A Photometric Variability Study Using Brown Dwarfs As Giant Planet Analogues: Investigating rotation periods and cloud structure

(1)

Department of Astronomy – Stockholm University

A Photometric Variability Study Using Brown Dwarfs As Giant Planet Analogues

Investigating rotation periods and cloud structure

Master of Science Thesis

3 June 2016

Author:

Simon Eriksson

simon.c.eriksson@gmail.com

Supervisor:

Markus Janson

(2)

Abstract

Recent discoveries of large numbers of low-mass field brown dwarfs below the deuterium-burning limit, offers up a substantial sample of giant planet analogues which can be directly imaged without the severe contrast difficulties that regularly bound planets suffer from. By detecting significant periodic variability in such objects, enhanced by their lower surface-gravities, over several hours we can obtain estimates of their rotation periods. As this periodicity is possibly the result of heterogeneous cloud features in the upper atmosphere of a brown dwarf, atmospheric cloud models can then be used to discern some properties of its cloud structure. In this work we independently investigate 19 L0-L7 and 2 T2.5-T3.5 brown dwarfs with a mass-range of ∼ 6 − 22 M_Jup, spanning the deuterium-burning limit. We detect significant large amplitude (> 2%) sinusoidal variability of < 9.3 ± 2.0% through near-infrared observations of PSO J318.5-22. This unusually red, 6.5 MJup, giant planet analogue was observed in J_Sand K_Sat the NTT/SOFI through the ESO observing program 194.C-0827(A) by PI: Biller, B. We are able to constrain the rotation period of PSO 318, estimating a likely period of at least 7 hours. We further detect entirely new and significant (> 99% confidence) variability in 3 targets, with tentative detections in another 10, out of which 9 of are new discoveries. Our results indicate a minimum variability fraction for these targets, primarily outside the L/T transition, as high as fmin= 70⁺⁸₋₁₂%. We conclude that very low-mass brown dwarfs, many of which show unusually red colours and signs of low-gravity, might be more likely to exhibit both greater amplitudes and frequencies of rotationally modulated variability.

ii

(3)

Contents

1 Introduction 1

2 Background and Theory 3

2.1 Brown Dwarfs . . . . 3

2.1.1 The Definition of BD vs. GP . . . . 3

2.1.2 Observational properties . . . . 4

2.1.3 Formation . . . . 7

2.2 Giant Planets . . . . 8

2.2.1 Observational properties . . . . 8

2.2.2 Formation . . . . 9

2.3 Previous Works . . . . 10

2.3.1 Observational . . . . 10

2.3.2 Modelling . . . . 13

2.4 Summary . . . . 13

3 Observations 14 3.1 NTT/SOFI . . . . 17

3.1.1 Data reduction . . . . 17

3.2 VLT/HAWK-I . . . . 19

3.2.1 Data reduction . . . . 20

4 Analysis 22 4.1 Aperture Photometry . . . . 22

4.2 Light Curve Calibration . . . . 26

4.3 Light Curve Analysis . . . . 28

4.3.1 Polynomial subtraction . . . . 28

4.3.2 Lomb-Scargle periodogram . . . . 29

5 Results 30 5.1 Significantly Variable Targets . . . . 31

5.2 Tentatively Variable Targets . . . . 38

5.3 Non-Variable Targets . . . . 45

6 Discussion 48 6.1 Implications of Binarity in the Sample . . . . 48

6.2 PSO 318 . . . . 49

6.3 HN Peg B . . . . 51

6.4 Photometric Precision and the Reduction Process . . . . 52

6.5 Frequency of Variability . . . . 53

6.6 Comparisons with Previous Works . . . . 53

6.7 Future Prospects . . . . 55

7 Conclusions 55

References 57

A Binned light curves & finding charts of non-variable targets 61 iii

(4)

B Polynomial subtraction results for tentative & non-variable targets 65 C L-S periodograms for tentative & non-variable targets 68

iv

(5)

