NGC 4147 revisited

Variable stars in NGC 4147 revisited: RR Lyrae stars new CCD Vi photometry and physical parameters

A. Arellano Ferro    11affiliation: Instituto de Astronomía, Universidad Nacional Autónoma de México, México. F.C. Rojas Galindo    22affiliation: Instituto de Física, Universidad de Antioquia, Colombia S. Muneer    33affiliation: Indian Institute od Astrophysics, Bangalore, India Sunetra Giridhar33affiliation: Indian Institute od Astrophysics, Bangalore, India
Abstract

We have calculated the physical parameters of the RR Lyrae stars in the globular cluster NGC 4147 via the Fourier decomposition of their light curves, using new data and well-established semi-empirical calibrations and zero points. The mean metallicity and distance estimated using the RRc stars are [Fe/H] and kpc respectively. The star V18, whose variability has been previously in dispute, is confirmed to be a variable of the SR type with a period of about 24.8d, and it has been used to get and independent distance estimate of the cluster. It is observed that the RRab and RRc stars do not share the inter-mode region in the horizontal branch. The cluster can be classified as of intermediate Oosterhoff type. Its horizontal branch structure and metallicity make a good case for extragalactic origin. It follows the distribution of Oo I type globular clusters in the [Fe/H] plane, as depicted from the RRc stars.

globular clusters: individual: NGC 4147 – stars: variables: RR Lyrae
\fulladdresses

A. Arellano Ferro: Instituto de Astronomía, Universidad Nacional Autónoma de México, Apdo. Postal 70-264, Ciudad de México, CP 04510, México. (armando@astro.unam.mx)

\SetYear

2018 \ReceivedDateJanuary 2018 \AcceptedDate——

\resumen

Los parámetros físicos en estrellas RR Lyrae en NGC 4147 se calcularon por medio de la descomposición de Fourier de sus curvas de luz, empleando calibraciones y puntos cero bien establecidos. Las estrellas RRc indican los valores medios de metalicidad y distancia al cúmulo de [Fe/H] and kpc respectivamente. La estrella V18, cuya variabilidad había sido puesta en duda, es confirmada ahora como una variable del tipo SR con un periodo de 24.8d y pudo ser empleada para estimar la distancia al cúmulo de manera independiente. Se observa que las estrellas RRab y RRc comparten la zona inter-modo en la zona de inestabilidad. El cúmulo puede clasificarse como del tipo intermedio de Oosterhoff. La estructura de su rama horizontal y su metalicidad favorecen la interpretación de su origen extragaláctico. En el plano [Fe/H] el cúmulo sigue la tendencia de los cúmulos tipo Oo I, definida por sus estrellas tipo RRc.

1 Introduction

The globular cluster NGC 4147 is a faint and distant cluster some 19 kpc from the Sun and 21 kpc from the Galactic Center (, , J2000; , ). It is one of the globular clusters immersed in the Saggitarius Stream and it has been suggested that originally it may have been a cluster member of the Sagittarius dSph galaxy (Bellazzini et al. 2003a, 2003b). Its classification as an Oosterhoff type I (Oo I) (Castellani & Quarta 1987) was controversial given its low metal abundance, blue horizontal branch (HB) and the large fraction of RRc type stars among the RR Lyrae population. This classification was confirmed by Arellano Ferro et al. 2004 (hereinafter AF04) from the revised periods of the RR Lyrae stars and by Stetson, Catelan & Smith (2005) (hereinafter SCS05) from the RR Lyrae distribution in the amplitude-period plane. It is probably the most metal poor globular cluster among the Oosterhoff type I clusters. However, considerations on the HB structure and amplitude-period distribution of the RRc stars, trigger the possibility that the clusters is of an Oosterhoff intermediate type (Oo-Int) and of extragalactic origin, as shall be discussed later in this paper.

