Properties of the cluster population of NGC 1566 and their implications
Katherine Hollyhead, Angela Adamo, Nate Bastian, Mark Gieles, Jenna Ryon
MMon. Not. R. Astron. Soc. , 1–18 (2016) Printed 9 October 2018 (MN L A TEX style file v2.2)
Properties of the cluster population of NGC 1566 andtheir implications
K. Hollyhead , A. Adamo , N. Bastian , M. Gieles , J. E. Ryon Astrophysics Research Institute, Liverpool John Moores University, 146 Brownlow Hill, Liverpool L3 5RF, UK Department of Astronomy, Oscar Klein Centre, Stockholm University, AlbaNova, Stockholm SE-106 91, Sweden Department of Physics, University of Surrey, Guildford, GU2 7XH, UK Department of Astronomy, University of Wisconsin-Madison, 475 North Charter Street, Madison, WI 53706, USA
Accepted. Received; in original form
ABSTRACT
We present results of a photometric study into the cluster population of NGC 1566, anearby grand design spiral galaxy, sampled out to a Galactocentric radius of ≈ . ≈ −
2, in agreement with other studies, and is found to agreewith a model luminosity function, which uses an underlying Schechter mass function.The recovered power law slope of the mass distribution shows a slight steepening as afunction of galactocentric distance, but this is within error estimates. It also displays apossible truncation at the high mass end. Additionally, the cluster formation efficiency(Γ) and the specific U-band luminosity of clusters ( T L ( U )) are calculated for NGC1566 and are consistent with values for similar galaxies. A difference in NGC 1566,however, is that the fairly high star formation rate is in contrast with a low Σ SF R and Γ, indicating that Γ can only be said to depend strongly on Σ
SF R , not the starformation rate.
Key words: galaxies: individual: ngc1566, galaxies: star clusters: general
The study of stellar clusters is vital to the understandingof star formation and galaxy evolution, as current theoryproposes that the majority of all stars form in groups orclustered environments (e.g. Hopkins 2013; Kruijssen 2012).A grouping is defined as any sized collection of stars, inde-pendent of whether or not the collection is gravitationallybound. More specifically, a cluster refers to a bound group-ing while associations are unbound groupings (Blaauw 1964;Gieles & Portegies Zwart 2011). It is difficult to define acluster at young ( <
10 Myr) ages, as without detailed kine-matical information of all group members (and potentiallythe gas in the region as well) it is not possible to determineif the grouping is bound. At young ages there exists a con-tinuous distribution of structures, whereas at ages greaterthan 10 Myr, a bimodal distribution arises with bound (com-pact) and unbound (expanding associations) groups (Porte-gies Zwart et al. 2010).Hence, an object can only definitely be defined and clas-sified as a cluster once it is dynamically evolved. This is in agreement with hierarchical star formation models, whichindicate that clusters are not well defined and unique ob-jects at young ages (Bastian 2011).The problem with defining and determining a clusterfrom an unbound grouping also lies in the limited spatialresolution of the telescope and lack of information on stellardynamics (e.g. Bastian et al. 2012). Without knowledge ofthe stellar dynamics within clusters/groups, it is impossibleto unambiguously determine whether the collection is boundor not. One simplistic way is to use the size of the grouping.As shown in the Small Magellanic Cloud, groupings with aneffective radius above 6 pc rapidly decline in number as afunction of age (t − ), i.e., 90% of groups get disrupted everydecade in age, but for groups with sizes below 6 pc, thereis a flat distribution suggesting little disruption (PortegiesZwart et al. 2010). By limiting cluster population studiesto systems containing dense, centrally concentrated groupswith ages >
10 Myr, issues with identifying bound structurescan be resolved.Much work has been done on cluster populations in sev- c (cid:13) a r X i v : . [ a s t r o - ph . GA ] M a y Hollyhead et al. eral nearby galaxies, most notably on M83 and the Small andLarge Magellanic Clouds. By studying the distributions ofdifferent cluster properties across the galaxy you can inferhow the clusters formed and determine how they evolve overtime.
Clusters that survive any initial mass loss during formationwill not survive indefinitely, as they will continue to dissolvethrough a combination of internal and external processes.This can be seen in the decrease in the number of clusterswith increasing age (e.g. Elmegreen & Hunter 2010).Gas loss at very young ages is expected to be entirelyenvironmentally independent as this should be an internalprocess, and occurs on very short timescales (less than acrossing time). Early cluster evolution due to gas expulsionshould additionally be mass independent, as violent relax-ation is responsible for dynamical restructuring after rapidgas loss (e.g. Bastian & Goodwin 2006). One the other hand,the gas rich birth environment of clusters has been suggestedto actually cause many of the young clusters to disrupt be-fore they can migrate to areas that are more gas poor (e.g.,Elmegreen & Hunter 2010; Kruijssen et al. 2011) in whichcase the local environment would play a strong role in thedetermination of the survival fraction of young clusters. The-oretically, disruption should depend on the cluster’s initialmass and its environment, with clusters in weaker tidal fieldsor higher masses surviving longer (e.g. Baumgardt & Makino2003; Gieles et al. 2006c). However, empirical studies haveresulted in two separate theories for the disruption process.The process of disruption over the lifetime of the clus-ters is more questionable. There are two main empiricalscenarios to explain the process: MID (Mass IndependentDisruption) and MDD (Mass Dependent Disruption). Theage and mass distributions of clusters, as studied in thisproject, strongly depend on how disruption is modelled dur-ing the cluster lifetime. MDD has been evidenced and dis-played via empirical studies (Boutloukos & Lamers 2003;Lamers et al. 2005) and N-body simulations (Baumgardt2001; Gieles et al. 2004) where disruption is found to de-pend on the initial mass of the cluster and the environ-ment within the galaxy. The timescale for disruption hasbeen found to depend on the cluster mass as M γ , where γ varies slightly between different galaxies, with a mean valueof γ = 0 .
62 (Boutloukos & Lamers 2003). Simply, this indi-cates that higher mass clusters live longer. In this scenario,disruption is also dependent on environment due to tidaleffects and the ambient density within the galaxy (Lamerset al. 2005; Lamers & Gieles 2006).The opposing idea to MDD has been proposed, claim-ing that disruption, up to an age of ∼ − (Whitmore et al. 2007).Potential models combining these two ideas have beenexplored and can be found to fit observed data for fast or slow disruption and disruption from internal mechanisms oroutside influence (such as nearby clouds) with certain as-sumptions within reasonable limits (Elmegreen & Hunter2010). Additionally, if tidal shocks are sufficiently strong,disruption may be mass independent (with an age distribu-tion as t − ) (Kruijssen et al. 2011), however there will still bea strong environmental influence. This indicates that fullyconstraining disruption mechanisms is a difficult process.Age distributions have been widely studied for differentgalaxies and can provide insight into the process of disrup-tion in a galaxy. The general shape of the distribution is apower law section with a steepening at high ages. The shapeof the distribution is determined by the star formation his-tory of the galaxy and the amount of disruption present. Ifapproximated as a single power-law, log(dN/dt) ∝ t ζ , wherestudies to date have found ζ to vary between 0 and -1 (e.g.Fall et al. 2005, Gieles et al. 2007, Chandar et al. 2010,Silva-Villa & Larsen 2011, Bastian et al. 2012, Ryon et al.2014).Studies of M83 show environmental dependence in theage distribution, ranging from nearly flat ( dN/dt ∼ t ) torelatively steep ( dN/dt ∼ t − . ) (Silva-Villa et al. 2014) atdifferent galactocentric distances. This was also found byChandar et al. (2014) (radially dependent index of the agedistribution) who needed to invoke radially dependent dif-ferences in the cluster formation history in order to bringthe age distributions in the inner and outer regions of thegalaxy into agreement.Bastian et al. (2012) found that both the MID andMDD scenarios could provide good fits to the observedage distributions of clusters in M83, however, disruptionneeded to be strongly dependent on environment. Addition-ally, these authors found that the mass function for the clus-ters was truncated, and the truncation value depended onenvironment. The truncation in the mass function was nec-essary to include in disruption analysis in order to explainthe age distribution in the MDD framework. The luminosity function (LF) of a cluster population pro-vides insight into the mass function of the clusters. It isfound to behave as dN/dL ∝ L − α , although some devi-ations from a pure single valued power-law have been re-ported (Gieles et al. 2006a), including a steepening at thebright end. An example is the bend observed in the LF inthe Antennae galaxies by Whitmore et al. (1999), which canbe fit with a double power law. When the power law sectionof the distribution is fit, α is usually found to be ≈
2, withsmall variations (e.g. de Grijs et al. 2003; Larsen 2002). Theluminosity function is related closely to the underlying massfunction of the clusters, and the cluster initial mass function(CIMF). A direct comparison may not be made, however,as clusters of the same mass but varying ages will have dif-ferent luminosities due to fading over time. A down-turn inthe LF can result from a truncation at the high mass endof the CIMF (e.g. Gieles 2010). However, this truncation inthe CIMF may be difficult to discern due to low numbers ofmassive clusters (Gieles et al. 2006b).The shape of the mass distribution has been questionedin a variety of studies, with some concluding that it is best fitwith a pure power law (e.g. Bik et al. 2003; Whitmore et al. c (cid:13) , 1–18 he cluster population of NGC 1566 Figure 1.
