source
stringlengths 1
2.05k
⌀ | target
stringlengths 1
11.7k
|
|---|---|
Because of the same reason as above. we could ouly estimate the phase of our spectra using the visual light curve plotted in Fig. 2.. | Because of the same reason as above, we could only estimate the phase of our spectra using the visual light curve plotted in Fig. \ref{fig_2}. |
Πονονα, because of the low value of A. this approximation probably does not introduce avec CLYOLs. | However, because of the low value of $\Delta$, this approximation probably does not introduce large errors. |
Tudeed. assunimg that the Nase of the first spectra. Πα...6 davs. A=0.008 could be obtained which would further reduce the expected citference )etwoeen the "real" light curve and the template leht curve. | Indeed, assuming that the phase of the first spectrum is $t=-6$ days, $\Delta=0.008$ could be obtained which would further reduce the expected difference between the “real” light curve and the template light curve. |
On the other hand. f=S days is improbable. jcause the Hand ieht iu B occurs carlicy than in V. | On the other hand, $t=-8$ days is improbable, because the maximum light in $B$ occurs earlier than in $V$. |
Again. this question should be re-investigated using calibrated enu photometry of SN 1998aq. | Again, this question should be re-investigated using calibrated long-term photometry of SN 1998aq. |
As far as the available photometry is concerned. here are some BW imeasurcincuts at the emer phases of SN 1998aq published in7AC Circulars. | As far as the available photometry is concerned, there are some $BV$ measurements at the earlier phases of SN 1998aq published in Circulars. |
Although he accuracy of the photometric data published in[AC Circulars is quite variable and sometimes inferior. but. as above. it is the ouly source of publicly available calibrated shotometiy of SN 1998aq at the date of the preparation of this paper. | Although the accuracy of the photometric data published in Circulars is quite variable and sometimes inferior, but, as above, it is the only source of publicly available calibrated photometry of SN 1998aq at the date of the preparation of this paper. |
We have collectec Έλι=12.67 and (D.V),4,=0.02 naenitudes. obscrvec at April 20.901 UT (Πα Caton. 1998)). | We have collected $V_{obs}=12.67$ and $(B-V)_{obs}=0.02$ magnitudes, observed at April 20.904 UT (Hanzl Caton, \cite{hanzl}) ). |
These measurcients were obtained with an ST-7 CCD-caimera attached to a 10 cir Casscerain telescope. according to one ofthe authors! (Tauzl) description. | These measurements were obtained with an ST-7 CCD-camera attached to a 40 cm Cassegrain telescope, according to one of the authors' (Hanzl) description. |
The accuracy of these data should be much higher than the ainateur visual light estimates showed in Fie. | The accuracy of these data should be much higher than the amateur visual light estimates showed in Fig. |
2. (which is used only for estimating the plases of our spectroscopic ueasureineuts). | \ref{fig_2} (which is used only for estimating the phases of our spectroscopic measurements). |
IIauzl (1998)) gives error estimates of Us nieasurenieuts m a follow-up publication. and typical values are óV=(0401 and e0B|y)0020.03 nae. | Hanzl \cite{hanzl2}) ) gives error estimates of his measurements in a follow-up publication, and typical values are $\delta V = 0.01$ and $\delta (B-V) = 0.02 - 0.03$ mag. |
Towever. the anonvinous referee of the present oper argued that his own lLieh-precision photometry gave BV=O17 on April 20. | However, the anonymous referee of the present paper argued that his own high-precision photometry gave $B-V = -0.17$ on April 20. |
This meaus that the BOY colour of SN L998aq may be much ducr than the single neasurciment of Πα] Caton (1 908)) iudicates. | This means that the $B-V$ colour of SN 1998aq may be much bluer than the single measurement of Hanzl Caton \cite{hanzl}) ) indicates. |
We cannot discuss this discrepancy mrther. because it isbased | We cannot discuss this discrepancy further, because it isbased |
5-raws. 5-rav (Albertetal.2007;Aharonianοἱ2007). | $\gamma$ $\gamma$ \citep{albert07,aharonian07}. |
. 5-ravs -yavs. (Urry&Padovani1995).. 5-ravs inparüculu. | $\gamma$ $\gamma$ \citep{up95}, $\gamma$ |
with constants ο and in. | with constants $A$ and $m$. |
The enthalpy P is denoted by other thermodynamic variables as hSetPip. | The enthalpy $h$ is denoted by other thermodynamic variables as $h\equiv\epsilon+P/\rho$. |
