Datasets:
ReadingTimeMachine
/
rtm-sgt-ocr-v1

Dataset card Data Studio Files Community
2
source
stringlengths
1
2.05k
⌀
target
stringlengths
1
11.7k
∙ -1 and 2. the window: functions. of bethe lieht often contain strong peaks at or close to particular curvesfrequencies.
\ref{fig:whiten} and \ref{fig:pdscalc}, the window functions of the light curves often contain strong peaks at or close to particular frequencies.
Even though the analvsis procedure tends to iuiminüze the appearance of these frequencies in the whitened power spectra. there are occurrences of peaks at these frequencies.
Even though the analysis procedure tends to minimize the appearance of these frequencies in the whitened power spectra, there are occurrences of peaks at these frequencies.
Iu the analyses done with filtering based on smoothing time scales of 10.0 days aud under. we ignore all peaks in the frequency ranges 1.0040.01. 2.00+0.01. 15.15+0.20. 30.3280,2. 15.15+£0.20. and 60.6£0.2 1.
In the analyses done with filtering based on smoothing time scales of 10.0 days and under, we ignore all peaks in the frequency ranges $1.00\pm0.04$, $2.00\pm0.04$, $15.15\pm0.20$, $30.3\pm0.2$, $45.45\pm0.20$, and $60.6\pm0.2$ $^{-1}$.
For the other analyses. we ignore all peaks iu the frequency ranges L3: 0.00270.00025.0.005Ls+ 0.00025. 0.01096+ 0.00025.
For the other analyses, we ignore all peaks in the frequency ranges $0.00274\pm0.00025$ ,$0.00548\pm0.00025$ , $0.01096\pm0.00025$ ,
as that suggested. first by Ando and. Osaki (1975) in an attempt to explain solar p-mocde excitation in the Sun. and is artificial.
as that suggested first by Ando and Osaki (1975) in an attempt to explain solar p-mode excitation in the Sun, and is artificial.
It is easy to understand why: at the photosphere. where the energy is carried mostly by radiation. the Lux »erturbation is negative in the hieh-temperature phase of he pulsation evele.
It is easy to understand why: at the photosphere, where the energy is carried mostly by radiation, the flux perturbation is negative in the high-temperature phase of the pulsation cycle.
Phis is a result. of the steep. increase of the opacity with temperature in the outer lavers.
This is a result of the steep increase of the opacity with temperature in the outer layers.
The raction of the energy carried by convection increases rapiclly inwards.
The fraction of the energy carried by convection increases rapidly inwards.
Since.assimplion. the convective Hux remains unperturbed. the energy. is forced. to be captured. by the Whotospherice [avers. and the putative heat engine works.
Since, the convective flux remains unperturbed, the energy is forced to be captured by the photospheric layers, and the putative heat engine works.
This phenomenon is sometimes called c'onvective blocking. which is confusing because what actuaIv. blocks he heat lux is the opacity variation.
This phenomenon is sometimes called convective blocking, which is confusing because what actually blocks the heat flux is the opacity variation.
IOwever. there is no physical justification for the neglect ofthe perturbed convective heat lux and. Itevnolds stresses.
However, there is no physical justification for the neglect of the perturbed convective heat flux and Reynolds stresses.
Indeed. pulsational modulation of the convectively unstable stratification of the star. is »ound to modulate the convective dvnamies. and dominate he driving or damping in regions where the convective IDuxes dominate in the equilibrium state.
Indeed, pulsational modulation of the convectively unstable stratification of the star is bound to modulate the convective dynamics, and dominate the driving or damping in regions where the convective fluxes dominate in the equilibrium state.
Etects of convection on the stability of radial pulsations in cool stars have been investigated since the early 1970s (see e.g.1998:2000).
Effects of convection on the stability of radial pulsations in cool stars have been investigated since the early 1970s (see e.g.;.
.. Reeent efforts have focused mainly on Mira stars and the Sun.
Recent efforts have focused mainly on Mira stars and the Sun.
According to the calculations of ((1998). low-order racial mocles of Mira mocoels are unstable. whereas those of orders nold were abwavs found to be damped (see also the work by ((1991) on Areturus).
According to the calculations of (1998), low-order radial modes of Mira models are unstable, whereas those of orders $n>4$ were always found to be damped (see also the work by (1991) on Arcturus).
In a study of p-mode stability in the Sun. by Dalmforth. (19922). all modes have been found to be sable.
