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MSI is the only massive galaxy of its group. surrounded by several small galaxies.
M81 is the only massive galaxy of its group, surrounded by several small galaxies.
The interaction of M8] with the dwarf galaxies of its group probably steepens the gradient of the major member due to the effect of stripping gas from the external regions of the major companion. while interaction of galaxies with more or less the same mass would redistribute the gas in both galaxies. and thus flatten the gradient.
The interaction of M81 with the dwarf galaxies of its group probably steepens the gradient of the major member due to the effect of stripping gas from the external regions of the major companion, while interaction of galaxies with more or less the same mass would redistribute the gas in both galaxies, and thus flatten the gradient.
The chemical evolution models of Valle et al. (
The chemical evolution models of Valle et al. (
2005) consider the effects of gas stripping due to galaxy encounters on the star formation rate and the evolution of the metallicity.
2005) consider the effects of gas stripping due to galaxy encounters on the star formation rate and the evolution of the metallicity.
They found that. for a stripping occurring. 1-3 Gyr after the formation of the galaxy and removing 97% of the gas. the region affected by the gas removal has a SFR almost a factor of 10 lower than in the model without stripping and the relative metallicity is then reduced by about 40%.
They found that, for a stripping occurring 1-3 Gyr after the formation of the galaxy and removing $\%$ of the gas, the region affected by the gas removal has a SFR almost a factor of 10 lower than in the model without stripping and the relative metallicity is then reduced by about $\%$.
The metallicity reduction is not strongly dependent on the time and duration of the stripping episode. but is quite sensitive to the relative amount of gas removed from the region.
The metallicity reduction is not strongly dependent on the time and duration of the stripping episode, but is quite sensitive to the relative amount of gas removed from the region.
This effect should be more pronounced in the outer than the inner galactic regions. due to the proximity of the interacting galaxies. and it might explain why M81 has steeper metallicity gradients than the Galaxy.
This effect should be more pronounced in the outer than the inner galactic regions, due to the proximity of the interacting galaxies, and it might explain why M81 has steeper metallicity gradients than the Galaxy.
Unfortunately. the models by Valle et al. (
Unfortunately, the models by Valle et al. (
2005) are limited to a single radial region. thus this conclusion ts of qualitative nature.
2005) are limited to a single radial region, thus this conclusion is of qualitative nature.
A radially-resolved chemical evolution modeling taking into account the effects of stripping would be necessary to determine the effect of tidal interaction on the gradient. and also to compare with other results.
A radially-resolved chemical evolution modeling taking into account the effects of stripping would be necessary to determine the effect of tidal interaction on the gradient, and also to compare with other results.
Hectospec/MMT spectroscopy of a sizable sample of PN and rregions in the nearby M81 galaxy has proven very efficient to find chemistry of the young and old stellar populations. and to pin point the radial metallicity gradients.
Hectospec/MMT spectroscopy of a sizable sample of PN and regions in the nearby M81 galaxy has proven very efficient to find chemistry of the young and old stellar populations, and to pin point the radial metallicity gradients.
We were able to detect the diagnostic lines for plasma and abundance analysis in 19 PNe and I4 rregions.
We were able to detect the diagnostic lines for plasma and abundance analysis in 19 PNe and 14 regions.
Their analysis indicates that the galaxy is clearly chemically enriched. with <O/HSyiiws./€Ῥννς 5. from MMT spectra where PNe and rregions were simultaneously acquired.
Their analysis indicates that the galaxy is clearly chemically enriched, with $\rm{<O/H>_{\hii\ reg.}/<O/H>_{PN}}$ =1.8, from MMT spectra where PNe and regions were simultaneously acquired.
We also found that there is a noticeable PN metallicity gradient in oxygen. with Alog(O/H)/ARGz-0.055 dex ΞšΟΞΏΟ„, and that neon and sulfur gradient slopes are within 15% of the oxygen one.
We also found that there is a noticeable PN metallicity gradient in oxygen, with $\Delta{\rm log(O/H)}/\Delta{\rm R_G}$ =-0.055 dex $^{-1}$, and that neon and sulfur gradient slopes are within $\%$ of the oxygen one.
The MMT sample of rregions have limited galactocentric distribution. thus they are insufficient probes of the metallicity gradient.
The MMT sample of regions have limited galactocentric distribution, thus they are insufficient probes of the metallicity gradient.
