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We fid that for separations =17.2. the recovered position is svstematically pulled towards the bright star by 07.1 — 07.2. | We find that for separations $\approx 4$ .2, the recovered position is systematically pulled towards the bright star by .1 – .2. |
This is small enough that wedo not apply this correction. | This is small enough that wedo not apply this correction. |
The same exercise led us to derive the photometric bias. | The same exercise led us to derive the photometric bias. |
The de-biased A-baud magnitude of Pis ing=213x 0.1. | The de-biased $R$ -band magnitude of P is $m_R = 24.3 \pm 0.1$ . |
To inter properties of the WD. we necd to calculate its absolute maguitude. | To infer properties of the WD, we need to calculate its absolute magnitude. |
To calculate the optical extinction. we asstuue that the ratio Διδν is constant along the ine of sight in the direction. of2230. | To calculate the optical extinction, we assume that the ratio $N_{\rm H}/N_e$ is constant along the line of sight in the direction of. |
.. The dispersion measure (DM) for iis (Demorestotal.2010).. aud. the otal DAL in this direction is lü0lppecan (Cordes&Lazio2002) about a factor of three higher hau the pulsar DM. | The dispersion measure (DM) for is $^{-3}$ \citep{heavy}, and the total DM in this direction is $^{-3}$ \citep{dispersion} — about a factor of three higher than the pulsar DM. |
This nuplies that the pulsar is lid approximately one third of the ealactic absorbing column. | This implies that the pulsar is behind approximately one third of the galactic absorbing column. |
We cau then scale the total R baud extinction iu his direction (Agora, = to ect ely= 0.22. | We can then scale the total $R$ band extinction in this direction \citep[$A_{R,{\rm total}} = to get $A_R = 0.22$ . |
We assume Age=0.17 jui for the g bandt.. and use the standard reddening law with Ry=3.1 to cot Ξ0.31 (Cox 2000).. Demorest | We assume $\lambda_{\rm eff} = 0.47\,\mu$ m for the $g$ , and use the standard reddening law with $R_V = 3.1$ to get $A_g = 0.34$ \citep{allens}. . |
Agctal.(2010)use the DM to estimate that lis at a LEdistanced.= L2kkpc. | \citet{heavy} use the DM to estimate that is at a distance$d = 1.2$ kpc. |
For this distance. the extinetion-corrected R-baud absolute maeuitude is | For this distance, the extinction-corrected $R$ -band absolute magnitude is |
bars on the plot. | bars on the plot. |
The total flux in the resolved component is 0.7+0.1 JJy. | The total flux in the resolved component is $\pm$ Jy. |
The general reduction and analysis strategy of the spectroscopic VISIR data is described in detail in?. | The general reduction and analysis strategy of the spectroscopic VISIR data is described in detail in. |
. For 995881 the telluric correction was done by means of an airmass interpolation of two calibrators. | For 95881 the telluric correction was done by means of an airmass interpolation of two calibrators. |
The observation of April 8, 2006, appeared to be suffering strong atmospheric residuals. | The observation of April 8, 2006, appeared to be suffering strong atmospheric residuals. |
The spectrum of December 16 2005 was thus chosen as most representative. | The spectrum of December 16 2005 was thus chosen as most representative. |
The missing observation of the zm setting was replaced with the poor one from April 8, 2006. | The missing observation of the $\mu$ m setting was replaced with the poor one from April 8, 2006. |
We scaled the VISIR spectrum to the Spitzer spectrum at um using1. | We scaled the VISIR spectrum to the Spitzer spectrum at $\mu$ m using. |
16.. The resulting spectrum in has a SNR of ~300. | The resulting spectrum in \\ref{fig:tenmicron}
has a SNR of $\sim$ 300. |
The agreement with the Spitzer spectrum is encouraging. | The agreement with the Spitzer spectrum is encouraging. |
The slight deviation observable just left of the ozone band at um is typical for the quality of the data taken on April 8, 2006. | The slight deviation observable just left of the ozone band at $\mu$ m is typical for the quality of the data taken on April 8, 2006. |
The Full Width at Half Maximum (FWHM) of the spatial emission profile of the target was determined by performing a Gauss-fit in 32 merged wavelength bins. | The Full Width at Half Maximum (FWHM) of the spatial emission profile of the target was determined by performing a Gauss-fit in 32 merged wavelength bins. |
Comparison of the science signals with the PSF shows that the target is unresolved in the continuum. | Comparison of the science signals with the PSF shows that the target is unresolved in the continuum. |
After quadratic subtraction of the PSF and averaging over the median values of all measurements we find a three sigma upper-limit to the FWHM extent of the continuum emission region of « 00.46", which corresponds to « AAU at the adopted distance of 170 pc. | After quadratic subtraction of the PSF and averaging over the median values of all measurements we find a three sigma upper-limit to the FWHM extent of the continuum emission region of $<$ $\arcsec$, which corresponds to $<$ AU at the adopted distance of 170 pc. |
