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Figure 11 compares the SPH and the rpSPH solution again for dv=0.01.
Figure \ref{fig:mm-RT} compares the SPH and the rpSPH solution again for $\delta v=0.01$.
Instead of showing the density field we show the particles painted by circles and colored by their density.
Instead of showing the density field we show the particles painted by circles and colored by their density.
This gives us an opportunity to see thatrpSPH does not show any clumping instability while it is severe for SPH.
This gives us an opportunity to see that does not show any clumping instability while it is severe for SPH.
In this run we only use 100 by 200 particles demonstrating thatrpSPH handles the Rayleigh-Taylor problem very well at small initial perturbations and low particle numbers.
In this run we only use 100 by 200 particles demonstrating that handles the Rayleigh–Taylor problem very well at small initial perturbations and low particle numbers.
The Sedov-Taylor blast wave above was also carried out with a staggered grid of particles of varying mass and retains a nice spherical shape despite the multiple squares
The Sedov-Taylor blast wave above was also carried out with a staggered grid of particles of varying mass and retains a nice spherical shape despite the multiple squares
assume that the distance of this source is the same as for the one associated with CCMa.
assume that the distance of this source is the same as for the one associated with CMa.
Lightcurves were extracted and searched for variability with a maximum likelihood method that divides the sequence of photons in intervals of constant signal (see7?) and, independently, with the Kolmogorov-Smirnov (KS) test.
Lightcurves were extracted and searched for variability with a maximum likelihood method that divides the sequence of photons in intervals of constant signal \citep[see ][]{Stelzer07.1} and, independently, with the Kolmogorov-Smirnov (KS) test.
According to this analysis both sources are not variable within the individual exposures.
According to this analysis both sources are not variable within the individual exposures.
The significance level of the KS statistic for each source is given in the last column of Table 2 (?)..
The significance level of the KS statistic for each source is given in the last column of Table \ref{tab:xrayparams} \citep{Kastner06.1}.
? ? (?).. (e.g.?)..
\cite{Audard05.2} \cite{Audard05.2} \citep{Lorenzetti06.1}. \citep[e.g.][]{Schmitt90.1}.
? ? (?) (?) (?),, (?).. (seesummaryby
\cite{Skinner09.1} \cite{Skinner09.1} \citep{Poetzel89.1} \citep{Velazquez01.1} \citep{zel66}, \citep{Poetzel89.1}. \citep[see summary by][]{Bonito07.1}.
In (his section. we show our results lor incompressible Riemann S-tvpe ellipsoids aud (heir quasi-equilibrium. compressible counterparts.
In this section, we show our results for incompressible Riemann S-type ellipsoids and their quasi-equilibrium, compressible counterparts.
Since (he available parameter space occupies a large portion of Figure 1.. we choose to build models only along the vertical dashed lines. which largely represent most of the configurations.
Since the available parameter space occupies a large portion of Figure \ref{triaxial}, we choose to build models only along the vertical dashed lines, which largely represent most of the configurations.
Our models are constructed on a evlindrieal grid with a resolution of 66x102128 in the a (evlindical radius). 2 (vertical). and © (azimuthal) directions. respectively.
Our models are constructed on a cylindrical grid with a resolution of $66 \times 102 \times 128$ in the $\varpi$ (cylindrical radius), $z$ (vertical), and $\phi$ (azimuthal) directions, respectively.
Following llachisu(1986a).. we adopt a set of polvtropie units in which the gravitational constant C. the radius of the entire grid ze. and maximum density Pumas are all set to 1.
Following \cite{H86A}, we adopt a set of polytropic units in which the gravitational constant $G$ , the radius of the entire grid $\varpi_{\mathrm{grid}}$, and maximum density $\rho_{\mathrm{max}}$ are all set to 1.
For all of our models. we set (he semiaxis a to 0.619.
For all of our models, we set the semiaxis $a$ to $0.619$.
We choose to present our results in such a wav that readers can readily. normalize our data to any unit svstem (μον are familiar with for the purpose of comparison.
We choose to present our results in such a way that readers can readily normalize our data to any unit system they are familiar with for the purpose of comparison.
Table 1 shows the results for direct configurations of incompressible (n= 0) Riemann S-type ellipsoids.
Table \ref{n0} shows the results for direct configurations of incompressible $n=0$ ) Riemann S-type ellipsoids.