Image of NGC 1566. The image was produced by equal-izing and combining fits images of the galaxy in the B, V and Ibands. The resulting image was then edited in the GNU GIMPimage processing utility to change the image to black and whiteand invert the colours. dN/dM ∝ M − β , has beenfound to be best fit in most cases with β ≈ M brightestV (Larsen 2002; Whitmore 2003). There is anobserved relation between this quantity and the star forma-tion rate (SFR) of the galaxy which is interpreted to be due(mainly) to a size-of-sample effect (see Adamo & Bastian(2015) for a recent review).Γ, or the cluster formation efficiency (CFE), is the frac-tion of stars that form within clusters in a given environ-ment/galaxy (see Bastian (2008)). Kruijssen (2012) pre-sented a model that relates the CFE to the formation processof clusters, so when local density distributions are taken intoaccount, the CFE should scale with the gas surface densityof the galaxy, leading to a decrease with distance from thecentre of any individual (spiral) galaxy. The cluster forma-tion efficiency should also then scale with the surface densityof star formation (Σ SFR ) in the galaxy via the Schmidt-Kennicutt law (Kennicutt 1998; Kennicutt & Evans 2012),which has been observed in many galaxies to date (e.g. God-dard et al. 2010; Ryon et al. 2014; Adamo et al. 2015). Thisindicates that Γ can be used to probe the effect of galacticenvironment on cluster population properties. Additionally,a variation in CFE with distance from the galactic centre has been found for M83 (Silva-Villa et al. 2013; Adamo et al.2015).Another correlation between cluster population proper-ties and their host galaxy has been investigated by Larsen &Richtler (2000), where they showed that the percentage oftotal U band luminosity of a galaxy contained within youngmassive clusters (YMCs) ( T L ( U )) shows a relationship withseveral host qualities including Σ SFR and the density ofHI emission. T L ( U ) can also provide insight into the envi-ronmental dependence of cluster populations in the galaxy(Larsen 2002). As U band luminosity traces young stellarpopulations, T L ( U ) can be related to star formation and con-sequently, CFE. The relationship between T L ( U ) and Σ SFR of the galaxy indicates that the amount of star formation oc-curring in clusters increases with Σ
SFR , and so CFE shouldalso increase, though the exact relation between the CFEand T L ( U ) has not yet been quantified. T L ( U ) is found torange from ≈ To address the open questions discussed in the previous sec-tion, we study the properties of the cluster population ofNGC 1566, the brightest member in the Dorado group ofgalaxies, as shown in Fig. 1. It is a face-on spiral Seyfertgalaxy (de Vaucouleurs 1973) at a distance of ∼
17 Mpc(Karachentsev & Makarov 1996), which makes it ideal foridentifying and studying its cluster population. At this dis-tance individual clusters can still be resolved using HSTdata meaning photometry can yield integrated magnitudesfor each cluster. Extensive HST data is already available forNGC 1566 on the Hubble Legacy Archive, covering the inner ∼ α , CO, X-ray and radiocontinuum (Kilborn et al. 2005; Korchagin et al. 2000).We have constructed a catalogue of clusters within thegalaxy and obtained photometry in a variety of photomet-ric bands using HST data. We fit simple stellar populationmodels to the photometry to obtain ages, masses and extinc-tions for each of the clusters and then inspect the age andmass distributions of clusters in different areas of the disc.Throughout this work we use three separate radial bins toinvestigate changes in properties with environment. Thesebins are approximately equal in cluster number and are ar-ranged from 0-3.3 kpc, 3.3-4.7 kpc and 4.7 kpc to the edgeof the image for radial bins 1, 2 and 3 respectively. A vari-able age distribution could also indicate an environmentaldependence in the disruption mechanism. We also compareour fits for the mass and age distributions for studies of othergalaxies.In § § § § § § § c (cid:13) , 1–18 Hollyhead et al.
The images used in this study were taken from the HubbleLegacy Archive (HLA), having previously been fully reducedand drizzled with exposures covering the inner regions ofNGC 1566 (out to ≈ . m − M ≈ .
