On the use of asymmetric PSF on NIR images of crowded stellar fields
Giuliana Fiorentino, Ivan Ferraro, Giacinto Iannicola, Giuseppe Bono, Matteo Monelli, Vincenzo Testa, Carmelo Arcidiacono, Marco Faccini, Roberto Gilmozzi, Marco Xompero, Runa Briguglio
OOn the use of asymmetric PSF on NIR images of crowdedstellar fields
Giuliana Fiorentino a , Ivan Ferraro b , Giacinto Iannicola b , Giuseppe Bono b,c , Matteo Monelli d,e ,Vincenzo Testa b , Carmelo Arcidiacono a , Marco Faccini b , Roberto Gilmozzi f , Marco Xompero g ,Runa Briguglio ga INAF-Osservatorio Astronomico di Bologna, via Ranzani 1, 40127, Bologna, Italy b INAF-Osservatorio Astronomico di Roma, via Frascati 33, Monte Porzio Catone, Rome, Italy c Dipartimento di Fisica, Universit`a di Roma Tor Vergata, via della Ricerca Scientifica 1, 00133Rome, Italy d Instituto de Astrof´ısica de Canarias, Calle Via Lactea, E38200 La Laguna, Tenerife, Spain e Departamento de Astrof´ısica, Universidad de La Laguna, Tenerife, Spain f European Southern Observatory, Karl-Schwarzschild-Str. 2, 85748 Garching bei Munchen,Germany g INAF-Osservatorio Astronomico di Arcetri, Largo Enrico Fermi, 5, 50125 Firenze, Italy
ABSTRACT
We present data collected using the camera PISCES coupled with the Firt Light Adaptive Optics (FLAO)mounted at the Large Binocular Telescope (LBT). The images were collected for two different pointings by usingtwo natural guide stars with an apparent magnitude of R ∼ <
13 mag. During these observations the seeing wason average ∼ ∼ ∼
23 mag.J–band images display a complex change in the shape of the PSF when moving at larger radial distances fromthe natural guide star. In particular, the stellar images become more elongated in approaching the corners of theJ-band images whereas the Ks–band images are more uniform. We discuss in detail the strategy used to performaccurate and deep photometry in these very challenging images. In particular we will focus our attention on theuse of an updated version of ROMAFOT based on asymmetric and analytical Point Spread Functions.The quality of the photometry allowed us to properly identify a feature that clearly shows up in NIR bands:the main sequence knee (MSK). The MSK is independent of the evolutionary age, therefore the difference inmagnitude with the canonical clock to constrain the cluster age, the main sequence turn off (MSTO), provides anestimate of the absolute age of the cluster. The key advantage of this new approach is that the error decreasesby a factor of two when compared with the classical one. Combining ground–based Ks with space F606Wphotometry, we estimate the absolute age of M15 to be 13.70 ± Keywords:
AO systems, globular clusters, data reduction
1. INTRODUCTION
One of the main unsolved question in astronomy is how galaxies form and evolve. Resolved Stellar Population(RSP) are one of the most powerful diagnostic to provide solid constraints on the early formation and evolutionof the Milky Way (MW). In this context Galactic Globular clusters (GGCs) play a crucial role, since they arethe oldest ( ∼ > Further author information: (Send correspondence to Giuliana Fiorentino)Giuliana Fiorentino: E-mail: giuliana.fi[email protected], Telephone: +39 051 209 53 18 a r X i v : . [ a s t r o - ph . I M ] J u l hat GGCs are fundamental laboratories to constrain the evolutionary properties of low–mass stars, but also forseveral open problems in modern Astrophysics. One of the key advantages in using GCs as tracers of the oldstellar populations is that they are ubiquitous in early and late galaxies and in massive dwarf galaxies. Absolute and relative ages of GCs together with their proper motions (PMs), galactocentric distances andradial velocities are required to properly understand the MW formation.
