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because they can be used as standard candles (?)).
because they can be used as standard candles \citealt{pozn2010}) ).
Here, we classify Type II-P supernovae in the SN Challenge data set using the above methods and analogous Type II-P figure of merit.
Here, we classify Type II-P supernovae in the SN Challenge data set using the above methods and analogous Type II-P figure of merit.
In we display the results of Type II-P supernova classification Table[7]with each of the 8 training sets, and in Fig.
In Table \ref{tab:classIIp} we display the results of Type II-P supernova classification with each of the 8 training sets, and in Fig.
we plot the distribution of the Type II-P FoM, purity βand efficiency with respect to each spectroscopic follow-up strategy.
\ref{fig:IIpphot} we plot the distribution of the Type II-P FoM, purity and efficiency with respect to each spectroscopic follow-up strategy.
Much like the Ia study, we find that the deeper magnitude-limited surveys perform the best.
Much like the Ia study, we find that the deeper magnitude-limited surveys perform the best.
We find that in terms of Type H-P figure of merit, a magnitude limited survey performs the best, achieving 24.5thfirp,prea=0.586, with purity and efficiency at and84%,, respectively.
We find that in terms of Type II-P figure of merit, a 24.5th magnitude limited survey performs the best, achieving $\widehat{f}_{\rm IIP, pred}=0.586$, with purity and efficiency at and, respectively.
Qualitatively, the Type II-P figures of merit resemble those of the type Ia study.
Qualitatively, the Type II-P figures of merit resemble those of the type Ia study.
For each training set, the purity of the classifications is quite high, above80%,, while the efficiency differs greatly, from a minimum of for S toa maximum of for Sm,25.
For each training set, the purity of the classifications is quite high, above, while the efficiency differs greatly, from a minimum of for $\mathcal{S}$ to a maximum of for $\mathcal{S}_{m,25}$ .
Compared to the training set, S, used in the SN Challenge, a 24.5th magnitude-limited survey achieves only a slightly better II-P purity, but a 1.6 times increase in II-P efficiency.
Compared to the training set, $\mathcal{S}$, used in the SN Challenge, a 24.5th magnitude-limited survey achieves only a slightly better II-P purity, but a 1.6 times increase in II-P efficiency.
Finally, we study the performance of the two methods of incorporating host-galaxy redshifts refss:redshiftDescription)).
Finally, we study the performance of the two methods of incorporating host-galaxy redshifts \\ref{ss:redshiftDescription}) ).
In Tables and [9] we show the results of classifying Type Ia and II-P SNe, respectively, using each of the two strategies for incorporating redshifts.
In Tables \ref{tab:zclassIa} and \ref{tab:zclassIIp} we show the results of classifying Type Ia and II-P SNe, respectively, using each of the two strategies for incorporating redshifts.
Results are shown for each of the 8 training sets, where the optimal redshift cutoff, n, in eq.
Results are shown for each of the 8 training sets, where the optimal redshift cutoff, $n_s$ in eq. \ref{eqn:hostz}) ),
was chosen by maximizing the cross-validated training set (9),FoM over a grid of integer values from 2 to 6.
was chosen by maximizing the cross-validated training set FoM over a grid of integer values from 2 to 6.
There is a clear improvement to the FoMs by including host-galaxy redshifts.
There is a clear improvement to the FoMs by including host-galaxy redshifts.
Compared to the non-redshift results in Tables [5H], the FoM values increase for every training set by the use of redshift to alter the diffusion map coordinates.
Compared to the non-redshift results in Tables \ref{tab:classIa}- \ref{tab:classIIp}, the FoM values increase for every training set by the use of redshift to alter the diffusion map coordinates.
Using redshifts to alter the diffusion map coordinates consistently performs better than using redshift as a covariate.
Using redshifts to alter the diffusion map coordinates consistently performs better than using redshift as a covariate.