The cluster variable stars were studied by AF04 in the and band passes and the light curves of the RR Lyrae were Fourier decomposed to estimate the mean metallicity and distance to the cluster. However, since then, we have improved upon several procedures related with the data reductions (Bramich et al. 2013) and transformations to the standard system, on the usage of the semi-empirical calibrations and their zero-points to estimate physical properties of RRab and RRc stars in a very homogeneous way (Arellano Ferro et al. 2013; 2017), and have expanded the critical analysis of the RR Lyrae distribution on the colour magnitude diagram (CMD) to a family of clusters of both Oosterhoff types I and II (Oo I and Oo II) (e.g. Yepez et al. 2018). A Fourier decomposition of both RRab and RRc stars was also performed by SCS05. In both the above studies, it became clear that the light curves morphology in all the five known RRab is peculiar, due to the observed amplitude modulations of their light curves (AF04) and consequently displaying a large parameter morphology (SCS05), which reveals the light curve as unsuitable for metallicity calibration. This is probably the reason why, both AF04 and SCS05, concluded on a much higher metallicity for the cluster. Among the RRc stars, numerous anomalies in the rather long period variables (V11, V13, V16, V17) were encountered in the above papers, such as erratic phasing and amplitude modulations that may be connected with the presence of secondary frequencies and/or the Blazhko effect. Thus, a reconsideration of the stellar physical quantities as obtained from the Fourier light curve decomposition is in order. For all the above reasons, the cluster was observed in 2012 with the aim of enriching the data collection and time-base for a proper comparison with previous discussions and to set the metallicity and distance to the cluster in the homogeneous scales of a family of some 24 clusters presented by Arellano Ferro et al. (2017) from the Fourier decomposition approach and their inference in the [Fe/H] relation.

The paper is organised as follows; we describe our observations and data reductions as well as the transformation to the Johnson-Kron-Cousins photometric system in 2, we perform the identification of the known variables, estimate the cluster reddening in 3, we calculate the physical parameters via the Fourier decomposition for RR Lyrae stars in 4, discuss the peculiarities of some individual stars in 5, comment on the distance to the cluster via several methods in 6, discuss the CMD and the isochrone and zero age horizontal branch (ZAHB) fitting in 7, the Oosterhoff type of NGC 4147, the cluster position in the Oosterhoff gap and hence its possible extragalactic origin are the topics treated in 8, we present NGC 4147 in the perspective of the -[Fe/H] relation determined from RRc stars in a family of globular clusters in 9, and finally we summarise our results in 10.

2 Observations and reductions

Date (s) (s) Avg seeing (”)
2012-02-05 35 140-350 18 30-150 2.5
2012-02-28 20 170 250 19 50-120 1.7
2012-02-29 12 300-450 11 90-250 3.0
2012-03-01 35 240-350 35 85-120 2.4
2012-03-02 18 150-300 19 60-150 2.2
2012-04-11 7 250-300 7 110-150 2.5
2012-04-28 11 300-350 2 100-150 2.7
2012-04-29 15 220-300 10 100-200 2.2
Total: 153 121
Table 1: The distribution of observations of NGC 4147. Columns and give the number of images taken with the and filters respectively. Columns and provide the range of exposure times. In the last column the average seeing is listed.
Figure 1: The transformation relationship between the instrumental and standard photometric systems using a set of standards of Stetson (2000) in the FoV of our images of NGC 4147 .

2.1 Observations

The CCD observations in the Johnson-Kron-Cousins VI-bands used in the present work, were obtained between 5 February and 29 April 2012 with the 2.0m-telescope at the Indian Astronomical Observatory (IAO), Hanle, India, located at 4500 m above sea level in the Himalaya. The detector was a Thompson CCD of 20482048 pixels with a scale of 0.296 arcsec/ pix, translating to a field of view (FoV) of approximately 10.110.1 arcmin. Our data consist of 153  and 121  images. Table 1 gives an overall summary of our observations and the seeing conditions.

2.2 Difference Image Analysis

Image data were calibrated using bias and flat-field correction procedures. We used the Difference Image Analysis (DIA) to extract high-precision time-series photometry of all point sources in the field of the cluster. We used the DanDIA111DanDIA is built from the DanIDL library of IDL routines available at http://www.danidl.co.uk pipeline for the data reduction process (Bramich et al. 2013), which includes an algorithm that models the convolution kernel matching the PSF of a pair of images of the same field as a discrete pixel array (Bramich 2008). A detailed description of the procedure is available in the paper by Bramich et al. (2011), to which the interested reader is referred for the relevant details.

We used the methodology of Bramich & Freudling (2012) to solve for the magnitude offset that may be introduced into the photometry by the error in the fitted value of the photometric scale factor corresponding to each image. The magnitude offset due to this error was of the order of  mmag.

2.3 Transformation to the Vi standard system

From the standard stars of Stetson (2000)222http://www3.cadc-ccda.hia-iha.nrc-cnrc.gc.ca/
community/STETSON/standards
in the field of NGC 4147, we identified 337 stars in the FoV of our images, with in the range 14.6–21.5 mag and V-I within  mag. These stars were used to transform our instrumental system to the Johnson-Kron-Cousins photometric system (Landolt 1992). The standard minus the instrumental magnitude differences show a mild dependence on the colour, as displayed in Fig. 1. The transformation equations are given in the corresponding panel of Fig. 1. The resulting VI photometry for all variables in our FoV is published in Table 2 which is an extract from the full table, available in electronic format. For completenes we also include in this table the VR photometry from AF04, which was not made public in that publication.