2. The galaxyis part of the Legacy ExtraGalactic UV Survey (LEGUS,Calzetti et al. (2015), HST project number GO-13364) andas such has complete and homogeneous imaging coverage inthe UV (F275W), U (F336W), B (F438W), V (F555W) andI (F814W) bands obtained using WFC3. No conversion wasmade to the Cousins-Johnson filter system, but the centralwavelengths of these bands are approximately equal to theWFC3 bands, so we use this nomenclature for simplicity.No prior catalogue was available for this galaxy, so wecarried out our own photometry on the images. We usedSource Extractor (Bertin & Arnouts 1996) within the Gaiapackage (Draper et al. 2014) included in the Starlink soft-ware to locate potential clusters throughout the galaxy usingthe V band image (the band where most clusters should bevisible). No limiting parameters were applied to the sourceextraction procedure to minimise the number of clusters un-intentionally omitted from the detection. Additionally, thecatalogue would undergo extensive refinement at a laterstage, so any unreliable sources or false detections wouldlater be removed. ∼ daophot package in iraf . Magnitudesfor each source were obtained using apertures of 1, 3 and5 pixels (corresponding to 0.04, 0.12 and 0.2 arcseconds re-spectively, or 3.3, 9.9 and 16.5 pc), with sky backgroundannuli between 15 and 17 pixels (0.60 and 0.68 arcsecondsor 49.5 and 56.0 pc respectively) for the UV, U, B, V, andI bands. The source catalogue included many false detections and un-wanted objects such as stars or possibly background galax-ies. The first cut made to the objects to reduce the numberof false detections involved removing any objects that werenot sufficiently detected in the U, B, V and I bands. Any ob-jects without photometric magnitudes in all of these bandswere removed.Similar to the work done by Chandar et al. (2010) andagain by Bastian et al. (2012) and Silva-Villa et al. (2014) forM83, we used concentration indices (CIs) to refine the sam-ple further. A CI is a measurement of how centrally concen-trated emission is for a source. This value helps distinguishbetween field stars and clusters; stars should be highly cen-trally concentrated as point sources, whereas clusters haveextended emission.Aperture corrections were calculated in each of thebands to account for flux missed by using a small aper-ture. This process involved visually selecting 30 sources thatpassed our selection criteria and were isolated in a variety oflocations in the galaxy. Photometry was carried out in iraf for each of the sources with apertures from 1-15 pixels at 1pixel intervals. These magnitudes were then used to create a radial profile for each cluster in each wavelength. Ideallythe profiles rise rapidly from the centre of the cluster for thefirst few pixels then begin to flatten asymptotically to themagnitude of the cluster equivalent to using an infinite aper-ture. In practice this is not always the case, so the profileof each cluster was inspected visually to remove any sourcesthat would pollute the final aperture corrections. This in-cluded sources with dips in the profiles, and those that hadnot flattened sufficiently, but were still rising at 15 pixels(likely due to the sampling of nearby sources).We were left with 8 clusters with reasonable profilesin all bands. The aperture corrections were calculated byaveraging the difference between the 5 pixel and 15 pixelapertures in each band: 0.40, 0.34, 0.34, 0.32 and 0.36 mag-nitudes for the UV, U, B, V and I bands respectively. Thesecorrections were subtracted from the magnitudes of eachcluster.To further reduce likely erroneous photometry, cutswere then applied across the U, B and I bands in additionto the current cut in the V band. Any sources fainter thanan apparent magnitude of 26 in all bands were removed.This ensured all final sources were reliably detected acrossthese key wavelengths for the purposes of age and mass fit-ting carried out later. Detection in the UV band was useful ifpossible but not essential to the study. A final cut in the pho-tometric errors was then applied across all sources. Objectswith an error (cid:62) . The magnitudes for each cluster obtained from photometrywere used to fit ages and masses for each of the clusters. Thefitting procedure was done as per Adamo et al. (2010a,b), bycomparison of each cluster’s SED with simple stellar pop-ulation Yggdrasil models (Zackrisson et al. 2011) using aKroupa IMF (Kroupa 2001). The models incorporate su-per solar metallicity and account for nebular and continuumemission.Traditionally, H α magnitudes are used to break the de-generacy between age and extinction at young ages (e.g. c (cid:13) , 1–18 he cluster population of NGC 1566 Whitmore et al. 2010) and give more accurate estimatesof cluster ages. However, the H α image for NGC 1566 isonly available in WFPC2 data, with smaller coverage of thegalaxy, missing many of our sources. SSP models assumethat contributions to the flux from ionised gas emission arepresent in young clusters, however it has been shown thatclusters as young as 3-4 Myr have expelled their remain-ing gas (Bastian et al. 2014; Hollyhead et al. 2015). Theearly removal of gas means that the H α emission is lowerthan model predictions, which likely gives an older age forthe cluster than required. Additionally, the distributed na-ture of H α means that it can be difficult to identify whetheremission is actually associated with the cluster or associ-ation itself. H α is also more susceptible to contaminationfrom nearby sources.Due to these factors we opted to use UV in the fittingprocedure instead of H α , as this can also disentangle de-generacies at young ages. Furthermore, UV emission is as-sociated with massive stars within clusters, and so is morereliably representative of the cluster. The potential for usingUV to disentangle degeneracies in age dating of clusters is akey aspect of the LEGUS survey (Calzetti et al. 2015). An interesting result of previous studies of cluster popula-tions has been that clusters closer to the central regions ofthe galaxy display different properties than those further to-wards the edge of the galaxy, showing variations in quantitiessuch as age and mass. We expect outer cluster populationsto contain more old clusters due to lower levels of disruption.A study of NGC 4041 found a marked difference in theposition of clusters in colour space, with clusters closer to thecentre of the galaxy in a bluer space than those in the outerregions (Konstantopoulos et al. 2013). Additionally to NGC4041, M83 also displays a variation in colour for clusters inouter and inner regions of the galaxy (Bastian et al. 2011).In contrast to this finding, Ryon et al. (2014) report nodifference in colour space for the cluster population of NGC2997, though this study compared clusters specifically in thecircumnuclear region to the rest of the disk, which could beconsidered slightly different to other studies.Fig. 2 shows our U-B vs V-I colour-colour plots for NGC1566. These plots include a mass cut of 5000 M (cid:12) applied tothe catalogue to account for stochastic sampling of the IMFand inaccuracies experienced in fitting low mass clusters,and includes only class 1 sources. The catalogue has beensplit into the three populations at different radial distancesfrom the centre of the galaxy as described in § ≈
270 clusters. The evolutionary models forthe clusters have been plotted over the points.The majority of the points lie in reasonable colour spacewith respect to the model track, meaning they can be tracedback along the extinction vector to an age on the model.These clusters are to the right of the track.To investigate the distributions, we found the medianU-B and V-I value for each population and found that theywere all located in approximately the centre of the distri-bution, as shown in Table 1. The observed trend is verysimilar to that found for M 83 (Bastian et al. 2011). Thereis no variation in V-I colour, however there is clearly a small
Av = 1−1.5−1.0−0.50.00.51.0−1.5−1.0−0.50.00.51.0 U V − U −0.5 0.0 0.5 1.0 1.5 2.0V−I−2.0−1.5−1.0−0.50.00.51.0 Radial bin 1Radial bin 2Radial bin 3 Figure 2.
Colour-colour plots for clusters in NGC 1566. Theclusters have been split into equal numbers in radial bins of 0-3.3 kpc, 3.3-4.7 kpc and 4.7 kpc outwards. The plots show thetraditional U-B vs V-I colours. They are overplotted with mod-els showing the evolutionary tracks of clusters and contours areplotted to show the concentration of the clusters in colour space.The extinction vector showing the movement of clusters on theplot due to extinction effects is in the top left corner. difference in the U-B colours, with the middle populationdisplaying 2 peaks in the density of points in the centre,with each corresponding approximately to the values of thesingle peaks of the other bins. This indicates that the medianU-B colour is continuously changing between bins. Clustersfurther towards the centre of the galaxy are slightly bluer,in agreement with the results for NGC 4041. The difference c (cid:13) , 1–18 Hollyhead et al.
Median U-B Median V-IBin 1 -0.90/ -0.64 /-0.33 0.46/ /0.78Bin 2 -0.92/ -0.57 /-0.18 0.46/ /0.77Bin 3 -0.68/ -0.38 /-0.11 0.44/ /0.78
Table 1.
The difference in colour properties for cluster popu-lations at different galacto-centric distances. The three bins arethose used throughout the analysis. The median U-B and V-Icolours (shown in bold) were calculated over the entire popula-tions and then compared to see if there were major differences inthe colour properties of the clusters at further distances from thecentre. Values to the left of the median are the lower quartilesand to the right are the upper quartiles. There is little differencein the values for V-I, but U-B shows more variation. The sec-ond bin with two maxima on the contour diagram has the largestinter-quartile range, which would be expected of a more spreaddistribution. indicates that there could be a small variations in the agesof the clusters radially from the centre, as age would be theprimary contributor to a change in colour. Potentially, thesevariations in age are due to the changing levels of disruptionthroughout the galaxy - with the highest near the galacticcentre meaning that fewer older clusters are present.
