Circumsubstellar disk SED in dependence on system parameters
Formulae for critical angles and areas that permit to imagine configurations of observed systems and to calculate their spectral energy distributions (SEDs) as dependencies on their geometrical parameters and inclination angles toward observer are obtained. Using these formulae an atlas of SEDs was...
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Головна астрономічна обсерваторія НАН України
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| Цитувати: | Circumsubstellar disk SED in dependence on system parameters / O. Zakhozhay // Advances in Astronomy and Space Physics. — 2012. — Т. 2., вип. 2. — С. 143-145. — Бібліогр.: 12 назв. — англ. |
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irk-123456789-1191862017-06-05T03:03:40Z Circumsubstellar disk SED in dependence on system parameters Zakhozhay, O. Formulae for critical angles and areas that permit to imagine configurations of observed systems and to calculate their spectral energy distributions (SEDs) as dependencies on their geometrical parameters and inclination angles toward observer are obtained. Using these formulae an atlas of SEDs was created. The SEDs were calculated for 1120 systems with different central object masses, ages, inner disk radii, flaring geometries and inclination angles. The dependencies of SED shapes on systems ages, inclinations and substellar masses are analysed. 2012 Article Circumsubstellar disk SED in dependence on system parameters / O. Zakhozhay // Advances in Astronomy and Space Physics. — 2012. — Т. 2., вип. 2. — С. 143-145. — Бібліогр.: 12 назв. — англ. 2227-1481 http://dspace.nbuv.gov.ua/handle/123456789/119186 en Advances in Astronomy and Space Physics Головна астрономічна обсерваторія НАН України |
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Formulae for critical angles and areas that permit to imagine configurations of observed systems and to calculate their spectral energy distributions (SEDs) as dependencies on their geometrical parameters and inclination angles toward observer are obtained. Using these formulae an atlas of SEDs was created. The SEDs were calculated for 1120 systems with different central object masses, ages, inner disk radii, flaring geometries and inclination angles. The dependencies of SED shapes on systems ages, inclinations and substellar masses are analysed. |
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Zakhozhay, O. |
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Zakhozhay, O. Circumsubstellar disk SED in dependence on system parameters Advances in Astronomy and Space Physics |
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Zakhozhay, O. |
| author_sort |
Zakhozhay, O. |
| title |
Circumsubstellar disk SED in dependence on system parameters |
| title_short |
Circumsubstellar disk SED in dependence on system parameters |
| title_full |
Circumsubstellar disk SED in dependence on system parameters |
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Circumsubstellar disk SED in dependence on system parameters |
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Circumsubstellar disk SED in dependence on system parameters |
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circumsubstellar disk sed in dependence on system parameters |
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Головна астрономічна обсерваторія НАН України |
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2012 |
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Circumsubstellar disk SED in dependence on system parameters / O. Zakhozhay // Advances in Astronomy and Space Physics. — 2012. — Т. 2., вип. 2. — С. 143-145. — Бібліогр.: 12 назв. — англ. |
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Advances in Astronomy and Space Physics |
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AT zakhozhayo circumsubstellardisksedindependenceonsystemparameters |
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2025-07-08T15:23:24Z |
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2025-07-08T15:23:24Z |
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Circumsubstellar disk SEDs in dependence
on system parameters
O.Zakhozhay∗
Advances in Astronomy and Space Physics, 2, 143-145 (2012)
© O.Zakhozhay, 2012
Main Astronomical Observatory of the National Academy of Sciences of Ukraine, Zabolotnoho 27, 03680, Kyiv, Ukraine
Formulae for critical angles and areas that permit to imagine con�gurations of observed systems and to calculate
their spectral energy distributions (SEDs) as dependencies on their geometrical parameters and inclination angles
toward observer are obtained. Using these formulae an atlas of SEDs was created. The SEDs were calculated for
1120 systems with di�erent central object masses, ages, inner disk radii, �aring geometries and inclination angles.
The dependencies of SED shapes on systems ages, inclinations and substellar masses are analysed.
Key words: protoplanetary disks, brown dwarfs, spectral energy distribution
introduction
At the beginning of this century a physical model
for substellar objects (Brown Dwarfs) evolution was
created by a research group from the Astronomical
Institute of V.N.Karazin Kharkiv National Univer-
sity [5]. This model represents the evolution of sub-
stellar objects with masses from 0.01 to 0.08M� and
with ages within the range from 1Myr to 10Gyr.
On the other hand, with the discovery of circum-
stellar disk around Vega by Aumann and co-authors
[1] the active investigation of protoplanetary disks
has begun. During the last decade the observations
of protoplanetary disks around substars were actively
carried out as well (e. g. [3, 4, 6]). So the aim of this
research is to create a new algorithm for calculation
of the spectral energy distribution (SED) of proto-
planetary disks that may surround such substellar
objects, inclined on a given angle, and to study how
the changing of di�erent parameters would a�ect the
SEDs shape.
Here we present the results for the following cases:
- substellar masses within the range of 0.01-
0.08M�;
- protoplanetary disks with di�erent inclination
(0°-80°);
- systems ages are 1-30Myr;
- substars and protoplanetary disks irradiate as a
black body;
- distance from the Sun to substar equals to 10 pc;
- inner disk radii equal to central object radius
and sublimation radius at the age of 1Myr.
method of calculations
SEDs for substars and surrounded disks were cal-
culated in a black body approximation. Disks' SEDs
were calculated using the model from [2] for a �at
passive circumstellar disk. Passive disk is a disk that
passively (without accretion) reradiates the energy
it absorbs from the central object. Its temperature
Tdisk changes with distance as:
Tdisk =
(
2
3π
)0.25(R
r
)0.75
Teff , (1)
where R is the central object radius, r is the dis-
tance within a disk, Teff is the e�ective temperature
of the central object. The outer disk radius Rout was
calculated with the formula that was obtained based
on the analysis of 107 protoplanetary disks around
single main sequence and T Tauri stars [11]:
Rout[AU] = 150
(
M
M�
)0.75
, (2)
where M is the mass of the central object.
