Datasets:
ReadingTimeMachine
/
rtm-sgt-ocr-v1

Dataset card Data Studio Files Community
2
source
stringlengths
1
2.05k
⌀
target
stringlengths
1
11.7k
This can be also seen in Figure 4.. which illustrates the similarity between the magnification fields for the two models of99-BLG-47.
This can be also seen in Figure \ref{fig:caust}, which illustrates the similarity between the magnification fields for the two models of.
. The very low A? between the two solutions despite the excellent data implies that it is extraordinarily difficult to break this degeneracy with photometric data.
The very low $\Delta\chi^2$ between the two solutions despite the excellent data implies that it is extraordinarily difficult to break this degeneracy with photometric data.
showed that for tthe two solutions were also astrometrically degenerate. at least for data streams lying within a few tg of the peak.
showed that for the two solutions were also astrometrically degenerate, at least for data streams lying within a few $t_{\rm E}$ of the peak.
They argued that this astrometric degeneracy. like the corresponding photometric degeneracy. was rooted in the lens equation.
They argued that this astrometric degeneracy, like the corresponding photometric degeneracy, was rooted in the lens equation.
However. as shown in this appendix. the correspondence between the equations describing close- and wide-binaries 1slocal2001).
However, as shown in this appendix, the correspondence between the equations describing close- and wide-binaries is.
. For example. there is a constant-offset term in equation (A10)). which does not give rise to any local photometric or astrometric effects. but which must "disappear" at late times.
For example, there is a constant-offset term in equation \ref{eqn:crl}) ), which does not give rise to any local photometric or astrometric effects, but which must “disappear” at late times.
Hence there must be a late-time astrometric shift between the two solutions.
Hence there must be a late-time astrometric shift between the two solutions.
Such a shift was noted explicitly by for the case of98-SMC-I.. and these are likely to be a generic feature of close/wide corresponding pairs of solutions.
Such a shift was noted explicitly by for the case of, and these are likely to be a generic feature of close/wide corresponding pairs of solutions.
We also plot the lines of (4.4) pairs that have the same shear as the best-fit wide-binary model or the same quadrupole moment ( as the best-fit elose-binary model on X?-surface contour plot shown in Figure 2..
We also plot the lines of $d$ $q$ ) pairs that have the same shear $\gamma$ as the best-fit wide-binary model or the same quadrupole moment $\hat Q$ as the best-fit close-binary model on $\chi^2$ -surface contour plot shown in Figure \ref{fig:chi2cont}.
While the iso-shear line for wide binaries lies nearly parallel to the direction of the principal conjugate near the best-fit model. it is clear from the figure that the condition of (Q—5<1 alone does not define the observed well-defined two-fold degeneracy. which involves the additional correspondence between higher order terms beyond the quadrupole moment (— c7) and the pure shear (—4,7).
While the iso-shear line for wide binaries lies nearly parallel to the direction of the principal conjugate near the best-fit model, it is clear from the figure that the condition of $\hat Q\simeq\gamma\ll 1$ alone does not define the observed well-defined two-fold degeneracy, which involves the additional correspondence between higher order terms beyond the quadrupole moment $\sim d_c^2$ ) and the pure shear $\sim d_w^{-2}$ ).
Further comparison between equations (A8)) and (A T14)) indicates that there exists a magnification correspondence up to the order of d)dP ifthecondition (1gj14)F9d,1qu).L7? is also satisfied in addition to (Q=~«1.
Further comparison between equations \ref{eqn:magc}) ) and \ref{eqn:magw}) ) indicates that there exists a magnification correspondence up to the order of $d_c^3\sim d_w^{-3}$ if the condition $d_c(1-q_c)(1+q_c)^{-1}=d_w^{-1}(1+q_w)^{-1/2}$ is also satisfied in addition to $\hat Q=\gamma\ll 1$.
We find that. for the two PLANET models. 4,(1.—ας14.)4—6.6«10.2? (the close binary) and 4,2(11q4)1?—6.7«10? (the wide binary).
We find that, for the two PLANET models, $d_c(1-q_c)(1+q_c)^{-1}=6.6\times 10^{-2}$ (the close binary) and $d_w^{-1}(1+q_w)^{-1/2}=6.7\times 10^{-2}$ (the wide binary).
Hence. we conclude that. in fact. these two conditions. define a unique correspondence between two extreme separation binaries.
