text: (cid:101) (cid:101) 4 of Qq heavy-light charm mesons are given as they are represented by g2 , g2 , Higher order correc- − − → − − HH SH (0 , 1 ) (0 , 1 ) + M tions for spin and ﬂavor violation of order 1 are ex- mQ cluded to avoid new unknown coupling constants. Equa- − → − g2 M p3 Γ(1 1 ) = C HH f M (16) tions 16-29 shows that the decay width of any state de- M 3πfπ2Mi pends on the initial and ﬁnal meson masses, their strong − → − g2 M p3 coupling constants, pion decay constant, energy scale Λ, Γ(1 0 ) = CM H6πHf2Mf M (17) mass and momentum of light pseudo-scalar mesons. Un- π i known coupling constants in these widths, can either be − → − g2 M p3 Γ(0 1 ) = C HH f M (18) theoretically predicted or can be determined indirectly M 2πfπ2Mi from the known experimental values of the decay widths. → − − Theoretically, lattice QCD [27], QCD sum rules [28] have (0+, 1+) (0 , 1 ) + M successfully predicted some of these coupling constants. The numerical masses of various mesons used in the cal- → − g2 M (p2 + m2 )p Γ(1+ 1 ) = C SH f M M M (19) culation are listed in Table II. M 2πf2M π i → − g2 M (p2 + m2 )p Γ(0+ 0 ) = C SH f M M M (20) M 2πf2M III. NUMERICAL ANALYSIS π i → − − (1+, 2+) (0 , 1 ) + M Assigning a proper JP(cid:48)s to the experimentally avail- able states are essential, as it helps in retrieving many → − 2g2 M p5 Γ(2+ 1 ) = C TH f M (21) properties like decay width, strong coupling constant, M 5πfπ2Λ2Mi branching ratios etc of these states. In this pa- → − 4g2 M p5 per, we reanalyze the previously available theoretical Γ(2+ 0 ) = C TH f M (22) ∗ M 15πfπ2Λ2Mi and experimental data o∗n the charm∗ states DJ(2460), D (2560), D (2740), D (2680), D (2760), D (3000) → − 2g2 M p5 J ∗ J J J J Γ(1+ 1 ) = C TH f M (23) and D (3000). This analysis is based on the available M 3πf2Λ2M J π i information on J values taken from LHCb in 2016. Hence − − → − − we identify these states as: (2 , 3 ) (0 , 1 ) + M ∗ Γ(2− → 1−) = CM 154πgfY2π2HΛ4 MMfi [p7M] (24) (DJ(256D0)J,(D24J∗6(206)8=0)()2=+)(320w−i,t1h−n)1=w1it,hLn==1,2, L =(03,0) 2 − → − 4g2 M (31) Γ(3 0 ) = CM 35πfYπ2HΛ4 Mfi [p7M] (25) (DJ(2740), DJ∗(2760)) = (2−, 3−)5 with n = 1, L = 2, Γ(3− → 1−) = C 16gY2 H Mf [p7 ] (26) 2 (32) M 105πfπ2Λ4 Mi M D∗(3000)), (D (3000) = (0+, 1+) with n = 2, L = 1 J J 1 → − − 2 (2+, 3+) (0 , 1 ) + M (33) The numerical value of the partial decay widths and ∗ → − 8g2 M the ratios for the charm states D (2460), D (2560), Γ(2+ 1 ) = C ZH f [p5 (m2 + p2 )] (27) ∗ ∗ 2 0∗ M 75πfπ2Λ4 Mi M M M D2(2740), D1(2680), D3(2760), D1(3000) and D0(3000) are listed in Table III. We equate the calculated decay → − 4g2 M Γ(2+ 0 ) = C ZH f [p5 (m2 + p2 )] (28) widths wit(cid:101)h the(cid:101)experimental data in Table III to obtain M 25πf2Λ4 M M M M π i the coupling constants which are listed in Table IV. The Γ(3+ → 1−) = C 4gZ2 H Mf [p5 (m2 + p2 )] (29) couplings gHH, gSH are obtaine∗d by averaging the val- M 25πf2Λ4 M M M M ues obtained from (D (2560), D (2680)) and (D (3000), π i ∗ 0 1 1 D (3000)) respectively. We have neglected the small 0 In the above decay widths, Mi and Mf stands for ini- value of the coupling gY H = 0.10, in comparison with tial and ﬁnal meson mass, pM and mM are the ﬁnal its other theoretically predicted values [26]. The range momentum and mass of the light pseudo-scalar meson in the coupling constant, comes from the error-bar in the respectively. The coeﬃcient Cπ±, CK±, CK0, CK0 = 1, experimental mass and decay width values. C = 1 and C = 2 or 1. Diﬀerent values of C corre- On the basis of the theoretically predicted masses π0 2 η 3 6 η ∗ sponds to the initial state being cu, cd or cs respectively. [8, 13, 15–18], D (3000) is assumed to belong to either 2 All hadronic coupling constants depends on the radial 1F5 (2+) or 2P3 (2+) state. The partial and the total de- 2 2 quantum number. For the decay within n=1 they are no- cay widths for both these states are shown in Table V. ∗ tated as g , g etc, and the decay from n=2 to n=1 To clear out the JP state for D (3000) between 1F(2+) HH SH 2 ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine##

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text: 7 TABLE IV: Value of various coupling constants obtained in the literature. Couplin(cid:101)g constant Our calculation Work in [26] Work in [9] ± ± ± g 0.40 0.01 0.43 0.05 0.43 0.01 TH ± ± ± g(cid:101) 0.31 0.05 0.14 0.03 0.28 0.01 HH ± ± ± g 0.61 0.05 0.53 0.13 0.42 0.02 Y H ± g 0.12 0.03 - - SH (cid:98) ∗ TABLE V: Strong decay width of D (3000) with the JP assignment as 1F (2+) and 2P (2+). Ratio represents 2 5 3 ∗ 2 2 Γ = ∗ Γ→ ∗ − for D (3000). Fraction gives the percentage of the particular decay width with respect to Γ(D (3000) D +π ) 2 2 the total decay width. nLs JP Decay channel Decay Width(MeV) Ratio Fraction Experimental Value(MeV) l ∗ − 1F (2+) D +π 1046.53g2 1 13.60 5/2 ∗ ZH D +π0 531.26g2 0.50 6.90 ∗ ZH D +η 109.14g2 0.10 1.41 ∗ − ZH D +K 422.87g2 0.40 5.49 s − ZH D+π 2630.35g2 2.51 34.20 ZH D+π0 1338.14g2 1.27 17.39 ZH D+η 307.35g2 0.29 3.99 − ZH D+K 1304.87g(cid:101)2 1.24 16.96 s ZH ± Total (cid:101) 186 38 ∗ − 2P (2+) D +π 4075.15(cid:101)g2 1 24.69 3/2 ∗ TH D +π0 2060.89g(cid:101)2 0.50 12.48 ∗ TH D +η 387.99g(cid:101)2 0.09 2.35 ∗ − TH D +K 1754.17g(cid:101)2 0.43 10.62 s − TH D+π 1952.32(cid:101)g2 0.94 23.36 TH D+π0 3856.13g(cid:101)2 0.47 11.83 TH D+η 413.76g2 0.10 2.50 − TH D+K 2002.65g2 0.49 12.13 s TH ± Total 186 38 V. ACKNOWLEDGEMENT port by the Department of Science and Technology (SB/FTP/PS-037/2014), New Delhi. The authors gratefully acknowledge the ﬁnancial sup- [1] R. Aaij et al, Phys. Rev. D 94, 072001 (2016). [11] Guo Liang Yu et. al., Chin.Phys. C 39, 063101 (2015). [2] R. Aaij et al, JHEP 1309 145 (2013). [12] Z. G. Wang, Commun. Theor. Phys. 66, 671 (2016). [3] P. del Amo Sanchez et al, Phys. Rev. D 82, 111101 (2010). [13] S. Godfrey and K. Moats, Phys. Rev. D 93, 034035 [4] K. A. Olive et al, Chin. Phys. C 38, 090001 (2014). (2016). [5] Guo Liang Yu, Zhi Gang Wang, Zhen Yu Li, Phys. Rev. [14] Jun-Zhang Wang et. al., Phys. Rev. D 94, 094044 (2016). D 94, 074024 (2016). [15] De-Min Li, Bing Ma, Yun-Hu liu, Eur.Phys.J.C 51, 359- [6] A. M. Badalian and B. L. G. Bakker, Phys. Rev. D 84, 365 (2007). 034006 (2011). [16] D. Ebert, et. al., Eur.Phys.J.C 66, 197-206 (2010). [7] P. Colangelo, F. De Fazio, F. Giannuzzi and S. Nicotri, [17] S. Godfrey and N. Isgur, Phys. Rev. D 32, 189 (1985). Phys. Rev. D 86, 054024 (2012). [18] M. Di Pierro and E. Eichten, Phys. Rev. D 64, 114004 [8] Q. T. Song, D. Y. Chen, X. Liu, and T. Matsuki, Phys. (2001). Rev. D 92, 074011 (2015). [19] J. L. Goity and W. Roberts, Phys. Rev. D 51 3459 (1995). [9] Z. G. Wang, Phys. Rev. D 88, 114003 (2013). [20] A. Falk and T. Mehen, Phys. Rev. D 53 231 (1996). [10] Meenakshi Batra, Alka Upadhyay, Eur.Phys.J. C 75, 319 [21] Iain W. Stewart, Nucl.Phys. B 529 62-80 (1998). (2015). [22] M. Neubert, Phys. Rept. 245, 259 (1994). ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine##

