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The equatorial outflow iu ;j Car has con. described as an extended equatorial disk expanding with velocity proportional to the angular distance to center (Davidsonetal.2001:στι2002).. while the physical structure of the equatorial outflow in 33 is best described. by an oblate shell. | The equatorial outflow in $\eta$ Car has been described as an extended equatorial disk expanding with velocity proportional to the angular distance to center \citep{Davidson01,Smith02}, while the physical structure of the equatorial outflow in 3 is best described by an oblate shell. |
Furthermore. their detailed norpholoeics are different aud very likely indicate ciffercut origins: m jj Car. the equatorial outflow secs to be composed of multiple jet-like features located alone the equatorial plane. while iu Mz233 the equatorial outflow shows the linmib-biieblitened morphology characteristic of a thin shell. | Furthermore, their detailed morphologies are different and very likely indicate different origins: in $\eta$ Car, the equatorial outflow seems to be composed of multiple jet-like features located along the equatorial plane, while in 3 the equatorial outflow shows the limb-brightened morphology characteristic of a thin shell. |
The formation of multipolar nebulae can be explained as the result of recurrent outbursts as those observed in lnassive stars in binary svstenis during the Luuinous Blue Variable (LBV) phase. e.g. 4 Car. | The formation of multipolar nebulae can be explained as the result of recurrent outbursts as those observed in massive stars in binary systems during the Luminous Blue Variable (LBV) phase, e.g. $\eta$ Car. |
In low ass stars. recurrent outbursts can be related to nova-like eruptions ou the accreting hot component of a syaubiotic star or to structural iustabilities iu the late evolution of the central star of a PN (οι, thermal pulses). | In low mass stars, recurrent outbursts can be related to nova-like eruptions on the accreting hot component of a symbiotic star or to structural instabilities in the late evolution of the central star of a PN (e.g., thermal pulses). |
Iu svaubiotie novae. the timescales of successive outbursts are determined by the mass of the acercting white dawarf. the mass loss rate of the red eiat. aud the accretion efficiency. of the wind capture which is related to the binary interaction (0.9.Priduik&Ixovetz 1995). | In symbiotic novae, the timescales of successive outbursts are determined by the mass of the accreting white dwarf, the mass loss rate of the red giant, and the accretion efficiency of the wind capture which is related to the binary interaction \citep[e.g.][]{PK95}. |
. Recurrence periods of a few hundred years are typical of svinbiotic novae (Priahük&IKovetz1995:Corradietal. 1999). | Recurrence periods of a few hundred years are typical of symbiotic novae \citep{PK95,Corradi99}. |
. The formation of multipolar PNe is far iore difficult to explain. as it requires the alternation between a dense. slow wind and a fast. tenuous wiud. | The formation of multipolar PNe is far more difficult to explain, as it requires the alternation between a dense, slow wind and a fast, tenuous wind. |
The evolution of the ceutral star of the PN in a binary svsteni provides a natural scenario for recurrent outbursts during the evolution through a common envelope phase or as the result of accretion and uova-like outbursts on the white cdwarf compoucut of a svinbiotic star. | The evolution of the central star of the PN in a binary system provides a natural scenario for recurrent outbursts during the evolution through a common envelope phase or as the result of accretion and nova-like outbursts on the white dwarf component of a symbiotic star. |
This raises the simularities between 33 aud other sviubiotic stars like R Δι and Heull0l. or other suspected svaubiotie stars vot classified as PNe. οι, 22-9. and casts doubts on the true nature of 33 axa PN. | This raises the similarities between 3 and other symbiotic stars like R Aqr and 104, or other suspected symbiotic stars yet classified as PNe, e.g., 2-9, and casts doubts on the true nature of 3 as a PN. |
Even if we accept that 32 has formed as the result of recurrent nova-like outbursts in a sviubiotie star. the phivsical structure of this bipolar nebula is rather unique. | Even if we accept that 3 has formed as the result of recurrent nova-like outbursts in a symbiotic star, the physical structure of this bipolar nebula is rather unique. |
The successive collimated ejections in 2323 are rather regular in time. but they have very different morphological and kinematical properties. which sugeest very distinct conditions and formation mechanisis. | The successive collimated ejections in 3 are rather regular in time, but they have very different morphological and kinematical properties, which suggest very distinct conditions and formation mechanisms. |
In 33. we are thus witnessing the formation of a 1iultipolar nebula which evolves dramatically between periodic outburst episodes. | In 3, we are thus witnessing the formation of a multipolar nebula which evolves dramatically between periodic outburst episodes. |
ALA.G. and L.F.M. acknowledge support from the eraut AYA 2002-00376 of the Spanish MCwT (cofunded by FEDER finds). | M.A.G. and L.F.M. acknowledge support from the grant AYA 2002-00376 of the Spanish MCyT (cofunded by FEDER funds). |