Variable Filter HJD
Star ID (d) (mag)
V1 V 2452651.90900 16.612
V1 V 2452651.92300 16.613
V1 R 2452651.912 16.421
V1 R 2452651.913 16.439
V1 I 2455963.22529 16.512
V1 I 2455963.22752 16.542
V2 V 2452651.89000 17.102
V2 V 2452651.89600 17.139
V2 R 2452651.932 17.020
V2 R 2452652.010 17.122
V2 I 2455963.22529 16.187
V2 I 2455963.22752 16.197
Table 2: Time-series V, R and I photometry for all the confirmed variables in NGC 4147 taken in 2003 (AF04) and 2012 (present work). This is an extract from the full table, which is available in electronic format.
Figure 2: Light curves of the RR Lyrae stars in NGC 4147 phased with the periods listed in Table 3. In the upper panels, black symbols correspond to data from 2003 and red to data from 2012.

3 Variable Stars in NGC 4147

All confirmed variable stars in our FoV are listed in Table 3 along with their mean magnitudes, amplitudes, and periods. The coordinates listed in columns 10 and 11 were taken from the Catalogue of Variable Stars in Globular Clusters (CVSGC) (Clement et al. 2001). For comparison we include in column 7, the periods as listed by SCS05, and it should be noted that in some cases the periods are significantly different from the ones found from our data, listed in column 9. For stars with light curves poorly covered by our photometry we have adopted the period of SCS05. The light curves of the RR Lyrae stars are shown in Fig. 2.

Variable Variable (SCS05) HJD (this work) RA Dec
Star ID Type (mag) (mag) (mag) (mag) (d) () (d) (J2000.0) (J2000.0)
V1 RRab Bl 17.066 16.535 1.05 0.70 0.500403 5988.49483 0.500393 12:09:59.38 +18:31:48.4
V2 RRab Bl 17.089 16.600 1.161 0.65 0.493180 5988.3470 0.493297 12:10:04.96 +18:32:04.5
V3 RRc 17.031 16.710 0.485 0.333 0.2805427 5986.5186 0.280543 12:10:04.38 +18:31:58.5
V4 RRc 17.047 16.750 0.482 0.389 0.300031 5963.2723 0.300066 12:10:06.39 +18:32:50.2
V6 RRab Bl 16.941 16.455 1.208 0.810 0.609730 5963.3748 0.609737 12:10:08.51 +18:33:00.0
V7 RRab 17.066 16.567 1.301 0.823 0.514245 5986.4396 0.514321 12:10:06.66 +18:32:39.7
V8 RRc 16.828 16.558 0.431 0.309 0.278652 5963.4587 0.278599 12:10:06.95 +18:32:34.8
V10 RRc 17.020 16.585 0.421 0.302 0.352301 5963.2378 0.352339 12:10:03.74 +18:31:48.4
V11 RRc 16.867 16.471 0.380 0.269 0.387419 5963.3836 0.387423 12:10:05.53 +18:31:51.8
V12 RRab 17.199 16.858 1.164 0.882 0.504700 5986.5132 0.504700 12:10:06.70 +18:32:28.4
V13 RRc 16.701 16.322 0.385 0.282 0.408320 5963.3660 0.408319 12:10:06.37 +18:32:14.1
V14 RRc 16.914 16.483 0.432 0.233 0.356376 5963.4586 0.356375 12:10:06.94 +18:32:32.4
V16 RRc 16.707 16.211 0.388 0.257 0.372259 5963.4587 0.372134 12:10:07.35 +18:32:40.1
V17 RRc 16.968 16.512 0.453 0.285 0.371229 5988.3095 0.374843 12:10:10.67 +18:34:51.2
V18 SR 13.929 12.391 0.2 24.8 12:10:05.63 +18:32:11.6
V19 RRc 17.03 16.72 0.28 0.14 0.273933 12:10:21.98 +18:35:02.1

a: Value taken from SCS05.

Table 3: General data for all of the confirmed variables in NGC 4147 in the FoV of our images. Period estimates from SCS05 are listed in column 7 for comparison with our periods listed in column 9.

All known variables in NGC 4147 are identified in the charts of Fig. 3 for the cluster peripheral and core regions.

Figure 3: Identification charts of all known variables in the field of NGC 4147. The field size in the upper and lower frames is 66 and 1.51.5 arcmin respectively. In both frames North is up and East is to the right.