label: paragraph

text: TABLE

text: IV:

text: Value

label: caption

text: of

text: various

text: coupling

text: constants

text: obtained

text: in

text: the

text: literature.

label: table

text: constant

text: Our

text: calculation

text: Work

text: in

text: Work

text: in

text: g

text: TH

text: HH

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text: Y

text: H

text: g

text: SH

text: TABLE

text: V:

text: Strong

text: decay

text: width

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text: D

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text: JP

text: assignment

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text: Ratio

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text: percentage

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text: Γ(D

text: D

text: +π

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text: total

text: decay

text: width.

text: nLs

text: JP

text: Decay

text: channel

text: Decay

text: Width(MeV)

text: Ratio

text: Fraction

text: Experimental

text: Value(MeV)

text: l

text: D

text: +π

text: ZH

text: D

text: ZH

text: D

text: +η

text: ZH

text: D

text: +K

text: s

text: ZH

text: D+π

text: ZH

text: ZH

text: D+η

text: ZH

text: D+K

text: s

text: ZH

text: Total

text: D

text: +π

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text: D

text: TH

text: D

text: +η

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text: D+π

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text: TH

text: D+η

text: TH

text: D+K

text: s

text: TH

text: Total

text: V.

text: ACKNOWLEDGEMENT

text: port

text: by

text: the

text: Department

text: of

text: Science

text: and

text: Technology

text: New

text: Delhi.

text: The

text: authors

text: gratefully

text: acknowledge

text: the

text: ﬁnancial

text: sup-

text: R.

text: Aaij

text: et

text: al,

text: Phys.

text: Rev.

text: D

text: Guo

text: Liang

text: Yu

text: et.

text: al.,

text: Chin.Phys.

text: C

text: R.

text: Aaij

text: et

text: al,

text: JHEP

text: Z.

text: G.

text: Wang,

text: Commun.

text: Theor.

text: Phys.

text: P.

text: del

text: Amo

text: Sanchez

text: et

text: al,

text: Phys.

text: Rev.

text: D

text: S.

text: Godfrey

text: and

text: K.

text: Moats,

text: Phys.

text: Rev.

text: D

text: K.

text: A.

text: Olive

text: et

text: al,

text: Chin.

text: Phys.

text: C

text: Guo

text: Liang

text: Yu,

text: Zhi

text: Gang

text: Wang,

text: Zhen

text: Yu

text: Li,

text: Phys.

text: Rev.

text: Jun-Zhang

text: Wang

text: et.

text: al.,

text: Phys.

text: Rev.

text: D

text: D

text: De-Min

text: Li,

text: Bing

text: Ma,

text: Yun-Hu

text: liu,

text: Eur.Phys.J.C

text: A.

text: M.

text: Badalian

text: and

text: B.

text: L.

text: G.

text: Bakker,

text: Phys.

text: Rev.

text: D

text: D.

text: Ebert,

text: et.

text: al.,

text: Eur.Phys.J.C

text: P.

text: Colangelo,

text: F.

text: De

text: Fazio,

text: F.

text: Giannuzzi

text: and

text: S.

text: Nicotri,

text: S.

text: Godfrey

text: and

text: N.

text: Isgur,

text: Phys.

text: Rev.

text: D

text: Phys.

text: Rev.

text: D

text: M.

text: Di

text: Pierro

text: and

text: E.

text: Eichten,

text: Phys.

text: Rev.

text: D

text: Q.

text: T.

text: Song,

text: D.

text: Y.

text: Chen,

text: X.

text: Liu,

text: and

text: T.

text: Matsuki,

text: Phys.

text: Rev.

text: D

text: J.

text: L.

text: Goity

text: and

text: W.

text: Roberts,

text: Phys.

text: Rev.

text: D

text: Z.

text: G.

text: Wang,

text: Phys.

text: Rev.

text: D

text: A.

text: Falk

text: and

text: T.

text: Mehen,

text: Phys.

text: Rev.

text: D

text: Meenakshi

text: Batra,

text: Alka

text: Upadhyay,

text: Eur.Phys.J.

text: C

text: Iain

text: W.

text: Stewart,

text: Nucl.Phys.

text: B

text: M.

text: Neubert,

text: Phys.

text: Rept.

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text: Draft version May 30, 2020 Typeset using LATEX twocolumn style in AASTeX61 ∗ ABSTRACT GJ 436b is a prime target for understanding warm Neptune exoplanet atmospheres and a target for multiple JWST GTO programs. Here, we report the ﬁrst space-based optical transmission spectrum of the planet using two HST/STIS transit observations from 0.53-1.03 µm. We ﬁnd no evidence for alkali absorption features, nor evidence of a scattering ∼ − × slope longward of 0.53 µm. The spectrum is indicative of moderate to high metallicity ( 100 1000 solar) while ∼ × moderate metallicity scenarios ( 100 solar) require aerosol opacity. The optical spectrum also rules out some highly scattering haze models. We ﬁnd an increase in transit depth around 0.8 µm in the transmission spectra of 3 diﬀerent sub-Jovian exoplanets (GJ 436b, HAT-P-26b, and GJ 1214b). While most of the data come from STIS, data from three other instruments may indicate this is not an instrumental eﬀect. Only the transit spectrum of GJ 1214b is well ﬁt by a model with stellar plages on the photosphere of the host star. Our photometric monitoring of the host star reveals a stellar rotation rate of 44.1 days and an activity cycle of 7.4 years. Intriguingly, GJ 436 does not become redder as it gets dimmer, which is expected if star spots were dominating the variability. These insights into the nature of the GJ 436 system help reﬁne our expectations for future observations in the era of JWST, whose higher precision and broader wavelength coverage will shed light on the composition and structure of GJ 436b’s atmosphere. Keywords: methods: observaional – planets and satellites: individual (GJ 436b) – optical: planetary systems – techniques: spectroscopic

text: Draft

label: section

text: version

text: May

text: Typeset

text: using

text: LATEX

text: twocolumn

text: style

text: in

text: ABSTRACT

text: GJ

label: abstract

text: is

text: a

text: prime

text: target

text: for

text: understanding

text: warm

text: Neptune

text: exoplanet

text: atmospheres

text: and

text: a

text: target

text: for

text: multiple

text: JWST

text: GTO

text: programs.