In a study of p-mode stability in the Sun by Balmforth (1992a), all modes have been found to be stable.
Dalmforth: used in his calculations Gough's (1976. 1971) nonlocal. tinie-dependent: mixine-leneth model for convection. improving on the code used by. Baker Goug1 (1979) to study RR Lyrae stars by incorporating the Ed:lington approximation to radiative transfer for both the equilibrium: structure and the pulsations. (
Balmforth used in his calculations Gough's (1976, 1977) nonlocal, time-dependent mixing-length model for convection, improving on the code used by Baker Gough (1979) to study RR Lyrae stars by incorporating the Eddington approximation to radiative transfer for both the equilibrium structure and the pulsations. (
(1999). applied. these calculations to solar-tvpe stars. and estimated amplitudes of intrinsically stable stochastically excited. racial oscillations in stars with masses between and MM. close to the main sequence.
1999) applied these calculations to solar-type stars, and estimated amplitudes of intrinsically stable stochastically excited radial oscillations in stars with masses between $_\odot$ and $_\odot$ close to the main sequence.
Lere we apply Balmforth's (1992a) treatment of pulsation to a model of a UAla.
Here we apply Balmforth's (1992a) treatment of pulsation to a model of $\alpha\,$ UMa.
In particular. we include turbulent pressure in the equilibrium mocel. and the stability analysis includes the Lagrangian perturbations of the convective heat and momentum UHuxes.
In particular, we include turbulent pressure in the equilibrium model, and the stability analysis includes the Lagrangian perturbations of the convective heat and momentum fluxes.
We use an envelope model calculated. with the surface parameters of model AL, given in Table 1. and an atmosphere using the 7-7 relation of model € of Vernazza. AXvrett Loeser (1981).
We use an envelope model calculated with the surface parameters of model $_\alpha$ given in Table 1, and an atmosphere using the $T$ $\tau$ relation of model C of Vernazza, Avrett Loeser (1981).
Tho value of the mixine-leneth parameter was adjusted such às to reproduce the same depth of the convective zone as was obtained from the evolutionary computation.
The value of the mixing-length parameter was adjusted such as to reproduce the same depth of the convective zone as was obtained from the evolutionary computation.
The nonlocal treatment of convection introduces two more parameters. ec and b. which characterize respectively the spatial coherence of the ensemble of eddies contributing to the total heat and momentum Ετος and the extent over which the turbulent eddies experience. an average of the local stratification.
The nonlocal treatment of convection introduces two more parameters, $a$ and $b$, which characterize respectively the spatial coherence of the ensemble of eddies contributing to the total heat and momentum fluxes and the extent over which the turbulent eddies experience an average of the local stratification.
Theory suggests approximate values for these parameters. but it is arguably better to treat them as free.
Theory suggests approximate values for these parameters, but it is arguably better to treat them as free.
Roughly speaking. the parameters control the degree of ‘nonlocality’ of convection: low values imply highly. nonlocal solutions. and in the limit a.b» the svstem of equations reduces to the local formulation (except near the boundaries of the convection zone. where the local equations are singular).
Roughly speaking, the parameters control the degree of `nonlocality' of convection; low values imply highly nonlocal solutions, and in the limit $a,b\rightarrow\infty$ the system of equations reduces to the local formulation (except near the boundaries of the convection zone, where the local equations are singular).
The energy. dissipation rate 2, of radial p modes was calculated as a continuous function of oscillation frequency bv relaxing the inner cdvnanmical boundary. condition.
The energy dissipation rate $D_{\rm p}$ of radial p modes was calculated as a continuous function of oscillation frequency by relaxing the inner dynamical boundary condition.
The results shown in the upper panel of Fig.
The results shown in the upper panel of Fig.
6 were obtained [or two sets of the nonlocal convection parameters e ancl b.
6 were obtained for two sets of the nonlocal convection parameters $a$ and $b$.
Phe choice of these parameters is important at high [requencies where unstable frequency ranges are found.
The choice of these parameters is important at high frequencies where unstable frequency ranges are found.
At low frequency. covering radial orders up to η=5. all modes are found to be stable for both sets of the e and b parameters.
At low frequency, covering radial orders up to $n=5$, all modes are found to be stable for both sets of the $a$ and $b$ parameters.
The values of [D] are significantly higher than the values of D, shown in the upper panel of Fig.