The gradient slope from the combined MMT and GS87 rregion samples is steeper (-0.093 dex kpe7!) than that of the PNe. possibly indicating an evolution of the radial metallicity gradients with time: older stellar population show shallower gradients. thus gradients are steepening with the time since galaxy formation.
The gradient slope from the combined MMT and GS87 region samples is steeper (-0.093 dex $^{-1}$ ) than that of the PNe, possibly indicating an evolution of the radial metallicity gradients with time: older stellar population show shallower gradients, thus gradients are steepening with the time since galaxy formation.
These results have been compared to their homologous for the Milky Way and M33. where similar (yet less marked) gradient steepening ts inferred.
These results have been compared to their homologous for the Milky Way and M33, where similar (yet less marked) gradient steepening is inferred.
We plan to
We plan to
seelent of the electron spectrun taking iuto account the anisotropic radiation pattern of the IC compoucut.
segment of the electron spectrum, taking into account the anisotropic radiation pattern of the IC component.
Secoud. we compute the expected value of R from the ratio of the cucrey densitics of the CMD to that in the magnetic field (both in the jet frame) (eq. A22)).
Second, we compute the expected value of R from the ratio of the energy densities of the CMB to that in the magnetic field (both in the jet frame) (eq. \ref{eq:rexp}) ).
Equating these two expressions. we are able to solve for the beaming parameters which satisfy the equality (eq. Γ€23)).
Equating these two expressions, we are able to solve for the beaming parameters which satisfy the equality (eq. \ref{eq:result}) ).
Since the jet parameters cuter the R equations in Leher complex wavs because of the anisotropic nature of the IC enussion. a nunerieald method is used.
Since the jet parameters enter the R equations in rather complex ways because of the anisotropic nature of the IC emission, a numerical method is used.
This is demonstrated in fig.
This is demonstrated in fig.
3. aud we obtain a result consistent with that of Celotti et al. (
\ref{fig:method} and we obtain a result consistent with that of Celotti et al. (
2001) for PKSO0637.
2001) for PKS0637.
We use the ollowius notation: woe prime all quautities iu the jet frame and. im cases where subieuities could arise. we characterize jet paraincters bv the subscript "j| aud electron paranieters by the subscript "e.
We use the following notation: we prime all quantities in the jet frame and, in cases where ambiguities could arise, we characterize jet parameters by the subscript β€œj” and electron parameters by the subscript β€œe”.
Tn this section. we provide some of the kev svuchrotron parameters aud beaming descriptors for a few knots in radio jets.
In this section, we provide some of the key synchrotron parameters and beaming descriptors for a few knots in radio jets.
For the svuchrotron parameters. we usc the standard expressions (6.8. DPacholczyk. 1970) with observables transformed. back to the jet frame.
For the synchrotron parameters, we use the standard expressions (e.g. Pacholczyk, 1970) with observables transformed back to the jet frame.
For the beaming parameters. our solution to eq.
For the beaming parameters, our solution to eq.
A23. requires ouly 1 auunubers: Table 1 eives the results and it can be seen that the beaming paraueters range from quite modest values (e.g. PISSLL27) to rather unbelievable extremes (3€ 120).
\ref{eq:result} requires only 4 numbers: Table \ref{tab:results} gives the results and it can be seen that the beaming parameters range from quite modest values (e.g. PKS1127) to rather unbelievable extremes (3C 120).
We have plotted the key results iu fig.
We have plotted the key results in fig.
Lo which is a represcutation of the beaming paraueters as a fiction of the observalles (eq. Γ€21)).
\ref{fig:results} which is a representation of the beaming parameters as a function of the observables (eq. \ref{eq:resulta}) ).
Iu this section. we deal with the conflicting evidence for seneral beaming nodels aud for svachrotron models.
In this section, we deal with the conflicting evidence for general beaming models and for synchrotron models.
Ou the oue hid. some sort of beanung appears to be required by the observation that all of the known jet sources (excluding of course the SSC terminal hotspots) produce X-ray Cluission ou only one side. ane that is the side which has the only or dominaut radio jet and for which relativistic effects have been demonstrated (usually on VLBI scales).
On the one hand, some sort of beaming appears to be required by the observation that all of the known jet sources (excluding of course the SSC terminal hotspots) produce X-ray emission on only one side, and that is the side which has the only or dominant radio jet and for which relativistic effects have been demonstrated (usually on VLBI scales).
