanar orbits with their star’s equator (Fabrycky & Winn 2009), something in line with predictions of disc migration (Lin et al. 1996; Ward 1997). However a number of papers have shown that hot Jupiters on non-coplanar orbits are common, including some planets on retrograde orbits (Hébrard et al. 2008; Moutou et al. 2009; Narita et al. 2009b; Winn et al. 2009a; Anderson et al. 2010; Queloz et al. 2010; Triaud et al. 2010). These measurements have been interpreted as showing that dynamical events are probably quite common and that not all systems can be understood by disc migration alone. Strong dynamical events such as planet-planet scattering (Rasio & Ford 1996; Jurić & Tremaine 2008; Chatterjee et al. 2008), more secular processes such as Kozai-Lidov oscillations (Wu et al. 2007; Fabrycky & Tremaine 2007; Nagasawa et al. 2008; Naoz et al. 2011), or chaotic interactions (Wu & Lithwick 2011) would place a planet on a highly eccentric orbit, whose passage at periastron is sufficiently close that tidal dissipation causes the planet to lose angular momentum and circularise around its star.

Understanding the origin of hot Jupiters is one of the keys to shedding light on the processes that act during planet formation as well as those acting after planets have formed. The constraint of these processes will help us determine what did and did not happen in our own Solar System, and match more accurately the theoretical predictions of planet formation done by population synthesis to the parameter space that planets currently occupy, as given by the observations (e.g., Ida & Lin 2004; and Mordasini et al. 2009).

Matsumura et al. (2010a) noted that if misaligned hot Jupiters do not require disc migration, aligned planets do not contradict a scenario involving dynamical interactions and tidal migration, as planets will tend to realign with the star (see also Hut 1981; and Barker & Ogilvie 2009).

Winn et al. (2010a) point out a correlation between the stellar effective temperature and the spin/orbit angle. For stars with Teff > 6250 K, fewer aligned systems are found than for stars with lower effective temperatures. This would imply that tidal realignment timescales are different for different stars, as proposed by Zahn (1977) in the context of binaries. Schlaufman (2010) presents an independent confirmation of that correlation, using a different methodology.

The aim of this Letter is to combine the observational findings and offer an explanation. The results will then be discussed in light of the currently available theoretical framework.

2. Motivation

The lack of aligned systems for stars with Teff > 6250 K noticed by Winn et al. (2010a) could also be explained by stellar physics combined with an observational bias: as predicted by stellar evolution, stars with masses higher than about  1.2 M start on the zero age main sequence with temperatures higher than 6250 K. When H-core burning has stopped, they have cooled by several hundred Kelvin (Fig. 1). They do so in 3 to 4 Gyr. This means that, while the planet and the star progressively realign, the star itself cools down. We are thus left with an aligned planet around an older, cooler star. Some, more massive, stars will cool to temperatures above 6250 K, but the timescale for realignment might be longer than the main sequence lifetime. Once they leave the main sequence, stars become too massive for planets to be discovered by ground-based transit surveys as the ratio of radii becomes too small. We are thus more likely to detect misaligned planets around hot stars, notably because we may not detect their aligned population.

This explanation could be combined with the different realignment timescales described in Winn et al. (2010a) and Zahn (1977) because, as the star ages and cools, its convective zone would also become larger. If that explanation were correct, we should expect a correlation between stellar age and alignment.

thumbnail Fig. 1

Main sequence showing the Geneva stellar evolution tracks for solar metallicity as presented in Mowlavi et al. (2011) and plotted using R   (in R) as a function of Teff. Tracks are labelled in units of M. Dashed line show the 2 Gyr isochrone. Overplotted are the systems for which we have Rossiter-McLaughlin measurements. Aligned systems are red circles, misaligned systems are blue triangles. Higher metallicities will move the tracks to the right. Data obtained from Exoplanet.eu.

The average stellar density, ρ  , is obtained directly from the planetary transit signal (Sozzetti et al. 2007); both effective temperature, Teff, and metallicity, Z, can be derived from spectral analysis. Stellar mass and stellar age can be estimated from interpolating the stellar evolution tracks in (ρ  ,Teff,Z) space. Interestingly, stars  > 1.2 M spend less time on the main sequence, but increase their radii more than solar mass stars do. We thus have a higher resolution on the tracks to estimate ages for more massive stars than for solar mass stars. Such a subsample should give the most precise and accurate ages that we can obtain. This is the sample used in this Letter.