The values of $\vert D_{\rm p}\vert$ are significantly higher than the values of $-D_{\rm p}$ shown in the upper panel of Fig.
3.
3.
This clearly indicates that by neglecting the perturbed convective Duxes we ignore the dominant contribution to the damping.
This clearly indicates that by neglecting the perturbed convective fluxes we ignore the dominant contribution to the damping.
The results shown in Fie.
The results shown in Fig.
6 are applicable also to nonracdial modes. because virtually all the contribution to LI, arises in the upper lavers where the value of(€ has little inlluence.
6 are applicable also to nonradial modes, because virtually all the contribution to $D_{\rm p}$ arises in the upper layers where the value of $\ell$ has little influence.
Llowever. damping effects in these lavers have consequences in the deep interior.
However, damping effects in these layers have consequences in the deep interior.
They change 7. and hence the amplitude behaviour in the e-mode propagation zone (see equation 3).
They change $\gamma$, and hence the amplitude behaviour in the g-mode propagation zone (see equation 3).
We have seen in Section 3.2 (Figs.
We have seen in Section 3.2 (Figs.
2 and 3) that ignoring driving effects in these lavers reduces the trapping.
2 and 3) that ignoring driving effects in these layers reduces the trapping.
Adding damping there would. reduced. it further.
Adding damping there would reduced it further.
Larger inertiae imply lower aniplituces for stochastically
Larger inertiae imply lower amplitudes for stochastically
star HR 6165 (7 Sco) was observed periodically for telluric corrections.
star HR 6165 $\tau$ Sco) was observed periodically for telluric corrections.
The telescope was gukled with the CSHELL internal CCD autoguicder during exposures of these telluric correction stars. while the telescope tracking rates were adjusted for minimum drift while observing the optically invisible p Oph YSOs.
The telescope was guided with the CSHELL internal CCD autoguider during exposures of these telluric correction stars, while the telescope tracking rates were adjusted for minimum drift while observing the optically invisible $\rho$ Oph YSOs.
Spectra of the internal CBHELL continuum lamp were taken for flat fields. and exposures of the internal CSHELL Ar and Wer lamps were used for wavelength calibrations.
Spectra of the internal CSHELL continuum lamp were taken for flat fields, and exposures of the internal CSHELL Ar and Kr lamps were used for wavelength calibrations.
All data were reduced with IRAE.
All data were reduced with IRAF.
First. object aud sky frames were clillerencecd and then divided by flat fields.
First, object and sky frames were differenced and then divided by flat fields.
Next. bad. pixels were fixed. via interpolation. aud spectra were extracted with the APALL task.
Next, bad pixels were fixed via interpolation, and spectra were extracted with the APALL task.
Extracted spectra were typically 2 pixels (1")) wide along the slit. (spatial) direction at their hal(-inteusity points.
Extracted spectra were typically 5 pixels ) wide along the slit (spatial) direction at their half-intensity points.
Spectra were waveleneth calibrated using low-order fits to lines in the are lamp exposures. and spectra at each slit. position of each object were co-adidec.
Spectra were wavelength calibrated using low-order fits to lines in the arc lamp exposures, and spectra at each slit position of each object were co-added.
Iustrumental aud atinospheric features. were removed by dividing waveleneth-calibratecl object spectra by spectra of early-type stars observed at similar airmass at each slit position.
Instrumental and atmospheric features were removed by dividing wavelength-calibrated object spectra by spectra of early-type stars observed at similar airmass at each slit position.
Final spectra were produced by combiningjs the spectra of both slit positions for each object.
Final spectra were produced by combining the spectra of both slit positions for each object.
The object sample was selected from the Class I aud Mat-spectrum YSOs observed at. low spectral resolution (2~ 500) in Paper I which were not subsequently observed at high. spectral resolution in Paper II.
The object sample was selected from the Class I and flat-spectrum YSOs observed at low spectral resolution $R \simeq 500$ ) in Paper I which were not subsequently observed at high spectral resolution in Paper II.
None of the newly observed sources (listed iu Table 1) showed any absorption features in their low resolution Ax-band spectra (Paper E). aud they are also relatively bright. Y mae ZON S10 mag.
None of the newly observed sources (listed in Table 1) showed any absorption features in their low resolution $K$ -band spectra (Paper I), and they are also relatively bright, 7 mag $\lesssim K \lesssim$ 10 mag.