Overall, the best strategy for including host-galaxy redshifts for Type Ia classification is to use eq. (9))
Overall, the best strategy for including host-galaxy redshifts for Type Ia classification is to use eq. \ref{eqn:hostz}) )
with n;=2 on the training set S,,,25.
with $n_s=2$ on the training set $\mathcal{S}_{m,25}$.
Using this prescription yields a Type Ia FoM of 0.355, an improvement of over the best FoM without redshift.
Using this prescription yields a Type Ia FoM of 0.355, an improvement of over the best FoM without redshift.
For Type II-P classification, the best strategy is to use n,—4, resulting in a FoM of 0.612, which represents an improvement of4.
For Type II-P classification, the best strategy is to use $n_s=4$, resulting in a FoM of 0.612, which represents an improvement of.
4%.. We plot the Type Ia FoM, purity, and efficiency as a function of redshift in Figure forthe analysis without using photometric redshifts, and in Figure for the analysis incorporating photo-z's with n,— 2.
We plot the Type Ia FoM, purity, and efficiency as a function of redshift in Figure \ref{fig:fomz} forthe analysis without using photometric redshifts, and in Figure \ref{fig:fomz4} for the analysis incorporating photo-z's with $n_s=2$ .
Within each
Within each
spectral data obtained by SylvesterandSkinner.(1996).. whose observations cover the 8-21 juu region. aud who used the photometry [rom another instrument in their modeling.
spectral data obtained by \citet{ss96}, whose observations cover the 8-24 $\mu$ m region, and who used the photometry from another instrument in their modeling.
The value of tlT BASS observations are that they cover the waveleneth regions dominated by both photospheri aud dust. emission simultaneously ancl ou the same photometric system. allowing the photospheric flux to be extrapolated out into the 10 jiu region using a single set of simultaneous data.
The value of the BASS observations are that they cover the wavelength regions dominated by both photospheric and dust emission simultaneously and on the same photometric system, allowing the photospheric flux to be extrapolated out into the 10 $\mu$ m region using a single set of simultaneous data.
The ISOPHOT observations of WalkeraudHeinrichsen(2000) cover the 5.8-11.6 jan region. but suffer [rom such large systematic fluctuatious in the sigual that the silicate feature cannot even be seen.
The ISOPHOT observations of \citet{wh00} cover the 5.8-11.6 $\mu$ m region, but suffer from such large systematic fluctuations in the signal that the silicate feature cannot even be seen.
The BASS spectrum shortward of 6 gam is well-fit by the photospheric model normalized near 3 yan. This is consistent with the results of Ixoerneretal.(2000).. who fit similar models to the iudividual A and B components of the system (each of which is a binary). and lind that the flux is dominated by photospheric emission out to 7 jun in both A aud B components.
The BASS spectrum shortward of 6 $\mu$ m is well-fit by the photospheric model normalized near 3 $\mu$ m. This is consistent with the results of \citet{koerner00}, who fit similar models to the individual A and B components of the system (each of which is a binary), and find that the flux is dominated by photospheric emission out to 7 $\mu$ m in both A and B components.
Iu Figures [and 5 we show the spectrum of HR. 10796À. and its appropriate model atmosphere.
In Figures 4 and 5 we show the spectrum of HR 4796A and its appropriate model atmosphere.
The 8-13.5 jun flux is weak. aud half is photospheric. Ixoernerοἱal.(19908).
The 8-13.5 $\mu$ m flux is weak, and half is photospheric. \citet{koerner98},
. using thermal imaging VIz‘ith the MERLIN instrument on Weck. derive a total [lux at 12.5 pim of 1 2. of which it was estimated that half was photospheric.
using thermal imaging with the MERLIN instrument on Keck, derive a total flux at 12.5 $\mu$ m of $^{-14}$ $^{-2}$, of which it was estimated that half was photospheric.
For the BASS observations. the 12-13 gam flux is higher than those derived from MERLIN. but the fraction due to photospheric emission is comparable.
