Loose Ends for the Exomoon Candidate Host Kepler-1625b

Alex Teachey; David Kipping; Christopher J. Burke; Ruth Angus; and; Andrew W. Howard

arXiv:1904.11896·astro-ph.EP·March 18, 2020

Loose Ends for the Exomoon Candidate Host Kepler-1625b

Alex Teachey, David Kipping, Christopher J. Burke, Ruth Angus, and, Andrew W. Howard

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TL;DR

This study critically examines the exomoon candidate in Kepler-1625b, exploring alternative explanations, data reduction differences, and the star's activity, ultimately questioning the original exomoon claim.

Contribution

It provides a detailed re-analysis of the Kepler-1625b data, highlighting the impact of data reduction methods and systematic effects on exomoon detection claims.

Findings

01

Flexible trend models can attenuate the exomoon signal.

02

The probability of a Neptune-sized planet causing the dip is less than 0.75%.

03

The star shows no significant stellar rotation period or false-positive signals.

Abstract

The claim of an exomoon candidate in the Kepler-1625b system has generated substantial discussion regarding possible alternative explanations for the purported signal. In this work we examine in detail these possibilities. First, the effect of more flexible trend models is explored and we show that sufficiently flexible models are capable of attenuating the signal, although this is an expected byproduct of invoking such models. We also explore trend models using X and Y centroid positions and show that there is no data-driven impetus to adopt such models over temporal ones. We quantify the probability that the 500 ppm moon-like dip could be caused by a Neptune-sized transiting planet to be < 0.75%. We show that neither autocorrelation, Gaussian processes nor a Lomb-Scargle periodogram are able to recover a stellar rotation period, demonstrating that K1625 is a quiet star with periodic…

Tables17

Table 1. Table 1: Additional AAS T e X symbols

$≲$	`\lesssim`, `\la`	$≳$	`\gtrsim`, `\ga`
µm	`\micron`	−	`\sbond`
=	`\dbond`	≡	`\tbond`
$☉$	`\sun`	$\oplus$	`\earth`
⌀	`\diameter`
°	`\arcdeg`, `\degr`	□	`\sq`
′	`\arcmin`	″	`\arcsec`
$\overset{d}{.}$	`\fd`	$\overset{h}{.}$	`\fh`
$\overset{m}{.}$	`\fm`	$\overset{s}{.}$	`\fs`
$\overset{\circ}{.}$	`\fdg`	$\overset{'}{.}$	`\farcm`
$\overset{''}{.}$	`\farcs`	$\overset{p}{.}$	`\fp`
½	`\onehalf`	UBVR	`\ubvr`
⅓	`\onethird`	U B	`\ub`
⅔	`\twothirds`	B V	`\bv`
¼	`\onequarter`	V R	`\vr`
¾	`\threequarters`	U R	`\ur`

Table 2. Table 2: Text-mode accents

ò	`\‘{o}`	ō	`\={o}`	o͡o	`\t{oo}`
ó	`\’{o}`	ȯ	`\.{o}`	o̧	`\c{o}`
ô	`\^{o}`	ŏ	`\u{o}`	ọ	`\d{o}`
ö	`\"{o}`	ǒ	`\v{o}`	o̱	`\b{o}`
õ	`\~{o}`	ő	`\H{o}`

Table 3. Table 3: National symbols

œ	`\oe`	å	`\aa`	ł	`\l`
Œ	`\OE`	Å	`\AA`	Ł	`\L`
æ	`\ae`	ø	`\o`	ß	`\ss`
Æ	`\AE`	Ø	`\O`

Table 4. Table 4: Math-mode accents

$\hat{a}$	`\hat{a}`	$\dot{a}$	`\dot{a}`
$\overset{ˇ}{a}$	`\check{a}`	$\ddot{a}$	`\ddot{a}`
$\tilde{a}$	`\tilde{a}`	$\overset{˘}{a}$	`\breve{a}`
$\overset{´}{a}$	`\acute{a}`	$\bar{a}$	`\bar{a}`
$\overset{`}{a}$	`\grave{a}`	$\vec{a}$	`\vec{a}`

