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2008). | 2008). |
The planet radius and mass are approximately 1 Ij; | The planet radius and mass are approximately 1 $_{\rm Jup}$ |
iron content ancl possibly cilferent ages have been revealed (Pancino et al. | iron content and possibly different ages have been revealed (Pancino et al. |
2002. Ferraro ct al. | 2002, Ferraro et al. |
2004. Sollima et al. | 2004, Sollima et al. |
2005. Villanova et al. | 2005, Villanova et al. |
2007. Calamida et al. | 2007, Calamida et al. |
2009). | 2009). |
Llowever w Cen may not be a genuine GC. but rather the remnant of a dwarf galaxy partially clisrupted by the interaction with he Milkv Way (Bekki Freeman 2003. Alackey Van den Bereh 2005). | However $\omega\,$ Cen may not be a genuine GC, but rather the remnant of a dwarf galaxy partially disrupted by the interaction with the Milky Way (Bekki Freeman 2003, Mackey Van den Bergh 2005). |
A similar system (Lerzan 5) harboring wo distinct. populations with dillerent. iron 'ontent and (possibly) ages has been recently found in the Galactic Bulge (Ferraro et al. | A similar system (Terzan 5) harboring two distinct populations with different iron content and (possibly) ages has been recently found in the Galactic Bulge (Ferraro et al. |
2009). | 2009). |
Similarly. this system is suspected to »e not a genuine GC. but instead the remnant of a [arger system that contributed to the formation of the Galactic Dulge. | Similarly, this system is suspected to be not a genuine GC, but instead the remnant of a larger system that contributed to the formation of the Galactic Bulge. |
A milder evidence of internal spread. of the metal content (A Fe/L ~ 0.1) has been observed also in M22 (Marino ct al. | A milder evidence of internal spread of the metal content $\Delta$ [Fe/H] $\sim 0.1$ ) has been observed also in M22 (Marino et al. |
2009: Da Costa et al. | 2009; Da Costa et al. |
2009). | 2009). |
In the context of the multi-population scenarios. one of the most puzzling cases is that of NGC 2808. | In the context of the multi-population scenarios, one of the most puzzling cases is that of NGC 2808. |
The first shotometrie observations (Llarris 1974. Ferraro ct al. | The first photometric observations (Harris 1974, Ferraro et al. |
1990) revealed a Horizontal. Branch (113). with a very complex structure. | 1990) revealed a Horizontal Branch (HB) with a very complex structure. |
The cluster LIB is well populated both at colours redder than the RR Lyrac instability strip and along its hot blue tail (BY) that covers a range of ~5 mag below the mean level of the instability strip. | The cluster HB is well populated both at colours redder than the RR Lyrae instability strip and along its hot blue tail (BT) that covers a range of $\sim5$ mag below the mean level of the instability strip. |
This morphology. is not casily explained in terms of the cluster metallicity {οΗ]~ 1.3). since it is well outside the common paradigm that inks red LBs to metal-rich GCs ane blue-HIDs to metal-»oor systems. | This morphology is not easily explained in terms of the cluster metallicity ${\rm [Fe/H]}\sim-1.3$ ), since it is well outside the common paradigm that links red HBs to metal-rich GCs and blue-HBs to metal-poor systems. |
In this sense NCC 2808 is similar to other very massive (and much more metal rich) GC's. like NGC 6388 and NOC 6441 (Rich et al. | In this sense NGC 2808 is similar to other very massive (and much more metal rich) GCs, like NGC 6388 and NGC 6441 (Rich et al. |
1997. Busso et al. | 1997, Busso et al. |
2007. Dalessandro et al. | 2007, Dalessandro et al. |
2008). | 2008). |
The cluster colour-magnituce-diagram. (CM) also shows puzzling cliscontinuities in the stellar clistribution along the BY (Sosin ct al. | The cluster colour-magnitude-diagram (CMD) also shows puzzling discontinuities in the stellar distribution along the BT (Sosin et al. |
LOOT. also Dedin et al. | 1997, also Bedin et al. |
2000. Castellani et al. | 2000, Castellani et al. |
2006. lannicola et al. | 2006, Iannicola et al. |
2009) similar to those found in several other GCs (Ferraro et al. | 2009) similar to those found in several other GCs (Ferraro et al. |
1998). | 1998). |
D'Antona et al. ( | D'Antona et al. ( |
2005) first noticed a broadening of the NGC 2808. MS which was incompatible with photometric errors. | 2005) first noticed a broadening of the NGC 2808 MS which was incompatible with photometric errors. |
