MNRAS 463, 2574–2582 (2016)

doi:10.1093/mnras/stw2148

Advance Access publication 2016 August 25

Transit timing variation and transmission spectroscopy analyses of the hot
Neptune GJ3470b
S. Awiphan,1‹ E. Kerins,1‹ S. Pichadee,2 S. Komonjinda,2 V. S. Dhillon,3,4
W. Rujopakarn,5,6 S. Poshyachinda,7 T. R. Marsh,8 D. E. Reichart,9 K. M. Ivarsen9
and J. B. Haislip9
1 Jodrell Bank Centre for Astrophysics, School of Physics and Astronomy, University of Manchester, Oxford Road, Manchester M13 9PL, UK
2 Department of Physics and Material Sciences, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand
3 Department of Physics and Astronomy, University of Sheffield, Sheffield S3 7RH, UK
4 Instituto de Astrofisica de Canarias, La Laguna, Tenerife E-38205, Spain
5 Department of Physics, Faculty of Science, Chulalongkorn University, 254 Phayathai Road, Pathumwan, Bangkok 10330, Thailand

Kashiwa, Chiba 277-8583, Japan
7 National Astronomical Research Institute of Thailand, 191 Siriphanich Bldg, Huay Kaew Road, Muang District, Chiang Mai 50200, Thailand
8 Department of Physics, University of Warwick, Coventry CV4 7AL, UK
9 Department of Physics and Astronomy, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599, USA

Accepted 2016 August 23. Received 2016 August 19; in original form 2016 May 24

ABSTRACTGJ3470b is a hot Neptune exoplanet orbiting an M dwarf and the first sub-Jovian planet
to exhibit Rayleigh scattering. We present transit timing variation (TTV) and transmission
spectroscopy analyses of multiwavelength optical photometry from 2.4-m and 0.5-m telescopes
at the Thai National Observatory, and the 0.6-m PROMPT-8 telescope in Chile. Our TTV
analysis allows us to place an upper mass limit for a second planet in the system. The presenceof a hot Jupiter with a period of less than 10 d or a planet with an orbital period between 2.5
and 4.0 d are excluded. Combined optical and near-infrared transmission spectroscopy favour
an H/He-dominated haze (mean molecular weight 1.08 ± 0.20) with high particle abundanceat high altitude. We also argue that previous near-infrared data favour the presence of methane
in the atmosphere of GJ3470b.
Key words: techniques: photometric – eclipses – planets and satellites: atmospheres – planetsand satellites: individual: GJ 3470b – stars: late-type – planetary systems.

1 I N T RO D U C T I O NOver the last decade, the search for and study of exoplanets has
been one of the most dynamic research fields of modern astronomy.
To date, more than 3200 planets have been confirmed by various
methods,1 including over 2000 by Kepler using the transit method(Morton et al. 2016). The transit method can detect planets ranging
in size from Earth to larger than Jupiter. Additionally, the transit
timing variation (TTV) method has been used to find at least 10
additional exoplanets and hundreds of candidates (Agol et al. 2005;
Holman & Murray 2005; Holman et al. 2010; Fabrycky et al. 2012;
Ford et al. 2012a,b; Steffen et al. 2012a,b, 2013; Mazeh et al. 2013).
In addition to the discovery of new exoplanets, the characterization of planetary interiors and atmospheres is a rapidly developing E-mail: supachai@narit.or.th (SA); eamonn.kerins@manchester.ac.uk(EK)
1 See http://exoplanet.eu/

area. One method that is used to study planetary atmospheres istransmission spectroscopy, which measures the variation of transit depth with wavelength (Seager & Deming 2010). From thetransmission spectroscopy technique, the absorption spectrum andthe composition of the planetary atmosphere can be deduced. Thismethod has been applied to several transiting exoplanets, for example, HD189733b (Grillmair et al. 2008; Swain et al. 2010), GJ1214b(Bean, Miller-Ricci Kempton & Homeier 2010; Kreidberg et al.
2014) and GJ436b (Knutson et al. 2014).
Kepler has discovered more than 4000 planetary candidates(Coughlin et al. 2016). Most of them are super-Earth and Neptunesize candidates (1.25−6 R⊕ ), which confirm the large fraction ofsmall planets within the exoplanet population (Howard et al. 2012;
Coughlin et al. 2016). Exoplanets within this radius range likely
comprise solid core (super-Earths), H/He gas and volatile envelopes(Neptune-like exoplanets).
In order to classify the transition between super-Earths and
Neptune-like exoplanets, Lopez & Fortney (2014) suggested thatplanets with a radius larger than about 1.75 R⊕ have H/He
C 2016 The Authors
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6 Kavli Institute for the Physics and Mathematics of the Universe (WPI), The University of Tokyo Institutes for Advanced Study, The University of Tokyo,