text: Here,

text: we

text: report

text: the

text: ﬁrst

text: space-based

text: optical

text: transmission

text: spectrum

text: of

text: the

text: planet

text: using

text: two

text: HST/STIS

text: transit

text: observations

text: from

text: µm.

text: We

text: ﬁnd

text: no

text: evidence

text: for

text: alkali

text: absorption

text: features,

text: nor

text: evidence

text: of

text: a

text: scattering

text: slope

text: longward

text: of

text: µm.

text: The

text: spectrum

text: is

text: indicative

text: of

text: moderate

text: to

text: high

text: metallicity

text: solar)

text: while

text: moderate

text: metallicity

text: scenarios

text: solar)

text: require

text: aerosol

text: opacity.

text: The

text: optical

text: spectrum

text: also

text: rules

text: out

text: some

text: highly

text: scattering

text: haze

text: models.

text: We

text: ﬁnd

text: an

text: increase

text: in

text: transit

text: depth

text: around

text: µm

text: in

text: the

text: transmission

text: spectra

text: of

text: diﬀerent

text: sub-Jovian

text: exoplanets

text: (GJ

text: and

text: GJ

text: While

text: most

text: of

text: the

text: data

text: come

text: from

text: STIS,

text: data

text: from

text: three

text: other

text: instruments

text: may

text: indicate

text: this

text: is

text: not

text: an

text: instrumental

text: eﬀect.

text: Only

text: the

text: transit

text: spectrum

text: of

text: GJ

text: is

text: well

text: ﬁt

text: by

text: a

text: model

text: with

text: stellar

text: plages

text: on

text: the

text: photosphere

text: of

text: the

text: host

text: star.

text: Our

text: photometric

text: monitoring

text: of

text: the

text: host

text: star

text: reveals

text: a

text: stellar

text: rotation

text: rate

text: of

text: days

text: and

text: an

text: activity

text: cycle

text: of

text: years.

text: Intriguingly,

text: GJ

text: does

text: not

text: become

text: redder

text: as

text: it

text: gets

text: dimmer,

text: which

text: is

text: expected

text: if

text: star

text: spots

text: were

text: dominating

text: the

text: variability.

text: These

text: insights

text: into

text: the

text: nature

text: of

text: the

text: GJ

text: system

text: help

text: reﬁne

text: our

text: expectations

text: for

text: future

text: observations

text: in

text: the

text: era

text: of

text: JWST,

text: whose

text: higher

text: precision

text: and

text: broader

text: wavelength

text: coverage

text: will

text: shed

text: light

text: on

text: the

text: composition

text: and

text: structure

text: of

text: GJ

text: atmosphere.

text: Keywords:

text: methods:

text: observaional

text: planets

text: and

text: satellites:

text: individual

text: (GJ

text: optical:

text: planetary

text: systems

text: techniques:

text: spectroscopic


text: 4 Lothringer et al. tion 3 describes our light curve ﬁtting techniques. In the 4 diﬀerence frames. The median diﬀerence frame Section 4, we show our results, including a look at the consists only of cosmic ray hits. Next, each pixel’s ﬂux eﬀects of stellar variability and the use of diﬀerent or- was compared to the standard deviation of its column. bital solutions. In Section 5, we compare our results If the pixel value was greater than 4 times this standard to other sub-Jovian exoplanets and describe a common deviation, it was ﬂagged as a cosmic ray hit. As a second trend found in their optical transmission spectrum. We method, a window of 20x20 pixels was then placed on close with a discussion of expectations for future JWST each pixel of the median diﬀerence frame and the me- transmission spectroscopy of GJ 436b. dian for that window was calculated. If the center pixel’s 2. OBSERVATIONS AND DATA REDUCTION value was greater than 4 standard deviations from this median window value, the center pixel was ﬂagged as 2.1. STIS Observations being contaminated by a cosmic ray strike. Two transits of GJ 436b were observed on 10 June Once all pixels were analyzed in this manner, the pixel 2015 UT and 14 June 2016 UT using the Space Telescope values were replaced by the corresponding pixel value in Imaging Spectrograph (STIS) on the Hubble Space Tele- − the median diﬀerence frame (i.e., the median for the four scope (HST) with the G750L grism (0.53 1.03 µm) as nearest frames). Pixels identiﬁed as ‘bad’ according to part of GO 13665 (PI Benneke). The 52x2 arsec2 slit was CALSTIS were replaced in this same manner. After be- used to minimize slit losses, while a 128 pixel subarray ing extracted from the 2 dimensional frames (see below), mode reduced readout overhead. Each transit consisted the 1D spectra were checked for cosmic rays that were of 4 total HST orbits. The ﬁrst orbit of a visit often missed by the 2D procedure. This is especially impor- exhibits strong systematic variations, inconsistent with tant for cosmic rays that occur near the bright spectral the systematics in subsequent orbits. For this reason, trace. The 1D stellar spectrum was compared to the two after conﬁrmation of this phenomenon, the ﬁrst orbit nearest spectra and two diﬀerence frames were created. was not included in the analysis. The second and fourth If the 1D spectrum exceeded the average of these diﬀer- orbits are used to characterize the stellar baseline ﬂux, ence frames at any point by 10 standard deviations, that while the transit occurs during the third orbit. Expo- pixel was ﬂagged as being contaminated by a cosmic ray sure times were 100 seconds resulting in 20 frames per strike. The large standard deviation cut-oﬀ serves to en- HST orbit. The ﬁrst frame of each orbit consistently sure that we are not erasing statistical noise. The value shows anomalous ﬂux, so this frame is not included in of the contaminated pixel is then replaced by the mean the light curve ﬁtting. Both visits were scheduled with of the 2 nearest values. the same orbital phasing, with the in-transit HST orbit 2.1.2. Spectral Extraction covering ingress through transit center to about 4 or 5 frames after transit center. A STIS pipeline was built for the program using ex- The data were dark subtracted, bias corrected, and isting CALSTIS routines in addition to custom proce- ﬂat ﬁelded using the appropriate CALSTIS routines. dures for cosmic ray identiﬁcation. This pipeline was The G750L grism on STIS has an obvious fringing eﬀect tested and validated using previous STIS data sets and longwards of 0.7 µm. To account for this, a fringe ﬂat is described below. was taken at the end of each HST visit (i.e., one for each 2.1.1. Cosmic Ray Identiﬁcation and Removal transit). This fringe ﬂat was then used to divide out the fringe pattern using the CALSTIS defringing procedure The long exposure times required for GJ 436 (I = 8.3) (Goudfrooij & Christensen 1998). We found that de- meant that most frames had multiple cosmic ray hits. fringing did not have a signiﬁcant eﬀect on the resulting It has also previously been found that the default CAL- planetary spectrum. STIS routines for cleaning cosmic ray hits were inade- Measurements of the spectral trace slope, the shift of quate for our purposes (Nikolov et al. 2014). For these the spectrum in the spatial direction and the shift of the reasons, a custom cosmic ray identiﬁcation and removal spectrum in the spectral direction were saved to be later procedure was developed, drawing on the technique de- used as covariates in the light curve analysis for system- scribed by Nikolov et al. (2014). For each frame to be atic detrending. The spectral trace slope and spatial cleaned, four diﬀerence images were created between the shift were found by ﬁtting a Gaussian proﬁle to each frame and the four frames nearest in time. Each diﬀer- column and then ﬁtting a line through the peaks of all ence image will subtract out the stellar ﬂux, leaving only the proﬁles. The shift of the spectrum in the disper- the cosmic rays from one frame being positive values and sion direction was measured by taking the wavelength the cosmic rays from the other frame being negative val- value at the center column after image rectiﬁcation in ues. A median diﬀerence frame was then created from CALSTIS.

text: Lothringer

text: et

text: al.

text: tion

text: describes

text: our

text: light

text: curve

text: ﬁtting

text: techniques.

text: In

text: the

text: diﬀerence

text: frames.

text: The

text: median

text: diﬀerence

text: frame

text: Section

text: we

text: show

text: our

text: results,

text: including

text: a

text: look

text: at

text: the

text: consists

text: only

text: of

text: cosmic

text: ray

text: hits.