Table 1 shows that the brighter point sources (i.e. Elias 29. IRS 51) were observed with higher signal-to-noise ratios than the fainter ones (Le. IRS 13. WL 6).
Table 1 shows that the brighter point sources (i.e. Elias 29, IRS 54) were observed with higher signal-to-noise ratios than the fainter ones (i.e. IRS 43, WL 6).
This is useful lor analvziuges the veiling in these objects if the brightness differeuces among the sources are mostly due to different. amount of IR excess emission from circumstellar regions.
This is useful for analyzing the veiling in these objects if the brightness differences among the sources are mostly due to different amount of IR excess emission from circumstellar regions.
If this is true. then the brighter objects have greater near-IR veiling aud greater sigual-to-uolse is required to detect their photospheric absorption lines.
If this is true, then the brighter objects have greater near-IR veiling and greater signal-to-noise is required to detect their photospheric absorption lines.
Ou the other haud. it may be possible that some of the bright protostars are featureless because they are of relatively early spectral type (C or earlier) ancl possess intrinsically weak {να absorption lines (besides H aud. He).
On the other hand, it may be possible that some of the bright protostars are featureless because they are of relatively early spectral type (G or earlier) and possess intrinsically weak $K$ -band absorption lines (besides H and He).
The uew flat-spectrum aud Class | YSO spectra are shown in Figures 1 aud 2. respectively.
The new flat-spectrum and Class I YSO spectra are shown in Figures 1 and 2, respectively.
None of the five Class I spectra show any. evideuce of CO absorptiou.
None of the five Class I spectra show any evidence of CO absorption.
Two of the flat-spectruui YSOs also show uo evideuce of auy CO absorption (CSS 26 aud YLW 1985). while the other two show evidence of weak. broad. baud. heads aid. perhaps some overlapping rotatiou-vibratiou lines as well (Figure 1).
Two of the flat-spectrum YSOs also show no evidence of any CO absorption (GSS 26 and YLW 13B), while the other two show evidence of weak, broad band heads and perhaps some overlapping rotation-vibration lines as well (Figure 1).
analvsis.
analysis.
Since Q>1. we are (hus assuming (hat (he star formation process in the central region of (he cluster is not LOO percent efficient.
Since $Q > 1$, we are thus assuming that the star formation process in the central region of the cluster is not 100 percent efficient.
The radius of the void surrounding the central star 15 obtained by setting Qui, equal to M(&.). thereby vielding when e=3.
The radius of the void surrounding the central star is obtained by setting $Q m_{max}$ equal to $M(\xi_c)$, thereby yielding when $c = 3$.
As wilh ορ. this quantity is best obtained numerically when e=4.
As with $q_{max}$, this quantity is best obtained numerically when $c = 4$ .
We assume a gas density p,(£)=(1—g)p(£) bevond a radius £..
We assume a gas density $\rho_g (\xi) = (1-\eta)\rho(\xi)$ beyond a radius $\xi_c$.
The optical depth outside the void is therefore given bythe expression where we adopt a value of opp:=8x107 em? [or the dust cross-section per ILvdrogen nucleus (Stórrzer Hollenbach 1999).
The optical depth outside the void is therefore given bythe expression where we adopt a value of $\sigma_{FUV} = 8\times 10^{-22}$ $^2$ for the dust cross-section per Hydrogen nucleus (Störrzer Hollenbach 1999).
We note that the integral in equation (13) can be solved analytically lor both e=3 ande4.
We note that the integral in equation (18) can be solved analytically for both $c = 3$ and $c = 4$.
For convenience. we introduce a dimensionless time 7=//75. where τῃ=r.//2V,.
For convenience, we introduce a dimensionless time $\tau \equiv t /\tau_{0}$, where $\tau_0 \equiv r_s/\sqrt{2\Psi_0}$.
The (climensionless) orbital period can be obtained through the expression and is shown in Figure 6 as a function of dimensionless enerev € for our three chosen values of No and (he (wo density profiles (we note that 7,5 1s nol sensitive to q).
The (dimensionless) orbital period can be obtained through the expression and is shown in Figure 6 as a function of dimensionless energy $\epsilon$ for our three chosen values of $N$ and the two density profiles (we note that $\tau_{orbit}$ is not sensitive to $q$ ).
The corresponding values of the orbital period are sialler [or (he ¢=4 case. as expected. given (he proportionality 7;xPy.
The corresponding values of the orbital period are smaller for the $c = 4$ case, as expected, given the proportionality $\tau_0 \propto \rho_0^{-1/2}$.
