ReadingTimeMachine/rtm-sgt-ocr-v1 · Datasets at Hugging Face

source stringlengths 1 2.05k ⌀	target stringlengths 1 11.7k
However. some electroi« wil je accelerated at the fo"wald shock whicl seyarates the siurroundiug medium from shocked Inhalter already. raked up by the ejecta.	However, some electrons will be accelerated at the forward shock which separates the surrounding medium from shocked matter already raked up by the ejecta.
Since the rate at which matter is raked up is roughly COLSalt. we cau take as a ivst’ approximatio1 that the total emitted power is a coustaut. [or whic Lan upper limit cau be fou as follows.	Since the rate at which matter is raked up is roughly constant, we can take as a first approximation that the total emitted power is a constant, for which an upper limit can be found as follows.
The shock slows down when the total swept up mass (inles >) equals the ejecta mass.	The shock slows down when the total swept up mass (times $\gamma$ ) equals the ejecta mass.
Witin this time interval. then. about hall of the total energy is transfered to the swept Up Lass: if this were hielily radiative. then the total emitted power would be of order Ezc£um which is much simaer (by the factor /5/£/4. where €cAv0.1 is the ratio of relative to bulk kineic energy of the winel) iur the burst luminosity.	Within this time interval, then, about half of the total energy is transfered to the swept up mass; if this were highly radiative, then the total emitted power would be of order $\dot{E} \approx \frac{E}{t_d}$ which is much smaller (by the factor $t_{b}/\xi t_d$, where $\xi \approx 0.1$ is the ratio of relative to bulk kinetic energy of the wind) than the burst luminosity.
However. this is au ipper lunit. because. thowel electrons are hieuly "adiative. this estimate imiplies that they are able to racliate away also al ol the thermal energy o ‘the protons.	However, this is an upper limit, because, though electrons are highly radiative, this estimate implies that they are able to radiate away also all of the thermal energy of the protons.
Since it is generally assuiued. (adit can be checked in the observatious of the afterglow of GRB 970508. Frail. Waxman aud Ixkarni 2000) that ouly a ractlon e«42:0.1 of the protons’ energy can be transfered from the protons to tle electrons. tlis assituption is excessive by the same factor. e;4.	Since it is generally assumed (and it can be checked in the observations of the afterglow of GRB 970508, Frail, Waxman and Kulkarni 2000) that only a fraction $\epsilon_{eq} \approx 0.1$ of the protons' energy can be transferred from the protons to the electrons, this assumption is excessive by the same factor, $\epsilon_{eq}$.
The exact luminosity racjated duri18oO this coasting pliase 1s «ilficult to predict exactly. since it depends criically upon rateruncertaiu lasina factors. like the elficiency e; with which energy is trauferred [rou protous to electrons. the iciency ej; with whie La near-equipartition magnetic field is built up. aud the relaive efficiency : quasi-therimal to Feruin processes.	The exact luminosity radiated during this coasting phase is difficult to predict exactly, since it depends critically upon ratheruncertain plasma factors, like the efficiency $\epsilon_{eq}$ with which energy is tranferred from protons to electrons, the efficiency $\epsilon_B$ with which a near–equipartition magnetic field is built up, and the relative efficiency of quasi–thermal to Fermi processes.
However. for the preseut aim. this exact value is unnecessary: {lice it to say that a 'easouable expectation is that What happeus alter shock deceleration has been described. for different values of the parameters. by Mésszárros. Laguna and Rees (1993).	However, for the present aim, this exact value is unnecessary: suffice it to say that a reasonable expectation is that What happens after shock deceleration has been described, for different values of the parameters, by Mésszárros, Laguna and Rees (1993).
Basically. a reverse shock wil propagate at moclerate Lorenz factors backwa«d into the ejecta. dissipating au appreciable fract101 of the kinetic energy of the shell within a tinescale Rug/>>7c. which. is. the appareut time. in" wlicl the shock crosses the ejecta shell. zz /y.	Basically, a reverse shock will propagate at moderate Lorenz factors backward into the ejecta, dissipating an appreciable fraction of the kinetic energy of the shell within a timescale $R_{ag}/\gamma^2 c$, which is the apparent time in which the shock crosses the ejecta shell, $\approx t_d$ .
Thus the maximum expeced power is exactly a [racion /5/£fq below hat of the burst.	Thus the maximum expected power is exactly a fraction $t_{b}/\xi t_d$ below that of the burst.
Notice that. in the previous sectiou. this was ouly au upper \|init.	Notice that, in the previous section, this was only an upper limit.
This internal shock provides a new. secouc phase of emission. of total duration comparable [9] he light crossing time oftle ejecta shell. fy.	This internal shock provides a new, second phase of emission, of total duration comparable to the light crossing time of the ejecta shell, $t_d$.
Alter this peak Iuulnosity we then expec the usual afterglow (x/' \|J o begin.	After this peak luminosity we then expect the usual afterglow $\propto t^{-\alpha}$ ) to begin.
A qualitative description of this cat be seen in Fie.	A qualitative description of this can be seen in Fig.
l.	1.
Diring the afterglow. emission is due to svuclrotron processes (Messzàrros :uc Rees 1997). as evideuced by the simulataneous spectrum of CRB t)r0508 that fits theoretical ex»ectations so nicely (Calama aL... 1998) aud by detectionof polarizatlou	During the afterglow, emission is due to synchrotron processes (Mèsszàrros and Rees 1997), as evidenced by the simulataneous spectrum of GRB 970508 that fits theoretical expectations so nicely (Galama , 1998) and by detectionof polarization
a rnudoni Poissoien field are less than 3% of the total uber.	a random Poissonian field are less than $3\%$ of the total number.
These spurIOUS SOTIEECS. causedk by local fluctuations of he background. can be eliminaed by means of a uinimuüal spanning tree (AIST) aleorithin (Ixxuskal 1956.. Pu1n LO57)). acceXtiug only those sources coutainines nore ha ja set mui.1i nunmber of photons.	These spurious sources, caused by local fluctuations of the background, can be eliminated by means of a minimal spanning tree (MST) algorithm (Kruskal \cite{kruska}, , Prim \cite{prim57}) ), accepting only those sources containing more than a set minimum number of photons.
Since we wait to fin close associaions of phoons. only those trees ο\| the MST are considered for which all edec-lenetls are si1aller haji à dnaximally allowed iuer-photon separation daa.	Since we want to find close associations of photons, only those trees of the MST are considered for which all edge-lengths are smaller than a maximally allowed inter-photon separation $d_{max}$ .
