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Again. the predicted black hole mass agrees very well with the dynamically determined mass (section 3).
Again, the predicted black hole mass agrees very well with the dynamically determined mass (section 3).
The possible relevance of the 3:2 resonance model to the periodicities reported for AA* has been mentioned in the papers of
The possible relevance of the 3:2 resonance model to the periodicities reported for A* has been mentioned in the papers of
black hole accretion aud feedback (c.e.. Di Matteo 2005. Topkins 2005).
black hole accretion and feedback (e.g., Di Matteo 2005, Hopkins 2005).
Successfully miecasuring the transverse proximuitv effect or finding a lieht echo would represent one way to test these models.
Successfully measuring the transverse proximity effect or finding a light echo would represent one way to test these models.
This paper is structured as follows.
This paper is structured as follows.
In 822 quasar light echoes are outlined in more detail.
In 2 quasar light echoes are outlined in more detail.
In 833 the sinmlatious used to produce spectra to which light echoes were artificially applied are described.
In 3 the simulations used to produce spectra to which light echoes were artificially applied are described.
In Ll a technique is described to search for quasar light echoes in sspectra.
In 4 a technique is described to search for quasar light echoes in spectra.
In 855 the results of searches for light echoes iu siuulated data are presented.
In 5 the results of searches for light echoes in simulated data are presented.
These results include the sensitivity of the test to different quasar luminosities aud to varviug the uuuber of aud resolution of sspectra.
These results include the sensitivity of the test to different quasar luminosities and to varying the number of and resolution of spectra.
In 866. we discuss our results. computing the chances of finding a light echo in observational data aud the vohune of data that would be required to do so.
In 6, we discuss our results, computing the chances of finding a light echo in observational data and the volume of data that would be required to do so.
The radiation enuütted from a quasar has au effect on the ionization state of the eas through which it passes.
The radiation emitted from a quasar has an effect on the ionization state of the gas through which it passes.
If a quasar produced high levels of radiation for some period of time a signature will be left iu the suiroundiug gas lone after this period has stopped.
If a quasar produced high levels of radiation for some period of time a signature will be left in the surrounding gas long after this period has stopped.
There will be lower levels of jeutral hydrogen in the region affected by the propagating radiation from the once active quasar. as described bv Equation 1l.
There will be lower levels of neutral hydrogen in the region affected by the propagating radiation from the once active quasar, as described by Equation \ref{fgpa}.
The equilibration time. the time taken for he ionization state to respond to small changes (factors of a few) in the iutensity of the ionizing radiation is of the order of 107 vr (Mautini 2003).
The equilibration time, the time taken for the ionization state to respond to small changes (factors of a few) in the intensity of the ionizing radiation is of the order of $10^{4}$ yr (Martini 2003).
As this is much shorter hau the quasar lifetimes we will be considering. the effect of the quasar radiation will effectively propagate through he intergalactic ποται at the speed of helt.
As this is much shorter than the quasar lifetimes we will be considering, the effect of the quasar radiation will effectively propagate through the intergalactic medium at the speed of light.
The width of the leht echo will be equal to the light travel time uultiplied by the leneth of time the quasar was radiating.
The width of the light echo will be equal to the light travel time multiplied by the length of time the quasar was radiating.
For simplicity. iu the present paper we approximate the quasar lightcmves by a top hat io. we assume that a quasar starts to emit a coustant level of radiation aud stops sharply some time £4 later.
For simplicity, in the present paper we approximate the quasar lightcurves by a top hat i.e., we assume that a quasar starts to emit a constant level of radiation and stops sharply some time $t_{q}$ later.
We will also asiune that this takes place at a redshift where the expansion timescale is significautly less than fj. so that we can model the quasar radiation using the inverse square law.
We will also assume that this takes place at a redshift where the expansion timescale is significantly less than $t_{q}$, so that we can model the quasar radiation using the inverse square law.
An additional sinplificatiou we use is to neelect the attenuation of the quasar due to intergalactic absorption.
An additional simplification we use is to neglect the attenuation of the quasar due to intergalactic absorption.
As the attcuuation leugth at 2=3 is of the order of 1005.!Mpe (Haardt Madan 1996) this is not a bad approximation.