For the BASS observations, the 12-13 $\mu$ m flux is higher than those derived from MERLIN, but the fraction due to photospheric emission is comparable.
The lack of any detectable excess flux shortward of & pm indicates that there is little dust hotter than 150 Ix or closer than about 2 AU (depeucling somewhat on the optical albedo aud infrared emissivity of the grains).
The lack of any detectable excess flux shortward of 8 $\mu$ m indicates that there is little dust hotter than 450 K or closer than about 2 AU (depending somewhat on the optical albedo and infrared emissivity of the grains).
Augereauetal.(1999) have modeled the spectral energy distribution of HR 1796À. including the hot inner region. with a 2-component dust mocel.
\citet{aug99} have modeled the spectral energy distribution of HR 4796A, including the hot inner region, with a 2-component dust model.
In their model. the excess emission near 10 jun comes primarily from huge (larger than 100 jun in size) grains locatec near 9 AU [rom the star.
In their model, the excess emission near 10 $\mu$ m comes primarily from huge (larger than 100 $\mu$ m in size) grains located near 9 AU from the star.
Unfortunately. the quality of the spectra here are inadequate the detailec spectral features expected [rom such material.
Unfortunately, the quality of the spectra here are inadequate the detailed spectral features expected from such material.
Some Wali sequence aud pre-main sequence stars with dusty debris disks possess silicate grains whose spectral features resemble those of loug-period comets.
Some main sequence and pre-main sequence stars with dusty debris disks possess silicate grains whose spectral features resemble those of long-period comets.
Ixuackeetal.(1993) were the first to demonstrate this by comparing the 10 san emission feature in ο Pic with 1P/Halles and Levy 1990 (C/1991 L3).
\citet{knacke93} were the first to demonstrate this by comparing the 10 $\mu$ m emission feature in $\beta$ Pic with 1P/Halley and Levy 1990 (C/1991 L3).
All three objects exhibit au emission baud with maxima or shoulders near 9.5 jm and 11.2 gam. the latter indicative of crystalline olivine.
All three objects exhibit an emission band with maxima or shoulders near 9.5 $\mu$ m and 11.2 $\mu$ m, the latter indicative of crystalline olivine.
Subsequently. HAEBEs embecded iu star-formiug regions have been exaimiued (i.e. Hauueretal. (1995))) and some. such as HD 150193
Subsequently, HAEBEs embedded in star-forming regions have been examined (i.e. \citet{hanner95}) ) and some, such as HD 150193
being scattered upward into space.
being scattered upward into space.
Furthermore. has a significant iron. content in its particles in the upper atmosphere. which is strongly absorbing.
Furthermore, has a significant iron content in its particles in the upper atmosphere, which is strongly absorbing.
If the iron content is lowered. the single scattering albedo also quickly rises.
If the iron content is lowered, the single scattering albedo also quickly rises.
To illustrate the effect of highly scattering particles. we also calculated a case where the particle single-scattering albedos are set to unity (Le. non-absorbing particles).
To illustrate the effect of highly scattering particles, we also calculated a case where the particle single-scattering albedos are set to unity (i.e. non-absorbing particles).
This is. the extreme case. but it ts realistic for particles larger than the wavelength with a low iron content.
This is the extreme case, but it is realistic for particles larger than the wavelength with a low iron content.
For ease of comparison between the cases with different single-scattering albedos. the phase functions and optical thicknesses are kept identical here.
For ease of comparison between the cases with different single-scattering albedos, the phase functions and optical thicknesses are kept identical here.
Figs.
Figs.
5. and 6 show this case as well (dot-dashed lines).
\ref{fig.spec1} and \ref{fig.spec2} show this case as well (dot-dashed lines).
It is clear that the scattering makes a very large difference in how the spectrum looks here: gas absorption features are much more apparent and overal brightness temperature levels are changed substantially.
It is clear that the scattering makes a very large difference in how the spectrum looks here: gas absorption features are much more apparent and overal brightness temperature levels are changed substantially.