text: Next,

text: each

text: pixel’s

text: ﬂux

text: eﬀects

text: of

text: stellar

text: variability

text: and

text: the

text: use

text: of

text: diﬀerent

text: or-

text: was

text: compared

text: to

text: the

text: standard

text: deviation

text: of

text: its

text: column.

text: bital

text: solutions.

text: In

text: Section

text: we

text: compare

text: our

text: results

text: If

text: the

text: pixel

text: value

text: was

text: greater

text: than

text: times

text: this

text: standard

text: to

text: other

text: sub-Jovian

text: exoplanets

text: and

text: describe

text: a

text: common

text: deviation,

text: it

text: was

text: ﬂagged

text: as

text: a

text: cosmic

text: ray

text: hit.

text: As

text: a

text: second

text: trend

text: found

text: in

text: their

text: optical

text: transmission

text: spectrum.

text: We

text: method,

text: a

text: window

text: of

text: pixels

text: was

text: then

text: placed

text: on

text: close

text: with

text: a

text: discussion

text: of

text: expectations

text: for

text: future

text: JWST

text: each

text: pixel

text: of

text: the

text: median

text: diﬀerence

text: frame

text: and

text: the

text: me-

text: transmission

text: spectroscopy

text: of

text: GJ

text: dian

text: for

text: that

text: window

text: was

text: calculated.

text: If

text: the

text: center

text: pixel’s

text: OBSERVATIONS

text: AND

text: DATA

text: REDUCTION

text: value

text: was

text: greater

text: than

text: standard

text: deviations

text: from

text: this

text: median

text: window

text: value,

text: the

text: center

text: pixel

text: was

text: ﬂagged

text: as

text: STIS

text: Observations

text: being

text: contaminated

text: by

text: a

text: cosmic

text: ray

text: strike.

text: Two

text: transits

text: of

text: GJ

text: were

text: observed

text: on

text: June

text: Once

text: all

text: pixels

text: were

text: analyzed

text: in

text: this

text: manner,

text: the

text: pixel

text: UT

text: and

text: June

text: UT

text: using

text: the

text: Space

text: Telescope

text: values

text: were

text: replaced

text: by

text: the

text: corresponding

text: pixel

text: value

text: in

text: Imaging

text: Spectrograph

text: (STIS)

text: on

text: the

text: Hubble

text: Space

text: Tele-

text: the

text: median

text: diﬀerence

text: frame

text: (i.e.,

text: the

text: median

text: for

text: the

text: four

text: scope

text: (HST)

text: with

text: the

text: grism

text: µm)

text: as

text: nearest

text: frames).

text: Pixels

text: identiﬁed

text: as

text: ‘bad’

text: according

text: to

text: part

text: of

text: GO

text: (PI

text: Benneke).

text: The

text: slit

text: was

text: CALSTIS

text: were

text: replaced

text: in

text: this

text: same

text: manner.

text: After

text: be-

text: used

text: to

text: minimize

text: slit

text: losses,

text: while

text: a

text: pixel

text: subarray

text: ing

text: extracted

text: from

text: the

text: dimensional

text: frames

text: (see

text: below),

text: mode

text: reduced

text: readout

text: overhead.

text: Each

text: transit

text: consisted

text: the

text: spectra

text: were

text: checked

text: for

text: cosmic

text: rays

text: that

text: were

text: of

text: total

text: HST

text: orbits.

text: The

text: ﬁrst

text: orbit

text: of

text: a

text: visit

text: often

text: missed

text: by

text: the

text: procedure.

text: This

text: is

text: especially

text: impor-

text: exhibits

text: strong

text: systematic

text: variations,

text: inconsistent

text: with

text: tant

text: for

text: cosmic

text: rays

text: that

text: occur

text: near

text: the

text: bright

text: spectral

text: the

text: systematics

text: in

text: subsequent

text: orbits.

text: For

text: this

text: reason,

text: trace.

text: The

text: stellar

text: spectrum

text: was

text: compared

text: to

text: the

text: two

text: after

text: conﬁrmation

text: of

text: this

text: phenomenon,

text: the

text: ﬁrst

text: orbit

text: nearest

text: spectra

text: and

text: two

text: diﬀerence

text: frames

text: were

text: created.

text: was

text: not

text: included

text: in

text: the

text: analysis.

text: The

text: second

text: and

text: fourth

text: If

text: the

text: spectrum

text: exceeded

text: the

text: average

text: of

text: these

text: diﬀer-

text: orbits

text: are

text: used

text: to

text: characterize

text: the

text: stellar

text: baseline

text: ﬂux,

text: ence

text: frames

text: at

text: any

text: point

text: by

text: standard

text: deviations,

text: that

text: while

text: the

text: transit

text: occurs

text: during

text: the

text: third

text: orbit.

text: Expo-

text: pixel

text: was

text: ﬂagged

text: as

text: being

text: contaminated

text: by

text: a

text: cosmic

text: ray

text: sure

text: times

text: were

text: seconds

text: resulting

text: in

text: frames

text: per

text: strike.

text: The

text: large

text: standard

text: deviation

text: cut-oﬀ

text: serves

text: to

text: en-

text: HST

text: orbit.

text: The

text: ﬁrst

text: frame

text: of

text: each

text: orbit

text: consistently

text: sure

text: that

text: we

text: are

text: not

text: erasing

text: statistical

text: noise.

text: The

text: value

text: shows

text: anomalous

text: ﬂux,

text: so

text: this

text: frame

text: is

text: not

text: included

text: in

text: of

text: the

text: contaminated

text: pixel

text: is

text: then

text: replaced

text: by

text: the

text: mean

text: the

text: light

text: curve

text: ﬁtting.

text: Both

text: visits

text: were

text: scheduled

text: with

text: of

text: the

text: nearest

text: values.

text: the

text: same

text: orbital

text: phasing,

text: with

text: the

text: in-transit

text: HST

text: orbit

text: Spectral

text: Extraction

text: covering

text: ingress

text: through

text: transit

text: center

text: to

text: about

text: or

text: frames

text: after

text: transit

text: center.

text: A

text: STIS

text: pipeline

text: was

text: built

text: for

text: the

text: program

text: using

text: ex-

text: The

text: data

text: were

text: dark

text: subtracted,

text: bias

text: corrected,

text: and

text: isting

text: CALSTIS

text: routines

text: in

text: addition

text: to

text: custom

text: proce-

text: ﬂat

text: ﬁelded

text: using

text: the

text: appropriate

text: CALSTIS

text: routines.

text: dures

text: for

text: cosmic

text: ray

text: identiﬁcation.

text: This

text: pipeline

text: was

text: The

text: grism

text: on

text: STIS

text: has

text: an

text: obvious

text: fringing

text: eﬀect

text: tested

text: and

text: validated

text: using

text: previous

text: STIS

text: data

text: sets

text: and

text: longwards

text: of

text: µm.

text: To

text: account

text: for

text: this,

text: a

text: fringe

text: ﬂat

text: is

text: described

text: below.

text: was

text: taken

text: at

text: the

text: end

text: of

text: each

text: HST

text: visit

text: (i.e.,

text: one

text: for

text: each

text: Cosmic

text: Ray

text: Identiﬁcation

text: and

text: Removal

text: transit).

text: This

text: fringe

text: ﬂat

text: was

text: then

text: used

text: to

text: divide

text: out

text: the

text: fringe

text: pattern

text: using

text: the

text: CALSTIS

text: defringing

text: procedure

text: The

text: long

text: exposure

text: times

text: required

text: for

text: GJ

text: (I

text: (Goudfrooij

text: Christensen

text: We

text: found

text: that

text: de-

text: meant

text: that

text: most

text: frames

text: had

text: multiple

text: cosmic

text: ray

text: hits.

text: fringing

text: did

text: not

text: have

text: a

text: signiﬁcant

text: eﬀect

text: on

text: the

text: resulting

text: It

text: has

text: also

text: previously

text: been

text: found

text: that

text: the

text: default

text: CAL-

text: planetary

text: spectrum.