As the attenuation length at $z=3$ is of the order of $100 \hmpc$ (Haardt Madau 1996) this is not a bad approximation.
If we were able to recieve information from all points in space at the same time. a Ποστ eclio would be a spherical shell.
If we were able to recieve information from all points in space at the same time, a light echo would be a spherical shell.
The outer boundary would correspond to the start of cluission and the inner one correspond to the eucl. with a separation cf, between them.
The outer boundary would correspond to the start of emission and the inner one correspond to the end, with a separation $ct_{q}$ between them.
However. when observing a heht echo one would not be able to see every poiut in space at the sune time.
However, when observing a light echo one would not be able to see every point in space at the same time.
The bouudarics of the regions coutainiug radiation can be described as follows.
The boundaries of the regions containing radiation can be described as follows.
Caven a Cartesian coordinate svstem with the 2 axis Όσιο orieuted directly away from the observer and the origin ceutered on the quasar: where Ro, is the distance the lisht has traveled since the start of radiation clission acl f,,, is the time since the start of this ciuission considered at the location of the quasar.
Given a Cartesian coordinate system with the $z-$ axis being oriented directly away from the observer and the origin centered on the quasar: where $R_{on}$ is the distance the light has traveled since the start of radiation emission and $t_{on}$ is the time since the start of this emission considered at the location of the quasar.
Changing to spherical coordinates one obtaius
Changing to spherical coordinates one obtains
We have presented computations indicating (hat a sienilicant reduction in the apparent molion can be expected for VLBI radio knots associated with an ultrarelativistic jet by Lalàng into account the jets opening angle.
We have presented computations indicating that a significant reduction in the apparent motion can be expected for VLBI radio knots associated with an ultrarelativistic jet by taking into account the jet's opening angle.
On the pe-seale which could be identilied with the collimation regime. the jets are likely to be at least several degrees wide: they may be substantially wider. as indicated for the best resolved case of M87 (Junor. Diretta Livio 1999).
On the pc-scale which could be identified with the collimation regime, the jets are likely to be at least several degrees wide; they may be substantially wider, as indicated for the best resolved case of M87 (Junor, Biretta Livio 1999).
For this situation. we find that the apparent (transverse velocity peaks al lower values. and these peaks can occur al significantly greater angles to the line of sieht than thev cdo for the usually assumed case of an infinitesimallv small jet opening angle on parsec scales 11).
For this situation, we find that the apparent transverse velocity peaks at lower values, and these peaks can occur at significantly greater angles to the line of sight than they do for the usually assumed case of an infinitesimally small jet opening angle on parsec scales 1).
These trends become stronger lor high E. for then c,55,,. is sharply peaked around some 8>1/T.
These trends become stronger for high $\Gamma$, for then $v_{app,w}$ is sharply peaked around some $\theta > 1/\Gamma$.
A reversal of the sign of contributions (o Coppi. arising from some parts of the jels cross-section occurs i 0«w/2.
A reversal of the sign of contributions to $v_{app,w}$ arising from some parts of the jet's cross-section occurs if $\theta < \omega/2$.
The resulting cancellation. which is further enhanced because of the sharply declining Doppler boost with 9. can often lead to a fairly drastic reduction in the apparent velocity of the knots. as compared to the canonical peak value of Jaeep 11).
The resulting cancellation, which is further enhanced because of the sharply declining Doppler boost with $\theta$, can often lead to a fairly drastic reduction in the apparent velocity of the knots, as compared to the canonical peak value of $\beta_{max} \simeq \Gamma$ 1).
In the core dominated samples that are characteristic of BL Lacs. (he usual expectation. based on w=0 jets. is to find sources with οapp widely distributed up to Pe. but with the distribution actually skewed toward the higher part of that range (as shown in 11: see also Vermeulen Cohen 1994).
In the core dominated samples that are characteristic of BL Lacs, the usual expectation, based on $\omega = 0$ jets, is to find sources with $v_{app}$ widely distributed up to $\Gamma c$, but with the distribution actually skewed toward the higher part of that range (as shown in 1; see also Vermeulen Cohen 1994).