Also note that the relative strengths of the water bands can change significantly by changing the single-scattering albedo of the particles.
Also note that the relative strengths of the water bands can change significantly by changing the single-scattering albedo of the particles.
Thus. if clouds would not be considered 11 the interpretation of this thermal emission spectrum. one could derive completely different temperature profiles and gas adundances than what is actually present in the atmosphere.
Thus, if clouds would not be considered in the interpretation of this thermal emission spectrum, one could derive completely different temperature profiles and gas adundances than what is actually present in the atmosphere.
If phase functions also would be more forward scattering. as Is generally the case with larger particles. this difference with non-scattering particles will be even more pronounced.
If phase functions also would be more forward scattering, as is generally the case with larger particles, this difference with non-scattering particles will be even more pronounced.
To illustrate the potential effect of à more forward-scattering phase function. we calculate two spectra with only a difference in the phase function.
To illustrate the potential effect of a more forward-scattering phase function, we calculate two spectra with only a difference in the phase function.
The temperature and optical thicknesses at 1 micron are taken from the 1500 K case. but instead of the particle wavelength-dependence of Fig.
The temperature and optical thicknesses at 1 micron are taken from the 1500 K case, but instead of the particle wavelength-dependence of Fig.
3 we assume optical thickness to be constant with wavelength and single-seattering albedos of unity. as is common for large non-absorbing particles.
\ref{fig.xsc1} we assume optical thickness to be constant with wavelength and single-scattering albedos of unity, as is common for large non-absorbing particles.
Also. all particles throughout the atmosphere were assumed identical.
Also, all particles throughout the atmosphere were assumed identical.
The two different phase functions were also assumed constant with wavelength and were taken from the T;= 1500 K Al:O; cloud at a wavelength of 0.3 micron (asymmetry parameter of g= 0.83) and the Tar 22000 K high silicate haze at 5 micron (e=3- 107+).
The two different phase functions were also assumed constant with wavelength and were taken from the $_{\mathrm{eff}} =$ 1500 K $_2$ $_3$ cloud at a wavelength of 0.3 micron (asymmetry parameter of $g=0.83$ ) and the $_{\mathrm{eff}} =$ 2000 K high silicate haze at 5 micron $g = 3 \cdot 10^{-4}$ ).
The first is thus strongly forward-scattering. whereas the latter is almost isotropically scattering.
The first is thus strongly forward-scattering, whereas the latter is almost isotropically scattering.
The two spectra with the two different particles are shown in Fig. 7..
The two spectra with the two different particles are shown in Fig. \ref{fig.gtest}.
Even though the particle optical thicknesses for both cases are identical. the spectra differ very strongly.
Even though the particle optical thicknesses for both cases are identical, the spectra differ very strongly.
The forward-scattering particles allow more heat from the warmer regions below the clouds to escape to space. giving higher radiances and stronger absorption features.
The forward-scattering particles allow more heat from the warmer regions below the clouds to escape to space, giving higher radiances and stronger absorption features.
Hence. assuming isotropic scattering can give errors of many tens of percent on the spectrum if the particles are in fact strongly forward-scattering.
Hence, assuming isotropic scattering can give errors of many tens of percent on the spectrum if the particles are in fact strongly forward-scattering.
Cloud and/or haze particles in. the atmospheres of hot exoplanets or brown dwarfs can have a strong effect on their thermal emission spectra. changing their brightness and colour at different wavelengths.
Cloud and/or haze particles in the atmospheres of hot exoplanets or brown dwarfs can have a strong effect on their thermal emission spectra, changing their brightness and colour at different wavelengths.
These thermal emission spectra can be measured either directly. or from their secondary eclipse.
These thermal emission spectra can be measured either directly, or from their secondary eclipse.
The effect of the clouds is strongest at shorter wavelengths and colder temperatures for the model. and generally for small particles.
