Simulation of polarimetric effects in planetary system HD 189733
In this paper we present results of linear polarization modelling for HD 189733 in the U filter using the Monte Carlo method. Our simulations are based on the well known effect that linear polarization of a entrosymmetri unresolved star becomes non-zero during the planet transit or in the presene of...
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Головна астрономічна обсерваторія НАН України
2012
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| Цитувати: | Simulation of polarimetric effects in planetary system HD 189733 / K. Frantseva, N.M. Kostogryz, T.M. Yakobchuk // Advances in Astronomy and Space Physics. — 2012. — Т. 2., вип. 2. — С. 146-148. — Бібліогр.: 11 назв. — англ. |
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irk-123456789-1191872017-06-05T03:03:27Z Simulation of polarimetric effects in planetary system HD 189733 Frantseva, K. Kostogryz, N.M. Yakobchuk, T.M. In this paper we present results of linear polarization modelling for HD 189733 in the U filter using the Monte Carlo method. Our simulations are based on the well known effect that linear polarization of a entrosymmetri unresolved star becomes non-zero during the planet transit or in the presene of spots on its surface. HD 189733 is urrently the brightest (mᵥ = 7.67ᵐ ) known star to harbour a transiting exoplanet. This fat, along with the short orbital period (2.2 d), makes it very suitable for different types of observations in luding polarimetry. Sine we are interested in oultation effects, a very important parameter is the ratio of the planet to star radii, which is also very large (0.15). As the host star is active and spots may over up to 1% of the planetary surfae, we perform our simulations for different spot parameters such as sizes, locations on the stellar disk, and temperatures. 2012 Article Simulation of polarimetric effects in planetary system HD 189733 / K. Frantseva, N.M. Kostogryz, T.M. Yakobchuk // Advances in Astronomy and Space Physics. — 2012. — Т. 2., вип. 2. — С. 146-148. — Бібліогр.: 11 назв. — англ. 2227-1481 http://dspace.nbuv.gov.ua/handle/123456789/119187 en Advances in Astronomy and Space Physics Головна астрономічна обсерваторія НАН України |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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In this paper we present results of linear polarization modelling for HD 189733 in the U filter using the Monte Carlo method. Our simulations are based on the well known effect that linear polarization of a entrosymmetri unresolved star becomes non-zero during the planet transit or in the presene of spots on its surface. HD 189733 is urrently the brightest (mᵥ = 7.67ᵐ ) known star to harbour a transiting exoplanet. This fat, along with the short orbital period (2.2 d), makes it very suitable for different types of observations in luding polarimetry. Sine we are interested in oultation effects, a very important parameter is the ratio of the planet to star radii, which is also very large (0.15). As the host star is active and spots may over up to 1% of the planetary surfae, we perform our simulations for different spot parameters such as sizes, locations on the stellar disk, and temperatures. |
| format |
Article |
| author |
Frantseva, K. Kostogryz, N.M. Yakobchuk, T.M. |
| spellingShingle |
Frantseva, K. Kostogryz, N.M. Yakobchuk, T.M. Simulation of polarimetric effects in planetary system HD 189733 Advances in Astronomy and Space Physics |
| author_facet |
Frantseva, K. Kostogryz, N.M. Yakobchuk, T.M. |
| author_sort |
Frantseva, K. |
| title |
Simulation of polarimetric effects in planetary system HD 189733 |
| title_short |
Simulation of polarimetric effects in planetary system HD 189733 |
| title_full |
Simulation of polarimetric effects in planetary system HD 189733 |
| title_fullStr |
Simulation of polarimetric effects in planetary system HD 189733 |
| title_full_unstemmed |
Simulation of polarimetric effects in planetary system HD 189733 |
| title_sort |
simulation of polarimetric effects in planetary system hd 189733 |
| publisher |
Головна астрономічна обсерваторія НАН України |
| publishDate |
2012 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/119187 |
| citation_txt |
Simulation of polarimetric effects in planetary system HD 189733 / K. Frantseva, N.M. Kostogryz, T.M. Yakobchuk // Advances in Astronomy and Space Physics. — 2012. — Т. 2., вип. 2. — С. 146-148. — Бібліогр.: 11 назв. — англ. |
| series |
