We present observations of the symbiotic star CH Cyg with a new JHK-band beam combiner mounted to the IOTA interferometer. The new beam combiner consists of an anamorphic cylindrical lens system and a grism, and allows the simultaneous recording of spectrally dispersed J-, H- and K-band Michelson interferograms. The observations of CH Cyg were conducted on 5, 6, 8 and 11 June 2001 using baselines of 17m to 25m. From the interferograms of CH Cyg, J-, H-, and K-band visibility functions can be determined. Uniform-disk fits to the visibilities give, e.g., stellar diameters of (7.8 ± 0.6) mas and (8.7 ± 0.8) mas in H and K, respectively. Angular stellar filter radii and Rosseland radii are derived from the measured visibilities by fitting theoretical center-to-limb intensity variations (CLVs) of Mira star models. The available HIPPARCOS parallax of CH Cyg allows us to determine linear radii. For example, on the basis of the K-band visibility, Rosseland radii in the range of 214 to 243 solar radii can be derived utilizing CLVs of different fundamental mode Mira models as fit functions. These radii agree well within the error bars with the corresponding theoretical model Rosseland radii of 230 to 282 solar radii. Models of first overtone pulsators are not in good agreement with the observations. The wavelength dependence of the stellar diameter can be well studied by using visibility ratios V(λ1)/V(λ2) since ratios of visibilities of different spectral channels can be measured with higher precision than absolute visibilities. We found that the 2.03 μm uniform disk diameter of CH Cyg is approximately 1.1 times larger than the 2.15 μm and 2.26 μm uniform-disk diameter

Beckmann, Udo

Berger, Jean-Philippe

Bloecker, Thomas

Brewer, Michael T.

Hofmann, Karl-Heinz

Lacasse, Marc G.

Malanushenko, Victor

Millan-Gabet, Rafael

Monnier, John D.

Ohnaka, Keiichi

Pedretti, Ettore

Schertl, Dieter

Schloerb, F. Peter

Scholz, Michael

Traub, Wesley A.

Weigelt, Gerd

Yudin, Boris

Hofmann, K.-H.

Beckmann, U.

Berger, J.-P.

Bloecker, T.

Brewer, M.~T.

Lacasse, M.~G.

Malanushenko, V.

Millan-Gabet, R.

Monnier, J.~D.

Ohnaka, K.

Pedretti, E.

Schertl, D.

Schloerb, F.~P.

Scholz, M.

Traub, W.~A.

Weigelt, G.

Yudin, B.

Heriot Watt Pure

Near-infrared IOTA interferometry of the symbiotic star CH Cyg

University of the Highlands and Islands Institutional Repository

Berger, J.

Blöcker, T.

Brewer, M. K.

Lacasse, M.

Monnier, J.

Schloerb, P.

Traub, W.