The value of d,,,, is determiied by the mean iuter-poiut separation expected im au isotropic aud homogeneous Olit distribution.	The value of $d_{max}$ is determined by the mean inter-point separation expected in an isotropic and homogeneous point distribution.
This separation is given by duy VALN, where Nis the tota -iiber of poiats ancl o ds he area of the region where th IN points are found (see WSV 1997)).	This separation is given by $d_{max}\approx\sqrt{A/N}$ , where $N$ is the total number of points and $A$ is the area of the region where the $N$ points are found (see WSV \cite{wiedenmann}) ).
An cxrample of the scaling-iidex spectrum is shown in Fie. 1..	An example of the scaling-index spectrum is shown in Fig. \ref{fig:simspec}.
The upper panes hishow a raudomlv-seucrated.Q smooth PSPC photon ma» (left) aud t1ο scaling iudex a-spectrum (ight).	The upper panels show a randomly-generated, smooth PSPC photon map (left) and the scaling index $\alpha$ -spectrum (right).
In au infinite. uuiform nuage. the sSpectruni NOILd be a delta "unction loc"uaed at a=2.	In an infinite, uniform image, the spectrum would be a delta function located at $\alpha =2$.
Because the feld is finite axd rot infinitely homogeneous. the spectrum is broadened. iid sleltly offset.	Because the field is finite and not infinitely homogeneous, the spectrum is broadened and slightly offset.
The lower panels show aji actual PSPC inage and is a-spectrun.	The lower panels show an actual PSPC image and its $\alpha$ -spectrum.
The spikes at k5v o are the xiehtest sources. aud the peak is broadened fiuther due to t1ο presence oD SOMICON.	The spikes at low $\alpha$ are the brightest sources, and the peak is broadened further due to the presence of sources.
Analyses ο: yxaudonmlv-seunerated μου] PSPC fields with backerotud levels siwil to those in our source fields revealed hat the SIM detected spurious sources with sonrce cotuts up to ~5 photous.	Analyses of randomly-generated smooth PSPC fields with background levels similar to those in our source fields revealed that the SIM detected spurious sources with source counts up to $\sim 5$ photons.
Iu oxer to ensure that no spuriots sources were included iu the source lists; we set the lower nuit ou source counts to teu protons.	In order to ensure that no spurious sources were included in the source lists, we set the lower limit on source counts to ten photons.
This lat ΠΠIv excluded real sources. but as of vet there is no estimae of source siguificance availadle for the SIM.	This limit undoubtedly excluded real sources, but as of yet there is no estimate of source significance available for the SIM.
We apied. the SIM. aleorithin he fields in this sunple. trereby creating source lists aud labelne each photon as a source or backeround phot3.	We applied the SIM algorithm to the fields in this sample, thereby creating source lists and labeling each photon as a source or background photon.
Upon removal of the soPCOS, it was obvious that fre SIM. had not correctly ideutified all photons. as bright sources reiuiinued in the imaees,	Upon removal of the sources, it was obvious that the SIM had not correctly identified all photons, as bright sources remained in the images.
Further investigatioi revealed that the SIM algoritlan rad dificulv ideutifving alp rotons associated with a sotree if the photon deusitv wew very high.	Further investigation revealed that the SIM algorithm had difficulty identifying all photons associated with a source if the photon density was very high.
We corrected. lis by identifving all piotons within the SIM-defined ηςmee boundaries as source protons.	We corrected this by identifying all photons within the SIM-defined source boundaries as source photons.
We then applied a ckeround correction based «n the umber of backeround photons «one would expect o find muder the source.	We then applied a background correction based on the number of background photons one would expect to find under the source.
Wule this method is less thau xcal. the resulting background photon maps appear to have! had. all detected ποος COupletely removed.	While this method is less than ideal, the resulting background photon maps appear to have had all detected sources completely removed.
Tn order to check the effectiveness of the scaliugdudex method. we also determined the diffuse x-ray background flux of cach field using the maxiuuu-likelihood. source-detection alexwithin included in the data r‘eduction software package {Zunuuernunun et al. 1992)).	In order to check the effectiveness of the scaling-index method, we also determined the diffuse x-ray background flux of each field using the maximum-likelihood source-detection algorithm included in the data reduction software package (Zimmermann et al. \cite{zman}) ).
Our lower likelihood πε was set oat 15. corresponding to a significauce level of ~Sa.	Our lower likelihood limit was set at 15, corresponding to a significance level of $\sim 5\sigma$.
We set the extrac‘tion radius at 2.5 times the FWIM of cach ποο	We set the extraction radius at 2.5 times the FWHM of each source.
The backeround-correctedC» plotou counts were then subtraced from the total photon count to eive the raw backeround ploton count.	The background-corrected photon counts were then subtracted from the total photon count to give the raw background photon count.
Vieuetting corrections were not appied. since we assume that vienettiug effects will be similar in cach image and since vignetti18o corrections were not availableal for the SIAL aleorithin.	Vignetting corrections were not applied, since we assume that vignetting effects will be similar in each image and since vignetting corrections were not available for the SIM algorithm.
We find that the SIAL aanalysis results in backegrouxd levels that are higher than the ΠΕΗΝxl technique backerounds by a Laverage of 158x95 counΤε	We find that the SIM analysis results in background levels that are higher than the maximum-likelihood technique backgrounds by an average of $158\pm 95$ counts.
The reasol. OY this ¢]screpancv Is not fully clear aud os1o0uld he πο¢xd. before tlre» STA js widely inplemenuted.	The reason for this discrepancy is not fully clear and should be understood before the SIM is widely implemented.
Ilowever. par of the discrepaicv can be explained by noting that oir SIM source flux cut-off of LO counts. while safelv ignoring spurious sources. almost certainly considere nunerous true low-flux sources as spurious. restting in these source photcuns beimg treated as bacseuu counts.	However, part of the discrepancy can be explained by noting that our SIM source flux cut-off of 10 counts, while safely ignoring spurious sources, almost certainly considered numerous true low-flux sources as spurious, resulting in these source photons being treated as background counts.
Tn this paper. we pertorÜ our analysis 1sine the background count evels as calculated bv. the SIN.	In this paper, we perform our analysis using the background count levels as calculated by the SIM.