Advances in Astronomy and Space Physics |
| work_keys_str_mv |
AT frantsevak simulationofpolarimetriceffectsinplanetarysystemhd189733 AT kostogryznm simulationofpolarimetriceffectsinplanetarysystemhd189733 AT yakobchuktm simulationofpolarimetriceffectsinplanetarysystemhd189733 |
| first_indexed |
2025-07-08T15:23:29Z |
| last_indexed |
2025-07-08T15:23:29Z |
| _version_ |
1837092795572027392 |
| fulltext |
Simulation of polarimetri
e�e
ts in planetarysystem HD189733K.Frantseva1∗, N.M.Kostogryz2, T.M.Yakob
huk2
Advan
es in Astronomy and Spa
e Physi
s, 2, 146-148 (2012)
© K.Frantseva, N.M.Kostogryz, T.M.Yakob
huk, 2012
1Taras Shev
henko National University of Kyiv, Glushkova ave., 4, 03127, Kyiv, Ukraine
2Main Astronomi
al Observatory of the National A
ademy of S
ien
es of Ukraine, Zabolotnoho 27, 03680, Kyiv, UkraineIn this paper we present results of linear polarization modelling for HD189733 in the U �lter using the MonteCarlo method. Our simulations are based on the well known e�e
t that linear polarization of a
entrosymmetri
unresolved star be
omes non-zero during the planet transit or in the presen
e of spots on its surfa
e. HD189733is
urrently the brightest (mV = 7.67
m) known star to harbour a transiting exoplanet. This fa
t, along with theshort orbital period (2.2 d), makes it very suitable for di�erent types of observations in
luding polarimetry. Sin
ewe are interested in o
ultation e�e
ts, a very important parameter is the ratio of the planet to star radii, whi
h isalso very large (0.15). As the host star is a
tive and spots may
over up to 1% of the planetary surfa
e, we performour simulations for di�erent spot parameters su
h as sizes, lo
ations on the stellar disk, and temperatures.Key words: polarization, HD189733, methods: numeri
al; planetary systemintrodu
tionMore than 700 exoplanets have been dis
overed todate and substantial e�orts are taken to determinethe
hara
teristi
s of these obje
ts.There are several su
essful methods for dete
tingand studying exoplanets su
h as the radial velo
ityte
hnique, transit photometry, mi
rolensing and soon. All of them have their pros and
ons, whi
hjusti�es the development of other te
hniques. Todete
t the polarization of the very weak �ux that
omes from exoplanets, the polarimeter must be ex-
eedingly sensitive. A
ording to theoreti
al predi
-tions, the polarimeter sensitivity should be at least
10−6 [9℄ to enable the dete
tion of the polarizationfrom the planetary atmosphere.In 2008 Berdyugina et al. [1℄ reported on the pos-sible dete
tion of polarized s
attered light in plane-tary atmosphere HD189733b. They performed po-larimetri
measurements of the orbital period in theB �lter, and obtained two polarization maxima nearelongation with an amplitude of ∼ 2 × 10−4. How-ever, Lu
as et al. [8℄
onsidered this value to betoo high for the planet and proposed that it
ouldalso be explained by the stellar a
tivity. In 2011Berdyugina et al. [2℄
on�rmed these results andshowed that polarization from the spots
an rea
hup to ∼ 3 × 10−6 and that the variations of lin-ear polarization obtained from observations
annotbe explained by spots. In all these papers the en-tire phase
urve was analysed, but linear polariza-tion arising during the planetary transit were not
taken into a
ount. Kostogryz et al. [6℄ obtainedlinear polarization (Stokes parameters Q and U) forHD189733 that appears during the planetary transitusing the Chandrasekhar's data [4℄, whi
h is similarin magnitude to the Berdyugina et al. [1℄ results. Inthis study we present the results of modelling the po-larization resulting from the planetary transits andstellar spots in the system HD189733, using the solarpolarization [10℄.the method of
al
ulationsThis method was thoroughly des
ribed by Car-
io� & Magalhães [3℄, Kostogryz et al. [6℄ and Kos-togryz et al. [7℄. Here we brie�y summarise only themain points of the simulations.For a given set of parameters (e. g., planetary-to-star radii ratio, semi-major axes and position onthe stellar disk) des
ribing
on�guration of the star-planet system, the following pro
edure was adopted.Ea
h photon pa
ket (PP), emitted from a randomlysele
ted point on the stellar surfa
e towards the ob-server, is determined by the weight:
εi =
f(µ)L∗
N
,where L∗ is the luminosity of the star, N is the num-ber of iterations, and f(µ) is a limb darkening law[5℄, whi
h depends on the wavelength, spe
tral type,surfa
e gravity, and metalli
ity.The weight indi
ates the radiation emanatingfrom the star and rea
hing the observer. In addi-
∗gagarin�f�gmail.