Tables 2.. 3..2 and 4 show the same results but for compressible counterparts of Riemann ellipsoids with »—0.5. »=1.0. and η=1.5. respectively.
Tables \ref{n05}, \ref{n10}, , and \ref{n15} show the same results but for compressible counterparts of Riemann ellipsoids with $n=0.5$ , $n=1.0$, and $n=1.5$ , respectively.
Tables 5.. 5..6.. and 7 show results for adjoint configurations with a=0.0.7 =0.5- and η= 1.0. respectively.
Tables \ref{n0a}, \ref{n05a}, and \ref{n10a} show results for adjoint configurations with $n=0.0$ , $n=0.5$ and $n=1.0$ , respectively.
In these tables. 7 is the rotational energy of the svstem. Af; is the total mass. «μι is the total angular momentum. fyc 15 Lhe mean density. WW. is the gravitational potential energy. and 5 is the thermal energy.
In these tables, $T$ is the rotational energy of the system, $M_{\mathrm{tot}}$ is the total mass, $J_{\mathrm{tot}}$ is the total angular momentum, $\rho_{\mathrm{mean}}$ is the mean density, $W$ is the gravitational potential energy, and $S$ is the thermal energy.
The quantity 654-7)/|W'| measures how well our models are in virialequilibrium: ideally. this ratio should have a value of 0.5.
The quantity $(S+T)/|W|$ measures how well our models are in virialequilibrium; ideally, this ratio should have a value of 0.5.
All of our models have values that are very. close to 0.5.5 especially for compressible configurations.
All of our models have values that are very close to 0.5, especially for compressible configurations.
In. Table 1.. the parameters w, and A, are analvlically computed results for w and A. respectively.
In Table \ref{n0}, the parameters $\omega_{\mathrm{a}}$ and $\lambda_{\mathrm{a}}$ are analytically computed results for $\omega$ and $\lambda$, respectively.
several properties of our models are worth discussing.
Several properties of our models are worth discussing.
First. for direct configurations wilh a fixed value of 5/a. as one proceeds [rom larger values of e/e to smaller values. A starts from a positive value. then continuously decreases: it reaches zero when (he rigidly rotating Jacobi sequence is hit. and then becomes negative aller passing the Jacobi sequence.
First, for direct configurations with a fixed value of $b/a$, as one proceeds from larger values of $c/a$ to smaller values, $\lambda$ starts from a positive value, then continuously decreases; it reaches zero when the rigidly rotating Jacobi sequence is hit, and then becomes negative after passing the Jacobi sequence.
The parameter / also switches sien when crossing the Jacobi/Dedekind sequences.
The parameter $f$ also switches sign when crossing the Jacobi/Dedekind sequences.
For adjoint configurations. a similar behavior is observed lor w. while / approaches dox around the Dedekind sequence because w=0.
For adjoint configurations, a similar behavior is observed for $\omega$, while $f$ approaches $\pm \infty$ around the Dedekind sequence because $\omega=0$.
second. in the parameter space above the Jacobi/Dedekind sequence where /« 0.27 is positive for direct configurations. and negative for adjoint configurations. which reflects the fact that the Jacobi mode in Maclaurin spheroids is the "forward moving wave butthe Dedekind mode is the "backwardmoving” wave.
Second, in the parameter space above the Jacobi/Dedekind sequence where $f<0$, $\omega$ is positive for direct configurations, and negative for adjoint configurations, which reflects the fact that the Jacobi mode in Maclaurin spheroids is the “forward moving” wave butthe Dedekind mode is the “backwardmoving” wave.
This alsoimpliesthat in (headjointconfigurations with f/< 0. the ellipsoidal pattern is moving in a direction that is opposite to the overall rotation!
This alsoimpliesthat in theadjointconfigurations with $f<0$ , the ellipsoidal pattern is moving in a direction that is opposite to the overall rotation!
Furthermore. when the critical Jacobi/Dedekind sequence is passed. /
Furthermore, when the critical Jacobi/Dedekind sequence is passed, $f$
Theoretically. the dominant and laregcly successful paraciem for understanding and modelling the universe is based on the theory of Cold. Dark Matter (CDM).
Theoretically, the dominant and largely successful paradigm for understanding and modelling the universe is based on the theory of Cold Dark Matter (CDM).
In this scenario. the first objects that form in the universe are low mass haloes that subsequcnthy merge. together to form. more massive structures as time progresses (e.g. 1978)).