Hence, we conclude that, in fact, these two conditions, define a unique correspondence between two extreme separation binaries.
We also note that the images (not shown) of the iso-A4? contours for the close binary models ofuunder the mapping defined by the above two relations follows extremely closely the corresponding iso-A4? contour for wide binary models. except for the difference of AX?~0.6 offset between two solutions.
We also note that the images (not shown) of the $\Delta\chi^2$ contours for the close binary models ofunder the mapping defined by the above two relations follows extremely closely the corresponding $\Delta\chi^2$ contour for wide binary models, except for the difference of $\Delta\chi^2\simeq 0.6$ offset between two solutions.
Over. the last two decades. evolutionary svutlesis uodeliug has become a common fool to study unresolved stellar populatious of galaxies in the optical aud UV passbauds (Druzual&Charlotal. 1999).
Over the last two decades, evolutionary synthesis modeling has become a common tool to study unresolved stellar populations of galaxies in the optical and UV passbands \citep{bru93,wor94a,vaz99,lei99}.
The heavy obscuration iu starburst IUIUS MES "o ∩⊾⋪↕⋪↧↸↕↸∖∖↴∪↕⋡↑↸∖∐↖↖↽↕↑∐≚↽⋝∖∕⋅↱⊐∐⊔∩⊾⋖⊏∐∩⊾↸∖∐⋝↥⋅⋪∥⊳∐↑°‘1997) requires an expansion of these models into the near infrared (CIR) domain. because the extinction there is reduced. teutold in comparison with the optical region: Ay /Ay-=0.112 (RicseLebofsky 1985).
The heavy obscuration in starburst galaxies – often with $_V$$\geq$ 5 mag \citep{eng97} – requires an expansion of these models into the near infrared (IR) domain, because the extinction there is reduced tenfold in comparison with the optical region: $_K$ $_V$ =0.112 \citep{rie85}.
Therefore, it is not strprising that many studies of eribeddedstellar popula19115 in galaxies have been conducted in the near-IR (Riekeetal,1980.1993).
Therefore, it is not surprising that many studies of embedded stellar populations in galaxies have been conducted in the near-IR \citep{rie80,rie93}.
IR. evolutionary svuthesis models base O1 syntheticu ⋅↴spectra.∙ (Ori↽∙⋅elia..Moorwood&{να1993:IKurucz1991) eenerallv have diffitics reproducing broad-band colors because of the complicated opacity calculations in the near-IR.
IR evolutionary synthesis models based on synthetic spectra \citep{ori93,kur94} generally have difficulties reproducing broad-band colors because of the complicated opacity calculations in the near-IR.
Eupirical libraries based predomunautly ou bright aud nearby Milkv. Wav stars
Empirical libraries based predominantly on bright and nearby Milky Way stars
To eliminate the from the physical parameters. we calculated their cle-trendecl counterparts emplovineS equations (4)) and (5)). as Absolute values of the de-trencdecl parameters are not meaningful. and we hereafter consider their relative values only.
To eliminate the from the physical parameters, we calculated their de-trended counterparts employing equations \ref{eq:1608_Ltot_Ldisk_Lbb}) ) and \ref{eq:1608_Ltot_t_r}) ), as Absolute values of the de-trended parameters are not meaningful, and we hereafter consider their relative values only.
Since r5, shows the largest variation among them. we plot the de-trended parameters as a function of ή.
Since $r'_{\rm in}$ shows the largest variation among them, we plot the de-trended parameters as a function of $r'_{\rm in}$.
Table 4. also summarizes those of Spec Ato Din § 3.1..
Table \ref{tab:detrend} also summarizes those of Spec A to D in $\S$ \ref{subsec:spec}.
From the behavior of the de-trended luminosities. the data points can be divided into (vo branches: one has almost constant luminosities as rj,varies. while the other is characterized by significant r5,-dependent variations both in [μι and Lt.
From the behavior of the de-trended luminosities, the data points can be divided into two branches; one has almost constant luminosities as $r'_{\rm in}$varies, while the other is characterized by significant $r'_{\rm in}$ -dependent variations both in $L'_{\rm disk}$ and $L'_{\rm BB}$.
Herealter. the two branches are denoted as “constant-luninosityv branch (CLDB) and "variable-Inminositv branch (VLB)'. respectively.
Hereafter, the two branches are denoted as “constant-luminosity branch (CLB)” and “variable-luminosity branch (VLB)”, respectively.
