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And that discrepancy between the two increases with wavelength as speckles move out of the slit.
And that discrepancy between the two increases with wavelength as speckles move out of the slit.
This implies that precise photometry of the star cannot be performed on the model spectrum.
This implies that precise photometry of the star cannot be performed on the model spectrum.
Intensive simulations were completed to simulate realistic spectra for testing the method.
Intensive simulations were completed to simulate realistic spectra for testing the method.
We used the complete simulation model of the VLT-SPHERE instrument developed for end-to-end simulations.
We used the complete simulation model of the VLT-SPHERE instrument developed for end-to-end simulations.
This model is a diffractive code written in IDL (Interactive Data Language) that is based on the CAOS (Code for Adaptive Optics Systems) problem solving environment (?) with a package developed for the SPHERE project (?)..
This model is a diffractive code written in IDL (Interactive Data Language) that is based on the CAOS (Code for Adaptive Optics Systems) problem solving environment \citep{carbillet2004} with a package developed for the SPHERE project \citep{carbillet2008}.
We do not to describe in detail the content of this simulation code, but present a global overview of the simulated.
We do not to describe in detail the content of this simulation code, but present a global overview of the simulated.
The SPHERE package for CAOS is a diffractive end-to- simulation code that takes into account multiple sources of aberrations, such as atmospheric residuals, AO correction and optical aberrations.
The SPHERE package for CAOS is a diffractive end-to-end simulation code that takes into account multiple sources of aberrations, such as atmospheric residuals, AO correction and optical aberrations.
It consists of separate modules, which simulate different parts of the instrument i.e. the extreme AO system SAXO, the optical common path, and the science modules.
It consists of separate modules, which simulate different parts of the instrument i.e. the extreme AO system SAXO, the optical common path, and the science modules.
A specific part of the code is dedicated to LSS simulations with coronagraphy.
A specific part of the code is dedicated to LSS simulations with coronagraphy.
This code does not simulate temporal variation in the aberrations: only the AO-filtered atmospheric residuals are changed during the simulation.
This code does not simulate temporal variation in the aberrations: only the AO-filtered atmospheric residuals are changed during the simulation.
The final output of the code are normalized images of the PSF, the coronagraphic PSF, and slit images at different wavelengths.
The final output of the code are normalized images of the PSF, the coronagraphic PSF, and slit images at different wavelengths.
A second code was developed to scale these normalized images to the correct photometric values according to the instrument design, the star being observed, the distance, the angular separation, and the of the companion.
A second code was developed to scale these normalized images to the correct photometric values according to the instrument design, the star being observed, the distance, the angular separation, and the of the companion.
In particular, the code accounts for the global throughput of the instrument, as well as the atmospheric transmission.
In particular, the code accounts for the global throughput of the instrument, as well as the atmospheric transmission.
The code considers OH lines but not their variability.
The code considers OH lines but not their variability.
The spectra used to model the companions in the simulations are the latest synthetic spectra generated by the ENS Lyon group with the PHOENIX code (?)..
The spectra used to model the companions in the simulations are the latest synthetic spectra generated by the ENS Lyon group with the PHOENIX code \citep{allard2001}.
More precisely, we used the models designated DUSTY-2000, COND-2002, and SETTL (??,andprivatecommunication).
More precisely, we used the models designated DUSTY-2000, COND-2002, and SETTL \citep[and private communication]{allard2001,allard2003}.
Finally, a realistic amount of noise was added depending on the characteristics of the particular next-generation AO imaging instruments i.e. detector noise, sky background and instrumental thermal background.
Finally, a realistic amount of noise was added depending on the characteristics of the particular next-generation AO imaging instruments i.e. detector noise, sky background and instrumental thermal background.
The final output was a two-dimensional spectrum of the star with one or more companions at different angular separations.
The final output was a two-dimensional spectrum of the star with one or more companions at different angular separations.