Thus. when the cap,s measured for VEDI knots are frequenUly < I10c. one of the following conclusions discussed in 81 is usually drawn: bulk D values are niodest: pattern velocities due to shock motions are slower than the jet flow: the VLBI knots are associated with a slower sheath of the jet: the angle to the line of sight is extremelv. small.
Thus, when the $v_{app}$ 's measured for VLBI knots are frequently $< 10$ c, one of the following conclusions discussed in $\S$ 1 is usually drawn: bulk $\Gamma$ values are modest; pattern velocities due to shock motions are slower than the jet flow; the VLBI knots are associated with a slower sheath of the jet; the angle to the line of sight is extremely small.
While all these are possible. here we have shown that none is necessary: rather. if the jet has a modest full-opening angle (w) on the scales probed by VLBI. then there is a very large reduction in the probability of measuring apparent velocities approaching Pr.
While all these are possible, here we have shown that none is necessary; rather, if the jet has a modest full-opening angle $\omega$ ) on the scales probed by VLBI, then there is a very large reduction in the probability of measuring apparent velocities approaching $\Gamma c$.
For instance. even lor (he extreme case of P=100 and a modest jet opening augle. vw—5. over of the radio components would be detected with tap,<I0c. while for w=LO”. over would fall into this category.
For instance, even for the extreme case of $\Gamma = 100$ and a modest jet opening angle, $\omega = 5^{\circ}$, over of the radio components would be detected with $v_{app} < 10c$, while for $\omega = 10^{\circ}$, over would fall into this category.
Over (Lor w= 5°) and over (for w= 107) would actually be seen as subliminal sources.
Over (for $\omega = 5^{\circ}$ ) and over (for $\omega = 10^{\circ}$ ) would actually be seen as subluminal sources.
Similarly. for P—50 and i=5°. over of the sources would be detected with top,«I0c. the median value is 2,5,=6. and still some would appear as subliminal sources.
Similarly, for $\Gamma = 50$ and $\omega = 5^{\circ}$, over of the sources would be detected with $v_{app} < 10c$, the median value is $\beta_{app} = 6$, and still some would appear as subluminal sources.
Therefore. the predominauce of mareinally superbuminal or even subliminal VLBI knots among TeV blazars does not imply that these radio knots cannot be physically. associated
Therefore, the predominance of marginally superluminal or even subluminal VLBI knots among TeV blazars does not imply that these radio knots cannot be physically associated
primordial power spectrum parameters produces a small degradation in the joint (wo, wa) errors and has little effect on the orientation of the ellipses.
primordial power spectrum parameters produces a small degradation in the joint $w_0,w_a$ ) errors and has little effect on the orientation of the ellipses.
We also investigate the effect adding both neutrinos and primordial power spectrum parameters (the sets v™QCDM+a and -ra.4- vQCDM
We also investigate the effect adding both neutrinos and primordial power spectrum parameters (the sets $\nu\mr{QCDM}+\alpha$ and $\nu\mr{QCDM}+\alpha+\beta$ ).
We note that the effect on the FoM is more significant than 8).with neutrinos or a and f alone (Table
We note that the effect on the FoM is more significant than with neutrinos or $\alpha$ and $\beta$ alone (Table
masses. and give their ages.
masses, and give their ages.
In the following. we refer to these special models as "transition. models".
In the following, we refer to these special models as “transition models”.
As the apparition. of this behaviour is related to the radius of the convective or helium core. negative small separations appear earlier when overshooting is introduced.
As the apparition of this behaviour is related to the radius of the convective or helium core, negative small separations appear earlier when overshooting is introduced.
This particular behaviour of the small separations could be used to derive the size of stellar cores and the presence of overshooting for stars at the end of the main-sequence.
This particular behaviour of the small separations could be used to derive the size of stellar cores and the presence of overshooting for stars at the end of the main-sequence.
À direct application to the exoplanet-host star j; Arae will be given in a forthcoming paper.
A direct application to the exoplanet-host star $\mu$ Arae will be given in a forthcoming paper.