3. Sample selection

Let us consider only the most secure measurements of the projected spin/orbit angle1, for planets with stars  ≥1.2 M. There are 22 objects in the sample (Table 1). The sample is divided into two: stars  ≥1.3 M (8 stars) and stars between 1.2 and 1.3 M (14 stars). The angle and age estimates were obtained from the literature, but for WASP-17, whose error bar in the age was large. It was re-estimated for this Letter, using the stellar parameters and density presented in Triaud et al. (2010) and interpolating in the Geneva tracks (Mowlavi et al. 2011). The new age estimate is 2.3 ± 0.6 Gyr. Its error bar is consistent with age measurements made by other teams. The new value is presented along with all other values in Table 1.

thumbnail Fig. 2

Secure  |β|  against stellar age (in Gyr), for stars with M   ≥ 1.2 M. Size of the symbols scales with planet mass. Blue squares indicate stars with M   ≥ 1.3 M; red diamonds, stars with 1.3 > M   ≥ 1.2 M. Horizontal dotted line show where aligned systems are. Vertical dotted line shows the age at which misaligned planets start to disappear.

Plotting the absolute values of the measured projected spin/orbit angle β against stellar age (Fig. 2), there is a pattern as distinctive as that presented in Winn et al. (2010a). While observationally, there should be no bias in preferentially detecting aligned systems instead of misaligned systems at any age, stars older than  ~2.5 Gyr mostly have aligned planets (rms = 22°, median = 5°). For younger stars we find a large range of inclinations (rms = 66°, median = 60°). Figure 3 displays the cumulative distributions on either side of the 2.5 Gyr age limit.

To test the robustness of the pattern, a Monte Carlo simulation was performed taking the data with ages  <2.5 Gyr as a fiducial zone from which random samples of eight measurements were drawn, allowing for repetitions. There is a lower than 4% probability of drawing a sample with median  <10° and rms  <60° which would allow a sample having seven aligned systems and one retrograde system. If we were to restrict the rms to within 30°, similar to that observed, there is a probability  <1% that the distributions on either side of the 2.5 Gyr age would be the same. Drawing randomly from the overall sample, there is a 2.6% chance of obtaining a cluster containing seven aligned systems and another at any angle  >20°. In addition, a Kolmogorov-Smirnov test was carried out, in which were compared the distribution in β on either side of the 2.5 Gyr limit. A value of D = 0.661 is obtained corresponding to a probability of 1.2% that both distributions are the same2. The same test shows that the distribution of angles around stars younger than 2.5 Gyr has about a 22% chance of being compatible with a uniform distribution, while for the older sample, this chance is of the order of 10-5. By rearranging the data, selecting various cut-offs and computing the KS test at each step, the probability of having two such different populations arising by chance is estimated to about 7%. It can be affirmed that there is tentative evidence of a pattern in the data.

We see that stars with masses  ≥ 1.3 M are all younger than 3 Gyr. In obtaining only a few aligned systems on stars hotter than 6250 K, Winn et al. (2010a) could in fact be detecting an effect due to stellar age, or rather, time since planet formation.

As for all multivariate problems, Fig. 2 offers an incomplete picture: it only shows two quantities in relation with time. At the moment, orbital separations and mass ratios are quite similar because the bulk of the discoveries have been made by ground-based transit search programs. With increasing numbers of measurements over a larger parameter space, we will eventually need to account for those extra parameters.

thumbnail Fig. 3

Cumulative distributions of orbital inclinations for systems younger than 2.5 Gyr (dashed blue), and older (plain red). For comparison, a uniform distribution (dotted black).

4. Discussion

The large variety of angles found on younger stars suggests that some misaligning mechanism operates during the youth of planetary systems. In combination with the results of Watson et al. (2011) showing no evidence of misaligned protoplanetary discs, it lends support to a planet-planet scattering scenario occurring during the last stages of planet formation or soon in the aftermath of disc dispersal as described by Matsumura et al. (2010b).

