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

source stringlengths 1 2.05k ⌀	target stringlengths 1 11.7k
2005: Falcone et al.	2005; Falcone et al.
2006: Romano et al.	2006; Romano et al.
20062: Lazzati Perna 2007: Masham Zhang 2009: see Zhang 2007 for review).	2006a; Lazzati Perna 2007; Maxham Zhang 2009; see Zhang 2007 for review).
Although X-rav flares are eenerallv regarded to arise frou the same physical region as prompt enüssion. they release their enerev mostlv iu the soft N-ray bad.	Although X-ray flares are generally regarded to arise from the same physical region as prompt emission, they release their energy mostly in the soft X-ray band.
GRDB 1107090D triggered the Durst Alert Telescope ou-boardSwift (Gohrels et al.	GRB 110709B triggered the Burst Alert Telescope on-board (Gehrels et al.
2001). twice.	2004) twice.
Each of the trigsers. separated by 11 minutes. consists of an otherwise typical lone GRB light curve in the hard N-ravσαλάτα band.	Each of the triggers, separated by 11 minutes, consists of an otherwise typical long GRB light curve in the hard X-ray/gamma-ray band.
X-ray observatious during the second burst show that this event also produced bright soft X-ray cussion.	X-ray observations during the second burst show that this event also produced bright soft X-ray emission.
This provides a rare opportuuitv to conduct a detailed broadband study of the central eugiue properties.	This provides a rare opportunity to conduct a detailed broadband study of the central engine properties.
Tn this paper. we first report the Suvfé aud	In this paper, we first report the and
of A(B ID/AMogr equal to -0.33 and -0.20 magdex\|. respectively. significantly smalor. in absolute value. than the average strength of A(B Mogr of the previous 6 blue earlv-type dwarls.	of $\Delta$ $-$ $\Delta log~r$ equal to -0.33 and -0.20 $\rm mag~dex^{-1}$, respectively, significantly smaller, in absolute value, than the average strength of $\Delta$ $-$ $\Delta log~r$ of the previous 6 blue early-type dwarfs.
None o “the 3 blue early-type cdvarfs with a blue central excess (000) has a negative 11 color &eracdient. so that the strong Xue central excess seenmis a sullicient explanation to their ow values of r.g/r.g within the subsample of blue earlv-ty ον	None of the 3 blue early-type dwarfs with a blue central excess (G01), has a negative $-$ H color gradient, so that the strong blue central excess seems a sufficient explanation to their low values of $r_{e B}/r_{e H}$ within the subsample of blue early-type dwarfs.
We conclude that stronger negative color gradients are necessarily associated with larger values of rog/r,a.	We conclude that stronger negative color gradients are necessarily associated with larger values of $r_{e B}/r_{e H}$.
llowever. since there is no reason a priori why strone negative color gradients should be associated with blue colors. we conclude hat the displacement of the average fus of the 7 blue early-type cdwarfs without a blue central excess from that ofthe 7 red cds and dSOs in Fig.	However, since there is no reason a priori why strong negative color gradients should be associated with blue colors, we conclude that the displacement of the average locus of the 7 blue early-type dwarfs without a blue central excess from that of the 7 red dEs and dS0s in Fig.
2 is a robist and interesting behaviour. though is only a 20 cllect.	2 is a robust and interesting behaviour, though is only a $\rm 2 \sigma$ effect.
Whatever the classification in terms of profile decomposition is (e.g. in the ll-band). regfirey does not seem to depend on the bulge-to-total Iuminosity ratio. either in the II-band. or in the DB-band. as shown in Fig.	Whatever the classification in terms of profile decomposition is (e.g. in the H-band), $r_{e B}/r_{e H}$ does not seem to depend on the bulge-to-total luminosity ratio, either in the H-band or in the B-band, as shown in Fig.
αι. respectively.	4a,b, respectively.
Interestingly. among the 5 blue objects which show an exponential-disk component only in the. D-band surface brightness profile. the highest value of D/Tg and 1e smaller value of regfie belong to the I pec/SO0 galaxy 11499.	Interestingly, among the 5 blue objects which show an exponential-disk component only in the B-band surface brightness profile, the highest value of $B/T_B$ and the smaller value of $r_{e B}/r_{e H}$ belong to the E pec/S0 galaxy 1499.
According to GOL. the very blue continuum and strong Balmer absorption lines of this object are typical of L.X. galaxies which have experienced an intense burst of star formation ended about 12 yrs ago (Poggianti Darbaro 1996).	According to G01, the very blue continuum and strong Balmer absorption lines of this object are typical of $+$ A galaxies which have experienced an intense burst of star formation ended about 1–2 Gyrs ago (Poggianti Barbaro 1996).
As well as ree/rea. LL does not seem to depend on he bulge-to-total luminosity ratio. as shown in Fig.	As well as $r_{e B}/r_{e H}$, $-$ H does not seem to depend on the bulge-to-total luminosity ratio, as shown in Fig.
5. where we plot B/Tg vs. HL (panel τα) and B/Tg vs. B. HL (panel b). the VCC galaxies being classified according to their H-xuxd surface brightness profile decomposition (cf.	5, where we plot $B/T_H$ vs. $-$ H (panel `a') and $B/T_B$ vs. $-$ H (panel `b'), the VCC galaxies being classified according to their H-band surface brightness profile decomposition (cf.
Fig.	Fig.
2a).	2a).
Both ByTy and οον are less than 0.5 for those galaxies with a confirmed. exponential-disk component. in hh. pass-bands. so that. in these galaxies. the stellar »opulations associated with the disk largely contribute to. if not dominate. the emission in the near-E ancl optical.	Both $B/T_H$ and $B/T_B$ are less than 0.5 for those galaxies with a confirmed exponential-disk component in both pass-bands, so that, in these galaxies, the stellar populations associated with the disk largely contribute to, if not dominate, the emission in the near-IR and optical.
Finally. we note that ο and D/Tg are to first order identical both for the 7. red earlv-type cwarfs and for the previous 6 blue earlv-tvpe cdwarls.	Finally, we note that $B/T_H$ and $B/T_B$ are to first order identical both for the 7 red early-type dwarfs and for the previous 6 blue early-type dwarfs.
In this section we investigate if the increase of regfry with 1I previously found in the earlv-type chvarts has an analogv in giant IZ ancl SO galaxies.	In this section we investigate if the increase of $r_{e B}/r_{e H}$ with $-$ H previously found in the early-type dwarfs has an analogy in giant E and S0 galaxies.
The findings may cast some light to the origin of the trend illustrated in Fig.2.	The findings may cast some light to the origin of the trend illustrated in Fig.2.
As a comparison. we adopt the sample of 29 carly-type giants of the Coma cluster listed in Tab.	As a comparison, we adopt the sample of 29 early-type giants of the Coma cluster listed in Tab.
3.	3.
Unfortunately. HL or V color profiles of these giant. galaxies are not available ous. so that we can not study the behaviour of total color. color gradient and ορ in these svstenis.	Unfortunately, $-$ H or $-$ V color profiles of these giant galaxies are not available to us, so that we can not study the behaviour of total color, color gradient and $r_{e B}/r_{e H}$ in these systems.