List of Figures

1 Optical spectra of SpT M7-T8 from 6800 to 8700 ˚A . . . . 5

2 Radigan et al. (2014) SpT vs. 2MASS J − K_S colour diagram . . . . 6

3 Planet-Metallicity Correlation . . . . 9

4 Biller et al. (2015) light curve for PSO 318 . . . . 10

5 Radigan et al. (2012) light curves for 2M2139 . . . . 11

6 Reduced light curves from Metchev et al. (2015) . . . . 12

7 Colour-Magnitude diagram of our sample . . . . 14

8 Single raw 60 s exposure from NTT/SOFI. . . . 18

9 Typical master dark frame from NTT/SOFI . . . . 18

10 Typical master flat field from NTT/SOFI . . . . 19

11 Illumination correction . . . . 19

12 HD 106906 b close-up . . . . 20

13 HD 106906 b median box filtering . . . . 21

14 HD 106906 b identification . . . . 22

15 Raw light curve examples . . . . 23

16 HD 106906 b Standard deviation vs. Median flux . . . . 24

17 PSO 318 Ks frame combination effects . . . . 25

18 PSO 318 Js Nov. raw light curves . . . . 25

19 Calibrated light curve of CB reference star . . . . 26

20 Binned light curve of CB reference star . . . . 27

21 Polynomial subtraction of the CB reference star . . . . 29

22 Simulated sinusoidal data . . . . 29

23 Lomb-Scargle periodogram of simulated data . . . . 29

24 Lomb-Scargle periodogram for the CB reference star . . . . 30

25 PSO 318 J_S Oct. binned light curves & finding chart . . . . 31

26 PSO 318 J_S Nov. binned light curves & finding chart . . . . 32

27 Polynomial subtraction results for PSO 318 J_S Oct, Nov. . . . 33

28 PSO 318 K_S Nov. binned light curves & finding chart . . . . 33

29 Polynomial subtraction result for PSO 318 K_S Nov. . . . 34

30 Lomb-Scargle periodograms for PSO 318 . . . . 34

31 2M0045 binned light curves & finding chart . . . . 35

32 Polynomial subtraction result for 2M0045. . . . 35

35 Polynomial subtraction results for 2M0117 and 2M0501. . . . . 37

36 Lomb-Scargle periodograms for 2M0045, 2M0117 and 2M0501 . . . . 38

44 GU Psc b binned light curves & finding chart . . . . 44

45 HN Peg B binned light curves & finding chart . . . . 44

46 SIMP2154 binned light curves & finding chart . . . . 45

47 HD 106906 b and control star comparison . . . . 46 v

(6)

48 Model fitting for PSO 318 by B15 . . . . 50

49 November 2014 light curve for PSO 318 by B15 . . . . 52

50 SpT vs. J-K_S diagram . . . . 54

57 HD 106906 b binned light curves & finding chart . . . . 64

58 2M0045 - Example with all RS . . . . 64

59 Polynomial subtraction plots I . . . . 65

60 Polynomial subtraction plots II . . . . 66

61 Polynomial subtraction plots III . . . . 67

62 Lomb-Scargle periodograms I . . . . 68

63 Lomb-Scargle periodograms II . . . . 69

List of Tables 1 SOFI observations . . . . 15

2 HAWK-I observations . . . . 15

3 Field object properties . . . . 16

4 Companion object properties . . . . 16

5 Detections of Variability . . . . 47

vi

(7)

1 Introduction - 1 - Section 1.0

1 Introduction

In this thesis project we investigate 21 directly imaged low-mass brown dwarfs (BD’s) for periodical photometric variability. With a mass-range of 6-22 Jupiter-masses (M_Jup) and with the majority at or just below the deuterium burning (DB) mass- limit of ∼ 13 M_Jup (Spiegel et al. 2011), these objects can be treated as free-floating giant planet (GP) analogues (Chabrier et al. 2014). For the sake of context however, before we get to the more detailed section of Background and Theory (§2), we first present a brief overview concerning recent advances made and techniques used in extrasolar planet, or exoplanet, research.

It has now been over two decades since the first exoplanet was discovered around the millisecond pulsar PSR B1257+12 (Wolszczan & Frail 1992), using pulsar timing variations. The fact that the host star of this planet, being a rapidly rotating neutron star, was as far from a ”normal” star as one can imagine, seems in hindsight to have been a very fitting omen of just how fantastically different and diverse the stellar environments of planets and star systems other than our own would turn out to be. The first bonafide exoplanet orbiting a main-sequence star was detected around 51 Pegasi a few years later (Mayor & Queloz 1995) and by the end of the decade dozens of worlds had been discovered.

The torrent of discoveries did not abate, but ac- celerated with missions like CoRoT (Auvergne et al. 2009) in 2006 and the start of the unimagin- ably successful Kepler mission in 2009 (Koch et al. 2010), which despite severe setbacks continues to this day to provide us with an ever increasing sample of planet candidates. Confirmed planets from the Kepler data range in mass from several MJupdown to Earth-mass planets and number al- most 2000, with over 5000 remaining candidates (Mullally et al. 2015). With the resounding suc- cess of these early missions the field of exoplane- tary science exploded and is still expanding rapidly with an ever increasing diversity, investigating ev- ery aspect of planetary formation, evolution, composition and habitability that current methods and

technology allows.

The detection method used for the Kepler mission focuses on photometric observations of planetary transits in front of their host stars (e.g. Char- bonneau et al. 2007), producing light curves with a clearly distinguishable drop in intensity which can be analysed to obtain constraints on planetary radius and parameters such as orbital period and eccentricity. Due to the principles of this method it works best on systems viewed near edge-on, and has a bias for detecting planets with short periods around cool stars. This naturally leads to large in- completeness effects when considering the full pop- ulation of extrasolar planets.

To confirm candidates discovered by Kepler as exoplanets, and to obtain mass limits, one generally looks to spectroscopic radial velocity (RV) measurements of candidate host stars, searching for a Doppler shift arising due to orbital move- ment around a common center of gravity (e.g.

Plavchan et al. 2015). Like the transit method, RV measurements are biased towards planets on tight orbits and more massive planets such as gas giants (or ”hot Jupiters”).

There are several other methods that can be used such as astrometry, polarimetry, other timing methods and gravitational microlensing, but we will move on to discussing the one most relevant for this work – direct imaging of exoplanets.

As the name implies, the aim of this method is to image the target directly which in the case of exoplanets is an extremely challenging prospect due to the extreme contrast difference between a planet and its host star.