We simulated and wide slits with a radius Lyot coronagraph at the center, for an 8 meter diameter telescope.
We simulated and wide slits with a radius Lyot coronagraph at the center, for an 8 meter diameter telescope.
The number of wavelengths and the spectral interval was carefully chosen to produce spectra at low and medium resolution, refered to as LRS and MRS respectively (see Table [i)).
The number of wavelengths and the spectral interval was carefully chosen to produce spectra at low and medium resolution, refered to as LRS and MRS respectively (see Table \ref{table:spectro_modes}) ).
The amount of optical aberrations was set to be 50 nm RMS before the coronagraph, and ~40 nm RMS after the coronagraph.
The amount of optical aberrations was set to be $\sim$ 50 nm RMS before the coronagraph, and $\sim$ 40 nm RMS after the coronagraph.
The atmosphere was simulated by a set of decorrelated phase screens, each corresponding to approximately 80 nm RMS of wavefront aberrations after AO correction.
The atmosphere was simulated by a set of decorrelated phase screens, each corresponding to approximately 80 nm RMS of wavefront aberrations after AO correction.
We limited our simulations to 100 phase screens to produce a smooth star halo.
We limited our simulations to 100 phase screens to produce a smooth star halo.
In theory, this number is too small to produce a “true” long exposure.
In theory, this number is too small to produce a “true” long exposure.
If we assume that atmospheric residuals have a correlation time of the order of 1 ms and that a typical exposure time for a DIT is 10 seconds, then 10,000 decorrelated phase screens would be required to produce a long exposure.
If we assume that atmospheric residuals have a correlation time of the order of 1 ms and that a typical exposure time for a DIT is 10 seconds, then 10,000 decorrelated phase screens would be required to produce a long exposure.
However, in practice using fewer phase screens has proven to give good results in various conditions, while significantly reducing the computing time of the simulations.
However, in practice using fewer phase screens has proven to give good results in various conditions, while significantly reducing the computing time of the simulations.
The total amount of aberrations is 110 nm RMS, which corresponds to a Strehl ratio of at 1.6 um. Although high compared to existing instruments with conventional AO (typical Strehl ratio for VLT-NACO in standard conditions is between andin K band, see ?)), these overall performances are realistic for new
The total amount of aberrations is $\sim$ 110 nm RMS, which corresponds to a Strehl ratio of at 1.6 $\mu$ m. Although high compared to existing instruments with conventional AO (typical Strehl ratio for VLT-NACO in standard conditions is between andin K band, see \citealt{clenet2004}) ), these overall performances are realistic for new
and ephemeral regions.
and ephemeral regions.
Here we divide the spectra into four classes according to the filling factors of individual structures. te. the fraction of the solar dise covered by an individual magnetic structure.
Here we divide the spectra into four classes according to the filling factors of individual structures, i.e. the fraction of the solar disc covered by an individual magnetic structure.
These classes are determined from the empirical cumulative distribution function (ECDF) of the features identified from Sep/2010 to Dec/2010.
These classes are determined from the empirical cumulative distribution function (ECDF) of the features identified from Sep/2010 to Dec/2010.
Figure 3. presents the ECDF obtained (blue line).
Figure \ref{Fig_ecdf} presents the ECDF obtained (blue line).
The boundaries between the four classes are defined approximately at the probability levels:33.3%..
The boundaries between the four classes are defined approximately at the probability levels:, and .
66.6%.. and 97%.. Table 1. shows the resulting classification according to the filling factors of the structures.
Table \ref{table1} shows the resulting classification according to the filling factors of the structures.
Following this classification scheme. we produce an image mask in which the active regions and the sunspots are represented.
Following this classification scheme, we produce an image mask in which the active regions and the sunspots are represented.
Figure 4+ displays an example of the image mask produce from the magnetogram and intensity image of 04-Aug-2011 at 09:00:00.
Figure \ref{Mask} displays an example of the image mask produce from the magnetogram and intensity image of 04-Aug-2011 at 09:00:00.