A reanalysis of the data using the numbers from the ΠΠ technique resulted in the same qualitative conclusions. although the resulting quantities dovary.	A reanalysis of the data using the numbers from the maximum-likelihood technique resulted in the same qualitative conclusions, although the resulting quantities dovary.
The SIM analysis has the benefit of iceutifviug cach backerouud photon. whicrinade spectral aalysis of the backeround photons straightforward.	The SIM analysis has the benefit of identifying each background photon, whichmade spectral analysis of the background photons straightforward.
he parameters in Table. 1).	the parameters in Table. \ref{tab:par}) ).
In the model used by vanZee Haynes (2006) (henceforth VHO6). this yield is consistent Gwithin he errorbars) with the theoretically expected closed-box yield of 9=0.0074 (Meynet Maeder. 2002).	In the model used by vanZee Haynes (2006) (henceforth VH06), this yield is consistent (within the errorbars) with the theoretically expected closed-box yield of p=0.0074 (Meynet Maeder, 2002).
On the other hand. using only he HI mass within the optical disk. the derived por7.510+ is much lower than that expected from closed-box chemical evolution.	On the other hand, using only the HI mass within the optical disk, the derived $\rm{_{eff}}\sim 7.5 \times 10^{-4}$ is much lower than that expected from closed-box chemical evolution.
If interpreted literally. the above exercise would suggest that NGC 3741 is evolving as a closed-box model. provided that the gas-phase metallicity in the inner disk is the same as the outer disk. i.e. that there is an efficient mixing of the metals throughout the HI disk.	If interpreted literally, the above exercise would suggest that NGC 3741 is evolving as a closed-box model, provided that the gas-phase metallicity in the inner disk is the same as the outer disk, i.e. that there is an efficient mixing of the metals throughout the HI disk.
However this seems unlikely. given the large size of the HI disk.	However this seems unlikely, given the large size of the HI disk.
Tassis et al. (	Tassis et al. (
2006) showed that the mixing length of metals in a galaxy increases with a decrease in the galaxy mass.	2006) showed that the mixing length of metals in a galaxy increases with a decrease in the galaxy mass.
However. whether there is mixing of metals even up to I+ times its optical extent is unclear.	However, whether there is mixing of metals even up to 14 times its optical extent is unclear.
On the other hand. what evidence do we have for closed-box chemical evolution in dwarf galaxies?	On the other hand, what evidence do we have for closed-box chemical evolution in dwarf galaxies?
And can one from the observational data try to make inferences about how much of the HI disk participates in the chemical evolution (i.e. is well mixed)?	And can one from the observational data try to make inferences about how much of the HI disk participates in the chemical evolution (i.e. is well mixed)?
The gravitational binding energy of faint dwarf irregular galaxies is not much larger than the energy output from a few supernovae. hence a priori. one might expect that low mass galaxies would depart from the closed-box chemical evolution. since enriched material could escape via stellar winds and supernova ejecta (Brooks et al.	The gravitational binding energy of faint dwarf irregular galaxies is not much larger than the energy output from a few supernovae, hence a priori, one might expect that low mass galaxies would depart from the closed-box chemical evolution, since enriched material could escape via stellar winds and supernova ejecta (Brooks et al.
2007).	2007).
We searched the literature for the HI interferometric images for the galaxies in VH06 sample and show in Fig. 9[[	We searched the literature for the HI interferometric images for the galaxies in VH06 sample and show in Fig. \ref{fig:overlay_yield}[ [
A] the effective yield plotted as a function of the HI extent of a sample of galaxies in VHO6 sample with available HI images (the sources of the HI images is given in the figure caption).	A] the effective yield plotted as a function of the HI extent of a sample of galaxies in VH06 sample with available HI images (the sources of the HI images is given in the figure caption).
The effective yield is computed by considering the entire gas mass.	The effective yield is computed by considering the entire gas mass.
NGC 3741 and DDOIS4 are shown in the plot with extreme values of the HI extent.	NGC 3741 and DDO154 are shown in the plot with extreme values of the HI extent.
As can be seen. there are some galaxies in the sample which are consistent with the closed-box model.	As can be seen, there are some galaxies in the sample which are consistent with the closed-box model.
However there is no clear trend seen between the effective yield and the extent of the HI disk.	However there is no clear trend seen between the effective yield and the extent of the HI disk.
Figure 9[[B] shows the effective yield for the same sample of galaxies as shown in Fig. 9[[	Figure \ref{fig:overlay_yield}[ [B] shows the effective yield for the same sample of galaxies as shown in Fig. \ref{fig:overlay_yield}[ [
A]. however this time the effective yield is computed by considering the gas fraction within the Holmberg radius.	A], however this time the effective yield is computed by considering the gas fraction within the Holmberg radius.
As can be seen. if the effective vield is computed within the Holmberg radius. (as would be appropriate in the case of inefficient mixing) none of these galaxies follow a closed-box model.	As can be seen, if the effective yield is computed within the Holmberg radius, (as would be appropriate in the case of inefficient mixing) none of these galaxies follow a closed-box model.
The theoretically expected closed-box chemical yield depends on assumptions about the IMF. stellar rotation as well as in details of stellar evolution models (Meynet Maeder. 2002).	The theoretically expected closed-box chemical yield depends on assumptions about the IMF, stellar rotation as well as in details of stellar evolution models (Meynet Maeder, 2002).
It may be more instructive hence to look for trends in the effective yield as a function of other galaxy properties. instead of comparing the observed yield against a model dependent expected yield.	It may be more instructive hence to look for trends in the effective yield as a function of other galaxy properties, instead of comparing the observed yield against a model dependent expected yield.
One possible parameter to use for such a correlation is the tota dynamical mass.	One possible parameter to use for such a correlation is the total dynamical mass.