om 146
Advan
es in Astronomy and Spa
e Physi
s K. Frantseva, N.M.Kostogryz, T.M.Yakob
huktion, PP is
hara
terised by linear polarization:
Qi = εiP (µ) cos(2ϕ),
Ui = −εiP (µ) sin(2ϕ),where P (µ) is the
entre-limb
ontinuum linear po-larization
al
ulated in [10℄.For PP emitted in the hemisphere opposite tothe observer the weight is equal to zero. On theother hand, when PP is emitted from the visiblehemisphere, we
an determine whether its traje
tory
rosses the planet or the spot. The latter ones absorbthe photon pa
ket and it is given a zero weight.After N iterations the �ux and Stokes parameters
an be found from the following formulae:
Fψ =
∑
N
εi, qψ =
∑
N
Qi
Fψ
, uψ =
∑
N
Ui
Fψ
,where the index ψ indi
ates the position of theplanet. F , q and u are
al
ulated using time intervalsfor di�erent positions of the planet.Assuming di�erent parameters of the spots su
has temperature, size and
oordinates, we evaluatedthe �ux and polarization variations resulting fromstellar a
tivity.results and
on
lusionsWe present the results of Monte-Carlo simulationsof �ux and linear polarization due to a planetarytransit and the presen
e of spots on the stellar sur-fa
e.Figure 1 shows the �ux, Stokes parameters (Qand U) and polarization degree in the U band. Itshould be mentioned that in [6℄ similar simulationsfor a planetary transit are des
ribed, but their resultsdi�er from those obtained here due to the di�eren
esin the
entre-to-limb stellar polarization and �ltersadopted. Kostogryz et al. [6℄ used Chandrasekhar's
entre-to-limb polarization [4℄ and limb darkeninglaw for B �lter as it was shown there that 3D mod-elling of the solar polarization [10℄ is not very suit-able for late spe
tral type stars. On the other hand,
Chandrasekhar's data are inappropriate for
ool late-type star as well. In this paper, we use the solar po-larization [10℄ for our simulations as any other
al
u-lations of
entre-to-limb polarization for
ooler starsdoes not exist. Therefore, the next step of our studyshould be the simulation of the
entre-to-limb polar-ization for
ooler atmospheres.As it was shown in [11℄, HD189733 is an a
tivestar and spots
an
over up to 1% of the stellar sur-fa
e. Figs. 2-8 show the same parameters as in Fig. 1but for di�erent positions of starspots.The largest value of the polarization degree isfound for the
ase when only one spot is present
overing an area of about 1% of the stellar surfa
e.When this 1% area is divided into 10 spots, the po-larization be
omes very small.We thus show that the in�uen
e of spots onthe total polarization for HD189733 is too small as
ompared to that resulting from the planet transit,
∼ 3 · 10−6 that is the same as in [2℄. These resultsne
essitate further planetary transit observations inorder to a
hieve better statisti
s and polarimetri
a
-
ura
y.referen
es[1℄ Berdyugina S.V., BerdyuginA.V., Fluri D.M. & Pi-irola V. 2008, ApJ, 673, L83[2℄ Berdyugina S.V., BerdyuginA.V., Fluri D.M. & Pi-irola V. 2011, ApJ, 728, L6[3℄ Car
io�A.C. & Magalhães A.M. 2005, ApJ, 635, 570[4℄ Chandrasekhar S., 1950, `Radiative Transfer', Oxford,Clarendon Press[5℄ Claret A. 2000, A&A, 363, 1081[6℄ KostogryzN.M., Yakob
hukT.M., MorozhenkoO.V. &Vid'ma
henkoA.P. 2011, MNRAS, 415, 695[7℄ KostogryzN. M., Yakob
hukT.M. & Vidma
henkoA.P.2012, IAU Symposium, 282, 209[8℄ Lu
as P.W., Hough J.H., Bailey J. A. et al. 2009, MN-RAS, 393, 229[9℄ Seager S., WhitneyB. A. & SasselovD.D. 2000, ApJ,540, 504[10℄ Trujillo Bueno J. & Sh
hukinaN. 2009, ApJ, 694, 1364[11℄ WinnJ. N., NoyesR.W., HolmanM. J. et al. 2005, ApJ,631, 1215
147
Advan
es in Astronomy and Spa
e Physi
s K. Frantseva, N.M.Kostogryz, T.M.Yakob
huk
0
1.5
3
4.5
6
7.5
0.03 0.06 0.09 0.12
p,
1
0-6
t, days
-6
-3
0
3
6
u,
1
0-6
-1.5
0
1.5
q,
1
0-6
0.97
0.98
0.99
1
F
lu
x
-1
-0.5
0
0.5
1
r
/
R
*
HD189733
Fig. 1: Modelling planettransit in U band withoutspots.
