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We initially scale bv ry so that 6,=orpits and use cvlndrical coordinates where 5,=v.|22 wheredien coi=-ijr. ruus along the optical axis aud ο-—s/re ds the scaled distance from the 2 axis. | We initially scale by $r_s$ so that $\tilde r_p = r_p/r_s$ and use cylindrical coordinates where $\tilde r_p = \sqrt{\tilde x^2+ \tilde
z^2}$ where $\tilde z = z/r_s$ runs along the optical axis and $\tilde x = s/r_s$ is the scaled distance from the $z$ axis. |
We define 5Ξή, to be an arbitrary scaled cutoff radius (we will later set (à.= royy).The surface mass deusitv is then eiven by and we make the ehiuge of variable 2=tame. | We define $\gamma = r_c/r_s$ to be an arbitrary scaled cutoff radius (we will later set $r_c = r_{200}$ ).The surface mass density is then given by and we make the change of variable $\tilde z=\tilde x\tan
u$ . |
Then the closed form expressionsfor the projected lass density are for — 1. aud for <1. | Then the closed form expressionsfor the projected mass density are for $\tilde x>1$ , and for $\tilde x<1$ , |
ó<10. which is itself a subsample of the Wall and Peacock (1985) sample of radio sources with Ilux densities e&reater than 2Jy at 2.7 CGllz. | $\delta < +10$, which is itself a subsample of the Wall and Peacock (1985) sample of radio sources with flux densities greater than 2Jy at 2.7 GHz. |
As discussed in Tadhunter et al. ( | As discussed in Tadhunter et al. ( |
1993. 1998) the z«0.7 sample has a high level of completeness. | 1993, 1998) the $z < 0.7$ sample has a high level of completeness. |
Low S/N optical spectra and. identifications [or the zo0.7 sample are. presented in Tadhunter et al. M | Low S/N optical spectra and identifications for all the $z < 0.7$ sample are presented in Tadhunter et al. ( |
"93) and di Serego Alighieri et al. ( | 1993) and di Serego Alighieri et al. ( |
1994): radio maps [or sample are presented in Morganti et al. ( | 1994); radio maps for this sample are presented in Morganti et al. ( |
1993. 1999); and X-ray observations are presented in Siebert et al. ( | 1993, 1999); and X-ray observations are presented in Siebert et al. ( |
1996). | 1996). |
Discussion of the radio observations in the context. of the unified schemes can be found in Morganti et al. ( | Discussion of the radio observations in the context of the unified schemes can be found in Morganti et al. ( |
1995. 199 while a discussion of the nature of the correlations between radio and optical emission line properties of the 2<0.7 sample is presented in Tadhunter et al. ( | 1995, 1997), while a discussion of the nature of the correlations between radio and optical emission line properties of the $z < 0.7$ sample is presented in Tadhunter et al. ( |
1998). | 1998). |
Although in section. 4+ below we will consider the UV excess in the z«0.7 sample of Fadhunter et. al. | Although in section 4 below we will consider the UV excess in the $z < 0.7$ sample of Tadhunter et al. |
1993 as a whole. most of this paper will be concerned with observations of a more restricted. sample. selected to facilitate a more. detailed: study of the optical/UV continuum. properties. | 1993 as a whole, most of this paper will be concerned with observations of a more restricted sample, selected to facilitate a more detailed study of the optical/UV continuum properties. |
The additional selection criteria for this restricted sample are: redshifts in the range0.15<2< and right. ascensions. in. the range 137ad«Hd<05". | The additional selection criteria for this restricted sample are: redshifts in the range $0.15 < z < 0.7$ and right ascensions in the range $13^{hr} < RA < 05^{hr}$. |
"Phe lower redshift limit for this restricted. sample. was chosen o ensure that the B-bane filter used. for the polarimetry observations covers the rest-frame UV. for all the sample objects. while the RA restriction was intended to ensure that we observed a complete. Αμμος sample of managable size. given the constraints on the observing time. | The lower redshift limit for this restricted sample was chosen to ensure that the B-band filter used for the polarimetry observations covers the rest-frame UV for all the sample objects, while the RA restriction was intended to ensure that we observed a complete RA-limited sample of managable size, given the constraints on the observing time. |