Earlier missions focused on space-based telescopes for very good reasons. The Earth’s atmosphere not only blocks several interesting wavelength-regions, but it also distorts the path of photons that manage to reach us. The result is an unavoidable smearing (seeing) effect on observations by any ground-based telescopes, which limits resolution and photometric precision. With the introduction of adaptive optics (AO; e.g. Davies

& Kasper 2012, Males et al. 2014) and further improvement of these systems (Extreme AO; e.g.

Jovanovic et al. 2015), the quality of ground-

(8)

1 Introduction - 2 - Section 1.0

based observations can start to approach parity with space-based telescopes. The 39.3 m diame- ter European Extremely Large Telescope (E-ELT) has the potential to revolutionize the search for and study of terrestrial-sized exoplanets, and would not be feasible without this technology.

The first exoplanet detection using direct imaging can be attributed to Chauvin et al. (2005), who detected the ∼ 5 M_Jup giant planet 2M1207b orbiting a ∼ 25 MJup BD at a distance of 55 AU.

Whether or not an object like 2M1207b actually qualifies as an exoplanet is a discussion for §2.

2M1207b is also of interest since Zhou et al. (2016) recently discovered that it displays low-amplitude (∼ 1%) peak-to-peak variability with a rotational modulation, most likely caused by heterogeneous cloud features.

It should come as no surprise that an object like 2M1207b was the first to be directly imaged, since it is a strong infrared emitter (T_eff∼ 1250 K) orbiting a relatively faint companion/host, allowing for high-contrast imaging without the use of a corona- graph that blocks out the light of a host star. Simi- larly, using the method on field BD’s or BD’s/GP’s with extreme separations from their companions or host stars has proven very successful, as this project is another example of.

Around main-sequence stars, direct imaging is biased towards planets with wide orbits, as contrast improves with distance from the star. The method also has the potential to reveal multiple planets at once, as was the case with the 1.47 Solar-mass (M) star HR 8799 where Marois et al.

(2008) presented multi-epoch high-contrast observations from the Very Large Telescope (VLT) of three planets, 5-13 M_Jup, orbiting the star with a top-down perspective. This system was later expanded to include the discovery of a fourth planet on an inner orbit, with recent observations possibly indicating a fifth (Booth et al. 2016). Further observations of these planets were later used by Madhusudhan et al. (2011) as a testing bed for their atmospheric models for massive gas giants, a set of models that we will be using and exploring further in Discussion (§6).

Closely linked with direct imaging is spec-

troscopy, and while not central to this project it is vital for the classification of BD’s and understanding their evolution using spectral features.

Obtaining spectra of exoplanets is inherently dif- ficult, given the problems of achieving high contrast and precision. The James Webb Space Tele- scope (JWST) has the potential to drastically improve the prospects for transit spectroscopy of terrestrial-sized worlds and characterization of their atmospheres (e.g. Barstow et al. 2016, Greene et al. 2016).

For faint low-mass objects such as the planets around HR 8799, field BD’s or GP’s with separations of 100’s of AU, direct spectroscopy is cer- tainly possible with many ground-based telescopes.

While excellent spectra have been obtained of the planets in the HR 8799 system and the number of directly imaged exoplanets is increasing, at present only around twenty have been observed (e.g. Kalas et al. 2008, Lagrange et al. 2010, Kraus & Ireland 2012, Kuzuhara et al. 2013, Liu et al. 2013 – PSO J318.5-22, Rameau et al. 2013)

The Wide-field Infrared Survey Explorer (WISE;

Wright et al. 2010), still going after more than six years, has so far discovered hundreds of low-mass BD’s in the Solar neighbourhood, with many of these below the DB-limit. As research into star, BD and GP formation continues it is becoming increasingly likely that BD and GP formation and evolution have a lot in common (Chabrier et al.

2014). If this is indeed the case, and similar-mass GP’s and BD’s are not that dissimilar, the WISE survey results offers up a vast amount of giant planet analogues that can be directly imaged and analysed without the headaches associated with the direct imaging of exoplanets.

While there has been extensive research into BD’s in general by looking for photometric variability (e.g. Apai et al. 2013, Biller et al. 2013, Buenzli et al. 2014, Metchev et al. 2015, Marley

& Robinson 2015, Radigan et al. 2012), until one week before the start of this project no photometric variability studies had been published for BD’s close to the DB-limit. So while the technique it- self is not new, the substantial sample offered by WISE allows for a new leap in its application.

(9)

2 Background and Theory - 3 - Section 2.1

Photometric variability studies of these lower- mass objects would therefore allow us to

1. constrain their rotation periods and compare with estimates obtained from radial velocity measurements. Better statistics on rotation periods across a broad range of masses could aid in the understanding of how it relates to the age of these objects and their formation and evolution.

2. aid the development of atmospheric models and through these improve our understanding of the evolution and structure of GP atmospheres.

3. make comparisons to the extensive literature that exists for photometric variability research done for more massive BD’s and look for cor- relations in e.g. lower surface gravity.

4. improve the methodology so it can be applied with higher precision to even lower-mass objects and GP’s.

As the technique becomes more widely applied and refined, it paves the way for potential future applications to Earth-sized exoplanets, where photometric variability could map cloud structures or even the shape of continents and oceans (e.g.

Kawahara & Fujii 2011). As such it could prove to be a powerful tool in the expanding toolbox that we need to finally answer Humanity’s ever-present question about life on other worlds.