VHO6 did not tind any significant trend between the dynamical mass and effective yield for the galaxies in their sample. however they computed the dynamical mass using the HI global velocity widths.	VH06 did not find any significant trend between the dynamical mass and effective yield for the galaxies in their sample, however they computed the dynamical mass using the HI global velocity widths.
We recomputed the dynamical masses for the galaxies in VHO6 sample for which rotation curves are available in literature.	We recomputed the dynamical masses for the galaxies in VH06 sample for which rotation curves are available in literature.
We show in Fig.	We show in Fig.
160. a plot of the effective yield against the total dynamical mass.	\ref{fig:yield_mass} a plot of the effective yield against the total dynamical mass.
The effective yield computec using the entire HI mass is shown as eross. while the effective yield computed using the HI mass within the Holmberg radius is shown as solid points.	The effective yield computed using the entire HI mass is shown as cross, while the effective yield computed using the HI mass within the Holmberg radius is shown as solid points.
As can be seen. in both cases the effective yield increases with increasing dynamical mass.	As can be seen, in both cases the effective yield increases with increasing dynamical mass.
The correlation is tighter if one uses the only HI mass within the Holmberg radius (correlation coefficient is 0.59) compared to using the entire HI mass (correlation coefficient is 0.47). suggesting that. if this model were to be correct. only the gas within the optical disk participates in the chemical evolution of the galaxy.	The correlation is tighter if one uses the only HI mass within the Holmberg radius (correlation coefficient is 0.59) compared to using the entire HI mass (correlation coefficient is 0.47), suggesting that, if this model were to be correct, only the gas within the optical disk participates in the chemical evolution of the galaxy.
However we note that the total number of galaxies in our analysis is too small to make any statistical conclusion.	However we note that the total number of galaxies in our analysis is too small to make any statistical conclusion.
Spectroscopic observations of a large sample of dwarf galaxies along with a knowledge of the gas distribution is hence required for a better understanding of chemical enrichment and mixing of enriched material in gas-rich. low mass galaxies.	Spectroscopic observations of a large sample of dwarf galaxies along with a knowledge of the gas distribution is hence required for a better understanding of chemical enrichment and mixing of enriched material in gas-rich, low mass galaxies.
In summary. we examine the dark and luminous matter in NGC 3741.	In summary, we examine the dark and luminous matter in NGC 3741.
Although this galaxy has one of the highest known ratios of dark to luminous (i.e. stellar) matter. its baryons to dark	Although this galaxy has one of the highest known ratios of dark to luminous (i.e. stellar) matter, its baryons to dark
that the entire triplet is too faint for studies of changes, the line complex around iis strong enough that residual He8 would be detectable.	that the entire triplet is too faint for studies of changes, the line complex around is strong enough that residual $\beta$ would be detectable.
Also, the higher Ly series lines of are not seen in the difference spectrum.	Also, the higher Ly series lines of are not seen in the difference spectrum.
We interpret the absence also of high Ly series lines in the difference spectrum as evidence for an increase in the optical depth of the scattering plasma, which could be part of the reformation process of the accretion disk.	We interpret the absence also of high Ly series lines in the difference spectrum as evidence for an increase in the optical depth of the scattering plasma, which could be part of the reformation process of the accretion disk.
A bit puzzling appears the presence of Lya in the difference spectrum while Ly is not present.	A bit puzzling appears the presence of $\alpha$ in the difference spectrum while $\beta$ is not present.
Except for the Lya line, the reduction in brightness during eclipse can therefore exclusively be attributed to the continuum.	Except for the $\alpha$ line, the reduction in brightness during eclipse can therefore exclusively be attributed to the continuum.
The shape of the continuum in the difference spectrum in Fig.	The shape of the continuum in the difference spectrum in Fig.
14 is the shape of the continuum component in the inner regions.	\ref{diffspec} is the shape of the continuum component in the inner regions.
It has roughly the same shape as the out-of-eclipse spectrum, supporting the interpretation of achromatic Thompson scattering.	It has roughly the same shape as the out-of-eclipse spectrum, supporting the interpretation of achromatic Thompson scattering.
Close inspection of the RGS and EPIC brightness maps in the bottom panels of Figs.	Close inspection of the RGS and EPIC brightness maps in the bottom panels of Figs.
12 and 13 reveals that the eclipse progresses in a slightly non-uniform way in wavelength/energy.	\ref{smap} and \ref{smap_epic} reveals that the eclipse progresses in a slightly non-uniform way in wavelength/energy.
In the Rayleigh-Jeans tail, betweenAA,, the continuum seems to go through a wider eclipse towards longer wavelength (Fig. 12)).	In the Rayleigh-Jeans tail, between, the continuum seems to go through a wider eclipse towards longer wavelength (Fig. \ref{smap}) ).
In the Wien tail, the eclipse seems to be narrower towards higher energieswhich is indicated by the contours in Fig. 13..	In the Wien tail, the eclipse seems to be narrower towards higher energieswhich is indicated by the contours in Fig. \ref{smap_epic}.
This could indicate a temperature gradient, however, the hardness light curve in the middle panel of Fig.	This could indicate a temperature gradient, however, the hardness light curve in the middle panel of Fig.
3 does not indicate a significant temperature change with the eclipse.	\ref{lc2} does not indicate a significant temperature change with the eclipse.
Only the softening after the eclipse appears noteworthy and may have to be attributed to the cooling while nuclear burning is turning off.	Only the softening after the eclipse appears noteworthy and may have to be attributed to the cooling while nuclear burning is turning off.
On the other hand, the hardness light curve contains the emission lines and is a less sensitive indicator for the photospheric temperature.	On the other hand, the hardness light curve contains the emission lines and is a less sensitive indicator for the photospheric temperature.
In the first of the two oobservations, starting day 22.9, the UV grism of the OM was employed, taking 27 consecutive spectra (see Table 1)).	In the first of the two observations, starting day 22.9, the UV grism of the OM was employed, taking 27 consecutive spectra (see Table \ref{obslog}) ).
In Fig. 15,,	In Fig. \ref{smap_om}, ,