In this scenario, the first objects that form in the universe are low mass haloes that subsequently merge together to form more massive structures as time progresses (e.g., ).
Phe hierarchical mass assembly by merging is in [act the cornerstone of CDM-based simulations and can be empirically tested. for example. by investigating the role of mergers in the formation and evolution of galaxies (e.g. Ixaulfimann 10921: Berricretal.2006: Wetzel.Cohn&White 2008)).
The hierarchical mass assembly by merging is in fact the cornerstone of CDM-based simulations and can be empirically tested, for example, by investigating the role of mergers in the formation and evolution of galaxies (e.g. \citealt{kauffmann1993}; ; \citealt{berrier2006}; \citealt{wetzel2008a}) ).
Galaxy formation and evolution is certainly driven in part bv galaxy mergers.
Galaxy formation and evolution is certainly driven in part by galaxy mergers.
There is no doubt that in the local universe there are examples of ealaxies merging with each other (e.e.. DeProprisetal.20072). which eventually
There is no doubt that in the local universe there are examples of galaxies merging with each other (e.g., \citealt{depropris2007})), which eventually
observed for individual stars in these clusters which suggests that these stars are probably embedded in dense structures, which explains the larger values of Ay estimated in the previous works, especially in the case of individual star analyses.
observed for individual stars in these clusters which suggests that these stars are probably embedded in dense structures, which explains the larger values of $A_V$ estimated in the previous works, especially in the case of individual star analyses.
Figs. 2,,
Figs. \ref{fig:02}, ,
3 and 11,, together with the age derived for the Sh2-235 Cluster (z5 Myr), indicate that the O star (=1 Myr) is not a member of this cluster.
\ref{fig:03} and \ref{fig:11}, together with the age derived for the Sh2-235 Cluster $\approx5$ Myr), indicate that the O star $\approx1$ Myr) is not a member of this cluster.
A possible explanation for the presence of the O star near this cluster is that winds from Sh2-235 Cluster, colliding with the surrounding gas, might have originated this star, CBB 2 and other clusters in the neighborhood.
A possible explanation for the presence of the O star near this cluster is that winds from Sh2-235 Cluster, colliding with the surrounding gas, might have originated this star, CBB 2 and other clusters in the neighborhood.
Assuming vzz20kms for the dense gas involved in the expansion (Kirsanovaet!al.2008),, the $h2-235 Cluster might be responsible for sequential star formation across a region of radius ~10 pc (Fig. 11)),
Assuming $v\approx20\,km\,s^{-1}$ for the dense gas involved in the expansion \citep{Kirsanova08}, the Sh2-235 Cluster might be responsible for sequential star formation across a region of radius $\approx10$ pc (Fig. \ref{fig:11}) ),
which includes also the clusters in a row in the southwest direction.
which includes also the clusters in a row in the southwest direction.
Sequential star formation is possible also for the pairs G173 and CBB 1, and Sh2-233SE Cluster and PCS 2.
Sequential star formation is possible also for the pairs G173 and CBB 1, and Sh2-233SE Cluster and PCS 2.
Recently, Dewangan&Anandarao(2011) point out that star formation continues to occur in the Sh2-235 complex, mainly within the ECs.
Recently, \citet{Dewangan11} point out that star formation continues to occur in the Sh2-235 complex, mainly within the ECs.
They identified 86 Class 0/I and 144 Class II YSOs, which reinforce the possibility of a sequential star formation event.
They identified 86 Class 0/I and 144 Class II YSOs, which reinforce the possibility of a sequential star formation event.
Colour-colour diagrams are useful tools to investigate the nature of ECs.
Colour-colour diagrams are useful tools to investigate the nature of ECs.
We show in Fig.
We show in Fig.
9 the decontaminated near-IR colour-colour diagram (J—K.)x(H of the member stars, together with PMS tracks (Siess,Dufour&Fores-tini 2000),, set with the reddening values derived above, to estimate ages.
\ref{fig:09} the decontaminated near-IR colour-colour diagram $(J-K_s)\times(H-K_s)$ of the member stars, together with PMS tracks \citep{Siess00}, set with the reddening values derived above, to estimate ages.
As a consequence of the presence of the PMS stars in the cluster, it is expected that some stars present near-IR excess.
As a consequence of the presence of the PMS stars in the cluster, it is expected that some stars present near-IR excess.