TTV and transmission spectroscopy of GJ3470b

h=

kb Tp
,
μgp

(1)

where kb , Tp , μ and gp are the Boltzmann constant, theplanet equilibrium temperature, the mean molecular weightof the planetary atmosphere and the planet surface gravity,
respectively.
In the case of a cloudless atmosphere, absorption lines fromvolatile molecules at near-infrared wavelengths should be detectable. On the other hand, an exoplanet with low atmospheric
H/He abundance provides a smaller scaleheight and flatter transmission spectrum. However, the presence of high-altitude hazes mightcause difficulty in distinguishing between H/He-rich and volatilerich envelopes, because the haze can hide molecules in the lower
atmosphere and produce near-infrared transmission spectra dominated by Mie scattering (Howe & Burrows 2012).
An exoplanet around a nearby M dwarf is favourable for transmission spectroscopy, due to its large planet-host radius ratio. In
this paper, a transmission spectroscopy study of GJ3470b, a hot
Neptune orbiting around an nearby M dwarf, is presented. GJ3470b
was first discovered with the HARPS spectrograph and confirmedwith follow-up transit observations with the TRAPPIST, Euler and
NITES telescopes (Bonfils et al. 2012). GJ3470b is a good target fortransmission spectroscopy because it has a large change in transit
depth with wavelength due to its large atmospheric opacity (Bentoet al. 2014). GJ3470b is also the first sub-Jovian planet that showsa significant Rayleigh scattering slope (Nascimbeni et al. 2013). To
date, GJ3470b has been observed at several optical and near-infrared
wavelengths (Crossfield et al. 2013; Demory et al. 2013; Fukui et al.
2013; Nascimbeni et al. 2013; Biddle et al. 2014; Ehrenreich et al.
2014; Dragomir et al. 2015).
Fukui et al. (2013) observed GJ3470b with simultaneous optical and near-infrared observations with the 0.5 m MITSuME and1.88 m telescopes at Okayama Astrophysical Observatory. Theysuggested that GJ3470b has a cloud-free atmosphere. Nascimbeni
et al. (2013) combined their optical observations with the Large
Binocular Telescope (Demory et al. 2013; Fukui et al. 2013). Theirresult suggests that the GJ3470b atmosphere is cloud-free with ahigh-altitude haze of tholins. They also found a strong Rayleighscattering slope at visible wavelengths.
However, Crossfield et al. (2013) performed an observation with
the MOSFIRE spectrograph at the Keck I telescope. They concluded
that the GJ3470b atmosphere provides a flat transmission spectrum

which indicates methane-poor, metal-rich, optically-thick clouds ora hazy atmosphere. Biddle et al. (2014) presented 12 new broadband optical transit observations and concluded that GJ3470b has ahydrogen-rich atmosphere exhibiting a strong Rayleigh scatteringslope from a hazy atmosphere with 50 times solar abundance.
A recent study by Ehrenreich et al. (2014) with the Wide Field
Camera-3 on the Hubble Space Telescope in the near-infraredalso suggested that GJ3470b is dominated by a cloudy hydrogenrich atmosphere with extremely low water volume mixing ratios(<1 ppm). Dragomir et al. (2015) provided shorter wavelengthtransmission spectroscopy results with the LCOGT network and theKuiper telescope in order to verify the Rayleigh scattering signal
in the 400–900 nm region. They found a strong Rayleigh scatteringslope that indicates an H/He atmosphere with hazes, as in previous
studies.
In this paper, TTV and transmission spectroscopy analyses fromadditional multiwavelength optical observations of GJ3470b arepresented. These data are combined with previous studies to provide improved measurements of the physical characteristics andephemeris of GJ3470b. We use these to deduce the first constraints
on the characteristics of additional planets in the system. In Section 2, the observational and data analysis details are presented.
The mid-transit times from the analysis, together with results fromprevious studies are used to analyse timing variations and to place
an upper mass limit for additional planets in Section 3. In Section 4, the atmosphere of GJ3470b is analysed using the transmission spectroscopy technique and finally, in Section 5, we present
our conclusions.

2 O B S E RVAT I O N S A N D DATA A N A LY S I S
2.1 Photometric observations
Photometric observations of exoplanet GJ3470b were conducted
between 2013 December and 2016 March. We obtained 10 transits,
including 6 full transits and 4 partial transits. The UT date of the
mid-transit time, instrument, filter, exposure time and number offrames in each observation are described below and are listed inTable 1. The 4-min binned light curves are shown in Fig. 1.

2.1.1 0.5 m telescope at Thai National Observatory
Two full transit observations of GJ3470b were obtained through a
Cousins-R filter using an Apogee Altra U9000 3056 × 3056 pixels
CCD camera attached to the 0.5 m Schmidt–Cassegrain Telescope
located at Thai National Observatory (TNO), Thailand. The field ofview of each image is 58 × 58 arcmin2 . For the first observation on
2013 December 17, the exposure time was set to be 20 s during thefirst half of observations (296 images) and 15 s during the second
half (288 images) due to the variation in seeing at the site. On 2014
January 6, observations with a 20 s exposure time were obtained.
The exposure overhead due to readout is ∼10 s.