Some properties of the resulting sample of 22 objects are presented in Table 1 | Some properties of the resulting sample of 22 objects are presented in Table 1. |
Vhe overall aim of our survey was to obtain accurate B-band. polarimetry measurements and deep spectra covering at least the rest wavelength. range 3500 for all of the restricted sample in Table. 1. | The overall aim of our survey was to obtain accurate B-band polarimetry measurements and deep spectra covering at least the rest wavelength range 3500 — for all of the restricted sample in Table 1. |
In. reality. while we succeeded in obtaining deep spectra for the whole sample. time restrictions meant that we failed to obtain. D-band | In reality, while we succeeded in obtaining deep spectra for the whole sample, time restrictions meant that we failed to obtain B-band |
Extinction corrections to theHa flux can be estimated using Ana=O.S3Ay with Ay This is similar to the visual extinction formula used by ? if the “fudge factor" used to infer the lumimosity outside the FUV band is replaced with the luminosity in the NUV. | Extinction corrections to the$\alpha$ flux can be estimated using $A_{H\alpha}=0.83 A_V$ with $A_V$ This is similar to the visual extinction formula used by \citet{2001PASP..113.1449C} if the “fudge factor” used to infer the luminosity outside the FUV band is replaced with the luminosity in the NUV. |
The luminosity function (LF) of YSCs ts a fundamental probe of the star formation process of a galaxy. | The luminosity function (LF) of YSCs is a fundamental probe of the star formation process of a galaxy. |
The cumulative LFs for the case of the inner and outer YSCs of M33 are shown in Fig. 3.. | The cumulative LFs for the case of the inner and outer YSCs of M33 are shown in Fig. \ref{lf}. |
We plot separately the results the cumulative function for the 24 jm flux for all the 915 24m sources (Fig. 3(( | We plot separately the results the cumulative function for the 24 $\mu$ m flux for all the 915 $24\,\mu$ m sources (Fig. \ref{lf}( ( |
a)). and the cumulative function for the TIR. luminosity relative only to sources with an 84m counterpart (Fig. 3(( | a)), and the cumulative function for the TIR luminosity relative only to sources with an $8\,\mu$ m counterpart (Fig. \ref{lf}( ( |
b)). | b)). |
We see that the shape of the two LFs is similar: their slopes are given in Table 3. | We see that the shape of the two LFs is similar; their slopes are given in Table 3. |
In the same figure we also plot the cumulative LFs of the selected 648 YSCs as a function of Li (Fig. | In the same figure we also plot the cumulative LFs of the selected 648 YSCs as a function of $L_{bol}$ (Fig. |
3(enandofthe2A um flux (Fig. | \ref{lf}$ $(c)$ ) and of the $24\,\mu$ m flux (Fig. |
3(d)). | \ref{lf}$ $(d)$ ). |
T hevalueso ftheslopeo fthebestleastsquare fittorhedatg ngyayys pepen FCFμαι) to 70 mJy are listed in Table 3 as 1" fit. while the 2” fit includes points with higher values of Εν im). | The values of the slope of the best least square fit to the data points between $F_{\nu}(24\,\mu$ $) = 0.4$ to 70 mJy are listed in Table 3 as $1^{st}$ fit, while the $2^{nd}$ fit includes points with higher values of $F_{\nu}(24\,\mu$ $)$. |
Since the values are lower than unity. the differential distribution ΝΕ1.xL"dL has y lower than 2. | Since the values are lower than unity, the differential distribution $N(L)dL \propto L^{-\gamma}dL$ has $\gamma$ lower than 2. |
Overall. the main features of the LFs are the following: (a) The slope of the cumulative function flattens at the faint end due to incompleteness. | Overall, the main features of the LFs are the following: (a) The slope of the cumulative function flattens at the faint end due to incompleteness. |
Crowding in the inner disk implies a somewhat higher completeness limit. ( | Crowding in the inner disk implies a somewhat higher completeness limit. ( |
b) The LF of the inner disk shows a definite change of slope for a TIR or Bolometric luminosity of order of 107° ere sv! | b) The LF of the inner disk shows a definite change of slope for a TIR or Bolometric luminosity of order of $^{40}$ erg $^{-1}$. |