2, 3
The GC absolute ages also providea lower limit on the epoch of pristine galaxy formation, and therefore, on the age of the Universe. The measure-ments of the above diagnostics do require: i ) high–quality multi–band images to perform accurate and precisephotometry in crowded stellar fields; ii ) high–resolution spectra collected with multi-object spectrographs toestimate heavy element (iron, α , CNO) abundances. The photometry allows us to construct Color-MagnitudeDiagrams (CMDs) and Luminosity Functions (LFs) to evaluate the cluster age and the proper motion. Thespectroscopy provides the chemical enrichment history and the kinematics.During the last twenty years the unprecedented image quality (stable Point Spread Function, PSF) andspatial resolution of the Hubble Space Telescope (HST) have been a quantum jump in the analysis of stellarpopulations in crowded stellar fields (Galactic Center, Bulge, innermost regions of GCs). The consequence isthat HST optical images allow us to build CMDs with accurate and deep photometry at least five magnitudesfainter than the main sequence turn–off (MSTO). The same outcome does not apply to near-infrared (NIR)images collected with HST (e.g., with the IR channel of the WFC3). The diffraction limit of HST in the Ks bandis ∼ ∼ ). Note that this means Ks–band images witha FWHM of ∼ ).The key advantage of the MCAO systems is their uniform correction across a quite large field of view(FOV ∼ ∼ (see Fig. 1 in Marchetti et al. 2008) and more recently by GeMS (Turri et al. 2014, this SPIE conference)available at the Gemini South Telescope. MAD had a limited sky-coverage, since the closure of the loop requiredan asterism of three stars brighter than V ∼
13 mag over two arcmin on the sky. However, MAD was a verysuccessful experiment, since delivered NIR images with a uniform PSF across the corrected FOV and producedseveral interesting investigations on RSP.
The accuracy and precision of the CMDs based on MAD images issimilar or even better than CMDs based on images collected with optical and NIR images collected with HST.Disentangling two different stellar populations in the bulge GGC Terzan 5, MAD observations suggested thatthis cluster is a candidate building block of the Galactic bulge. However, the complex variation of the PSFacross the FOV and in time makes the analysis of MCAO data quite challenging.Equipped with one deformable secondary mirror and a high-order pyramid wave-front sensor, each LBT eyecan work with a SCAO system that coupled with the high spatial resolution of PISCES (pixel scale = 0.0193”)can deliver high quality NIR images of crowded stellar fields. When first mounted on one of the LBTs (early2010), the adaptive optics system–FLAO –provided the best NIR images ever collected with a ground–basedtelescope. The new systems succeeded in delivering images with a PSF across the FOV that was more than threetimes sharper than images collected with HST. Moreover, during the initial testing phase, the LBTs adaptiveptics system was able to achieve and unprecedented Strehl Ratio in the Ks–band: from 60 to 80 percent. Thismeans an improvement of two-third in image sharpness when compared with similar AO systems available at8-m class telescopes. Current generation of AO systems are a fundamental playground not only for the technological challenges,but also to sharpen our fingernail in analyzing NIR images of crowded stellar fields that will be collected withMCAO systems. This will offer the unique opportunity to revolutionize our approach to Galaxy evolution andto pave the way for future ELTs (diameter ≥ ). It is of critical importance for the full exploitation of ELTfacilities that NIR RSP are explored and successfully modeled. AO deep NIR data will provide crucial inputs forthe modeling of cool stars, mainly emitting in NIR, for which uncertainties related to the effective temperatureevaluation and to the colour-temperature transformations require further investigation.
16, 17
Moreover, recent deep NIR studies indicate a new robust method to estimate the age of GGCs using thesignature of collisional induced absorption of molecular hydrogen in low-mass (M ∼ (cid:12) ) MS stars (seeFig. 2 in Bono et al. 2010). This opacity mechanism shows up as a well–defined Knee observable in the faintMS (MSK), and its position is, at fixed chemical composition, independent of the cluster age (Mk ∼ ∼ σ (MSK–MSTO) ∼ σ (MSTO)/2 ∼ ∼ < -2 dex]). Moreover, M15 appears to be in an advanced dynamical state (post core collapsed), thismeans that the innermost cluster regions display a well defined sharp peak in luminosity, and in turn in densityprofile. It has also been suggested that M15 harbors an Intermediate Mass Black Hole. The above featuremade M15 a fundamental laboratory to test the accuracy and the precision of the approach adopted to performphotometry in crowded stellar fields (ALLFRAME ).