3.1 Reddening

It is well known from the work of Sturch (1966) that RRab stars have nearly the same intrinsic colour at minimum light. The value was calibrated by Guldenschuh et al. (2005). We have used these results to calculate the reddening of four RRab stars in NGC 4147 from their minimum value in V-I and found an average . Taking E(V-I)/E(B-V)= 1.259 (Schlegel et al. 1998) we get an average E(B-V). This value is a little smaller than the value 0.02, listed by Harris (1996) or the value given by the reddening maps of Schlafly & Finkbeiner (2011) 0.022. We shall adopt E(B-V)= 0.01 in the remainder of the paper.

4 Physical parameters of RR Lyrae stars

Physical quantities of individual RR Lyrae stars can be estimated via the Fourier decomposition of the light curve and the employment of ad-hoc well-tested calibrations. A full description of the method and the specific calibrations and their zero points used in a homogeneous way in several of our previous papers for a family of globular clusters, can be seen in the paper by Arellano Ferro, Bramich & Giridhar (2017). For briefness we do not reproduce the details here, however, for the sake of clearness in the nomenclature we remind that the light curve can be represented by the equation,

(1)

where is the magnitude at time , is the period, and is the epoch. A linear minimization routine is used to derive the best fit values of the amplitudes and phases of the sinusoidal components. From the amplitudes and phases of the harmonics in Eq. 1, the Fourier parameters, defined as , and , are computed.

We have argued in previous papers in favour of the calibrations developed by Jurcsik & Kovács (1996) and Kovács & Walker (2001) for the iron abundance and absolute magnitude of RRab stars, and those of Morgan, Wahl & Wieckhorts (2007) and Kovács (1998) for RRc stars. The effective temperature is estimated using the calibration of Jurcsik (1998). These calibrations and their zero points have been discussed in detail in Arellano Ferro et al. (2013).

The calculation of the physical quantities is very sensitive to the morphology of the light curve and spurious results can be obtained if light curves with peculiarities are considered, for example those with amplitude and/or phase modulations, or cases of incomplete light curves. In particular, for the calculation of [Fe/H] in RRab stars, Jurcsik & Kovács (1996) and Kovács & Kanbur (1998) have defined a ”compatibility parameter” which should be smaller than 3.0 if the light curve under analysis is consistent with the calibrators used to establish the Jurcsik & Kovács (1996) iron abundance calibration. In the present case we note that all five known RRab star show amplitude variations and their values are all very large (column 10 in Table 4), hence they are neither fit for [Fe/H] calculation nor for a distance estimation since the absolute magnitude depends on the amplitudes of the first and third harmonics (Kovács & Walker 2001), thus they were ignored. Likewise, some peculiar RRc stars with erratic phasing (V8, V13 and V16) were also not included in the physical parameters calculations.

Nevertheless, the value of and the Fourier light-curve fitting parameters for the 5 RRab and 9 RRc stars are given in Table 4. When amplitude variations are present, we have taken care in fitting the maximum amplitude curve. The corresponding physical parameters for the most stable RRc stars are listed in Table 5. The absolute magnitude was converted into luminosity with ). The bolometric correction was calculated using the formula given by Sandage & Cacciari (1990). We adopted  mag. For the distance calculation, we have adopted E(B-V)=0.01, estimated in 3.1.

Variable
ID ( mag) ( mag) ( mag) ( mag) ( mag)
RRab
V1 17.066(2) 0.440(3) 0.164(3) 0.131(3) 0.084(3) 3.855(21) 7.981(31) 5.864(45) 16.7
V2 17.089(4) 0.413(5) 0.229(6) 0.108(6) 0.054(6) 3.674(40) 7.581(73) 5.435(126 8.4
V6 16.941(2) 0.343(4) 0.211(4) 0.152(4) 0.105(4) 4.092(30) 8.314(45) 6.241(62) 22.7
V7 17.066(5) 0.454(7) 0.177(7) 0.145(7) 0.108(7) 3.850(51) 7.722(69) 5.686(92) 12.4
V12 17.197(3) 0.431(4) 0.195(4) 0.146(4) 0.088(4) 3.781(29) 7.933(41) 6.071(61) 20.5
RRc