When preparing Fig. 2, reason dictated that a dearth of old, misaligned systems was expected, not an absence. The complete lack of misaligned planets orbiting stars older than 2.5 Gyr in the current sample came somewhat as a surprise as secular interactions could place planets on inclined orbits well after the disc dissipated. A system with these characteristics can be found among the “older” systems: HAT-P-13, whose current configuration may have originated from secular interactions (Mardling 2010). If that history is right, its observed coplanarity may be a chance alignment, which can occur easily because firstly, we observe a projected angle, β, and not the real obliquity ψ and secondly, theoretical predictions such as Wu et al. (2007), Fabrycky & Tremaine (2007), and Nagasawa et al. (2008) predict very high orbital inclinations, but also a number of aligned systems.

There is great interest in matching those theoretical distributions to observations (notably for young hot Jupiters), but the evolving nature of the spin/orbit angle distribution makes this a tricky task. Multi-body dynamics are less concerned with absolute masses than mass ratio. In systems where no Jupiter has formed, we would expect planet-planet scattering between Neptune-mass planets producing an inclined hot Neptune population. If the inital stages are similar, the later ones will not be: tidal circularisation and realignment timescales will be different. Spin/orbit angles for planets of masses  <0.1 MJup will be less affected by tidal realignment and offer a closer picture of the initial spin/orbit angle distribution than hot Jupiters. A hot Neptune, Hat-P-11 b has been found misaligned by Winn et al. (2010c) and confirmed by Sanchis-Ojeda & Winn (2011).

This work has focused on stars with masses  ≥1.2 M. If age is what determines primarily whether a hot Jupiter is observed aligned or misaligned, because solar mass stars are found to be on average older than more massive stars, it is unsurprising that their planets are coplanar. Nevertheless, there is interest in carefully studying that population, which stems from work by Burkert & Ida (2007), Currie (2009), and Alibert et al. (2011), who argue that discs around the more massive stars are not long lived enough to produce an aligned hot Jupiter population via disc migration. In the mean time, if planet formation is more efficient in more massive discs (found around more massive stars), then one could expect a higher occurrence of planet-planet scattering around these stars. If this were true, it could point towards two pathways for bringing hot Jupiters to their observed location, which would depend on stellar mass. Unfortunately, stellar ages are less precisely determined for solar mass stars as illustrated by the isochrone in Fig. 1.

The change in the shape of the distribution of spin/orbit angles with time is indicative of some orbital evolution, presumably by means of tidal interactions between the star and the planet. Barker & Ogilvie (2009) show that retrograde planets decay onto their star on timescales two to three times shorter than prograde planets would do, for given initial conditions. Their infall timescale for a typical, retrograde hot Jupiter are of the order of a few Gyr. Winn et al. (2010a) identify a similar behaviour, and show that, for a given stellar mass, a more massive planet will realign and in-spiral faster than a lighter one3. In both papers, the retrograde planets realign with the star but only shortly before falling onto it. It would thus be unlikely to observe them at these very particular phases. Nevertheless, possible examples might have been found in WASP-12, 18, and 19 (e.g., Hellier et al. 2011). Matsumura et al. (2010a) describe how planets initially placed on mildly inclined or aligned orbits, are less likely to in-fall and more likely to survive until observed. Nevertheless, in most cases tidal realignment corresponds to the disappearance of the planet.

If retrograde planets were to plunge towards their star as they tidally realign, a decreasing number of hot Jupiters should be observed with time. No such decreasing trend can be found when considering all the hot Jupiters presented in the literature around stars in the mass range considered for this paper. This is at odds with evidence of a trend between semimajor axis and stellar age showing a lack of very short orbits around older stars as presented by Jackson et al. (2009), who interpreted this as evidence of the destructive tidal orbital decay of hot Jupiters. Looking at the semimajor axes of the targets in Table 1, a similar trend appears. This may indicate we have not yet observed enough objects to detect the expected decreasing fraction of hot Jupiters with time. Alternatively, the results presented here, and those of Winn et al. (2010a), could be seen as evidence that realignment occurs faster than orbital decay. Lai (2011) demonstrate how planets could realign their orbit more rapidly than their semimajor axis would decay.

