Study of dynamical status of the globular cluster NGC 1851 using Ultraviolet Imaging Telescope
Gaurav Singh, R. K. S. Yadav, Snehalata Sahu, Annapurni Subramaniam
aa r X i v : . [ a s t r o - ph . GA ] F e b J. Astrophys. Astr. (0000) :
Study of dynamical status of the globular cluster NGC 1851using Ultraviolet Imaging Telescope
Gaurav Singh , R. K. S. Yadav , Snehalata Sahu and Annapurni Subramaniam Aryabhatta Research Institute of Observational Sciences (ARIES), Manora Peak, Nainital, 263001 Department of Physics and Astrophysics, University of Delhi, Delhi 110007 Indian Institute of Astrophysics, Koramangala II Block, Bangalore-560034, India * Corresponding author. E-mail: [email protected]
Abstract.
We present the study of dynamical status of the globular cluster NGC 1851. A combination of multi-wavelength space and ground-based data sets are used for the present analysis. In order to select the genuinecluster members, we used the astro-photometric data available from HST and GAIA-DR2 catalogs. The BSSradial distribution of the cluster is plotted from the center of the cluster to the outskirts. The radial distribution ofBSS shows a central peak, followed by a dip at the intermediate radii ( r min ∼ ′′ ) and a rising trend in the outskirts.We also estimated A + rh parameter as 0.391 ± A + rh parameter, we conclude that NGC 1851belongs to Family II classification and is an intermediate dynamical state cluster.
Keywords. (Galaxy:) globular clusters: individual: NGC 1851 - (stars:) blue stragglers - (stars:) Hertzsprung-Russell and colour-magnitude diagrams
1. Introduction
Globular clusters (GCs) are compact, centrally concen-trated and gravitationally bound systems of stars. Thehigh density in the central region of globular clusterslead to frequent gravitational interactions. The gravita-tional interactions among stars result in various dynam-ical processes i.e., two-body relaxation, core collapse,mass segregation, stellar collisions, stellar mergers etc(Meylan & Heggie 1997). These dynamical processesgive rise to several exotic populations i.e., millisecondpulsars, cataclysmic variables, and blue straggler stars(BSSs), etc (Ferraro et al. ff (MS-TO). Based onisochrone fitting technique, Shara et al. (1997) foundBSSs to be more massive ( M ∼ M ⊙ ) than the aver-age mass of stars in the GCs ( M ∼ M ⊙ ). Using Spec-tral energy distribution (SED) fitting technique, Raso etal. (2019) found similar estimates of BSS masses, witha few BSSs having masses larger that 2 times of MS-TO. Being more massive than the normal stars, they are subject to dynamical friction, which segregates theBSSs towards the centre of the cluster (Ferraro et al. DR et al. (2012) (hereafter F12) classified GCs into three maincategories;1. Family I : The radial distribution of BSSs show aflat distribution, and are classified as dynamicallyyoung systems. The examples of GCs classifiedin
Family I are e.g., Palomar 14 (Beccari et al. et al. ω Centauri (Ferraro et al.
Family II : The radial distribution of BSSs showa bimodal distribution with a central peak, fol-lowed by a minima at some intermediate radii( r min ), and an external rising trend. These clustersare classified as dynamically intermediate clus-ters. The example of the clusters showing bi-modal distribution are: NGC 6388 studied byDalessandro et al. (2008a), M53 by Beccari et © Indian Academy of Sciences 1
J. Astrophys. Astr. (0000) : al. (2008), M5 by Lanzoni et al. (2007a), and 47Tuc by Ferraro et al. (2004), M55 by Lanzoni etal. (2007c), NGC 6752 by Sabbi et al. (2004)and NGC 5824 by Sanna et al. (2014).3.