text: STIS

text: routines

text: for

text: cleaning

text: cosmic

text: ray

text: hits

text: were

text: inade-

text: Measurements

text: of

text: the

text: spectral

text: trace

text: slope,

text: the

text: shift

text: of

text: quate

text: for

text: our

text: purposes

text: (Nikolov

text: et

text: al.

text: For

text: these

text: the

text: spectrum

text: in

text: the

text: spatial

text: direction

text: and

text: the

text: shift

text: of

text: the

text: reasons,

text: a

text: custom

text: cosmic

text: ray

text: identiﬁcation

text: and

text: removal

text: spectrum

text: in

text: the

text: spectral

text: direction

text: were

text: saved

text: to

text: be

text: later

text: procedure

text: was

text: developed,

text: drawing

text: on

text: the

text: technique

text: de-

text: used

text: as

text: covariates

text: in

text: the

text: light

text: curve

text: analysis

text: for

text: system-

text: scribed

text: by

text: Nikolov

text: et

text: al.

text: For

text: each

text: frame

text: to

text: be

text: atic

text: detrending.

text: The

text: spectral

text: trace

text: slope

text: and

text: spatial

text: cleaned,

text: four

text: diﬀerence

text: images

text: were

text: created

text: between

text: the

text: shift

text: were

text: found

text: by

text: ﬁtting

text: a

text: Gaussian

text: proﬁle

text: to

text: each

text: frame

text: and

text: the

text: four

text: frames

text: nearest

text: in

text: time.

text: Each

text: diﬀer-

text: column

text: and

text: then

text: ﬁtting

text: a

text: line

text: through

text: the

text: peaks

text: of

text: all

text: ence

text: image

text: will

text: subtract

text: out

text: the

text: stellar

text: ﬂux,

text: leaving

text: only

text: the

text: proﬁles.

text: The

text: shift

text: of

text: the

text: spectrum

text: in

text: the

text: disper-

text: the

text: cosmic

text: rays

text: from

text: one

text: frame

text: being

text: positive

text: values

text: and

text: sion

text: direction

text: was

text: measured

text: by

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text: the

text: wavelength

text: the

text: cosmic

text: rays

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text: the

text: other

text: frame

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text: value

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text: the

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text: image

text: rectiﬁcation

text: in

text: ues.

text: A

text: median

text: diﬀerence

text: frame

text: was

text: then

text: created

text: from

text: CALSTIS.


text: HST/STIS Observations of GJ436b 5 An extraction aperture size of 13 pixels was found to The rotational period we measure for GJ 436 is similar minimize the scatter in the residuals to the ﬁt. Other ex- to periods observed in many low-mass stars (Irwin et al. traction aperture sizes lead to equivalent results. Both 2011; Su´arez Mascaren˜o et al. 2016). This measurement the CALSTIS X1D routine and IRAF/APALL were is also consistent with an early rotation period derived used to extract the spectrum, each producing consistent from spectroscopic indicators (Demory et al. 2007), but results. inconsistent with the 57 d period derived using a one- 2.2. Photometric Monitoring: A Precise Rotation year segment of our data (Knutson et al. 2011). When Period using those same data we also see a 57 d periodogram peak, but that season is the only one of our fourteen GJ 436 (M2.5V) has been monitored in Str¨omgren whose periodogram shows a peak at that period. We b and y ﬁlters for the past fourteen years using the ± conclude that GJ 436’s rotation period is indeed 44.1 Tennessee State University’s T12 0.8 m Automatic Pho- 0.2 d. This rotation rate is consistent with the interpre- toelectric Telescope (APT) at Fairborn Observatory in tation that GJ 436 is not an active star and is at least a southern Arizona (Henry 1999; Eaton et al. 2003; Henry few Gyr old (Maness et al. 2007; Kiraga & Stepien´ 2007; & Winn 2008) in order to better characterize the star Saﬀe et al. 2005; Jenkins et al. 2009; Sanz-Forcada et al. and how star spots may aﬀect our transit observations. 2010). With respect to the relationship between rota- In these observations we nod the telescope between tional period and activity cycle, GJ 436 ﬁts in with other GJ 436 and comparison stars of comparable or greater M-stars (Su´arez Mascaren˜o et al. 2016). brightness; we use these stars to remove extinction and Figure 2 shows the same photometric observations, seeing eﬀects. Of the 3 comparison stars analyzed, HD but for the individual b and y ﬁlters, showing that as 102555 (hereafter C1) and HD 103676 (C2) were the GJ 436 ﬁrst gets dimmer, the star becomes bluer. Most most constant, with very little variation between them chromospherically active stars get redder as the star gets over the 14 years. The third star, HD 99518, showed fainter, implying that dark spots dominate the variabil- a gradual brightening throughout the 14 year observa- ity (e.g., Innis et al. 1997); however, another well-known tions. Altogether we have obtained 1735 measurements, chromospherically active RS CVn variable binary, UX which we present in Table 1 and Figure 1 and 2. Ari, trends as GJ 436 does, becoming bluer as it be- The photometry of GJ 436 in Figure 1 shows an obvi- comes dimmer (Padmakar & Pandey 1999; Aarum Ulv˚as ous long-term variation with a period of roughly 7.4 yr & Henry 2003). For GJ 436, this behavior does not and a peak-to-peak amplitude of 10 mmag. This co- seem repetative, since during the next dimming phase, herent signal is consistent in period and amplitude with the star becomes slightly more red. During the current observations of many low-mass stars that are interpreted brightening phase, GJ 436 remains red compared to the as stellar activity cycles (Su´arez Mascaren˜o et al. 2016). 14-year mean color. We therefore conclude that we have measured GJ 436’s UX Ari’s behavior of becoming bluer as it gets dim- stellar activity cycle for the ﬁrst time. This activity cy- mer is seen both within the binary’s orbital period of cle is consistent with the ﬁnding that early M-type stars ± 6.4 days (Carlos & Popper 1971) and throughout the 25 have magnetic cycles that are on average 6.0 2.9 years ± year activity cycle (Aarum Ulv˚as & Henry 2003). Two and mid-M-type stars average 7.1 2.7 years (Su´arez explanations for this behavior include ﬂare and facular Mascaren˜o et al. 2016). activity (Rodono & Cutispoto 1992) or that the relative After removing this signal and a linear trend, a peri- component of the hotter (and bluer) member of the bi- odogram analysis reveals a strong signal with a period ± nary contributes more ﬂux as the cooler one becomes of 44.1 0.2 d and peak-to-peak amplitude of 3 mmag. more spotted (Mohin & Raveendran 1989; Raveendran To estimate the uncertainty on the rotation period, we & Mohin 1995). Aarum Ulv˚as & Engvold (2003) showed split the data into 3-year blocks and computed a Lomb- that this behavior can be successfully reproduced using Scargle periodogram of each data subset. The 44 d sig- a model that includes dark spots surrounded by bright nal is not detectable in each individual season’s pho- faculae on the active K star. We thus suggest that GJ tometry, but a strong peak is visible in the periodogram 436’s odd color behavior as activity changes may be due for each of these ﬁve contiguous sub-blocks. We mea- to the interplay between dark star spots and the faculae sured the location of the peak of each of these ﬁve pe- that surround them. It may be the case that diﬀerent riodograms and ﬁnd the mean and standard deviation ± activity cycles have diﬀerent proportions of star spots of the mean to be 44.1 0.2 d, which we interpret as and faculae. GJ 436’s stellar activity cycles be further GJ 436b’s rotation period and the uncertainty on that studied by continuing long-term stellar monitoring of GJ parameter.

text: HST/STIS

text: Observations

text: of

text: An

text: extraction

text: aperture

text: size

text: of

text: pixels

text: was

text: found

text: to

text: The

text: rotational

text: period

text: we

text: measure

text: for

text: GJ

text: is

text: similar

text: minimize

text: the

text: scatter

text: in

text: the

text: residuals

text: to

text: the

text: ﬁt.