V3
17.031(1) 0.229 (2) 0.051 (2) 0.012 (2) 0.009 (1) 4.567 (49) 2.470 (188) 0.942 (262)
V4 17.047(2) 0.202 (3) 0.053 (3) 0.016 (3) 0.019 (3) 4.478 (78) 1.979 (242) 0.413 (209)
V8 16.828(3) 0.178 (4) 0.032 (4) 0.008 (4) 0.007 (4) 4.561 (157) 2.599 (606) 1.342 (680)
V10 17.020(1) 0.211 (1) 0.025 (1) 0.014 (1) 0.009 (1) 4.672 (63) 3.616 (118) 2.124 (181)
V11 16.867(1) 0.186 (1) 0.007 (1) 0.015 (1) 0.007 (1) 5.252 (193) 4.243 (95) 2.242 (185)
V13 16.701(1) 0.181 (2) 0.004 (2) 0.013 (2) 0.004 (2) 5.833 (701) 2.053 (204) 5.861 (605)
V14 16.914(2) 0.176 (3) 0.021 (3) 0.016 (3) 0.005 (3) 4.718 (173) 3.879 (230) 1.988 (732)
V16 16.707(1) 0.192 (1) 0.014 (1) 0.018 (1) 0.011 (1) 5.134 (120) 3.902 (99) 2.713 (159)
V17 16.968(2) 0.198 (3) 0.013 (3) 0.006 (3) 0.006 (3) 4.728 (311) 3.490 (712) 5.884 (589)

Table 4: Fourier coefficients of RRab and RRc stars in NGC 4147. The numbers in parentheses indicate the uncertainty on the last decimal place. Also listed is the deviation parameter  for the RRab stars.
Star [Fe/H] [Fe/H] log  log (kpc)
V3 -1.57(31) -1.49(35) 0.620(5) 3.869(1) 1.652(2) 18.88(4) 0.59(1) 4.12(2)
V4 -1.91(41) -1.96(56) 0.560(14) 3.862(1) 1.676(6) 19.55(13) 0.62(1) 4.37(3)
V10 -1.74(24) -1.72(30) 0.546(5) 3.861(1) 1.682(2) 19.44(5) 0.51(1) 4.42(1)
V11 -1.72(21) -1.70(26) 0.496(10) 3.858(1) 1.702(4) 18.54(8) 0.48(1) 4.58(2)
V14 -1.65(47) -1.60(56) 0.558(15) 3.861(1) 1.677(6) 18.41(13) 0.49(1) 4.38(3)
V17 -1.95(33) -2.01(36) 0.535(19) 3.856(4) 1.686(8) 19.07(17) 0.49(3) 4.54(4)
Weighted mean 1.72(13) 1.68(16) 0.571(3) 3.861(1) 1.671(1) 19.05(3) 0.52(1) 4.30(1)
0.15 0.15 0.040 0.004 0.016 0.46 0.06 0.16
Table 5: Physical parameters of the RRc stars. The numbers in parentheses indicate the uncertainty on the last decimal places.

The resulting physical parameters of the RRc stars are summarized in Table 5. The mean values given in the bottom of the table are weighted by the statistical uncertainties. The iron abundance is given in the scale of Zinn & West (1984) and in the scale of Carretta et al. (2009). The transformation between these two scales is of the form:

(2)

Also listed are the corresponding distances. Given the period, luminosity, and temperature for each RR Lyrae star, its mass and radius can be estimated from the equations: (van Albada & Baker 1971), and = respectively. The masses and radii given in Table 5 are expressed in solar units.

Figure 4: The left panel shows the amplitude modulation of the magnitude in V6 phased with a period of 67.46d; black symbols are observations from 2003 (AF04) and red symbols are 2012 observations from the present work. In the central and right panels the time scale in the horizontal axis is HAD2452654.935 and the sinusoidal curve has a period of 67.46d.

5 Notes on individual stars.

In the following paragraphs we comment on certain peculiarities of specific anomalous stars.

V6. This RRab star has pronounced Blazhko amplitude modulations. Analysing the magnitude at maximum light variations, AF04 estimated a likely Blazhko period of about 67.9d. In the present data we have identified three more times of maximum. In Table 6 we list the times of maximum and their corresponding magnitudes . The modulations are shown in first panel of Fig. 4. We calculated a periodicity of 67.46d which agrees very well with the original estimation of AF04. In the central and right panels one can see that the sinusoidal model with d does fit the modulations very well.

V12. In the paper of AF04 the light curve is rather incomplete but shows a very large amplitude, likely due to the presence of four spurious data near minimum light. The light curve of SCS05 is of smaller amplitude with a flat bottom, attributed by SCS05 to the possible presence of an unseen companion. In the present paper the light curve (Fig. 2) is clean and complete, with an amplitude similar to that of SCS05. A comparison of all available data suggest some small amplitude modulations. The intensity weighted colour - from our data is 0.340 and in the CMD (Fig. 7) the star falls in the inter-mode region. The colour from SCS05 is 0.48 which moves the star to the fundamental mode region. Given the uncertainties in the colour estimates of this peculiar star, we chose to omit it in the discussion involving the RRab-RRc distribution in the instability strip.