Many previous cluster population studies have explored theluminosity function of clusters in other galaxies. As luminos-ity is proportional to mass (modulo age), this can provideinsight into the behaviour of the cluster mass function us-ing an observed quantity, rather than a modelled one. Whilethis section explores our observed luminosity functions, in § NdL ∼ L − α dL , though the shape is not usually apure power law, but one that is truncated at the brighter endand can sometimes be better approximated with a doublepower law function (e.g. Gieles et al. 2006a). Fig. 3 shows alevelling at the faintest end, likely due to a combination ofreaching the reliable detection limit and potentially the dis-ruption process, which primarily affects lower mass clustersif a MDD disruption regime is considered. The truncationat the brighter end is caused by a truncation in the clustermass function at high masses, though this is not always ina one-to-one ratio as differential fading across wavelengthsalters the position of clusters of the same mass in the lu-minosity function. We find the gradient of the power lawsection ( α ) of the curve by using the linfit utility in idl ,which minimises χ .The range of luminosities selected for the fits variedslightly between each band, as the position of the power lawsection changed. The flat end of the distribution at faintluminosities was never included in the fit as the cause of theshape is most likely dominated by our detection limits and Figure 3.
Luminosity functions of the three binned regions ofthe galaxy as a log plot of the cumulative fraction, shown foreach band. The shape of the function can be approximated by apower law, as we would expect, and has been observed for othergalaxies with similar studies, such as M83. The values displayedon the plots are the gradient of the fit to the power law section ofthe function, using the linfit line-fitting utility in idl with errorsfound from fitting synthetic populations created by Monte Carlotechniques. c (cid:13)000
Luminosity functions of the three binned regions ofthe galaxy as a log plot of the cumulative fraction, shown foreach band. The shape of the function can be approximated by apower law, as we would expect, and has been observed for othergalaxies with similar studies, such as M83. The values displayedon the plots are the gradient of the fit to the power law section ofthe function, using the linfit line-fitting utility in idl with errorsfound from fitting synthetic populations created by Monte Carlotechniques. c (cid:13)000 , 1–18 he cluster population of NGC 1566 α = 2.13 α = 1.98 Log ( d N / dL ) + c Fixed bin widthFixed cluster number
Figure 4.
The luminosity functions for the whole cluster popu-lation above 5000 M (cid:12) for class 1 sources in the B band createdby binning the clusters, rather than using a cumulative function.The purple points show a binned function using variable bin widthwith equal numbers of clusters in each bin and he blue points rep-resent a function with fixed bin width and variable numbers ofclusters. The turnover at low luminosity is due to incompletenessand occurs at approximately the same values as for our cumula-tive function. Far less of a truncation at the bright end is seenin the binned functions, which can easily be dismissed as beingwithin Poisson noise, when in fact this could be a physical effect.Band Min fit Max fitUV 23.5 21U 23 21.5B 23.5 22V 23.5 22I 22.5 21.5
Table 2.
The maximum and minimum magnitudes used for thefit of each of the lines in the first radial bin. Other bins were fittedwith approximately the same values. magnitude cuts, with little influence from physical effects.Additionally, the brighter end of the distributions were alsonot included due to the low number of clusters and thereforepoor statistical significance. The ranges of fits were within21-24 magnitudes across each band and each bin; Table 2shows the exact fit ranges for the first bin, with other binsbeing approximately the same values. The fits are plottedover the curves for each band, and the values of α for eachfit are displayed on the plot.Other similar studies may use a binned luminosity func-tion, as shown in Fig. 4 for the B band. All class 1 clustersabove our mass cut of 5000M (cid:12) are used and we show theresults for variable bin width (purple) and fixed bin width(blue). The turnover at the faint end is due to incomplete-ness and occurs at approximately the same magnitude asthe equivalent turnover in Fig. 3. There is less evidence of atruncation at the bright end as seen in the cumulative func-tions, however the dramatic increase in bin size (for variablebin width) in the bright bins containing the same numberof clusters indicates that there are far fewer bright clustersand that there could potentially be a truncation, which is not clearly evident from a binned function. The slight dipin the fixed bin width distribution could be easily dismissedas Poisson noise, when in fact the effect could be physical.A cumulative function is more sensitive to changes at thebright end, though with the caveat of low cluster numbersand therefore poorer statistics.Previous studies have found that the value of α is usu-ally ≈
2, with small variations (de Grijs et al. 2003). Studiesof M83 show that the value is slightly higher for clusters inthe outer regions of the galaxy, indicating a decrease in thenumber of bright clusters (Bastian et al. 2012). The inner ar-eas of galaxies (just outside of the bulge) would be expectedto experience higher levels of star formation than furtherout into the arms due to a higher density of molecular gas.Ryon et al. (2014) find slightly different results for NGC2997. The circumnuclear regions were found to be slightlyshallower than the disk in the U and B bands but steeper inthe V and I bands.Our results agree with the other cluster populationstudies; α ≈ c (cid:13) , 1–18 Hollyhead et al.
The mass and age distributions of a population of clustersare highly useful for studying the star formation history ofthe galaxy and the effects of the disruption process. Clusterpopulation studies (including this one) generally impose amass cut on the population. This accounts for inaccuraciesin age and mass fitting and stochastic sampling of the stellarIMF (Silva-Villa & Larsen 2011; Fouesneau & Lan¸con 2010).Additionally, a mass-limited sample prevents bias in the agedistribution caused by young clusters. Fig. 5 is the age-massdiagram for class 1 sources in our catalogue. There appearsto be very little difference between the three populations ofclusters in varying distances from the galactic centre. Theblue line indicates the mass cut we applied to the cataloguefor our analyses at 5000 M (cid:12) . We lose a large percentage ofclusters after applying the cut, ( ∼ ≈ −
200 Myr, when lower mass clusters become too faintto observe.The age-mass diagram also displays some less populatedareas, such as the gap around 10-30 Myr. This is a well-known artefact from the mass and age fitting process andhas been previously identified in other galaxies such as M51(Bik et al. 2003; Bastian et al. 2005) and M83 (Chandaret al. 2010).
Age distributions of clusters across the galaxy can provideinformation on the formation history of the clusters and thescale or strength of the effect of disruption. By studying dif-ferent areas of the galaxy you can also determine whetherthe disruption process is environmentally dependent. It canbe assumed that the shape of the age distribution is onlydependent on cluster formation and disruption as our sam-ple is mass-limited. This means that a minimum detectionluminosity should not be shaping the distribution until af-ter 100 Myr (e.g. Gieles et al. 2007), as can be seen in theage-mass diagram.Fig. 6 shows the age distributions of clusters in thethree radial subsections of the galaxy, separated by distancesof 0.5 in log space to clearly show their shape. The bluesquares show the shape for the entire cluster population,while the purple, teal and red points show the consecutiveradial bins. We use overlapping bins to minimise the effectsof the stochastic nature of bin fitting, with the bin sizesshown at the bottom of the plot.The shape of an age distribution can generally beroughly approximated by a single power law with steepen-ing at high ages due to incompleteness. Our plot displayspotential evidence of a three component shape predicted bya system of mass dependent disruption, as summarised by l og ( d N / d t ) Radial bin 1Radial bin 2Radial bin 3All clusters
Figure 6.
The age distributions for different sections of thegalaxy. Only class 1 sources above 5000 M (cid:12) have been included.Overlapping bins have been used to remove unphysical variationscaused by the binning procedure, with the coverage of each binshown by the bars at the bottom of the plot. As shown, there islittle difference between the shapes of the distributions. A factorhas been added to each of the lines to separate the points andmake the shape of the distribution easier to see. The two bluevertical lines indicate the separate regimes within the age distri-bution, as described in the text. The plot is shaded after 200 Myras we are incomplete here, and may be partially incomplete from100 Myr.