These results indicate that stars will complete at least one orbit before the gas and dust are removed by the action of stellar winds (which. as noted in 82. occurs on a timescale of 3—5 Myr).
These results indicate that stars will complete at least one orbit before the gas and dust are removed by the action of stellar winds (which, as noted in 2, occurs on a timescale of $3 - 5$ Myr).
In the absence of dust attenuation. the orbit-averaged EUV [lis is given by (he expression where the orbital radius € of the star as a function of time is obtained by numerical integration of the governing lorce equations.
In the absence of dust attenuation, the orbit-averaged FUV flux is given by the expression where the orbital radius $\xi$ of the star as a function of time is obtained by numerical integration of the governing force equations.
The effects of dust attenuation are easily included by multiplving the integrand in equation (20)) by a factor of exp[7754:4:]. where Trey is the optical depth to FUV radiation for a given point along the orbit.
The effects of dust attenuation are easily included by multiplying the integrand in equation \ref{meanflux}) ) by a factor of$\exp[-\tau_{FUV}]$ , where $\tau_{FUV}$ is the optical depth to FUV radiation for a given point along the orbit.
depth in Ks-band the lower atmosphere needs to be made hotter.
depth in Ks-band the lower atmosphere needs to be made hotter.
However, this also increases the eclipse depth in L-band, another spectral region of low absorption (red cureve in Fig. 9)).
However, this also increases the eclipse depth in L-band, another spectral region of low absorption (red cureve in Fig. \ref{fig:models}) ).
L-band emission can be suppressed somewhat by including large amounts of CO2 and CHA (calculated here from HITEMP and HITRAN 2008 (?) data respectively), but this also reduces the signal in Ks-band (blue curve in Fig. 9)).
L-band emission can be suppressed somewhat by including large amounts of CO2 and CH4 (calculated here from HITEMP and HITRAN 2008 \citep{rothmanetal09} data respectively), but this also reduces the signal in Ks-band (blue curve in Fig. \ref{fig:models}) ).
Reducing the water or CO abundances also do not produce a better fit.
Reducing the water or CO abundances also do not produce a better fit.
Hence, we cannot fit all data points well using any clear atmosphere with gases that are predicted to be abundant on hot exoplanets.
Hence, we cannot fit all data points well using any clear atmosphere with gases that are predicted to be abundant on hot exoplanets.
One remedy to fit both the Spitzer data and our Ks-band eclipse depth is to include a Venus-like cloud.
One remedy to fit both the Spitzer data and our Ks-band eclipse depth is to include a Venus-like cloud.
The clouds on Venus are made of concentrated sulphuric acid droplets, which have the property that they are strongly scattering below wavelengths of ~3um and strongly absorbing above 3 um, with only little variation of extinction with wavelength (e.g.?)..
The clouds on Venus are made of concentrated sulphuric acid droplets, which have the property that they are strongly scattering below wavelengths of $\sim$ $\mu$ m and strongly absorbing above 3 $\mu$ m, with only little variation of extinction with wavelength \citep[e.g.][]{grinspoonetal93}.
Because of the scattering nature of the clouds, radiation from Venus' hot lower atmosphere still reaches space at the night side below 3um, despite an optically thick cloud layer surrounding the planet.
Because of the scattering nature of the clouds, radiation from Venus' hot lower atmosphere still reaches space at the night side below $\mu$ m, despite an optically thick cloud layer surrounding the planet.
Above 3 um the night side emission originates from the clouds.
Above 3 $\mu$ m the night side emission originates from the clouds.
To show this potential effect for HAT-P-Ib, we inserted a cloud layer with an optical depth of 1.5 at the tropopause with properties identical to those of Venus' 1-um sized cloud-particles.
To show this potential effect for HAT-P-1b, we inserted a cloud layer with an optical depth of 1.5 at the tropopause with properties identical to those of Venus' $\mu$ m sized cloud-particles.
Indeed, brightness temperatures at Ks-band are higher than anywhere else in Fig.
Indeed, brightness temperatures at Ks-band are higher than anywhere else in Fig.
and all data points could potentially be fitted well if the lower atmosphere is made even hotter.
\ref{fig:models} and all data points could potentially be fitted well if the lower atmosphere is made even hotter.
However, we could not find a physically plausible candidate for cloud materials that could mimic Venus' clouds on a hot exoplanet.