However the science signal displays a relative increase at 8.6 and m and an upturn to the left of 8 um, which are exactly the wavelengths at which the PAH molecules have emission features?). | However the science signal displays a relative increase at 8.6 and $\mu$ m and an upturn to the left of $\sim$ $\mu$ m, which are exactly the wavelengths at which the PAH molecules have emission features. |
. We checked the significance of these FWHM features with respect to to-pixel variations and concluded thatcontinuum. | We checked the significance of these FWHM features with respect to pixel-to-pixel variations and concluded that. |
In order to estimate the spatial extent of the PAH emission we measured the spatial emission profile at the peak wavelengths of the PAH bands and we subtracted the spatial emission profile of the continuum contribution. | In order to estimate the spatial extent of the PAH emission we measured the spatial emission profile at the peak wavelengths of the PAH bands and we subtracted the spatial emission profile of the continuum contribution. |
This continuum profile was determined by interpolating the intensities and spatial profiles adjacent to the PAH bands. | This continuum profile was determined by interpolating the intensities and spatial profiles adjacent to the PAH bands. |
The resulting observed spatial profile of the PAH emission was Gaussian fitted to obtain the FWHM. | The resulting observed spatial profile of the PAH emission was Gaussian fitted to obtain the FWHM. |
Finally, the instrumental width (i.e. the PSF) was quadratically subtracted to obtain a measure for the intrinsic extent of the PAH emission. | Finally, the instrumental width (i.e. the PSF) was quadratically subtracted to obtain a measure for the intrinsic extent of the PAH emission. |
We found FWHM values of 0.34*005 and 0.39*05* for the 8.6 and um PAH bands respectively, which results in absolute sizes of 58 and AAU. | We found FWHM values of $\arcsec^{+0.05}_{-0.08}$ and $\arcsec^{+0.04}_{-0.06}$ for the 8.6 and $\mu$ m PAH bands respectively, which results in absolute sizes of 58 and AU. |
In a Gaussian distribution of the PAH emission this would mean that is confined in a radius of ~100 AAU. | In a Gaussian distribution of the PAH emission this would mean that is confined in a radius of $\sim$ AU. |
Note that this is a conservative estimate of the PAH emission scale since the PAH surface brightness is expected to fall off with distance from the star together with the flux as 1/7?. | Note that this is a conservative estimate of the PAH emission scale since the PAH surface brightness is expected to fall off with distance from the star together with the flux as $r^2$. |
In reffig:tenmicron we compare the spectrum as seen by MIDI, to the spectra observed by VISIR and Spitzer. | In \\ref{fig:tenmicron} we compare the spectrum as seen by MIDI, to the spectra observed by VISIR and Spitzer. |
The correlated flux spectrum is dominated by the central few AU of the disk, the Spitzer and VISIR spectra probe the entire disk. | The correlated flux spectrum is dominated by the central few AU of the disk, the Spitzer and VISIR spectra probe the entire disk. |
Note the difference in the strength of the 8.6 and m PAH bands in the spectra. | Note the difference in the strength of the 8.6 and $\mu$ m PAH bands in the spectra. |
These bands are prominent in the total flux spectra, but essentially absent in the correlated flux spectrum. | These bands are prominent in the total flux spectra, but essentially absent in the correlated flux spectrum. |
The PAH emission region is apparently outside of the disk region probed by MIDI. | The PAH emission region is apparently outside of the disk region probed by MIDI. |
This shows by direct measurement that95881. | This shows by direct measurement that. |
To stress this point we also plotted the difference between the Spitzer and the MIDI correlated flux spectrum in reffig:tenmicron.. | To stress this point we also plotted the difference between the Spitzer and the MIDI correlated flux spectrum in \\ref{fig:tenmicron}. |
This difference spectrum is dominated by the emission of the outer disk and shows very distinct PAH features. | This difference spectrum is dominated by the emission of the outer disk and shows very distinct PAH features. |
To investigate spatial differences in the weak silicate emission we considered the shape of the feature in the Spitzer, | To investigate spatial differences in the weak silicate emission we considered the shape of the feature in the Spitzer, |
SLL. YF. PL and PDC acknowledge financial support from the Belgian Federal Science Policy (rel: NMO/33/018). | SH, YF, PL and PDC acknowledge financial support from the Belgian Federal Science Policy (ref: MO/33/018). |