The two branches may connect at rj,~0.85. rather than behaving independently fom each other.
The two branches may connect at $r'_{\rm in} \sim 0.85$, rather than behaving independently from each other.
—| the CLD. the de-trended BB luminosity stays nearly constant at Li),~0.8: so are the (vo DD parameters. A75,o1.6 and ry),0.9.
In the CLB, the de-trended BB luminosity stays nearly constant at $L'_{\rm BB} \sim 0.8$; so are the two BB parameters, $kT'_{\rm BB} \sim 1.6$ and $r'_{\rm BB} \sim 0.9$.
Similarly. the de-trended disk luminosity remains al La~0.9.
Similarly, the de-trended disk luminosity remains at $L'_{\rm disk} \sim 0.9$.
As a result. the CLB data points are distributed in Figure 6. (a) along the majorcorrelation trends.
As a result, the CLB data points are distributed in Figure \ref{fig:spec_1608_all1} (a) along the majorcorrelation trends.
Nevertheless. 7, varies by ~z204.. accompanied by a clear decrease in the de-trended. disk temperature as A77,11xri. (
Nevertheless, $r'_{\rm in}$ varies by $\sim \pm 20$, accompanied by a clear decrease in the de-trended disk temperature as $kT'_{\rm in} \propto r_{\rm in} $$^{-0.5}$. (
This scaling is a natural consequence of the constant μι and the relation of L4/QOXoT!ruA da)Y T
This scaling is a natural consequence of the constant $L'_{\rm disk}$ and the relation of $L'_{\rm disk} \propto r'_{\rm in}$$^{2} T'_{\rm in}$$^{4}$ .)
here are twotw possibilities to explain this ri, behavior.
There are two possibilities to explain this $r'_{\rm in}$ behavior.
One is real changes in rj,. and the other is those in the color hardening factor & of the disk.
One is real changes in $r_{\rm in}$, and the other is those in the color hardening factor $\kappa$ of the disk.
Since Li.) is kept constant in the CLD. the latter case may be more likely.
Since $L'_{\rm disk}$ is kept constant in the CLB, the latter case may be more likely.
In the VLD. r7, varies over a relatively small range (o 410%)). whereas the two luninosities both vary significantly in an anti-correlated way: L4, decreases from 1.9 to 1.5 as xri, I. while Lj, increases from 0.8 to 1.2 as x 747.
In the VLB, $r'_{\rm in}$ varies over a relatively small range $\sim \pm 10$ ), whereas the two luminosities both vary significantly in an anti-correlated way; $L'_{\rm disk}$ decreases from 1.9 to 1.5 as $\propto r'_{\rm in}$$^{-1}$ , while $L'_{\rm BB}$ increases from 0.8 to 1.2 as $\propto r'_{\rm in}$$^{2}$ .
This complementary behavior between the MCD and BB components appears in Figure G as the large fluctuations away
This complementary behavior between the MCD and BB components appears in Figure \ref{fig:spec_1608_all1} as the large fluctuations away
observations can be clearly identified in the simulations, except in the temporal range between t=27 and t—40 min.
observations can be clearly identified in the simulations, except in the temporal range between $t=27$ and $t=40$ min.
The match between the observed and simulated amplitudes is also remarkable.
The match between the observed and simulated amplitudes is also remarkable.
Both maps seem to be almost in phase.
Both maps seem to be almost in phase.
There is some phase delay which coincides with the strongest shocks, but it is smaller than the one obtained for the ccore.
There is some phase delay which coincides with the strongest shocks, but it is smaller than the one obtained for the core.
Only those waves with frequency above the cutoff can reach the chromosphere.
Only those waves with frequency above the cutoff can reach the chromosphere.
The increase of the amplitude of these waves with height is larger than that of the evanescent low frequency waves, and the power spectra at the chromosphere is dominated by the peak at 6 mHz.
The increase of the amplitude of these waves with height is larger than that of the evanescent low frequency waves, and the power spectra at the chromosphere is dominated by the peak at 6 mHz.
For example, in the case of the power spectra of the lline (Figure 11)), both the observations and simulation have their power concentrated around this frequency.
For example, in the case of the power spectra of the line (Figure \ref{fig:he_spectra}) ), both the observations and simulation have their power concentrated around this frequency.
The observational power has three power peaks in the 3 minute band, located at 5.5, 6 and 7 mHz.