However, we could not find a physically plausible candidate for cloud materials that could mimic Venus' clouds on a hot exoplanet.
So, at present we do not find any suitable atmosphere that could explain the high Ks-band eclipse depth.
So, at present we do not find any suitable atmosphere that could explain the high Ks-band eclipse depth.
Using the LIRIS infrared camera on the WHT, we determine the eclipse depth of the extrasolar planet HAT-P-1b in K,-band to be
Using the LIRIS infrared camera on the WHT, we determine the eclipse depth of the extrasolar planet HAT-P-1b in $_s$ -band to be
the distance traveled toward the surface in V scatterings. which is proportional to N77.mot we [ind that photons escape after τα.D scatterings ancl therefore the total path length traversed bv a photon is. about πο1/3d (where d is. the depth of the line. producing. region).
the distance traveled toward the surface in $N$ scatterings, which is proportional to $N^{3/2}$, we find that photons escape after $\tau_\alpha^{2/3}$ scatterings and therefore the total path length traversed by a photon is about $\tau_\alpha^{1/3}d$ (where $d$ is the depth of the line producing region).
.x When the absorption mean Iree path of the photon is comparable to the photoionization depth [or Si atoms. the line-photon flux will be suppressed bv a [actor of about 71.
When the absorption mean free path of the photon is comparable to the photoionization depth for Si atoms, the line-photon flux will be suppressed by a factor of about $\tau_\alpha^{1/3}$ .
For an ionization parameter of 400 and 77=0.1. or for £=100 and 77=l1. the two mean yee paths are equal ancl the line {lis is small.
For an ionization parameter of $400$ and $T_7=0.1$, or for $\xi=100$ and $T_7=1$, the two mean free paths are equal and the line flux is small.
However. as we increase € (he neutral atonic Taction decreases and the path length over which a line photon is absorbed by neutral atoms ol lower atomic number goes up.
However, as we increase $\xi$ the neutral atomic fraction decreases and the path length over which a line photon is absorbed by neutral atoms of lower atomic number goes up.
An increase in the ionization parameter by a [actor of four increases (he photo-absorption leneth by a factor of four. aud the emergent line emission is 10 longer suppressed by Lue trapping.
An increase in the ionization parameter by a factor of four increases the photo-absorption length by a factor of four, and the emergent line emission is no longer suppressed by line trapping.
The enhanced photo-absorption of line photons due to resonant line trapping is included in the numerical results shown in Fig.
The enhanced photo-absorption of line photons due to resonant line trapping is included in the numerical results shown in Fig.
1.
1.
Our basic result is (hat the maximum {his in the Si XIV Ix, line is a few percent of the irraciating x-ray continuum flux. and (hat (le maximum flux is attained when £~10* for solar composition and [or T=ΙΟ (lor T=4x10* Ik. ἕ~100 as reported in Lazzatli et aL.
Our basic result is that the maximum flux in the Si XIV $_\alpha$ line is a few percent of the irradiating x-ray continuum flux, and that the maximum flux is attained when $\xi\sim 10^3$ for solar composition and for $T=10^6$ K (for $T=4\times10^7$ K, $\xi\sim100$ as reported in Lazzati et al.,
2002).
2002).
The optimum € increases further if the Si abundance is above solar.
The optimum $\xi$ increases further if the Si abundance is above solar.
Let us assume that the most abundant ionic species in the plasma has an atomic number z.
Let us assume that the most abundant ionic species in the plasma has an atomic number $z$.
Hs number density. compared (o electrons is sumaller by a factor of z. and the bremsstrahlunege enereve. loss rate per electron in the egas is exgiven bv If we approximate the geometry of the region as locally plane-parallel. (hen the x-ray continuum [πας due (to bremsstrahlung is given by Comparing (his with the estimate for (he Si line [Iux given in equation (2). we find (for LI21]7έν 1) Observations of GRB 011211 indicate that the continuum fIux is no more than ten times the Si line f[Iux.
Its number density compared to electrons is smaller by a factor of $z$, and the bremsstrahlung energy loss rate per electron in the gas is given by If we approximate the geometry of the region as locally plane-parallel, then the x-ray continuum flux due to bremsstrahlung is given by Comparing this with the estimate for the Si line flux given in equation (2), we find (for $z=z_{14}=\tau=\epsilon_3=1$ ) Observations of GRB 011211 indicate that the continuum flux is no more than ten times the Si line flux.