2. PHOTOMETRIC DATA
The NIR images adopted in this investigation were secured in October 2011 with PISCES by using the DX(right) 8.4 m telescope of LBT where the FLAO was originally mounted. This AO system relies on two keycomponents, namely an adaptive secondary mirror with 672 actuators and an innovative high-order pyramidwave-front sensor.The scientific target was the Galactic Globular M15 (RA=21:29:58.33, DEC=+12:10:01.2) visible for morethan about four hours with an air mass smaller than 1.3. Data were acquired for two different different pointings,the former is centrally located, while the latter is located at 3 arcmin form the center in the South-Westdirection. Two natural guide stars adopted to close the loop of the AO system are: NGS1, RA= 21:29:58.616,DEC=+12:09:56.34, R=12.6 mag central pointing and NGS2, RA= 21:29:44.6457, DEC=+12:07:30.697, R=12.9mag off–center pointing. One of the key advantages in observing Galactic Globulars is that NGSs can be easilyidentified in the innermost cluster regions. Cluster red giant stars are typically brighter than R ∼
13 mag up todistances of 10–16 kpc.We collected 18 J-band and 20–Ks band images for the central pointing with a total exposure time of 108and 170 s, while for the off–center pointing we secured 20 J-band and 42 Ks–band images for a total 600 and 630s (see Table 1). The external DIMM seeing ranges from 0.7 to 1.1 arcsec for the central pointing and from 0.6to 0.95 arcsec for the off–center pointing. These weather conditions and the selected NGSs allowed us to reacha Strehl ratio up to 65% in Ks and 30% in J in the central pointing and up to 50% in Ks and 13% in J in theoff–center pointing. Fig. 1 shows the position of the pointings together with the position of the adopted NGSs.In order to provide a more clear idea concerning the AO performance that can be reached with PISCES,Fig. 2 shows two images collected in the J (left) and in the Ks (right) band for the central pointing. A glanceat the shape of the stars plotted in these images clearly shows that the PSF in J-band become more and moreelliptical as a function of the distance from the NGS. The FWHM increases from 0.04 arcsec in the very centerof the image to about 0.07 arcsec in its outskirt. This effect is more mitigated in the Ks–band, and indeed the
ISCES EXT. FOVPISCES Central FOV
Figure 1. Finding chart of M15 showing the two PISCES pointings (red squares) with a FOV of 21 × t exp =10 s, see Table 1). The two small images located onthe left side display the zoom of two regions located at different distances from the NGS highlighted with a red cross inthe image. The difference in the shape of the stars between the two regions clearly show a difference in the perfomanceof the AO system. Right: Same as the left, but for a Ks–band image ( t exp =15 s) . The Ks–band image shows a bettercorrection than J-band image, and indeed the shape of the stars is more regular and circular across the FOV. The specklesgenerated by the AO correction are present both in the J and in the Ks–band images, the extended seeing halos can alsobe easily identified.able 1. Observing log. INSTRUMENT PASSBAND N obs × TEXPPISCES-central FOV J 9 × ×
10 sPISCES-central FOV Ks 10 × ×
15 sPISCES-external FOV J 20 ×
30 sPISCES-external FOV Ks 42 ×
15 sshape of the PSF remains almost circular across the entire image (see the zoom on individual stars). The FWHMis on average ∼ × × ∼
3. DATA REDUCTION
Photometry of crowded stellar fields became a solid opportunity during the late eighties thanks to the developmentof sophisticated automatic techniques to perform the photometry on digitalized photographic plate images. Theuse and the role played by these packages became even more crucial in handling hundreds of optical imagescollected with modern CCDs. The most commonly used packages to perform PSF fitting photometry in crowdedstellar fields are DAOPHOT (ALLSTAR/ALLFRAME),
21, 22
ROMAFOT,
23, 24
DOPHOT, SExtractor,
26, 27
Starfinder and software ad hoc developed to deal with HST images.