Next, Background and Theory (§2) goes into more detail concerning previous studies of BD’s, their formation, evolution and connection to GP’s.

Observations (§3) and follows thereafter detailing the data sets, their reduction and continuing with the Analysis (§4). The outcomes of which are then presented in Results (§5). Finally we end with the Discussion (§6) and Conclusions (§7).

2 Background and Theory

There is one trait common to all of the targets investigated in this work, which is that the vast majority are very young objects, with ages of ∼

10−100 Myr and located at a distance of ∼ 10−60 parsec (pc) (Gagn´e et al. 2014a). The age estima- tions of BD’s are generally obtained by looking at their motion in space, i.e. determining their radial velocities and assigning them to stellar associations or moving groups with objects that exhibit similar motion (e.g. Ducourant et al. 2014). The ages of these associations can be estimated by the use of e.g. stellar models and theories of star formation or kinematic analysis (tracing motions back in time). These young objects are intrinsically very hot as they are still in the process of gravitationally contracting, and as a result emit strongly in the infrared (IR). In general, this provides the observer with a natural high-contrast condition, improv- ing the possibility to observe such objects closer to their host stars (e.g. Oppenheimer & Hinkley 2009) than would be possible for older and cooler objects. As the targets in this work are reasonably close to us in space, they are relatively bright with apparent J-band magnitudes of ∼ 14 − 17 mag.

Before we move on, we need to decide how to tackle a somewhat controversial issue, namely one of definition.

2.1 Brown Dwarfs

2.1.1 The Definition of BD vs. GP

When discussing BD’s and GP’s in this context, one must first establish a definition that distin- guishes between the two. Unfortunately this is not a simple task, and any attempts at a strict definition is often highly controversial, even more so considering the increasing number of discoveries of BD’s well below the DB-limit (e.g. Chauvin et al.

2005, Todorov et al. 2010, Delorme et al. 2012).

Distinguishing between a star and a BD is more straight-forward, with the natural hard cut-off point between the two being a core temperature high enough to initiate hydrogen-burning (HB).

Since core temperature is tied to stellar mass, this gives us a HB minimum-mass for stars of ∼ 0.075 M or ∼ 80 MJup(e.g. Chabrier et al. 2000).

The ”classical” definition used by the Interna- tional Astronomical Union (IAU) states that if the object is above the DB-limit (∼ 13 M_Jup) but be-

(10)

low the hydrogen fusion limit it is classified as a BD. This definition seemed reasonable at a time when our knowledge of BD’s and GP’s outside our Solar system was limited, but with recent ad- vancements in astronomy, this limit appears un- necessarily arbitrary and confusing. To account for free-floating objects below the DB-limit, the term planetary-mass object (PMO, planemo) is some- times used. Rather than perpetuating this definition we choose to follow a different one.

Chabrier et al. (2014), henceforth C14, argue this point extensively, as they detail the observational properties of BD’s and GP’s, their formation and evolution. Their classification, which we feel is more suitable for this work, states the following.

BD’s denominates any

1. free-floating object below the HB minimum- mass, irrespective of it being above or below the DB-limit.

2. objects that are companions to a host star or another BD, and exhibit properties consistent with that of a gaseous sphere with a global chemical composition similar to the host star or BD.

The last point is especially important as chemical composition is affected by the mechanism behind the formation of the object, as we will see later on in this section. In short, this definition separates BD’s and GP’s depending on the way they formed, rather than an arbitrary line at the DB-limit.

While this is not by any means a final or perfect definition, and becomes ambiguous for e.g. objects with very wide separations from their companion/host or when considering ejected/scattered planets, it does offer an overlap between the two object classes which does not exist under the IAU definition. We will return to C14 as we continue our discussion on BD formation later on.

2.1.2 Observational properties

Since BD’s by definition lack a persistent internal energy source, they slowly cool over time as they radiate away the energy they obtained during formation and subsequent gravitational contraction.

As the effective temperature decreases, the conditions and chemistry in the atmosphere changes, leading to different atoms and molecules being favoured over others, which in turn leads to sedimentation into clouds (e.g. Marley et al. 2002).

As such, the observational properties of BD’s can change drastically during their evolution, and being able to differentiate between them becomes a necessity.

The primary classification of BD’s is made by assigning them a spectral type (SpT) in a similar way as is done for stars, which are classified as SpT O B A F G K M. As a first step, this represents a relatively simple way of ensuring that the object you are looking at is not a regular star or galaxy.

The last type in the traditional classification, M, primarily contains red dwarfs, giants and super- giants but also hosts young and hot BD’s at around

∼M6. As the number of BD detections increased as observations improved, additional spectral classes needed to be defined to include (the fainter) cooler and older objects of lower mass. Kirkpatrick et al. (1999) and Kirkpatrick (2005) introduced the two SpT’s L and T, and detailed optical spectra showing the transition from late-M to late-T can be seen below in Figure (1), illustrating how the spectral features evolve. Finally, for the ultra-cool dwarfs discovered by WISE there is the class Y (Cushing et al. 2011). The stellar SpT sequence can also be thought of as a temperature sequence, with temperatures increasing from M to O. The same holds overall for T to L, except in the transition region between the two, from mid-/late-L to mid-T – also known as the L/T transition. As we will see later, it is in this spectral region where clouds in the photosphere are expected to play a significant role in influencing the spectral and photometric appearance of BD’s.