2.1.2 PROMPT 8 telescope (0.6 m)
We observed two full transits with PROMPT 8, a 0.6 m robotic telescope at Cerro Tololo Inter-American Observatory (CTIO), Chile,with a 2048 × 2048 pixels CCD camera with a scale of 0.624 arcsec pixel−1 . The observations were performed through a Cousins-R
filter on 2014 January 10 and 2015 January 22 with 10 s exposuresand an ∼20 s overhead between each.
MNRAS 463, 2574–2582 (2016)

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envelopes. Nevertheless, the transition point may vary between 1.5
and 2.0 R⊕ (Marcy et al. 2014; Weiss & Marcy 2014). Instead ofclassification by planetary radius, Rafikov (2011) studied envelope
accretion of Neptune-like planets and suggested a mass transition
limit at 10 M⊕ or larger for close-in planets. Piso, Youdin & MurrayClay (2015) also suggested that the minimum core mass to forma Neptune-like planet is ∼8 M⊕ at 5 au and ∼5 M⊕ at 100 au.
However, in the case of low-density super-Earth-sized exoplanets,
the mass of the planet alone cannot be used for classification [e.g.
Kepler-11f (Lissauer et al. 2011) and Kepler-51b (Masuda 2014)].
Planetary average densities are also unable to confirm the transition
between super-Earths and Neptune-like exoplanets, due to the broad
range of detected planet densities that overlap the transition range(Howe, Burrows & Verne 2014).
One feature that can be used to determine the solid core to H/He
envelope transition regime is the amount of hydrogen and heliumin the planet envelope, which can be obtained from transmission
spectroscopy measurements (Miller-Ricci & Fortney 2010). An
exoplanet with an H/He-rich atmosphere has a large atmosphericscaleheight, h, due to a low mean molecular weight.

2575

2576

S. Awiphan et al.
Table 1. Observation details for our transmission spectroscopy measurements of GJ3470b.
Observation date

Telescope

FilterExposure (s)Number of images2013 December 17
2014 January 06
2014 January 10
2014 March 04
2014 March 14
2014 April 03
2015 January 222015 March 06
2015 March 16
2016 March 17

TNO 0.5 m
TNO 0.5 m
PROMPT-8
TNT
TNT
TNT
PROMPT-8
TNT
TNT
TNT

Cousins-R
Cousins-R
Cousins-R
Sloan z
Sloan r
Sloan z
Cousins-R
Sloan r
Sloan iSloan g20.0,15.0a
15.0
10.0
5.65
8.29
5.65
10.0
3.13
3.13
14.85

584
500
425
1883
1777
1254
449
1500
2755
550

a The exposure time of the first 296 images is 20 s and the exposure time of the last 288 images is 15 s.

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Figure 1. Light curves of GJ3470b with 4 min binning and with the best-fitting model from the TAP analysis. The best-fitting model light curves in all filters areshown in the bottom-right panel with arbitrary off-sets (−0.0025, −0.0050, −0.0075 and −0.0100). Thick yellow, red, orange, green and blue lines represent
the best-fitting model in Cousins-R, z , i , r and g filters, respectively.

MNRAS 463, 2574–2582 (2016)

TTV and transmission spectroscopy of GJ3470b

2577

Table 2. GJ3470b orbital elements from our TAP analysis and from previous studies.
Orbital period(d)Inclination
(◦ )

a/R∗

Rp /R∗

u1

u2

FilterBonfils et al. (2012)

3.337 14 ± 0.000 17>88.8

14.9 ± 1.2

0.0755 ± 0.0031

0.04 10.38 10.19 10.40 1

Gunn-ZNo filter

Demory et al. (2013)

3.336 65 ± 0.000 05

88.3+0.5−0.4

13.42+0.55−0.53

0.07798+0.00046−0.00045

0.033 ± 0.015

0.181 ± 0.10

IRAC 4.5 µm–

14.02+0.33−0.39

0.07577+0.00072−0.00075

0.137+0.077−0.0730.255 1J

Reference

Fukui et al. (2013)

Nascimbeni et al. (2013)

0.0802 ± 0.0013

0.19 ± 0.11

0.338 1

Ic

0.0776 ± 0.0038
0.0809 ± 0.0031

0.25 ± 0.15
0.486 1

0.322 10.289 1Rc
g

0.07484+0.00052−0.00048

0.25 ± 0.04

0.49 ± 0.03

F972N200.0821 ± 0.0013

0.30 ± 0.03

0.29 ± 0.03

U
2.09–2.36 µm

88.12+0.34
−0.30

–

3.336 665 ± 0.000 002

88.98+0.94
−1.25

–

0.0789+0.0021−0.0019−0.351+0.025−0.023−0.889+0.051−0.0520043
3.336 648+0.000−0.000 0033

88.88+0.44−0.45

13.94+0.44−0.49

0.0766+0.0019−0.00200.017+0.014−0.0120.5030 ± 0.0068

Gunn-Z

0.5030 ± 0.014

Panstarrs-Z

0.488 ± 0.020

i

3.336 649 ± 0.000 002

Biddle et al. (2014)

0.0766+0.0019−0.00200.0765+0.0027−0.0030
0.0780+0.0015−0.00160.0736+0.0029−0.00310.0803 ± 0.0025

Dragomir et al. (2015)