Ou the other haud. for knots such as AL/3C273 or B/3C390.3. the observed X-ray iutensitv is accommodated by an extension of the power law connecting the radio and optical Ξ½ΞΏ, the svuchrotrou spectrin).
On the other hand, for knots such as A1/3C273 or B/3C390.3, the observed X-ray intensity is accommodated by an extension of the power law connecting the radio and optical (i.e. the synchrotron spectrum).
If
If
Siuce. both. (b,1&) aud the density Nfp. are monotonically β‰Όβˆβˆ–β†ΈβŠ³β†₯β‹…β†Έβˆ–β‹œβ†§β†΄βˆ–β†΄β†•βˆβˆΆβ†΄βˆ™βŠΎβ†•β‹Ÿβˆβˆβ†ΈβŠ³β†‘β†•βˆͺβˆβ†΄βˆ–β†΄β†•β‹Ÿβˆͺβ†₯β‹…β‰Όβ†§β‹œβ†§βˆβ†˜β†½β‹―β‹œβ†§β†‘β†‘β†Έβˆ–β†₯β‹…βˆβ‹œβ†§β†•βˆͺβ†΄βˆ–β†΄βˆ™β†‘βˆβ†Έβˆ–β†Έβˆ–βŠΌβ†»βˆͺβˆβ†Έβˆ–βˆβ†‘ must be positive.
Since, both, $(\Phi_{\rm{out}} - \Phi)$ and the density $\rho$, are monotonically decreasing functions for dark matter halos, the exponent must be positive.
Therefore. the factor Β’ has to be in the range O<aΒ« l.
Therefore, the factor $a$ has to be in the range $0<a<1$ .
We can coustrain Β« further by msertiug Eq. (5))
We can constrain $a$ further by inserting Eq. \ref{eq-rho-phi-isotrop}) )
iuto the Poisson equation.
into the Poisson equation.
This results in the Lane-Emden equation (?) (22b Dux Qi) | Ο€ΟŒ ΓΌ
This results in the Lane-Emden equation \citep{binney:87} r^2 ) + 4 G c = 0 .
Oue solution of the Laue-Emden equation is a power-law for the relative poteutial and with Eq.| (5))
One solution of the Lane-Emden equation is a power-law for the relative potential ) , m = -1) and with Eq. \ref{eq-rho-phi-isotrop}) )
also for the densitvthe
also for the density. ,
"Oo πα, y=ὦBal f(a).
n = -1) = (2-2a)/(1-2a) .
Tn order to obtain a solution for a finite mass halo the β†΄βˆ–β†΄β†•βˆͺβ†»β†Έβˆ–βˆͺβ†•β‹Ÿβ‰Όβˆβˆ–βˆβ†΄βˆ–β†΄β†•β†‘β‹…β†–β†½β†»β†₯β‹…βˆͺβˆβ†•β†Έβˆ–βˆβ‹―β†΄βˆ–β†΄β†‘β†΄β‹β†Έβˆ–β†΄βˆ–β†΄β†Ώβˆβˆ’βŠ”β†ΈβŠ³β†•β†Έβˆ–β†•β†•β†‘β†•β‹…β†–β†½β†΄βˆ–β†΄β†‘β†Έβˆ–β†Έβˆ–β†»βˆ™βˆβ‹œβ‹―βˆβˆ–β†•β‹…β†–β†½ nc3.
In order to obtain a solution for a finite mass halo the slope of density profile must be sufficiently steep, namely $n>3$.
Therefore. the factor Γ  must be in the range L/liljajl/=/2
Therefore, the factor $a$ must be in the range 1/4<a<1/2 .
Note the asvimptotic slope of the NEW-profile. ΞΏ>x)= 3. results from. a=4l/l.
Note the asymptotic slope of the NFW-profile, $n(r\to \infty)= 3$ , results from $a=1/4$.
The simulations.: show that the auisotropy of the velocity dispersion iucreases with radius and amounts to 20.3 at the virial radius.
The simulations show that the anisotropy of the velocity dispersion increases with radius and amounts to $\beta \approx 0.3$ at the virial radius.
This anisotropy affects the allowed parameter range for a: luteeratiug the Jeans equation uuder the condition of a constant anisotropy paraiueter ΞΏ) leads to ↕
This anisotropy affects the allowed parameter range for $a$: Integrating the Jeans equation under the condition of a constant anisotropy parameter $\beta$ leads to. ,
βˆβ†΄βˆ–β†΄β†Έβˆ–β†₯⋅↑
r) = .