Caltech Authors - Main

Zabot, Alexandre

Repositório Institucional da UFSC

Astrofísica GeralTema 14: Aglomerados deestrelasAlexandre ZabotÍndiceAglomerados estelaresPopulações estelaresMedidas com aglomeradosBibliografia1 | 22ÍndiceAglomerados estelaresPopulações estelaresMedidas com aglomeradosBibliografia2 | 22Aglomerados estelares Estrelas ligadasgravitacionalmente Formadas juntas Dois tipos: Aglomerados abertos Aglomerados globularesAglomerado globular M 13, descobertopor Edmond Halley em 1714, tem cercade 1 milhão de estrelas.3 | 22Aglomerados abertos De dezenas a poucos milhares deestrelas Jovens Tamanho  10 pc Formas irregulares fraca atração gravitacional Vida curta desfazem-se em poucos milharesde anosAglomerado aberto das Pleiades (M 45),contém cerca de 3 mil estrelas, mas só 7são visíveis a olho nu.4 | 22Aglomerados abertosMosaico de aglomerados abertos detectados pelo telescópio VISTA.5 | 22Aglomerados globulares De  103 a  106 estrelas Velhos (até 13 bilhões de anos) Esféricos forte atração gravitacional Cerca de 150 na nossa GaláxiaAglomerado globular ! Centauri. Contém cerca de10 milhões de estrelas.6 | 22Catálogo Messier Busca por cometas Lista de objetos nebulosos Galáxias e aglomerados estelaresO astrônomo francês Charles Messier (1730 –1817) catalogou mais de 100 objetos nebulosos.Os objetos do seu catálogo são conhecidos atéhoje pela inicial M seguida de um número.7 | 22Catálogo NGC New General Catalogue ofNebulae and Clusters of Stars Ampliação do catálogo Messier esimilares 7840 objetosO astrônomo dinamarquês John Dreyer (1852 –1926) estendeu o catálogo Messier em 1888.8 | 22ÍndiceAglomerados estelaresPopulações estelaresMedidas com aglomeradosBibliografia9 | 22Formação conjuntaFormação de um Aglomerado Estelarhttps://www.youtube.com/watch?v=3z9ZKAkbMhY10 | 22Formação conjuntaPodemos estudar o envelhecimento do ser humano observando um só ou umapopulação.O mesmo pode ser feito com as estrelas (felizmente!)11 | 22Formação conjunta As estrelas de um aglomerado sãotodas irmãs Cada uma com uma Massa Inicial Uma posição no HR Evolução diferenteUm diagrama HR com isócronas teóricas. Odiagrama HR de um aglomerado nos permiteestudar a evolução estelar.12 | 22ÍndiceAglomerados estelaresPopulações estelaresMedidas com aglomeradosBibliografia13 | 22Medidas com aglomeradosDiagramas HR de algomerados. Há estrelas na sequência principal e em ramos maisevoluídos. É possível identificar os turn-off points.14 | 22Medidas com aglomeradosFormas dos diagramas HR de vários aglomerados abertos. É possível ver a diferençade idade entre eles pela posição do turn-off point.15 | 22Medidas com aglomeradosDiagrama HR de dois aglomerados com isócronas que melhor ajustam. O estudo foifeito em várias bandas, dando mais confiabilidade aos ajustes.16 | 22Medidas com aglomeradosDiagrama HR de ! Centauri e ajustes de isócronas teóricas para medir os parâmetros.17 | 22Medidas com aglomeradosÉ possível estudar a metalicidade das estrelas do aglomerado.Aglomerados globulares contém poucos metais, indicando que são mais velhos.Os aglomerados abertos são contém mais metais, portanto são mais jovens.18 | 22Medidas com aglomeradosÉ possível observar e estudar aglomerados em outras galáxias, como estes na galáxiavizinha, Centaurus A.19 | 22Dinâmica estelarComo as estrelas se movimentam na presença de um campo gravitacional médio?20 | 22ÍndiceAglomerados estelaresPopulações estelaresMedidas com aglomeradosBibliografia21 | 22BibliografiaFontes para estudo Fascínio do Universo, capítulo 5 Curso de Astronomia do Prof. Steiner, aula 31. Seção “Estrelas e Diagrama HR” em http://astro.if.ufrgs.br/22 | 22

Tema 14: Aglomerados de estrelas

PROCEEDINGS OF SPIE
SPIEDigitalLibrary.org/conference-proceedings-of-spie
Near-infrared IOTA interferometry of
the symbiotic star CH Cyg
Karl-Heinz  Hofmann, Udo  Beckmann, Jean-Philippe
Berger, Thomas  Bloecker, Michael T. Brewer, et al.
Karl-Heinz  Hofmann, Udo  Beckmann, Jean-Philippe  Berger, Thomas
Bloecker, Michael T. Brewer, Marc G. Lacasse, Victor  Malanushenko, Rafael
Millan-Gabet, John D. Monnier, Keiichi  Ohnaka, Ettore  Pedretti, Dieter
Schertl, F. Peter  Schloerb, Michael  Scholz, Wesley A. Traub, Gerd  Weigelt,
Boris  Yudin, "Near-infrared IOTA interferometry of the symbiotic star CH
Cyg," Proc. SPIE 4838, Interferometry for Optical Astronomy II,  (21 February
2003); doi: 10.1117/12.458904
Event: Astronomical Telescopes and Instrumentation, 2002, Waikoloa,
Hawai'i, United States
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Near-infrared IOTA interferometry
of the symbiotic star CHCyg
K.-H. Hofmann
a
, U. Beckmann
a
, J. Berger
b
, T. Blocker
a
, M.K. Brewer
c
,
M. Lacasse
b
, V. Malanushenko
e
, R. Millan-Gabet
b
,
J. Monnier
b
, K. Ohnaka
a
, E. Pedretti
b
, D. Schertl
a
, P. Schloerb
c
,
M. Scholz
f
, W. Traub
b
, G. Weigelt
a
, B. Yudin
d
a
Max-Planck-Institut fur Radioastronomie, 53121 Bonn, Germany
b
Harvard-Smithsonian Center for Astrophysics, Cambridge, MA 02138, USA
c
Physics and Astronomy Dept., Univ. Massachusetts, Amherst, MA 01003, USA
d
Sternberg Astronomical Institute, 119899 Moscow, Russia
e
Crimean Astrophysical Observatory, 98409 Crimea, Ukraine
f
Institut fur Theoretische Astrophysik der Universitat Heidelberg,
69121 Heidelberg, Germany, and Institute of Astronomy,
School of Physics, University of Sydney NSW 2006, Australia
ABSTRACT
We present observations of the symbiotic star CH Cyg with a new JHK-band beam combiner mounted to the
IOTA interferometer
1
. The new beam combiner consists of an anamorphic cylindrical lens system and a grism,
and allows the simultaneous recording of spectrally dispersed J-, H- andK-band Michelson interferograms. The
observations of CHCyg were conducted on 5, 6, 8 and 11 June 2001 using baselines of 17 m to 25 m. From the
interferograms of CHCyg, J-, H-, and K-band visibility functions can be determined. Uniform-disk ts to the
visibilities give, e.g., stellar diameters of (7.8  0.6) mas and (8.7  0.8) mas in H and K, respectively. Angular
stellar lter radii and Rosseland radii are derived from the measured visibilities by tting theoretical center-to-
limb intensity variations (CLVs) of Mira star models
2;3
. The available HIPPARCOS parallax of CHCyg allows
us to determine linear radii. For example, on the basis of the K-band visibility, Rosseland radii in the range
of 214 to 243R