“Phey suggested. that the MS. consisted. of two components with the same age and Fe/ll]. but. cifferent initial Hle. abundances. with YονOA for the Le-rich component. | They suggested that the MS consisted of two components with the same age and [Fe/H], but different initial He abundances, with $Y\sim0.4$ for the He-rich component. |
“Phe complex AES structure was confirmed by an accurate photometric and proper motion analysis with deep Llubble Space Telescope (LIST) data (Piotto et al. | The complex MS structure was confirmed by an accurate photometric and proper motion analysis with deep Hubble Space Telescope (HST) data (Piotto et al. |
2007). | 2007). |
They found that the MS of NGC 280s splits into three sub-populations. all with age 12.5 αν and Yo~0.248 for the red-MS. Y—0.30 for the mean-ALS ancl 0.35.<)«040 for the blue-MS. | They found that the MS of NGC 2808 splits into three sub-populations, all with age $\sim12.5$ Gyr and $Y\sim0.248$ for the red-MS, $Y\sim0.30$ for the mean-MS and $0.35<Y<0.40$ for the blue-MS. |
D'Xntona οἱ al. ( | D'Antona et al. ( |
2005) further hypothesized that the complex LLB is connected to the MS components with cillerent He abundances. | 2005) further hypothesized that the complex HB is connected to the MS components with different He abundances. |
However their LIB morphology analysis was performed in the optical bands where the increase of the bolometric corrections at. high ellective temperature turns the LEB into an almost vertical structure (rather than horizontal) when 710.000 Ix. Along this vertical part. of the LEB. models with clleren initial He abundance tend to overlap. ancl the identification of sub-populations with dilferent initial 3 is not independen of assumptions about the amount of mass lost along the RGB phase. | However their HB morphology analysis was performed in the optical bands where the increase of the bolometric corrections at high effective temperature turns the HB into an almost vertical structure (rather than horizontal) when $T>10,000\,
$ K. Along this vertical part of the HB, models with different initial He abundance tend to overlap, and the identification of sub-populations with different initial $Y$ is not independent of assumptions about the amount of mass lost along the RGB phase. |
Ferraro et al. ( | Ferraro et al. ( |
10998) and. Rood et al. ( | 1998) and Rood et al. ( |
2008) sugeest that the optimal diagram for the study of blue HB stars is the (mpisogiv- MaelooBNmpsssw) CMD in the LIST filter system. | 2008) suggest that the optimal diagram for the study of blue HB stars is the $m_{F160BW}$, $m_{F160BW}-m_{F555W}$ ) CMD in the HST filter system. |
In this CMD the hottest LIB stars are the most luminous and lic along almost horizontal sequences. whose Luminosity is very sensitive to the initial Y abundance irrespective of the precise value of the stellar mass. | In this CMD the hottest HB stars are the most luminous and lie along almost horizontal sequences, whose luminosity is very sensitive to the initial $Y$ abundance irrespective of the precise value of the stellar mass. |
Llere we present an accurate photometric study of the central regions of NGC 2808. based on high-resolution LIST observations in far-UV and optical filters. | Here we present an accurate photometric study of the central regions of NGC 2808, based on high-resolution HST observations in far-UV and optical filters. |
With evolutionary models and constraints on the initial 3 clistribution coming from the analysis of the multiple MS. we investigate the complex structure of the HD of this massive GC. | With evolutionary models and constraints on the initial $Y$ distribution coming from the analysis of the multiple MS, we investigate the complex structure of the HB of this massive GC. |
The paper is structured as follows. | The paper is structured as follows. |
Section 2 describes the observational data. their reduction ancl calibration. Sect. | Section 2 describes the observational data, their reduction and calibration, Sect. |
3 presents an analvsis of the observed properties of the cluster LLB. and Sect. | 3 presents an analysis of the observed properties of the cluster HB, and Sect. |
4 details their interpretation in term of theoretical models. | 4 details their interpretation in term of theoretical models. |
A summary and the conclusions follow in Sect. | A summary and the conclusions follow in Sect. |
5. | 5. |
We used a set of images (Prop. | We used a set of images (Prop. |