β†•βˆβˆΆβ†΄β‹β†‘β†•βˆβ†΄βˆ–β†΄β†₯β‹…β†Έβˆ–β†•β‹œβ†§β†‘β†•βˆͺβˆβ‹œβ†§βˆΆβ†΄βˆ™βŠΎβ‹œβ†§β†•βˆβ†•βˆβ†‘βˆͺβ†‘β†•βˆβˆ–β†•β‹Ÿβˆͺβ†•β†΄βˆ–βˆ·βˆ–β†΄βˆͺβˆβ†Έβˆ–β‰Ίβˆ£βˆβ‹œβ†§β†‘β†•βˆͺ∐ β‹œβ†§βˆβˆͺβ†–β†–β‡β†΄βˆ–β†΄βˆβ†΄βˆ–β†΄β†‘βˆͺβˆβˆβ‰Όβ†§β†»βˆͺβ†–β†–β‡β†Έβˆ–β†₯β‹…β‰“β†•β‹œβˆβ†–β‡β†΄βˆ–β†΄βˆͺβ†•βˆβ†‘β†•βˆͺβˆβ†΄βˆ–β†΄β†•β‹Ÿβˆͺβ†₯β‹…β†‘βˆβ†Έβˆ–β†»βˆͺβ†‘β†Έβˆ–βˆβ†‘β†•β‹œβ†•β†•β‹œβ‹―β‰Όβ†§ density (D., (Dayne ni = 1) ΞΏ.
Inserting this relation again into the Poisson equation allows us to find power-law solutions for the potential andthe density ) m = -1) . ,
since (he inverse (ransform does not involve an integral. issues of quadrature accuracy do nol arise.
Since the inverse transform does not involve an integral, issues of quadrature accuracy do not arise.
We can again use the Wigner function relation to write this as The m and m' sums can be computed using FFTs. and are sub-dominant to the scaling. using OL?logL) operations.
We can again use the Wigner function relation to write this as The $m$ and $m'$ sums can be computed using FFTs, and are sub-dominant to the scaling, using ${\cal O}(L^2\log L)$ operations.
The FFTs will produce (0.6) as a regularly sampled [function on a 2-torus.
The FFTs will produce $f(\theta,\phi)$ as a regularly sampled function on a 2-torus.
Onlv half of this torus is of interest ancl the 0>7 portion can be ignored.
Only half of this torus is of interest and the $\theta > \pi$ portion can be ignored.
An appendix to? also noted this algorithm for the inverse transform (but does not address the forward transform).
An appendix to also noted this algorithm for the inverse transform (but does not address the forward transform).
Computation of ΞΏ... (β€”1)TE-. sls again scales as Q(L).
Computation of = (-1)^s _s again scales as ${\cal O}(L^3)$.
Mirror svmmetries of the Wigner matrices again allow the expression to be rewritten using only (he non-negative quadrant.
Mirror symmetries of the Wigner matrices again allow the expression to be rewritten using only the non-negative quadrant.
The mirror svuunetry on the first azimuthal index of A leads to β€”"C"IPIE which cuts the computation time in hall.
The mirror symmetry on the first azimuthal index of $\Delta$ leads to = which cuts the computation time in half.
For a transform {ΞΏ a real-valued function. the additional symmetry C44a=65mm can again cul the computation timeby (wo.
For a transform to a real-valued function, the additional symmetry $G_{(-m')(-m)} = G_{m'm}^* $ can again cut the computation timeby two.
difference iu both metallicity aud age within cach galaxy. and therefore a recent eas-ricl luecrger (zΒ«1) et al. 19985)).
difference in both metallicity and age within each galaxy, and therefore a recent gas-rich merger $<$ 1) (Kissler-Patig et al. \cite{kissfor}) ).
The availability of the D-I colors for he GCs of NGC Ο„Ξ™ΞŸΞ€ allows us o Β£o further iu the aualvsis.
The availability of the B-I colors for the GCs of NGC 7457 allows us to go further in the analysis.
Tudeed the D-I color is roughly twice as sensitive to metallicity han the V-I color (Couture et al. 1990)).
Indeed the B-I color is roughly twice as sensitive to metallicity than the V-I color (Couture et al. \cite{couture}) ).