Given that the range of ~ 600 in L-bancl luminosity (i.c. mass) spanned by earlv-tvpe giants and cwarfs implies cilferences in structural. kinematical and photometric properties. first we display he distribution of carly-type dwarls and giants in the planes Mg II (Fig.	Given that the range of $\sim$ 600 in H-band luminosity (i.e. mass) spanned by early-type giants and dwarfs implies differences in structural, kinematical and photometric properties, first we display the distribution of early-type dwarfs and giants in the planes $\rm M_H$ $-$ H (Fig.
6) and Aly Γρέν (Vie.	6) and $\rm M_H$ $r_{e B}/r_{e H}$ (Fig.
7).	7).
Each sample of galaxies spans a range of ~ 10 in L-bancl luminosity (Fig.	Each sample of galaxies spans a range of $\sim$ 10 in H-band luminosity (Fig.
6). but the early-type elants. plotted as small empty squares. span a narrow rangeanes in color (5cB Il κ 42). which overlaps the range in BLU spannecl by the red subsample of the early-type charts. hereafter plotted. as large filled squares.	6), but the early-type giants, plotted as small empty squares, span a narrow range in color $3.3 <$ $-$ H $< 4.2$ ), which overlaps the range in $-$ H spanned by the red subsample of the early-type dwarfs, hereafter plotted as large filled squares.
HE colors bluer than 3.1 are found. only in. earlv-tvpe dwarfs.	$-$ H colors bluer than 3.1 are found only in early-type dwarfs.
Conversely. the earlv-type giants span a broad range in ree/rea. their roeite ranging [rom ~0.2 to ~ with a mean value equal to 1.13 and an rms dispersion of 0.48 (cf.	Conversely, the early-type giants span a broad range in $r_{e B}/r_{e H}$, their $r_{e B}/r_{e H}$ ranging from $\sim 0.2$ to $\sim 2.2$ , with a mean value equal to 1.13 and an rms dispersion of 0.48 (cf.
Fig.	Fig.
7).	7).
Such a broad range. due in part to the non-homogeneous source of the photometric parameters of the giants (cf.	Such a broad range, due in part to the non-homogeneous source of the photometric parameters of the giants (cf.
Sect.	Sect.
2). embraces the distribution of the early-twpe dwarls at the σσ level.	2), embraces the distribution of the early-type dwarfs at the $\rm 2 \sigma$ level.
No trend of regfrog with H-band magnitude is found. either overall or within cach sample.	No trend of $r_{e B}/r_{e H}$ with H-band magnitude is found, either overall or within each sample.
Finally. we reproduce the distributionof the early-type	Finally, we reproduce the distributionof the early-type
moment that they exit the presumed acceleration site near the solar surface.	moment that they exit the presumed acceleration site near the solar surface.
The injected (accelerated) beams of electrons are assumed to be power-laws, with a low-energy cutoff Ej: The distribution Fo(F) is expressed in electrons ! keV~!, 6 is the spectral index, and ΕΙ the total number of injected electrons per second above E;?)..?,	The injected (accelerated) beams of electrons are assumed to be power-laws, with a low-energy cutoff $E_1$: The distribution $F_0(E)$ is expressed in electrons $^{-1}$ $^{-1}$, $\delta$ is the spectral index, and $F_1$ the total number of injected electrons per second above $E_1$.,
, have associated the HXR emission from a flare (GOES class C9.6) with a beam of electrons propagating downward, toward the denser chromosphere, and, assuming a target model(?),, have found the following characteristics for the injected electron beam: 0—4, E4—10 keV, and F\=2.7x10* electrons/s. Despite its relatively small X-ray thermal footprint, this flare was particularly hard, and was even a gamma-ray line emitter.	have associated the HXR emission from a flare (GOES class C9.6) with a beam of electrons propagating downward, toward the denser chromosphere, and, assuming a thick-target model, have found the following characteristics for the injected electron beam: $\delta$ =4, $E_1$ =10 keV, and $F_1$ $\times 10^{36}$ electrons/s. Despite its relatively small X-ray thermal footprint, this flare was particularly hard, and was even a gamma-ray line emitter.
For comparison, the 2002 July 23 flare (GOES class X4.8), had an average electron flux of about 1035 electrons/s (electrons above 35 keV) during its zz15-minute long main impulsive phase(?),, translating to about 1036 electrons above 10 keV per second (using an averaged electron spectral index 6 of 72.5).	For comparison, the 2002 July 23 flare (GOES class X4.8), had an average electron flux of about $^{35}$ electrons/s (electrons above 35 keV) during its $\approx$ 15-minute long main impulsive phase, translating to about $^{36}$ electrons above 10 keV per second (using an averaged electron spectral index $\delta$ of $\approx$ 2.5).
In situ and remote observations from indicate that the number of electrons in interplanetary beams is 720.296 of the number derived from the temporally associated HXR flare beams.	In situ and remote observations from indicate that the number of electrons in interplanetary beams is $\approx$ of the number derived from the temporally associated HXR flare beams.
This relationship was established for electrons >50 keV. Assuming it holds for energies down to 10 keV, this means that the interplanetary counterpart of the first flare beam has F;z 1033 electrons/s above 10 keV. We will henceforth call astrong beam a beam of electrons with F\ strong=2.7X1096 electrons/s, and aweak beam one with Fy wear=1.010™ electrons/s (Fiweak70.0037xΕΙ strong). As	This relationship was established for electrons $>$ 50 keV. Assuming it holds for energies down to 10 keV, this means that the interplanetary counterpart of the first flare beam has $F_1\approx$ $^{34}$ electrons/s above 10 keV. We will henceforth call a beam a beam of electrons with $F_{1,strong}$ $\times 10^{36}$ electrons/s, and a beam one with $F_{1,weak}$ $\times 10^{34}$ electrons/s $F_{1,weak} \approx 0.0037 \times F_{1,strong}$ ).
trong beam is of the type usually associated with flares, whereas aweak beam is of the type usually associated with Solar Energetic Particles (SEP).	A beam is of the type usually associated with flares, whereas a beam is of the type usually associated with Solar Energetic Particles (SEP).
The HXR-producing electron beams in had a typical duration of 100 s, and this is the duration that will be used throughout this paper, unless otherwise specified.	The HXR-producing electron beams in had a typical duration of 100 s, and this is the duration that will be used throughout this paper, unless otherwise specified.
For comparison, the 100 s typical duration leads to a total number ofweak beam electrons above 10 keV of z1x10?9 electrons, or ~9x10*4 electrons above 22 keV, hence about an order of magnitude more than has been reported so far??),, but still below the 4χ 1056 electrons above 10 keV that would have come out of the 2002 July 23 flare, assuming the 20.296 relationship holds.	For comparison, the 100 s typical duration leads to a total number of beam electrons above 10 keV of $\approx$ $\times$ $^{36}$ electrons, or $\approx$ $\times$ $^{34}$ electrons above 22 keV, hence about an order of magnitude more than has been reported so far, but still below the $\times$ $^{36}$ electrons above 10 keV that would have come out of the 2002 July 23 flare, assuming the $\approx$ relationship holds.
Asin? (and using the same assumptions), the electron spectrum changes shape as it	As in (and using the same assumptions), the electron spectrum changes shape as it
Ilielh-: that he preseut expanding Universe is ectting eradual acceleration.	$z$ that the present expanding Universe is getting gradual acceleration.