6864. P.L. busi Pecci) covering optical to. far-UV. wavelengths. obtained with the Wide Field Planetary Camera 2 (WEDPC2) on board the HIST. | 6864, P.I. Fusi Pecci) covering optical to far-UV wavelengths, obtained with the Wide Field Planetary Camera 2 (WFPC2) on board the HST. |
The ΛΕΡΟΣ is à mosaic made of four SOONOO pixels cameras. with angular resolutions of 0.046" /pixel for. the anetzwy. Camera (PC) and ~0.1" /pixel for the three Wide Field. Cameras \(WE2. WES ancl WEA). | The WFPC2 is a mosaic made of four $800\times800$ pixels cameras, with angular resolutions of $0.046\arcsec/$ pixel for the Planetary Camera (PC) and $\sim0.1\arcsec/$ pixel for the three Wide Field Cameras (WF2, WF3 and WF4). |
The optical dataset consists of ο£5551" images. three with exposure ime fos,= LOOssee and two with fos,=Tssec. plus 4.P3360 images with exposure time fox;=1000 ssec. | The optical dataset consists of $5 \times F555W$ images, three with exposure time $t_{\rm exp}=100$ sec and two with $t_{\rm
exp}=7$ sec, plus $4 \times F336W$ images with exposure time $t_{\rm exp}=1600$ sec. |
Phe zr-UV database comprises 3.£IGOBW images with fij=1200 ssec each. | The far-UV database comprises $3 \times
F160BW$ images with $t_{\rm exp}=1200$ sec each. |
AL the images have the same pointing. with he cluster centre roughly centred in the PC (see Figure 1). | All the images have the same pointing, with the cluster centre roughly centred in the PC (see Figure 1). |
We combined the images using the ΗΛΙΟ task in order to improve the signal to noise ratio and decontaminate hem from cosmic ravs. which are particularly prominent in ong exposure data. | We combined the images using the IRAF task in order to improve the signal to noise ratio and decontaminate them from cosmic rays, which are particularly prominent in long exposure data. |
For a given passband and exposure time we adopted the resulting median frame as reference image or the data reduction. | For a given passband and exposure time we adopted the resulting median frame as reference image for the data reduction. |
As done in our previous work (see or example. Dalessandro ct al. | As done in our previous work (see for example Dalessandro et al. |
2009). the data reduction of the optical images was performed. using the IRRONLAEOT xvkage (Buonanno et al. | 2009), the data reduction of the optical images was performed using the ROMAFOT package (Buonanno et al. |
1983). specifically. developed. to perform accurate photometry in erowcded regions (Duonanno lannicola. 1984). | 1983), specifically developed to perform accurate photometry in crowded regions (Buonanno Iannicola 1984). |
Because of uncder-sanipling problems related to the Point Spread Function (PSE) of stars in the rUV images. we used aperture photometry performed with the publich available software Source. Extractor (SLExtractor. Bertin Arnouts 1996). | Because of under-sampling problems related to the Point Spread Function (PSF) of stars in the far-UV images, we used aperture photometry performed with the publicly available software Source Extractor (SExtractor, Bertin Arnouts 1996). |
The adopted aperture radii were 2 pixels (corresponding to 0.27) for the WE chips and 3 pixels ( 0.15") for the PC. | The adopted aperture radii were 2 pixels (corresponding to $0.2\arcsec$ ) for the WF chips and 3 pixels $\sim0.15\arcsec$ ) for the PC. |
For the WE cameras. because of strong vignetting problems allecting the upper right. corners of all the FIGOBW images. the regions 550ο2y©S00] have been excluded from the analysis. | For the WF cameras, because of strong vignetting problems affecting the upper right corners of all the $F160BW$ images, the regions $[550\lsim
x\lsim800; 550\lsim y\lsim800]$ have been excluded from the analysis. |
In each filter for every star detected. the photometri¢ error has been defined as the standard deviation of all the measures obtained. | In each filter for every star detected, the photometric error has been defined as the standard deviation of all the measures obtained. |
The final star list includes all the sources detected. in at least 2 filters. | The final star list includes all the sources detected in at least 2 filters. |
Hot. stars detected in £1605YV and. not automatically found in the optical data were force-fitted in | Hot stars detected in $F160BW$ and not automatically found in the optical data were force-fitted in |
Direct measurements of stellar masses provide an essential foundation [or theoretical models of stars. | Direct measurements of stellar masses provide an essential foundation for theoretical models of stars. |