The observational power has three power peaks in the 3 minute band, located at 5.5, 6 and 7 mHz.
The simulated power is concentrated at a single peak between the two highest peaks of the observations.
The simulated power is concentrated at a single peak between the two highest peaks of the observations.
The simulated peak at 5.5 mHz is lower than the observed one.
The simulated peak at 5.5 mHz is lower than the observed one.
The simulations also reproduce the power peaks at 7.7 mHz and 9 mHz, and the low power at frequencies below 5 mHz.
The simulations also reproduce the power peaks at 7.7 mHz and 9 mHz, and the low power at frequencies below 5 mHz.
At frequencies above 13 mHz the simulated power is larger than the observational one.
At frequencies above 13 mHz the simulated power is larger than the observational one.
The propagation properties of waves are analysed by means of the phase difference (A9) and amplification spectra.
The propagation properties of waves are analysed by means of the phase difference $\Delta \phi$ ) and amplification spectra.
The value of A$ gives the time delay between the oscillatory velocity signals from two spectral lines.
The value of $\Delta \phi$ gives the time delay between the oscillatory velocity signals from two spectral lines.
We assume that the difference between them is mainly due to the difference of the formation height of the two lines.
We assume that the difference between them is mainly due to the difference of the formation height of the two lines.
The amplification spectra are calculated as the ratio between the wave power at two layers.
The amplification spectra are calculated as the ratio between the wave power at two layers.
They give us information about variations of oscillation amplitude with height.
They give us information about variations of oscillation amplitude with height.
The estimation of the statistical validity of the amplification and phase difference spectra can be done by calculation of the coherence spectra.
The estimation of the statistical validity of the amplification and phase difference spectra can be done by calculation of the coherence spectra.
This calculations for the observed dataset were presented previously in Felipeetal.
This calculations for the observed dataset were presented previously in \citet{Felipe+etal2010b}.
In order to reproduce(2010b).. correctly the phase and amplification spectra, the introduction of the term Q4 in the energy equation for the simulations (see Section 2)), to take into account the energy losses, has proved to be fundamental.
In order to reproduce correctly the phase and amplification spectra, the introduction of the term $Q_{rad}$ in the energy equation for the simulations (see Section \ref{sect:procedures}) ), to take into account the energy losses, has proved to be fundamental.
This is so due to several reasons.
This is so due to several reasons.
Firstly, the radiative losses produce some damping of the waves, reducing their amplitude.
Firstly, the radiative losses produce some damping of the waves, reducing their amplitude.
Secondly, the cutoff frequency of the waves is also affected by radiative transfer (Roberts1983;Khomenkoetal. 2008).
Secondly, the cutoff frequency of the waves is also affected by radiative transfer \citep{Roberts1983,Khomenko+etal2008c}.
When the radiative timescale Tg is small enough, the cutoff frequency is expected to decrease, compared to the adiabatic case.
When the radiative timescale $\tau_R$ is small enough, the cutoff frequency is expected to decrease, compared to the adiabatic case.
Finally, the inclusion of radiative losses also produces an increase of the phase difference compared to adiabatic case (seeFigure7fromCentenoetal.2006).
Finally, the inclusion of radiative losses also produces an increase of the phase difference compared to adiabatic case \citep[see Figure 7 from][]{Centeno+etal2006}.
. Figure 12 shows the phase difference and amplification spectra between the photospheric Iline and the chromospheric line, for both observational and simulated velocities.
Figure \ref{fig:spiegel_sihe} shows the phase difference and amplification spectra between the photospheric line and the chromospheric line, for both observational and simulated velocities.
From 1 to 7 mHz, where the coherence of the observations is high, the simulated phase difference precisely matches the observed one, with a null phase difference for frequencies below 4 mHz and an almost linear increase between 4 and 7 mHz.
From 1 to 7 mHz, where the coherence of the observations is high, the simulated phase difference precisely matches the observed one, with a null phase difference for frequencies below 4 mHz and an almost linear increase between 4 and 7 mHz.
At higher frequencies the coherence of the observed phase difference is lower, but the simulated one keeps its linear increase.
At higher frequencies the coherence of the observed phase difference is lower, but the simulated one keeps its linear increase.
With regards to the amplification spectra, for frequencies above 1.5 mHz the simulated spectra reproduces properly the observed one.
