The optical variability of Supermassive Black Hole Binary Candidate   PG1302-102: Periodicity and perturbation in the light curve

Andjelka B. Kovacevic; Luka C. Popovic; Sasa Simic; Dragana Ilic

arXiv:1812.03370·astro-ph.HE·January 30, 2019

The optical variability of Supermassive Black Hole Binary Candidate PG1302-102: Periodicity and perturbation in the light curve

Andjelka B. Kovacevic, Luka C. Popovic, Sasa Simic, Dragana Ilic

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TL;DR

This study models the optical light curve of PG1302-102, a supermassive black hole binary candidate, showing that perturbations can explain observed periodicity fluctuations and predicting a slightly longer period consistent with observations.

Contribution

The paper introduces a physical model with disk perturbations that explains the light curve variability and period fluctuations of PG1302-102, supporting its binary black hole nature.

Findings

01

Model reproduces observed light curve with perturbation.

02

Predicted period of about 1899 days aligns with observations.

03

Periodic fluctuations are confirmed by hybrid periodicity detection.

Abstract

The photometric light curve of PG1302-102 shows periodic variability which makes this object one of the most plausible supermassive black hole binary candidate. Interestingly, the most recent study of its updated optical light curve reports a decrease in significance of periodicity which may suggest that the binary model is less favorable. Here, we model the PG 1302-102 light curve, spanning almost 20 years, with a supermassive black hole binary system in which a perturbation in the accretion disk of more massive component is present. Our model reproduces well the observed light curve with a slight perturbation of a sinusoidal feature and predicts that a slightly larger period than previously reported, of about 1899 days, could arise due to a cold spot in the disk of {\bf more massive} component of a close, unequal-mass ( $\frac{m _{1}}{m _{2}} = 0.1$ ) black hole binary…

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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