can be derived utilizing CLVs of dierent fundamental mode Mira models as t functions.
These radii agree well within the error bars with the corresponding theoretical model Rosseland radii of 230 to
282R

. Models of rst overtone pulsators are not in good agreement with the observations. The wavelength
dependence of the stellar diameter can be well studied by using visibility ratios V(
1
)/V(
2
) since ratios of
visibilities of dierent spectral channels can be measured with higher precision than absolute visibilities. We
found that the 2.03m uniform disk diameter of CHCyg is 1.1 times larger than the 2.15m and 2.26m
uniform-disk diameter.
Keywords: interferometry, symbiotic stars, near-infrared
1. INTRODUCTION
Symbiotic stars are close binary systems consisting of a cool red giant and a hot blue star. Interaction of both
components can lead to accretion phenomena and highly variable lightcurves. CHCyg is one of the best studied
members of this class of stars. It is a luminous triple symbiotic system with a very complicated photometric and
spectroscopic behaviour
4
. The red giant's diameter is one crucial parameter for the investigation of such systems
and therefore high-resolution interferometric measurements may provide important information
1
. Previous
interferometric K-band observations of CH Cyg carried out by Dyck et al.
5
(1996 Oct. 7) yielded a uniform
disk diameter of 10.40.6mas.
The size of a star can be derived by observing the brightness distribution on its stellar disk. For the
interpretation detailed dynamic atmosphere models have to be taken into account which predict, for instance,
center-to-limb intensity variations and corresponding visibilities
6
. By comparing the observations with such
Interferometry for Optical Astronomy II, Wesley A. Traub, Editor,
Proceedings of SPIE Vol. 4838 (2003) © 2003 SPIE · 0277-786X/03/$15.00
1043
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models, fundamental stellar parameters can be derived. It is well known that the stellar diameter may vary
with wavelength
7
. Accordingly, simultaneous measurements in dierent spectral bands greatly constrain the
analysis.
2. OBSERVATIONS AND UNIFORM-DISK FITS
CHCyg was observed with the IOTA interferometer using a new JHK beam combiner developed at the Max-
Planck Institute for Radioastronomy. This NIR beam combiner consists of an anamorphic lens system and a
grism, and is similar to the dispersed-fringe instruments used at the I2T/GI2T interferometer in the optical
wavelength range
8
. A full description will be given elsewhere. The observations were carried out on June 5,
6, 8 and 11, 2001 with baselines between 17 m and 25 m. The observational parameters are given in Table 1.
The raw visibilities of each spectral channel and each baseline were derived by evaluating the power spectra
of the interferograms (determination of the ratio of o-axis and central peak). The calibrated visibilities were
reconstructed from the raw visibilities of the object and the raw visibilities of reference stars. Figure 1 (see also
Table 1) shows the calibrated H and K visibilities and their uniform-disk (UD) ts which yield H- and K-band
UD stellar diameters of 7.8 mas  0.6 mas and 8.7 mas  0.8 mas, respectively (along position angle  0
o
).
Table 1. IOTA observations of CH Cyg. B
p
is the projected baseline, N denotes the total number of recorded interfer-
ograms, and V
K
and V
H
are the measured visibilities in the K and H, respectively.
Date B
p
[m] N V
K
V
H
Ref. stars
2001 June 05/06 20.08 12200 0.810.05 0.740.06 d Cyg, HR 7924
2001 June 08 24.55 11000 0.730.05 0.660.05 d Cyg, HR 7924
2001 June 11 17.37 11200 0.840.07 0.810.08 d Cyg, e Dra
0
0.2
0.4
0.6
0.8
1
0 20 40 60 80 100 120
vi
si
bi
lity
spatial frequency (cycles/arcsec)
visibility of a 7.77 mas UD
measured visibilities of CH Cyg in H
0
0.2
0.4
0.6
0.8
1
0 20 40 60 80 100 120
vi
si
bi
lity
spatial frequency (cycles/arcsec)
visibility of a 8.75 mas UD
measured visibilities of CH Cyg in K
Figure 1. Uniform-disk (UD) ts to the visibilities of CHCyg measured in the H (left) and K band (right).
3. COMPARISON OF THE OBSERVATION WITH MIRA STAR MODELS
3.1. Mira star models
Angular diameters can be derived from the observations by tting the measured visibilities with theoretical
center-to-limb intensity variations of Mira star models (Bessel, Scholz & Wood
2
; Hofmann, Scholz & Wood
3
).
These models were developed as possible representations of the prototype Mira variable o Ceti, and hence have
periods P very close to the 332 day period of o Ceti; they dier in pulsation mode (fundamental, f , or rst
overtone, o), assumed mass M and luminosity L, and in modelling assumptions. Table 2 lists the properties
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0100
200
300
400
500
600
700
800
0 5 10 15 20
R
os
se
la
nd
 ra
di
us
 (in
 S
ola
r r
ad
ii)
model phase combinations m
D E P M O
K band observations
Theory
0
100
200
300
400
500
600
700
800
0 5 10 15 20
St
el
la
r f
ilte
r r
ad
iu
s 
(in
 S
ola
r r
ad
ii)
model phase combinations m
D E P M O
lin. stellar K-band radii
Theory
Figure 2. Comparison of derived CHCyg radii (lled squares) with theoretical model radii (open circles). Left: linear
Rosseland radii R
m
for all 22 model-phase combinations m. Dierent values of m correspond to dierent phases or cycles
(see Ref. 9). Right: linear stellar K-band radii for all 22 model-phase combinations m.
of the model series used (R
p
= Rosseland radius of the non-pulsating "parent" star of the Mira variable
2;3
;
T
e
= eective temperature). These models predict monochromatic radii R