As a cause of this acceleration it is argued that a kind of exotic matter having repulsive force is responsible for speeding up the Universe some 7 billion vears ago.	As a cause of this acceleration it is argued that a kind of exotic matter having repulsive force is responsible for speeding up the Universe some $7$ billion years ago.
To nuderstaud the nature of this hypothetical energy that tends to increase the rate of expansion of the Universe several unodels have been proposed by the scieutists so far (OverduinandCooperstockL998:Starobiuskv 2000).	To understand the nature of this hypothetical energy that tends to increase the rate of expansion of the Universe several models have been proposed by the scientists so far \citep{Overduin1998,Sahni2000}.
As far as imatter content of the Universe is concerned. it is convincinely interred from distant superuovac. lavee scale structure aud CMD. that 96% of matter is hidden mass coustituted by 23© dark matter aud 73%( nuknown exotic matter known as dark energy whereas ouly [4 quass in the form of ordinary mass which is visible coutrary to the non-bhuuinous dark matter (Pretzl2001:Freemanand\leNamara2006:Wheeler2007:(απ 2007).	As far as matter content of the Universe is concerned, it is convincingly inferred from distant supernovae, large scale structure and CMB, that $96\%$ of matter is hidden mass constituted by $23\%$ dark matter and $73\%$ unknown exotic matter known as dark energy whereas only $4\%$ mass in the form of ordinary mass which is visible contrary to the non-luminous dark matter \citep{Pretzl,Freeman,Wheeler,Gribbin}.
. On the other haud. theoretically awormhole. which is sluuilar to a tunnel with two ends cach iu separate points iu spacetime or two connecting black holes. was conjectured first by Wevl (Colemanand[do-rteL985) aud ater on bv Wheeler(1957).	On the other hand, theoretically a, which is similar to a tunnel with two ends each in separate points in spacetime or two connecting black holes, was conjectured first by Weyl \citep{Coleman1985} and later on by \citet{Wheeler1957}.
.. This is essentially some kind of hypothetical topological feature of spacetime which iav acts as through spacetime.	This is essentially some kind of hypothetical topological feature of spacetime which may acts as through spacetime.
Iu principle this means that a wormhole would allow travel in time as well as in space aud can be shown explicitly how to couvert a wormbhole traversing space mto one traversing time (Morrisetal. 1988).	In principle this means that a wormhole would allow travel in time as well as in space and can be shown explicitly how to convert a wormhole traversing space into one traversing time \citep{Morris1988a}.
The possibility of traversable wormloles in general relativity was demonstrated by MorrisaudThorne(1988) which held open by a spherical shell of exotic inatter whereas quite a nunber of wormlole solutions were obtained much carlier with differeut physical motivation by other scicutists 1981).	The possibility of traversable wormholes in general relativity was demonstrated by \citet{Morris1988b} which held open by a spherical shell of exotic matter whereas quite a number of wormhole solutions were obtained much earlier with different physical motivation by other scientists \citep{Ellis1973,Bronnikov1973,Clement1984}. .
carbon chemistry is included in the numerical algorithm.	carbon chemistry is included in the numerical algorithm.
This consists of 218 reactions of 32 chemical species. which are coupled with the thermocwnamics.	This consists of 218 reactions of 32 chemical species, which are coupled with the thermodynamics.
A background. UV radiation field. which is responsible for photodissociation. is treated. through the six-ray approximation as described in 7..	A background UV radiation field, which is responsible for photodissociation, is treated through the six-ray approximation as described in \citet{Glover&MacLow07I}.
In our investigation of emission from CO molecules. we consider one snapshot of these simulations at a late time > 5 Myr. after which the simulation has reached a statistically steady state.	In our investigation of emission from CO molecules, we consider one snapshot of these simulations at a late time $>$ 5 Myr, after which the simulation has reached a statistically steady state.
The numerical modeling. deseribed above follows the combined ellects of turbulence. magnetic fields. thermodynamics. anc chemical evolution as structures— such as filaments and. dense cores twpically found in MCS forms out of the gas (see Paper Lb for more details).	The numerical modeling described above follows the combined effects of turbulence, magnetic fields, thermodynamics, and chemical evolution as structures such as filaments and dense cores typically found in MCs forms out of the gas (see Paper I for more details).
In our investigation of CO emission. emerging from the MC simulations. we consider a suit of models designed. to represent various astrophysical environments.	In our investigation of CO emission emerging from the MC simulations, we consider a suit of models designed to represent various astrophysical environments.
The relevant parameters of cach model are listed in Table 1..	The relevant parameters of each model are listed in Table \ref{exptab}.
Column l shows the name of each run.	Column 1 shows the name of each run.
The main user defined parameters are the initial density vy. metallicity Z.and background. UV. radiation field. Co. indicated. in. Columns 2-4. respectively.	The main user defined parameters are the initial density $n_0$, metallicity $Z$,and background UV radiation field $G_0$, indicated in Columns 2-4, respectively.
We assume that the clust-to-gas ratio is clirecthy proportional to the gas-phase metallicity and. do not vary these quantities independently.	We assume that the dust-to-gas ratio is directly proportional to the gas-phase metallicity and do not vary these quantities independently.
Column 5 shows the numerical resolution: as noted in Paper LH. simulations with identical initial conditions but resolutions of 256% and 1287 produce very similar The last column lists the representative environment corresponding to the simulated. cloud: a high density cloud found in the galactic center (n1000). a typical Milkv Way cloud. (1200.2).. clouds in low metallicity svstems like the LMC or SAIC (n300-Z03 and n300-Z01). a low censitv cloud in a dwarf ealaxy (n100). ancl clouds in weak ancl strong starbursts (n300-UV10 ane n300-UV100. respectively).	Column 5 shows the numerical resolution; as noted in Paper II, simulations with identical initial conditions but resolutions of $^3$ and $^3$ produce very similar The last column lists the representative environment corresponding to the simulated cloud: a high density cloud found in the galactic center (n1000), a typical Milky Way cloud \citep[n300,][]{Ferriere01}, clouds in low metallicity systems like the LMC or SMC (n300-Z03 and n300-Z01), a low density cloud in a dwarf galaxy (n100), and clouds in weak and strong starbursts (n300-UV10 and n300-UV100, respectively).
We use the racliative transfer code RADAIC-3D (Dullemond et al.	We use the radiative transfer code RADMC-3D (Dullemond et al.
in preparation) to mocel the molecular line emission of the MIID. MC models.	in preparation) to model the molecular line emission of the MHD MC models.
IUADMC-3D is a 3-climensional code that performs dust. and/or line radiative transfer on Cartesian or spherical erids (including adaptive mesh refinement).	RADMC-3D is a 3-dimensional code that performs dust and/or line radiative transfer on Cartesian or spherical grids (including adaptive mesh refinement).