We computed series of evolutionary tracks using the Toulouse Geneva Evolution Code (see Hui Bon Hoa 2007 for a general deseription of this code) with the OPAL equation of state anc opacities (Rogers Nayfonov 2002:: Iglesias Rogers 1996)) and the NACRE nuclear reaction rates (Angulo et al. 1999)).
We computed series of evolutionary tracks using the Toulouse Geneva Evolution Code (see Hui Bon Hoa \cite{hui07} for a general description of this code) with the OPAL equation of state and opacities (Rogers Nayfonov \cite{rogers02}; ; Iglesias Rogers \cite{iglesias96}) ) and the NACRE nuclear reaction rates (Angulo et al. \cite{angulo99}) ).
I1 all our models. we included mieroscopie diffusion as described in Michaud et al. (2004))
In all our models, we included microscopic diffusion as described in Michaud et al. \cite{michaud04}) )
and Paquette et al. (1986)).
and Paquette et al. \cite{paquette86}) ).
The convection was treated in the framework of the mixing length theory and the mixing length parameter was adjusted as in the Sun: a1.8 (Richard et al. 2004)).
The convection was treated in the framework of the mixing length theory and the mixing length parameter was adjusted as in the Sun: $\alpha=1.8$ (Richard et al. \cite{richard04}) ).
Models were computed for a range of masses from 1.05 to 1.25Mo.
Models were computed for a range of masses from 1.05 to 1.25.
.. We computed six series of models.
We computed six series of models.
The first three series were computed without overshooting and the second three series with overshooting at the limit of the stellar core.
The first three series were computed without overshooting and the second three series with overshooting at the limit of the stellar core.
Here overshooting 1s described as an extension of the central convective zone by a length αμΠρ. where Hp is the pressure height scale. and αμ the overshooting parameter.
Here overshooting is described as an extension of the central convective zone by a length $\alpha_{ov}H_P$, where $H_P$ is the pressure height scale, and $\alpha_{ov}$ the overshooting parameter.
In. our computations. we fixed a, to 0.20.
In our computations, we fixed $\alpha_{ov}$ to 0.20.
In each case. the three series differ from their abundances: We computed adiabatic oscillation frequencies for a large number of models along each evolutionary. track. using the PULSE code (Brassard et al. 1992)).
In each case, the three series differ from their abundances: We computed adiabatic oscillation frequencies for a large number of models along each evolutionary track, using the PULSE code (Brassard et al. \cite{brassard92}) ).
The oscillation frequencies were computed for degrees £=0 to £=3. which are the only degrees observable for solar-like stars. because of the lack of spatial resolution.
The oscillation frequencies were computed for degrees $\ell=0$ to $\ell=3$, which are the only degrees observable for solar-like stars, because of the lack of spatial resolution.
We only kept frequencies between 1.5 and 3.5 mHz. corresponding to the typical observational range for solar-type stars.
We only kept frequencies between 1.5 and 3.5 mHz, corresponding to the typical observational range for solar-type stars.
Their radial orders range between 4 to 100.
Their radial orders range between 4 to 100.
Using these frequencies. we computed the small separations for each model and analysed in what conditions these quantities can become negative.
Using these frequencies, we computed the small separations for each model and analysed in what conditions these quantities can become negative.
For all evolutionary tracks. we found models where the small separations become negative at some frequencies. which means that the £ = 0 and € = 2 lines cross over at a given point in the echelle diagram (cf Fig. 3..
For all evolutionary tracks, we found models where the small separations become negative at some frequencies, which means that the $\ell$ = 0 and $\ell$ = 2 lines cross over at a given point in the echelle diagram (cf Fig. \ref{fig3},
for example).
for example).
In all cases. the frequencies of these crossing points decrease for increasing stellar age.
In all cases, the frequencies of these crossing points decrease for increasing stellar age.
For each computed track. we picked up the “transition model” for which the frequency of the crossing point is 3.5 mHz.
For each computed track, we picked up the “transition model” for which the frequency of the crossing point is 3.5 mHz.
These models are represented by crosses in Figs.
These models are represented by crosses in Figs.
1. and 2.. and their characteristics are given in Tables | to 6..
\ref{fig1} and \ref{fig2}, and their characteristics are given in Tables \ref{tab1} to \ref{tab6}.