Family III : The radial distribution of BSSs showa monotonic behaviour, with a central peak fol-lowed by a decreasing trend and no signs of anexternal rise. These clusters are classified as dy-namically old systems. The examples of GCsshowing unimodal behavior are e.g., M79 stud-ied by Lanzoni et al. (2007b), M80 & M30 byF12, and M75 by Contreras Ramos et al. (2012).In the recent years, a new parameter ( A + rh ) hasbeen proposed to measure the dynamical segregation ofBSSs by Alessandrini et al. (2016), which is given asthe area between the cumulative distribution curves ofthe reference population ( φ REF (x)) and BSSs ( φ BS S (x)): A + rh ( x ) = Z xx min φ BS S ( x ′ ) − φ REF ( x ′ ) dx ′ (1)In the above equation, x ( = log( r / r h )) is defined asthe logarithmic distance from the center of the clusterand scaled over the half-mass radius r h of the cluster.Lanzoni et al. (2016) (hereafter L16) found a directcorrelation between r min and A + rh parameter, suggestingthat both the parameters are governed by a basic mech-anism i.e., dynamical friction.UVIT / AstroSat observations have also been bene-ficial in the BSS radial distribution studies. Sahu etal. (2019) studied the specific frequency of BSS in thecluster NGC 288 and found a bimodal radial distribu-tion using UVIT / AstroSat data.In this paper, we present the study of dynamicalstatus of the cluster, NGC 1851. This is a high den-sity globular cluster with the core ( r c ) and tidal ( r t )radii around 5 ′′ . ′′ .
6, respectively (Ferraro etal. α J = h m s . δ J = − ◦ ′ ′′ . l = ◦ .51, b = − ◦ .03, Harris 1996(2010 edition) (hereafter HA10)) is located at a dis-tance of 12.1 kpc from the Sun. NGC 1851 is an in-termediate metallicity cluster ([Fe / H] = − et al. (2017) and Singh etal. (2020) presented the UV and Optical CMDs of thecluster using UVIT / AstroSat data.The paper is organized in the following manner:data used for the present analysis is presented in Sec-tion 2, the selection of BSS and reference population Table 1 . Parameters of the cluster NGC 1851 used in thispaper.
Parameter Value ReferencesRA (J2000) 5 h m s .
76 HA10DEC (J2000) − ◦ ′ ′′ . / H] − et al. (2013)Distance modulus 15.47 mag Cassisi et al. (2008)Age 10 Gyr Cassisi et al. (2008)Core radius ( r c ) 5 ′′ . et al. r t ) 481 ′′ . et al.
2. Data sets
To study the dynamical status and to create the radialdistribution of BSS in the cluster NGC 1851, we usespace and ground-based data sets in NUV and Opticalwavelengths. We aim to study the BSSs located in theentire cluster extension i.e., from the cluster centre tothe tidal radii ( r t ).We use the astro-photometric catalog fromNardiello et al. (2018) in the central dense region( r ≤ ′′ ) of the cluster, observed as a part of theHST UV Legacy Survey of Galactic Globular Cluster(HUGS) program (Piotto et al. F275W , F336W ,and
F438W pass-bands, which were observed throughWFC3 / UVIS channel. The
F606W and
F814W pass-bands were observed through ACS / WFC channel.The catalog also contains the membership informationof all the stars that are common to WFC3 / UVIS andACS / WFC field of view (FOV).To select the BSSs from the outer region (90 ′′ ≤ r ≤ ′′ ), we use Near-UV (NUV) data in N279N fil-ter, observed through
Ultra Violet Imaging Telescope(UVIT) on board
AstroSat satellite during 19 th -21 st March 2016, as a part of Performance Verification (PV)phase. UVIT / AstroSat provides a simultaneous obser-vations in a wide range of electromagnetic spectrumfrom Far-UV (130-180 nm) to NUV (200-300 nm)wavelengths. It provides a circular field of view ofabout ∼ ′ and an angular resolution better than 1 . ′′ et al. (2016) and Tan-don et al. (2017) presented the details of instrumentand calibration of the UVIT data. For this cluster, thedata acquisition and reduction procedures are describedin detail in Subramaniam et al. (2017). . Astrophys. Astr. (0000) : Figure 1 . The frequency vs membership probability for allthe stars lying in the outer region is shown. In this histogramstar counts start rising after 50 % membership probabil-ity. Therefore, we can use membership criteria of P ≥
50% for the selection of cluster members in the further analysis.