Lamers (2009). The first section ranges from the beginningof the plot to ∼
10 Myr. This decline is caused by the dis-solution of young clusters as they expel any gas left overfrom the star formation process, and should be independentof mass (Bastian et al. 2006). However, at least part of thisdrop is likely due to the inclusion of unbound associationsin our cluster sample (Bastian et al. 2012).As our data is mass-limited, the next section, up to ∼
100 Myr for NGC 1566 (though this can extend to muchmore advanced ages in other galaxies), is fairly flat, whichindicates little disruption. The age-dating artefact at 10-30Myr could be affecting the shape of the distribution in thissection, however we think this is unlikely, as clusters in thisage range will still be accounted for in nearby bins, and shift-ing bins still produces a flat section (see Fig. 7). The finalsection is a strong decrease again, which could potentiallybe due to mass-dependent disruption of clusters due to tidaleffects with a large contribution from incompleteness of thefainter, older clusters (Boutloukos & Lamers 2003). As weare incomplete after 200 Myr (and potentially partially in-complete from 100 Myr) these two mechanisms cannot beentirely disentangled. Approximate values of the changes inthe sections are shown as vertical lines on the plot, and theshading indicates the age regime in which we are incomplete.The age distribution can be highly susceptible tochanges in the binning procedure used to represent the data,though binning is important to overcome small variationscaused by artefacts in age fitting. Fig. 7 shows how shiftingbins can alter the age distribution. Each shift still displaysevidence of a flattening in the ≈ −
100 Myr range. Thetop plot fits from 10-100 Myr as done in (Chandar et al. c (cid:13)000
100 Myr range. Thetop plot fits from 10-100 Myr as done in (Chandar et al. c (cid:13)000 , 1–18 he cluster population of NGC 1566 Log(age)
Log ( m a ss ) Radial bin 1 Radial bin 2Radial bin 3 All clusters
Bin 1
Figure 5.
Age vs mass for all class 1 sources in the catalogue. Each bin is displayed separately, with the combined population in thefinal plot. The blue line indicates the age cut we apply to the catalogue for the other analyses. We lose ∼ half of all clusters by applyingthe mass cut. The lower limit line on the right side of the plots represent the detection limits in the catalogue, as well as the magnitudecut imposed during the catalogue creation. The apparent ceiling to the data is due to the mass function. (cid:12) yr − (Thilker et al. 2007) (amended, discussed laterin § ∼ − . − −
1. (e.g. Whitmore et al. 2007). More recently,Chandar et al. (2014) have claimed that variations in fitbetween fields in M 83 is due to differences in the SFH be-tween fields, rather than varying levels of disruption. NGC1566 displays the same shaped distribution for each bin andan overall shape potentially indicative of a disruption mech-anism dependent on mass. The flat section seen between 10and 100 Myr argues strongly against a quasi-universal agedistribution. However, if a single power-law is fit to the dataover the full range a relatively steep index is found, due toincompleteness at high ages, and the abundance of youngclusters in our sample at ages less than 10 Myr. c (cid:13) , 1–18 Hollyhead et al. ζ = 0.077 ζ = −0.47 ζ = −0.55 ζ = 0.036 Log ( d N / d t ) + c Bin shift 0.1Bin shift 0.2Bin shift 0.3Bin shift 0.4 ζ = −0.43 ζ = −0.50 ζ = −0.59 ζ = −0.49 Log ( d N / d t ) + c Bin shift 0.1Bin shift 0.2Bin shift 0.3Bin shift 0.4
Figure 7.
The effect of shifting bins in the age distribution forall clusters more massive than 5000 M (cid:12) and only class 1 sources.The shape still displays evidence of a flattening in the 10-100 Myrrange so fitting single power laws to the data can be misleading.For this reason we do not attempt to fit our age distributions. Thisplot uses the same binning procedure as our age distribution. Thetop plot is fitted from 10-100 Myr, not including clusters < Another reason for the steepening of the age distribu-tion at young ages could be observational biases. NGC 1566is a fairly distant galaxy at ≈
17 Mpc, and therefore thedensest clusters in the galaxy may appear as point sources,which would be removed by the concentration index cut orvisual inspection phases. If the age distribution is biased to-wards larger clusters or associations that appear as clusters,the age distribution would decline more quickly due to theshorter lifetimes of less dense systems.
The mass distribution of clusters can be described by
Ndm ∼ M − β dm ; a function well approximated by a powerlaw with a possible truncation at the high mass end. Fig. 8shows the mass distributions for the three radial bins for β = 1.79 ± β = 1.96 ± β = 2.00 ± Log c u m u l a t i v e f r a c t i on Radial bin 1Radial bin 2Radial bin 3
Figure 8.
The mass distribution for clusters in bins of distancefrom the centre of the galaxy. The fit to distribution is highlydependent on the range over which the line is fitted. Clustersolder than ≈
100 Myr were removed as we are incomplete at highages. Clusters younger than 10 Myr have also been removed dueto possible incompleteness and difficulty in age and mass fittingin this age regime. clusters older than 10 Myr and younger than ≈
100 Myr.This age range was selected as we are likely partially incom-plete after 100 Myr (as shown by the age-mass diagram inFig. 5) and potentially affected by contamination from as-sociations in the sample below 10 Myr (e.g. Bastian et al.2012). Additionally age and mass fitting is less accurate be-low 10 Myr. Only class 1 sources and those more massivethan 5000 M (cid:12) are included. The distributions were fitted byminimising χ from ≈ − (cid:12) . There is a variationseen in the best fit for the power law section with respectto galactic radius, with a steeper slope for the outer clustersthan for the inner two bins, potentially indicating the pres-ence of more lower mass clusters than in the inner regions,which would agree with an environmentally dependent pro-cess of disruption. However, the differences are within theestimated errors on the fits and therefore no definite trendcan be determined.Fig. 9 shows the distribution for all clusters youngerthan 100 Myr and older than 10 Myr. The high mass end ofthe distribution does display evidence of a truncation as itdeviates from the power law fit line (shown as black dashedline), but as this could be due to dwindling numbers of clus-ters at these masses. This effect is unlikely to be due todisruption in a MDD regime, as more massive clusters areaffected less by disruption but it could play a part if MID isconsidered. The errors on the fits are found through MonteCarlo simulations of mass distributions. While much information can be gleaned from studying theobserved distributions of quantities such as age, mass or lu-minosity for the clusters, the underlying processes causingtheir appearance are not always evident solely from obser- c (cid:13)000
100 Myr.This age range was selected as we are likely partially incom-plete after 100 Myr (as shown by the age-mass diagram inFig. 5) and potentially affected by contamination from as-sociations in the sample below 10 Myr (e.g. Bastian et al.2012). Additionally age and mass fitting is less accurate be-low 10 Myr. Only class 1 sources and those more massivethan 5000 M (cid:12) are included. The distributions were fitted byminimising χ from ≈ − (cid:12) . There is a variationseen in the best fit for the power law section with respectto galactic radius, with a steeper slope for the outer clustersthan for the inner two bins, potentially indicating the pres-ence of more lower mass clusters than in the inner regions,which would agree with an environmentally dependent pro-cess of disruption. However, the differences are within theestimated errors on the fits and therefore no definite trendcan be determined.Fig. 9 shows the distribution for all clusters youngerthan 100 Myr and older than 10 Myr. The high mass end ofthe distribution does display evidence of a truncation as itdeviates from the power law fit line (shown as black dashedline), but as this could be due to dwindling numbers of clus-ters at these masses. This effect is unlikely to be due todisruption in a MDD regime, as more massive clusters areaffected less by disruption but it could play a part if MID isconsidered. The errors on the fits are found through MonteCarlo simulations of mass distributions. While much information can be gleaned from studying theobserved distributions of quantities such as age, mass or lu-minosity for the clusters, the underlying processes causingtheir appearance are not always evident solely from obser- c (cid:13)000 , 1–18 he cluster population of NGC 1566 β = 1.91 ± Log c u m u l a t i v e f r a c t i on Figure 9.