As expected from the CMDs of ECs (Figs.
As expected from the CMDs of ECs (Figs.
to 8)), a significant fraction of the stars appears to be very reddened.
\ref{fig:04} to \ref{fig:08}) ), a significant fraction of the stars appears to be very reddened.
Most stars, specially MS stars, have (H—Ks) colours close to the isochrone, within the uncertainties.
Most stars, specially MS stars, have $(H-K_s)$ colours close to the isochrone, within the uncertainties.
Besides, most of the very red PMS stars are displaced parallel to the respective reddening vectors.
Besides, most of the very red PMS stars are displaced parallel to the respective reddening vectors.
However, a significant fraction appears to present an abnormal excess in (J—K;) and (Η—Ks), especially Sh2-235B, which may come from PMS stars still bearing circumstellar discs.
However, a significant fraction appears to present an abnormal excess in $(J-K_s)$ and $(H-K_s)$, especially Sh2-235B, which may come from PMS stars still bearing circumstellar discs.
MS stars lie on the blue side of the diagrams and there occurs a gap between MS and PMS stars in the CMDs.
MS stars lie on the blue side of the diagrams and there occurs a gap between MS and PMS stars in the CMDs.
The structure of the ECs is analysed bymeans of the stellar radial density profile (RDP), defined as the
The structure of the ECs is analysed bymeans of the stellar radial density profile (RDP), defined as the
surface density is proportional to the epicyelic leqenev,
surface density is proportional to the epicyclic frequency.
I&oviuua&Ostriker(2000). state that he eu]ourical result tha Ryo Is proportional to he uecan midplane pressure of the ISALD implies hat the epicevclic freeποιον, the gas surface density. and the star oration rate per uni voluue are interdepceneeut. most probably due Oa eaOs:axv evolution wih the Toonire parameter Qcose to unitv.
\citet{KoyamaOstriker} state that the empirical result that $R_{\rm mol}$ is proportional to the mean midplane pressure of the ISM implies that the epicyclic frequency, the gas surface density, and the star formation rate per unit volume are interdependent, most probably due to a galaxy evolution with the Toomre parameter $Q$ close to unity.
If eravitational instability of a chuupy aid turbulen eas disk is taken iuto accottr .tur»ileuce drives he disc to a regime of trausition between iustailitv at simall scales ane stabilitv iu he classical seuse (Toole Q~ 1: Romeoetal. (2010))).
If gravitational instability of a clumpy and turbulent gas disk is taken into account, turbulence drives the disc to a regime of transition between instability at small scales and stability in the classical sense (Toomre $Q \sim 1$ ; \citet{Romeo}) ).
Most receutlv. παλιοί&Burkert(2010) have developed an analytical model for the evolution of a thin disk of seas aid stars with zu arbitrary rotation curve that is kept in a state of mareinal gravitational instability (Q~ 1) and enerev equilibrium due to the balance between enerev released by accretion and cherey lost duc to decay of turbuleice;
Most recently, \citet{KrumholzBurkert} have developed an analytical model for the evolution of a thin disk of gas and stars with an arbitrary rotation curve that is kept in a state of marginal gravitational instability $Q \sim 1$ ) and energy equilibrium due to the balance between energy released by accretion and energy lost due to decay of turbulence.
Equilibrnui disks of this kind have beeu investigate by Volliuer&Beckert (
Equilibrium disks of this kind have been investigated by \citet{VollmerBeckert}.
20023.. Katuholz&Burkert(2010) showed that disks iuitially out of equilixiu evolve iuto it on tinescaCs ΟΟΙΙΤdle to t16 orbital period if the externa eas accretiou rate is high.
\citet{KrumholzBurkert} showed that disks initially out of equilibrium evolve into it on timescales comparable to the orbital period if the external gas accretion rate is high.
lu this article we lise the analvtical meocels of Vollner&Beckert(2003.hereafterVDO3) to ostnuate the radial mass accretion rate of a saiple of nearby spira ealaxies.
In this article we use the analytical models of \citet[][hereafter VB03]{Vollmer} to estimate the radial mass accretion rate of a sample of nearby spiral galaxies.
The VDU3 model reats galaxies as οπής accretion disks using a simplified description of turbulence driveu by supenova (SN) explosions.
The VB03 model treats galaxies as clumpy accretion disks using a simplified description of turbulence driven by supernova (SN) explosions.