For the optical wavelength in the outer region, weused the
UBVRI photometric catalog provided by Stet-son et al. (2019). The Gaia DR2 catalog provides theinformation of photometry and astrometry of all thestars down to G ∼
21 mag (Gaia Collaboration et al. ≥
50 % forthe selection of cluster members in the further analysis.So, by combining the HST membership catalog withthe Gaia DR2 membership data, we now have member-ship information of most of the stars used in the presentanalysis.
3. Analysis and Results
BSS and reference population selection
The first step towards studying the BS radial distribu-tion is to carefully select the genuine BSS and a refer-ence population. For this purpose, we will use NUV pass-bands for the primary selection of the BSSs. Toselect the reference population and complete BSS pop-ulation, we will use the Optical pass-bands for the se-lection, as described in (Singh & Yadav 2019).3.2
BSS population selection
For selecting the BSSs in the inner region, we useHST CMD (F275W, (F275W − F606W)) and for select-ing BSSs from the outer region we use UVIT CMD(N279N, (N275N − V)). The NUV-Optical CMDs arefitted with the hybrid models i.e., the isochrone is fit-ted with the the Flexible Stellar Population Synthesis(FSPS) models of Conroy et al. (2009) and HB se-quence is fitted with the HB model generated using theupdated Bag of Stellar Tracks and Isochrones (BaSTI-IAC , Hidalgo et al. / H] = − . et al. et al. et al. (2017) have used UV CMD (F275W,(F275W − F336W)) to select the BSSs from the cen-tral region of the cluster. In the UV CMD, BSS sam-ple can be selected both e ffi ciently and reliably, sinceit can be easily separated from the optical blends justabove the MS-TO. Therefore, to select the BSSs fromthe entire region, we use NUV-Optical CMD (HST andUVIT CMDs) as our primary selection criteria wherethe contamination from the optical blends can be mini-mized. In the NUV-Optical CMD, the BSSs can be sep-arated from the optical blends which extends a verticalsequence just above the main sequence while in Opti-cal CMD it is di ffi cult to separate these two sequences.The selection box criteria is shown in the Figure 2.Since, in NUV-Optical CMDs the BSSs can be easilydistinguished and are separated from the optical blendsand visible plumes. The evolutionary track of BSS inthe theoretical isochones also provides useful informa-tion for defining the selection criteria for the selectionof BSSs. In Figure 2, the BSSs defines a vertical se-quence, while the cooler giants like SGB, RGB are sup-pressed. The selected BSSs are shown with filled cir-cles. To minimize the contamination from the MS-TOand the sub-giant branch, we adopted a limiting magni-tude of F275W = = http://basti-iac.oa-abruzzo.inaf.it/hbmodels.html J. Astrophys. Astr. (0000) :
Once the BSSs are selected from the NUV-OpticalCMDs, they are used to define the selection box crite-ria in the Optical CMD (V, (V − I)), as shown in Figure3. By combining the Stetson’s catalog with the
Gaia
DR2 data and HST photometry, it is possible to coverboth the inner and outer regions (Stetson et al. et al. (2005). We found 3 additional BSSsfrom the Optical CMD in the inner region and 5 addi-tional BSSs in the outer region. The reason for gettingthese additional BSSs is attributed to the fact that thereare 3 BSSs that lies in the ACS FOV but are not presentin the WFC3 FOV. However, the 4 additional BSSs inthe outer region are due to the incompleteness of theUVIT N279N and one is the BSS + EHB photometricbinary companion identified by Singh et al. (2020), thatis located in the EHB sequence in the UVIT CMD.Therefore, in total we have found 172 BSSsthroughout the entire cluster region, 157 in the innerand 15 in the outer region. All the BSSs are genuinecluster members with a membership probability, P ≥