text: Other

text: ex-

text: to

text: periods

text: observed

text: in

text: many

text: low-mass

text: stars

text: (Irwin

text: et

text: al.

text: traction

text: aperture

text: sizes

text: lead

text: to

text: equivalent

text: results.

text: Both

text: Su´arez

text: Mascaren˜o

text: et

text: al.

text: This

text: measurement

text: the

text: CALSTIS

text: routine

text: and

text: IRAF/APALL

text: were

text: is

text: also

text: consistent

text: with

text: an

text: early

text: rotation

text: period

text: derived

text: used

text: to

text: extract

text: the

text: spectrum,

text: each

text: producing

text: consistent

text: from

text: spectroscopic

text: indicators

text: (Demory

text: et

text: al.

text: but

text: results.

text: inconsistent

text: with

text: the

text: d

text: period

text: derived

text: using

text: a

text: one-

text: Photometric

text: Monitoring:

text: A

text: Precise

text: Rotation

text: year

text: segment

text: of

text: our

text: data

text: (Knutson

text: et

text: al.

text: When

text: Period

text: using

text: those

text: same

text: data

text: we

text: also

text: see

text: a

text: d

text: periodogram

text: peak,

text: but

text: that

text: season

text: is

text: the

text: only

text: one

text: of

text: our

text: fourteen

text: GJ

text: has

text: been

text: monitored

text: in

text: Str¨omgren

text: whose

text: periodogram

text: shows

text: a

text: peak

text: at

text: that

text: period.

text: We

text: b

text: and

text: y

text: ﬁlters

text: for

text: the

text: past

text: fourteen

text: years

text: using

text: the

text: conclude

text: that

text: GJ

text: rotation

text: period

text: is

text: indeed

text: Tennessee

text: State

text: University’s

text: m

text: Automatic

text: Pho-

text: d.

text: This

text: rotation

text: rate

text: is

text: consistent

text: with

text: the

text: interpre-

text: toelectric

text: Telescope

text: (APT)

text: at

text: Fairborn

text: Observatory

text: in

text: tation

text: that

text: GJ

text: is

text: not

text: an

text: active

text: star

text: and

text: is

text: at

text: least

text: a

text: southern

text: Arizona

text: (Henry

text: Eaton

text: et

text: al.

text: Henry

text: few

text: Gyr

text: old

text: (Maness

text: et

text: al.

text: Kiraga

text: Stepien´

text: Winn

text: in

text: order

text: to

text: better

text: characterize

text: the

text: star

text: Saﬀe

text: et

text: al.

text: Jenkins

text: et

text: al.

text: Sanz-Forcada

text: et

text: al.

text: and

text: how

text: star

text: spots

text: may

text: aﬀect

text: our

text: transit

text: observations.

text: With

text: respect

text: to

text: the

text: relationship

text: between

text: rota-

text: In

text: these

text: observations

text: we

text: nod

text: the

text: telescope

text: between

text: tional

text: period

text: and

text: activity

text: cycle,

text: GJ

text: ﬁts

text: in

text: with

text: other

text: GJ

text: and

text: comparison

text: stars

text: of

text: comparable

text: or

text: greater

text: M-stars

text: (Su´arez

text: Mascaren˜o

text: et

text: al.

text: brightness;

text: we

text: use

text: these

text: stars

text: to

text: remove

text: extinction

text: and

text: Figure

text: shows

text: the

text: same

text: photometric

text: observations,

text: seeing

text: eﬀects.

text: Of

text: the

text: comparison

text: stars

text: analyzed,

text: HD

text: but

text: for

text: the

text: individual

text: b

text: and

text: y

text: ﬁlters,

text: showing

text: that

text: as

text: (hereafter

text: and

text: HD

text: were

text: the

text: GJ

text: ﬁrst

text: gets

text: dimmer,

text: the

text: star

text: becomes

text: bluer.

text: Most

text: most

text: constant,

text: with

text: very

text: little

text: variation

text: between

text: them

text: chromospherically

text: active

text: stars

text: get

text: redder

text: as

text: the

text: star

text: gets

text: over

text: the

text: years.

text: The

text: third

text: star,

text: HD

text: showed

text: fainter,

text: implying

text: that

text: dark

text: spots

text: dominate

text: the

text: variabil-

text: a

text: gradual

text: brightening

text: throughout

text: the

text: year

text: observa-

text: ity

text: (e.g.,

text: Innis

text: et

text: al.

text: however,

text: another

text: well-known

text: tions.

text: Altogether

text: we

text: have

text: obtained

text: measurements,

text: chromospherically

text: active

text: RS

text: CVn

text: variable

text: binary,

text: UX

text: which

text: we

text: present

text: in

text: Table

text: and

text: Figure

text: and

text: Ari,

text: trends

text: as

text: GJ

text: does,

text: becoming

text: bluer

text: as

text: it

text: be-

text: The

text: photometry

text: of

text: GJ

text: in

text: Figure

text: shows

text: an

text: obvi-

text: comes

text: dimmer

text: (Padmakar

text: Pandey

text: Aarum

text: Ulv˚as

text: ous

text: long-term

text: variation

text: with

text: a

text: period

text: of

text: roughly

text: yr

text: Henry

text: For

text: GJ

text: this

text: behavior

text: does

text: not

text: and

text: a

text: peak-to-peak

text: amplitude

text: of

text: mmag.

text: This

text: co-

text: seem

text: repetative,

text: since

text: during

text: the

text: next

text: dimming

text: phase,

text: herent

text: signal

text: is

text: consistent

text: in

text: period

text: and

text: amplitude

text: with

text: the

text: star

text: becomes

text: slightly

text: more

text: red.

text: During

text: the

text: current

text: observations

text: of

text: many

text: low-mass

text: stars

text: that

text: are

text: interpreted

text: brightening

text: phase,

text: GJ

text: remains

text: red

text: compared

text: to

text: the

text: as

text: stellar

text: activity

text: cycles

text: (Su´arez

text: Mascaren˜o

text: et

text: al.

text: mean

text: color.

text: We

text: therefore

text: conclude

text: that

text: we

text: have

text: measured

text: GJ

text: UX

text: Ari’s

text: behavior

text: of

text: becoming

text: bluer

text: as

text: it

text: gets

text: dim-

text: stellar

text: activity

text: cycle

text: for

text: the

text: ﬁrst

text: time.

text: This

text: activity

text: cy-

text: mer

text: is

text: seen

text: both

text: within

text: the

text: binary’s

text: orbital

text: period

text: of

text: cle

text: is

text: consistent

text: with

text: the

text: ﬁnding

text: that

text: early

text: M-type

text: stars

text: days

text: (Carlos

text: Popper

text: and

text: throughout

text: the

text: have

text: magnetic

text: cycles

text: that

text: are

text: on

text: average

text: years

text: year

text: activity

text: cycle

text: (Aarum

text: Ulv˚as

text: Henry

text: Two

text: and

text: mid-M-type

text: stars

text: average

text: years

text: (Su´arez

text: explanations

text: for

text: this

text: behavior

text: include

text: ﬂare

text: and

text: facular

text: Mascaren˜o

text: et

text: al.

text: activity

text: (Rodono

text: Cutispoto

text: or

text: that

text: the

text: relative

text: After

text: removing

text: this

text: signal

text: and

text: a

text: linear

text: trend,

text: a

text: peri-

text: component

text: of

text: the

text: hotter

text: (and

text: bluer)

text: member

text: of

text: the

text: bi-

text: odogram

text: analysis

text: reveals

text: a

text: strong

text: signal

text: with

text: a

text: period

text: nary

text: contributes

text: more

text: ﬂux

text: as

text: the

text: cooler

text: one

text: becomes

text: of

text: d

text: and

text: peak-to-peak

text: amplitude

text: of

text: mmag.