29, 30
The use of these packages madepossible the construction of very deep and precise CMDs based on ground–based and space images that allowedus to investigate in detail RSPs in the very center of GGCs and in the Bulge. Note that the use of thePSF photometry in crowded stellar fields is mandatory not only to improve the precision of the photometry(identification of faint companions), but also to improve the limiting magnitude (identification of faint objects).The latter point is even more crucial in dealing with NIR images, since they are sky limited.The use of ground–based NIR images collected with AO systems seems to suggest that a further developmentof the packages currently available is required. The shorter wavelength images (tipically J–band) display acomplex change of the shape of the PSF across the FOV. This evidence further support the suggestion that theperformance of a AO system does depend on the Strehl ratio, but also on the image quality and on the temporalstability of the PSF. In the following we discuss in more detail while the latter parameters play a crucial role inthe photometry of crowded stellar fields. Note that there is mounting evidence that NIR images collected withMCAO systems (MAD at VLT, ) have a more uniform and stable PSF across the FOV. This is the reason whyin dealing with these images have been adopted classical approaches.
12, 13
In dealing with NIR images collected with SCAO systems (NACO at VLT, PISCES at LBT) we decidedto use ROMAFOT. The key advantage in using ROMAFOT is that we can check the different steps (fit, mapof the residuals) of the individual PSF fitting thanks to the graphical interface. The main drawback is that itis lengthy. The key advantages in using analytical PSF fitting of crowded stellar fields when compared withaperture photometry and with numerical PSF have been widely discussed in the literature. We mention thatthe analytical PSF improves at fixed magnitude the photometric precision thanks to the identification of faint riginal data reconstructed data Symmetric Mo at function
O. D. R. D. residuals original data reconstructed data
R. D. residuals
Asymmetric Mo at function
O. D.
Figure 3. Left: 2D projection of the analytical PSF fitting on two close stars performed with ROMAFOT on a singleJ-band image. The fit uses a classical symmetric Moffat function. The green lines shows the original data (O.D.), whilethe red one the expected profile (reconstructed data, R.D.). The left and middle plots on top of the figure display theprojection along the X- and the Y-axis. The left and middle contours in the middle display the view from the Z-axis. Theleft and the middle images in the bottom display the original data and the reconstructed data. The right contours in themiddle and the right image in the bottom display the residuals once the deconvolution of the original data was performed.Right: Same as the right, but the analytical PSF fitting was performed by using an asymmetric Moffat function. Theuse of the this PSF significantly improves the quality of the fitting, and indeed the residuals decrease over the entire areacovered by the two close stars. companions and the opportunity to discriminate between stars and galaxies. Moreover, it improves, at fixedexposure time, the limiting magnitude thanks to the identification of faint stellar sources. The latter point iseven more crucial in dealing with NIR images, since they are sky limited.In the following we use a Moffat function that can be expressed as
P SF ( h, x , y , σ, β, x, y ) = h ∗ (1 + ( x − x ) + ( y − y ) σ ) − β (1) The β parameter fixes the slope of the wings, larger is the value steeper is the slope. We adopted this analyticalPSF because it provides a good description of the stellar profiles both in seeing limited and in diffractionlimited images. In the ROMAFOT environment the analytical PSF fitting is performed simultaneously with anassumption that accounts for the local sky–background. This means that once the shape of the PSF has beenfixed ( β and σ values), by using PSF stars, the number of unknowns for an isolated stellar profile is three (x , y ,h) plus the term that accounts for the local sky–background. This is the main reason why accurate and precisephotometry of