The effect of the clouds is strongest at shorter wavelengths and colder temperatures for the model, and generally for small particles.
This makes the brown dwarf more ‘red’ in the infrared.
This makes the brown dwarf more `red' in the infrared.
Although the latter effect is clear from previous studies. not much attention has been given in the past to the contribution from scattered light to the spectrum.
Although the latter effect is clear from previous studies, not much attention has been given in the past to the contribution from scattered light to the spectrum.
Here. we show that not only the extinction of the cloud. but also the scattering nature of the particles can be important in determining the emission spectra for these objects.
Here, we show that not only the extinction of the cloud, but also the scattering nature of the particles can be important in determining the emission spectra for these objects.
Scattering can affect the emission spectra especially when the particles are large and have little iron in them.
Scattering can affect the emission spectra especially when the particles are large and have little iron in them.
Hence. knowledge of the scattering properties such as single-scattering albedo and phase functior can be crucial in calculating accurate spectra of sub-stellar atmospheres.
Hence, knowledge of the scattering properties such as single-scattering albedo and phase function can be crucial in calculating accurate spectra of sub-stellar atmospheres.
Errors 1n these parameters will result in errors in atmospheric properties derived. from infrared direct measurements or secondary eclipses.
Errors in these parameters will result in errors in atmospheric properties derived from infrared direct measurements or secondary eclipses.
Also the self-consistent calculation of the temperature structure in such an atmosphere can thus depend significantly on the assumed or calculated scattering. properties in the atmosphere.
Also the self-consistent calculation of the temperature structure in such an atmosphere can thus depend significantly on the assumed or calculated scattering properties in the atmosphere.
For instance. Fig.
For instance, Fig.
7 shows that more forward-scattering phase functions. allow more heat from lower altitudes to escape to space. leading to an increase in cooling of these lower regions compared to more isotropically scattering particles.
\ref{fig.gtest} shows that more forward-scattering phase functions allow more heat from lower altitudes to escape to space, leading to an increase in cooling of these lower regions compared to more isotropically scattering particles.
This also will affect calculations made using the isotropically scattering model. if the particles are more scattering than the silicate haze in the two cases presented here.
This also will affect calculations made using the isotropically scattering model, if the particles are more scattering than the silicate haze in the two cases presented here.
The errors due to the parameterisation of the phase function in terms of g are bound to be less severe. but probably can reach several percent in the calculated radiance.
The errors due to the parameterisation of the phase function in terms of $g$ are bound to be less severe, but probably can reach several percent in the calculated radiance.
Thus. care must be taken in the choice of radiative transfer method for heat balance or spectral calculations. depending on the type of particles that are predicted.
Thus, care must be taken in the choice of radiative transfer method for heat balance or spectral calculations, depending on the type of particles that are predicted.
volume of the shell) for he simulations.
volume of the shell) for the simulations.
The media- anit value for the ciission measure from all tle simulated eyceles is shown in σοι 6.
The median maximum value for the emission measure from all the simulated cycles is shown in column 6.
Fig.3 shows how the radius. velocity. aud ewission measure changes with time through a shell episode.
Fig.3 shows how the radius, velocity, and emission measure changes with time through a shell episode.
We have ideutified the shell at the point where there is a local masini in deusity (svheu the shell is close to he star it becomes difficult to identify unambiguously ai so these points have been left οτι of fig.3).
We have identified the shell at the point where there is a local maximum in density (when the shell is close to the star it becomes difficult to identify unambiguously and so these points have been left out of fig.3).
The wind iutially sweeps up the ambicut gas creating a low clensity-coutrast shell.
The wind initially sweeps up the ambient gas creating a low density-contrast shell.
Iu this phase the shell is decelerating from the decoupling radius. aud moving out in radius.
In this phase the shell is decelerating from the decoupling radius, and moving out in radius.
Finally the shell comes to rest (0;=0 at rowBOR. 9). and it starts to eain mass.