In addition to the optical SpT, which is mainly affected by temperature, there is also a near- infrared (NIR) SpT for BD’s which is more affected by clouds, surface gravity and metallicity (e.g. Mc- Govern et al. 2004, Kirkpatrick 2006, Burgasser et al. 2008, Cushing et al. 2008, Bonnefoy et al.

2014, Schmidt et al. 2014).

(11)

Figure 1: Optical spectra of SpT M7-T8 from 6800 to 8700 ˚A (Kirkpatrick 2005).

Since surface-gravity in particular is thought to have a large impact on the formation of condensate clouds that strongly affect the observational properties of BD’s, the classification of the L and T SpT’s was expanded to include a suffix denoting the surface-gravity (Cruz et al. 2009). Normal gravity is indicated by α or a lack of suffix, β for intermediate-gravity and γ for very-low gravity (log(g) ∼ 4). Allers & Liu (2013) arrive at a similar classification, but the use of the greek suffix seems to have caught on. Kirkpatrick (2006) also suggests a suffix be used for metallicity, but as that has not been relevant for the objects studied in this work, we will not go into it any further. For more details on the specifics of spectral features, effective temperatures and luminosity the review by Luhman (2012) is recommended.

Since the cooler L and T BD’s are generally too faint in the optical, most observations are done in the NIR bands of J, H and K. Typical wavelength midpoints for these bands are (e.g. ESO) λ_{mean, J}

= 1.25 µm, λmean, H= 1.63 µm and λmean, K= 2.19 µm respectively. There are further variations to these, such as having a shorter wavelength range with a similar midpoint, e.g. JS and KS which are filters used for the majority of the observations analysed in this work. As the 2MASS survey (Skrutskie et al. 2006) provided vast catalogues of photometric data in J, H and Ks, the colour J −K_Sis often used in combination with the L and T SpT’s when discussing the observational properties of BD’s, with an increasing value representing a reddening of the object.

L-dwarfs become progressively redder with de- creasing effective temperature (Teff), down to a SpT of around L7 where there is a drastic shift towards bluer colours, which represents the start of the so called L/T transition (∼L7-T4). Seek- ing to investigate which physical parameters provide the strongest influence on the observed colour, Stephens et al. (2009) conducted a detailed study on an assortment of early- to mid-L and T dwarfs (L3.5-T5.5) and used a range of atmospheric mod-

(12)

els to create synthetic spectra to compare with observations. They find that the L/T transition between L7-T4 corresponds to a T_eff between 1400 K to 1100 K, which represents a relatively small change in temperature over a wide range of SpT’s, a similar result to that obtained by Saumon &

Marley (2008). The colour difference is then not specifically temperature dependant, but rather the result of a change in cloud opacity in the upper atmosphere, so that less cloudy atmospheres are bluer (see also e.g. Cushing et al. 2008). By varying the grain sedimentation in the atmosphere they could recreate the change in SpT’s over the L/T transition while keeping T_eff constant. The dramatic shift towards bluer colours is therefore thought to be caused by a more rapid sedimentation of these condensate clouds to a region below the photosphere, creating a cloud-free atmosphere after SpT ∼T4. Additionally their results suggest that this rate of sedimentation is dependent

on surface-gravity, so therefore lower-mass BD’s ought to stay redder at even lower temperatures.

They acknowledge that the models are compara- tively simple compared to the full hydrodynamical simulations that would be ideal, but still manage to recreate the observed spectra with good accu- racy.

Further works since this study have reinforced these assertions (e.g. Marley et al. 2010, Morley et al. 2014) and as we will see towards the end of this section, numerous observational works fo- cusing on photometric variability support the idea that the changing spectral features over the L/T transition is primarily caused by changes in cloud opacity, which is influenced by surface-gravity. A diagram from Radigan et al. (2014) that illustrates the L/T transition in a helpful manner can be seen below in Figure (2), and we will return to this when discussing Previous Works (§2.3).

Figure 2: SpT vs. 2MASS J − K_S colour diagram from Radigan et al. (2014). Grey points represent known field L and T dwarfs. Purple circles indicate detection of variability, and the L/T transition is indicated by the dashed ellipse.

(13)

2.1.3 Formation

There are several theories concerning the formation of BD’s (e.g. Whitworth et al. 2007), and while none of them exclude any of the others, there are some that are likely to be more dominant. Here we will briefly discuss these formation scenarios, one of which is shared with GP’s as a possible formation mechanism, and the Initial Mass Function (IMF, e.g. Bonnell et al. 2007, Offner et al. 2014) for BD’s. For a more in-depth exploration of the formation scenarios of BD’s and GP’s we also rec- ommend e.g. Chabrier et al. (2014, i.e. C14), and Luhman (2012, henceforth L12) for a more general review on the IMF and formation of low-mass stars and BD’s.

In the first hundred BD’s discovered by WISE (Kirkpatrick 2011), the vast majority of them were cold ≥ T6 dwarfs, too faint to be have been found previously. With WISE, BD’s had now been observed all the way down to very-low masses (∼ 5 M_Jup) and the question about whether or not the regular stellar IMF could extend down to such low masses became even more relevant – i.e what is the minimum mass of the IMF? C14 argue that the recent WISE discoveries agree well with the IMF proposed by Chabrier (2005, see also 2001

& 2002), and find no strong arguments as to why BD’s should not share the same underlying IMF as stars. They list numerous properties that seem to be shared by young stars and BD’s, indicating a close connection in regards to their formation.