crowded stellar fields does require that stars cover at least 2 × and/or numerical PSFs has been suggested. Fortunately, the new CCD imageshave appropriate pixel scales.To perform accurate PSF photometry of stellar images with asymmetric profiles have been suggested differentapproaches. The most simple approach is to split the FOV in a number of smaller subfields and to perform theselection of PSF stars on these individual subfields. A similar approach relies on the selection of a sizable sampleof PSF stars across the entire field of view and to assume either a quadratic or a cubic change of the PSF acrossthe image. However, these approaches become quite complicated in dealing with crowded stellar fields, since riginal data reconstructed data
Symmetric Mo at function
O. D. R. D. residuals original data reconstructed data
Asymmetric Mo at function
O. D. R. D. residuals
Figure 4. Same as in Figure 3, but for an analytical PSF fitting performed on three close stars of a Ks–band image.The asymmetric PSF is still improving the quality of the fit, but the improvement is smaller than for the J-band image. the number of good isolated PSF stars is limited. The use of specific algorithms overcomes some of the quotedproblems and appears quite useful in dealing with images that are on the verge to be undersampled. It hasalso been suggested to use a “Penny” function i.e. the sum of a Gaussian and of a Lorenz function, in which thelatter one can be either tilted or not tilted when compared with the Gaussian function. The quoted approaches present several clear advantages, however, after different tests and trials on SCAOimages we decided to perform the analytical PSF fitting by using a new asymmetric Moffat function:
PSF(h, x , y , a, b, c, θ , β , x, y)= h ∗ (1 + (( x − x ) cosθ + ( y − y ) sinθ ) a + (( y − y ) cosθ + ( x − x ) sinθ ) ∗ ( c ∗ (( x − x ) cosθ + ( y − y ) sinθ )) b ) − β (2) In spite of the apparently complicated analytical representation, the new analytical function is relativelysimple. The main features are the following: •
1) Wings – The β paramater of the Moffat function is fixed using PSF stars and does not change acrossthe image. •
2) Ellipse – The core of the Moffat function is no more a circle, but an ellipse characterized by its semi–major(a) and semi–minor (b) axes. •
3) Tilt – The ellipse is not aligned with the X and Y axis, but has an inclination angle– θ –with the X axis. •
4) Asymmetry – The 3D shape of stellar images can be asymmetric thanks to the c parameter, i.e. thisconstrains the departure from an ellipsoidal shaped volume into an egg shaped volume. igure 5. Synthetic J- (left) and Ks–band (right) images of the adopted PSF stars based on the new asymmetric Moffatfunction (see eq. 2.). The location of the NGS is marked in red.. The number of unknowns of the new asymmetric Moffat function are eight (plus the sky–background value).The four unknowns affecting the shape of the PSF (a, b, c, θ ) change across the image and they are fixed byfitting the stellar profile of several, possibly isolated, PSF stars across the frame. We derive for every image, onthe basis of the PSF stars, an almost spatially uniform grid of values for the five unknowns. This approach allowus to decrease the number of unknowns, and in turn to speed up the PSF fitting of both isolated and blendedstars. The new ROMAFOT according to the position of the star in the grid performs a quadratic interpolation ofthe four shape parameters across the grid and then performs the fit of individual stellar profile. This means thatthe unknowns of the new approach are still three ( h , the height; x , y , the centroid) plus the sky–backgroundvalue. The reasons why we devised the above reduction strategy are the following: 1) Current ground-basedNIR images collected with AO systems are typically oversampled. Indeed, the sampling parameter, defined asFWHM/Pixel scale, is of the order of ∼ ∗ This means that the deconvolutionof isolated stars does allow us to provide solid measurements of the unknowns affecting the shape of the PSF.2) We performed series of numerical experiments on synthetic images and we found that the asymmetricalanalytical PSF with four unknowns and five parameters fixed a priori works very well across the entire image.In this context it is worth mentioning that the fit of individual stellar profiles with an asymmetric PSF (nineunknowns) provides less accurate deconvolutions of blended stars in the innermost cluster regions and of fainterstars. 