Table 5. Table 5: Greek and Hebrew letters (math mode)

$α$	`\alpha`	$ν$	`\nu`
$β$	`\beta`	$ξ$	`\xi`
$γ$	`\gamma`	$o$	`o`
$δ$	`\delta`	$π$	`\pi`
$ϵ$	`\epsilon`	$ρ$	`\rho`
$ζ$	`\zeta`	$σ$	`\sigma`
$η$	`\eta`	$τ$	`\tau`
$θ$	`\theta`	$υ$	`\upsilon`
$ι$	`\iota`	$ϕ$	`\phi`
$κ$	`\kappa`	$χ$	`\chi`
$λ$	`\lambda`	$ψ$	`\psi`
$μ$	`\mu`	$ω$	`\omega`
$ϝ$	`\digamma`	$ϰ$	`\varkappa`
$ε$	`\varepsilon`	$ς$	`\varsigma`
$ϑ$	`\vartheta`	$φ$	`\varphi`
$ϱ$	`\varrho`
$Γ$	`\Gamma`	$Σ$	`\Sigma`
$Δ$	`\Delta`	$Υ$	`\Upsilon`
$Θ$	`\Theta`	$Φ$	`\Phi`
$Λ$	`\Lambda`	$Ψ$	`\Psi`
$Ξ$	`\Xi`	$Ω$	`\Omega`
$Π$	`\Pi`
$ℵ$	`\aleph`	$ℶ$	`\beth`
$ℷ$	`\gimel`	$ℸ$	`\daleth`

Table 6. Table 6: Binary operators (math mode)

$\pm$	`\pm`	$\cap$	`\cap`
$\mp$	`\mp`	$\cup$	`\cup`
$∖$	`\setminus`	$⊎$	`\uplus`
$\cdot$	`\cdot`	$⊓$	`\sqcap`
$\times$	`\times`	$⊔$	`\sqcup`
$*$	`\ast`	$◁$	`\triangleleft`
$⋆$	`\star`	$▷$	`\triangleright`
$⋄$	`\diamond`	$≀$	`\wr`
$\circ$	`\circ`	$○$	`\bigcirc`
$∙$	`\bullet`	$△$	`\bigtriangleup`
$\div$	`\div`	$▽$	`\bigtriangledown`
$⊲$	`\lhd`	$⊳$	`\rhd`
$\lor$	`\vee`	$⊙$	`\odot`
$\land$	`\wedge`	$†$	`\dagger`
$\oplus$	`\oplus`	$‡$	`\ddagger`
$⊖$	`\ominus`	$∐$	`\amalg`
$\otimes$	`\otimes`	$⊴$	`\unlhd`
$⊘$	`\oslash`	$⊵$	`\unrhd`

Table 7. Table 7: AMS binary operators (math mode)

$∔$	`\dotplus`	$⋉$	`\ltimes`
$∖$	`\smallsetminus`	$⋊$	`\rtimes`
$⋒$	`\Cap`, `\doublecap`	$⋋$	`\leftthreetimes`
$⋓$	`\Cup`, `\doublecup`	$⋌$	`\rightthreetimes`
$⊼$	`\barwedge`	$⋏$	`\curlywedge`
$⊻$	`\veebar`	$⋎$	`\curlyvee`
$⩞$	`\doublebarwedge`
$⊟$	`\boxminus`	$⊝$	`\circleddash`
$⊠$	`\boxtimes`	$⊛$	`\circledast`
$⊡$	`\boxdot`	$⊚$	`\circledcirc`
$⊞$	`\boxplus`	$∙$	`\centerdot`
$⋇$	`\divideontimes`	$⊺$	`\intercal`

Table 8. Table 8: Miscellaneous symbols

†	`\dag`	§	`\S`
©	`\copyright`	‡	`\ddag`
¶	`\P`	£	`\pounds`
#	`\#`	$	`\$`
%	`\%`	&	`\&`
_	`\_`	{	`\{`
}	`\}`

Table 9. Table 9: Miscellaneous symbols (math mode)