In this work. since we are only interested. in CO molecular line emission along a chosen direction. we use the rav. tracing capability of IUADMC-3D. One of the primary challenges in line radiative transfer is to solve for the population levels. of the molecular (or atomic) species under consideration.	In this work, since we are only interested in CO molecular line emission along a chosen direction, we use the ray tracing capability of RADMC-3D. One of the primary challenges in line radiative transfer is to solve for the population levels of the molecular (or atomic) species under consideration.
The occupation of a given (rotational/vibrational) οποιον level of a molecule depends on the incident. radiation field. as well as the collision properties. (c.g. frequency). with other atoms or molecules. both of which act as excitation or de-excitation mechanisms.	The occupation of a given (rotational/vibrational) energy level of a molecule depends on the incident radiation field, as well as the collision properties (e.g. frequency) with other atoms or molecules, both of which act as excitation or de-excitation mechanisms.
In statistical equilibrium. the relative population of level ;. f; is governed by the equation of detailed balance: The last summation accounts for collisions. where C; is 1e collisional rate for a transition from level 7 to level j.	In statistical equilibrium, the relative population of level $i$, $f_i$, is governed by the equation of detailed balance: The last summation accounts for collisions, where $C_{ij}$ is the collisional rate for a transition from level $i$ to level $j$.
Phe collisionalrate is dependent on the rate coctlicient A';; and re density of the collisional partner no: C5;=movi.	The collisionalrate is dependent on the rate coefficient $K_{ij}$ and the density of the collisional partner $n_{col}$: $C_{ij} = n_{col} K_{ij}$.
1n p»ICs. the main collisional partner of CO isL».	In MCs, the main collisional partner of CO is.
. We use the rate coellicients for collisional excitation ancl de-exeitations of CO by tlabulatecl and. freely available from. the Leiden: clatahbase (?)..	We use the rate coefficients for collisional excitation and de-excitations of CO by tabulated and freely available from the Leiden database \citep{Schoieretal05}.
These are based on calculations by 2..	These are based on calculations by \citet{Yangetal10}.
We neglect the cHleet of collisions with partners other thanοι.	We neglect the effect of collisions with partners other than.
We justify this by noting that almost all of the CO in our simulations is found in regions of the gas that are dominated. byH».. rather than atomic hydrogen.	We justify this by noting that almost all of the CO in our simulations is found in regions of the gas that are dominated by, rather than atomic hydrogen.
The intluence of radiation on setting the level populations is captured by the first two summations in Equation 2.. which include the mean integrated: intensity Ji; of the radiation field in the line corresponding to the transition [rom i to jf.	The influence of radiation on setting the level populations is captured by the first two summations in Equation \ref{poplevel}, , which include the mean integrated intensity $\bar{J}_{ij}$ of the radiation field in the line corresponding to the transition from $i$ to $j$.
The constants are ;1;. the Einstein coefficient for spontaneous emission for a transition [rom level / to level j. ει. the Einstein. cocllicient for stipulated. emission. from / to. level j. anc Dj;. the corresponding coellicient for absorption (also given by the Leiden database).	The constants are $A_{ij}$, the Einstein coefficient for spontaneous emission for a transition from level $i$ to level $j$ , $B_{ij}$, the Einstein coefficient for stimulated emission from $i$ to level $j$, and $B_{ji}$ , the corresponding coefficient for absorption (also given by the Leiden database).
Equation 2. is coupled withthe equation of racdative transfer where J, is the specific intensity. 5, the source function. ancl 7, is the optical depth.	Equation \ref{poplevel} is coupled withthe equation of radiative transfer where $I_\nu$ is the specific intensity, $S_\nu$ the source function, and $\tau_\nu$ is the optical depth.
Phe coupling between Equations 2 and 3. occurs through the dependence. of the source function CS,= 5;;) on the relative population levels: as well as the dependence of the ο f: where the integral is taken over all solid angles ©.	The coupling between Equations \ref{poplevel} and \ref{rteqn} occurs through the dependence of the source function $S_\nu = S_{ij}$ ) on the relative population levels: as well as the dependence of the $\bar{J}$ on $I$: where the integral is taken over all solid angles $\Omega$.
The normalized profile function ὧν determines the emission and absorbtion probability of a photon with frequency ο. due to a line with rest frequency £;;.	The normalized profile function $\phi_{ij}$ determines the emission and absorbtion probability of a photon with frequency $\nu$ due to a line with rest frequency $\nu_{ij}$ .
For a photon propagatingin a direction & through a medium with velocity v. where ce ids the light) speed.	For a photon propagatingin a direction ${\bf \hat{n}}$ through a medium with velocity ${\bf v}$, where $c$ is the light speed.
The thermal and microturbulent broadening ofthe line is accounted for through	The thermal and microturbulent broadening ofthe line is accounted for through
follows: where the subseripted variables represent the actual values independent of measurement uucertaimties. aud the non-subseripted variables represent the observed values imcludiug measurement uncertainties.	follows: where the subscripted variables represent the actual values independent of measurement uncertainties, and the non-subscripted variables represent the observed values including measurement uncertainties.
Eq.	Eq.
6 allows us to split the dependence of sin; mto two parts: the actual value of sin’ (the term outside the brackets) aud the contributions of 1ucasureimoent wncertaiuties (the term inside the brackets).	\ref{sinim} allows us to split the dependence of $\sin i$ into two parts: the actual value of $\sin i$ (the term outside the brackets) and the contributions of measurement uncertainties (the term inside the brackets).
The (ini), distribution is generated from Eq.	The $(\sin i)_{m}$ distribution is generated from Eq.
6 sing a Monte Carlo routine.	\ref{sinim} using a Monte Carlo routine.
Each term of the form AXXu (where represcutsany of the variables P. ¢sin/. Toyg ov L) is calculated Dy drawing raucdomly frou +he appropriate error distribution for our dataset. as escribed iu 6 1.3..	Each term of the form $X/X_{0}$ (where $X$ representsany of the variables $P$, $v \sin i$, $T_{eff}$ or $L$ ) is calculated by drawing randomly from the appropriate error distribution for our dataset, as described in $\S$ \ref{error_distribution}.
This process assumes that fractional errors in csiu. Toy; aud £ are independent of the values of these variables.	This process assumes that fractional errors in $v \sin i$, $T_{eff}$ and $L$ are independent of the values of these variables.
While this assumption is somewhat questionable. the deviation from the true error distribution is likely small	While this assumption is somewhat questionable, the deviation from the true error distribution is likely small.