80 %.3.3
Reference population selection
Reference populations are important to understand thesegregation of BSSs and we used post-MS stars, sincethey define a natural trend in radial distribution againstwhich the radial distribution of the BSSs can be com-pared. The number of stars in a Post-MS stage is di-rectly proportional to its evolutionary time scales (Lan-zoni et al. (2007c); Renzini & Fusi Pecci (1988)).These Post-MS stars are, therefore, important for qual-itative study of BSS specific frequency and radial dis-tribution studies. The specific frequency of thesebranches are constant throughout the entire cluster re-gion and are equal to the evolutionary time scales of theHB and GB (SGB + RGB) phase respectively. There-fore, these branches are considered as the referencepopulation.For the reference population selection, we considerthe same limiting magnitudes subtended by the BSSpopulation in the optical CMD. Therefore, our selectionof reference population are not a ff ected by the com-pleteness of the sample. To select the genuine refer-ence population, we have adopted the membership cri-teria of P ≥
50 %, since at higher membership cuto ff s,we found a significant change in the number of refer-ence population. In Figure 3, the selection criteria forreference population is shown. We used the same se- Figure 2 . The selection of BSSs from the NUV-OpticalCMDs, with (F275W, (F275W − F606W)) in the le f t panel and (N279N, (N275N − V)) in the right panel , respectively.The selected BSSs are shown with filled circles and theyextends a vertical sequence in the NUV-Optical CMDs. TheNUV-Optical CMDs are fitted with the hybrid models i.e.,the isochrone is fitted with the FSPS models and the HBsequence is fitted with the HB model generated throughBaSTI-IAC models. The selection box criteria is shown inboth the panels. lection criteria followed by Singh & Yadav (2019) toselect the reference population. Hence, we found 394and 127 HB stars in the inner and outer sample respec-tively. Also, 2690 and 634 GB stars from the inner andouter regions, respectively.In total, we found, 521 HB and 3324 GB stars fromthe entire cluster region.Figure 4, show the spatial distribution of BSSs se-lected from the entire cluster region. The BSSs aremore concentrated towards the center and a large frac-tion of them are located in the inner region, muchwithin the half-mass radius ( r h ). However, significantnumber of BSSs are present in the outer region of thecluster as well. We also plotted the spatial distributionof GB population which is nearly symmetric in com-parison to the spatial distribution of BSSs.3.4 BSS radial distribution
In this section, we present the radial distribution of BSSwith respect to the reference population. To obtain theradial distribution plot of BSS with respect to the ref-erence population, we divided the cluster area into six . Astrophys. Astr. (0000) :
Figure 3 . The selection of the BSS and the referencepopulation using Optical CMD (V, (V − I)). The selection boxcriteria of BSS and reference population are shown for boththe inner and outer regions in the le f t and the right panels ,respectively. The selected BSSs are marked by filled circles.
Figure 4 . The plot show the spatial distribution of BSSsin the entire cluster region and are marked by filled bluecircles. The GB population is shown as black dots. concentric circles. In the Table 2, we listed the numberof genuine BSS and reference population correspond-ing to each of the radial bin ( N BS S , N GB and N HB .). We Table 2 . The log of the Number counts for BSS andreference population.