With regards to the amplification spectra, for frequencies above 1.5 mHz the simulated spectra reproduces properly the observed one.
The smallest frequencies show a high numerical amplification, which is possibly due to the difficulties of the PML to damp these long period waves.
The smallest frequencies show a high numerical amplification, which is possibly due to the difficulties of the PML to damp these long period waves.
The thickness of the PML layer should be proportional to the wavelength of the wave that must be absorbed, and the employed PML is obviously not optimized for such long period waves.
The thickness of the PML layer should be proportional to the wavelength of the wave that must be absorbed, and the employed PML is obviously not optimized for such long period waves.
However, since the power at these low frequencies is small, their overall influence on the simulations is negligible.
However, since the power at these low frequencies is small, their overall influence on the simulations is negligible.
A similar result is found between the velocity obtained with the aand the ccore (Figure 13)), since the latter is formed just around 100 km below the Nine.
A similar result is found between the velocity obtained with the and the core (Figure \ref{fig:spiegel_sica}) ), since the latter is formed just around 100 km below the line.
The simulated phase difference is zero for frequencies below 4 mHz, and it increases at higher frequencies.
The simulated phase difference is zero for frequencies below 4 mHz, and it increases at higher frequencies.
It matches the observed phase shift between
It matches the observed phase shift between
throug
baryon.
h (6)) from avalence diquark behaves like avalence diquark and produce aleading
From the data on $\bar{\Sigma}^-$ polarization, we set the parameter for the probability of
WV. aud also a faculty member in the Departineut o£ Plysies at. Virgiuia Tech.
WV, and also a faculty member in the Department of Physics at Virginia Tech.
This work was supported by the Claxo-Wellcome Endowment at the University of North Carolina-Asheville aud by National Science Foundation grant AS'T-0008[8T to Vireinia Tech.
This work was supported by the Glaxo-Wellcome Endowment at the University of North Carolina-Asheville and by National Science Foundation grant AST-0098487 to Virginia Tech.
The National Racio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities. Inc.
The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc.
Studies; of⋅ star-forming⋅; galaxies; at high; redshift.τρ {ς 1.5) over the past decade have mapped. the demographics of⋅ the populations. as a whole vielding"m valuable data on Iκ. ⋡⋅⋅⋅⋡⋪ κ ars ⇂↓↥∢⊾↓↓↓⊔↿⋖⊾⋏∙≟↓≼⋯⊾∠⇂⊳∖↿≼⊔⇂∪↓⊔↓≼⊔↓∪⊔↓≺⋯⊾⊳∖⊳⊳∖∩⋅∐≼⊔≼⋃⊔⇂∠⇂∙∖⊔≺⋯↓⊔≼↧↓⇁⋡⊀⋅⋡
Studies of star-forming galaxies at high redshift $z > 1.5$ ) over the past decade have mapped the demographics of the populations as a whole yielding valuable data on their integrated star formation rates, stellar and dynamical masses, metallicities and morphologies \citep{Shapley01,Shapley03,Reddy04,Erb06, Law07a}.
data. a consistent picture of the development of the comoving density of star formation and its contribution to theh presenpresent clayle stellarolla densitylenit? hasmergedemerged (77)(2?)..
From these data, a consistent picture of the development of the comoving density of star formation and its contribution to the present day stellar density has emerged \citep{Dickinson03, Hopkins06}.
IFollowingowing a rapid rise in activity at early hatimes. corresponding to the redshilledshift rang range2<6. the star starformation rate has declinedeclin ⊔↓⋜⊔⋅↳∢⊾∠∐∙∖⇁∪∖⇁⋖⋅↓⋅⇂↓↥∢⊾↓⋯⊳∖⇂↖∖≺∶∙∖⇁↓⋅≼∼∪↓⋅↓⋅∢⋅⊳∖↓≻∪⊔∠⇂⊲↓⊔∙≟↿∪↿↓↕∢⋅⊲↓⊔∩⋅↓⋅∖⇁⋜↧↓ 0«2I.
Following a rapid rise in activity at early times, corresponding to the redshift range $2<z<6$, the star formation rate has decline markedly over the past 8 Gyr corresponding to the interval $0<z<1$.