V13. This RRc star was noted by AF04 to show amplitude modulations. SCS05 in their investigation calculated a period of 0.408319d but comment that the resulting light curve is somewhat noisy. Combining AF04, SCS05 and the present paper data we found a period of 0.408318d, in excellent agreement with that of SCS05. The resulting phased and light curves are shown in Figs. 2 and 5. In the later we include the data from SCS05. The light curve displays amplitude and phase displacements. It has been suggested by SCS05 that these erratic phasing may be the consequence of interference of fundamental and first overtone pulsation modes but they failed identifying the two modes. An alternative explanation might be the interference of two modes of very similar frequencies, and at least one of them being non-radial, similar to the case of V37 in NGC 6362 (Smolec et al. 2017; Arellano Ferro et al. 2018). Detecting the two frequencies requires dense high quality observations that are not presently available for V13. Possible light contamination by an unseen companion also cannot be ruled out.

Figure 5: light curve of V13. Green symbols are data from SCS05, red are from AF04 and black are data from the present paper.

V16. Similarly to V13, this star shows erratic phasing, which was also noted by SCS05. It falls about 0.02 mag to the red of the red edge of the first overtone instability strip (Fig. 7), but its position may be spurious given the amplitude and phase variations.

HJD
2452654.935 16.140
2452770.192 16.400
2452791.514 16.148
2452813.481 16.607
2452818.382 16.618
2455963.366 16.175
2455988.398 16.666
2456029.223 16.246
Table 6: Variation of the magnitude at maximum in V6 due to the Blazhko effect (see Fig. 3).

V18. This is the brightest star in the field of the cluster near the central region. The star was classified by AF04 as a possible RRc and later denied as variable by SCS05, who considered the star a bright red giant but failed finding a convincing variability. We have reconsidered the case employing the historical data of SCS05 taken between 1983 and 2003 by an assortion of instruments, the data from AF04 taken during 24 nights between January and July, 2003, and the data of the present paper taken in 2012 as detailed in Table 1. In Fig. 6, the top panel shows the long-term brightening of the star, while the panel in the middle shows the clear dimming in 2012. This demonstrates beyond doubt the variable nature of the star. The following questions are if the star is periodic and what the period might be. We have performed a series of test for several data blocks and found that the AF04 and 2012 data are well phased by a period of about 46.1d, the combination of all available data suggests about half that period, 24.8d. The bottom panel shows the light curve phased with this period.

The star is saturated in our -band images, hence we cannot calculate V-I. Adopting the and from SCS05 we were able to plot the star on the CMD of Fig. 7. The star is near the tip of the red giant branch (RGB) as pointed out by SCS05. Based on these evidences we classify the star as a semi-regular late-type variable (SR) whose characteristic time of variation or semi-period is to be better estimated when new accurate data become available.

Figure 6: Historical light variations in the -band of the star V18. Top panel shows a long term brightening over the last nearly 27 years. Green circles are data from SCS05, red from AF04 and black from the present paper. The middle panel is an enlargement of the 2012 data that clearly show a slow light dimming. This demonstrates the variable nature of the star. The bottom panel shows the light curve with phase with a period of 24.8d. We classify the star as semi-regular red variable of the SR type.

V19. This RRc star discovered by SCS04 is near the edge of our images and very near to a bad pixel column of our CCD chip, thus we were unable to secure any confident photometry.

6 Distance to NGC 4147 from its variable stars

The distance to NGC 4147 obtained from the Fourier decomposition of RRc stars is 19.050.46 kpc.

Also for the RR Lyrae stars one can make use of the P-L relation for the magnitude derived by Catelan et al. (2004):

(3)

with and and log f = [/Fe] (Salaris et al. 1993). For the sake of direct comparison with the results of Fourier decomposition we applied the above equations to the measurements of the 6 RRc stars in Table 5 and found a mean distance of 18.890.57 kpc, in good agreement with the Fourier results.

In principle, another approach to estimate the cluster distance is using the variables near the tip of the RGB (TRGB). We can take advantage of the fact that V18 is semi-regular red variable or SR type, and sits near the TRGB. The method, originally developed to estimate distances to nearby galaxies (Lee et al. 1993) has already been applied by our group for the distance estimates of other clusters e.g. Arellano Ferro et al. (2015) for NGC 6229 and Arellano Ferro et al. (2016) for M5 and it is described in detail in these papers. In brief, the idea is to use the bolometric magnitude of the tip of the RGB as an indicator, which can be estimated using the calibration of Salaris & Cassisi (1997):

(4)

where and log f = [/Fe] (Salaris et al. 1993). However, as argued by Viaux et al. (2013) in their analysis of M5, the brightest stars on the RGB might not be exactly at the TRGB but some dimmer leading to an overestimation of the distance. According to these authors the TRGB may be between 0.05 and 0.16 mag brighter than the brightest stars on the RGB. For V18 in NGC 4147, if we assume that it is exactly at the TRGB, which is unlikely, we find a distance of 20.3 kpc. To bring this distance into agreement with the results from the RRc star we must assume that V18 is 0.14 mag below the true TRGB, in this case we find a distance of 19.08 kpc.