Radial bin N BS S N HB N GB L samp / L totsamp (arcsec)0 - 15 118 125 839 0.3415 - 30 18 96 619 0.2030 - 60 15 103 791 0.1960 - 120 7 113 591 0.15120 - 240 11 60 342 0.10240 - 480 3 22 141 0.06also obtain the specific frequency ( F BS SGB = N BS S / N GB , F BS SHB = N BS S / N HB and F HBGB = N HB / N GB ) of BSS andplotted them in Figure 5. The errors are plotted with 1sigma error bar. The specific frequency of BSS show abimodal distribution with a central peak followed by aminima and an external rising trend in the outer region,while the reference population show a flat radial distri-bution. In order to check the significance of the rise inthe external region, we performed Z-test and foundthe significance level of rise in the outer region to be ∼
77 %.We also obtained the doubly normalized ratio forBSS with respect to the reference population. Thesepopulation (“Pop”) could be BSS, HB or RGB. It isdefined as the number of “Pop” observed in a regionto the total number of “Pop” divided by the fractionof light sampled in the same region with respect to thetotal measured luminosity (Ferraro et al. R Pop = N Pop / N totPop L samp / L totsamp (2)We estimated the sampled to the total luminosityfor each radial bin by integrating the isotropic single-mass King profile using parameters taken from HA10catalog. We assumed the Poisson error in the values ofluminosities and numbers. Using the formula describedin Sabbi et al. (2004), we considered propagation oferrors to estimate the errors in the double normalizedratios. In Table 2, we listed the luminosity ratios com-puted in the corresponding annulus.In Figure 6, we plot the radial distribution of BSS,HB and GB, using double normalized ratios with re-spect to the radial distance scaled over r c . In the upperpanel , double normalized ratio of BSS with respect toHB is plotted and the lower panel shows the variationof double normalized ratio of BSS with respect to GB. J. Astrophys. Astr. (0000) :
Figure 5 . The specific frequency of BSS with respect to HBand GB are plotted in the upper and middle panels , respec-tively, while the specific frequency of HB and GB is plottedin the lower panel . The specific frequency distribution ofBSS show a bimodal distribution, whereas for the referencepopulation, it shows a constant value throughout the entirecluster region.
The value of R BS S shows a bimodal distribution with apeak in the center, a minima at r ∼ r c and an out-ward rising trend. The double normalized ratios of thereference population ( R HB and R GB ), however show aflattened behaviour ( ∼ A + rh parameter defined by L16, as thearea enclosed between the cumulative radial distribu-tion of BSS and the reference populations scaled over r h . In Figure 7, the cumulative radial distributions ofBSS with respect to HB and GB are plotted in the le f t and right panels , respectively. The value of A + rh areestimated as 0.394 and 0.386 with respect to GB andHB respectively. The corresponding values of meanand standard deviation of A + rh are therefore 0 .
391 and0 . upper panel of Figure 8, we plot the em-pirical dynamical clock relation defined by F12, whichcorrelates the position of minima of the BSS radial dis-tribution ( r min / r c ) with the core relaxation time ( t rc / t H ).In the lower panel of Figure 8, we plot the correlationof A + rh parameter and t rc / t H . The cluster NGC 1851 isshown with filled circle. The value of error in r c is takenfrom Miocchi et al. (2013) for estimating the error in Figure 6 . The double normalized ratios of BSS are plottedwith respect to HB and GB in the upper and lower panels ,respectively. The BSS radial distribution show a peak in thecenter, a minima at the intermediate radii ( r min ∼ ′′ ), andthe external rising trend. Figure 7 . The cumulative distribution plot of BSS, HB andGB. The A + rh parameter is obtained as area between thecurves of BSS with respect to HB and GB and are found tobe 0.386 and 0.394, respectively. the r min / r c . The values of r min , t rc , and r c of other clus-ters are adopted from F12. . Astrophys. Astr. (0000) : Figure 8 . The plot showing the location of the cluster NGC1851 in the empirical dynamical clock relation defined byF12 in the upper panel . The filled triangles are dynam-ically old clusters while open circles are the dynamicallyintermediate age clusters. The dynamically young clustersare plotted as lower-limit arrows at r min ∼ lower panel .