A first analysis of the possibilities of negative small separations in stars was given in Soriano et al.(2007)) for the specific case of the exoplanet-host star HD 52265.
A first analysis of the possibilities of negative small separations in stars was given in Soriano et \cite{soriano07}) ) for the specific case of the exoplanet-host star HD 52265.
When we computed models for this star. taking spectroscopic constraints into account. we were surprised to find two models that showed this specific behaviour: one model at the end of the main sequence with a mass of 1.31.Mo... which had a convective core. and one model at the beginning of the subgiant branch with à mass of 1.20M... in which the convective core. present during the main sequence. had disappeared.
When we computed models for this star, taking spectroscopic constraints into account, we were surprised to find two models that showed this specific behaviour: one model at the end of the main sequence with a mass of 1.31, which had a convective core, and one model at the beginning of the subgiant branch with a mass of 1.20, in which the convective core, present during the main sequence, had disappeared.
For both cases we realised that the main reason for the negative small separations was related to the high helium content of the cores.
For both cases we realised that the main reason for the negative small separations was related to the high helium content of the cores.
The basic role of convection in this respect was its action of concentrating helium inside a sharp core during the main We showed how negative small separations could be a signature of the size of a helium core. as well as that of a convective core when it ts still present.
The basic role of convection in this respect was its action of concentrating helium inside a sharp core during the main We showed how negative small separations could be a signature of the size of a helium core, as well as that of a convective core when it is still present.
We give below a more complete analysis of the results we obtained by doing systematic studies of this effect for solar-type stars.
We give below a more complete analysis of the results we obtained by doing systematic studies of this effect for solar-type stars.
We first recall useful theoretical points. then we discuss our computational results.
We first recall useful theoretical points, then we discuss our computational results.
In all our models. the acoustic frequencies were computed precisely using the PULSE adiabatic code (Brassard et al. 1992)).
In all our models, the acoustic frequencies were computed precisely using the PULSE adiabatic code (Brassard et al. \cite{brassard92}) ).
The results take the particular features of the stellar interiors into account.
The results take the particular features of the stellar interiors into account.
That the small separations become negative in some cases Is real.
That the small separations become negative in some cases is real.
This seems surprising at first sight because 1t contradicts what is usually called “asymptotic theory”. as developed by Tassoul (1980)).
This seems surprising at first sight because it contradicts what is usually called “asymptotic theory”, as developed by Tassoul \cite{tassoul80}) ).
According to this analytical deseription of the oscillations. the large separations should be constant. equal to half of the inverse of the acoustic time. defined as the time needed for the acoustic waves to cross the stellar radius.
According to this analytical description of the oscillations, the large separations should be constant, equal to half of the inverse of the acoustic time, defined as the time needed for the acoustic waves to cross the stellar radius.
Meanwhile. the small separation should vary quite slowly and remain positive.
Meanwhile, the small separation should vary quite slowly and remain positive.
Although these approximate expressions are not used in realcomputations. they are very useful for understanding the underlying physics.
Although these approximate expressions are not used in realcomputations, they are very useful for understanding the underlying physics.
The data preseuted above strongly suggest that most of the 12 and 25 ffiux from the NE vim ofIC£13 is due to ionic me enissiou rather than continui enussion from. wari. cust.
The data presented above strongly suggest that most of the 12 and 25 flux from the NE rim of IC443 is due to ionic line emission rather than continuum emission from warm dust.
We address here the following questions.
We address here the following questions.
Cau this result be eeneralized to other radiative SNRs?
Can this result be generalized to other radiative SNRs?
Ave there otler lines which may severely contaminate IRAS measurements of this aud other remuauts?
Are there other lines which may severely contaminate IRAS measurements of this and other remnants?
The easiest auc most direct estimate of the line contribution to the IRAS fluxes requires a iieasurement of the FIR line intensity from the whole SNR.
The easiest and most direct estimate of the line contribution to the IRAS fluxes requires a measurement of the FIR line intensity from the whole SNR.