Because we focus O1) LOCchne the ealactic disk within the optical radius. we neglect eravitational lustahilities as energv source for turbulence (seeAgertzctal.Ww 00).
Because we focus on modeling the galactic disk within the optical radius, we neglect gravitational instabilities as energy source for turbulence \citep[see][]{Agertz}.
A cas disk witlkmit star formation might eenerate turbulence via graviational iustabilitios. out oncο stars form. we asste that SN dominate euergv injection.
A gas disk without star formation might generate turbulence via gravitational instabilities, but once stars form, we assume that SN dominate energy injection.
The formalisi ofour equilibrium uodel is close to that of Kruuholz&Burkert(20) 0).
The formalism of our equilibrium model is close to that of \citet{KrumholzBurkert}.
. The inodel raturally links the physical ILOvertices of the ealac‘tic eas disk (9rface deusity. nolecular fraction. star orlation rate) to the widplane pressure wich mainly depends ou the stelar surface densiY. spievclic frequency. the Toonre parameter. :uid the seas mass accretion rate (similutoIxwana&Ostriker2009).
The model naturally links the physical properties of the galactic gas disk (surface density, molecular fraction, star formation rate) to the midplane pressure which mainly depends on the stellar surface density, epicyclic frequency, the Toomre parameter, and the gas mass accretion rate \citep[similar to][]{KoyamaOstriker}.
Furherimore. we assuue the classical scale-indepeudeut 'Toonure stability criterion.
Furthermore, we assume the classical scale-independent Toomre stability criterion.
We compare these models to multiwavelength observations of I8 spiral galaxies youn the THINGS siuuple (Walteretal.2008). compiled by Leroyetal.(2008).
We compare these models to multiwavelength observations of 18 spiral galaxies from the THINGS sample \citep{Walter} compiled by \citet{Leroy}.
. From the comparison. we estimate the radial mass accretion rate of cach galaxy.
From the comparison, we estimate the radial mass accretion rate of each galaxy.
The VDOS model considers the easons disk of a ealaxy as a single turbulent imedimn.
The VB03 model considers the gas disk of a galaxy as a single turbulent medium.
The dissipation timescale of turbulent kinetic CLOYSVo on galactic scales is about the crossing tie (Ehucercen2000).. so that for a typica drivius scale leneth of ~1X) pc of the turbulent flow the dissipation time τι~10 Myv.
The dissipation timescale of turbulent kinetic energy on galactic scales is about the crossing time \citep{Elmegreen2000}, so that for a typical driving scale length of $\sim 100$ pc of the turbulent flow the dissipation time $\tau_{\rm d} \sim 10$ Myr.
Therefore in order to luaintain turbulence. an efficient. conutiuuous. daiving mechanisin is needed.
Therefore in order to maintain turbulence, an efficient, continuous, driving mechanism is needed.
Possible caucdidates for such a driving uechauisui are: Of these only SN. explosions can balance the enerev loss due to turbulent energy dissipation if the driving leugth scale is ~100 pc (MacLow&]xXlesseu2001) aud the star Orialon rate ds = AL vrtkpe 7 (Agertz¢al.209)..
Possible candidates for such a driving mechanism are: Of these only SN explosions can balance the energy loss due to turbulent energy dissipation if the driving length scale is $\sim 100$ pc \citep{MacLow} and the star formation rate is $\geq 10^{-3}$ $_{\odot}$ $^{-1}$ $^{-2}$ \citep{Agertz}.
. Th cases where the driving leugth scale is oft1e order of he disk thickness (~500 pc). the energy input cπο to eravitational instabilities can maintain turbilence in the interstellar medi (ISAT) (Volliiuer&Beck-ert2002:Ixiuubolz&Burkert 2010).
In cases where the driving length scale is of the order of the disk thickness $\sim 500$ pc), the energy input due to gravitational instabilities can maintain turbulence in the interstellar medium (ISM) \citep{VollmerBeckert,KrumholzBurkert}.
. The VDO03 model aud this paper consider only turbulence driven bySN.
The VB03 model and this paper consider only turbulence driven bySN.
Iu the VDU3 inodel. SN-driven turbulence sets the disk structure and the disk structure
In the VB03 model, SN-driven turbulence sets the disk structure and the disk structure
GBOS that To,= Τοπ.
GB05 that $T_{0,{\rm E}}=T$ ]).