3) The numerical complexity of the PSF fitting significantly decreases.In order to provide a more quantitative analysis of the difference between symmetric and asymmetric analyt-ical PSF Figs. 3–4 display the details of the fit. The plots on the left display the Original Data (OD, green) andthe reconstructed Data (RD, red) of the stellar profile projected onto the X- (left) and onto the Y-axis (middle)by using a symmetric Moffat function. The comparison shows that the analytical symmetric PSF does notproperly fit the peak of the observed profile. The contours at three arbitrary cuts plotted in the middle panelsdisplay a similar problem, but in the wings of the profiles (see also the images plotted in the bottom panel).The discrepancy between observed and reconstructed profile is even more clear in the residual map plotted inthe right bottom panel. ∗ Note that the typical FWHM for J- and Ks–band images is 0.05 and 0.06 arcsec, while the PISCES pixel–scale is0.0193”/pixel. he comparison between observed and reconstructed profile based on an analytical asymmetric PSF is showedin the right panels of Fig. 4. Data plotted in these panels display that the new fits takes account of both thepeak and the wings. Indeed the map of the residuals attains vanishing values over the entire area covered bythe two close stars. Fig 4 shows the same comparison, but for three nearby stars on Ks–band image. The use ofthe asymmetric analytical PSF still improves the quality of the fit, but the difference is less clear than for theJ-band.In order to constrain on a quantitative basis the difference between the fit performed with the symmetricand the asymmetric Moffat Function, we estimated the difference in flux, over an area of 10 ×
10 pixels aroundthe center of the star, between the reconstructed and the original data. In particular, we adopted the followingformula for the residuals:
RESIDUAL F LUX = N ∗ (cid:113) ( (cid:88) (( O.D. i − R.D. i ) ) /N ) / (cid:88) ( O.D. i − background ) ∗
100 (3)
We found that the residuals in the J-band when using the asymmetric and the symmetric Moffat function are ∼
16% and ∼ † and the orientation of the stellar images of the left panel clearlydisplay the same radial trend from the NGS (red dot) showed by real images (see Fig. 2). The similarity alsoapplies to stars located in the corners of the image. The mild change in the shape of the stellar images can alsobe easily identified in the Ks–band image, but it is less evident when compared with the J-band.
4. CLUSTER PHOTOMETRY
We first performed the photometry on the stacked J- and Ks–band image. The master list includes stars withone measurement in the two bands. The same list was then used to perform the photometry on individual J,and Ks–band images. The final catalog includes stars with at least one measurement per band. Fig. 6 shows theNIR J, J-Ks CMD of the very crowded central pointing. The improvements in using an asymmetric analyticalPSF fitting are quite clear. Data plotted in the left panel (asymmetric PSF) display well defined sequencesalong the Red Giant Branch (RGB, J–Ks=-0.7 mag), the Horizontal Branch (HB, Ks ∼ ∼
17 J–Ks=-0.75 mag) and in particular across the MSTO region (Ks ∼
18, J–Ks=0.9 mag). On the other hand, the CMD based on a symmetric analytical PSF fitting shows broader evolvedsequences (RGB, HB, SGB) and a steady decrease in photometric accuracy approaching the MSTO. This is acrucial difference since the precision in the evaluation of the absolute age of GCs is strongly affected by thephotometric precision of the MSTO. Note that an uncertainty of the order of one tenth of a magnitude typicallyintroduces in the comparison with cluster isochrones an uncertainty of the order of 1 Gyr.The above evidence suggests that the new reduction strategy devised to perform accurate analytical PSFphotometry on NIR images collected with SCAO systems appears very promising. Current preliminary resultsappear even more interesting if we take into account the fact that the cluster regions covered by the centralpointing are characterized by a very high central stellar density Indeed, M15 belongs to the small sample of postcore–collapsed GCs. † The semi–major axis in the J-band ranges from 0.7 to 2.9 pixels, while in the Ks–band from 2.6 to 5.9 pixels. Thesemi-minor axis attains similar values, and indeed it ranges from 0.6 to 1.9 pixels (J-band) and from 2.3 to 4.4 (Ks–band). .50 -2.1 -0.1 -0.1 -2.1 J J-K