Equation (5)) vields Equations (6)) can be rewritten as Equatious (11))-(13)) together with the relation 5,—yinoIDs at r=Rs lead to the folowing equation where.r=53/D5. | Equation \ref{density}) ) yields Equations \ref{em}) ) can be rewritten as Equations \ref{sc1}) \ref{sc3}) ) together with the relation $\gamma_{\rm e} = \sqrt{m+1} \Gamma_2$ at $r = R_2$ lead to the following equation where $x = \gamma_2 / \Gamma_2$. |
This equation has the only one positive solution between 1 and Yi+1 lor m>—1. | This equation has the only one positive solution between 1 and $\sqrt{m+1}$ for $m>-1$. |
HE this solution is denoted as .r=να. the Lorentz factor. density. and pressure at the lront in the shocked matter will be derived as These relations are used to obtain the boundary. conditions for flows in the shocked ejecta. | If this solution is denoted as $x=\sqrt{q}$, the Lorentz factor, density, and pressure at the front in the shocked matter will be derived as These relations are used to obtain the boundary conditions for flows in the shocked ejecta. |
If (he constant 5 ds smaller than univ as is usually the case. (he compression is so weak that the thermal energv. cannot dominate the rest mass οποιον in the shocked ejecta. | If the constant $m$ is smaller than unity as is usually the case, the compression is so weak that the thermal energy cannot dominate the rest mass energy in the shocked ejecta. |
Therefore we cannot use the ultra-relativistic equation of state there while the equation of state is always a good approximation in the shocked ambient medium as long as the shock Lorentz [actor is much larger than unity. | Therefore we cannot use the ultra-relativistic equation of state there while the ultra-relativistic equation of state is always a good approximation in the shocked ambient medium as long as the shock Lorentz factor is much larger than unity. |
prescription (Pressetal.1992). | prescription \citep{press92}. |
. Tere the superscripts refer to the time judex and subscripts the spatial index aud the factors of two come about from the averaging of Dore between adjacent cells. | Here the superscripts refer to the time index and subscripts the spatial index and the factors of two come about from the averaging of $D, r, v$ between adjacent cells. |
The first two terius eive the diffusive fluxcs through the top aud bottom of the mass shell at radius r;. | The first two terms give the diffusive fluxes through the top and bottom of the mass shell at radius $r_i$. |
The second two teris give the same for the drifting fluxes. | The second two terms give the same for the drifting fluxes. |
The boundary conditions are Jo.= Oat r=0.R. where R is the WD radius; | The boundary conditions are $J_{22} = 0$ at $r=0,R$, where $R$ is the WD radius. |
We use poy instead of concentration as our dependent variable since this simplifies the form of the coutiuuitv equation. | We use $\rho_{22}$ instead of concentration as our dependent variable since this simplifies the form of the continuity equation. |
The rate at which flows through the interior is completely determined by D. | The rate at which flows through the interior is completely determined by $D$. |
Iu the liquid regious of the star. we set D=D, (equation CI). | In the liquid regions of the star, we set $D = D_s$ (equation \ref{eq:diff}) )). |
The E depeudenuce of D, means that as the WD cools. D. aud hence c. decrease aud flow slows. | The $\Gamma$ dependence of $D_s$ means that as the WD cools, $D$, and hence $v$, decrease and flow slows. |
We expect diffusion to halt iu regions of the WD that have crystallized. | We expect diffusion to halt in regions of the WD that have crystallized. |
There is thus an abrupt transition in the flow rate at the crvstal/liquid interface. | There is thus an abrupt transition in the flow rate at the crystal/liquid interface. |
Combined with the fact that the neon concentration is fixed behind the ervstal/Tiquid boundary. the crvstallizine of the WD leaves a siguificaut iuprint on the concentration profile in the star. as we discuss in &81.1.. | Combined with the fact that the neon concentration is fixed behind the crystal/liquid boundary, the crystallizing of the WD leaves a significant imprint on the concentration profile in the star, as we discuss in \ref{sec:cool:diffusion}. . |