But an intrinsic difficulty with low-IunΓΌnositv ooOalaxies is) their sunall nunuber of GCs,
But an intrinsic difficulty with low-luminosity galaxies is their small number of GCs.
Diuuodalitv was shown to be undetectable in a dataset containing less than 50 objects (see section 5.3).
Bimodality was shown to be undetectable in a dataset containing less than 50 objects (see section 5.3).
Nevertheless. as we will see below. we can expect to observe some differeuces between the widths of a πλοία and a bimodal cistributious.
Nevertheless, as we will see below, we can expect to observe some differences between the widths of a unimodal and a bimodal distributions.
The dispersion in color of a "suele population of GCs can be estimated from the halo GCs of the AIW.
The dispersion in color of a β€œsingle” population of GCs can be estimated from the halo GCs of the MW.
On the one haud. we cau conver the imetallicity dispersion iuto a color dispersion.
On the one hand, we can convert the metallicity dispersion into a color dispersion.
With c([Fe/TI])=0.3 dex (Armandroff Zinn 1988)) we expec aayI)0.05 mag andoa(BI)=0.1 mae from the calibration relations of section 5.
With $\rm \sigma ([Fe/H])=0.3$ dex (Armandroff Zinn \cite{armandroff}) ) we expect a $\rm \sigma (V-I) \sim 0.05$ mag and $\rm \sigma (B-I)=0.1$ mag from the calibration relations of section 5.
Ou the other haud. we can measure the dispersion from the V-I aud. 0-1 data of the ~8O halo GCs in the MeMaster catalog (Iris 1996). and obtain a(VΒ₯I)=0.05x0.01 mae aud (BoD=0.09-E0.01 mag in excellent agreement with the first values.
On the other hand, we can measure the dispersion from the V-I and B-I data of the $\sim 80$ halo GCs in the McMaster catalog (Harris 1996), and obtain $\rm \sigma (V-I)=0.05\pm 0.01$ mag and $\rm \sigma (B-I)=0.09\pm 0.01$ mag in excellent agreement with the first values.
Iu V-L the genuime dispersion iu metallicity is extremely difficult to derive from the V-I colors. the expected dispersion being lower han the typical photometric errors of 0.1 mae.
In V-I, the genuine dispersion in metallicity is extremely difficult to derive from the V-I colors, the expected dispersion being lower than the typical photometric errors of 0.1 mag.
Iu D-I. however. typical photometric errors aud intrinsic dispersion of a sinele population are comparable. so that several populations would broaden the color distribution to a detectable level.
In B-I, however, typical photometric errors and intrinsic dispersion of a single population are comparable, so that several populations would broaden the color distribution to a detectable level.
Tn NGC 7157 the dispersion in V-I is oulv slightly avecr than the internal error (0.15 mag agaist L10 mag) and we estima| that the true. dispersion is ~Oll+011 mag according to the relation
In NGC 7457 the dispersion in V-I is only slightly larger than the internal error (0.15 mag against 0.10 mag) and we estimate that the true dispersion is $\rm \sim 0.11\pm 0.11$ mag according to the relation $\rm \sigma^2_{obs} = \sigma^2_{err}+\sigma^2_{true}$.
This standard deviation in V-I rauslates ΞΏ~0.120.1 dex when using the calibration relation given in the precedent section.
This standard deviation in V-I translates to a $\rm \sigma([Fe/H])\sim 0.4\pm 0.4$ dex when using the calibration relation given in the precedent section.
The error is estimated bv accounting for he unucertaiuties ou he determination of the standard deviatious aud on the calibration formmla given iu section 5.
The error is estimated by accounting for the uncertainties on the determination of the standard deviations and on the calibration formula given in section 5.
The estimate is very insecure due to the large error on a(VI). For the D-I color we fux a dispersion (0.25 mag) clearly broader than the combination of a single population aud photometric errors.
The estimate is very insecure due to the large error on $\rm \sigma(V-I)$ For the B-I color we find a dispersion (0.25 mag) clearly broader than the combination of a single population and photometric errors.
The above relation leads to Oru.=0.2340.07 nag or o([Fe/T])=0.6Β£0.2 dex.
The above relation leads to $\rm \sigma_{true}=0.23 \pm 0.07$ mag or $\rm \sigma([Fe/H])=0.6\pm 0.2$ dex.
This value is conipatible with the value tentatively deduced from the V-I distribution.
This value is compatible with the value tentatively deduced from the V-I distribution.