The contribution of the solar features to the solar irradiance also depends on the position of the features on the solar disk.
The contribution of the solar features to the solar irradiance also depends on the position of the features on the solar disk.
In order to take this in to account. we compute the area covered by bipolar features in concentric rings.
In order to take this in to account, we compute the area covered by bipolar features in concentric rings.
These rings are determined according to the heliographic angle (40).
These rings are determined according to the heliographic angle $\mu$ ).
Figure 5. shows the eleven (11) rings considered in this work.
Figure \ref{Fig_mu_rings} shows the eleven (11) rings considered in this work.
As we will show later. there is no need for increasing that number.
As we will show later, there is no need for increasing that number.
The input vector (p) of the network is defined as the filling factors of the 10 inner rings of each class considered.
The input vector $p$ ) of the network is defined as the filling factors of the 10 inner rings of each class considered.
Following à common pratice. we normalize the input time series proportionally to the standard deviation before they enter in the neural network.
Following a common pratice, we normalize the input time series proportionally to the standard deviation before they enter in the neural network.
Note that the thresholds employed for the segmentation of the Images are fixed taking into account that the noise should be removed.
Note that the thresholds employed for the segmentation of the images are fixed taking into account that the noise should be removed.
Although the threshold values affect the distribution of the filing factors of individual structures. the training procedure accommodate the ANN coetficients in order to generalize properly the output.
Although the threshold values affect the distribution of the filing factors of individual structures, the training procedure accommodate the ANN coefficients in order to generalize properly the output.
Figure 6aa shows the evolution of the various filling factors from Sep/2010 to Oct/2011.
Figure \ref{fig_small_areas}a a shows the evolution of the various filling factors from Sep/2010 to Oct/2011.
Each line presents the fraction of the solar disk covered by structures that belong to one class. re. the filling factors of each class.
Each line presents the fraction of the solar disk covered by structures that belong to one class, i.e. the filling factors of each class.
The yellow, red. and green lines display the evolution of ephemeral regions (ER) that are members of the Classes I. IL and ΠΠ. respectively.
The yellow, red, and green lines display the evolution of ephemeral regions (ER) that are members of the Classes I, II, and III, respectively.
The blue line exhibits
The blue line exhibits
(characterised as a modulation of the lightcurve evolution) was interpreted as being due to a precessing, eccentric disk (e.g. Whitehurst 1988; Hirose Osaki 1990; Lubow 1991).
(characterised as a modulation of the lightcurve evolution) was interpreted as being due to a precessing, eccentric disk (e.g. Whitehurst 1988; Hirose Osaki 1990; Lubow 1991).
Lubow (1991) presented a fluid dynamical theory that explained the origin of the eccentric disk as being due to an instability at the 3:1 Lindblad resonance generated by non linear mode coupling, leading to the growth of disk eccentricity for a circular binary orbit.
Lubow (1991) presented a fluid dynamical theory that explained the origin of the eccentric disk as being due to an instability at the 3:1 Lindblad resonance generated by non linear mode coupling, leading to the growth of disk eccentricity for a circular binary orbit.
The interaction between massive companions (giant planets and brown dwarfs) and accretion disks in which they were initially embedded was considered by Papaloizou, Nelson Masset (2001).
The interaction between massive companions (giant planets and brown dwarfs) and accretion disks in which they were initially embedded was considered by Papaloizou, Nelson Masset (2001).
Here the tidal interaction creates an inner cavity within which the primary star and companion orbit, and as such these systems are similar to the binary plus circumbinary disks that we are concerned with in this paper.
Here the tidal interaction creates an inner cavity within which the primary star and companion orbit, and as such these systems are similar to the binary plus circumbinary disks that we are concerned with in this paper.
Papaloizou et al. (
Papaloizou et al. (
2001) showed that a massive companion on a circular orbit could cause the surrounding disk to become eccentric.