Iu order to avoid nunuerical difficultics. we haudle the transition iu the value of D to zero in crystallizing regious by iiotlhliug the transition with the foriuula Tere 1/5 sets the factor by which D is reduced from D, in the crystalline state auc 2A; sets the width im DP over which the transition frou liquid to crystal occur in the // shell. | In order to avoid numerical difficulties, we handle the transition in the value of $D$ to zero in crystallizing regions by smoothing the transition with the formula Here $1/h$ sets the factor by which $D$ is reduced from $D_s$ in the crystalline state and $2 \Delta_i$ sets the width in $\Gamma$ over which the transition from liquid to crystal occur in the $i^{th}$ shell. |
By sinoothing out the transition frou liquid to crystal states. we effectively resolve the propagation of the crvstal/liquid boundary within a sinele shell of our exid in the seuse that it now takes a finite time for the shell to eo from fully liquid to fully crystalline. | By smoothing out the transition from liquid to crystal states, we effectively resolve the propagation of the crystal/liquid boundary within a single shell of our grid in the sense that it now takes a finite time for the shell to go from fully liquid to fully crystalline. |
This is important because the width of the transition reeion affects the profile ucar the crvstal/liquid boundary. | This is important because the width of the transition region affects the profile near the crystal/liquid boundary. |
We choose A; so that the time it takes for cach shell to transition from liquid to crystal (the transition regine beiug defined by (1|101ο>Dla 50.) equals the amount of time it takes the crystal frout to move across the shell. | We choose $\Delta_i$ so that the time it takes for each shell to transition from liquid to crystal (the transition regime being defined by $(1+10^{-3})^{-1}D_s \geq D \geq 10^{-3} D_s$ ) equals the amount of time it takes the crystal front to move across the shell. |
An easy wav of approximating A; is to consider the 7, at which the adjacent cells in our grid crystallize. | An easy way of approximating $\Delta_i$ is to consider the $T_c$ at which the adjacent cells in our grid crystallize. |
These two temperatures set the lower and upper bounds of the ranec in D in the j between which the cell undergoes crvstallization. | These two temperatures set the lower and upper bounds of the range in $\Gamma$ in the $j^{th}$ between which the cell undergoes crystallization. |
From this A is determined bv the simple relation where Ἐν=173. | From this $\Delta$ is determined by the simple relation where $\Gamma_{crit}=173$. |
For our models. the right haud side of equation (13)) is~ 10.P and A~0.1. | For our models, the right hand side of equation \ref{eq:dgamma}) ) is $\sim 10^{-3}$ and $\Delta \sim 0.1$. |
We prestume tha the lateut head is released iustautaueouslv when P=173 in the shell. | We presume that the latent head is released instantaneously when $\Gamma = 173$ in the shell. |
As imentioned prior. we also utilize the diffusion coefficient. inplied by the Stokes-Eiusteiu relation. and equation (5)) to calculate the effects of diffusion in WDs if the interior plasma undergoes a glassv transition instead of crystallizing. | As mentioned prior, we also utilize the diffusion coefficient implied by the Stokes-Einstein relation and equation \ref{eq:etaglfit}) ) to calculate the effects of diffusion in WDs if the interior plasma undergoes a glassy transition instead of crystallizing. |
In the elassyv state. we expect diffusion to contine. | In the glassy state, we expect diffusion to continue. |
Thus sedineutatiou wil continue to eenerate οποιον loug past the time whe1 sedimentation would have stopped in a crystallized WD. | Thus sedimentation will continue to generate energy long past the time when sedimentation would have stopped in a crystallized WD. |
Obviously. such a process has the potential to maintain a WD at a higher Iuunünositv than it otherwise would have at very late times. | Obviously, such a process has the potential to maintain a WD at a higher luminosity than it otherwise would have at very late times. |
We explore this possibility in section 1.3.. | We explore this possibility in section \ref{sec:cool:cool}. |
Before includiug the thermal evolution of the WD. we performed checks ou the accuracy of our algorithui at constant T. ina 0.63. mass WD. | Before including the thermal evolution of the WD, we performed checks on the accuracy of our algorithm at constant $T_c$ in a $0.6 \msun$ mass WD. |
The motion of over most of the WD is dominated bv falling at the local drift speed. ον allowing an analytical calculation of the concentration as a function of time by considering ouly the drift coutributions to the flux. | The motion of over most of the WD is dominated by falling at the local drift speed, $v$, allowing an analytical calculation of the concentration as a function of time by considering only the drift contributions to the flux. |