Finally the shell comes to rest $v_s = 0$ at $r \approx 3.5$ ), and it starts to gain mass.
The ciuissiou neasure starts to increase sigenificautlv diving this time.
The emission measure starts to increase significantly during this time.
When it cannot be supported anv longer the shell starts ο fall back toward the star. finally coming iuto contact ith the star at a velocity of around
When it cannot be supported any longer the shell starts to fall back toward the star, finally coming into contact with the star at a velocity of around.
All of the simulations produce very similar plots except he scaling5 iu time aud positioi aye differcut.
All of the simulations produce very similar plots except the scaling in time and position are different.
We find that he stalling radii are very siniar to those predicted using eq.2 (table 1. column 3).
We find that the stalling radii are very similar to those predicted using eq.2 (table 1, column 3).
The iod for initial shell erowth has already: becu shown to be dependent on the mass-loss rate via the stalliug radius (eq.5) which ds dn tur. set bv the decoupling radius.
The period for initial shell growth has already been shown to be dependent on the mass-loss rate via the stalling radius (eq.5) which is, in turn, set by the decoupling radius.
As the mass-loss rate increases. the CCOIpling velocity/racius increases (sec table 1). axd so the sagnation radius (at which the shell forms) aSO increases.
As the mass-loss rate increases, the decoupling velocity/radius increases (see table 1), and so the stagnation radius (at which the shell forms) also increases.
We expect that the scaling relationships in the Lerowth timescale (eq.5) is similar for the timescale he shel episode as a whole. although the time for shell erowth is only a fraction of the shell evcle.
We expect that the scaling relationships in the shell-growth timescale (eq.5) is similar for the timescale of the shell episode as a whole, although the time for shell growth is only a fraction of the shell cycle.
ence expect that the period shotld be proportiona to the hue radius squared.
Hence we expect that the period should be proportional to the stalling radius squared.
In fie.l1 the logarithmic hue radius relatiouship is displaved.
In fig.4 the logarithmic period-stalling radius relationship is displayed.
We have performed a least-squares fit to the above data aud find that the period P is related to the stalling radius via P=3.2271" which is close to the expected scaling.
We have performed a least-squares fit to the above data and find that the period $P$ is related to the stalling radius via $P = 3.22 r_s^{1.7}$ which is close to the expected scaling.
We also find that the maxim emission nieasure follows the same scaling with radius.
We also find that the maximum emission measure follows the same scaling with radius.
The total mass in the shell will typically be the wind mass-loss rate multiplied by the total lifetime of the shell.
The total mass in the shell will typically be the wind mass-loss rate multiplied by the total lifetime of the shell.
Timescales of ~cdav have been found from the previous section. vielding maximuun shell masses of Maji~10.1? LOTAL.
Timescales of $\sim$ day have been found from the previous section, yielding maximum shell masses of $M_{\rm shell} \sim 10^{-13}$ $10^{-12}\msun$.
Clearly such a low mass will not have a large influence on the eross observational properties of the star.
Clearly such a low mass will not have a large influence on the gross observational properties of the star.
The most obvious effect of decouple is that the muaxiumiü wind velocity will be observed to be lower than the terminal velocities frou theoretical studies a phenomenon which has been known observationallv for
The most obvious effect of decoupling is that the maximum wind velocity will be observed to be lower than the terminal velocities from theoretical studies – a phenomenon which has been known observationally for
flix due to rather poor observing conditions in terms of seeing and transparency.
flux due to rather poor observing conditions in terms of seeing and transparency.
The calibrator stars for the data reduction were chosen by analyzing all calibrator stars observed over the whole night.
The calibrator stars for the data reduction were chosen by analyzing all calibrator stars observed over the whole night.
We selected those showing a good agreement in their transfer [unctions. ie. their instrumental visibilities alter the assumed sizes were taken into account.
We selected those showing a good agreement in their transfer functions, i.e. their instrumental visibilities after the assumed sizes were taken into account.