We thanks Miguel Sautander Garciaa for providing us with the results on their spatio-kineimatical iuodeling of 33 before publication. | We thanks Miguel Santander a for providing us with the results on their spatio-kinematical modeling of 3 before publication. |
We also thauk the referee. MMatt Ποια, for lis valuable conmucuts. | We also thank the referee, Matt Redman, for his valuable comments. |
The cmicroquasar GRS 1915)105 is one of the most celebrated and widelv-studied astrophysical objects of recent vears. | The `microquasar' GRS 1915+105 is one of the most celebrated and widely-studied astrophysical objects of recent years. |
The system is extremely luminous ancl variable in both hard and soft N-ravs (e.g. Foster et al. | The system is extremely luminous and variable in both hard and soft X-rays (e.g. Foster et al. |
1996: Morgan. Remillard Greiner 1997: Belloni et al. | 1996; Morgan, Remillard Greiner 1997; Belloni et al. |
2000) and is a source of relativistic jets observed on aresec and milliaresce angular scales (Alirabel σος 1994. hereafter. ALRO4: Fender et al. | 2000) and is a source of relativistic jets observed on arcsec and milliarcsec angular scales (Mirabel guez 1994, hereafter MR94; Fender et al. |
1999. hereafter 1799: guez Alirabel 1990. hereafter. RAIOO: Dhawan. Alirabel guez 2000). | 1999, hereafter F99; guez Mirabel 1999, hereafter RM99; Dhawan, Mirabel guez 2000). |
Sams. Eckart Sunvaey (1996) have reported extended infrared. emission from. GRS 1915]105. but. its relation to the radio ejections is at present unclear. | Sams, Eckart Sunyaev (1996) have reported extended infrared emission from GRS 1915+105, but its relation to the radio ejections is at present unclear. |
Neray clips) on timescales of minutes have been interpreted. by Belloni et. al. ( | X-ray dips on timescales of minutes have been interpreted by Belloni et al. ( |
lO97a.b) as the repeated disappearance and refill of the inner aceretion disce. possibly due to extremely. rapid. transitions between "canonical black hole accretion states (Belloni et al. | 1997a,b) as the repeated disappearance and refill of the inner accretion disc, possibly due to extremely rapid transitions between `canonical' black hole accretion states (Belloni et al. |
2000). | 2000). |
Pooley Fender (1997: hereafter. PE97) reported: radio oscillations associated with such dips. and Fender et al. ( | Pooley Fender (1997; hereafter PF97) reported radio oscillations associated with such dips, and Fender et al. ( |
1997: hereafter 197) discovered. infrared. analogs of these oscillations. | 1997; hereafter F97) discovered infrared analogs of these oscillations. |
The lat spectrum and correlated: radio: infrared. behaviour suggested that nonthermal svnchrotron enission. extended rom the radio to the infrared regimes. the first time such ueh-[requeney svnchrotron emission. had. been observed. rom an X-ray binary (E97). | The flat spectrum and correlated radio: infrared behaviour suggested that nonthermal synchrotron emission extended from the radio to the infrared regimes, the first time such high-frequency synchrotron emission had been observed from an X-ray binary (F97). |
Combined. with the unstable accretion dise model of Belloni et al. ( | Combined with the unstable accretion disc model of Belloni et al. ( |
1997a.b) we suggested hat a fraction of the inner disc was being repeatedly accelerated: and: ejected. from. the system. (οτι PE97). | 1997a,b) we suggested that a fraction of the inner disc was being repeatedly accelerated and ejected from the system (F97; PF97). |
Eikenberry et al. ( | Eikenberry et al. ( |
1998a) confirmed the association between X-ray anc infrared events. ando Mirabel ct al. ( | 1998a) confirmed the association between X-ray and infrared events, and Mirabel et al. ( |
1998. hereafter M98) clearly observed the correlation between X-rav. infrared. and radio behaviour in the source. | 1998, hereafter M98) clearly observed the correlation between X-ray, infrared and radio behaviour in the source. |
Additional | Additional |
fluneuts from the Μππάς to the disk-center-sicde in peuunbral sections where the filameuts are oriented at angles inaller than z607 to the nearest part of the solar limb. | filaments from the limb-side to the disk-center-side in penumbral sections where the filaments are oriented at angles smaller than $\pm$$60^\circ$ to the nearest part of the solar limb. |
We have studied such motious im relation to other properties of 21 filaments in the uortheru section and 22 ju the southern section. | We have studied such motions in relation to other properties of 21 filaments in the northern section and 22 in the southern section. |
We note that such twists are discernable oulv within a certain portion of the length of a filament. | We note that such twists are discernable only within a certain portion of the length of a filament. |
We divided cach filament mto 3 parts (cf. | We divided each filament into 3 parts (cf. |
Fie. | Fig. |
2). a central part displaving a twist (henceforth called he body of the filament) and two parts bouncing this central part that do not display anv discernable twisting notions. | 2), a central part displaying a twist (henceforth called the body of the filament) and two parts bounding this central part that do not display any discernable twisting motions. |