2001) showed that a massive companion on a circular orbit could cause the surrounding disk to become eccentric.
The origin of the eccentricity was found to be due to a similar instability mechanism to that proposed by Lubow (1991), namely non linear coupling between an initial m=1 eccentric disturbance in the disk and the m=1 component of the binary potential leading to an m=2 wave being excited at the 1:3 resonance in the circumbinary disk.
The origin of the eccentricity was found to be due to a similar instability mechanism to that proposed by Lubow (1991), namely non linear coupling between an initial $m=1$ eccentric disturbance in the disk and the $m=1$ component of the binary potential leading to an $m=2$ wave being excited at the 1:3 resonance in the circumbinary disk.
Based on this we expect to see the circumbinary disk in our simulations become eccentric.
Based on this we expect to see the circumbinary disk in our simulations become eccentric.
Eccentricity growth will saturate when viscous damping matches the eccentricity forcing rate.
Eccentricity growth will saturate when viscous damping matches the eccentricity forcing rate.
Secular interaction between the eccentric disk and binary should force the binary to become eccentric also.
Secular interaction between the eccentric disk and binary should force the binary to become eccentric also.
There are important resonant interactions between the disk and binary that can lead to modification of the binary orbital elements.
There are important resonant interactions between the disk and binary that can lead to modification of the binary orbital elements.
For a binary on a modestly eccentric orbit interaction at outer Lindblad resonances is expected to cause a decay of the semimajor axis in a viscous disk, where the decay rate depends on the disk viscosity.
For a binary on a modestly eccentric orbit interaction at outer Lindblad resonances is expected to cause a decay of the semimajor axis in a viscous disk, where the decay rate depends on the disk viscosity.
Interaction at eccentric Lindblad resonances is expected to cause growth of the eccentricity.
Interaction at eccentric Lindblad resonances is expected to cause growth of the eccentricity.
Working to first order in the binary eccentricity, ej, the 1:2 corotation resonance should induce eccentricity damping and the 1:3 eccentric Lindblad resonance should cause eccentricity growth.
Working to first order in the binary eccentricity, $e_{b}$, the 1:2 corotation resonance should induce eccentricity damping and the 1:3 eccentric Lindblad resonance should cause eccentricity growth.
If the disk is tidally truncated beyond the 1:2 Lindblad resonance, as is expected for massive companions (e.g. Artymowicz 1992; Lin Papaloizou 1993), then eccentricity growth is expected.
If the disk is tidally truncated beyond the 1:2 Lindblad resonance, as is expected for massive companions (e.g. Artymowicz 1992; Lin Papaloizou 1993), then eccentricity growth is expected.
Thus we expect the eccentricity of the binary system to grow in our simulations, provided the disk inner cavity does not extend beyond the 1:3 resonance.
Thus we expect the eccentricity of the binary system to grow in our simulations, provided the disk inner cavity does not extend beyond the 1:3 resonance.
Should this occur the eccentricity should still grow, but at a lower rate since higher order resonances will be required to drive the eccentricity.
Should this occur the eccentricity should still grow, but at a lower rate since higher order resonances will be required to drive the eccentricity.
At the present time there is not a well developed theory that can be used to predict when the binary eccentricity should saturate.
At the present time there is not a well developed theory that can be used to predict when the binary eccentricity should saturate.
We note, however, that as the eccentricity grows the interaction at the most significant eccentric Lindblad resonances may become increasingly non linear such that they saturate (i.e. the density there is decreased), causing the growth rate to slow.
We note, however, that as the eccentricity grows the interaction at the most significant eccentric Lindblad resonances may become increasingly non linear such that they saturate (i.e. the density there is decreased), causing the growth rate to slow.
We see from the above discussion that we expect there to be both secular and resonant interactions occuring between the disk and binary, leading to the growth of their eccentricity.
We see from the above discussion that we expect there to be both secular and resonant interactions occuring between the disk and binary, leading to the growth of their eccentricity.