(radius at which the optical
depth equals unity, i.e. 

=1), Rosseland radii R (radius at which the Rosseland optical depth equals unity,
i.e. 
Ross
=1), and stellar lter radii R
f
(=
R
R

I

f

d =
R
I

f

d, with f

being the lter transmission, R

the monochromatic radius, and I

the intensity spectrum) at dierent pulsational phases and cycles. These
predictions are compared with our measurements in the following section.
Table 2. Mira model series (see text). For more details we refer to Ref. (2,3).
Series Mode P (d) M=M

L=L

R
p
=R

T
eff
/K
D f 330 1.0 3470 236 2900
E o 328 1.0 6310 366 2700
P f 332 1.0 3470 241 2860
M f 332 1.2 3470 260 2750
O o 320 2.0 5830 503 2250
3.2. Derived angular stellar lter radii, angular Rosseland radius and linear radii
The derived angular stellar lter radii R
a
K;m
and R
a
H;m
(m: model-phase combinations) were determined by
least-squares ts of the model
2;3
CLV visibilities to the measured visibilities. From the obtained stellar lter
radii and the theoretical ratios of R/R
p
to R
K
/R
p
and R
H
/R
p
, respectively, predicted by the above Mira star
models (see Table 3 in Ref. 9), the angular Rosseland radii R
a
m
can be derived.
Linear stellar lter radii (R
K;m
, R
H;m
), and linear Rosseland radii (R
m
) of CHCyg were determined from
the derived angular stellar lter radii (R
a
K;m
, R
a
H;m
) and Rosseland radii (R
a
m
) using the CHCyg HIPPARCOS
parallax of 3.730.85mas
10;11
. Fig. 2 shows the obtained linear Rosseland radii R
m
(derived from the K-band
visibilities) and the stellar lter radii R
K;m
for all model-phase combinations m. The theoretical Rosseland radii
of the fundamental mode D, M and P model series are at almost all available phases close to the Rosseland
radii of CH Cyg derived from the observations. On the other hand, the rst-overtone models E and O give
Rosseland radii which are too large. Table 3 compares the theoretical D-, P- and M-model Rosseland radii with
the derived linear Rosseland radii determined from the K-band visibilities and the D-, P- and M-model CLVs.
The phase-averaged derived linear Rosseland radii are averages over all pulsational phases. Table 3 shows that
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Table 3. Comparison of the derived linear Rosseland radii of CHCyg with the corresponding theoretical Rosseland radii.
For comparison, the linear UD K-band radius is 251
+100
 63
R