$ℵ$	`\aleph`	$'$	`\prime`
$ℏ$	`\hbar`	$\emptyset$	`\emptyset`
$ı$	`\imath`	$\nabla$	`\nabla`
$ȷ$	`\jmath`	$\sqrt$	`\surd`
$ℓ$	`\ell`	$⊤$	`\top`
$℘$	`\wp`	$⊥$	`\bot`
$ℜ$	`\Re`	$∥$	`\\|`
$ℑ$	`\Im`	$∠$	`\angle`
$\partial$	`\partial`	$△$	`\triangle`
$\infty$	`\infty`	$\$	`\backslash`
$□$	`\Box`	$◇$	`\Diamond`
$\forall$	`\forall`	$♯$	`\sharp`
$\exists$	`\exists`	$♣$	`\clubsuit`
$\neg$	`\neg`	$♢$	`\diamondsuit`
$♭$	`\flat`	$♡$	`\heartsuit`
$♮$	`\natural`	$♠$	`\spadesuit`
$℧$	`\mho`

Table 10. Table 10: AMS miscellaneous symbols (math mode)

$ℏ$	`\hbar`	$‵$	`\backprime`
$ℏ$	`\hslash`	$\emptyset$	`\varnothing`
$△$	`\vartriangle`	$▲$	`\blacktriangle`
$▽$	`\triangledown`	$▼$	`\blacktriangledown`
$□$	`\square`	$■$	`\blacksquare`
$◆$	`\lozenge`	$◆$	`\blacklozenge`
$Ⓢ$	`\circledS`	$★$	`\bigstar`
$∠$	`\angle`	$∢$	`\sphericalangle`
$∡$	`\measuredangle`
$∄$	`\nexists`	$∁$	`\complement`
$℧$	`\mho`	$ð$	`\eth`
$Ⅎ$	`\Finv`	$╱$	`\diagup`
$⅁$	`\Game`	$╲$	`\diagdown`
$𝕜$	`\Bbbk`	$↾$	`\restriction`

Table 11. Table 11: Arrows (math mode)

$\leftarrow$	`\leftarrow`	$⟵$	`\longleftarrow`
$\Leftarrow$	`\Leftarrow`	$⟸$	`\Longleftarrow`
$\to$	`\rightarrow`	$⟶$	`\longrightarrow`
$\Rightarrow$	`\Rightarrow`	$⟹$	`\Longrightarrow`
$\leftrightarrow$	`\leftrightarrow`	$⟷$	`\longleftrightarrow`
$\Leftrightarrow$	`\Leftrightarrow`	$⟺$	`\Longleftrightarrow`
$\mapsto$	`\mapsto`	$⟼$	`\longmapsto`
$↩$	`\hookleftarrow`	$↪$	`\hookrightarrow`
$↼$	`\leftharpoonup`	$⇀$	`\rightharpoonup`
$↽$	`\leftharpoondown`	$⇁$	`\rightharpoondown`
$⇌$	`\rightleftharpoons`	$↝$	`\leadsto`
$↑$	`\uparrow`	$⇕$	`\Updownarrow`
$⇑$	`\Uparrow`	$↗$	`\nearrow`
$↓$	`\downarrow`	$↘$	`\searrow`
$⇓$	`\Downarrow`	$↙$	`\swarrow`
$↕$	`\updownarrow`	$↖$	`\nwarrow`

Table 12. Table 12: AMS arrows (math mode)