The mass distribution for all class 1 sources in thecatalogue, with a mass cut of 3.7 in log space. The best fit to thepower law section is shown in the top right. vations. The modelling of physical processes underpinningthe evolution of clusters is important in relating observablesto the physics behind them. In this section we fit data toobtain information about the cluster population and thenuse this to form model functions to which we can compareour data and further understand its qualities.
Age and mass distributions can provide empirical reason-ing for the strength and scale of disruption in NGC 1566,however further information requires modelling and fittingdata. Fig. 10 displays maximum likelihood fits to the ageand mass plots for the three radial bins and the total pop-ulation, as done for M 83 by Bastian et al. (2012). Clustersolder than 10 Myr are selected for the fits, with an addi-tional constraint of a minimum V band magnitude of 23.5magnitudes, to ensure completeness.The fits employ the relationship between disruptiontimescale and cluster mass, scaling as M γ with γ = 0 . M c and t (the turnover mass and averagetime scale of disruption for a 10 M (cid:12) cluster respectively).We estimate M c ≈ . × M (cid:12) and t as ≈
100 Myr forNGC 1566, taken from the fit for the entire cluster popula-tion.There is little difference in M c for each successive radialbin. This suggests the truncation value in the mass functionfor each section should occur at the same mass. The trun-cation value in Fig. 8 is difficult to determine accuratelyfor the three populations due to dwindling cluster numbersat high masses. t is very similar for the inner two radialbins, however is around a factor of 2 larger in the outermostbin. This result may not be significant but indicates thatouter clusters are possibly disrupted more slowly than innerclusters.The values for M c and t were used to model the con-tributions from different aged stellar populations to the lu-minosity function for NGC 1566, as discussed in the nextsection. t was scaled to t (the average disruption timescale Figure 11.
Modelled relative contributions of varying clusterages made to the luminosity function for a Schechter mass func-tion. The three panels are as follows: the shape of the luminosityfunction, the value of α for the function at each point and the con-tributions of clusters in four different age bands. The blue bandis clusters aged 10 − years, the green is 10 − years, theyellow 10 − years and the red 10 − years. t is theaverage disruption timescale of a 1 M (cid:12) cluster. Figure 12.
The luminosity functions in the U, B, V and I bandswith magnitudes converted to luminosities. The top panel on theplot shows the shape of the functions for all class 1 clusters above5000 M (cid:12) and younger than our incompleteness limit of ∼ α ) along the curves. α is found by fitting the functionsabove by minimising χ , with overlapping bins of 0.5 dex. of a 1 M (cid:12) cluster), as required for the model. t was foundto be 100-200 Myr, for which we took the average of the twovalues. The shape of the luminosity function depends on the clusterformation history, the mass function of the clusters, their c (cid:13) , 1–18 Hollyhead et al.
Figure 10.
Maximum likelihood fits of the age mass distributions for the three different radial bins used throughout this study, andadditionally the fit for the entire cluster population in the lowest plots. The left column shows the age mass plots of the clusters, whilethe right plots show the maximum likelihood fit for the truncation value of the mass function ( M c ) and the corresponding timescale fordisruption of a 10 M (cid:12) cluster. The clusters in black are used for the fit and are selected using an age cut of 10 Myr and a magnitudecut in the V band of 23.5. c (cid:13)000
Maximum likelihood fits of the age mass distributions for the three different radial bins used throughout this study, andadditionally the fit for the entire cluster population in the lowest plots. The left column shows the age mass plots of the clusters, whilethe right plots show the maximum likelihood fit for the truncation value of the mass function ( M c ) and the corresponding timescale fordisruption of a 10 M (cid:12) cluster. The clusters in black are used for the fit and are selected using an age cut of 10 Myr and a magnitudecut in the V band of 23.5. c (cid:13)000 , 1–18 he cluster population of NGC 1566 mass evolution and extinction. Clusters fade as they age andthere are, therefore, clusters with different ages and massescontributing to the number of clusters at a given luminosity.To get a better understanding of how the LF depends on thevarious implied properties of the cluster population in NGC1566, we here model the LF based on the underlying massfunctions and cluster disruption timescale we derived earlier.We assume a constant cluster formation rate of 10 yrand a Schechter function for the cluster initial mass function(CIMF), with an index of α = − M ∗ = 2 . × M (cid:12) , as obtained fromthe maximum likelihood fitting method in § t = 0 .
35 Myr, also as found in § B , V and I filters is found from the age-dependentmass-to-light ratios of the single stellar population modelsof Bruzual & Charlot (2003). The logarithmic slope ( α ) isderived from the LF using the symmetric difference quotient.Similar procedures to model the LF are presented in Fall(2006); Larsen (2009); Gieles (2010).Fig. 11 shows the resulting LF model. The top panelshows the LF in the three filters, the middle panel shows theluminosity dependent α and the bottom panel displays therelative contributions of different age bins. Young clustersdominate at the bright-end as the result of the truncationin the CIMF and evolutionary fading (i.e. old M ∗ clustersare fainter than young M ∗ clusters). At low luminosities themajority of the clusters are also young, which is due to dis-ruption.In Fig. 12 we show the LF (top panel) and α (bottompanel) for the clusters in NGC 1566. We find α by usingthe linfit procedure in idl . We use overlapping bins of 0.5dex to ensure that no anomalous peaks in the luminosityfunction dominate the fit for α .The general behaviour of the LF and α in different filtersis similar to that of the model in Fig. 11. The LF is steeper athigher L , which in our model is the result of the exponentialtruncation (at high L ) and mass dependent disruption (atlow L ). The LF is steeper in redder filters, which in ourmodel is due to the truncation of the mass function and morerapid fading in bluer filters. We note that if the steepeningof the LF was due to a luminosity dependent extinction,we would expect to see the opposite: a steeper LF in thebluer filters. The average and median value for α for ourdata corresponds very well to the average and median forthe model values of α , as shown in Table 3.This modelling exercise further supports the finding ofa truncation or steepening in the underlying mass function. Clusters and associations are the building blocks of galax-ies, and therefore are vital to understanding star formationprocesses. Adamo et al. (2015) recently showed how tracingthe properties of clusters across M 83 provides information
Mean values for α Band Observed ModelB -2.08 -2.02V -2.19 -2.16I -2.25 -2.27
Median values for α Band Observed ModelB -1.99 -1.97V -2.14 -2.11I -2.29 -2.18
Table 3.
Average and median values for α for our observed lu-minosity function and our model function. The values are verysimilar across all bands, indicating that our results are compara-ble. on how the galactic environment has influenced the clusterformation process, and consequently gives insight into starformation throughout the galaxy. In this section we discussseveral galactic parameters that provide insight into clusterpopulations and their histories, including M brightestV , Γ and T L ( U ). Fig. 13 shows the absolute V band magnitude of the bright-est cluster in our NGC 1566 catalogue plotted against thelog star formation rate of the galaxy. Our SFR was foundby reducing the value for the SFR of NGC 1566 provided inThilker et al. (2007) to account for the area of the galaxycovered by the HST WFC3 images, which is smaller. Thilkeret al. (2007) use the same distance for NGC 1566 as ourstudy, which makes this calculation trivial. The calculationis based on Hα flux extracted from an image covering the en-tire galaxy from the SINGS survey. The ratio of the flux forthe areas covered by Thilker et al. (2007) and HST allowedus to reduce their estimate of the SFR accordingly, givingus a value of 4 . (cid:12) yr − . Our data point is displayed as thered star. The other data points for other galaxies were takenfrom Adamo et al. (2015) (please see Table B1 of that paperfor the full list of objects included). The clear correlationbetween these two parameters is the result of the stochas-ticity of the cluster formation process and size of sampleeffect, where higher SFR galaxies are able to sample the ini-tial mass and luminosity functions to brighter and highermass clusters (Larsen 2002; Bastian 2008). NGC 1566 is noexception to this effect, lying comfortably at the end withthe higher rate of star formation. As discussed in § SFR ) (e.g.Goddard et al. 2010; Ryon et al. 2014), with which it corre-lates. Γ is also found to decrease within the same galaxy fur-ther from the galactic centre (Silva-Villa et al. 2013; Adamoet al. 2015). As the CFE can provide information on how c (cid:13) , 1–18 Hollyhead et al.