3.336 6413 ± 0.000 0060

This work0039
3.336 6496+0.000−0.000 0033–

89.13+0.26−0.34

12.92+0.72−0.65

13.98+0.20−0.28

0.029+0.025−0.0180.123+0.038−0.047

0.517+0.010−0.0099

I

0.083+0.035−0.0320.403+0.040−0.0440.519 ± 0.016

Arizona-I

0.390+0.036−0.038r

0.070 ± 0.025



0.084+0.013−0.0160.0771+0.0012−0.00110.0770+0.0020−0.0019––

Bessel-B

0.123 ± 0.050

0.489 ± 0.050

i 2

0.360 ± 0.050

0.411 ± 0.050

Harris-V

0.0833 ± 0.0019

0.398 ± 0.050

0.390 ± 0.050

g

0.0827+0.0022−0.00200.0744+0.0020−0.00200.0785+0.0008−0.00080.0765+0.0017−0.00150.0787+0.0016−0.00220.0832+0.0027−0.0027
0.0752+0.0030−0.0029
0.0913+0.0047−0.0053

0.421 ± 0.050

0.398 ± 0.050

Harris-B

0.356+0.081−0.0940.469+0.026−0.046
0.585+0.023−0.0540.540+0.079−0.0470.568+0.062−0.0940.22+0.14−0.11
0.45+0.17−0.20

0.307+0.091−0.1120.350+0.031−0.0740.278+0.045−0.0910.212+0.081−0.0770.304+0.068−0.0990.15+0.17−0.09
0.33+0.22
−0.20

z



i







Rc
r



g



Gunn-Z 3
No filter 3

Remarks: 1 Fixed value; 2 Re-analyzed Biddle et al. (2014) data; 3 Re-analyzed Bonfils et al. (2012) data.

2.1.3 TNO (2.4 m)
We conducted photometric observations of GJ3470 with ULTRASPEC (Dhillon et al. 2014), a 1k × 1k pixels high-speed frametransfer EMCCD camera, on the 2.4 m Thai National Telescope(TNT) at TNO during the 2013–2016 observing seasons. The camera has a field of view 7.68 × 7.68 arcmin2 . The readout time
between exposures is only 14 ms. Optical multiwavelength observations though the z , i , r and g filters were performed on separatenight.
The host star, GJ3470, is an M-dwarf. Therefore, in Fig. 1, theg -band light curve provides smaller signal-to-noise ratio comparedto other light curves. Although the g filter light curve shows alarge scatter, it is still an important inclusion for planetary atmosphere modelling, especially for Rayleigh scattering curve fitting(Section 4.1).

2.2 Light-curve analysis
In the following work, the calibration was carried out using the
DAOPHOT package and the photometry was carried out using PYTHON
scripts which perform aperture photometry. In order to fit the light

curves, we use the Transit Analysis Package (TAP; Gazak et al. 2012),
a set of IDL routines which employs the Markov Chain Monte Carlo(MCMC) technique of Mandel & Agol (2002).
We combined our 10 light curves with 4 light curves from Bonfils et al. (2012), in order to fit their mid transit times. AlthoughBiddle et al. (2014) re-analyzed and fit the mid-transit times of the
Bonfils et al. (2012) data, they did not include the 12th April 2012transit.
We set scales for semi-major axis (a/R∗ ), period (P) and inclination (i) to be consistent for all light curves. The planet-star radiusratio (Rp /R∗ ) and quadratic limb darking coefficients are taken to
be filter dependent. The mid-transit times (T0 ) observed at the same
epoch are also fixed to be the same value. From the previous studies, the eccentricity of the system is less than 0.051 (Bonfils et al.
2012). Therefore, in this work, a circular orbit is assumed. 1,000 000
MCMC steps are performed and the best fits from TAP are shown in
Fig. 1.
The orbital elements calculated by TAP are compared with the results from previous studies in Table 2. The results from TAP provide acompatible planetary orbital period, inclination and scaled semimajor axis that agree to within 2σ with results from previous studies.
Table 3 compares the quadratic limb darkening coefficients (u1 and
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Crossfield et al. (2013)

3.336 648 ± 0.000 005

2578

S. Awiphan et al.

Table 3. GJ3470 quadratic limb darkening coefficients from our TAP analysis together with predicted coefficients from the models of Claret et al.
(2011), with both least-square (L) and flux conservation (F) fitting methods(see the text).
FilterR

Best fitu1

u2

0.585+0.023−0.0540.278+0.045−0.091

0.568+0.062−0.0940.540+0.079−0.0470.469+0.026−0.046
0.356+0.081−0.094

g
r
i
z

0.304+0.068−0.0990.212+0.081−0.0770.350+0.031−0.0740.307+0.091−0.112Claret Lu1
u2

Claret F
u1
u2

0.49980.23290.51790.21010.51540.30460.54050.27240.54190.22210.55720.20280.37820.28300.40530.24860.3804

0.23610.27460.3311

Reference

Stellar density (ρ  )Bonfils et al. (2012)
Demory et al. (2013)
Pineda, Bottom & Johnson (2013)
Fukui et al. (2013)
Nascimbeni et al. (2013)
Crossfield et al. (2013)