J-K
M15 photometry
Asymmetric Mo (cid:1) at function Symmetric Mo (cid:1) at function
Figure 6. Left: NIR J,J–Ks CMD of the central pointing of M15. The photometry was performed by using an asymmetricMoffat function. The photometry is very accurate well below the turn–off region ( J ∼ The photometric catalog released by 2MASS has been a quantum jump in the improvement of the absolutecalibration of NIR ground-based photometry. However, this catalog can be barely used to provide local standardsto new AO systems available at the 8-m class telescopes. The reasons are manifold. The limiting magnitude ofthe 2MASS catalog is
J, H, Ks =14–15 mag. This limit becomes even brighter in crowded stellar fields. Theseobjects are typically saturated in NIR images collected with AO systems. The FOV of NIR detectors used withAO systems is at most of the order of 2 × J, H, Ks =16–18mag. To overcome this problem have been adopted both NIR images collected with both 4m and 8m telescopes(Bono et al. 2010; Stetson et al. 2014).To calibrate NIR images collected with PISCES at LBT, we secured a set of NIR images collected withLUCI1 on June 2012. The key advantage of the LUCI1 images is that the LUCI1 FOV is 4 × The LUCI1 NIR images werecalibrated using 2MASS local standards. The NIR photometry based on LUCI1 images is very accurate down to
J, Ks ∼
19 mag and they were adopted to calibrate the photometric catalogs based on PISCES images (Monelliet al. 2014, to be submitted). Finally, we mention that the use of a sizable sample of local standards overcomesthe problem of the aperture correction.
5. THE ABSOLUTE AGE OF M15
In this section we anticipate a new result detailed in Monelli et al. (2014, to be submitted) concerning theabsolute age of M15. This result is based on data collected for the off–center pointing of M15. To perform stellarphotometry, we have used the same procedure described above to analyse PISCES@LBT images: an updatedversion of ROMAFOT with the new asymmetric PSF function (eq. 2). This resulted to be the best choice toobtain the deepest CMD ever observed in near IR by reaching a Ks limiting magnitude of ∼
23 mag, see Fig. 7 .0 0.5 1.0 1.5 2.0J - K s [mag]222018161412108 K s s [mag] 0.0 0.5 1.0 1.5 2.0F160W - K s [mag] Figure 7. Left: NIR Ks, J–Ks CMD based on seeing limited images collected with LUCI1 at LBT (left). The red errorbars on the left display the error both in magnitude and in color. Middle: Same as the left, but the photometry is based onimages collected with PISCES at LBT with a SCAO (FLAO) system. Note that the limiting magnitude in the Ks–bandis the deepest ever collected with a ground–based telescope. Right: Same as the left, but for the Ks, F160W-Ks CMD.The Fi60W photometry is based on space images collected with WFC3 at HST, while the Ks–band was collected withPISCES at LBT. Note that the F160W photometry is approximately one magnitude shallower. (middle panel). In this figure we have also shown the Ks, J-Ks CMD obtained using the camera [email protected] described above, these data were taken mainly for calibration purpose and show the seeing–limited behaviorof data taken using the same telescope but a different camera with a pixel scale of 0.118”/px, about 10 timeslarger than PISCES’one.We have performed standard data reduction to analyse space telescope data from WFC3@HST usingF814W, F606W, and F160W bands. In this paper we show only the results obtained with the near IR channelusing F160W passband (see right panel in Fig. 7) to make a fair comparison between space and AO imagestaken from the ground with LBT. The CMDs coming from the combination of the full set of optical and nearIR bands are presented in Monelli et al. 2014 (to be submitted). The resulting near IR CMDs show clearly thejump in limiting magnitude obtained when moving from seeing–limited IR collected with LUCI1 and the AOassisted taken with PISCES@LBT. The reached limiting magnitude is Ks ∼