Figure 13.
A collection of clusters in nearby galaxies’ with thebrightest V band magnitude in their respective populations plot-ted against the galaxies’ total star formation rates. There is a clearrelationship between these two quantities, displaying the stochas-tic element of the cluster formation process. The value for NGC1566 is shown as a red star. Major contributors to the number ofsources on the plot are listed to the right, please see Table B1 ofAdamo et al. (2015) for the literature containing this information. galactic environment can affect cluster population proper-ties, we calculated the value for NGC 1566 to compare withother galaxies.
Γ is calculated for two different age ranges of clusters: 0-10 Myr and 10-50 Myr. The division at 10 Myr is due tothe difficulty in fitting ages and masses to clusters youngerthan this age, which introduces inaccuracy in the calculationof Γ for 0-10 Myr. The mass cut of 5000 M (cid:12) applied tothe rest of this work was again applied here to attempt toaccount for stochastic IMF sampling by using a mass-limitedsample. Additionally, we only included class 1 sources toavoid contamination of a ’true cluster’ population.Γ is found by dividing the cluster formation rate (CFR)by the total star formation rate of the galaxy. So in orderto find Γ we need to estimate a CFR, which can be definedas the total mass of clusters formed divided by the timeover which they form. The first step in calculating a CFRis the integration of a chosen cluster mass function (CMF)over 2 sets of limits. The first set corresponds to finding atheoretical total cluster mass ( M c,tot ), with a lower limit of100 M (cid:12) and an upper limit of 1 . × M (cid:12) , the observedhighest mass cluster. The second set provides an estimate ofa theoretical observed cluster mass ( M c,obs ), and uses a lowerlimit of our mass cut of 5000M (cid:12) and the same upper limitas the previous integration. Using the ratio of the resultingintegrated functions, we can estimate the cluster formationrate in the two selected age ranges and therefore calculateΓ. The CMF we have chosen to use is a simple power law,as observed to fit well to many cluster populations’ mass dis-tributions, including NGC 1566, of the form dN ∝ m − β dm . The validity of using a power law function is discussed inthe next section. The value of β we chose was 2, the averagevalue found for most galaxies. The ratio of the two integra-tions provides the factor for calculating a total cluster massin NGC 1566 based on data, rather than theoretical. Forexample, if the theoretical ratio of observed to total clustermass is 0.5, then an estimate of a total cluster mass based ondata would be double the summation of all observed clustersin our catalogue. This value is then carried forward to finda CFR by dividing the total mass by 10 for CF R − Myr and 40 for
CF R − Myr and Γ is then
CF R/SF R × Fig. 14 shows the trend between Γ and log of Σ
SFR (surfacedensity of star formation) observed for a variety of objectstaken from the literature by Adamo et al. (2015) (again,please see Table B1 in this paper for the full details of thepoints and their sources), with values calculated for NGC1566 shown by the red and teal stars. The value of log Σ
SFR is found by dividing our SFR by the area covered in kpc, andis found to be ≈ .
033 M (cid:12) yr − kpc − . For NGC 1566 we findthat Γ ≈ . ± . ≈ . ± . SFR and therefore a higher CFEis that NGC 1566 has a fairly high star formation rate (whencompared to similar galaxies) and yet has a lower than ex-pected cluster formation efficiency and Σ
SFR . This indicatesthat the galaxy is primarily forming stars outside of boundclustered environments possibly because of insufficient gasdensity. It may be possible, therefore that Γ is not stronglyrelated to the star formation rate in the galaxy, and canonly be reliably dependent on gas density. Additionally, thiscould be possible with significant disruption within 100 Myr.There are many limitations to our calculation of Γ, asdiscussed in detail for NGC 3625 by Goddard et al. (2010).In their work they used synthetic cluster populations to ex-amine the accuracy and effectiveness of their calculations.They identified many potential sources of error, which canalso be applied to NGC 1566.Firstly, by using our total observed cluster mass dur-ing the conversion from integrated quantities to estimatesbased on our data, we assume that we have detected allclusters in the galaxy. Some clusters are inevitably missedduring the detection and catalogue refinement phase, espe-cially the youngest clusters that may be obscured by dust.Our catalogue likely misses few of these clusters, however asWhitmore & Zhang (2002) found that when comparing thedetection of the youngest clusters in radio bands and opticalbands, there is ∼
85% overlap. Hollyhead et al. (2015) founda similar result for M 83, where detections in the H bandconfirmed few clusters would be missed.Ages and masses of clusters are obtained by fitting pho-tometric data to SSP models. The parameters of the SSPmodel, for example the metallicity used, can strongly affectthe resulting cluster properties by altering the numbers of c (cid:13) , 1–18 he cluster population of NGC 1566 clusters at different ages or masses (Bastian et al. 2005).Goddard et al. (2010), however, report a difference of 5-10%for differing SSP models, so the effect is likely negligible.The assumed mass function also plays an important rolein the calculation. We have used a power law with an indexof − M (cid:12) or higher. The estimate ofthe truncation value for NGC 1566, however, is ≈ . M (cid:12) ,which is shown to have a larger difference. The differencein integrated mass between a power law and a Schechterfunction with turnover mass equal to that of NGC 1566 is ≈ .
75. This means that our total mass could be ≈ . ≈ . ≈ . SFR for the young ( <
10 Myr) clusterpopulation in their sample. When using an older popula-tion (100-300 Myr), they did find similar trends as expectedbased on previous works using Γ (e.g. Adamo et al. 2015).Their CMF/SFR is not subject to all of the same uncertain-ties as Γ, though ages, masses and extinctions do still needto be modelled. Kruijssen & Bastian (2016) showed that thediscrepancy, at least in part is due to a lack of distinctionof bound and unbound aggregates at young ages in Chan-dar et al. (2015) as well as the need to account for clusterdisruption at later ages. It is worth noting, however, thatsome of the galaxies presented in Adamo et al. (2015) alsodo not make the distinction between bound and unboundaggregates, though several make age cuts to remove youngclusters that likely cause contamination of unbound sources.This lack of uniformity is addressed by the LEGUS survey(Calzetti et al. 2015). T L ( U )Another quantity that is related to Γ and gives an indica-tion of the effect that environment plays on cluster popula-tions is the percentage of U band light from a galaxy that isemitted by clusters, or T L ( U ). U band light primarily tracesthe young clusters in the population, as they are usuallybrighter in bluer bands, while older clusters have faded andemit more strongly in redder bands, so therefore should belinked to star formation. Unlike Γ however, T L ( U ) is a purelyobservational quantity, therefore free of the biases and errorsintroduced by selecting an approximate mass function andusing quantities derived from SSP models. T L ( U ) is also notstrongly affected by extinction.We took the data for other galaxies from Larsen & Figure 14.
Cluster formation efficiency against the surface den-sity of star formation for a variety of objects, including NGC1566. The correlation indicates that clusters form in denser ar-eas of cold gas. NGC 1566 is shown by the red and teal stars,which display a fairly low CFE and surface density in comparisonto the SFR. Major contributors to the data points are listed onthe right, the other sources can be found in Table B1 of Adamoet al. (2015). The blue line represents the model to the data fromKruijssen (2012).