A consequence of this argument is that they should then be formed predominantly by a similar mechanism – e.g. gravitational compression and fragmentation (Hartmann 2002). This has been suggested in other works as well, such as Scholz et al. (2012) who observed very low-mass objects in a young star cluster and estimated a minimum mass of at least 6 MJup. L12 does not come down strongly in favour of any particular resolution to the question of a shared IMF between BD’s and stars, but rather discusses the IMF in general, as observed in the Solar neighbourhood, Galactic disk and young clusters. Both L12 and C14 agree however, that the continuously improved statistics from the WISE data has the potential to give a

definitive answer eventually.

Regardless of the fundamental mechanisms behind BD formation, all scenarios naturally include some way of limiting the final mass, to prevent the formation of a low-mass star rather than a BD.

This is either inherent in the formation scenario or included as an environmental factor as a means of halting accretion.

Bonnell et al. (2008) investigated, through numerical simulations, the issue of whether or not it should be possible for BD’s to form via gravitational fragmentation in the same way as stars.

They conclude that both BD’s and low-mass stars can form from the fragmentation of high-density gas in a stellar cluster, even if they are in the mi- nority. In their simulations, the mechanism preventing further accretion for BD’s is the strong tidal shear of the cluster combined with the fact that its gravitational potential imparts high velocities to the fragments.

An alternative way of halting accretion is the ejection of the BD core-fragments out of the cluster through dynamical interactions. This accretion-ejection scenario was originally proposed by Reipurth & Clarke (2001), with subsequent simulations done by e.g. Bate (2009, 2012).

C14 argues extensively as to why this is likely not the dominant formation mechanism for BD’s.

Two main points of the argument being that 1) accretion-ejection would not work for low-density environments where dynamical interaction is not strong enough, and that 2) observed average dis- persion velocities of prestellar cores are low enough to suggest that no substantial dynamical evolution takes place at that stage.

A fairly situational halting mechanism includes the idea that photoionization from close-by O,B stars are responsible for preventing further accretion on the prestellar cores (Whitworth & Zin- necker 2004). However, the BD mass-function re- mains the same for clusters with or without these stars and the fact that BD’s also form in isolated environments suggests that this is not a dominant mechanism (C14).

Concluding the BD-specific formation scenarios is the one of turbulent fragmentation (Padoan &

(14)

Nordlund 2002, 2004). Instead of primarily being driven by gravity, fragmentation is induced by large-scale turbulence that propagates down the hierarchy of the molecular cloud to smaller scales.

C14 comes down in favour of this ”gravoturbulent fragmentation” as the dominant formation mechanism and while not excluding the other potential scenarios, argue that this agrees the best with current observations.

The final scenario, disk instability/fragmentation, is one shared between both GP’s and BD’s.

The physics and conditions behind disk instabilities in protostellar or protoplanetary disks are detailed further in §4 in C14.

Originally formulated by Kuiper (1951), it primarily gained traction over the past two decades as a way of explaining GP’s located at wide- separations from their host stars (Boss 1997). Cen- tral to the theory is that disks are expected to be gravitationally unstable during the early stages of star formation, with massive disks being especially prone to gravitational instabilities (GI). This is unlikely to happen in the inner part of the disk, due to conditions required for cooling, but could occur further out, leading to partial fragmentation in the disk, a part of which in turn collapses into a clump that can contract into a GP. Whether such an object will survive or not (e.g. Boss 2005, Galvagni

& Mayer 2014), due to migrating into the star or being disrupted in the disk, is still very much up for debate (e.g. Helled et al. 2014).

As has been discussed earlier, direct imaging is especially well-suited for observing wide- separation companions after formation, and the extremely high-resolution observations possible with the recently completed ALMA radio telescope offers the ability to observe a disk during the formation stages (e.g. Douglas et al. 2013, Dipierro et al. 2014). Janson et al. (2011) observed nearby B & A stars, which are thought to have the most massive disks and therefore the most prone to GI, and found that their number of wide companion detections fell far short of that predicted by models, indicating that disk fragmentation is likely not the dominant formation mechanism.

So while it is still unclear how big a role disk in-

stabilities play in the formation of BD’s and GP’s, and C14 considers the contribution of GI to their overall formation to be limited, it should become more evident in the coming years.

2.2 Giant Planets

2.2.1 Observational properties

Unlike BD’s, where one often has to rely on mass estimates being derived from models that in turn use e.g. age estimates and observed bolomet- ric luminosity as parameters, we can determine both mass and radius accurately for many GP’s.

The methods used in these observations were discussed previously, namely radius measurements from transits and mass estimates from RV, and one or the other are applicable to many GP’s, as- suming they are relatively close to their host stars.

There are however some complications that exist specifically for observing short-period GP’s that have been given the nickname hot Jupiters, or inflated hot Jupiters (e.g. Laughlin et al. 2011, Lopez & Fortney 2016). While both young GP’s and BD’s will be naturally inflated due to still being in the process of gravitationally contracting, hot Jupiters are generally billions of years old but appear to have radii as large as ∼ 2R_Jup, nearly twice the typical radius for an older GP. They re- main a curious anomaly as no real consensus on the exact underlying mechanic of inflation has been reached, other than that it is closely connected to how much irradiance the planet receives from the host star.