However. some electroi« wil je accelerated at the fo"wald shock whicl seyarates the siurroundiug medium from shocked Inhalter already. raked up by the ejecta.

However, some electrons will be accelerated at the forward shock which separates the surrounding medium from shocked matter already raked up by the ejecta.

Since the rate at which matter is raked up is roughly COLSalt. we cau take as a ivst’ approximatio1 that the total emitted power is a coustaut. [or whic Lan upper limit cau be fou as follows.

Since the rate at which matter is raked up is roughly constant, we can take as a first approximation that the total emitted power is a constant, for which an upper limit can be found as follows.

The shock slows down when the total swept up mass (inles >) equals the ejecta mass.

The shock slows down when the total swept up mass (times $\gamma$ ) equals the ejecta mass.

Witin this time interval. then. about hall of the total energy is transfered to the swept Up Lass: if this were hielily radiative. then the total emitted power would be of order Ezc£um which is much simaer (by the factor /5/£/4. where €cAv0.1 is the ratio of relative to bulk kineic energy of the winel) iur the burst luminosity.

Within this time interval, then, about half of the total energy is transfered to the swept up mass; if this were highly radiative, then the total emitted power would be of order $\dot{E} \approx \frac{E}{t_d}$ which is much smaller (by the factor $t_{b}/\xi t_d$, where $\xi \approx 0.1$ is the ratio of relative to bulk kinetic energy of the wind) than the burst luminosity.

However. this is au ipper lunit. because. thowel electrons are hieuly "adiative. this estimate imiplies that they are able to racliate away also al ol the thermal energy o ‘the protons.

However, this is an upper limit, because, though electrons are highly radiative, this estimate implies that they are able to radiate away also all of the thermal energy of the protons.

Since it is generally assuiued. (adit can be checked in the observatious of the afterglow of GRB 970508. Frail. Waxman aud Ixkarni 2000) that ouly a ractlon e«42:0.1 of the protons’ energy can be transfered from the protons to tle electrons. tlis assituption is excessive by the same factor. e;4.

Since it is generally assumed (and it can be checked in the observations of the afterglow of GRB 970508, Frail, Waxman and Kulkarni 2000) that only a fraction $\epsilon_{eq} \approx 0.1$ of the protons' energy can be transferred from the protons to the electrons, this assumption is excessive by the same factor, $\epsilon_{eq}$.

The exact luminosity racjated duri18oO this coasting pliase 1s «ilficult to predict exactly. since it depends criically upon rateruncertaiu lasina factors. like the elficiency e; with which energy is trauferred [rou protous to electrons. the iciency ej; with whie La near-equipartition magnetic field is built up. aud the relaive efficiency : quasi-therimal to Feruin processes.

The exact luminosity radiated during this coasting phase is difficult to predict exactly, since it depends critically upon ratheruncertain plasma factors, like the efficiency $\epsilon_{eq}$ with which energy is tranferred from protons to electrons, the efficiency $\epsilon_B$ with which a near–equipartition magnetic field is built up, and the relative efficiency of quasi–thermal to Fermi processes.

However. for the preseut aim. this exact value is unnecessary: {lice it to say that a 'easouable expectation is that What happeus alter shock deceleration has been described. for different values of the parameters. by Mésszárros. Laguna and Rees (1993).

However, for the present aim, this exact value is unnecessary: suffice it to say that a reasonable expectation is that What happens after shock deceleration has been described, for different values of the parameters, by Mésszárros, Laguna and Rees (1993).

Basically. a reverse shock wil propagate at moclerate Lorenz factors backwa«d into the ejecta. dissipating au appreciable fract101 of the kinetic energy of the shell within a tinescale Rug/>>7c. which. is. the appareut time. in" wlicl the shock crosses the ejecta shell. zz /y.

Basically, a reverse shock will propagate at moderate Lorenz factors backward into the ejecta, dissipating an appreciable fraction of the kinetic energy of the shell within a timescale $R_{ag}/\gamma^2 c$, which is the apparent time in which the shock crosses the ejecta shell, $\approx t_d$ .

Thus the maximum expeced power is exactly a [racion /5/£fq below hat of the burst.

Thus the maximum expected power is exactly a fraction $t_{b}/\xi t_d$ below that of the burst.

Notice that. in the previous sectiou. this was ouly au upper |init.

Notice that, in the previous section, this was only an upper limit.

This internal shock provides a new. secouc phase of emission. of total duration comparable [9] he light crossing time oftle ejecta shell. fy.

This internal shock provides a new, second phase of emission, of total duration comparable to the light crossing time of the ejecta shell, $t_d$.

Alter this peak Iuulnosity we then expec the usual afterglow (x/' |J o begin.

After this peak luminosity we then expect the usual afterglow $\propto t^{-\alpha}$ ) to begin.

A qualitative description of this cat be seen in Fie.

A qualitative description of this can be seen in Fig.

l.

1.

Diring the afterglow. emission is due to svuclrotron processes (Messzàrros :uc Rees 1997). as evideuced by the simulataneous spectrum of CRB t)r0508 that fits theoretical ex»ectations so nicely (Calama aL... 1998) aud by detectionof polarizatlou

During the afterglow, emission is due to synchrotron processes (Mèsszàrros and Rees 1997), as evidenced by the simulataneous spectrum of GRB 970508 that fits theoretical expectations so nicely (Galama , 1998) and by detectionof polarization

a rnudoni Poissoien field are less than 3% of the total uber.

a random Poissonian field are less than $3\%$ of the total number.