23 mag, that means about 3 magfainter in Ks band when AO systems are used on the same telescope. In spite of the small FOV corrected foratmosphere turbulence, thanks the AO we are able for the first time to detect the MSK in a very metal poorGGC. The quality obtained using J and Ks bands with PISCES is very likely comparable to what is obtainedusing a combination of space (F160W) and ground based (Ks) filters. However the intrinsic errors given in Jband are much larger than in F160W, this is mainly due to the larger exposure time used for space observationwhich is 3.5 times larger than what used to integrate J band data.In order to determine the absolute age of M15, we decided to use the best photometry available, this means acombination of Ks–band from PISCES and optical (F606W) space observations. We have used evolutionary tracksfor an old age range (from 12 to 15 Gyr, Vandenberg priv. comm.) with [Fe/H]=-2.4 dex, an α − enhancement α =+0.4 and a primordial helium abundance Y=0.25. These tracks were transformed into the observational planeusing colour–temperature relation provided by Casagrande (priv. comm.). To match the data with isochroneswe have adopted a distance modulus of µ =15.14 mag and a reddening E(B–V)=0.08. At this point, we have all the ingredients to derive the absolute age of M15. We approach at this estimationby using two independent methods: the detection of the MSTO and the difference between the MSTO and theSK magnitudes, i.e. MSTO–MSK (fully described in Bono et al. 2010 ). We notice that the first methoddoes dependent on distance and reddening whereas the second one, being a differential method, is free from theuncertainties affecting these parameters. In fact, the distance modulus assumed for M15 is given with an errorof ± We have used CMD ridge lines to define both the MSTO and the MSK as follows. The MSTO is identified asthe bluer point in the TO region. The MSK is defined as the maximum curvature point in the low part of the MS.The same definition has been used to determine the magnitude and colours of these two points for both data andobservations. In particular for near IR data, we have constrained the MSTO and MSK locations using LUCI1and PISCES data respectively. The evolutionary tracks allow us, at fixed chemical composition, to estimate thederivative of the MSTO magnitude as a function of age: ∆F606W/∆t= 0.083 mag/Gyr and ∆Ks/∆t= 0.051mag/Gyr. The age corresponding to M15 is derived by interpolating the previous relation assuming the observedMSTO magnitude. The error budget has to take into account various sources. From the observational side,we included the error on the TO magnitude, the reddening and distance. In the case of the present data set,the photometric error varies depending on the filter used, from ∼ ∼ ± ± ‡ .
6. CONCLUSIONS AND FINAL REMARKS
We present new and accurate NIR (J,Ks) photometry for the Galactic globular cluster M15. The images werecollected with PISCES at LBT with an innovative SCAO system equipped with high-order pyramid wave-frontsensor (FLAO). The images were collected for two different pointings by using two natural guide stars with anapparent magnitude of R ∼ <
13 mag. The images were collected with medium seeing condition ( ≈ ∼
23 mag. This means, to our knowledge, the deepest K-bandphotometry ever collected with a ground–based telescope. The new NIR photometry and a well defined kneealong the lower main sequence allowed us to estimate the absolute age of M15 with a precision that is a factorof two better when compared with similar estimates based on the MSTO available in the literature, i.e. usingthe MSTO–MSK we obtain 13.70 ± ‡ The interested reader will find much more details in Monelli et al. (2014, to be submitted).
CKNOWLEDGMENTS
GF has been supported by the Futuro in Ricerca di Base 2013 (RBFR13J716). This work was partially supportedby PRIN–INAF 2011 “Tracing the formation and evolution of the Galactic halo with VST” (P.I.: M. Marconi)and by PRIN–MIUR (2010LY5N2T) “Chemical and dynamical evolution of the Milky Way and Local Groupgalaxies” (P.I.: F. Matteucci).
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