The distances found above are in excellent agreement with the values listed by Harris (1996) of 19.3 kpc and by SCS05 of 19.05 kpc.

7 The CMD of NGC 4147

The CMD of the cluster is shown in Fig. 7, where the location of all known variables is marked. All variable stars are plotted using their intensity-weighted means and corresponding colour .

Figure 7: CMD of NGC 4147. The plotted magnitudes and colors for all non-variable stars are magnitude-weighted means of their light curves. Variables are plotted using their intensity-weighted means and . Symbols and colors are: blue and green circles RRab and RRc stars respectively. The SR star V18 is shown with a red symbol. Since the star is saturated in our images we used the values of SCS05 to plot the star. Isochrones for 12 Gyr, Y=0.25 and [/Fe]=0.4 for metallicities –1.75 (blue) and –1.80 (red), and the ZAHB for [Fe/H]=–1.75, shifted to a distance of 19.05 kpc and come from the model collection of VandenBerg et al. (2014). For comparison the green segmented isochrone is for [Fe/H]=–2.0 and assuming . The black vertical line in the HB is the empirical red edge of the first overtone instability strip at (Arellano Ferro et al. 2016) duly reddened. See text for a discussion.

The age of NGC 4147 has been estimated via a differential approach by De Angeli et al. (2005) as 12.23 Gyrs. On the other hand, SCS05 have argued that the ages of M3 and NGC 4147 are virtually identical. For M3 De Angeli et al. (2005) estimated 12.0 Gyrs. We have adopted 12.0 Gyrs with the aim of overplotting an isochrone on our CMD.

We have plotted the isochrone and ZAHB models from VandenBerg et al. (2014) for [Fe/H]=–1.75, Y=0.25 and [/Fe]=0.4. The models were shifted according to the distance and reddening calculated in previous sections from the RRc and RRab stars respectively, i.e. the model parameters closely correspond to our determinations [Fe/H]=, 19.05 kpc (apparent distance modulus of 16.43) and =0.01. Immediate peculiarities stand out from this exercises: The isochrone does not fit the RGB but falls to the red by about 0.05 mag (blue isochrone in Fig. 7). Note that assuming =0.02 would make things worse. Adopting [Fe/H]=–1.80 from the listing of Harris (1996, 2010 edition) the situation improves only a little (red isochrone). It would be necessary, with this distance and reddening, to claim a much lower [Fe/H] to better fit the RGB. For the sake of comparison we plotted the isochrone for [Fe/H]=–2.0 and =0.0 (green dashed isochrone), while it gives better fit at RGB, it is at odds with our determined parameters.

If we look at the ZAHB, the peculiarities continue, the blue tail of the HB bents down at a redder colour than the theoretical model by about 0.1 mag. We stress that the RR Lyrae positions are correct since the red edge of the first overtone mode, i.e. the vertical black line in the CMD, falls exactly where it has been observed in other clusters. If we adopt of 0.02 the problem is lessened (not fully solved) at the expense of a larger red wards shift of the isochrone

We have not found a CMD for NGC 4147 in the literature for a direct comparison. A comparison with the and CMD’s from SCS05 is not illustrative since their isochrone and ZAHB are fiducial hand draws and are not suitable for comparison with theoretical models.

8 Oosterhoff type and the HB of NGC 4147

8.1 The Oosterhoff type

NGC 4147 has been considered as an Oo I type cluster in spite its low metallicity and the rather large fraction of RRc stars, , typical of Oo II clusters. The reason for this is the low average period of its RRab stars,  d, which unfortunately is based only on its five known RRab stars. The period-amplitude plane, or Bailey diagram, for NGC 4147 is shown in Fig. 8 in the VI-bands. The details are given in the caption. Given the low number of RRab stars and their strong amplitude modulations, it is not possible to decide from their distribution, whether they are confined preferentially towards the Oo I locus defined from the M3 globular cluster (Cacciari et al. 2005). The distribution of RRc stars is more suggestive and they display a dual distribution about the loci for Oo I (red parabola) and Oo II (black parabola). This reminds the distribution for NGC 6402 (Contreras Peña et al. 2018; their Figures 9 and 10) for which arguments in favour of being an Oo-Int cluster were offered.