These spurIOUS SOTIEECS. causedk by local fluctuations of he background. can be eliminaed by means of a uinimuüal spanning tree (AIST) aleorithin (Ixxuskal 1956.. Pu1n LO57)). acceXtiug only those sources coutainines nore ha ja set mui.1i nunmber of photons.

These spurious sources, caused by local fluctuations of the background, can be eliminated by means of a minimal spanning tree (MST) algorithm (Kruskal \cite{kruska}, , Prim \cite{prim57}) ), accepting only those sources containing more than a set minimum number of photons.

Since we wait to fin close associaions of phoons. only those trees ο| the MST are considered for which all edec-lenetls are si1aller haji à dnaximally allowed iuer-photon separation daa.

Since we want to find close associations of photons, only those trees of the MST are considered for which all edge-lengths are smaller than a maximally allowed inter-photon separation $d_{max}$ .

The value of d,,,, is determiied by the mean iuter-poiut separation expected im au isotropic aud homogeneous Olit distribution.

The value of $d_{max}$ is determined by the mean inter-point separation expected in an isotropic and homogeneous point distribution.

This separation is given by duy VALN, where Nis the tota -iiber of poiats ancl o ds he area of the region where th IN points are found (see WSV 1997)).

This separation is given by $d_{max}\approx\sqrt{A/N}$ , where $N$ is the total number of points and $A$ is the area of the region where the $N$ points are found (see WSV \cite{wiedenmann}) ).

An cxrample of the scaling-iidex spectrum is shown in Fie. 1..

An example of the scaling-index spectrum is shown in Fig. \ref{fig:simspec}.

The upper panes hishow a raudomlv-seucrated.Q smooth PSPC photon ma» (left) aud t1ο scaling iudex a-spectrum (ight).

The upper panels show a randomly-generated, smooth PSPC photon map (left) and the scaling index $\alpha$ -spectrum (right).

In au infinite. uuiform nuage. the sSpectruni NOILd be a delta "unction loc"uaed at a=2.

In an infinite, uniform image, the spectrum would be a delta function located at $\alpha =2$.

Because the feld is finite axd rot infinitely homogeneous. the spectrum is broadened. iid sleltly offset.

Because the field is finite and not infinitely homogeneous, the spectrum is broadened and slightly offset.

The lower panels show aji actual PSPC inage and is a-spectrun.

The lower panels show an actual PSPC image and its $\alpha$ -spectrum.

The spikes at k5v o are the xiehtest sources. aud the peak is broadened fiuther due to t1ο presence oD SOMICON.

The spikes at low $\alpha$ are the brightest sources, and the peak is broadened further due to the presence of sources.

Analyses ο: yxaudonmlv-seunerated μου] PSPC fields with backerotud levels siwil to those in our source fields revealed hat the SIM detected spurious sources with sonrce cotuts up to ~5 photous.

Analyses of randomly-generated smooth PSPC fields with background levels similar to those in our source fields revealed that the SIM detected spurious sources with source counts up to $\sim 5$ photons.

Iu oxer to ensure that no spuriots sources were included iu the source lists; we set the lower nuit ou source counts to teu protons.

In order to ensure that no spurious sources were included in the source lists, we set the lower limit on source counts to ten photons.

This lat ΠΠIv excluded real sources. but as of vet there is no estimae of source siguificance availadle for the SIM.

This limit undoubtedly excluded real sources, but as of yet there is no estimate of source significance available for the SIM.

We apied. the SIM. aleorithin he fields in this sunple. trereby creating source lists aud labelne each photon as a source or backeround phot3.

We applied the SIM algorithm to the fields in this sample, thereby creating source lists and labeling each photon as a source or background photon.

Upon removal of the soPCOS, it was obvious that fre SIM. had not correctly ideutified all photons. as bright sources reiuiinued in the imaees,

Upon removal of the sources, it was obvious that the SIM had not correctly identified all photons, as bright sources remained in the images.

Further investigatioi revealed that the SIM algoritlan rad dificulv ideutifving alp rotons associated with a sotree if the photon deusitv wew very high.

Further investigation revealed that the SIM algorithm had difficulty identifying all photons associated with a source if the photon density was very high.

We corrected. lis by identifving all piotons within the SIM-defined ηςmee boundaries as source protons.

We corrected this by identifying all photons within the SIM-defined source boundaries as source photons.

We then applied a ckeround correction based «n the umber of backeround photons «one would expect o find muder the source.

We then applied a background correction based on the number of background photons one would expect to find under the source.

Wule this method is less thau xcal. the resulting background photon maps appear to have! had. all detected ποος COupletely removed.

While this method is less than ideal, the resulting background photon maps appear to have had all detected sources completely removed.

Tn order to check the effectiveness of the scaliugdudex method. we also determined the diffuse x-ray background flux of cach field using the maxiuuu-likelihood. source-detection alexwithin included in the data r‘eduction software package {Zunuuernunun et al. 1992)).

In order to check the effectiveness of the scaling-index method, we also determined the diffuse x-ray background flux of each field using the maximum-likelihood source-detection algorithm included in the data reduction software package (Zimmermann et al. \cite{zman}) ).

Our lower likelihood πε was set oat 15. corresponding to a significauce level of ~Sa.

Our lower likelihood limit was set at 15, corresponding to a significance level of $\sim 5\sigma$.

We set the extrac‘tion radius at 2.5 times the FWIM of cach ποο

We set the extraction radius at 2.5 times the FWHM of each source.

The backeround-correctedC» plotou counts were then subtraced from the total photon count to eive the raw backeround ploton count.

The background-corrected photon counts were then subtracted from the total photon count to give the raw background photon count.

Vieuetting corrections were not appied. since we assume that vienettiug effects will be similar in cach image and since vignetti18o corrections were not availableal for the SIAL aleorithin.