text: more

text: spotted

text: (Mohin

text: Raveendran

text: Raveendran

text: To

text: estimate

text: the

text: uncertainty

text: on

text: the

text: rotation

text: period,

text: we

text: Mohin

text: Aarum

text: Ulv˚as

text: Engvold

text: showed

text: split

text: the

text: data

text: into

text: blocks

text: and

text: computed

text: a

text: Lomb-

text: that

text: this

text: behavior

text: can

text: be

text: successfully

text: reproduced

text: using

text: Scargle

text: periodogram

text: of

text: each

text: data

text: subset.

text: The

text: d

text: sig-

text: a

text: model

text: that

text: includes

text: dark

text: spots

text: surrounded

text: by

text: bright

text: nal

text: is

text: not

text: detectable

text: in

text: each

text: individual

text: season’s

text: pho-

text: faculae

text: on

text: the

text: active

text: K

text: star.

text: We

text: thus

text: suggest

text: that

text: GJ

text: tometry,

text: but

text: a

text: strong

text: peak

text: is

text: visible

text: in

text: the

text: periodogram

text: odd

text: color

text: behavior

text: as

text: activity

text: changes

text: may

text: be

text: due

text: for

text: each

text: of

text: these

text: ﬁve

text: contiguous

text: sub-blocks.

text: We

text: mea-

text: to

text: the

text: interplay

text: between

text: dark

text: star

text: spots

text: and

text: the

text: faculae

text: sured

text: the

text: location

text: of

text: the

text: peak

text: of

text: each

text: of

text: these

text: ﬁve

text: pe-

text: that

text: surround

text: them.

text: It

text: may

text: be

text: the

text: case

text: that

text: diﬀerent

text: riodograms

text: and

text: ﬁnd

text: the

text: mean

text: and

text: standard

text: deviation

text: activity

text: cycles

text: have

text: diﬀerent

text: proportions

text: of

text: star

text: spots

text: of

text: the

text: mean

text: to

text: be

text: d,

text: which

text: we

text: interpret

text: as

text: and

text: faculae.

text: GJ

text: stellar

text: activity

text: cycles

text: be

text: further

text: GJ

text: rotation

text: period

text: and

text: the

text: uncertainty

text: on

text: that

text: studied

text: by

text: continuing

text: long-term

text: stellar

text: monitoring

text: of

text: GJ

text: parameter.


text: HST/STIS Observations of GJ436b 9 7200 9000 9000 Visit 1 Visit 1 Visit 2 Visit 2 8500 8500 7000 8000 8000 6800 7500 7500 7000 7000 6600 6500 6500 6000 6000 6400 5000 6000 7000 8000 9000 10000 5800 5850 5900 5950 6000 7600 7650 7700 7750 7800 Wavelength (Å) Wavelength (Å) Wavelength (Å) Figure 6. Transmission spectra of GJ 436b from the indi- Figure 4. Left: Higher resolution binning around the Na absorption doublet (5890 & 5900 ˚A). Right: Higher resolu- vidual HST/STIS visits. Each data point is an average of 108 diﬀerent systematic models weighted by their evidence tion binning around the K absorption doublet (7667 & 7701 ˚A). Neither visits show any additional absorption at these (see Section 6). Both visits are in general agreement. wavelengths. tral trace in the dispersion direction. S1, S3, S4, and S5 are well-known parameters used to describe system- atics caused by HST’s low Earth orbit; HST is contin- 1.005 ually cycling through day-night temperature variations throughout its 90-minute orbit. This results in small changes in the telescope’s focus as components expand 1.000 and contract (Hasan & Bely 1994; Sing et al. 2013). S2 accounts for a visit-long linear change in the measured 0.995 ﬂux from the star and is similarly thought to be an eﬀect from the telescope itself. S3 and S4 are found through a linear ﬁt to the spectral trace before image rectiﬁcation. 0.990 S5 is found through the cross-correlation of the spec- trum with a reference spectrum (in this case the fringe 0.985 ﬂat) in the cross-dispersion direction during 1D spectral extraction. Each covariate is ﬁt with diﬀerent orders of polyno- 0.980 -0.08 -0.04 0.0 0.04 0.08 mial: S1 is ﬁt from 1st up to 4th order, which previ- Days from Transit Center ous STIS studies have shown to adequately capture this trend (e.g., Sing et al. 2013; Nikolov et al. 2014). S2 is Figure 5. Fits to the raw data for two diﬀerent models for kept as a 1st order linear trend, as we ﬁnd no evidence of the systematics. The solid blue line is a ﬁt to the raw data a quadratic variation in ﬂux with time and such a vari- in a wavelength bin from 7721 to 8210 ˚A from visit 1 (blue ation would be degenerate with the transit model. S3, points) using the most complex systematics model: 4th order S4, and S5 are all ﬁt up to 2nd order. As we show be- polynomial ﬁt to S1, 1st order ﬁt to S2, and 2nd order ﬁt to low, our analysis and previous analyses have not found it S3, S4, and S5 (see text for details). The blue dashed line is a ﬁt to the visit 1 raw data only using a 1st order ﬁt to S1 justiﬁed to include any higher orders. Each systematic and S2. The red lines and points are the same as above, but model is then used to ﬁt the data as described in Sec- for visit 2, oﬀset by -0.01. tion 3, resulting in 108 diﬀerent ﬁts to the data. Figure 5 shows the diﬀerence in the ﬁt using the least versus data: S1) HST orbital phase S2) Time S3) the posi- the most complex systematics model for each visit. The tion of the spectral trace in the spatial direction S4) evidence-of-ﬁt, or the marginal likelihood, of each model Slope of the spectral trace S5) the position of the spec- is calculated in order to compare each of the models. xulF dezillamroN )mpp( htpeD tisnarT )mpp( htpeD tisnarT )mpp( htpeD tisnarT ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine##

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text: three decades have led to greater accessibility to advanced imaging techniques in clinical practice and research settings. Such technologies include magnetic resonance imaging (MRI), dual-energy X-ray absorptiometry, ultrasonography and computed tomography. They are widely used by clinicians to scan body segments to diagnose injury or disease [8, 9]. These imaging techniques are also used by researchers interested in studies of human anatomy and physiology in health and disease across the lifespan. These techniques produce precise, high-quality distinctions between diﬀerent tissue and cell types. In computer vision analysis and medical imaging, semantic segmentation is an attempt to partition meaningful parts that belong to the same object class of an image together and is mostly applied in object detection and localization [10, 11]. In this work, ﬁve state-of-the-art semantic segmentation deep learning architectures for regions of interest (ROI) in MRI of thigh muscles are reviewed. The signiﬁcant contributions of this work are: 1. To provide a review of current state-of-the-art image processing, tradi- tional machine learning and deep learning approaches for segmentation of MRI thigh muscles. 2. We present the largest dataset of MRI thigh muscles with annotated ROI that consists of quadriceps, bone and marrow as ground truths from the experts. 3. To date, this is the ﬁrst time deep learning methods are used to segment the ROI from the MRI of thigh muscles and results are compared with the traditional methods. 4. We propose a post-processing technique which helps in further reﬁnement of segmentation of ROI in MRI of thigh muscles. 2. Related Work From 2002 until 2015, twelve automated segmentation attempts on the MRI thigh muscles have been recorded [12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23]), 3

text: three

text: decades

text: have

text: led

text: to

text: greater

text: accessibility

text: to

text: advanced

text: imaging

text: techniques

text: in

text: clinical

text: practice

text: and

text: research

text: settings.

text: Such

text: technologies

text: include

text: magnetic

text: resonance

text: imaging

text: (MRI),

text: dual-energy

text: X-ray

text: absorptiometry,

text: ultrasonography

text: and

text: computed

text: tomography.

text: They

text: are

text: widely

text: used

text: by

text: clinicians

text: to

text: scan

text: body

text: segments

text: to

text: diagnose

text: injury

text: or

text: disease

text: These

text: imaging

text: techniques

text: are

text: also

text: used

text: by

text: researchers

text: interested

text: in

text: studies

text: of

text: human

text: anatomy

text: and

text: physiology

text: in

text: health

text: and

text: disease

text: across

text: the

text: lifespan.