$⇠$	`\dashleftarrow`	$⇢$	`\dashrightarrow`
$⇇$	`\leftleftarrows`	$⇉$	`\rightrightarrows`
$⇆$	`\leftrightarrows`	$⇄$	`\rightleftarrows`
$⇚$	`\Lleftarrow`	$⇛$	`\Rrightarrow`
$↞$	`\twoheadleftarrow`	$↠$	`\twoheadrightarrow`
$↢$	`\leftarrowtail`	$↣$	`\rightarrowtail`
$↫$	`\looparrowleft`	$↬$	`\looparrowright`
$⇋$	`\leftrightharpoons`	$⇌$	`\rightleftharpoons`
$↶$	`\curvearrowleft`	$↷$	`\curvearrowright`
$↺$	`\circlearrowleft`	$↻$	`\circlearrowright`
$↰$	`\Lsh`	$↱$	`\Rsh`
$⇈$	`\upuparrows`	$⇊$	`\downdownarrows`
$↿$	`\upharpoonleft`	$↾$	`\upharpoonright`
$⇃$	`\downharpoonleft`	$⇂$	`\downharpoonright`
$⊸$	`\multimap`	$↝$	`\rightsquigarrow`
$↭$	`\leftrightsquigarrow`
$↚$	`\nleftarrow`	$↛$	`\nrightarrow`
$⇍$	`\nLeftarrow`	$⇏$	`\nRightarrow`
$↮$	`\nleftrightarrow`	$⇎$	`\nLeftrightarrow`

Table 13. Table 13: Relations (math mode)

$\leq$	`\leq`	$\geq$	`\geq`
$≺$	`\prec`	$≻$	`\succ`
$⪯$	`\preceq`	$⪰$	`\succeq`
$≪$	`\ll`	$≫$	`\gg`
$\subset$	`\subset`	$\supset$	`\supset`
$\subseteq$	`\subseteq`	$\supseteq$	`\supseteq`
$⊏$	`\sqsubset`	$⊐$	`\sqsupset`
$⊑$	`\sqsubseteq`	$⊒$	`\sqsupseteq`
$\in$	`\in`	$∋$	`\ni`
$⊢$	`\vdash`	$⊣$	`\dashv`
$⌣$	`\smile`	$∣$	`\mid`
$⌢$	`\frown`	$∥$	`\parallel`
$\neq$	`\neq`	$⟂$	`\perp`
$\equiv$	`\equiv`	$≅$	`\cong`
$\sim$	`\sim`	$⋈$	`\bowtie`
$≃$	`\simeq`	$\propto$	`\propto`
$≍$	`\asymp`	$⊧$	`\models`
$\approx$	`\approx`	$≐$	`\doteq`
		$⨝$	`\Join`

Table 14. Table 14: AMS binary relations (math mode)

$≦$	`\leqq`	$≧$	`\geqq`
$⩽$	`\leqslant`	$⩾$	`\geqslant`
$⪕$	`\eqslantless`	$⪖$	`\eqslantgtr`
$≲$	`\lesssim`	$≳$	`\gtrsim`
$⪅$	`\lessapprox`	$⪆$	`\gtrapprox`
$≊$	`\approxeq`	$≂$	`\eqsim`
$⋖$	`\lessdot`	$⋗$	`\gtrdot`
$⋘$	`\lll`, `\llless`	$⋙$	`\ggg`, `\gggtr`
$≶$	`\lessgtr`	$≷$	`\gtrless`
$⋚$	`\lesseqgtr`	$⋛$	`\gtreqless`
$⪋$	`\lesseqqgtr`	$⪌$	`\gtreqqless`
$≑$	`\doteqdot`, `\Doteq`	$≖$	`\eqcirc`
$≓$	`\risingdotseq`	$≗$	`\circeq`
$≒$	`\fallingdotseq`	$≜$	`\triangleq`
$∽$	`\backsim`	$\sim$	`\thicksim`
$≌$	`\backsimeq`	$\approx$	`\thickapprox`
$⫅$	`\subseteqq`	$⫆$	`\supseteqq`
$⋐$	`\Subset`	$⋑$	`\Supset`
$⊏$	`\sqsubset`	$⊐$	`\sqsupset`
$≼$	`\preccurlyeq`	$≽$	`\succcurlyeq`
$⋞$	`\curlyeqprec`	$⋟$	`\curlyeqsucc`
$≾$	`\precsim`	$≿$	`\succsim`
$⪷$	`\precapprox`	$⪸$	`\succapprox`
$⊲$	`\vartriangleleft`	$⊳$	`\vartriangleright`
$⊴$	`\trianglelefteq`	$⊵$	`\trianglerighteq`
$⊨$	`\vDash`	$⊩$	`\Vdash`
$⊪$	`\Vvdash`
$⌣$	`\smallsmile`	$∣$	`\shortmid`
$⌢$	`\smallfrown`	$∥$	`\shortparallel`
$≏$	`\bumpeq`	$≬$	`\between`
$≎$	`\Bumpeq`	$⋔$	`\pitchfork`
$\propto$	`\varpropto`	$϶$	`\backepsilon`
$◀$	`\blacktriangleleft`	$▶$	`\blacktriangleright`
$∴$	`\therefore`	$∵$	`\because`