0
2
4
6
8
0.03 0.06 0.09 0.12
p,
1
0-6
t, days
-3
0
3
6
9
u,
1
0-6
0
1.5
3
q,
1
0-6
0.97
0.98
0.99
1
F
lu
x
-1
-0.5
0
0.5
1
r
/
R
*
HD189733
Fig. 2: Modelling planettransit in U band with 1spot at latitude from -20◦to -50◦.
0
2
4
6
0.03 0.06 0.09 0.12
p,
1
0-6
t, days
-6
-3
0
3
6
u,
1
0-6
-1
0
1
2
q,
1
0-6
0.97
0.98
0.99
1
F
lu
x
-1
-0.5
0
0.5
1
r
/
R
*
HD189733
Fig. 3: Modelling planettransit in U band with 10spots at latitude from -20◦to -50◦.
0
3
6
9
0.03 0.06 0.09 0.12
p,
1
0-6
t, days
-9
-6
-3
0
3
u,
1
0-6
-1.2
0
1.2
2.4
q,
1
0-6
0.97
0.98
0.99
1
F
lu
x
-1
-0.5
0
0.5
1
r
/
R
*
HD189733
Fig. 4: Modelling planettransit in U band with 1spot at latitude from 20◦ to50◦.
0
1.7
3.4
5.1
6.8
0.03 0.06 0.09 0.12
p,
1
0-6
t, days
-6
-3
0
3
6
u,
1
0-6
-1.2
0
1.2
2.4
q,
1
0-6
0.97
0.98
0.99
1
F
lu
x
-1
-0.5
0
0.5
1
r
/
R
*
HD189733
Fig. 5: Modelling planettransit in U band with 10spots at latitude from 20◦to 50◦.
0
2
4
6
0.03 0.06 0.09 0.12
p,
1
0-6
t, days
-6
-3
0
3
6
u,
1
0-6
-1.3
0
1.3
q,
1
0-6
0.97
0.98
0.99
1
F
lu
x
-1
-0.5
0
0.5
1
r
/
R
*
HD189733
Fig. 6: Modelling planettransit in U band with 10spots at latitude from -50◦to 50◦.
0
2
4
6
0 2 4 6 8 10
p,
1
0-6
t, days
-6
-3
0
3
6
u,
1
0-6
-1
0
1
2
q,
1
0-6
0.97
0.98
0.99
1
F
lu
x
-1
-0.5
0
0.5
1
r
/
R
*
HD189733
Fig. 7: Modelling planettransit in U band with 10spots at latitude from -20◦to -50◦ and from 20◦ to 50◦during period of the star.
1.5
3
4.5
6
0 2 4 6 8 10
p,
1
0-6
t, days
-5
-2.5
0
2.5
5
u,
1
0-6
-2.4
-1.2
0
1.2
q,
1
0-6
0.97
0.98
0.99
1
F
lu
x
-1
-0.5
0
0.5
1
r
/
R
*
HD189733
Fig. 8: Modelling planettransit in U band with 10spots at latitude from -50◦to 50◦ during period of thestar.148
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