We consider the im a thin shell (at radius r and thickuess Ar). | We consider the in a thin shell (at radius $r$ and thickness $\Delta r$ ). |
Frou e(r) we calculate the position at later times of ious starting at the iuner and outer boundaries of this shell. | From $v(r)$ we calculate the position at later times of ions starting at the inner and outer boundaries of this shell. |
Then. the new ρου in the shell can be calculated from th5 old pos. r. and Ar and the new + and Ar. | Then, the new $\rho_{22}$ in the shell can be calculated from the old $\rho_{22}$, $r$, and $\Delta r$ and the new $r$ and $\Delta r$. |
The resulting at f—6.3 Cyr is displaved in Figure Α΄ along with he full nunerical results at the same WD age. | The resulting at $t=6.3$ Gyr is displayed in Figure \ref{fig:xcomp1} along with the full numerical results at the same WD age. |
The lower xuel of the plot displavs the relative difference between he two calculations. which show a good agreement in the Inner regions of the WD. | The lower panel of the plot displays the relative difference between the two calculations, which show a good agreement in the inner regions of the WD. |
We also compared the uumueric aud. analytic results for he diffusive equilibrium of. | We also compared the numeric and analytic results for the diffusive equilibrium of. |
. With D aud e specified. he profiles iu diffusive equilibriuu (Jo.=0) is given N which gives with. po», normalized. by total mass. | With $D$ and $v$ specified, the profiles in diffusive equilibrium $\vec{J}_{22}=0$ ) is given by which gives with $\rho_{22_0}$ normalized by total mass. |
A comparixou. between this expression aud the equilibrium reached iu the muuneric integration shows very good agreement. | A comparison between this expression and the equilibrium reached in the numeric integration shows very good agreement. |
We utilize equation (11)) and the discretization of equation (9)) to perform: the mutual evolution of T, aud pe» nunerically. | We utilize equation \ref{eq:numcont}) ) and the discretization of equation \ref{eq:Tc}) ) to perform the mutual evolution of $T_c$ and $\rho_{22}$ numerically. |
Here 19. Τό, CX.. aud fare the Inuuinosity. central temperature. total heat capacity of the WD. aud ateut heat released duringthe j* timestep. | Here $L^j$, $T_C^j$, $C_V^j$, and $l^j$ are the luminosity, central temperature, total heat capacity of the WD, and latent heat released duringthe $j^{th}$ timestep. |
In what ollows we cousder a WD composed of a single iou species as the background. | In what follows we consider a WD composed of a single ion species as the background. |
Figure Al is tvpical of the C/O ratio in WD interiors predicted by stellar evolution uodels; | Figure \ref{fig:xinit} is typical of the C/O ratio in WD interiors predicted by stellar evolution models. |
We can approximate this composition profile bv serforming calculations taking the cutire star to have a | We can approximate this composition profile by performing calculations taking the entire star to have a |
Conmminug back to the svstem of elasticity. it is possible (o compute the clisplacement. | Comming back to the system of elasticity, it is possible to compute the displacement. |
We [ind wy,=uy0 and In Figure 5.. we show successively the initial state of the crystal at time /=0 without anv applied stress. (hen the instantaneous (elastic) deformation of the crvstal when we apply the shear stress 7> αἱ time /=0. | We find $u_1=u_3=0$ and In Figure \ref{f5}, we show successively the initial state of the crystal at time $t=0$ without any applied stress, then the instantaneous (elastic) deformation of the crystal when we apply the shear stress $\tau>0$ at time $t=0^+$. |
The deformation of the crvstal evolves in time and finally converges numerically to some particular delormation which is shown on the last picture alter a very long time. | The deformation of the crystal evolves in time and finally converges numerically to some particular deformation which is shown on the last picture after a very long time. |
This kind of behaviour is called in mechanics. | This kind of behaviour is called elasto-visco-plasticity in mechanics. |
Moreover. on (hie last. picture. we observe (he presence of boundary laver deformations. | Moreover, on the last picture, we observe the presence of boundary layer deformations. |
This effect is directilv related to the introduction of the back stress 7 in the model. | This effect is directly related to the introduction of the back stress $\tau_b$ in the model. |