These include the head of a filament ie. the xieht mnermost part of the flament. aud the ‘tail’ of a filament. the often faint outer part in which no twist Is ποσα anviuore in space-time diagrams. | These include the 'head' of a filament i.e. the bright innermost part of the filament, and the 'tail' of a filament, the often faint outer part in which no twist is seen anymore in space-time diagrams. |
Here. ΠΙΟ) and outer parts of filaments refer to the parts closer o the inner and to the outer boundary ofthe peuunibra. respectively. | Here, 'inner' and 'outer' parts of filaments refer to the parts closer to the inner and to the outer boundary of the penumbra, respectively. |
The locations of the boundaries between read. body aud tail vary from filament to filament. | The locations of the boundaries between head, body and tail vary from filament to filament. |
Γιος, we find that filaments which extend iuto the unibra. oosess twist over their whole leneth. although iu the darker outer (1.0. away frou unibra) part of the flament it becomes difficult to identify such a twisting motion. | E.g., we find that filaments which extend into the umbra, possess twist over their whole length, although in the darker outer (i.e. away from umbra) part of the filament it becomes difficult to identify such a twisting motion. |
We call the length of the twisting portion (body) of the filament its twisting leneth. | We call the length of the twisting portion (body) of the filament its twisting length. |
The ‘twisting leneth defined above may not be constant over the time series for cach filament. | The 'twisting length' defined above may not be constant over the time series for each filament. |
The wisting leneth of filaments discussed later (Fie. | The twisting length of filaments discussed later (Fig. |
1 (vieht)) refers to the begiuuiug of the time series. | 4 (right)) refers to the beginning of the time series. |
The wisting leneth of flamcuts which exteud iuto the mubra. displays some ambieuity. | The twisting length of filaments which extend into the umbra, displays some ambiguity. |
We made space time diagrams for three locatious in he body of the filament. | We made space time diagrams for three locations in the body of the filament. |
These three locations are the duner cut? which is close to the imuer edge of the body of the filament. the “muddle cut’ is the middle poiut of the body of the filament aud the “outer cut’? which is 2-3 pixels inside the outer edge of the body of the filament. such that dark stripes cau still be seen iu the space-time diagram. | These three locations are the 'inner cut' which is close to the inner edge of the body of the filament, the 'middle cut' is the middle point of the body of the filament and the 'outer cut' which is 2-3 pixels inside the outer edge of the body of the filament, such that dark stripes can still be seen in the space-time diagram. |
The locations of all these parts are sketched for filament €" in Fig. | The locations of all these parts are sketched for filament 'C' in Fig. |
2. | 2. |
The location of this articular filament CU ds marked iu Figure 1. | The location of this particular filament 'C' is marked in Figure 1. |
Note that he absence of a clear sigual does not imply the abseuce of corresponding motions in the head or tail of a filament. just the absence of dark stripes parallel to the flament’s axis that make such motions visible. | Note that the absence of a clear signal does not imply the absence of corresponding motions in the head or tail of a filament, just the absence of dark stripes parallel to the filament's axis that make such motions visible. |
The width of a (twisting) filament is the distance vetween the inflection points of the iutensitv profiles xwallel to the filamenut’s nünor axis. | The width of a (twisting) filament is the distance between the inflection points of the intensity profiles parallel to the filament's minor axis. |
Frou, Fig. | From Fig. |
1l oue can see that the inner part of a vpical peumubral filament is brighter aud the brightuess decreases eradually towards the outer part. | 1 one can see that the inner part of a typical penumbral filament is brighter and the brightness decreases gradually towards the outer part. |
This is eenerallv true. irrespective of whether the fluuenut is ocated iu the inner. middle or outer penumbra. | This is generally true, irrespective of whether the filament is located in the inner, middle or outer penumbra. |
The intensity profile along a fibuuneuts major axis as plotted in Fie. | The intensity profile along a filament's major axis as plotted in Fig. |
2. is thus relatively typical of many fibuuceuts. | 2, is thus relatively typical of many filaments. |
Space-time diagrams of various locations. marked bv arrows and white lines in Fie. | Space-time diagrams of various locations, marked by arrows and white lines in Fig. |
1. iu some of the studied. filaments are shown in Fie. | 1, in some of the studied filaments are shown in Fig. |
3. | 3. |
The motion of thin dark stripes across the filameuts is apparent as inclined dark stripes in Figs. | The motion of thin dark stripes across the filaments is apparent as inclined dark stripes in Figs. |