4.26±0.53
2.91±0.37
4.25±0.40
3.32±0.27
2.74±0.19
3.49±1.13

Biddle et al. (2014)

3.39+0.30−0.32This work

3.30±0.17

u2 ) with the values from the Claret & Bloemen (2011) catalogue,
which is based on the PHOENIX model,2 with both least-squareand flux conservation fitting methods. We use the limb darkening
coefficients of a star with stellar temperature Teff = 3500 K, surface
gravity log(g∗ ) = 4.5 and metallicity [Fe/H] = 0.2, which is thenearest grid point(Teff = 3600 ± 100 K, log(g∗ ) = 4.658 ± 0.035
and [Fe/H] = 0.20 ± 0.10 (Demory et al. 2013)). The Claret &Bloemen (2011) catalogue provides compatible (within 2σ variation) limb darkening coefficients with the best-fitting coefficientsfrom TAP.
2.3 Stellar and planetary characterizations
In order to obtain planetary physical parameters, the parameters of
the host star must also be considered. The mean stellar density is
calculated by Kepler’s third law neglecting planetary mass. From
the TAP result, the mean density of GJ3470 is ρ∗ = 3.30 ± 0.17ρ .
This result is consistent with the value derived by other works (seeTable 4).
To find other stellar and planetary parameters, we adopt a stellar mass, M∗ = 0.539+0.047−0.043 M from Demory et al. (2013), whichwere obtained from the average of the J-, H-, and K-band mass–
luminosity relations of Delfosse et al. (2000). We also adopt a radialvelocity amplitude parameter K = 13.4 ± 1.2 m s−1 d1/3 from Demory et al. (2013), where

K = KP 1/3 =(2πG)1/3 Mp sini(M∗ + Mp )2/3

(2)

for a circular orbit. In the above equation, K is the radial velocity
semi-amplitude, Mp is the planet mass, M∗ is the host mass and G
is the gravitational constant.
2 See http://phoenix.ens-lyon.fr/simulator/

MNRAS 463, 2574–2582 (2016)

Parameter
Stellar parameters
Stellar mass
Stellar radius
Stellar density
Stellar surface gravity
Stellar effective
temperature
Stellar metallicity
Planetary parameters
Orbital period

Symbol

Value

Unit

M∗

a
0.539+0.047−0.043MR∗ρ∗log(g∗ )Teff

0.547 ± 0.018
3.30 ± 0.17
4.695 ± 0.046
3600 ± 100a

[Fe/H]

0.20 ± 0.10a

P0039
3.336 6496+0.000−0.000 0033

89.13+0.26
−0.34

R
g cm−3
cgs
K

d
deg

Orbital inclinationi

Semimajor axis
Epoch of mid-transit(BJD)
Radial velocity amplitude
parameter
Planetary mass
Planetary radiusPlanetary density
Planetary equilibrium
temperature
Planetary surface gravity
Planetary atmosphericscaleheight
Planetary atmosphericmean molecular weightaT0

0.0355 ± 0.0019
2455 983.704 21

au
d



13.4 ± 1.2m s−1 d1/3

Mp
Rp
ρp
Tp

13.9 ± 1.5
4.57 ± 0.18
0.80 ± 0.13
497–690

M⊕R⊕
g cm−3Klog (gp )h2.815 ± 0.057
760 ± 140

cgs
km

μ

1.08 ± 0.20

Ka Adopted value from Demory et al. (2013).

Combining with the mean density, the calculated radius of theGJ3470 host star is R∗ = 0.547 ± 0.018R . The planetary radius
is calculated from the planet-star radius ratio, which is wavelengthdependent. We use the ratio in the Cousins-R waveband to calculate
a radius, Rp = 4.57 ± 0.18R⊕ .
The calculated planetary mass and density are Mp = 13.9 ±1.5M⊕ and ρ p = 0.80 ± 0.13 g cm−3 . The range of planetary
equilibrium temperature, Tp , can be derived from the relation,  
1 − A 1/4 R∗ 1/2
Tp = Teff
,
(3)
4F
2a
where Teff = 3600 ± 100 K is the effective temperature of the hoststar, A is the Bond albedo (0–0.4) and F is the heat redistribution
factor (0.25–0.50) (Demory et al. 2013; Biddle et al. 2014). In thecalculation, we use Teff = 3600 K and a/R∗ = 13.98 and theiruncertainties are not taken into account. The temperature range in
our work, due to the possible range of Bond albedo and the heat
redistribution factor, is Tp = 497–690 K. The list of all parametersfrom the analysis is shown in Table 5.

3 T R A N S I T T I M I N G VA R I AT I O N S
3.1 O–C diagram
The measured mid-transit time of a photometric light curve always has some variation due to noise. However, variations can becaused by the gravitational interaction of other objects in the system, such as other exoplanets or exomoons. Therefore, we can use
the mid-transit times of GJ3470b to place limits on TTVs. From the
TAP analysis, the mid-transit times of 14 light curves are shown in
Table 6.

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Table 4. Mean stellar density of GJ3470 from our TAP
analysis and previous studies.

Table 5. Summary of GJ3470b properties.