Finding out about the ultimate fate of hot Jupiters is of great interest and a subject of intense ongoing research, fraught with challenges. For example, the tidal circularisation and realignment timescales notably depend on the orbital obliquity ψ, the ratio of masses, the scaled radius (a/R  ), and the tidal quality factors for the planet, , and for the star, (Hut 1981; Barker & Ogilvie 2009). Most of the theoretical work currently assumes constant Q′ values, whereas Ogilvie & Lin (2004) showed that they depend on tidal frequency. Lai (2011) indicates that Q′ could vary for different physical processes. Similarly, R   is often assumed constant when clearly, in Fig. 1 a 1.3 M star increases its radius by about 30% in about 4 Gyr.

Stellar age estimates are notoriously difficult to obtain. The estimates used here have been extracted by a variety of authors using different techniques on different sets of evolution models. The pattern between β and stellar age resisted to a blurring caused by systematic effects, displaying a certain robustness. Nevertheless, this study should provide an incentive to continue obtaining Rossiter-McLaughlin measurements as well as check stellar ages and derive them in a uniform manner. Similarly, accurate and precise age estimates for solar mass stars are clearly needed. One can obtain those via a good determination of stellar parameters, using higher resolution spectroscopy for the Teff and Z, and high precision photometry to determine ρ  . Stellar ages can also be estimated from asteroseismologic time-series underlying the interest in having a planet-finding space mission with such capacity, such as the proposed PLATO. Astrometric distance measurements from the GAIA satellite will soon give us independent access to stellar radii.


Some measurements have been omitted for the following reasons: CoRoT-3 (sampling is poor Triaud et al. 2009), CoRoT-11 and Kepler-8 (transits are incomplete Gandolfi et al. 2010; Jenkins et al. 2010) and WASP-1 (angle is unsure Albrecht et al. 2011).


The same test for the pattern presented in Winn et al. (2010a) gives a 6.1% chance that the distributions on either side of 6250 K are the same.


Incidentally, this could explain a second feature linked to the angle β. As shown in Moutou et al. (2011), there is a lack of retrograde massive planets (>5 MJup), something expected if retrograde, massive planets realign with their star faster than other planets do.


Many thanks are given to those whose many discussions helped me to produce this work, in particular Rosemary Mardling, Soko Matsumura and Johannes Sahlmann, but also Christoph Mordasini, Pedro Figueira, Josh Winn, Andrew Collier Cameron, Georges Meynet, Michaël Gillon, and Damien Ségransan. Thanks to Nami Mowlavi and the Geneva stellar evolution group for preparing stellar tracks to my specifications. Eternal recognition also go to Didier Queloz, my PhD supervisor for teaching me how to research while giving me freedom and independence. I wish to convey thanks to my editor, Tristan Guillot, and to an anonymous referee for greatly improving this work and understanding it. I would also like to acknowledge the use of Jean Schneider’s exoplanet.eu and René Heller’s encyclopaedia for the Rossiter-McLaughlin effect. This work is supported by the Swiss Fond National de Recherche Scientifique.


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Online material

Table 1

Stellar and planetary parameters used to create Fig. 2.

All Tables

Table 1

Stellar and planetary parameters used to create Fig. 2.

All Figures

thumbnail Fig. 1

Main sequence showing the Geneva stellar evolution tracks for solar metallicity as presented in Mowlavi et al. (2011) and plotted using R   (in R) as a function of Teff. Tracks are labelled in units of M. Dashed line show the 2 Gyr isochrone. Overplotted are the systems for which we have Rossiter-McLaughlin measurements. Aligned systems are red circles, misaligned systems are blue triangles. Higher metallicities will move the tracks to the right. Data obtained from Exoplanet.eu.

In the text
thumbnail Fig. 2

Secure  |β|  against stellar age (in Gyr), for stars with M   ≥ 1.2 M. Size of the symbols scales with planet mass. Blue squares indicate stars with M   ≥ 1.3 M; red diamonds, stars with 1.3 > M   ≥ 1.2 M. Horizontal dotted line show where aligned systems are. Vertical dotted line shows the age at which misaligned planets start to disappear.

In the text
thumbnail Fig. 3

Cumulative distributions of orbital inclinations for systems younger than 2.5 Gyr (dashed blue), and older (plain red). For comparison, a uniform distribution (dotted black).

In the text

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