.
Model Phase-averaged linear Rosseland Theoretical linear
radius (R

) derived from the K-band obs. Rosseland radius (R

)
D 243
+98
 62
230
P 214
+87
 55
282
M 220
+89
 56
275
there is good agreement within the error bars between the measured uniform-disk radius, the derived Rosseland
radii, and the theoretical Rosseland radii. We note that the HIPPARCOS parallax error contributes most to
the given total error bars.
Iijima
4
detected eclipsing phenomena of the inner binary of the CHCyg system with a period of 756d
by spectrophotometric observations. From the duration of the hot component's eclipse by the red giant, a
radius of 288R

was estimated for the red giant slightly larger than the one inferred from our interferometric
measurements.
4. DIAMETER RATIOS
D(
1
)
D(
2
)
DERIVED FROM VISIBILITY RATIOS
V(
1
)
V(
2
)
Our JHK interferograms allow us to derive from each interferogram the visibilities of many dierent spec-
tral channels in the wavelength range of 1-2.3m. We use these visibilities to determine the diameter ratios
D(
1
)/D(
2
) and compare these observed ratios with theoretical model ratios
12
.
For this goal we have divided our K-band interferograms into three wavelength bins of approximately 0.1m
width and derived the visibility ratios V
2:03m
/V
2:26m
, V
2:15m
/V
2:26m
and V
2:03 m
/V
2:15m
. From these
visibility ratios we can derive diameter ratios which show that the diameter of CH Cyg is larger at 2.03m than
at 2.15 m or 2.26 m. If the CH Cyg visibilities V
2:03m
, V
2:15m
, and V
2:26m
are tted by uniform-disks,
diameter ratios of D
2:03m
/D
2:26m
= 1.11, D
2:03m
/D
2:15m
= 1.12, and D
2:15m
/D
2:26m
= 0.99 are obtained.
These ratios agree with both the predicted theoretical diameter ratios
12
and observations presented in Ref. 13.
A full account of the above studies (comparison with Mira models at JHK, wavelength dependence of the
diameter in JHK, derivation of eective temperature from JHK radii and coeval UBV JHKLM photometry)
will be presented in Ref. 14.
5. REFERENCES
1. W.A. Traub, SPIE 3350, 848, 1998
2. M.S. Bessell, M. Scholz, M., and P.R. Wood 1996, A&A, 307, 481
3. K.-H. Hofmann, M. Scholz, and P.R. Wood 1998, A&A, 339, 846
4. T. Iijima, 1998, MNRAS 297, 77
5. H.M. Dyck, G.T. van Belle, R.R. Thompson 1998, AJ, 116, 981
6. M. Scholz, 2001, MNRAS 321, 347
7. A. Labeyrie, L. Koechlin, D. Bonneau, A. Blazit, R. Foy. 1977, ApJ 218, L75
8. A. Labeyrie, G. Schumacher, M.Dugue, C.Thom, P.Bourlon, F. Foy, D.Bonneau, R. Foy 1986,A&A 162, 359
9. K.-H. Hofmann, U. Beckmann, T. Blocker, et al. 2001, New Astronomy, 7, 9-20
10. ESA 1997, The Hipparcos & Tycho Catalog, ESA SP-1200, Noordwijk: ESA
11. F. Van Leeuwen, M.W. Feast, P.A. Whitelock, and B. Yudin 1997, MNRAS, 287, 955
12. A.P. Jacob and M. Scholz "Eects of molecular contamination of IR near-continuum bandpasses on mea-
surements of M-type Mira diameters", MNRAS, in press
13. R.R. Thompson, M.J. Creech-Eakman and G.T. van Belle "Multi-epoch interferometric study of Mira vari-
ables I. Narrowband diameters of RZ Peg and S Lac", ApJ, in press
14. K.-H. Hofmann et al., 2002, "Near-infrared IOTA interferometry of the symbiotic star CHCyg", in prep.
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Tema 14: Aglomerados de estrelas

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