We acknowledge funding by the Optical Infrared. Co-ordination network (OPTICON). a major. international collaboration supported. by the Research Infrastructures Programme of the European Commissions Sixth Framework Programme. | We acknowledge funding by the Optical Infrared Co-ordination network (OPTICON), a major international collaboration supported by the Research Infrastructures Programme of the European Commission's Sixth Framework Programme. |
This research was in part supported. by the European Lelio- ancl Asteroscismoloey Network (LIELAS). a major international collaboration funded by the European Commission's Sixth Framework Programme. | This research was in part supported by the European Helio- and Asteroseismology Network (HELAS), a major international collaboration funded by the European Commission's Sixth Framework Programme. |
We would like to thank the anonymous referee. for valuable comments. which helped to improved the manuscript considerably. | We would like to thank the anonymous referee for valuable comments, which helped to improved the manuscript considerably. |
παπο substellar companions. | unknown substellar companions. |
However. for follow-up observations of higl-contrast objects detected. by. other means. Where spectral properties need to be determined. the method has excellent prospects. | However, for follow-up observations of high-contrast objects detected by other means, where spectral properties need to be determined, the method has excellent prospects. |
On this subject. we will briefly discuss the spectral deconvolution (SD) technique. | On this subject, we will briefly discuss the spectral deconvolution (SD) technique. |
SD was suegeested for detection of substellar coupaious »* Sparks Ford (2002). and has been applied to AB Dor obscrvatious with SINFONI by Thatte et al. ( | SD was suggested for detection of substellar companions by Sparks Ford (2002), and has been applied to AB Dor observations with SINFONI by Thatte et al. ( |
2007). | 2007). |
The latter show that the SNR of AD Dor € (a low-mass companion close to AD Dor A) can be increased by applying SD aud using a priori information about the position of AB Dor C. They also give a general radial contrast profile based on the standard deviation of the final nuaec. | The latter show that the SNR of AB Dor C (a low-mass companion close to AB Dor A) can be increased by applying SD and using a priori information about the position of AB Dor C. They also give a general radial contrast profile based on the standard deviation of the final image. |
Trauslatine their quoted Loa points into 30 and including them in Fig. | Translating their quoted $1 \sigma$ points into $3 \sigma$ and including them in Fig. |
1 iuplies that SD with SINFONI cau reach almost as high contrast as NACO-SDI. if we geucrously assuine that its SNR develops according to £7. | \ref{sdi_img} implies that SD with SINFONI can reach almost as high contrast as NACO-SDI, if we generously assume that its SNR develops according to $t^{1/2}$. |
However. this coutrast is ouly valid well outside of au angular separation quantified bv Thatte et al. ( | However, this contrast is only valid well outside of an angular separation quantified by Thatte et al. ( |
2007) as the bifurcation radius. | 2007) as the bifurcation radius. |
For the SINFONI "IL|R mode. the biftweation radius is about 250 mas. | For the SINFONI “H+K” mode, the bifurcation radius is about 250 mas. |
Tusicde of this radius. a large fraction of the companion fux will inevitably be subtracted out bv the SD technique Gf its position is not known a priori or. equivalently. can be seen in the data already prior to | Inside of this radius, a large fraction of the companion flux will inevitably be subtracted out by the SD technique (if its position is not known a priori or, equivalently, can be seen in the data already prior to |
from nearly zero up to ~0.3Mo. | from nearly zero up to $\sim0.3 M_{\odot}$. |
Mergers leading to significant disks occur in a small (but not negligible) region of parameter space and could produce a sGRB. | Mergers leading to significant disks occur in a small (but not negligible) region of parameter space and could produce a sGRB. |
In follow up work we plan to extend the parameter space survey, varying the NS EOS and BH spin. | In follow up work we plan to extend the parameter space survey, varying the NS EOS and BH spin. |
We also intend to explore the detectability of these events with GW detectors, and conclude with brief preliminary comments. | We also intend to explore the detectability of these events with GW detectors, and conclude with brief preliminary comments. |
These signals may be difficult to detect with instruments such as LIGO since they lack a long inspiral phase and most of the power is at high frequencies (1500-2000 Hz for the masses considered here). | These signals may be difficult to detect with instruments such as LIGO since they lack a long inspiral phase and most of the power is at high frequencies (1500-2000 Hz for the masses considered here). |
Using the broadband AdLIGO noise curve, we find sky-averaged | Using the broadband AdLIGO noise curve, we find sky-averaged |
and 75 - the Pauli matrix. | and $\sigma_3$ - the Pauli matrix. |