Such measurements must be [ree of model-dependent. assumptions about the stars internal physics aud so can be obtained only [rom the star's gravitational ellects on external objects. | Such measurements must be free of model-dependent assumptions about the star's internal physics and so can be obtained only from the star's gravitational effects on external objects. |
Almost all stars with directly measured masses are components of binaries. | Almost all stars with directly measured masses are components of binaries. |
However. binary stars may not always evolve as do single stars. and thus direct mass nmeasurenienis of single stars are of prime importance. | However, binary stars may not always evolve as do single stars, and thus direct mass measurements of single stars are of prime importance. |
The Sun's mass has been measured using (wo completely independent methods: first by applving Newton's generalization of Kepler's Third Law to the motion its companions (the planets): second Irom its deflection ol light [rom distant stars (Dyson.Eddington.&Davis 1997). | The Sun's mass has been measured using two completely independent methods: first by applying Newton's generalization of Kepler's Third Law to the motion its companions (the planets); second from its deflection of light from distant stars \citep{eddington,fma}. |
. For all stars other than the Sun. direct mass measurements have. until recently. only been possible with the first method. | For all stars other than the Sun, direct mass measurements have, until recently, only been possible with the first method. |
That is. direct mass measurements have been restricted to components of binary svstenis wilh orbital periods of decades or less. | That is, direct mass measurements have been restricted to components of binary systems with orbital periods of decades or less. |
All light-deflection methods rely fundamentally on the equation. where 8j is the angular Einstein radius. A/ is the mass of the lens. and πιο is the relative parallax. | All light-deflection methods rely fundamentally on the equation, where $\theta_\e$ is the angular Einstein radius, $M$ is the mass of the lens, and $\pi_\rel$ is the lens-source relative parallax. |
Relscal(1964). was the first to propose that the masses of stars could be measured [rom light deflection. | \citet{refsdal} was the first to propose that the masses of stars could be measured from light deflection. |
Lis method was purely astrometric. | His method was purely astrometric. |
By measuring the relative separation of a nearby lens ancl a more distant source. one could directly determine the relative parallax πιο. the angular impact parameter 2. and the maximal deflection «0. | By measuring the relative separation of a nearby lens and a more distant source, one could directly determine the relative parallax $\pi_\rel$, the angular impact parameter $\beta$, and the maximal deflection $\Delta\theta$ . |
In the simplest (ancl tvpical) case. ο>064. llence. combining equations (1)) and (2)) leads to a simple expression for the mass. Relsdal ( | In the simplest (and typical) case, $\beta\gg \theta_\e$, Hence, combining equations \ref{eqn:thetadef}) ) and \ref{eqn:widesep}) ) leads to a simple expression for the mass. \citet{refsdal}' |
1964)s method. will be carried out for perhaps a dozen nearby stars using the(SIM. Salim&Gould 2000)). | 's method will be carried out for perhaps a dozen nearby stars using the, \citealt{sg00}) ). |
A second method was proposed by Gould(1992) and. first. carriecl out by (1995). | A second method was proposed by \citet{gould92} and first carried out by \citet{alcock95}. |
. Here one uses the accelerated platform of the Earth to measure the microlens parallax. and combines thiswith an independent measurement of 6 (o obtain (he mass. | Here one uses the accelerated platform of the Earth to measure the microlens parallax, and combines thiswith an independent measurement of $\theta_\e$ to obtain the mass. |
The | The |
where f(r.E) is the solution of Eq. (5)). | where $f(r,E)$ is the solution of Eq. \ref{pr_state}) ). |
The second is the spatial distribution of the IC fIux in the energy range Ae as observed from Earth: llere / is the line of sight and © is the angular distance from the center as observed from Earth. | The second is the spatial distribution of the IC flux in the energy range $\Delta\epsilon$ as observed from Earth: Here $l$ is the line of sight and $\phi$ is the angular distance from the center as observed from Earth. |