2005: Falcone et al.

2005; Falcone et al.

2006: Romano et al.

2006; Romano et al.

20062: Lazzati Perna 2007: Masham Zhang 2009: see Zhang 2007 for review).

2006a; Lazzati Perna 2007; Maxham Zhang 2009; see Zhang 2007 for review).

Although X-rav flares are eenerallv regarded to arise frou the same physical region as prompt enüssion. they release their enerev mostlv iu the soft N-ray bad.

Although X-ray flares are generally regarded to arise from the same physical region as prompt emission, they release their energy mostly in the soft X-ray band.

GRDB 1107090D triggered the Durst Alert Telescope ou-boardSwift (Gohrels et al.

GRB 110709B triggered the Burst Alert Telescope on-board (Gehrels et al.

2001). twice.

2004) twice.

Each of the trigsers. separated by 11 minutes. consists of an otherwise typical lone GRB light curve in the hard N-ravσαλάτα band.

Each of the triggers, separated by 11 minutes, consists of an otherwise typical long GRB light curve in the hard X-ray/gamma-ray band.

X-ray observatious during the second burst show that this event also produced bright soft X-ray cussion.

X-ray observations during the second burst show that this event also produced bright soft X-ray emission.

This provides a rare opportuuitv to conduct a detailed broadband study of the central eugiue properties.

This provides a rare opportunity to conduct a detailed broadband study of the central engine properties.

Tn this paper. we first report the Suvfé aud

In this paper, we first report the and

of A(B ID/AMogr equal to -0.33 and -0.20 magdex|. respectively. significantly smalor. in absolute value. than the average strength of A(B Mogr of the previous 6 blue earlv-type dwarls.

of $\Delta$ $-$ $\Delta log~r$ equal to -0.33 and -0.20 $\rm mag~dex^{-1}$, respectively, significantly smaller, in absolute value, than the average strength of $\Delta$ $-$ $\Delta log~r$ of the previous 6 blue early-type dwarfs.

None o “the 3 blue early-type cdvarfs with a blue central excess (000) has a negative 11 color &eracdient. so that the strong Xue central excess seenmis a sullicient explanation to their ow values of r.g/r.g within the subsample of blue earlv-ty ον

None of the 3 blue early-type dwarfs with a blue central excess (G01), has a negative $-$ H color gradient, so that the strong blue central excess seems a sufficient explanation to their low values of $r_{e B}/r_{e H}$ within the subsample of blue early-type dwarfs.

We conclude that stronger negative color gradients are necessarily associated with larger values of rog/r,a.

We conclude that stronger negative color gradients are necessarily associated with larger values of $r_{e B}/r_{e H}$.

llowever. since there is no reason a priori why strone negative color gradients should be associated with blue colors. we conclude hat the displacement of the average fus of the 7 blue early-type cdwarfs without a blue central excess from that ofthe 7 red cds and dSOs in Fig.

However, since there is no reason a priori why strong negative color gradients should be associated with blue colors, we conclude that the displacement of the average locus of the 7 blue early-type dwarfs without a blue central excess from that of the 7 red dEs and dS0s in Fig.

2 is a robist and interesting behaviour. though is only a 20 cllect.

2 is a robust and interesting behaviour, though is only a $\rm 2 \sigma$ effect.

Whatever the classification in terms of profile decomposition is (e.g. in the ll-band). regfirey does not seem to depend on the bulge-to-total Iuminosity ratio. either in the II-band. or in the DB-band. as shown in Fig.

Whatever the classification in terms of profile decomposition is (e.g. in the H-band), $r_{e B}/r_{e H}$ does not seem to depend on the bulge-to-total luminosity ratio, either in the H-band or in the B-band, as shown in Fig.

αι. respectively.

4a,b, respectively.

Interestingly. among the 5 blue objects which show an exponential-disk component only in the. D-band surface brightness profile. the highest value of D/Tg and 1e smaller value of regfie belong to the I pec/SO0 galaxy 11499.

Interestingly, among the 5 blue objects which show an exponential-disk component only in the B-band surface brightness profile, the highest value of $B/T_B$ and the smaller value of $r_{e B}/r_{e H}$ belong to the E pec/S0 galaxy 1499.

According to GOL. the very blue continuum and strong Balmer absorption lines of this object are typical of L.X. galaxies which have experienced an intense burst of star formation ended about 12 yrs ago (Poggianti Darbaro 1996).

According to G01, the very blue continuum and strong Balmer absorption lines of this object are typical of $+$ A galaxies which have experienced an intense burst of star formation ended about 1–2 Gyrs ago (Poggianti Barbaro 1996).

As well as ree/rea. LL does not seem to depend on he bulge-to-total luminosity ratio. as shown in Fig.

As well as $r_{e B}/r_{e H}$, $-$ H does not seem to depend on the bulge-to-total luminosity ratio, as shown in Fig.

5. where we plot B/Tg vs. HL (panel τα) and B/Tg vs. B. HL (panel b). the VCC galaxies being classified according to their H-xuxd surface brightness profile decomposition (cf.

5, where we plot $B/T_H$ vs. $-$ H (panel `a') and $B/T_B$ vs. $-$ H (panel `b'), the VCC galaxies being classified according to their H-band surface brightness profile decomposition (cf.

Fig.

2a).

Both ByTy and οον are less than 0.5 for those galaxies with a confirmed. exponential-disk component. in hh. pass-bands. so that. in these galaxies. the stellar »opulations associated with the disk largely contribute to. if not dominate. the emission in the near-E ancl optical.

Both $B/T_H$ and $B/T_B$ are less than 0.5 for those galaxies with a confirmed exponential-disk component in both pass-bands, so that, in these galaxies, the stellar populations associated with the disk largely contribute to, if not dominate, the emission in the near-IR and optical.

Finally. we note that ο and D/Tg are to first order identical both for the 7. red earlv-type cwarfs and for the previous 6 blue earlv-tvpe cdwarls.

Finally, we note that $B/T_H$ and $B/T_B$ are to first order identical both for the 7 red early-type dwarfs and for the previous 6 blue early-type dwarfs.

In this section we investigate if the increase of regfry with 1I previously found in the earlv-type chvarts has an analogv in giant IZ ancl SO galaxies.

In this section we investigate if the increase of $r_{e B}/r_{e H}$ with $-$ H previously found in the early-type dwarfs has an analogy in giant E and S0 galaxies.

The findings may cast some light to the origin of the trend illustrated in Fig.2.

As a comparison. we adopt the sample of 29 carly-type giants of the Coma cluster listed in Tab.

As a comparison, we adopt the sample of 29 early-type giants of the Coma cluster listed in Tab.