Then we ect where fy. NV=1.2.3... di au iufinite time hierarchy. | Then we get where $t_N$, $N = 1, 2, 3, ...$ is an infinite time hierarchy. |
In the linear approximation. when &—0. the recursion: operator is: just. the momcutuu operator ERy=10357.j and the NLS hierarchy (CI) becomes the linear Schrodiuger hierarchy from Section 1. | In the linear approximation, when $\kappa = 0$, the recursion operator is just the momentum operator ${\cal{R}}_0 = i \sigma_3 \frac{\partial}{\partial x}$ and the NLS hierarchy \ref{NLShierarchy}) ) becomes the linear Schrodinger hierarchy from Section 1. |
The Madehme representation for this hierarchy. produced bv the complex Cole-ITopf. trausformation. is given by the complex Durgers hierarchy |I]. | The Madelung representation for this hierarchy, produced by the complex Cole-Hopf transformation, is given by the complex Burgers hierarchy \cite{PG}. |
Every equation of hierarchy. (11)) is iutegrable. | Every equation of hierarchy \ref{NLShierarchy}) ) is integrable. |
The linear problem for the N-th equation is elven by the Zakharov-Shabat problemi (36)) for the space part aud for the time part. | The linear problem for the $N$ -th equation is given by the Zakharov-Shabat problem \ref{ZS11}) ) for the space part and for the time part. |
Coefficient functions Cy. can be found conveniently as To rewrite this expression in a compact form we introduce notation of the q-uuuber operator where gis à linear operator. | Coefficient functions $C_N$ can be found conveniently as To rewrite this expression in a compact form we introduce notation of the q-number operator where $q$ is a linear operator. |
Hence. with operator q=Rp we lave following finite Laurent form in the spectral parameter p Tn a similar wav Equatious (13)).C17)) aud (18)) eive the time part of the lear problem (the Lax represeutation) for the N-th flow of NLS hierarchy CI) iu the q-caleulus fori. | Hence, with operator $q \equiv
{\cal{R}}/p$ we have following finite Laurent form in the spectral parameter $p$ Then we have shortly In a similar way Equations \ref{ZSTN}) \ref{CN}) ) and \ref{AN}) ) give the time part of the linear problem (the Lax representation) for the N-th flow of NLS hierarchy \ref{NLShierarchy}) ) in the q-calculus form. |
We thank the anonymous referee for the helpful comments/suggestions. T. G. Wang and Y. F. Yuan for discussion. and N. Tamura for providing us the data of the spheroid-BHMEFs. | We thank the anonymous referee for the helpful comments/suggestions, T. G. Wang and Y. F. Yuan for discussion, and N. Tamura for providing us the data of the spheroid-BHMFs. |
This work is supported by the NSFC (grant. 10773020). and the CAS (erant KICX2-YW-TO3). | This work is supported by the NSFC (grant 10773020), and the CAS (grant KJCX2-YW-T03). |
2550. 6300. ancl 10050. vr. for species that are. potentially observable. | 2550, 6300, and 10050 yr, for species that are potentially observable. |
The earliest epoch is approximately when the interclump abundances are at à maximum. while the values in the clump of species formed by degradation are low. | The earliest epoch is approximately when the interclump abundances are at a maximum, while the values in the clump of species formed by degradation are low. |
For such species. then the ratio Is low. | For such species, then the ratio is low. |
At epoch 6300vr. many of the degradation. products have declined. in abundance in the interclump gas. while their abundances in the clump gas are growing. so the ratio is generally large. | At epoch ${\rm 6300~yr}$, many of the degradation products have declined in abundance in the interclump gas, while their abundances in the clump gas are growing, so the ratio is generally large. |
At the latest epoch shown in Table 1. then most of the degradation products have. declined. in abundance in the clump gas. and have declined even further in the interclump eas. so the ratio is in many cases again large. | At the latest epoch shown in Table 1, then most of the degradation products have declined in abundance in the clump gas, and have declined even further in the interclump gas, so the ratio is in many cases again large. |
However. by this stage the abundances in the clump eas max have declined so far as to make many of the species uneletectable. | However, by this stage the abundances in the clump gas may have declined so far as to make many of the species undetectable. |
Lowe take a fractional abundance of 10.7 to represent a characteristic detection limit at 10000vr. where the clump extinction is 1 magnitude. then about of the species listed are possibly not detectable at this epoch. whereas only about 30 percent are not detectable at 6500vr. | If we take a fractional abundance of $10^{-8}$ to represent a characteristic detection limit at ${\rm 10000~yr}$, where the clump extinction is $\sim 1$ magnitude, then about of the species listed are possibly not detectable at this epoch, whereas only about 30 percent are not detectable at ${\rm 6500~yr}$. |