The bright end slope is similar to that found for bright HII regions in M33 (?) and in late-type spirals (?).. ( | The bright end slope is similar to that found for bright HII regions in M33 \citep{1997PASP..109..927W} and in late-type spirals \citep{1991ApJ...370..526C}. ( |
c) The LF of the inner and outer YSCs differ markedly: there are very few bright outer sources and the LF is steeper at the faint end. | c) The LF of the inner and outer YSCs differ markedly: there are very few bright outer sources and the LF is steeper at the faint end. |
The presence of a break is not evident and. if present. it occurs at a lower luminosity. | The presence of a break is not evident and, if present, it occurs at a lower luminosity. |
The distribution can be well deseribed by a single power law. | The distribution can be well described by a single power law. |
From the flattening of the distribution at the faint end. we estimate the completeness limit of the catalog around 0.4 mJy or Lj~5x10 erg s7!. | From the flattening of the distribution at the faint end, we estimate the completeness limit of the catalog around 0.4 mJy or $L_{TIR} \sim 5 \times 10^{37}$ erg $^{-1}$. |
This corresponds to the bolometric luminosity of a single BI.SV. star (?).. indicating that our sample is close to being complete even for faint obscured HII regions. | This corresponds to the bolometric luminosity of a single B1.5V star \citep{2000asqu.book.....C}, indicating that our sample is close to being complete even for faint obscured HII regions. |
The difference in the slopes of the inner and outer LFs between F,(24jm)=0.4 to 70 mJy can be explained by a difference in the population of the star clusters. | The difference in the slopes of the inner and outer LFs between $F_{\nu}(24\,\mu$ $) = 0.4$ to 70 mJy can be explained by a difference in the population of the star clusters. |
Namely.e the inner regions have more massive clusters with the IMF fully populated up to the upper mass end. | Namely, the inner regions have more massive clusters with the IMF fully populated up to the upper mass end. |
Conversely. the outer regions form predominantly clusters of lower mass and hence the presence of massive stars is rare and stochastic. as we shall discuss in Section 5. | Conversely, the outer regions form predominantly clusters of lower mass and hence the presence of massive stars is rare and stochastic, as we shall discuss in Section 5. |
Owing to the similarity between the LFs for the infrared and bolometric luminosity. we can exclude the possibility that. YSCs in the outer regions are fainter in. the IR due to the formation in an environment with a lower dust-to-gas mass ratio. | Owing to the similarity between the LFs for the infrared and bolometric luminosity, we can exclude the possibility that YSCs in the outer regions are fainter in the IR due to the formation in an environment with a lower dust-to-gas mass ratio. |
As we will see below. the estimated YSC extinctions show no radial variation. | As we will see below, the estimated YSC extinctions show no radial variation. |
In fact. beyond the edge of active star formation the MIR-to-FUV or to-He ratios increase. | In fact, beyond the edge of active star formation the MIR-to-FUV or $\alpha$ ratios increase. |
YSCs in the outer regions are intrinsically of lower luminosity: we will discuss in the next Section whether this is due to an aging effect or to a different distribution in mass. | YSCs in the outer regions are intrinsically of lower luminosity: we will discuss in the next Section whether this is due to an aging effect or to a different distribution in mass. |
As for the inner clusters. the distribution from the faint to the bright end can be broadly divided into two regimes with different slopes. | As for the inner clusters, the distribution from the faint to the bright end can be broadly divided into two regimes with different slopes. |
The steep slope at high luminosity ts often observed in the LF of HII regions. open clusters and associations (?).. | The steep slope at high luminosity is often observed in the LF of HII regions, open clusters and associations \citep{1997ApJ...476..144M}. |