Richtler (2000) and Adamo et al. (2011) and calculated T L ( U ) for NGC 1566 to investigate where it lay in rela-tion to other galaxies on the plot. T L ( U ) was calculatedby summing the U band luminosities of all clusters in thecatalogue, dividing by the total measured U band luminos-ity for the entire galaxy obtained by aperture photometryand multiplying by 100. We applied the usual mass cut of5000 M (cid:12) and split the catalogue into class 1 and class 2sources. We find that T L ( U ) ≈ .
1% for class 1 sources and T L ( U ) ≈ .
7% for class 1 and 2 sources.Fig. 15 shows the relationship between Σ
SFR and T L ( U ). The purple, teal and black points are those takenfrom Larsen & Richtler (2000), where purple points are star-burst galaxies and mergers, while the black and teal pointsare other galaxies. The blue points are BCGs taken fromAdamo et al. (2011) and the red star is for NGC 1566. Theplot demonstrates that the galaxy fits well onto the currentrelationship and is also in the section of the plot populatedby starburst galaxies and merging systems. This would beexpected of a galaxy with a high star formation rate, though T L ( U ) correlates less strongly with SFR than Σ SFR (Larsen& Richtler 2000; Larsen 2002).In addition to T L ( U ), Larsen & Richtler (2000) providedvalues for T L ( V ) for all of the galaxies. Fig. 16 shows therelationship of T L ( V ) with Σ SFR . Little difference is seenbetween the plots for the two different bands. NGC 1566however, shows a fairly large difference between the U andV bands. If the star formation history has been increasing,this could be due to the galaxy having many young clusters,so they contribute more strongly to T L ( U ) than T L ( V ). Weinvestigated the effect on the percentage of the total lumi-nosity emitted from clusters in the U, B, V and I bands.Table 4 shows the data for the different bands, givingthe total magnitude of the galaxy and the percentages for c (cid:13) , 1–18 Hollyhead et al.
Figure 15. T L ( U ) for galaxies taken from Larsen & Richtler(2000) and Adamo et al. (2011) and now including the data forNGC 1566. The teal points indicate galaxies that were taken fromLarsen & Richtler (1999), the purple points are starburst andmerger galaxies introduced in Larsen & Richtler (2000), the blackpoints are other galaxies from Larsen & Richtler (2000) and theblue are BCG galaxies from Adamo et al. (2011). The red star isour data for NGC 1566. Both axes are log units. Figure 16. T L ( V ) for galaxies taken from Larsen & Richtler(2000) and now including the data for NGC 1566. The colours in-dicate the same separation of galaxies as described in the previousfigure. Band M gal T L T L U 11.59 10.1 12.7B 11.81 4.8 5.9V 10.94 2.3 2.8I 9.76 1.3 1.5
Table 4.
Percentage of total galaxy luminosity emitted from clus-ters in the U, B, V and I bands. M gal is the magnitude of thewhole galaxy in each band, T L is the percentage given for onlyclass 1 sources and T L is for class 1 and 2 sources. Radial bin 1 Radial bin 2 Radial bin 3 N
274 274 278 N
70 85 56 α V β M c (M (cid:12) ) 2 × × × t (Myr) 80 80 200 Table 5.
Summary of data for the three radial bins used through-out this study. These are values as calculated using a mass cutof 5000 M (cid:12) with full detections in the UV band. The bins werechosen to accommodate approximately equal numbers of clustersin each bin for our plots. However, this applies only to class 1sources, as these were used for the analysis. N and N refer tothe number of class 1 and class 2 sources respectively. α V is thefit to the V band luminosity function, while β is the fit to themass function. M c is the truncation mass and t is the averagedisruption timescale of a 10 M (cid:12) cluster. only class 1 sources and class 1 and 2 sources. There appearsto be a general trend, as we could expect, in the values of T L . Less luminosity in redder bands is omitted by clusters,as older clusters that emit primarily at redder colours arefainter and will contribute less than other sources. This in-dicates that by calculating T L ( I ) we are comparing the lightfrom clusters to the large field stellar population throughoutthe galaxy, consisting of older stars, which will contributemuch more strongly at longer wavelengths. Younger clus-ters are usually the brightest, which emit more heavily inbluer bands. NGC 1566 displays negligible variations in several clusterproperties at different galactocentric distances within the ∼ . • There is a small variation in colour space with respectto galactocentric distance. The most concentrated areas ofcolour space are slightly redder in the outer radial bins. Thisis likely due to small variations in the age of the clusterswith distance, as age is the primary factor affecting colourdistribution (extinction is expected to go in the oppositedirection). Similar variations are also seen in other galaxies,such as NGC 4041 and M 83. • The shape of the luminosity functions for all radial binsare as expected, with the power law section of the best fitwith an index value of α ≈ −
2, as found in numerous otherstudies and galaxies. We found negligible differences in theindices fitted for different radial bins, with the largest differ-ences in the UV and U bands, though all are within errors onthe fit. In agreement with the luminosity function, as theyare potentially related, the mass distributions also show onlysmall variations. We find a steepening of α for redder bands,which is predicted if the cluster mass function is truncatedat the end mass end. This is due to the more rapid fading ofclusters in bluer bands, as clusters with the same mass, but c (cid:13)000
2, as found in numerous otherstudies and galaxies. We found negligible differences in theindices fitted for different radial bins, with the largest differ-ences in the UV and U bands, though all are within errors onthe fit. In agreement with the luminosity function, as theyare potentially related, the mass distributions also show onlysmall variations. We find a steepening of α for redder bands,which is predicted if the cluster mass function is truncatedat the end mass end. This is due to the more rapid fading ofclusters in bluer bands, as clusters with the same mass, but c (cid:13)000 , 1–18 he cluster population of NGC 1566 different ages, are more spread across a luminosity range inbluer bands, giving rise to a shallower function. • The age distribution for NGC 1566 is also of the shapewe would expect. Little difference in colour distribution forclusters in the three radial bins indicated a fairly uniformrange of cluster ages throughout the galaxy. The age distri-bution shows that this is likely the case, as the three binsdisplay only small variations between them. There is somedifference between the shape of the distribution for NGC1566 and other galaxies such as M 31 and M 83. The in-ner regions of M 83 have a much steeper age distributionbetween 10 −
100 Myr, suggesting that cluster disruption ismuch more efficient there than in NGC 1566 or M 31. • The mass distributions show a slight steepening withincreasing radial distance, but within error estimates. Addi-tionally, the data suggest a truncation in the mass function,though this could be due to low numbers of clusters at highmasses. This finding is supported by our comparison of theobserved luminosity function with models, which show thata Schechter function is a good fit. The index of the slopesare all ∼
2, as observed for other galaxies.
We have calculated T L ( U ) and Γ for NGC 1566 and findboth values to lie within the correlations with Σ SFR . Aninteresting result of the study was that we found Γ to beslightly lower than expected for a galaxy with a fairly highSFR. This is when compared to galaxies similar to NGC1566. While the galaxy still fits into the current scaling rela-tions for these properties, Γ could indicate that the galaxy isless efficient at forming stars in clusters than we may expect.
ACKNOWLEDGEMENTS
Based on observations made with the NASA/ESA Hub-ble Space Telescope, and obtained from the Hubble LegacyArchive, which is a collaboration between the Space Tele-scope Science Institute (STScI/NASA), the Space TelescopeEuropean Coordinating Facility (ST-ECF/ESA) and theCanadian Astronomy Data Centre (CADC/NRC/CSA).
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