Such a dispersion 1- netallicity seenis intermediate between the oue of a suele population aud the tota dispersion of the GC populations im bright cllipticals.
Such a dispersion in metallicity seems intermediate between the one of a single population and the total dispersion of the GC populations in bright ellipticals.
Iudeed single populations such as the Galactic halo GCs (Armanudroff Zinn 1988)). or the GCs around M 81 or Γ€ 31 (Pereliuuter Racine 1995)) have ot[FeT)~0.3 dex: the individual components of the biumodal distribution iu NGC L172 have similar dispersions of ~0.38 dex in [Fe/TT (Geisler et al. 19963).
Indeed single populations such as the Galactic halo GCs (Armandroff Zinn \cite{armandroff}) ), or the GCs around M 81 or M 31 (Perelmuter Racine \cite{perelmuter}) ) have $\rm \sigma ([Fe/H])\sim 0.3$ dex; the individual components of the bimodal distribution in NGC 4472 have similar dispersions of $\sim 0.38$ dex in $\rm [Fe/H]$ (Geisler et al. \cite{geisler}) ).
In coutrast. the total dispersion of the system in M 87 is o(|Fo/II|)=0.65 dex (Lee Coisler 1993)). in NGC 1172 et(|Fe/II|)=0.7 dex (Geisler et al. 1996).
In contrast, the total dispersion of the system in M 87 is $\rm \sigma([Fe/H])=0.65$ dex (Lee Geisler \cite{lee}) ), in NGC 4472 $\rm \sigma([Fe/H])=0.7$ dex (Geisler et al. \cite{geisler}) ).
Therefore. while the distribution iu metallicity of the GCs around NCC 7157 is found to be mnimodal. the width of the CC metallicity distribution is compatible with the presence of different populations probably less separated in inetallicity than in the eiut clusters ellipticals.
Therefore, while the distribution in metallicity of the GCs around NGC 7457 is found to be unimodal, the width of the GC metallicity distribution is compatible with the presence of different populations probably less separated in metallicity than in the giant clusters ellipticals.
This sugeests a siguificautly cliffcrent chemical euricliieut. of the GCs in NGC 7157 than. c.go.. the halo population of the Calaxy.
This suggests a significantly different chemical enrichment of the GCs in NGC 7457 than, e.g., the halo population of the Galaxy.
With Ms=19.55 anda meau metallicity of -.1 dex for its GCs. NGC 7157 follows the general treud found between the absolute maguitude of he galaxies (spirals | ellipticals) and the |Fe/II]| value of their GCs (e.g. Drodie Huchra 1991.. Ashinan Zepf 1998)).
With $\rm M_V=-19.55$ and a mean metallicity of $\ \simeq -1$ dex for its GCs, NGC 7457 follows the general trend found between the absolute magnitude of the galaxies (spirals $+$ ellipticals) and the [Fe/H] value of their GCs (e.g. Brodie Huchra \cite{brodie}, Ashman Zepf \cite{ashzepf}) ).
Nevertheless. the spirals ποσα to have a lower GC metallicity as compared to elliptieals of similar luminosity aud the memi metallicity of ~1 dex for the GCs around NGC 7157 is cousistent with the mean values found for he metallicitics of the GCs around the bright elliptical galaxies Ww ) oe. Ashman Zepf 1998)).
Nevertheless, the spirals seem to have a lower GC metallicity as compared to ellipticals of similar luminosity and the mean metallicity of $\ \simeq -1$ dex for the GCs around NGC 7457 is consistent with the mean values found for the metallicities of the GCs around the bright elliptical galaxies $\rm M_V\le -20$ , e.g. Ashman Zepf \cite{ashzepf}) ).
We can also compare more quantitatively the color distribution of he GCs around NCC 7157 with that of the Galactic GCs.
We can also compare more quantitatively the color distribution of the GCs around NGC 7457 with that of the Galactic GCs.
Iu addition to its broad dispersion. the mean D-I color found for the GCs of NGC 7157 =1.9 mae. see section 5.2) is comparable to the mean of the Galactic disc/bulee GCs z1.9 inag. as derived frou the MeMaster Moreover. Aloute Carlo slinulations ΞΏαΌ³ B-I color distributions simular to ours show hat auv metal-poor (B-T=1.55 mag. the mean color of he metal-poor clusters in the Galaxy) population as large as o of the metalaich (B-I=1.92 mae) oue would be detected.