3.

Unfortunately. HL or V color profiles of these giant. galaxies are not available ous. so that we can not study the behaviour of total color. color gradient and ορ in these svstenis.

Unfortunately, $-$ H or $-$ V color profiles of these giant galaxies are not available to us, so that we can not study the behaviour of total color, color gradient and $r_{e B}/r_{e H}$ in these systems.

Given that the range of ~ 600 in L-bancl luminosity (i.c. mass) spanned by earlv-tvpe giants and cwarfs implies cilferences in structural. kinematical and photometric properties. first we display he distribution of carly-type dwarls and giants in the planes Mg II (Fig.

Given that the range of $\sim$ 600 in H-band luminosity (i.e. mass) spanned by early-type giants and dwarfs implies differences in structural, kinematical and photometric properties, first we display the distribution of early-type dwarfs and giants in the planes $\rm M_H$ $-$ H (Fig.

6) and Aly Γρέν (Vie.

6) and $\rm M_H$ $r_{e B}/r_{e H}$ (Fig.

7).

Each sample of galaxies spans a range of ~ 10 in L-bancl luminosity (Fig.

Each sample of galaxies spans a range of $\sim$ 10 in H-band luminosity (Fig.

6). but the early-type elants. plotted as small empty squares. span a narrow rangeanes in color (5cB Il κ 42). which overlaps the range in BLU spannecl by the red subsample of the early-type charts. hereafter plotted. as large filled squares.

6), but the early-type giants, plotted as small empty squares, span a narrow range in color $3.3 <$ $-$ H $< 4.2$ ), which overlaps the range in $-$ H spanned by the red subsample of the early-type dwarfs, hereafter plotted as large filled squares.

HE colors bluer than 3.1 are found. only in. earlv-tvpe dwarfs.

$-$ H colors bluer than 3.1 are found only in early-type dwarfs.

Conversely. the earlv-type giants span a broad range in ree/rea. their roeite ranging [rom ~0.2 to ~ with a mean value equal to 1.13 and an rms dispersion of 0.48 (cf.

Conversely, the early-type giants span a broad range in $r_{e B}/r_{e H}$, their $r_{e B}/r_{e H}$ ranging from $\sim 0.2$ to $\sim 2.2$ , with a mean value equal to 1.13 and an rms dispersion of 0.48 (cf.

Fig.

7).

Such a broad range. due in part to the non-homogeneous source of the photometric parameters of the giants (cf.

Such a broad range, due in part to the non-homogeneous source of the photometric parameters of the giants (cf.

Sect.

2). embraces the distribution of the early-twpe dwarls at the σσ level.

2), embraces the distribution of the early-type dwarfs at the $\rm 2 \sigma$ level.

No trend of regfrog with H-band magnitude is found. either overall or within cach sample.

No trend of $r_{e B}/r_{e H}$ with H-band magnitude is found, either overall or within each sample.

Finally. we reproduce the distributionof the early-type

Finally, we reproduce the distributionof the early-type

moment that they exit the presumed acceleration site near the solar surface.

The injected (accelerated) beams of electrons are assumed to be power-laws, with a low-energy cutoff Ej: The distribution Fo(F) is expressed in electrons ! keV~!, 6 is the spectral index, and ΕΙ the total number of injected electrons per second above E;?)..?,

The injected (accelerated) beams of electrons are assumed to be power-laws, with a low-energy cutoff $E_1$: The distribution $F_0(E)$ is expressed in electrons $^{-1}$ $^{-1}$, $\delta$ is the spectral index, and $F_1$ the total number of injected electrons per second above $E_1$.,

, have associated the HXR emission from a flare (GOES class C9.6) with a beam of electrons propagating downward, toward the denser chromosphere, and, assuming a target model(?),, have found the following characteristics for the injected electron beam: 0—4, E4—10 keV, and F\=2.7x10* electrons/s. Despite its relatively small X-ray thermal footprint, this flare was particularly hard, and was even a gamma-ray line emitter.

have associated the HXR emission from a flare (GOES class C9.6) with a beam of electrons propagating downward, toward the denser chromosphere, and, assuming a thick-target model, have found the following characteristics for the injected electron beam: $\delta$ =4, $E_1$ =10 keV, and $F_1$ $\times 10^{36}$ electrons/s. Despite its relatively small X-ray thermal footprint, this flare was particularly hard, and was even a gamma-ray line emitter.

For comparison, the 2002 July 23 flare (GOES class X4.8), had an average electron flux of about 1035 electrons/s (electrons above 35 keV) during its zz15-minute long main impulsive phase(?),, translating to about 1036 electrons above 10 keV per second (using an averaged electron spectral index 6 of 72.5).

For comparison, the 2002 July 23 flare (GOES class X4.8), had an average electron flux of about $^{35}$ electrons/s (electrons above 35 keV) during its $\approx$ 15-minute long main impulsive phase, translating to about $^{36}$ electrons above 10 keV per second (using an averaged electron spectral index $\delta$ of $\approx$ 2.5).

In situ and remote observations from indicate that the number of electrons in interplanetary beams is 720.296 of the number derived from the temporally associated HXR flare beams.

In situ and remote observations from indicate that the number of electrons in interplanetary beams is $\approx$ of the number derived from the temporally associated HXR flare beams.

This relationship was established for electrons >50 keV. Assuming it holds for energies down to 10 keV, this means that the interplanetary counterpart of the first flare beam has F;z 1033 electrons/s above 10 keV. We will henceforth call astrong beam a beam of electrons with F\ strong=2.7X1096 electrons/s, and aweak beam one with Fy wear=1.010™ electrons/s (Fiweak70.0037xΕΙ strong). As

This relationship was established for electrons $>$ 50 keV. Assuming it holds for energies down to 10 keV, this means that the interplanetary counterpart of the first flare beam has $F_1\approx$ $^{34}$ electrons/s above 10 keV. We will henceforth call a beam a beam of electrons with $F_{1,strong}$ $\times 10^{36}$ electrons/s, and a beam one with $F_{1,weak}$ $\times 10^{34}$ electrons/s $F_{1,weak} \approx 0.0037 \times F_{1,strong}$ ).

trong beam is of the type usually associated with flares, whereas aweak beam is of the type usually associated with Solar Energetic Particles (SEP).

A beam is of the type usually associated with flares, whereas a beam is of the type usually associated with Solar Energetic Particles (SEP).

The HXR-producing electron beams in had a typical duration of 100 s, and this is the duration that will be used throughout this paper, unless otherwise specified.

For comparison, the 100 s typical duration leads to a total number ofweak beam electrons above 10 keV of z1x10?9 electrons, or ~9x10*4 electrons above 22 keV, hence about an order of magnitude more than has been reported so far??),, but still below the 4χ 1056 electrons above 10 keV that would have come out of the 2002 July 23 flare, assuming the 20.296 relationship holds.