Then &x can be determined from Eq. (11).
Then $\theta x^2$ can be determined from Eq. \ref{t22}) ),
where ΤΗΝ=TCHR.Toi. Ty.= Tor).
where $T(\ion{H}{i})=T(\ion{H}{i})(t^2_{\rm E},T_{0,{\rm E}})$, $T_{\rm h}=T([\ion{O}{iii}])(t^2_{\rm E},T_{0,{\rm E}})$ .
Although the values of T(O impar.Toi) thus obtained are slightly higher than the actual values deduced from observations (see Table 1)). the resulting &3 are hardly affected.
Although the values of $T$ $t^2_{\rm E}$ $T_{0,{\rm E}}$ ) thus obtained are slightly higher than the actual values deduced from observations (see Table \ref{est}) ), the resulting $\theta x^2$ are hardly affected.
In Table | we compare our &x values to those of GBOS (given in parentheses); for low values of #17 differences of up to a factor of a hundred are found.
In Table \ref{est} we compare our $\theta x^2$ values to those of GB05 (given in parentheses); for low values of $\theta x^2$ differences of up to a factor of a hundred are found.
It can easily be seen that the discrepancies increase with decreasing temperature of the cold gas. as suggested by Fig. 1..
It can easily be seen that the discrepancies increase with decreasing temperature of the cold gas, as suggested by Fig. \ref{tsq}. .
For 7,= 100KK. our derived values of #17 are very low. suggesting that the values of r reported by Esteban et al. (2002))
For $T_{\rm c}=100$ K, our derived values of $\theta x^2$ are very low, suggesting that the values of $t^2$ reported by Esteban et al. \cite{e02}) )
can be explained by the existence of a very small amount of cold gas.
can be explained by the existence of a very small amount of cold gas.
Table | also gives 7 and Ty values derived from the Eqs. (12))
Table \ref{est} also gives $t^2$ and $T_0$ values derived from the Eqs. \ref{t3}) )
and (13).
and \ref{t4}) ).
As the Table shows. the real (£ values are lower when Τι«T, than those derived from the empirical method.
As the Table shows, the real $t^2$ values are lower when $T_{\rm c} \ll T_0$ than those derived from the empirical method.
As a result. values of the cosmic ray ionization rate. £. derived by GBOS have been grossly overestimated |[c.f.
As a result, values of the cosmic ray ionization rate, $\zeta$, derived by GB05 have been grossly overestimated [c.f.
their Eq. (
their Eq. (
17)].
17)].
Our conclusion is consistent with the range of values inferred for the Orion nebula from Gamma ray observations.
Our conclusion is consistent with the range of values inferred for the Orion nebula from Gamma ray observations.
We have studied the relationship between values of t7 predicted by a two-phase model and those derived empirically from observations (empirical method).
We have studied the relationship between values of $t^2$ predicted by a two-phase model and those derived empirically from observations (empirical method).
Our results show that the existence of extremely cold gas within regions may lead to overestimated /£ calculated from empirically determined T(Oiup and T(H1).
Our results show that the existence of extremely cold gas within regions may lead to overestimated $t^2$ calculated from empirically determined $T([\ion{O}{iii}])$ and $T(\ion{H}{i})$.
We stress that care should be taken when using the two-phase model to study large temperature fluctuations of regions.
We stress that care should be taken when using the two-phase model to study large temperature fluctuations of regions.
In this model. CELs are hardly produced by the cold gas. which on the other hand makes a large contribution to the flux at the Balmer jump. due to the TO. dependence of /(Bal.3646).
In this model, CELs are hardly produced by the cold gas, which on the other hand makes a large contribution to the flux at the Balmer jump, due to the $T_{\rm e}^{-3/2}$ dependence of $I({\rm Bal}, 3646)$.
Accordingly. the existence of a very small amount of cold material may lead to a large discrepancy between 7Z([Oi]) and T(H1.
Accordingly, the existence of a very small amount of cold material may lead to a large discrepancy between $T([\ion{O}{iii}])$ and $T(\ion{H}{i})$.
In other words. in spite of its small mass. the existence of extremely cold material ean reproduce apparently large f (as derived from the empirical method). much larger than the actual value [as defined by Eq. (
In other words, in spite of its small mass, the existence of extremely cold material can reproduce apparently large $t^2$ (as derived from the empirical method), much larger than the actual value [as defined by Eq. (
2)].
2)].