In addition to its broad dispersion, the mean B-I color found for the GCs of NGC 7457 $\ \simeq1.9$ mag, see section 5.2) is comparable to the mean of the Galactic disc/bulge GCs $\ \simeq 1.9$ mag, as derived from the McMaster Moreover, Monte Carlo simulations of B-I color distributions similar to ours show that any metal-poor (B-I=1.55 mag, the mean color of the metal-poor clusters in the Galaxy) population as large as to of the metal-rich $=1.92$ mag) one would be detected.
Therefore we can couclude to the absence of auy siguificaut population of metal-poor clusters similar to that of the AAW 1alo.
Therefore we can conclude to the absence of any significant population of metal-poor clusters similar to that of the MW halo.
It is likely that such blue elobular clusters were never presenut in NGC 7157 since NGC TLST ds an isolated ealaxy (p=0.13. galaxies/Mpc?) aud shows no sigus of any interaction.
It is likely that such blue globular clusters were never present in NGC 7457 since NGC 7457 is an isolated galaxy $\rm \rho=0.13~~ galaxies/Mpc^{3}$ ) and shows no signs of any interaction.
Thus the loss of blue GCs loss through stripping seenis. The ormnation i a spiral merger would imply the presence of blue GCs from the progenitor spirals unless the latter did not host blue CC's like the MW.
Thus the loss of blue GCs loss through stripping seems The formation in a spiral–spiral merger would imply the presence of blue GCs from the progenitor spirals unless the latter did not host blue GCs like the MW.
Iu situ ornmation models usually explain blue CCS as formed in the carly stage of the galaxy.
In situ formation models usually explain blue GCs as formed in the early stage of the galaxy.
To fit the absence of blue clusters in such scenarios an early epoch of star formation (to curich the eas) without any formation of
To fit the absence of blue clusters in such scenarios an early epoch of star formation (to enrich the gas) without any formation of
where στ is the Thomson cross-section. and poli) = niktitre) is the electron. pressure of the ICAL where Ξ ΞΏ = OATSpeasftiy) is the clectrom umber density. Ay, is the Boltzmann constant. and Zi) is the electron teiperature.
where $\sigma_{\rm T}$ is the Thomson cross-section, and $p_{\rm e}(r)$ = $n_{\rm e}(r)k_{\rm b}T_{\rm e}(r)$ is the electron pressure of the ICM, where $n_{\rm e}(r)$ = $0.875 (\rho_{\rm gas}/m_{\rm p})$ is the electron number density, $k_{\rm b}$ is the Boltzmann constant, and $T_{\rm e}(r)$ is the electron temperature.
The iutegral is performed along the of sight (/) through the cluster aud the upper lait of the imteeral R) is the extent of the cluster along uv particular of sight.
The integral is performed along the $\hbox{--}$ of $\hbox{--}$ sight $l$ ) through the cluster and the upper limit of the integral $+R$ ) is the extent of the cluster along any particular $\hbox{--}$ $\hbox{--}$ sight.
We do not include the effects of beam size iu caleulatiug the y parameter.
We do not include the effects of beam size in calculating the $y$ parameter.
This approxination is justified by the fact that the pressure profiles are relatively flat iu the iuner region.
This approximation is justified by the fact that the pressure profiles are relatively flat in the inner region.
The variation of pressure integrated along the lineofsight as a function the projected radius is even flatter thus providing more stification for the above approximation.
The variation of pressure integrated along the line–of–sight as a function of the projected radius is even flatter thus providing more justification for the above approximation.
The augular temperature profile projected on the sky due to SZ effect. AT(A)/Toary is given in terms of the Compton parameter in equation (19)) where g(r)= occothGe/2)-]1. oeβ€”hvfkpgTesn. Tex=2.728 (Fixsen ct al.
The angular temperature profile projected on the sky due to SZ effect, $\Delta T(\theta)/T_{\rm CMB}$ is given in terms of the Compton parameter in equation \ref{eq:y_sph_sym}) ) where $g(x)\equiv x$ $x/2$ $4$, $x\equiv h\nu/k_{\rm B}T_{\rm CMB}$, $T_{\rm CMB}=2.728$ (Fixsen et al.
1996).
1996).
In the Ravleigh-Jeaus approximation. g(r)zβ€”2.
In the Rayleigh-Jeans approximation, $g(x)\approx -2$.