The work of Santerne et al. (2016) offers an excellent and detailed view of the process of con- firming and characterizing the properties of GP’s, and as such we refer the reader to their work for a view at an in-depth analysis.

In addition the various physical properties of GP’s that one seeks to determine, there is a vital and more fundamental relation connecting the formation of GP’s with their stars – the Planet- Metallicity correlation (Santos et al. 2004, Fischer

& Valenti 2005). Formulated by Fischer & Valenti (2005) as a result of an extensive spectral analysis

(15)

of 850 FGK-type stars where Doppler observations were also available, it correlates planet abundance with the metallicity of the host star. Metallicity (Z) refers to the fraction of elements heavier than Helium (i.e. ”metals”) compared to Hydrogen, and for this relation the fraction is typically expressed as the logarithmic value [Fe/H], where [Fe/H] = 0 is Solar metallicity and [Fe/H] = -1 a tenth of that.

In their analysis, they find a strong correlation between the iron abundance in the host star and the probability of finding a GP orbiting it (see Fig- ure 3 below) and are able to fit a power-law to this relation using finer binning of the data.

Figure 3: The Planet-Metallicity correlation as found by Fischer & Valenti (2005), indicating a clear increase in the percentage of stars hosting massive planets with increasing iron abundance.

Since their findings were published there has been continued research (e.g. Johnson et al. 2010, Miller & Fortney 2011, Thorngren et al. 2015) into this correlation and its importance in different applications in regards to exoplanets. For our purposes we will focus on its relevance for the formation of GP’s specifically, and will continue discussing it in the next section.

2.2.2 Formation

There are predominantly two formation mechanics to consider for GP’s – core accretion (CA) and gravitational/disk-instability, with the latter being discussed previously in §2.1.3. Backed up by extensive numerical simulations, Pollack et al. (1996)

presented their case for CA as a formation mechanic that could help explain why the Solar system gas giants had a different proportion of elements compared to the Sun, and how such gas giants would have had time to form before the gas dissipates from the protoplanetary disk. We will here focus on the overall mechanics, and direct the reader to C14 who present an in-depth discussion on CA, and specifically the issue of how GP’s can form fast enough while there is still gas to accrete, an issue that so far has not been entirely resolved.

CA for GP’s is essentially a two-stage bottom- up process, where the first stage is the accretion of planetesimals, similar to the formation of terrestrial-mass planets. For GP’s however, the accretion continues to a critical point (∼ 10 Earth-masses, M⊕) where gas can now be accreted from the disk and retained (stage two) in an envelope around the core. At this point the mass of the envelope increases faster than the core, leading to a continued rapid gas accretion. The first stage would therefore be the primary reason for the difference in relative composition between the star and the GP, as it naturally leads to a higher concentration of heavier elements compared to a collapse scenario where both star and GP form from the same nebular gas.

This mechanism provides an elegant explanation for the observed planet-metallicity correlation for GP’s, and why there seems to be no such correlation for the probability of finding terrestrial-mass planets. The greater the abundance of heavy elements in the nebular gas, the easier it is to form cores massive enough to start accreting gas, and if the metallicity is substantially lower, the critical mass might not be attainable and GP formation becomes highly unlikely.

Johnson et al. (2010) analysed 1266 stars in a mass range of 0.2 < M< 1.9 and concluded that, in addition to again verifying the correlation, GP occurrence also seems to increase with the stellar mass. This could be seen to favour GI, as we previously discussed that more massive stars can host larger disks and thus be more prone to GI, but as Johnson et al. (2010) argues, GI is supposed to have no environmental dependence, so there-

(16)

fore GP’s should be prevalent even among low- metallicity stars.

Thorngren et al. (2015) study 38 transiting GP’s and find a clear correlation between the heavy ele- ment mass of a planet (MZ) and the total mass M , so that M_Z ∝√

M . In addition to finding further support for CA, they also suggest that the majority of the heavy elements should be present in the gaseous envelope of the planet, and not exclu- sively in the core. If this is the case for GP’s, they should exhibit enriched atmospheres compared to BD’s, and as such enable a distinction between the two to be made based on atmospheric composition. This is explored in their work as they compare the less massive HAT-P-20b (7.2 M_Jup) to Kepler-75b (10.1 M_Jup), where the former shows a substantially greater enrichment than the latter, from which one could suppose that they formed by different mechanisms.

So to conclude, there does seem to be substantial evidence in the literature discussed here and else- where that CA is the dominant formation mechanism rather than GI, and that it seems likely that a definitive answer to the question could be found in the coming years. Combined with the fact that there should be observable compositional differ- ences between BD’s and GP’s due to the enrichment as a result of CA, we should also see more arguments being made for a less arbitrary distinction between the two objects.

2.3 Previous Works

In this section we present an overview of the observational and modelling works that have been done recently in regards photometric variability studies of BD’s.

2.3.1 Observational

At the inception of this project there were no published detections of photometric variability in very low-mass objects below the DB-limit that could be thought of as GP analogues, and the extensive work that had been done was for more massive BD’s.