In the simple scenario. the change of slope represents the transition from poor to rich clusters. where the latter are populous enough to reproduce the high-mass IMF (?).. | In the simple scenario, the change of slope represents the transition from poor to rich clusters, where the latter are populous enough to reproduce the high-mass IMF \citep{1998AJ....115.1543O}. |
In this case. the transition point between the two regimes marks the luminosity of the single brightest star: below this value. the observed statistics is modified by the sampling variance. | In this case, the transition point between the two regimes marks the luminosity of the single brightest star: below this value, the observed statistics is modified by the sampling variance. |
We find that the transition occurs around F,(244m) 60 mJy. i.e. 10 erg s7'. close to the luminosity of an O3V star (?).. | We find that the transition occurs around $F_{\nu}(24\,\mu$ $) \sim 60$ mJy, i.e. $10^{40}$ erg $^{-1}$, close to the luminosity of an O3V star \citep{1996ApJ...460..914V}. |
This implies that most of the bright MIR sources are in fact luminous YSCs. | This implies that most of the bright MIR sources are in fact luminous YSCs. |
Using the photometry in the FUV. NUV. H«c and MIR. we have constructed the SED of each YSC. | Using the photometry in the FUV, NUV, $\alpha$ and MIR, we have constructed the SED of each YSC. |
By acomparison with model SEDs from Starburst99 (??.SB99).. we can then derive the individual age. extinction, and mass: in addition. we provide some estimate of the average properties of the whole YSC population with implications on the IMF and on the ambient ISM. | By a comparison with model SEDs from Starburst99 \citep[][SB99]{1999ApJS..123....3L,2005ApJ...621..695V}, we can then derive the individual age, extinction, and mass; in addition, we provide some estimate of the average properties of the whole YSC population with implications on the IMF and on the ambient ISM. |
Below. we illustrate the procedure. | Below, we illustrate the procedure. |
We model the YSC SEDs with the SB99 single-age stellar population synthesis. | We model the YSC SEDs with the SB99 single-age stellar population synthesis. |
We consider that YSCs formed in an instantaneous burst and assume a sub-solar metallicity of 0.004 (?).. | We consider that YSCs formed in an instantaneous burst and assume a sub-solar metallicity of $Z = 0.004$ \citep{2010A&A...512A..63M}. |
The IMF is chosen to be the default Kroupa IMF. that is a broken power law (6(M)x M") with a slope a=1.3 for 0.1M««0.5M. anda=2.3 for0.5Ma«€M<Migs (?).. | The IMF is chosen to be the default Kroupa IMF, that is a broken power law $\phi(M) \propto M^{-\alpha}$ ) with a slope $\alpha=1.3$ for $0.1\,\msun < M < 0.5\,\msun$ and $\alpha=2.3$ for $0.5\,\msun < M < M_{max}$ \citep{2001MNRAS.322..231K}. |
Two sets of models were generated for different upper mass cutoffs: Mig.=40M. and M,,,,=100M... respectively. | Two sets of models were generated for different upper mass cutoffs: $M_{max}=40\,\msun$ and $M_{max}=100\,\msun$, respectively. |
We use the Padova evolutionary tracks with full AGB evolution to account for their non negligible contribution to MIR fluxes. | We use the Padova evolutionary tracks with full AGB evolution to account for their non negligible contribution to MIR fluxes. |
However. we did ot consider the contribution of thermally pulsating AGB stars that should be minimal for associations younger than | Gyr (2).. | However, we did not consider the contribution of thermally pulsating AGB stars that should be minimal for associations younger than 1 Gyr \citep{2006ApJ...652...85M}. |
The time evolution is followed with logarithmie sampli5 (30 steps) from 1 to 100 Myr. | The time evolution is followed with logarithmic sampling (30 steps) from 1 to 100 Myr. |
The SB99 calculations refer to a total stellar mass of 10 M... and no allowance is made for dust extinction or emission. | The SB99 calculations refer to a total stellar mass of $10^6\,\msun$ , and no allowance is made for dust extinction or emission. |
The mat output of the simulation is the emerging spectrum at each sampled age which we then convolve with the GALEX and Spitzer filter bandpasses to generate the synthetic photometry. | The main output of the simulation is the emerging spectrum at each sampled age which we then convolve with the GALEX and Spitzer filter bandpasses to generate the synthetic photometry. |