Vignetting corrections were not applied, since we assume that vignetting effects will be similar in each image and since vignetting corrections were not available for the SIM algorithm.

We find that the SIAL aanalysis results in backegrouxd levels that are higher than the ΠΕΗΝxl technique backerounds by a Laverage of 158x95 counΤε

We find that the SIM analysis results in background levels that are higher than the maximum-likelihood technique backgrounds by an average of $158\pm 95$ counts.

The reasol. OY this ¢]screpancv Is not fully clear aud os1o0uld he πο¢xd. before tlre» STA js widely inplemenuted.

The reason for this discrepancy is not fully clear and should be understood before the SIM is widely implemented.

Ilowever. par of the discrepaicv can be explained by noting that oir SIM source flux cut-off of LO counts. while safelv ignoring spurious sources. almost certainly considere nunerous true low-flux sources as spurious. restting in these source photcuns beimg treated as bacseuu counts.

However, part of the discrepancy can be explained by noting that our SIM source flux cut-off of 10 counts, while safely ignoring spurious sources, almost certainly considered numerous true low-flux sources as spurious, resulting in these source photons being treated as background counts.

Tn this paper. we pertorÜ our analysis 1sine the background count evels as calculated bv. the SIN.

In this paper, we perform our analysis using the background count levels as calculated by the SIM.

A reanalysis of the data using the numbers from the ΠΠ technique resulted in the same qualitative conclusions. although the resulting quantities dovary.

A reanalysis of the data using the numbers from the maximum-likelihood technique resulted in the same qualitative conclusions, although the resulting quantities dovary.

The SIM analysis has the benefit of iceutifviug cach backerouud photon. whicrinade spectral aalysis of the backeround photons straightforward.

The SIM analysis has the benefit of identifying each background photon, whichmade spectral analysis of the background photons straightforward.

he parameters in Table. 1).

the parameters in Table. \ref{tab:par}) ).

In the model used by vanZee Haynes (2006) (henceforth VHO6). this yield is consistent Gwithin he errorbars) with the theoretically expected closed-box yield of 9=0.0074 (Meynet Maeder. 2002).

In the model used by vanZee Haynes (2006) (henceforth VH06), this yield is consistent (within the errorbars) with the theoretically expected closed-box yield of p=0.0074 (Meynet Maeder, 2002).

On the other hand. using only he HI mass within the optical disk. the derived por7.510+ is much lower than that expected from closed-box chemical evolution.

On the other hand, using only the HI mass within the optical disk, the derived $\rm{_{eff}}\sim 7.5 \times 10^{-4}$ is much lower than that expected from closed-box chemical evolution.

If interpreted literally. the above exercise would suggest that NGC 3741 is evolving as a closed-box model. provided that the gas-phase metallicity in the inner disk is the same as the outer disk. i.e. that there is an efficient mixing of the metals throughout the HI disk.

If interpreted literally, the above exercise would suggest that NGC 3741 is evolving as a closed-box model, provided that the gas-phase metallicity in the inner disk is the same as the outer disk, i.e. that there is an efficient mixing of the metals throughout the HI disk.

However this seems unlikely. given the large size of the HI disk.

However this seems unlikely, given the large size of the HI disk.

Tassis et al. (

2006) showed that the mixing length of metals in a galaxy increases with a decrease in the galaxy mass.

However. whether there is mixing of metals even up to I+ times its optical extent is unclear.

However, whether there is mixing of metals even up to 14 times its optical extent is unclear.

On the other hand. what evidence do we have for closed-box chemical evolution in dwarf galaxies?

On the other hand, what evidence do we have for closed-box chemical evolution in dwarf galaxies?

And can one from the observational data try to make inferences about how much of the HI disk participates in the chemical evolution (i.e. is well mixed)?

The gravitational binding energy of faint dwarf irregular galaxies is not much larger than the energy output from a few supernovae. hence a priori. one might expect that low mass galaxies would depart from the closed-box chemical evolution. since enriched material could escape via stellar winds and supernova ejecta (Brooks et al.

The gravitational binding energy of faint dwarf irregular galaxies is not much larger than the energy output from a few supernovae, hence a priori, one might expect that low mass galaxies would depart from the closed-box chemical evolution, since enriched material could escape via stellar winds and supernova ejecta (Brooks et al.

2007).

We searched the literature for the HI interferometric images for the galaxies in VH06 sample and show in Fig. 9[[

We searched the literature for the HI interferometric images for the galaxies in VH06 sample and show in Fig. \ref{fig:overlay_yield}[ [

A] the effective yield plotted as a function of the HI extent of a sample of galaxies in VHO6 sample with available HI images (the sources of the HI images is given in the figure caption).

A] the effective yield plotted as a function of the HI extent of a sample of galaxies in VH06 sample with available HI images (the sources of the HI images is given in the figure caption).

The effective yield is computed by considering the entire gas mass.

NGC 3741 and DDOIS4 are shown in the plot with extreme values of the HI extent.

NGC 3741 and DDO154 are shown in the plot with extreme values of the HI extent.

As can be seen. there are some galaxies in the sample which are consistent with the closed-box model.

As can be seen, there are some galaxies in the sample which are consistent with the closed-box model.

However there is no clear trend seen between the effective yield and the extent of the HI disk.

Figure 9[[B] shows the effective yield for the same sample of galaxies as shown in Fig. 9[[

Figure \ref{fig:overlay_yield}[ [B] shows the effective yield for the same sample of galaxies as shown in Fig. \ref{fig:overlay_yield}[ [

A]. however this time the effective yield is computed by considering the gas fraction within the Holmberg radius.

A], however this time the effective yield is computed by considering the gas fraction within the Holmberg radius.

As can be seen. if the effective vield is computed within the Holmberg radius. (as would be appropriate in the case of inefficient mixing) none of these galaxies follow a closed-box model.

As can be seen, if the effective yield is computed within the Holmberg radius, (as would be appropriate in the case of inefficient mixing) none of these galaxies follow a closed-box model.