For comparison, the 100 s typical duration leads to a total number of beam electrons above 10 keV of $\approx$ $\times$ $^{36}$ electrons, or $\approx$ $\times$ $^{34}$ electrons above 22 keV, hence about an order of magnitude more than has been reported so far, but still below the $\times$ $^{36}$ electrons above 10 keV that would have come out of the 2002 July 23 flare, assuming the $\approx$ relationship holds.

Asin? (and using the same assumptions), the electron spectrum changes shape as it

As in (and using the same assumptions), the electron spectrum changes shape as it

Ilielh-: that he preseut expanding Universe is ectting eradual acceleration.

$z$ that the present expanding Universe is getting gradual acceleration.

As a cause of this acceleration it is argued that a kind of exotic matter having repulsive force is responsible for speeding up the Universe some 7 billion vears ago.

As a cause of this acceleration it is argued that a kind of exotic matter having repulsive force is responsible for speeding up the Universe some $7$ billion years ago.

To nuderstaud the nature of this hypothetical energy that tends to increase the rate of expansion of the Universe several unodels have been proposed by the scieutists so far (OverduinandCooperstockL998:Starobiuskv 2000).

To understand the nature of this hypothetical energy that tends to increase the rate of expansion of the Universe several models have been proposed by the scientists so far \citep{Overduin1998,Sahni2000}.

As far as imatter content of the Universe is concerned. it is convincinely interred from distant superuovac. lavee scale structure aud CMD. that 96% of matter is hidden mass coustituted by 23© dark matter aud 73%( nuknown exotic matter known as dark energy whereas ouly [4 quass in the form of ordinary mass which is visible coutrary to the non-bhuuinous dark matter (Pretzl2001:Freemanand\leNamara2006:Wheeler2007:(απ 2007).

As far as matter content of the Universe is concerned, it is convincingly inferred from distant supernovae, large scale structure and CMB, that $96\%$ of matter is hidden mass constituted by $23\%$ dark matter and $73\%$ unknown exotic matter known as dark energy whereas only $4\%$ mass in the form of ordinary mass which is visible contrary to the non-luminous dark matter \citep{Pretzl,Freeman,Wheeler,Gribbin}.

. On the other haud. theoretically awormhole. which is sluuilar to a tunnel with two ends cach iu separate points iu spacetime or two connecting black holes. was conjectured first by Wevl (Colemanand[do-rteL985) aud ater on bv Wheeler(1957).

On the other hand, theoretically a, which is similar to a tunnel with two ends each in separate points in spacetime or two connecting black holes, was conjectured first by Weyl \citep{Coleman1985} and later on by \citet{Wheeler1957}.

.. This is essentially some kind of hypothetical topological feature of spacetime which iav acts as through spacetime.

This is essentially some kind of hypothetical topological feature of spacetime which may acts as through spacetime.

Iu principle this means that a wormhole would allow travel in time as well as in space aud can be shown explicitly how to couvert a wormbhole traversing space mto one traversing time (Morrisetal. 1988).

In principle this means that a wormhole would allow travel in time as well as in space and can be shown explicitly how to convert a wormhole traversing space into one traversing time \citep{Morris1988a}.

The possibility of traversable wormloles in general relativity was demonstrated by MorrisaudThorne(1988) which held open by a spherical shell of exotic inatter whereas quite a nunber of wormlole solutions were obtained much carlier with differeut physical motivation by other scicutists 1981).

The possibility of traversable wormholes in general relativity was demonstrated by \citet{Morris1988b} which held open by a spherical shell of exotic matter whereas quite a number of wormhole solutions were obtained much earlier with different physical motivation by other scientists \citep{Ellis1973,Bronnikov1973,Clement1984}. .

carbon chemistry is included in the numerical algorithm.

This consists of 218 reactions of 32 chemical species. which are coupled with the thermocwnamics.

This consists of 218 reactions of 32 chemical species, which are coupled with the thermodynamics.

A background. UV radiation field. which is responsible for photodissociation. is treated. through the six-ray approximation as described in 7..

A background UV radiation field, which is responsible for photodissociation, is treated through the six-ray approximation as described in \citet{Glover&MacLow07I}.

In our investigation of emission from CO molecules. we consider one snapshot of these simulations at a late time > 5 Myr. after which the simulation has reached a statistically steady state.

In our investigation of emission from CO molecules, we consider one snapshot of these simulations at a late time $>$ 5 Myr, after which the simulation has reached a statistically steady state.

The numerical modeling. deseribed above follows the combined ellects of turbulence. magnetic fields. thermodynamics. anc chemical evolution as structures— such as filaments and. dense cores twpically found in MCS forms out of the gas (see Paper Lb for more details).

The numerical modeling described above follows the combined effects of turbulence, magnetic fields, thermodynamics, and chemical evolution as structures such as filaments and dense cores typically found in MCs forms out of the gas (see Paper I for more details).

In our investigation of CO emission. emerging from the MC simulations. we consider a suit of models designed. to represent various astrophysical environments.

In our investigation of CO emission emerging from the MC simulations, we consider a suit of models designed to represent various astrophysical environments.

The relevant parameters of cach model are listed in Table 1..

The relevant parameters of each model are listed in Table \ref{exptab}.

Column l shows the name of each run.

Column 1 shows the name of each run.

The main user defined parameters are the initial density vy. metallicity Z.and background. UV. radiation field. Co. indicated. in. Columns 2-4. respectively.

The main user defined parameters are the initial density $n_0$, metallicity $Z$,and background UV radiation field $G_0$, indicated in Columns 2-4, respectively.

We assume that the clust-to-gas ratio is clirecthy proportional to the gas-phase metallicity and. do not vary these quantities independently.

We assume that the dust-to-gas ratio is directly proportional to the gas-phase metallicity and do not vary these quantities independently.

Column 5 shows the numerical resolution: as noted in Paper LH. simulations with identical initial conditions but resolutions of 256% and 1287 produce very similar The last column lists the representative environment corresponding to the simulated. cloud: a high density cloud found in the galactic center (n1000). a typical Milkv Way cloud. (1200.2).. clouds in low metallicity svstems like the LMC or SAIC (n300-Z03 and n300-Z01). a low censitv cloud in a dwarf ealaxy (n100). ancl clouds in weak ancl strong starbursts (n300-UV10 ane n300-UV100. respectively).

Column 5 shows the numerical resolution; as noted in Paper II, simulations with identical initial conditions but resolutions of $^3$ and $^3$ produce very similar The last column lists the representative environment corresponding to the simulated cloud: a high density cloud found in the galactic center (n1000), a typical Milky Way cloud \citep[n300,][]{Ferriere01}, clouds in low metallicity systems like the LMC or SMC (n300-Z03 and n300-Z01), a low density cloud in a dwarf galaxy (n100), and clouds in weak and strong starbursts (n300-UV10 and n300-UV100, respectively).

We use the racliative transfer code RADAIC-3D (Dullemond et al.