When the angular momentum content of disk and binary are similar then we expect that they may participate in a joint secular mode in which they precess at the same rate (Papaloizou 2002).
When the angular momentum content of disk and binary are similar then we expect that they may participate in a joint secular mode in which they precess at the same rate (Papaloizou 2002).
In fact the angular momentum in the binary exceeds that in the disk by about a factor of 4 in our simulations, so the existence of a joint mode is probably marginal.
In fact the angular momentum in the binary exceeds that in the disk by about a factor of 4 in our simulations, so the existence of a joint mode is probably marginal.
When their apsidal lines are misaligned the disk and binary will exert secular torques leading to changes in their eccentricities (by analogy with the Jupiter-Saturn system).
When their apsidal lines are misaligned the disk and binary will exert secular torques leading to changes in their eccentricities (by analogy with the Jupiter–Saturn system).
If the apsidal lines become closely aligned, however, then these torques will diminish.
If the apsidal lines become closely aligned, however, then these torques will diminish.
Thus, we expect that a steady state configuration will consist of an eccentric binary system surrounded by an eccentric disk precessing at the same rate in a prograde direction with with apsidal lines closely aligned.
Thus, we expect that a steady state configuration will consist of an eccentric binary system surrounded by an eccentric disk precessing at the same rate in a prograde direction with with apsidal lines closely aligned.
and the collocation poiuts in plivsical space are the mapped collocation points along cach dimension. where the coordinate. along the -th dimension.): (fy). is given: by Eq.
and the collocation points in physical space are the mapped collocation points along each dimension, where the coordinate along the $l$ -th dimension $x^{(l)}_{i_l}$ is given by Eq.
using: xU)
using $X^{(l)}$.
Note that such a ¢-dimenusional rectanele has as many spectral cocticicuts Ohh, as erid point values 1),00),=ulti...rz).
Note that such a $d$ -dimensional rectangle has as many spectral coefficients $\tilde u_{k_1\cdots k_d}$ as grid point values $u_{i_1\ldots i_d}=u(x_{i_1}, \ldots, x_{i_d})$.
Therefore we cau equivalently solve for the spectral cocfiicicuts or the real space values.
Therefore we can equivalently solve for the spectral coefficients or the real space values.
We will solve for the real space values tj)ju.
We will solve for the real space values $u_{i_1\ldots i_d}$.
Iu a spherical shell with iuuner aud outer radii 0<RyRe we use a mapping for the radial coordinate.
In a spherical shell with inner and outer radii $0<R_1<R_2$ we use a mapping for the radial coordinate.
A function e(r.0.0) is thus expanded as where real-valued spherical harmouics are used: DI"(cos0) ave the associated Logeudre polvuomials.
A function $u(r,\theta,\phi)$ is thus expanded as where real-valued spherical harmonics are used: $P_l^m(\cos\theta)$ are the associated Legendre polynomials.
Associating tho sin-ternis with negative is ids uot standard. but chininates the need to refer to two sets of spectral coefficients. one cach for the cos-terms aud the sin-terms.
Associating the $\sin$ -terms with negative $m$ is not standard, but eliminates the need to refer to two sets of spectral coefficients, one each for the $\cos$ -terms and the $\sin$ -terms.
The radial mapping X:[/4.πο»|.1.1] cau be auy of the choices in Eq.
The radial mapping $X:[R_1,R_2]\to[-1,1]$ can be any of the choices in Eq.
(27).. The radial collocation poiuts rj;/=0.....N, are given by Eq.
The radial collocation points $r_i, i=0, \dots, N_r$ are given by Eq.
(26).. For the augle o. Eq.
For the angle $\phi$, Eq.
leads to a Fourier series with equally spaced azimuthal collocation poiuts There is a total of No=E|l1 augular collocation poiuts 0;. which are the abscissas of Gauss-Legeudre mtegration.
leads to a Fourier series with equally spaced azimuthal collocation points There is a total of $N_\theta=L+1$ angular collocation points $\theta_i$, which are the abscissas of Gauss-Legendre integration.