Al sufficiently low temperature. dislocation curves are contained in the ervstallographie planes of the (hree-dimensional crvstal and can only move in those planes. | At sufficiently low temperature, dislocation curves are contained in the crystallographic planes of the three-dimensional crystal and can only move in those planes. |
Let us consiler a closed. and smooth curve D, moving in (he plane (yy.y). | Let us consider a closed and smooth curve $\Gamma_t$ moving in the plane $(y_1,y_2)$. |
The evolution of this dislocation ean be modelled by a dvnamies with normal velocity e(y./) (see Figure 6)). | The evolution of this dislocation can be modelled by a dynamics with normal velocity $c(y,t)$ (see Figure \ref{F2}) ). |
their actual flux densities would be ~100 Jy, which is an atypically large amplitude for a water maser at these outlying velocities. | their actual flux densities would be $\sim 100$ Jy, which is an atypically large amplitude for a water maser at these outlying velocities. |
The only water maser known to occur at a velocity and position comparable to a !NH3 (9,6) maser is at vsg—56.9kms-! (Paper I; Kameya et 11990; Galvánn- et | The only water maser known to occur at a velocity and position comparable to a $^{14}$ $_3$ (9,6) maser is at $v_{\rm LSR} = -56.9\,{\rm km}\,{\rm s}^{-1}$ (Paper I; Kameya et 1990; Galv\'ann-Madrid et 2010). |
This water maser exhibits a four- intensity 22010).fluctuation during our observations while the corresponding ammonia maser exhibits no variability. | This water maser exhibits a four-fold intensity fluctuation during our observations while the corresponding ammonia maser exhibits no variability. |
If these two maser species are associated with the same physical volume example, a molecular then their pumping mechanisms(for or saturation states clump)must be substantially different from each other. | If these two maser species are associated with the same physical volume (for example, a molecular clump) then their pumping mechanisms or saturation states must be substantially different from each other. |
In comparing our results with other maser studies, we classify the masers in NGC 7538 into three groups: (1) those in the narrow velocity range —61kms!«ULSsR<—5lkms-! having positions near the continuum peak of IRS 1, presumably related to the inner regions of a circumstellar disk and torus, including rare species such as 23.1-GHz CH3OH and 4.8-GHz H3CO (Galvánn-Madrid et 22010; Hoffman et (2) the OH masers in the same narrow velocity 22003),range but with positions relatively far from the continuum peak and unassociated with the central disk structure (Hutawarakorn Cohen 2003), and (3) the H3O and l4NH3 masers that have velocities outside of the narrow range. | In comparing our results with other maser studies, we classify the masers in NGC 7538 into three groups: (1) those in the narrow velocity range $-61\,{\rm km}\,{\rm s}^{-1} < v_{\rm LSR} < -51\,{\rm km}\,{\rm s}^{-1}$ having positions near the continuum peak of IRS 1, presumably related to the inner regions of a circumstellar disk and torus, including rare species such as 23.1-GHz $_3$ OH and 4.8-GHz $_2$ CO (Galv\'ann-Madrid et 2010; Hoffman et 2003), (2) the OH masers in the same narrow velocity range but with positions relatively far from the continuum peak and unassociated with the central disk structure (Hutawarakorn Cohen 2003), and (3) the $_2$ O and $^{14}$ $_3$ masers that have velocities outside of the narrow range. |
Since we find no significant correlated velocities or variability between the water and ammonia masers, it remains an open question what relationship, if any, exists between water and ammonia. | Since we find no significant correlated velocities or variability between the water and ammonia masers, it remains an open question what relationship, if any, exists between water and ammonia. |
The drawing of further conclusions about the physical conditions illuminated by the ammonia sources awaits interferometric imaging of the new ammonia masers. | The drawing of further conclusions about the physical conditions illuminated by the ammonia sources awaits interferometric imaging of the new ammonia masers. |
In the case of the water masers, interferometric positions are already known from Kameya et ((1990). | In the case of the water masers, interferometric positions are already known from Kameya et (1990). |