The model spectrum we use is the one taking into account both stellar and nebular emission. the latter being | The model spectrum we use is the one taking into account both stellar and nebular emission, the latter being |
upper limits. | upper limits. |
We therefore have no indication of variability between the ROSAT observations. | We therefore have no indication of variability between the ROSAT observations. |
On the other hand. a variation bv a factor 2 in the countrate between the 1991 and the 1993 detections is well within the range allowed by the linited statistics. | On the other hand, a variation by a factor 2 in the countrate between the 1991 and the 1993 detections is well within the range allowed by the limited statistics. |
The oulv source. other than the ceutral source. detected significantly in anv of the ROSAT TRI pointines.o Is a point source in the 1993 observation. listed as N3 in roftabpos.. | The only source, other than the central source, detected significantly in any of the ROSAT HRI pointings, is a point source in the 1993 observation, listed as X3 in \\ref{tabpos}. |
There is no bright (Vx 1l) optical counterpart to this source in the digitized sky survey: and no objectim SIMDAD within 1/ of its position. | There is no bright $V\ltap14$ ) optical counterpart to this source in the digitized sky survey; and no objectin SIMBAD within $'$ of its position. |
We therefore cannot determine zn accurate bore sigh correction. and the uncertainty in the position of the central N-rav source is dominated by the maceuracy of the bore sight deteruumation. which is about 5" (1-0: see David et 11995). | We therefore cannot determine an accurate bore sight correction, and the uncertainty in the position of the central X-ray source is dominated by the inaccuracy of the bore sight determination, which is about $''$ $\sigma$; see David et 1995). |
With this uncertainty. he three positions found for the central source in 1991. 1993 ane 1991 Sep are all compatible. | With this uncertainty, the three positions found for the central source in 1991, 1993 and 1994 Sep are all compatible. |
For each of the two longest observations. the stancare analysis indicates that the central source is extended. tthe distributions of the photons is not compatible with that of a single poiut source. | For each of the two longest observations, the standard analysis indicates that the central source is extended, the distributions of the photons is not compatible with that of a single point source. |
No such indication is presc1 in the 1991 observation. which has a verv small umber of detected counts. | No such indication is present in the 1991 observation, which has a very small number of detected counts. |
To establish the nature of the extension of the ceutral source we first study the longest observation. obtained iu 1993. | To establish the nature of the extension of the central source we first study the longest observation, obtained in 1993. |
A siunoothed X-ray nuage of the central region of NGC66LL0. shown in roffüeuul.. sugecsts that two sources are present. | A smoothed X-ray image of the central region of 6440, shown in \\ref{figml}, suggests that two sources are present. |
They are too close to be separated by the standard analysis. | They are too close to be separated by the standard analysis. |
We therefore iuplement ai further analysis. based on the imaxiumn-likelihood. method (sce CCash 1979. Alattox et 11996). as follows. | We therefore implement a further analysis, based on the maximum-likelihood method (see Cash 1979, Mattox et 1996), as follows. |
The probability at detector pixel / to obtain »; photons when a model xediets i; photons is described by Poissou statistics The probability. that the model describes the observations 1s elven by the product of the probabilities for all / iu the region cousidercd: Z/=ILP;. | The probability at detector pixel $i$ to obtain $n_i$ photons when a model predicts $m_i$ photons is described by Poisson statistics The probability that the model describes the observations is given by the product of the probabilities for all $i$ in the region considered: $L'=\Pi P_i$. |