To take into account the disk inclination the spe-
cial algorithm for emitting areas projection on the
sky plane was created. The formula that permits
to calculate limiting angles for systems inclination
at �rst and then the areas of emitting surfaces pro-
jections for systems that contain spherical central
source and surrounded disk was obtained. This
method was previously described in [7, 8, 12].
Using these formulae 1120 SEDs for substars with
disks with di�erent geometry and inclination angle
were calculated. Calculated arrays for irradiated
�uxes that were obtained with the new algorithm
are analysed.
The developed calculations algorithm was veri-
�ed on �uxes received with ground-based and space
observations [6]. Simulated SEDs and determined
system characteristics for 10 substars from the Up-
per Scorpius open cluster were presented in [9, 12].
As a result of SED simulations new parameters for
inner disk radii, inclination angles and system ages
were obtained. New physical parameters (masses,
∗zkholga@mail.ru
143
Advances in Astronomy and Space Physics O. Zakhozhay
Fig. 1: SEDs for substars with disks located face on without inner holes with age 1Myr in logarithmic (left) and
absolute (right) scales. Di�erent lines correspond to di�erent masses (form top to bottom): 0.08-0.01M� with a step
0.01M�.
radii and e�ective temperatures) for central substars
were estimated as well. Substellar parameters do not
di�er essentially from that found in [6] (the compar-
ison for 6 systems is shown in a table in [12]) but
these data should be improved in future by taking
into account atmospheric features of every particu-
lar Brown Dwarf.
results
Mass, chemical composition and age determine
the radius of substar, its e�ective temperature and
luminosity. Geometrical parameters of the adopted
model are �xed, except the disk inclination, on which
the integral �ux depends essentially. Therefore, the
dependence of �ux on substellar mass and age, and
the disk inclination toward observer, is analysed.
The maximum �ux (in systems with de�ned pa-
rameters) belongs to a system with substellar mass
0.08M�, age 1Myr, and disk located face on.
Figs. 1-5 show the SED shape of systems without
and with an inner hole as a dependence on central
Brown Dwarf mass (Fig. 1), age (Fig. 2-3) and incli-
nation (Fig. 4-5) in logarithmic and absolute scale.
The SED shape dependence on the inclination an-
gle was studied in detail in [10]. It was noticed that
at small inclination angles the �ux from the gapless
system will be always stronger because the emitting
area of such disk is larger. But at large inclination
angles the �ux from system with inner hole is more
intensive. This fact can be interpreted as follows:
when disk has no inner hole its inner edge starts to
cover a part of the central object at the moment
when inclination is j > 0°. And when the disk in-
ner hole exists, the inner edge of the disk starts to
cover a part of the central object at quite large an-
gles (its exact value depends on system geometrical
parameters, for the systems that are presented here
its value is ∼75°). And as a �ux from the central
object always give the largest contribution to the to-
tal �ux, SED of a system with inner hole will have a
maximum at largest values.
conclusions
The SED shape of Brown Dwarf with protoplane-
tary disk strongly depends on the age and inclination
of the system. The mass of the central object a�ects
mostly its intensity. So exploration makes it possible
to determine: �rstly, the mass of the central object,
and then the presence of inner hole of the system,
the approximate age of the system (that permits to
exclude an idea of simultaneous star formation in a
cluster) and the system inclination.
references
[1] AumannH.H., BeichmanC.A., Gillett F.C. et al. 1984,
ApJ, 278, L23
[2] ChiangE. I. & GoldreichP. 1997, ApJ, 490, 368
[3] Mohanty S., JayawardhanaR., NattaA. et al. 2004, ApJ,
609, L33
[4] NattaA., Testi L., ComerónF. et al. 2002, A&A, 393,
597
[5] PisarenkoA. I., YatsenkoA.A. & ZakhozhayV.A. 2007,
Astron. Rep., 51, 605
[6] ScholzA., JayawardhanaRay, WoodK. et al. 2007, ApJ,
660, 1517
[7] ZakhozhayO.V. 2011, Radio Phys. and Radio Astron.,
2, 125
[8] ZakhozhayO.V. 2011, Radio Phys. and Radio Astron.,
2, 211
[9] ZakhozhayO. 2011, IAU Symposium, 276, 467
[10] ZakhozhayO. 2012, IAU Symposium, 282, 448
[11] ZakhozhayV.A. 2005, Vysnyk Astronomichnoi Shkoly,
4, 55
[12] ZakhozhayV.A., ZakhozhayO.V. & VidmachenkoA.P.
2011, Kinematics and Physics of Celestial Bodies, 27,
140
144
Advances in Astronomy and Space Physics O. Zakhozhay
Fig. 2: SEDs for substars with disks located face on without inner holes with substellar mass 0.08M� in logarithmic
(left) and absolute (right) scales. Systems ages (form top to bottom): 1-30Myr with step 5Myr.
Fig. 3: The same as in Fig. 2, but with inner holes.
Fig. 4: SEDs for substars with disks without inner holes, with substellar mass 0.08M� and age 1Myr in logarithmic
(left) and absolute (right) scales. System inclinations (form top to bottom): 0°-80° with step 20°.
Fig. 5: The same as in Fig. 4, but with inner holes.
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