We enploy the software package Spherepack|?| which provides routines to conirpute the collocation poiuts. transforms and aneular derivatives.
We employ the software package \cite{spherepack-home-page} which provides routines to compute the collocation points, transforms and angular derivatives.
Iu order to resolve the full Fourier series iu o up tom=L. oue uceds l. since for [N,,=2L. the term siu(Lo) vanishes at all collocation points o;.
In order to resolve the full Fourier series in $\phi$ up to $m=L$, one needs $N_\phi\ge 2L+1$ , since for $N_\phi=2L$, the term $\sin(L\phi)$ vanishes at all collocation points $\phi_i$.
We use N,,22(L|1) since FETs are more efficient with an even umnber of points.
We use $N_\phi=2(L+1)$ since FFTs are more efficient with an even number of points.
The expansion has a total of CV,|LCL1)? spectral coefficients but a total of CN,|DNDN,=2CN,LCE1)? collocation points.
The expansion has a total of $(N_r+1)(L+1)^2$ spectral coefficients but a total of $(N_r+1) N_\theta N_\phi=2(N_r+1)(L+1)^2$ collocation points.
This mieaus a spherical shell hasiore collocation points than spectral coefficients and the expansion approximates the grid point values in a least-square seuse ouly|?]..
This means a spherical shell has collocation points than spectral coefficients and the expansion approximates the grid point values in a least-square sense \cite{Swarztrauber:1979}.
Performing a spectral transform aud its inverse will thus project the erid poit values into a subspace with dimension equal to the πο of spectral cocticicuts.
Performing a spectral transform and its inverse will thus project the grid point values into a subspace with dimension equal to the number of spectral coefficients.
The implications of this fact for our code are discussed below in section 3.6..
The implications of this fact for our code are discussed below in section \ref{sec:S-in-Spheres}. .
20pt The basic cosinological parameters that describe our universe Lave now been measurecl with compelliug precision.
20pt $\,$ The basic cosmological parameters that describe our universe have now been measured with compelling precision.
Recent measurements of the cosmic microwave background radiation indicate that the universe is spatially flat [1].
Recent measurements of the cosmic microwave background radiation indicate that the universe is spatially flat [1].
Complementary measurements of the redshift-distauce relation using Type Ia supernovae stronglv suggest that the universe is now accelerating [2].
Complementary measurements of the redshift-distance relation using Type Ia supernovae strongly suggest that the universe is now accelerating [2].
Taken together. the current astronomical data argue for a cosmological model with matter deusity O4, = 0.3. dark vacuum euergy density £44, = 0.7. curvature coustaut &=0. and Hubble constant. Hy = 70 kin ! |.
Taken together, the current astronomical data argue for a cosmological model with matter density $\om$ = 0.3, dark vacuum energy density $\vac$ = 0.7, curvature constant $k=0$ , and Hubble constant $H_0$ = 70 km $^{-1}$ $^{-1}$.
Although the time dependence of the dark energy iis not been fully determined. the current. data are cousistent with the vacuui energy density eine temporally coustaut. as this work assumes.
Although the time dependence of the dark energy has not been fully determined, the current data are consistent with the vacuum energy density being temporally constant, as this work assumes.
This newly cousolicatecl cosmological model represents a milestoue in our uucerstauding of the iniverse.
This newly consolidated cosmological model represents a milestone in our understanding of the universe.
The large scale space-time of the uuiverse is now= kuown aud its corresponding metric cau ye specified.
The large scale space-time of the universe is now known and its corresponding metric can be specified.
Iu the absence of structure formation. the universe is homogeneous aud isotropic. aud he space-time would be described by the maximally svimmetric Robertson-Walker metric [3].
In the absence of structure formation, the universe is homogeneous and isotropic, and the space-time would be described by the maximally symmetric Robertson-Walker metric [3].