3. producing the impression of twisting filaments. or. more precisely. of horizoutal | 3, producing the impression of twisting filaments, or, more precisely, of horizontal |
the halo centre is especially interesting. | the halo centre is especially interesting. |
In particular, the halo-dark matter correlation function is related in a straightforward way to the density profile. | In particular, the halo–dark matter correlation function is related in a straightforward way to the density profile. |
Although the transition from the one-halo term to the two-halo term in this correlation function is present before 10Ryir, our approximation has turned out to be a reasonable description of the DM distribution even at these distances. | Although the transition from the one-halo term to the two-halo term in this correlation function is present before $10R_{\rmn{vir}}$, our approximation has turned out to be a reasonable description of the DM distribution even at these distances. |
In order to build the numerical mean density profiles, we averaged over many hundreds of haloes from high-resolution cosmological simulations so that the profiles corresponding to most of our mass bins are entirely unaffected by statistics. | In order to build the numerical mean density profiles, we averaged over many hundreds of haloes from high-resolution cosmological simulations so that the profiles corresponding to most of our mass bins are entirely unaffected by statistics. |
This procedure for averaging density profiles is analogue to the stacking method, used in observational studies like the one by ? to infer the density profile of a cluster of galaxies. | This procedure for averaging density profiles is analogue to the stacking method, used in observational studies like the one by \citet{Ma08} to infer the density profile of a cluster of galaxies. |
This similarity is useful for the comparison of the results from cosmological simulations to the real data. | This similarity is useful for the comparison of the results from cosmological simulations to the real data. |
'This parametrization for the average density profile is accurate to within in the range from 0.05Ri. to 10Ryir. | This parametrization for the average density profile is accurate to within in the range from $0.05R_{\rmn{vir}}$ to $10R_{\rmn{vir}}$. |
There are two main discrepancies from the numerical density profile which have a different origin: whereas the overestimation around r=r, is inherited from NFW profile, the overestimation just beyond the virial radius suggests that our model is not able to reproduce the steepest region. | There are two main discrepancies from the numerical density profile which have a different origin: whereas the overestimation around $r=r_s$ is inherited from NFW profile, the overestimation just beyond the virial radius suggests that our model is not able to reproduce the steepest region. |
This steep region just outside Ryir is more pronounced for most massive haloes, suggesting a depletion of the halo outskirts due to dark matter infall (?,, ?)). | This steep region just outside $R_{\rmn{vir}}$ is more pronounced for most massive haloes, suggesting a depletion of the halo outskirts due to dark matter infall \citealt{Pr06}, \citealt{Cu07}) ). |
The presence of our additional terms with respect to the NFW formula has only a very small influence on the inner regions of the density profile, so that our approximation can also be considered as an extension of the NFW profile. | The presence of our additional terms with respect to the NFW formula has only a very small influence on the inner regions of the density profile, so that our approximation can also be considered as an extension of the NFW profile. |
At larger distances our model shows deviations around in the range Πνιν just before entering the asymptotic regime. | At larger distances our model shows deviations around in the range $R_{\rmn{vir}}$ just before entering the asymptotic regime. |
These deviations are caused by our additional (r/Ryir)~+ terms which improve the fit in the interesting region below 10Rvir where the density is much higher. | These deviations are caused by our additional $(r/R_{\rmn{vir}})^{-1}$ terms which improve the fit in the interesting region below $10R_{\rmn{vir}}$ where the density is much higher. |
In any case, we must remark that our approximation implements the correct asymptotic behaviour: the density profile tends to the asymptotic value of the mean matter density of the Universe p. | In any case, we must remark that our approximation implements the correct asymptotic behaviour: the density profile tends to the asymptotic value of the mean matter density of the Universe $\bar{\rho}$. |
'The cumulative mass inside a sphere of a given radius is underestimated by more than at 10Ryir by the NFW formula. | The cumulative mass inside a sphere of a given radius is underestimated by more than at $10R_{\rmn{vir}}$ by the NFW formula. |
On the contrary, it is much better approximated (to within 12%)) when the NFW profile is modified by addition of the mean matter density, although with our model the difference with numerical density profiles is reduced even up to in the range Ryi,. | On the contrary, it is much better approximated (to within ) when the NFW profile is modified by addition of the mean matter density, although with our model the difference with numerical density profiles is reduced even up to in the range $R_{\rmn{vir}}$. |