The distance from the center of the cluster r can be estimated in the following wav (see Fig. 2)): | The distance from the center of the cluster $r$ can be estimated in the following way (see Fig. \ref{schm}) ): |
The Eq. (14)) | The Eq. \ref{spec_r}) ) |
max be rewritten as where The enereyo. of primary electrons E and seattered —gamma-ray photons ει1 are related with each other as: | may be rewritten as where The energy of primary electrons $E$ and scattered gamma-ray photons $\epsilon_1$ are related with each other as: |
observations provide lig1 count-rate data with a noniwl time resolution of 1255458 in 61 spectral chanucls over the whole cnerey range (64 keV) of the PCA detector. | observations provide high count-rate data with a nominal time resolution of $\mu$ s in 64 spectral channels over the whole energy range $-$ 60 keV) of the PCA detector. |
Folowing Calloway et 22008a. we extracted spectra integrated over 0.25. 0.5. 1. aud 2 « nne intervals. de)endiue on the! Source count rate durug the burst. so that the total umber of counts in cach προςἔτιuu is roughly conustaut. ( | Following Galloway et 2008a, we extracted spectra integrated over 0.25, 0.5, 1, and 2 s time intervals, depending on the source count rate during the burst, so that the total number of counts in each spectrum is roughly constant. ( |
Iu α few cases. data gaps during the observations result in N-rav spectra integrated over sjorter exposure times). | In a few cases, data gaps during the observations result in X-ray spectra integrated over shorter exposure times). |
We tooς the spectruii over a 16 s time interval prior to the ouset of cach burst as the spectraii of the persisteit onudsslon. Which we subtracted frou the burst spectra as backeround. | We took the spectrum over a 16 s time interval prior to the onset of each burst as the spectrum of the persistent emission, which we subtracted from the burst spectra as background. |
We venerated separate response matrix files for cach burst usiie the PCARSP version 11.7. HEASOFT release OT. ixl TEASARC'’s reuote calibration ¢latabase ancl ook into account tfhe offset poiutiug of he PCA during the creaticn of the response matrix files. | We generated separate response matrix files for each burst using the PCARSP version 11.7, HEASOFT release 6.7, and HEASARC's remote calibration database and took into account the offset pointing of the PCA during the creation of the response matrix files. |
This atest version of the PCA response matrix makes the instrument calibration self-consistent over the PCA lifetime aud vields a normalization of t1ο Crab ]oulsar that is within σ of the calibration lueastrelent of Toor Seward (1971) for that source. | This latest version of the PCA response matrix makes the instrument calibration self-consistent over the PCA lifetime and yields a normalization of the Crab pulsar that is within $-\sigma$ of the calibration measurement of Toor Seward (1974) for that source. |
In lL. we disCuss ILL πι1ue detail the effect othe uncertaiuties iu the absolute fux calibration ou the moeastremment of the apparent surface area o| neutron stars. | In 4, we discuss in some detail the effect of the uncertainties in the absolute flux calibration on the measurement of the apparent surface area of neutron stars. |
Finally. we corrected all of he X-ray spectra for PCA deadtine following the method sevested by tlie RXTEteu. | Finally, we corrected all of the X-ray spectra for PCA deadtime following the method suggested by the RXTE. |
. To :uialvze the spectra. we 1sed the Iucractive Spectral Iiterpretation Systeii (ISIS). versio1 1.1.9-55 (IIouck Deniceda 2000). | To analyze the spectra, we used the Interactive Spectral Interpretation System (ISIS), version 1.4.9-55 (Houck Denicola 2000). |
For cach fit. we! mneluded a systematic error oOLD as sugeeste by the RNTE calibrationteam?. | For each fit, we included a systematic error of as suggested by the RXTE calibration. |
. We Bt cach spectrum with a dackbody fuuctiou using theedanodel (as defined in NSPEC. Arnaud 1996) aud multiplied it bv the iiodel (Wilius. Allen. MeCray 2100) hat takes iuto account the interstellar extinction. assumndues ISM abuudances. | We fit each spectrum with a blackbody function using the model (as defined in XSPEC, Arnaud 1996) and multiplied it by the model (Wilms, Allen, McCray 2000) that takes into account the interstellar extinction, assuming ISM abundances. |
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