Table 15. Table 15: AMS negated relations (math mode)

$≮$	`\nless`	$≯$	`\ngtr`
$≰$	`\nleq`	$≱$	`\ngeq`
$⩽̸$	`\nleqslant`	$⩾̸$	`\ngeqslant`
$≦̸$	`\nleqq`	$≧̸$	`\ngeqq`
$⪇$	`\lneq`	$⪈$	`\gneq`
$≨$	`\lneqq`	$≩$	`\gneqq`
$≨$	`\lvertneqq`	$≩$	`\gvertneqq`
$⋦$	`\lnsim`	$⋧$	`\gnsim`
$⪉$	`\lnapprox`	$⪊$	`\gnapprox`
$⊀$	`\nprec`	$⊁$	`\nsucc`
$⋠$	`\npreceq`	$⋡$	`\nsucceq`
$⪵$	`\precneqq`	$⪶$	`\succneqq`
$⋨$	`\precnsim`	$⋩$	`\succnsim`
$⪹$	`\precnapprox`	$⪺$	`\succnapprox`
$≁$	`\nsim`	$≇$	`\ncong`
$∤$	`\nshortmid`	$∦$	`\nshortparallel`
$∤$	`\nmid`	$∦$	`\nparallel`
$⊬$	`\nvdash`	$⊭$	`\nvDash`
$⊮$	`\nVdash`	$⊯$	`\nVDash`
$⋪$	`\ntriangleleft`	$⋫$	`\ntriangleright`
$⋬$	`\ntrianglelefteq`	$⋭$	`\ntrianglerighteq`
$⊈$	`\nsubseteq`	$⊉$	`\nsupseteq`
$⫅̸$	`\nsubseteqq`	$⫆̸$	`\nsupseteqq`
$⊊$	`\subsetneq`	$⊋$	`\supsetneq`
$⊊$	`\varsubsetneq`	$⊋$	`\varsupsetneq`
$⫋$	`\subsetneqq`	$⫌$	`\supsetneqq`
$⫋$	`\varsubsetneqq`	$⫌$	`\varsupsetneqq`

Table 16. Table 16: Variable-sized symbols (math mode)

$\begin{matrix} \sum & \sum & \sum & ⋂ & ⋂ & \bigcap \\ \prod & \prod & \prod & ⋃ & ⋃ & \bigcup \\ ∐ & ∐ & \coprod & ⨆ & ⨆ & \bigsqcup \\ \int & \int & \int & ⋁ & ⋁ & \bigvee \\ \oint & \oint & \oint & ⋀ & ⋀ & \bigwedge \\ ⨀ & ⨀ & \bigodot & ⨂ & ⨂ & \bigotimes \\ ⨁ & ⨁ & \bigoplus & ⨄ & ⨄ & \biguplus \end{matrix}$

Table 17. Table 17: Delimiters (math mode)

$($	`(`	$)$	`)`
$[$	`[`	$]$	`]`
${$	`\{`	$}$	`\}`
$⌊$	`\lfloor`	$⌋$	`\rfloor`
$⌈$	`\lceil`	$⌉$	`\rceil`
$⟨$	`\langle`	$⟩$	`\rangle`
$/$	`/`	$\$	`\backslash`
$\|$	`\vert`	$∥$	`\Vert`
$↑$	`\uparrow`	$⇑$	`\Uparrow`
$↓$	`\downarrow`	$⇓$	`\Downarrow`
$↕$	`\updownarrow`	$⇕$	`\Updownarrow`
$⌜$	`\ulcorner`	$⌝$	`\urcorner`
$⌞$	`\llcorner`	$⌟$	`\lrcorner`

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