4. Discussions
The specific frequency and double normalized ratio ofBSS show bimodal distribution, with a peak in the cen-tral region, followed by a clear dip at the intermediateradii ( r min ∼ ′′ ) and a rising trend in the external re-gion. The BSSs are more massive than the referencepopulation and therefore are subjected to the dynami-cal friction which plays a crucial role in segregating theBSSs towards the cluster center. However, the BSSsthat are located in the outskirts, show a flat distributionand are not yet a ff ected by the action of dynamical fric-tion. The radial distribution of BSS observed in NGC1851 are in agreement with the previous studies (i.e.,F12) on the cluster showing bimodal radial distribution.Ferraro et al. (2018) found the value of A + rh param-eter of the cluster NGC 1851 to be 0.48 ± A + rh parameter is slightly less than the valueestimated by Ferraro et al. (2018), and it could be dueto the strict condition of membership probability, P ≥
50 % for the selection of BSS and reference population.Although, Ferraro et al. (2018) included proper motionselection criteria using the Vector-Point diagram (VPD)from the HUGS data set. The di ff erence in the A + rh pa- rameter could be largely due to the selection of refer-ence population. Ferraro et al. (2018) used 5 σ selec-tion box criteria for the selection of MS-TO as the ref-erence population in the UV-CMD, while in the presentanalysis, we have done the selection of reference popu-lation (HB and GB) from the Optical CMD, due to in-completeness of the MS-TO sample in the UVIT CMD.The A + rh parameter of the NGC 1851, studied byFerraro et al. (2018) does provides the informationabout the level of segregation of BSSs in the clustersample, but in the central dense region of the cluster(up to r h ), therefore, BSS radial distribution is need tounderstand the level of segregation of BSSs located inthe outskirts (after r h ) of the cluster. Also, it providesa very useful information about the cluster dynamicalstate. Therefore, we have estimated both the r min and A + rh parameters to obtain the dynamical state of the clus-ter, NGC 1851.The position of the r min is defined by F12 as an indi-cator of the level of segregation of BSSs or dynamicalstatus of the cluster. There is a well established empir-ical dynamical clock relation between r min and core orhalf-mass relaxation times ( t rc or t rh ) defined by F12.Also, L16 uses A + rh parameter and show that there ex-ists a direct correlation between r min and A + rh . There-fore, based on the position of the minima in the BSSradial distribution and A + rh parameter, we suggest thatNGC 1851 belongs to Family II classification and is anintermediate dynamical state cluster. The bimodal ra-dial distribution suggest that, BSSs located in the out-skirts of the cluster are still not a ff ected by the role ofdynamical friction. The spatial distribution of the BSSsalso suggest that most of the BSSs are located in thecentral region, while some BSSs are located in the out-skirts, which validates our findings. In the outskirts ofthe GC, NGC 1851, Singh et al. (2020) found a can-didate BSS + EHB binary system, suggesting that someBSSs are located in the outskirts of NGC 1851, wheredensity is low and binary BSSs can form through trans-fer mass from the companion star.
5. SUMMARY AND CONCLUSIONS
1. We present the dynamical status of the clusterNGC 1851, using data from HST, UVIT / AstoSat,GAIA DR J. Astrophys. Astr. (0000) :
3. The observed radial distribution of BSS shows apeak in the central region, a dip at the interme-diate radii ( r min ∼ ′′ ) and a rising trend in theexternal region. We also estimated A + rh parameterto be 0 . ± . r min and A + rh parameter therefore indicate that NGC1851 is an intermediate dynamical state clusterand it belongs to Family II classification. Thisindicates that the BSSs located in the outskirts ofthe cluster are still not a ff ected by the action ofdynamical friction. Acknowledgements
We are thankful to the reviewer for the thoughtfulcomments and suggestions that improved the quality ofthe manuscript. This publication uses the data from theAstroSat mission of the Indian Space Research Organ-isation (ISRO), archived at the Indian Space ScienceData Centre (ISSDC). UVIT project is a result of thecollaboration between IIA, Bengaluru, IUCAA, Pune,TIFR, Mumbai, several centers of ISRO, and CSA.This publication uses the data from the
ASTROSAT mission of the Indian Space Research Organisation(ISRO), archived at the Indian Space Science DataCentre (ISSDC). This work has made use of datafrom the European Space Agency (ESA) mission
Gaia ( ),processed by the Gaia
Data Process-ing and Analysis Consortium (DPAC, ).Funding for the DPAC has been provided by nationalinstitutions, in particular, the institutions participatingin the
Gaia
Multilateral Agreement. This researchhas made use of data, software and / or web toolsobtained from the High Energy Astrophysics ScienceArchive Research Center (HEASARC), a service ofthe Astrophysics Science Division at NASA / GSFC andof the Smithsonian Astrophysical Observatory’s HighEnergy Astrophysics Division.
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