Of∙ particular. interest: is. the relationship". between
Of particular interest is the relationship between
second simulation is one by Cen(2002b) in which Qy=0.3. Q4=0.7. OIO.O17. h=0.67. n= 1. and o4=0.9.
second simulation is one by \citet{Cen02b} in which $\Omega_0=0.3$ , $\Omega_\Lambda=0.7$ , $\Omega_b h^2 = 0.017$ , $h = 0.67$, $n=1$ , and $\sigma_8 = 0.9$.
The values of 2 ancl oy are given for both and Cen(2002b) are provided in Table 1.
The values of $\beta$ and $\delta_0$ are given for both \citet{MHR00} and \citet{Cen02b} are provided in Table 1.
As is clear [rom Table 1. the value of 6) and to a lesser extent 2 depend on cosmology.
As is clear from Table 1, the value of $\delta_0$ and to a lesser extent $\beta$ depend on cosmology.
This is not surprising given (hat dy depend on the power spectrum.
This is not surprising given that $\delta_0$ depend on the power spectrum.
The cosmological dependence on 5j ds less clear. especially since (he best fit value of 9 depends significantly on the density run in collapsed halos.
The cosmological dependence on $\beta$ is less clear, especially since the best fit value of $\beta$ depends significantly on the density run in collapsed halos.
Because the Cen(2002b) simulation is at much hieher resolution and includes more realistic physics. we simply fit ;? to the Cen results as a function of redshift. with a maximum of 2,444=2.5. corresponding to an isothermal sphere: where we are only considering redshills 2>4.
Because the \citet{Cen02b} simulation is at much higher resolution and includes more realistic physics, we simply fit $\beta$ to the Cen results as a function of redshift, with a maximum of $\beta_{\rm max} = 2.5$, corresponding to an isothermal sphere: where we are only considering redshifts $z \geq 4$.
As [or a prescription for finding oy. we note that the gas PDF also preclicts the fraction of mass in collapsed virialized halos: ↴∏∐↲↕∐∩↲↖≺↽↔↴↕⋅≀↧↴∐∪∐↕↽≻∪↕∐↥≺≨⊼⇉∎⋟∖⊽≺⇂≼↲↕⋅↕∖↽≼↲≼⊔⋟↕⋅∪∐↓⊔∐↲↓⋟≀↧↴≺∢↥⊔⋯↴↥↓⋟∪↕⋅≀↧⊔∖⊽↕∐≸↽↔↴∏↥≀↧↴↕⋅↕⋟∖⊽∪⊔∐↲↕⋅∐↓≀↧↴↥⋟∖⊽↕↽≻↥∐↲↕⋅≼↲⋅ ⊔∐↲↥∪≺∢≀↧↴↥∪∖↽≼↲↕⋅≺⇂≼↲∐⋟∖⊽∐⋡∖↽≼⇂≼↲∐⋟∖⊽∐∡∖
As for a prescription for finding $\delta_0$, we note that the gas PDF also predicts the fraction of mass in collapsed virialized halos: The integration point $6\pi^2$ is derived from the fact that for a singular isothermal sphere, the local overdensity density at the virial radius is $6\pi^2$.
↽≀↧↴↥⊔∐↲∖⇁∐⋅↕≀↧↴↥↕⋅≀↧↴≼∐∏⋟∖⊽↕⋟∖⊽≺≻∣∆−⋅⊺↥∐↲↕⋅≼↲↓∪↕⋅≼↲⋅∖∖⇁≼↲≀⋯↲≀↧↴↕↽≻↕↽≻↕⋅∪⇀↸∐∐≀↧↴↥≼↲↥⋡∖↽ Laking into account all gas within virialized halos.
Therefore, we are approximately taking into account all gas within virialized halos.
Similarly. from linear theory. we can use the Press-Schechter formalism (PressanclSchechter1974). (o find the same quantity il we know the correct filtering radius Z1: where 0.z1.69 and op, is the linear RATS mass fluctuation filtered with a tophat οἱ radius Z?;.
Similarly, from linear theory, we can use the Press-Schechter formalism \citep{PS74} to find the same quantity if we know the correct filtering radius $R_f$: where $\delta_c \approx 1.69$ and $\sigma_{R_f}$ is the linear RMS mass fluctuation filtered with a tophat of radius $R_f$.