This is virtually inipossible iun IC£03 aud other radiative remnants in the Galaxy because of their very large projected sizes. but is feasible in the LMC where e.g. the remnaut N19. has been mapped with SWS bv Oliva ct al (
This is virtually impossible in IC443 and other radiative remnants in the Galaxy because of their very large projected sizes, but is feasible in the LMC where e.g. the remnant N49 has been mapped with SWS by Oliva et al. (
iu preparation).
in preparation).
They find a total [NeITALL2.8 line intensity of 2101! W 7 aud equal. within the errors. to the F(12;11))22.2101D Won 2 IRAS dus reported by Craham et al. CLO87)).
They find a total 12.8 line intensity of $2\,10^{-14}$ W $^{-2}$ and equal, within the errors, to the $2.2\,10^{-14}$ W $^{-2}$ IRAS flux reported by Graham et al. \cite{graham87}) ).
For remuauts where direct measurements of FIR lines is not available. a reasonable estimate of their fluxes cau be obtained by scaling optical line measurements using available ISO. spectral observatious of radiative SNRs. namely IC113 (this paper). RCWIO3 (Oliva et al. 1998))
For remnants where direct measurements of FIR lines is not available, a reasonable estimate of their fluxes can be obtained by scaling optical line measurements using available ISO spectral observations of radiative SNRs, namely IC443 (this paper), RCW103 (Oliva et al. \cite{rcw103_iso}) )
and N19 (Oliva et al.
and N49 (Oliva et al.
in preparation).
in preparation).
These indicate that the [NeIH] aud [Fel]||SITI]|OIV] line contribution to the 12 and 25 filters are both roughly equal to the flux ofIL».
These indicate that the [NeII] and [FeII]+[SIII]+[OIV] line contribution to the 12 and 25 filters are both roughly equal to the flux of.
Uufortuuatelv. relatively few optical spectroplotometric observations of SNRs are available iu the literature aud are altogether uussine for several nuportaut radiative relmnauts such as Wil aud W19D. Nevertheless. the SW filament of ROWs6 has X(ILJ)~110 (Leibowitz Dauziger 1983)) aud verv similar to the X2310DW 7 | ΠΑΣ 12 and 25 fluxes found by As9..
Unfortunately, relatively few optical spectrophotometric observations of SNRs are available in the literature and are altogether missing for several important radiative remnants such as W44 and W49B. Nevertheless, the SW filament of RCW86 has $\Sigma(\HB)\!\simeq\!4\,10^{-7}$ (Leibowitz Danziger \cite{leibowitz}) ) and very similar to the $\Sigma\!\simeq\!3\,10^{-7}$ W $^{-2}$ $^{-1}$ IRAS 12 and 25 fluxes found by \cite{A89}.
Similarly. the NE filament of the Cyenus Loophas X(IT2)zz110* (Fesen et al. 1982))
Similarly, the NE filament of the Cygnus Loophas $\Sigma(\HB)\!\simeq\!1\,10^{-7}$ (Fesen et al. \cite{fesen82}) )
aud close to the IRAS surface biightuess X8105 Wu? + (AS9))
and close to the IRAS surface brightness $\Sigma\!\simeq\!8\,10^{-8}$ W $^{-2}$ $^{-1}$ \cite{A89}) ).
These results suggest. therefore. that lines account or niost of he IRAS 12 and 25 chussion from line cutting filaments of radiative SNRs.
These results suggest, therefore, that lines account for most of the IRAS 12 and 25 emission from line emitting filaments of radiative SNRs.
Another interesting exercise is to Compare optical liue and IRAS fluxes in a vouuger remuant such as the Nepler SNR for which accurate line photometric nieasurenments are available (D'Odorco et al. 1986)).
Another interesting exercise is to compare optical line and IRAS fluxes in a younger remnant such as the Kepler SNR for which accurate line photometric measurements are available (D'Odorico et al. \cite{dodorico}) ).
The total ID} cuuission from the whole remuaut is 2.9101° Wan ? and onlv aud 0.6 of the TRAS flux iu the 12 aud 25 bands. respectively,
The total $\beta$ emission from the whole remnant is $2.9\,10^{-15}$ W $^{-2}$ and only and 0.6 of the IRAS flux in the 12 and 25 bands, respectively.