The theoretically expected closed-box chemical yield depends on assumptions about the IMF. stellar rotation as well as in details of stellar evolution models (Meynet Maeder. 2002).

The theoretically expected closed-box chemical yield depends on assumptions about the IMF, stellar rotation as well as in details of stellar evolution models (Meynet Maeder, 2002).

It may be more instructive hence to look for trends in the effective yield as a function of other galaxy properties. instead of comparing the observed yield against a model dependent expected yield.

It may be more instructive hence to look for trends in the effective yield as a function of other galaxy properties, instead of comparing the observed yield against a model dependent expected yield.

One possible parameter to use for such a correlation is the tota dynamical mass.

One possible parameter to use for such a correlation is the total dynamical mass.

VHO6 did not tind any significant trend between the dynamical mass and effective yield for the galaxies in their sample. however they computed the dynamical mass using the HI global velocity widths.

VH06 did not find any significant trend between the dynamical mass and effective yield for the galaxies in their sample, however they computed the dynamical mass using the HI global velocity widths.

We recomputed the dynamical masses for the galaxies in VHO6 sample for which rotation curves are available in literature.

We recomputed the dynamical masses for the galaxies in VH06 sample for which rotation curves are available in literature.

We show in Fig.

160. a plot of the effective yield against the total dynamical mass.

\ref{fig:yield_mass} a plot of the effective yield against the total dynamical mass.

The effective yield computec using the entire HI mass is shown as eross. while the effective yield computed using the HI mass within the Holmberg radius is shown as solid points.

The effective yield computed using the entire HI mass is shown as cross, while the effective yield computed using the HI mass within the Holmberg radius is shown as solid points.

As can be seen. in both cases the effective yield increases with increasing dynamical mass.

As can be seen, in both cases the effective yield increases with increasing dynamical mass.

The correlation is tighter if one uses the only HI mass within the Holmberg radius (correlation coefficient is 0.59) compared to using the entire HI mass (correlation coefficient is 0.47). suggesting that. if this model were to be correct. only the gas within the optical disk participates in the chemical evolution of the galaxy.

The correlation is tighter if one uses the only HI mass within the Holmberg radius (correlation coefficient is 0.59) compared to using the entire HI mass (correlation coefficient is 0.47), suggesting that, if this model were to be correct, only the gas within the optical disk participates in the chemical evolution of the galaxy.

However we note that the total number of galaxies in our analysis is too small to make any statistical conclusion.

Spectroscopic observations of a large sample of dwarf galaxies along with a knowledge of the gas distribution is hence required for a better understanding of chemical enrichment and mixing of enriched material in gas-rich. low mass galaxies.

Spectroscopic observations of a large sample of dwarf galaxies along with a knowledge of the gas distribution is hence required for a better understanding of chemical enrichment and mixing of enriched material in gas-rich, low mass galaxies.

In summary. we examine the dark and luminous matter in NGC 3741.

In summary, we examine the dark and luminous matter in NGC 3741.

Although this galaxy has one of the highest known ratios of dark to luminous (i.e. stellar) matter. its baryons to dark

Although this galaxy has one of the highest known ratios of dark to luminous (i.e. stellar) matter, its baryons to dark

that the entire triplet is too faint for studies of changes, the line complex around iis strong enough that residual He8 would be detectable.

that the entire triplet is too faint for studies of changes, the line complex around is strong enough that residual $\beta$ would be detectable.

Also, the higher Ly series lines of are not seen in the difference spectrum.

We interpret the absence also of high Ly series lines in the difference spectrum as evidence for an increase in the optical depth of the scattering plasma, which could be part of the reformation process of the accretion disk.

A bit puzzling appears the presence of Lya in the difference spectrum while Ly is not present.

A bit puzzling appears the presence of $\alpha$ in the difference spectrum while $\beta$ is not present.

Except for the Lya line, the reduction in brightness during eclipse can therefore exclusively be attributed to the continuum.

Except for the $\alpha$ line, the reduction in brightness during eclipse can therefore exclusively be attributed to the continuum.

The shape of the continuum in the difference spectrum in Fig.

14 is the shape of the continuum component in the inner regions.

\ref{diffspec} is the shape of the continuum component in the inner regions.

It has roughly the same shape as the out-of-eclipse spectrum, supporting the interpretation of achromatic Thompson scattering.

Close inspection of the RGS and EPIC brightness maps in the bottom panels of Figs.

12 and 13 reveals that the eclipse progresses in a slightly non-uniform way in wavelength/energy.

\ref{smap} and \ref{smap_epic} reveals that the eclipse progresses in a slightly non-uniform way in wavelength/energy.

In the Rayleigh-Jeans tail, betweenAA,, the continuum seems to go through a wider eclipse towards longer wavelength (Fig. 12)).

In the Rayleigh-Jeans tail, between, the continuum seems to go through a wider eclipse towards longer wavelength (Fig. \ref{smap}) ).

In the Wien tail, the eclipse seems to be narrower towards higher energieswhich is indicated by the contours in Fig. 13..

In the Wien tail, the eclipse seems to be narrower towards higher energieswhich is indicated by the contours in Fig. \ref{smap_epic}.

This could indicate a temperature gradient, however, the hardness light curve in the middle panel of Fig.

3 does not indicate a significant temperature change with the eclipse.

\ref{lc2} does not indicate a significant temperature change with the eclipse.

Only the softening after the eclipse appears noteworthy and may have to be attributed to the cooling while nuclear burning is turning off.

On the other hand, the hardness light curve contains the emission lines and is a less sensitive indicator for the photospheric temperature.

In the first of the two oobservations, starting day 22.9, the UV grism of the OM was employed, taking 27 consecutive spectra (see Table 1)).

In the first of the two observations, starting day 22.9, the UV grism of the OM was employed, taking 27 consecutive spectra (see Table \ref{obslog}) ).

In Fig. 15,,

In Fig. \ref{smap_om}, ,