TTV and transmission spectroscopy of GJ3470b

2579

Table 6. Mid transit time and O–C residuals for GJ3470b from our
TAP analysis.
Observing date2012 February 2012a2012 March 2012a2012 April 12a2013 December 17
2014 January 06
2014 January 10
2014 March 04
2014 March 14
2014 April 03

2015 March 16
2015 March 17

O–C
(d)

5983.7015+0.0015−0.0015−0.00265993.7152+0.0014−0.00140.00126644.3602+0.0011−0.0014−0.0006

6667.7169+0.0021−0.0021−0.00046030.4177+0.0010−0.00106664.3812+0.0017−0.00176721.1038+0.0004−0.0005

6731.1162+0.0011−0.00116751.1332+0.0007−0.00087044.7603+0.0019−0.00247088.1370+0.0008−0.00077098.1455+0.0004−0.00057465.1750+0.0017−0.00140.00060.00050.00010.0026−0.0004
0.00150.0018Figure 3. Upper mass limit of a second planet in the GJ3470 system. The
blue dash–dotted, green dashed and red solid lines represent the upper mass
limit for 400, 500 and 600 s TTV amplitudes. The contours show the χr2
between the best TTV fit and the best linear fit. The black dotted line presents
the best χr2 within a 0.05 period ratio bin. From left to right, the black
vertical lines show 3:1, 2:1, 3:2, 4:3, 5:6, 4:5, 3:4, 2:3, 1:2, 1:3 and 1:4
resonance periods. The white vertical dashed line shows the orbital period
of GJ3470b.

0.0003−0.0017a Re-analyzed Bonfils et al. (2012) data.

Figure 2. O–C diagram of exoplanet GJ3470b. Epoch = 0 is the transit on2012 February 26. The red filled, cyan half-filled and unfilled markers represent the mid-transit time from our observations, re-analysed Bonfils et al.
(2012) observations and other previous published observations, respectively.

We use these mid-transit times, and those from previous studies, to plot the epoch of each transit against the observed minus
the calculated time (O–C) in order to find the TTV of GJ3470b.
We perform a linear fit to the O–C diagram to correct GJ3470b’s
2= 2.11)ephemeris. The best linear fit (reduced chi-squared, χr,L
gives a corrected ephemeris of
T0 (E) = 2455 983.704 21 + 3.336 65E(BJD),(4)

where E is the number of epochs from the 2012 February 26 transit,
the first transit of Bonfils et al. (2012). In Fig. 2, the O–C diagramshows that there is no significant variation of the mid-transit time.
Almost all of them are consistent within 2σ .
3.2 Upper mass limit of the second planet
From Section 3.1, the O–C diagram shows no significant TTV
signal, indicating that there are no nearby massive objects, whichhave strong gravitational interaction with GJ3470b. We use thisto compute an upper mass limit on a second planet in the sys-tem. We assume that the second planet is in a circular orbit thatis also coplanar with GJ3470b’s orbit. We use the TTVFASTER code
(Agol & Deck 2016), which computes the TTV signal from analytic
formulae.
We employ two methods to measure the upper mass limit. First,
we calculate the TTV signal for the second planet over a mass range
from 10−1 to 103 M⊕ with 100.01 M⊕ steps on a logarithmic scale.
We sample a period ratio of the perturbing planet and GJ3470b overa ratio range from 0.30 to 4.50 with 0.01 steps. At each grid point,
the initial phase of the perturber is varied between 0 and 2π with
π /18 000 steps in order to cover all alignments of the second planet
at E = 0. For each period of the perturber planet, the minimum
mass which produces a TTV signal higher than the measured TTV
limit is taken to be the upper mass limit for that period. As thehighest TTV signal from the O–C diagram is 498 s, upper mass
limits corresponding to TTV amplitudes of 400, 500 and 600 s arecalculated and shown in Fig. 3.
The second method uses the reduced chi-squared of the best fit
between the observed TTV signal and the signal from TTVFASTER.
The grid points and the initial phase of second planet are varied
as in the first method. From Section 3.1, the best linear fit using2= 2.11. We assess the improvementa single-planet model is χr,Lto the fit of introducing a second planet though the delta reduced2, where χr2 is the best-fitting
chi-squared statistic, χr2 = χr2 − χr,L
TTV model at the given mass and period. In Fig. 3, χr2 is shown
as a function of perturber mass and period. The preferred planet
models are shown in Fig. 3 as negative-valued χr2 regions. The
best-fitting TTV models are shown with the black dotted line in
Fig. 3, which is produced by averaging over period ratio bins ofwidth 0.05.
Unstable orbit regions are calculated from the mutual Hill spherebetween GJ3470b and the perturber. For two-planet systems in
coplanar and circular orbits, the boundary of the stable orbit is
MNRAS 463, 2574–2582 (2016)

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Mid-transit time (BJD)(BJD-2450000)

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S. Awiphan et al.

when the separationof the planets’ semimajor axes (aout − ain ) is√larger than 2 3 of the mutual Hill sphere (Fabrycky et al. 2012)
ain + aout Min + Mout 1/3
.
(5)
rH =
2
3M∗