For computational case woe maximize the logarithm of this quautity: The last term in this equation doesnt depend ou the assunied model. and in terms of selecting the best mocel iav be considered as a constant. | For computational ease we maximize the logarithm of this quantity: The last term in this equation doesn't depend on the assumed model, and – in terms of selecting the best model – may be considered as a constant. |
Thus maximizine £/ is equivalent to minimizing L. where Our further analysis of the 1993 ROSAT IRI observation is limited to the central 50"4 area. and consists of four steps. in which we fit à constant background. or a constant backeround plus one. two. or three sources. | Thus maximizing $L'$ is equivalent to minimizing $L$, where Our further analysis of the 1993 ROSAT HRI observation is limited to the central $50''\times50''$ area, and consists of four steps, in which we fit a constant background, or a constant background plus one, two, or three sources. |
The values of lui for the best models of these fits are denoted as lu£y. ln £4. Info. aud luL5 respectively, | The values of $\ln L$ for the best models of these fits are denoted as $\ln L_0$, $\ln L_1$ , $\ln L_2$, and $\ln L_3$ respectively. |
The siguificauce of the mth source is found by comparing liL,» with a «7 distribution for | The significance of the $n$ th source is found by comparing $\ln L_{n-1}-\ln L_n$ with a $\chi^2$ distribution for |
by unstable detector response. all the features inον: should be confirmed by future observations. | by unstable detector response, all the features in$A_V$ should be confirmed by future observations. |
The shy value is roughly in the 881 disc. | The $A_V$ value is roughly in the 81 disc. |
Buatet(2005). show that FIR to ultraviolet (UV) luminosity ratio of galaxies is related to the dust extinction because the efficiency of UV reprocessing into PIR by dust is related to the dust extinction. | \citet{buat05} show that FIR to ultraviolet (UV) luminosity ratio of galaxies is related to the dust extinction because the efficiency of UV reprocessing into FIR by dust is related to the dust extinction. |
The UV flux of M881 at the band (1528 Aj) of the (GALEX)) is |j,=179 mJy (Daleetal.2007). | The UV flux of 81 at the band (1528 ) of the ) is $F_\nu =179$ mJy \citep{dale07}. |
. Thus. Perey—es3515lo? erg 26 i, | Thus, $F_\mathit{FUV}\equiv\nu F_\nu =3.51\times 10^{-9}$ erg $^{-2}$ $^{-1}$. |
The extinction at the band can be estimated by usingthe fitting formula derived from the model calculations by Buatetal.(2005): where y—οσαμεν}. | The extinction at the band can be estimated by usingthe fitting formula derived from the model calculations by \citet{buat05}: where $y\equiv\log (F_\mathrm{TIR}/F_\mathit{FUV})$. |
Using the value for Zi in Section 3.2.. we obtain celery=L46. | Using the value for $F_\mathrm{TIR}$ in Section \ref{subsec:global}, we obtain $A_\mathit{FUV}=1.46$. |
This matches the mean value for the UV-selected sample in Buatetal.(2005) in the local Universe. | This matches the mean value for the UV-selected sample in \citet{buat05} in the local Universe. |
Now using the Galactic extinction curve given by Weingartner&Draine(2001) with ἐν=3.1 Glyfleey= 0389). we obtain do=0.57. | Now using the Galactic extinction curve given by \citet{weingartner01}
with $R_V=3.1$ $A_V/A_\mathit{FUV}=0.389$ ), we obtain $A_V=0.57$. |
The extinction shown in rettig:distyanisihconcovertheentirecolumninthegalacticdis | The extinction shown in \\ref{fig:dist_T_tau} is the one over the entire column in the galactic disc. |
e fir μμ ΙΙ ΕΣ Ihestellarectin distyrau::thatis. Ayx 0.25-1. | If the stars are on average located in the middle of the disc thickness, the stellar extinction would be half of the values obtained in \\ref{fig:dist_T_tau}; that is, $A_V\simeq 0.25$ –1. |
Ay=0.57 is within this range. | $A_V=0.57$ is within this range. |
The relation among the intensities at the three bands is investigated here. | The relation among the intensities at the three bands is investigated here. |
Following Hibietal.(2006).. we investigate the FIR colour-eolour relation. | Following \citet{hibi06}, we investigate the FIR colour–colour relation. |
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