They find the water maser at —46.4kms~! to lie within IRS 1, but the remainder of the high-velocity masers at —48.5kms! and —45.4kms! have positions well removed from any other infrared source or maser (see their Figure 3), although still in the main beam of our GBT observations. | They find the water maser at $-46.4\,{\rm km}\,{\rm s}^{-1}$ to lie within IRS 1, but the remainder of the high-velocity masers at $-48.5\,{\rm km}\,{\rm s}^{-1}$ and $-45.4\,{\rm km}\,{\rm s}^{-1}$ have positions well removed from any other infrared source or maser (see their Figure 3), although still in the main beam of our GBT observations. |
Qiu et have recently reported cores of millimeter-wave ((2011)emission (MM2 and MM3) at the positions of the —48.5kms"! and —45.4kms water masers. | Qiu et (2011) have recently reported cores of millimeter-wave emission (MM2 and MM3) at the positions of the $-48.5\,{\rm km}\,{\rm s}^{-1}$ and $-45.4\,{\rm km}\,{\rm s}^{-1}$ water masers. |
The MM2 and MM3 sources are interpreted as embedded stars that are comparable in gas mass to the power source of IRS 1, | The MM2 and MM3 sources are interpreted as embedded stars that are comparable in gas mass to the power source of IRS 1, |
Lt is. of course. not obvious that. the mocde-coupling calculation should give the same answer as the Floquet analysis of S44. even after this correction. | It is, of course, not obvious that the mode-coupling calculation should give the same answer as the Floquet analysis of 4, even after this correction. |
Phe gas considered here is compressible. whereas ino S44 it was assumed incompressible. | The gas considered here is compressible, whereas in 4 it was assumed incompressible. |
As nx. however. the modes of interest. which belong to the “inertial” branch (833). are ellectiveA incompressible near the mid-plane. | As $n\to\infty$, however, the modes of interest, which belong to the “inertial” branch 3), are effectively incompressible near the mid-plane. |
At high. altitudes (2> I1) the inertial modes are nearly isobaric. and. the local contribution to the coupling cocllicient (43)) varies with height. | At high altitudes $z
> H$ ) the inertial modes are nearly isobaric, and the local contribution to the coupling coefficient \ref{coupling}) ) varies with height. |
But when modes of many. (large) values of ϱ and the same [A] grow together. it can be shown that the relative phasing of the mode amplitudes demanded: by parametric instability results in à total wavefunction that is concentrated toward the mid-plane. | But when modes of many (large) values of $n$ and the same $|k|$ grow together, it can be shown that the relative phasing of the mode amplitudes demanded by parametric instability results in a total wavefunction that is concentrated toward the mid-plane. |
The analyses of 4 and 5 establish the existence of a linear instability of hvedrodsnamic warps. | The analyses of 4 and 5 establish the existence of a linear instability of hydrodynamic warps. |
We would now like to understand the non-linear outcome of the instability. ancl its non-axisvnimetric development. whieh was ignored in the analytic analysis. | We would now like to understand the non-linear outcome of the instability, and its non-axisymmetric development, which was ignored in the analytic analysis. |
To do this. we have integrated the hyelrodvnamic equations in a series. of numerical experiments. | To do this, we have integrated the hydrodynamic equations in a series of numerical experiments. |
The numerical model retains the basic assumptions used in the linear analysis. | The numerical model retains the basic assumptions used in the linear analysis. |
The parent warp mode is axisvmmetric. | The parent warp mode is axisymmetric. |
The equations of motion are those appropriate to the local model (see equation 1). | The equations of motion are those appropriate to the local model (see equation 1). |
The dise is Keplerian. so q=3/2. | The disc is Keplerian, so $q = 3/2$. |
The BDuid is assumed strictly isothermal. | The fluid is assumed strictly isothermal. |
We do not require that the svstem remain axisvmmetric. | We do not require that the system remain axisymmetric. |
1n the initial conditions we set Here Jo]«107 is a uniformly distributed: random variable with mean zero chosen independently for. each variable in each zone. | In the initial conditions we set Here $|\delta| < 10^{-3}$ is a uniformly distributed random variable with mean zero chosen independently for each variable in each zone. |
Subsets and Splits
No saved queries yet
Save your SQL queries to embed, download, and access them later. Queries will appear here once saved.