4 T R A N S M I S S I O N S P E C T RO S C O P Y
4.1 Rayleigh scattering
Transmission spectroscopy of an exoplanet can be seen as a change
in planet-star radius ratio as a function of wavelength. At a wavelength with higher atmospheric absorption, the planet appears larger,
due to the opaque atmosphere. For an ideal gas atmosphere in hydrostatic equilibrium, the slope of the planetary radius as a function of
wavelength can be expressed as dRp /dln λ = αH, where α is a scale
factor (Lecavelier Des Etangs et al. 2008). From the atmosphericscaleheight relation (equation 1), the mean molecular weight of theplanetary atmosphere can be estimated asdRp −1.
(6)μ = αTp kB gp
d ln λWe adopt a Bond Albedo, A = 0.3 and an equilibrium temperature,
T = 624 ± 25 K from Demory et al. (2013). We assume the main
physical process involved in GJ3470b’s atmosphere is Rayleighscattering (α = −4) without atomic or molecular absorption. In
order to find dRp /dln λ, we combine our planet-star radius ratiowith previous optical observations. The plot of planet-star radiusratio versus wavelength and the best-fitting model of the GJ3470b
data with mean molecular weight 1.00, 1.50, 2.22 (Jupiter) and 2.61
(Neptune) atmospheres are shown in Fig. 4.
From the curve fit to the data in Fig. 4, a low mean molecularweight of 1.08 ± 0.20 is obtained. This low mean molecular weightis consistent with an H/He-dominated atmosphere as in previous
studies (Nascimbeni et al. 2013: 1.32+0.27−0.19 and Dragomir et al. 2015:
1.35 ± 0.44).
4.2 Atmospheric composition
To determine the atmospheric composition, ideally, a detailed atmospheric model of GJ3470b is required. We re-scale the planetaryatmosphere models of Howe & Burrows (2012). We use 114 models
spanning a range of atmospheric compositions including: sub-solar,
solar and supersolar metallicity compositions, as well as single
component atmospheres of methane, carbon dioxide and water. For
each of these atmospheric models, we test several different assumptions of atmospheric contaminant including: cloud-free and cloudy
atmospheres, and polyaceylene and tholin hazes.
MNRAS 463, 2574–2582 (2016)

Figure 4. (Top) Relation between planet-star radius ratio and wavelength
in optical filters with dRp /dln λ slope fitting (Black thick line). The blue
solid, dashed, dash–dotted and dotted lines represent the best fit with mean
molecular weight 1.00, 1.50, 2.22 (Jupiter) and 2.61 (Neptune), respectively.
The markers have the same description as Fig. 2. (Bottom) The bandpass of
our filters: g , r , Cousins-R, i and z band (from left to right). The bandpass
colours have the same description as Fig. 1.

We adopt only models with a planetary equilibrium temperatureand mass close to GJ3470b (Tp = 700 K, Mp = 10M⊕ ). The opticalplanet-star radius ratio data from Section 4.1 and infrared datafrom Demory et al. (2013) and Ehrenreich et al. (2014) are used2
) between the re-scaled
to compute a reduced chi-squared (χr,atm
models and the data. In Table 7, examples of the atmosphere models
2
are shown.
with their best-fitting χr,atm
From the fitting, a CH4 atmosphere with a 100 cm−3 particle abun2=
dance haze at 1–1000 μbar altitude provides the best fit with χr,atm
1.40 or 1.38 for polyacetylene or tholin haze, respectively. At nearinfrared wavelengths, CH4 models provide the best fit and the data
are not compatible with a cloudy atmosphere model. However, themodels of Howe & Burrows (2012) do not provide an atmospherewith mixed composition (the CH4 atmosphere is a 100 per centmethane atmosphere), which might be the cause of the poor fit to
the data at optical wavelengths. From the Rayleigh scattering slope,the mean molecular weight is too low to be a methane-dominatedatmosphere. Therefore, the H/He-dominated haze with high particle abundance, such as high-altitude polyacetylene and tholin witha methane contaminant, is preferred. A model atmosphere with amixed-ratio composition should provide a better description of theGJ3470b atmosphere.
5 CONCLUSIONSIn this work, we observed and studied a transiting hot Neptune, GJ3470b, which is the first sub-Jovian planet with detected
Rayleigh scattering. Optical multifilter observations of the exoplanet were obtained with the 2.4-m and 0.5-m telescopes at the
TNO and the 0.6-m telescope at CTIO in 2013–2016. 10 transit
light curves were obtained and analyzed using the TAP program(Agol et al. 2005). The derived data from the analysis provide a

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In equation (5), ain and aout are the semimajor axis of the innerand outer planets, respectively. The area of unstable orbits is shownby the black shaded region of Fig. 3. Orbital resonances between
GJ3470b and the second planet are shown as vertical lines. In thecases where GJ3470b and the perturber are in a first-order mean
motion resonance, the upper mass limits are lower.
From Fig. 3, the preferred-TTV area with a χr2 between −0.7
and −0.4 is shown near the upper mass limit of 400 s TTV amplitude. A nearby second planet with period between 2.5 and 4.0
d is ruled out by both upper mass limit tests and the mutual Hill
sphere area. A Jupiter-mass planet with period less than 10 d is also
excluded. From this result, we can conclude that there is no nearby
massive planet to GJ3470b.