However. the mass fraction shouldbe equalbythetwo calculations Dv analvzing both simulations. we find the following relation leads (ο satisfactory results: where /?y is the Jeans length defined by
However, the mass fraction shouldbe equalbythetwo calculations By analyzing both simulations, we find the following relation leads to satisfactory results: where $R_J$ is the Jeans length defined by
T D>651, T>65! (BM)7?=17Ei,/16nmmyc?. (Blandfordr n Fi,,is Ej«=102Ei, 6o T>691 1/T l'=05! corresponding to an observer's frame time where 09=10:10., Exo=1093Eiso,53 erg and n=ΊπροπιὉ. (
$\Gamma$ $\Gamma>\theta_0^{-1}$ $\Gamma>\theta_0^{-1}$ $\Gamma^2r^3=17E_{\rm iso}/16\pi nm_pc^2$ $r$ $n$ $E_{\rm iso}$ $E_{\rm jet}=\frac{1}{2}\theta_0^2E_{\rm iso}$ $\theta_0$ $\Gamma>\theta_0^{-1}$ $1/\Gamma$ $\Gamma=\theta_0^{-1}$ corresponding to an observer's frame time where $\theta_{0}=10^{-1}\theta_{0,-1}$, $E_{\rm iso}=10^{53}E_{\rm iso,53}$ erg and $n=1n_0\rm cm^{-3}$. (
For a burst located at redshift z, all observed times should be increased by a factor 1+z; we do not explicitly show this correction in our eqs.)
For a burst located at redshift $z$, all observed times should be increased by a factor $1+z$; we do not explicitly show this correction in our eqs.)
The sideways expansion is expected to be relativistic as long as the blast wave is relativistic and the post-shock energy density is relativistic1999).
The sideways expansion is expected to be relativistic as long as the blast wave is relativistic and the post-shock energy density is relativistic.
. If this is the case, at t>tg the lateral expansion rapidly increases the jet opening angle and accelerates its deceleration1999),, reducing T to ~1 with only a logarithmic increase of r (to In65!x rg).
If this is the case, at $t>t_\theta$ the lateral expansion rapidly increases the jet opening angle and accelerates its deceleration, reducing $\Gamma$ to $\sim1$ with only a logarithmic increase of $r$ (to $\sim\ln\theta_0^{-1}\times r_\theta$ ).
Thus, the observed time scale for the flow to become transrelativistic is On similar time scale, the flow is expected to become quasi-spherical,a i.e. the jet is expected to expand to 0~ 1,and the outflow is subsequently expected to evolve into the spherical non-relativistic Sedov-von Neumann-Taylor (ST) flow.
Thus, the observed time scale for the flow to become transrelativistic is On a similar time scale, the flow is expected to become quasi-spherical, i.e. the jet is expected to expand to $\theta\sim1$ ,and the outflow is subsequently expected to evolve into the spherical non-relativistic Sedov-von Neumann-Taylor (ST) flow.
This simple analytic description of jet expansion was challenged by a series of numerical calculations2010).
This simple analytic description of jet expansion was challenged by a series of numerical calculations.
. It was argued, based on the numerical results, that the sideways expansion of the jet is not relativistic, and that the jet retains its narrow original opening angle, 69, as long as it is relativistic2009).
It was argued, based on the numerical results, that the sideways expansion of the jet is not relativistic, and that the jet retains its narrow original opening angle, $\theta_0$, as long as it is relativistic.
. This implies that (Granotthe jet continues to evolve like a conical sectionofa sphericaloutflow with energy Ei,withLorentzfactor followingtheBM solution, up to the radius rnp=ctnr at which it becomes sub-relativistic,
This implies that the jet continues to evolve like a conical sectionofa sphericaloutflow with energy$E_{\rm iso}$ ,withLorentzfactor followingtheBM solution, up to the radius $r_{\rm NR}=ct_{\rm NR}$ at which it becomes sub-relativistic,
109an f,»"3 f,»9
$\mu$ \citet{van71}. \citep[see][ for a review]{Condon92}.
. ~90%
$_{\nu}$ $\propto$ $\nu^{-0.1}$ $_{\nu}$ $\propto$ $\nu^{-0.8}$ $\sim$ \citep{Harwit75}.
been shown that the far-infrared (FIR. jn). to radio correlation holds well over a remarkably wide range of star forming galaxies. spannuius several orders of magnitude in Iunuinosities (IHelouctal.1985:deJong 2001).
been shown that the far-infrared (FIR, $\mu$ m) to radio correlation holds well over a remarkably wide range of star forming galaxies, spanning several orders of magnitude in luminosities \citep{Helou85, Dejong85, Condon91,Yun01}.