text: These

text: techniques

text: produce

text: precise,

text: high-quality

text: distinctions

text: between

text: diﬀerent

text: tissue

text: and

text: cell

text: types.

text: In

text: computer

text: vision

text: analysis

text: and

text: medical

text: imaging,

text: semantic

text: segmentation

text: is

text: an

text: attempt

text: to

text: partition

text: meaningful

text: parts

text: that

text: belong

text: to

text: the

text: same

text: object

text: class

text: of

text: an

text: image

text: together

text: and

text: is

text: mostly

text: applied

text: in

text: object

text: detection

text: and

text: localization

text: In

text: this

text: work,

text: ﬁve

text: state-of-the-art

text: semantic

text: segmentation

text: deep

text: learning

text: architectures

text: for

text: regions

text: of

text: interest

text: (ROI)

text: in

text: MRI

text: of

text: thigh

text: muscles

text: are

text: reviewed.

text: The

text: signiﬁcant

text: contributions

text: of

text: this

text: work

text: are:

text: To

text: provide

text: a

text: review

text: of

text: current

text: state-of-the-art

text: image

text: processing,

text: tradi-

text: tional

text: machine

text: learning

text: and

text: deep

text: learning

text: approaches

text: for

text: segmentation

text: of

text: MRI

text: thigh

text: muscles.

text: We

text: present

text: the

text: largest

text: dataset

text: of

text: MRI

text: thigh

text: muscles

text: with

text: annotated

text: ROI

text: that

text: consists

text: of

text: quadriceps,

text: bone

text: and

text: marrow

text: as

text: ground

text: truths

text: from

text: the

text: experts.

text: To

text: date,

text: this

text: is

text: the

text: ﬁrst

text: time

text: deep

text: learning

text: methods

text: are

text: used

text: to

text: segment

text: the

text: ROI

text: from

text: the

text: MRI

text: of

text: thigh

text: muscles

text: and

text: results

text: are

text: compared

text: with

text: the

text: traditional

text: methods.

text: We

text: propose

text: a

text: post-processing

text: technique

text: which

text: helps

text: in

text: further

text: reﬁnement

text: of

text: segmentation

text: of

text: ROI

text: in

text: MRI

text: of

text: thigh

text: muscles.

text: Related

text: Work

text: From

text: until

text: twelve

text: automated

text: segmentation

text: attempts

text: on

text: the

text: MRI

text: thigh

text: muscles

text: have

text: been

text: recorded


text: and analysis were done to all muscles, individually, on MRI of the thigh. In 1992, Morrison et al. [29] made an attempt on MRI thigh segmentation by using neural network. The network model integrates a probabilistic neural network to facilitate the generation of probability estimates at each pixel for use in an iterative segmentation process. This preliminary study on MRI thigh segmentation by using one of the simplest forms of neural network reported that the segmentation result is unaﬀected by the quality of the training dataset. Today, the concept of neural network has been revolutionised and diversely applied, including in segmentation of medical imaging. Recently, deep learning has provided various end-to-end solutions for the semantic segmentation of abnormalities such as breast cancer, brain tumour, skin lesions, foot ulcers in various image modalities of medical imaging [30, 31, 32]. At the time of writing, there is no other study has been made in the segmentation of MR images of human thigh muscles with deep learning methods. Current state-of-the-art methods, especially image processing based techniques, are not robust, due to their nature of reliance on speciﬁc regulators and rules, with certain assumptions. In contrast to conventional machine learning, deep learning methods do not require such strong assumptions and have demonstrated superiority in region and object segmentation and classiﬁcation, which suggests that the robust fully automated MRI segmentation of human thigh muscles may be achieved, by adopting such approach. Moreover, the segmentation output performance from most recent applications of network models in MRI of diﬀerent domains [33, 34, 35], in association with image processing technique [36] and in conjunction with the utilization of better and upgradable graphics processing unit (GPU), is remarkably accurate and fast. 3. Experiments This section discusses the selection and labelling of datasets of MRI of thigh muscles, the preparation of the ground truth image and object labelling and the proposed methods for experimentation of semantic segmentation. 3.1. MRI Datasets of Thigh Muscles 7

text: and

text: analysis

text: were

text: done

text: to

text: all

text: muscles,

text: individually,

text: on

text: MRI

text: of

text: the

text: thigh.

text: In

text: Morrison

text: et

text: al.

text: made

text: an

text: attempt

text: on

text: MRI

text: thigh

text: segmentation

text: by

text: using

text: neural

text: network.

text: The

text: network

text: model

text: integrates

text: a

text: probabilistic

text: neural

text: network

text: to

text: facilitate

text: the

text: generation

text: of

text: probability

text: estimates

text: at

text: each

text: pixel

text: for

text: use

text: in

text: an

text: iterative

text: segmentation

text: process.

text: This

text: preliminary

text: study

text: on

text: MRI

text: thigh

text: segmentation

text: by

text: using

text: one

text: of

text: the

text: simplest

text: forms

text: of

text: neural

text: network

text: reported

text: that

text: the

text: segmentation

text: result

text: is

text: unaﬀected

text: by

text: the

text: quality

text: of

text: the

text: training

text: dataset.

text: Today,

text: the

text: concept

text: of

text: neural

text: network

text: has

text: been

text: revolutionised

text: and

text: diversely

text: applied,

text: including

text: in

text: segmentation

text: of

text: medical

text: imaging.

text: Recently,

text: deep

text: learning

text: has

text: provided

text: various

text: end-to-end

text: solutions

text: for

text: the

text: semantic

text: segmentation

text: of

text: abnormalities

text: such

text: as

text: breast

text: cancer,

text: brain

text: tumour,

text: skin

text: lesions,

text: foot

text: ulcers

text: in

text: various

text: image

text: modalities

text: of

text: medical

text: imaging

text: At

text: the

text: time

text: of

text: writing,

text: there

text: is

text: no

text: other

text: study

text: has

text: been

text: made

text: in

text: the

text: segmentation

text: of

text: MR

text: images

text: of

text: human

text: thigh

text: muscles

text: with

text: deep

text: learning

text: methods.

text: Current

text: state-of-the-art

text: methods,

text: especially

text: image

text: processing

text: based

text: techniques,

text: are

text: not

text: robust,

text: due

text: to

text: their

text: nature

text: of

text: reliance

text: on

text: speciﬁc

text: regulators

text: and

text: rules,

text: with

text: certain

text: assumptions.

text: In

text: contrast

text: to

text: conventional

text: machine

text: learning,

text: deep

text: learning

text: methods

text: do

text: not

text: require

text: such

text: strong

text: assumptions

text: and

text: have

text: demonstrated

text: superiority

text: in

text: region

text: and

text: object

text: segmentation

text: and

text: classiﬁcation,

text: which

text: suggests

text: that

text: the

text: robust

text: fully

text: automated

text: MRI

text: segmentation

text: of

text: human

text: thigh

text: muscles

text: may

text: be

text: achieved,

text: by

text: adopting

text: such

text: approach.

text: Moreover,

text: the

text: segmentation

text: output

text: performance

text: from

text: most

text: recent

text: applications

text: of

text: network

text: models

text: in

text: MRI

text: of

text: diﬀerent

text: domains

text: in

text: association

text: with

text: image

text: processing

text: technique

text: and

text: in

text: conjunction

text: with

text: the

text: utilization

text: of

text: better

text: and

text: upgradable

text: graphics

text: processing

text: unit

text: (GPU),

text: is

text: remarkably

text: accurate

text: and

text: fast.

text: Experiments

text: This

text: section

text: discusses

text: the

text: selection

text: and

text: labelling

text: of

text: datasets

text: of

text: MRI

text: of

text: thigh

text: muscles,

text: the

text: preparation

text: of

text: the

text: ground

text: truth

text: image

text: and

text: object

text: labelling

text: and

text: the

text: proposed

text: methods

text: for

text: experimentation

text: of

text: semantic

text: segmentation.

text: MRI

text: Datasets

text: of

text: Thigh

text: Muscles