This is especially interesting for new measurements of the enclosed mass beyond virial radius in X-ray clusters (?),, where plain NFW is still used even at r>1Ryir. | This is especially interesting for new measurements of the enclosed mass beyond virial radius in X-ray clusters \citep{Ge08}, where plain NFW is still used even at $r>1R_{\rmn{vir}}$. |
While current observations cannot distinguish between modified NFW and our approximation, in the near future they should be able to find the need for adding the mean matter density term to the density profile. | While current observations cannot distinguish between modified NFW and our approximation, in the near future they should be able to find the need for adding the mean matter density term to the density profile. |
We have also presented an application for our approximation in the context of mass estimation using gravitational lensing effect. | We have also presented an application for our approximation in the context of mass estimation using gravitational lensing effect. |
We derived expressions for tangential shear corresponding to different regions around the halo, which are in turn related to the different terms in our approximation. | We derived expressions for tangential shear corresponding to different regions around the halo, which are in turn related to the different terms in our approximation. |
The contribution from the outer regions is small as compared to the contribution of the inner region, as expected. | The contribution from the outer regions is small as compared to the contribution of the inner region, as expected. |
We calculated the difference between this tangential shear and the one derived from the NFW profile as a function of distance, showing that the inclusion of the outer regions produces a difference around. | We calculated the difference between this tangential shear and the one derived from the NFW profile as a function of distance, showing that the inclusion of the outer regions produces a difference around. |
This small difference could provide an observational test for the validity of our approximation, which has been derived from the results of cosmological N-body simulations. | This small difference could provide an observational test for the validity of our approximation, which has been derived from the results of cosmological $N$ –body simulations. |
Although present resolution of weak lensing experiments prevents us from drawing a robust conclusion, the stacking of different observations should prove that this approximation, which includes the contribution of external regions, is more realistic than most of the so far proposed density profiles, which do not account for HT wants to thank the I.E.S. José Cadalso for allowing him to combine this research with his teaching duties. | Although present resolution of weak lensing experiments prevents us from drawing a robust conclusion, the stacking of different observations should prove that this approximation, which includes the contribution of external regions, is more realistic than most of the so far proposed density profiles, which do not account for HT wants to thank the I.E.S. José Cadalso for allowing him to combine this research with his teaching duties. |
FP, AJC and MASC thank the Spanish MEC under grant PNAYA 2005-07789 for their support. | FP, AJC and MASC thank the Spanish MEC under grant PNAYA 2005-07789 for their support. |
AK acknowledges support from NASA and NSF grants to NMSU. | AK acknowledges support from NASA and NSF grants to NMSU. |
AJC acknowledges the financial support of the MEC through Spanish grant FPU AP2005-1826. | AJC acknowledges the financial support of the MEC through Spanish grant FPU AP2005-1826. |
MASC acknowledges the financial support of the CSIC through Spanish grant I3P. | MASC acknowledges the financial support of the CSIC through Spanish grant I3P. |
magnitude lower than in model B, for both the shocked ISM and RSG wind (see Fig. | magnitude lower than in model $_{\rm ad}$ for both the shocked ISM and RSG wind (see Fig. |
8 [top, middle]). | \ref{fig: nprof} [top, middle]). |
Furthermore, by reducing the thermal pressure of the gas, the strong cooling also enables further compression in the shock, resulting in greater post-shock densities (see Fig. | Furthermore, by reducing the thermal pressure of the gas, the strong cooling also enables further compression in the shock, resulting in greater post-shock densities (see Fig. |
8 [top, left]) than in model Bag. | \ref{fig: nprof} [top, left]) than in model $_{\rm ad}$. |
Consequently, the time scale for the growth of R-T instabilities is reduced and, similar to the models of ? (their Fig. | Consequently, the time scale for the growth of R-T instabilities is reduced and, similar to the models of \cite{Bri95} (their Fig. |
2.), | 2.), |
R-T *fingers' develop faster than the K-H rolls that characterised the adiabatic case (see Secs. | R-T `fingers' develop faster than the K-H rolls that characterised the adiabatic case (see Secs. |
3.2 and 4.1.1)). | \ref{sec: adinstab} and \ref{sec: instab}) ). |
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