TTV and transmission spectroscopy of GJ3470b

2581

Table 7. Atmospheric models of Howe & Burrows (2012) with the best2
χr,atmfit. The highlight best fit atmospheric models are shown in Fig 5.

planet mass Mp = 13.9 ± 1.5M⊕ , radius Rp = 4.57 ± 0.18R⊕ ,0039+0.26 ◦
period P = 3.336 6496+0.000−0.000 0033 d, and inclination i = 89.13−0.34 .
A new ephemeris for GJ3470b is also provided.
We perform the TTV analysis with the TTVFASTER code of Agol &Deck (2016), in order to determine an upper mass limit for a second
planet in the system. The TTV signal indicates little variation, which
excludes the presence of a hot Jupiter with orbital period less than
10 d in the system. The mutual Hill sphere also excludes the presenceof a nearby planet with orbital period between 2.5 and 4.0 d.
For the transmission spectroscopy analysis, GJ3470b’s low atmosphere mean molecular weight (μ = 1.08 ± 0.20) is obtained fromthe Rayleigh scattering fitting of the planet-star radius ratio variation in the optical. We confirm the steep Rayleigh scattering slope
favoured by previous studies. Previous near-infrared data favour
a methane atmosphere with high particle abundance (100 cm−3of tholin or polyaceylen) at high altitude (1000–1 μbar) whencompared to the model atmosphere of Howe & Burrows (2012).
However, the models do not fit the data at optical wavelengths,

Composition

Cloud toppressure2
χr,atmNo Cloud
No Cloud
No Cloud
No Cloud
No Cloud
No Cloud
Cloud
Cloud
Cloud
Cloud
Cloud
Cloud
Cloud
Cloud
Cloud
Cloud
Cloud
Cloud
0.1 µm 100 cm−3 polyaceylene
0.1 µm 100 cm−3 polyaceylene
0.1 µm 100 cm−3 polyaceylene
0.1 µm 100 cm−3 polyaceylene
0.1 µm 100 cm−3 polyaceylene
0.1 µm 100 cm−3 polyaceylene
0.1 µm 100 cm−3 polyaceylene
0.1 µm 1000 cm−3 polyaceylene
1.0 µm 0.01 cm−3 polyaceylene
1.0 µm 0.1 cm−3 polyaceylene
0.1 µm 100 cm−3 tholin
0.1 µm 100 cm−3 tholin
0.1 µm 100 cm−3 tholin
0.1 µm 100 cm−3 tholin
0.1 µm 100 cm−3 tholin
0.1 µm 100 cm−3 tholin
0.1 µm 100 cm−3 tholin
0.1 µm 1000 cm−3 tholin
1.0 µm 0.01 cm−3 tholin
1.0 µm 0.1 cm−3 tholin

0.3 × solar
1 × solar
3 × solar
CH4
CO2
H2 O
0.3 × solar
1 × solar
3 × solar
CH4
CO2
H2 O
0.3 × solar
1 × solar
3 × solar
CH4
CO2
H2 O
0.3 × solar
1 × solar
3 × solar
CH4
CH4
CO2
H2 O
CH4
CH4
CH4
0.3 × solar
1 × solar
3 × solar
CH4
CH4
CO2
H2 O
CH4
CH4
CH4

1 bar
1 bar
1 bar
1 bar
1 bar
1 bar
1 mbar
1 mbar
1 mbar
1 mbar
1 mbar
1 mbar
1 µbar
1 µbar
1 µbar
1 µbar
1 µbar
1 µbar
1 µbar
1 µbar
1 µbar
1 µbar
1 mbar
1 µbar
1 µbar
1 µbar
1 µbar
1 µbar
1 µbar
1 µbar
1 µbar
1 µbar
1 mbar
1 µbar
1 µbar
1 µbar
1 µbar
1 µbar

3.24
4.05
4.64
1.49
1.79
1.86
1.80
2.04
2.33
1.64
1.76
1.77
1.71
1.71
1.71
1.71
1.72
1.71
2.14
2.36
2.51
1.40
1.47
1.78
1.76
1.49
1.50
1.47
2.13
2.31
2.44
1.38
1.46
1.78
1.74
1.48
1.50
1.51

which might be a consequence of the single atmosphere composition within the models. A mixed-ratio composition model could
provide a better understanding of the planet’s atmosphere.
AC K N OW L E D G E M E N T S
This work has made use of data obtained at the TNO on Doi
Inthanon, operated by NARIT, and the PROMPT-8 telescope, operated by the Skynet Robotic Telescope Network. SA gratefully acknowledges the support from the Thai Government Scholarship andthe University of Manchester President’s Doctoral Scholar Award.
VSD acknowledges the support of the Science and Technology
Facilities Council (STFC) and the Leverhulme Trust for ULTRASPEC operations. TRM acknowledges the support of STFC throughgrant ST/L0007333.
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Figure 5. GJ3470b atmosphere models: (a) 0.1 µm 100 cm−3 Tholin with2
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