Thus. there is a very significant change in the detectable chemistry of the clump eas the PN ages. | Thus, there is a very significant change in the detectable chemistry of the clump gas the PN ages. |
The column density of any species is mace up of contributions from both clump ancl interclump gas. | The column density of any species is made up of contributions from both clump and interclump gas. |
At the earliest PPN epoch illustrated. Table I shows that ehemistry is largely. determined by the interelump eas. while at later epochs it is determined in the cbumps. | At the earliest PPN epoch illustrated, Table 1 shows that chemistry is largely determined by the interclump gas, while at later epochs it is determined in the clumps. |
Fable 2 lists molecules that are likely to be the most important. tracers of either chump or interclump gas. at the three epochs chosen. | Table 2 lists molecules that are likely to be the most important tracers of either clump or interclump gas, at the three epochs chosen. |
llere the results will. be compared. very. generally with observations of three objects: CRLGLIS. NOGCTO27 and. the llelix. nebula. | Here the results will be compared very generally with observations of three objects: CRL618, NGC7027 and the Helix nebula. |
These objects span progressively acivanced evolutionary stages with CRLGIS being a PPN. NGC 7027 a voung PN and the Ilelix an evolved PN. | These objects span progressively advanced evolutionary stages with CRL618 being a PPN, NGC 7027 a young PN and the Helix an evolved PN. |
As discussed. immediately. below. comparison with CLRLGIS is made cilfieult by the complex geometry of the source. | As discussed immediately below, comparison with CRL618 is made difficult by the complex geometry of the source. |
The comparisons with NGC 7027 ancl the LHelix are more straight-Forward. | The comparisons with NGC 7027 and the Helix are more straight-forward. |
Carbon-rich protoplanctary nebulae such as 1015 and APCGL268s8 have been the subject of several molecular studies in recent vears. | Carbon-rich protoplanetary nebulae such as CRL618 and AFGL2688 have been the subject of several molecular studies in recent years. |
Ln particular. CIRLGIS has been used. as à tvpical example of an asvmptotic giant branch (AGB) star in the transition evolving toward the planetary nebula stage (Llerpin&Cernicharo2000:: Cernicharo ct al. | In particular, CRL618 has been used as a typical example of an asymptotic giant branch (AGB) star in the transition evolving toward the planetary nebula stage \citealt{herpin&chernicharo00}; Cernicharo et al. |
2001a.b: Woods et al. | 2001a,b; Woods et al. |
2002). | 2002). |
Llere we attempt a qualitative comparison of our models with some observations and theoretical work on this object. | Here we attempt a qualitative comparison of our models with some observations and theoretical work on this object. |
show that to reproduce the observed emission of CO. LICN. UNC. H2O0. OLI and O. à 3-component geometry is needed (see their figure 3). with a central torus at high density (~I0'em.7) and a gradient of temperatures ranging [rom 250 to 1000 Ix: an extended AGB remnant envelope with a density of 5.LOem. and temperature of LOOK: and finally the lobes. where high velocity. gas is emitted. from. with a density of 10cm and a lwo-component teniperature of 200 and 1000 Ix. In follow up papers. Cernicharo οἱ (2001a.b) observed methylpolyvnes. small hydrocarbons and benzene along the same line of sight and conclude that the emission of these species must. come from the central torus region. | show that to reproduce the observed emission of CO, HCN, HNC, $_2$ O, OH and O, a 3-component geometry is needed (see their figure 3), with a central torus at high density $\sim 5 \times 10^7~{\rm cm}^{-3}$ ) and a gradient of temperatures ranging from 250 to 1000 K; an extended AGB remnant envelope with a density of $5\times 10^5~{\rm cm^{-3}}$ and temperature of 100K; and finally the lobes, where high velocity gas is emitted from, with a density of $10^7~{\rm cm^{-3}}$ and a two-component temperature of 200 and 1000 K. In follow up papers, Cernicharo et (2001a,b) observed methylpolyynes, small hydrocarbons and benzene along the same line of sight and conclude that the emission of these species must come from the central torus region. |
The scenario we model. is. different from. the. 3-component geometry but we can attempt a comparison with the species emitted from the AGB remnant component where the temperature is close to the one derived. in our model (see Table 1). although the density is much higher. | The scenario we model is different from the 3-component geometry but we can attempt a comparison with the species emitted from the AGB remnant component where the temperature is close to the one derived in our model (see Table 1), although the density is much higher. |
We find that our best match with the PPN CRLGIS occurs at early times few hundred vears. | We find that our best match with the PPN CRL618 occurs at early times $\sim $ few hundred years. |
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