We use the radiative transfer code RADMC-3D (Dullemond et al.

in preparation) to mocel the molecular line emission of the MIID. MC models.

in preparation) to model the molecular line emission of the MHD MC models.

IUADMC-3D is a 3-climensional code that performs dust. and/or line radiative transfer on Cartesian or spherical erids (including adaptive mesh refinement).

RADMC-3D is a 3-dimensional code that performs dust and/or line radiative transfer on Cartesian or spherical grids (including adaptive mesh refinement).

In this work. since we are only interested. in CO molecular line emission along a chosen direction. we use the rav. tracing capability of IUADMC-3D. One of the primary challenges in line radiative transfer is to solve for the population levels. of the molecular (or atomic) species under consideration.

In this work, since we are only interested in CO molecular line emission along a chosen direction, we use the ray tracing capability of RADMC-3D. One of the primary challenges in line radiative transfer is to solve for the population levels of the molecular (or atomic) species under consideration.

The occupation of a given (rotational/vibrational) οποιον level of a molecule depends on the incident. radiation field. as well as the collision properties. (c.g. frequency). with other atoms or molecules. both of which act as excitation or de-excitation mechanisms.

The occupation of a given (rotational/vibrational) energy level of a molecule depends on the incident radiation field, as well as the collision properties (e.g. frequency) with other atoms or molecules, both of which act as excitation or de-excitation mechanisms.

In statistical equilibrium. the relative population of level ;. f; is governed by the equation of detailed balance: The last summation accounts for collisions. where C; is 1e collisional rate for a transition from level 7 to level j.

In statistical equilibrium, the relative population of level $i$, $f_i$, is governed by the equation of detailed balance: The last summation accounts for collisions, where $C_{ij}$ is the collisional rate for a transition from level $i$ to level $j$.

Phe collisionalrate is dependent on the rate coctlicient A';; and re density of the collisional partner no: C5;=movi.

The collisionalrate is dependent on the rate coefficient $K_{ij}$ and the density of the collisional partner $n_{col}$: $C_{ij} = n_{col} K_{ij}$.

1n p»ICs. the main collisional partner of CO isL».

In MCs, the main collisional partner of CO is.

. We use the rate coellicients for collisional excitation ancl de-exeitations of CO by tlabulatecl and. freely available from. the Leiden: clatahbase (?)..

We use the rate coefficients for collisional excitation and de-excitations of CO by tabulated and freely available from the Leiden database \citep{Schoieretal05}.

These are based on calculations by 2..

These are based on calculations by \citet{Yangetal10}.

We neglect the cHleet of collisions with partners other thanοι.

We neglect the effect of collisions with partners other than.

We justify this by noting that almost all of the CO in our simulations is found in regions of the gas that are dominated. byH».. rather than atomic hydrogen.

We justify this by noting that almost all of the CO in our simulations is found in regions of the gas that are dominated by, rather than atomic hydrogen.

The intluence of radiation on setting the level populations is captured by the first two summations in Equation 2.. which include the mean integrated: intensity Ji; of the radiation field in the line corresponding to the transition [rom i to jf.

The influence of radiation on setting the level populations is captured by the first two summations in Equation \ref{poplevel}, , which include the mean integrated intensity $\bar{J}_{ij}$ of the radiation field in the line corresponding to the transition from $i$ to $j$.

The constants are ;1;. the Einstein coefficient for spontaneous emission for a transition [rom level / to level j. ει. the Einstein. cocllicient for stipulated. emission. from / to. level j. anc Dj;. the corresponding coellicient for absorption (also given by the Leiden database).

The constants are $A_{ij}$, the Einstein coefficient for spontaneous emission for a transition from level $i$ to level $j$ , $B_{ij}$, the Einstein coefficient for stimulated emission from $i$ to level $j$, and $B_{ji}$ , the corresponding coefficient for absorption (also given by the Leiden database).

Equation 2. is coupled withthe equation of racdative transfer where J, is the specific intensity. 5, the source function. ancl 7, is the optical depth.

Equation \ref{poplevel} is coupled withthe equation of radiative transfer where $I_\nu$ is the specific intensity, $S_\nu$ the source function, and $\tau_\nu$ is the optical depth.

Phe coupling between Equations 2 and 3. occurs through the dependence. of the source function CS,= 5;;) on the relative population levels: as well as the dependence of the ο f: where the integral is taken over all solid angles ©.

The coupling between Equations \ref{poplevel} and \ref{rteqn} occurs through the dependence of the source function $S_\nu = S_{ij}$ ) on the relative population levels: as well as the dependence of the $\bar{J}$ on $I$: where the integral is taken over all solid angles $\Omega$.

The normalized profile function ὧν determines the emission and absorbtion probability of a photon with frequency ο. due to a line with rest frequency £;;.

The normalized profile function $\phi_{ij}$ determines the emission and absorbtion probability of a photon with frequency $\nu$ due to a line with rest frequency $\nu_{ij}$ .

For a photon propagatingin a direction & through a medium with velocity v. where ce ids the light) speed.

For a photon propagatingin a direction ${\bf \hat{n}}$ through a medium with velocity ${\bf v}$, where $c$ is the light speed.

The thermal and microturbulent broadening ofthe line is accounted for through

follows: where the subseripted variables represent the actual values independent of measurement uucertaimties. aud the non-subseripted variables represent the observed values imcludiug measurement uncertainties.

follows: where the subscripted variables represent the actual values independent of measurement uncertainties, and the non-subscripted variables represent the observed values including measurement uncertainties.

Eq.

6 allows us to split the dependence of sin; mto two parts: the actual value of sin’ (the term outside the brackets) aud the contributions of 1ucasureimoent wncertaiuties (the term inside the brackets).

\ref{sinim} allows us to split the dependence of $\sin i$ into two parts: the actual value of $\sin i$ (the term outside the brackets) and the contributions of measurement uncertainties (the term inside the brackets).

The (ini), distribution is generated from Eq.

The $(\sin i)_{m}$ distribution is generated from Eq.

6 sing a Monte Carlo routine.

\ref{sinim} using a Monte Carlo routine.

Each term of the form AXXu (where represcutsany of the variables P. ¢sin/. Toyg ov L) is calculated Dy drawing raucdomly frou +he appropriate error distribution for our dataset. as escribed iu 6 1.3..

Each term of the form $X/X_{0}$ (where $X$ representsany of the variables $P$, $v \sin i$, $T_{eff}$ or $L$ ) is calculated by drawing randomly from the appropriate error distribution for our dataset, as described in $\S$ \ref{error_distribution}.

This process assumes that fractional errors in csiu. Toy; aud £ are independent of the values of these variables.

This process assumes that fractional errors in $v \sin i$, $T_{eff}$ and $L$ are independent of the values of these variables.

While this assumption is somewhat questionable. the deviation from the true error distribution is likely small

While this assumption is somewhat questionable, the deviation from the true error distribution is likely small.