Shortly after our work began, Biller et al. (2015)

published the results of their observations of PSO J318.5338-22.8603 (Liu et al. 2013, also 2MASS J21140802-2251358, hereafter PSO 318), a free- floating ∼7 MJup BD which showed clear signs of significant variability (> 10 ± 1.3%), that evolved over multiple observations (Figure 4).

Figure 4: Final reduced light curves for PSO 318 and reference stars from Biller et al. (2015), showing a peak-to-peak amplitude of > 10% with a period of at least 5 hours.

These observations were part of a larger observing programme of over 20 low-mass BD’s, the data of which was publicly released as this project started. This data set has been the primary focus of our work, as it represents the latest and most extensive source of photometric variability data for low-mass BD’s, and will be explored further in Observations (§3).

Early efforts on studying variability in BD’s focused on optical (I-band) observations of late- M or early-L dwarfs (e.g. Bailer-Jones & Mundt 2001, Gelino et al. 2002, Enoch et al. 2003) and found amplitudes of a few percent, concluding that they were most likely caused by either inhomogeneous cloud coverage, but that magnetic spots, although assumed to be increasingly rare in ultra-cool dwarfs, could be another source. Con- trary to more recent studies, Enoch et al. (2003) found no increased variability fraction in the L/T transition. Following this, there was not much

(17)

progress in terms of new detections until Clarke et al. (2008) found < 4% variability in a number of L7-T6 BD’s and Artigau et al. (2009) detected multi-wavelength variability at 10σ in their previously discovered L/T transition BD SIMP0136 (T2.5). This detection set it apart from previous studies, particularly in terms of the precision of the observations, and was soon followed by many more surveys presenting high-precision photometry.

With their multi-wavelength observations of the BD 2MASS J21392676+0220226 (2M2139), Radi- gan et al. (2012) advanced the field in a number of ways, and their exhaustive analysis illustrates a far more detailed application of modelling than what has been possible for this work.

2M2139 became the second L/T transition BD to show significant variability and still holds the record as the most variable BD discovered thus far. The first four days of multi-wavelength observations, seen in Figure (5), also clearly indicate

that the rotationally modulated variability is dependant on wavelength, which indicates an atmospheric origin.

They rule out the possibility of a binary system giving rise to the variability and conclude that the evolution of the light curve over a four-month period strongly indicates that it is caused by atmospheric changes. Through modelling, and given that L/T transition BD’s are expected to have patchy clouds due to their spectral evolution in this region, they also argue in favour of heterogeneous clouds rather than magnetically induced spots as the underlying cause. In short, their work provided further critical empirical results that back up the hypothesis of fragmenting clouds being primarily responsible for the spectral changes observed during the L/T transition.

Continuing their work with the largest survey yet, Radigan et al. (2014) looked at 62 L4-T9 BD’s for photometric variability and a summary of their detections could be seen previously in Figure (2).

Figure 5: The reduced multi-wavelength light curves for 2M2139, with reference stars in the panel below, showing a peak-to-peak amplitude of up to 26% in the J-band with a period of 7.72 hours if the light curve has a single peak (Radigan et al. 2012).

(18)

Buenzli et al. (2015a, 2015b) used the Hubble Space Telescope (HST) to observe the closest BD binary system Luhman 16AB, searching for photometric variability and found significant amplitudes (4.5 and 9.3%) for both components (L7.5/T0.5).

This result is particularly surprising as while Radi- gan et al. (2014) found that most L/T transition BD’s are weakly variable at the percent level, it seems unusual to find two strongly variable BD’s in the same system, which could indicate that they both have common, and as of yet unclear, properties that favour variability.

Metchev et al. (2015) present an extensive space-based survey of 44 L3-T8 BD’s with both unparalleled photometric precision and duration of the time-series data, using the Spitzer Space Tele- scope. They find that the vast majority (∼ 80%) of L dwarfs are variable by ≥ 0.2% and that ∼ 36%

of T dwarfs vary by ≥ 0.4%. The light curves of some of these shown below in Figure (6), and take note of the light curve for HN Peg B (right panel), as we will return to it later in our own analysis.

Taking different inclinations into consideration, they conclude that essentially all L dwarfs should have spots and exhibit some variability. In com- paring with other surveys (Radigan et al. 2014, Buenzli et al. 2014), their results suggests that variability in L/T transition BD’s, while ubiqui- tous, is not as prominent at the Spitzer IRAC wavelengths (approximately L- and M-bands) as it is for the shorter J, H and K bands. This lends further credence to the idea that cloud structures are responsible for this type of variability, and that different wavelengths are sensitive to changes in different layers of the atmosphere. Furthermore they suggest that their data could also be used in the Doppler imaging of clouds/surface features, an interesting technique utilized by Crossfield (2014) for Luhman 16B, revealing a patchy photosphere.

In addition to the works discussed above, there are several others focused on observations of L/T transition BD’s, such as Buenzli et al. (2012), Biller et al. (2013), Apai et al. (2013) and Radigan (2014).

Figure 6: Reduced light curves from Metchev et al. (2015) of 11 (out of 21) variable L and T BD’s, displaying Spitzer IRAC data [3.6 µm] (filled symbols) and [4.5 µm] (open symbols), including fitted curves. For future reference (§5), make note of the long-period and weakly variable HN Peg B light curve.