Another interesting feature of NGC 4147 is its HB structure parametrised by the quantity = (B - R)/(B + V + R) with B, V, R, representing the number of stars on the HB to the blue, inside and to the red of the instability strip. Fig. 9 displays the positions of Galactic globular clusters on the -[Fe/H] plane. The different Oosterhoff types are indicated. Similar versions of this figure have been used to illustrate the Oosterhoff dichotomy in Galactic globular clusters which is not present in extragalactic clusters and spheroidal galaxies (e.g. Bono et al. 1994, Catelan 2009, Contreras Peña 2018). The upper and lower limits of the Oostherhoff gap are shown by the solid lines in the figure calculated by Bono et al. (1994). This region is mostly populated by extragalactic systems, for instance those listed in Table 3 of Catelan (2009). For the sake of clearness we only display Galactic globulars in Fig. 9.

Figure 8: The Period-Amplitude plane in the VI-bands for NGC 4147. Filled and open symbols represent RRab and RRc stars, respectively. Triangles represent stars with Blazhko modulations. In the top panel the continuous and segmented lines are the loci for evolved and unevolved stars in M3 according to Cacciari et al. (2005). The black parabola was found by Kunder et al. (2013a) from 14 OoII clusters. The red parabolas were calculated by Arellano Ferro et al. (2015) from a sample of RRc stars in five OoI clusters and avoiding Blazhko variables. In the bottom panel the black segmented locus was found by Arellano Ferro et al. (2011; 2013) for the OoII clusters NGC 5024 and NGC 6333. The blue loci are from Kunder et al. (2013b).

The position of NGC 4147 inside the Oosterhoff gap, although marginal, is remarkable and consistent with the classification of the cluster as an Oo-Int type from the RRc stars amplitude distributions. This together with association of the cluster to the Sagittarius dSph galaxy stream discussed by Bellazzini et al. (2003a, 2003b), supports the scenario that NGC 4147 was accreted by our Galaxy during the merging of the satellite Sagittarius dSph galaxy.

From, Fig. 9, three more clusters in the Oosterhoff gap call our attention; M14 which has been recently argued to be an Oo-Int cluster and whose extragalactic origin also cannot be discarded (Contreras Peña et al. 2018), NGC 6558 which is an Oo I of the old halo pupulation, and NGC 4590 an Oo II type cluster with a red HB for its [Fe/H] and which has been considered a relatively young cluster (Chaboyer et al. 1996). The period-amplitude diagram for NGC 4590 is an interesting one (Kains et al. 2015) since the distribution of RRab stars hints the possibility of an Oo-Int classification.

8.2 Distribution of pulsating modes in the HB

NGC 4147 being a cluster of low metallicity, having a rather blue HB and an intermediate Oosterhoff type, the distribution of RRab and RRc stars in the HB is of particular interest since a clean mode splitting has been found in all studied Oo II type clusters (nine so far), but only in some Oo I (four out of seven so far) (Yepez et al. 2018).

Except for the RRc V16 and the RRab V12, the distribution of RR Lyrae stars on the HB suggest a clean segregation of the RRab and RRc stars at red edge of the first overtone instability strip at (V-I) (Arellano Ferro et al. 2016) duly reddened in Fig. 7. Given the peculiarities of V12 and V16 ( 5), we believe they can be omitted and hence we can conclude that in the case of NGC 4147 the fundamental and first overtone stars are clearly segregated in the HB.

Figure 9: Galactic globular clusters in the HB structure parameter vs. [Fe/H] plane. Circles and squares are used for inner and outer halo clusters respectively. The black-rimmed symbols represent globular clusters where the fundamental and first overtone modes are well segregated around the first overtone red edge of the instability strip, as opposed to filled non-rimmed symbols. Empty symbols are clusters not yet studied by our group. The case of M14 is adapted from Contreras Peña et al. (2018). The upper and lower solid lines are the limits of the Oosterhoff gap according to Bono et al. (1994). NGC 4147 stands out as the most metal poor Oo I cluster but it is obviously not the one with bluest HB in this class (see cluster labels in blue). Its position inside the Oosterhoff gap is in consonance with the possibility of its extragalactic origin. See 8.1 for a discussion.

Fig. 9 illustrates the occurrence of mode-splitting or mode-mixing observed in a family of clusters of both Oosterhoff types, as observed in recent papers of our group, on the plane HB type–[Fe/H].

As it has been discussed by Caputo et al. (1978), the mode segregation versus the mingled mode distribution in the inter-mode or ”either-or” region is a direct result of the mass distribution of ZAHB stars in the instability strip, which in turn depends on the mass loss rates at the RGB (e.g. Silva-Aguirre et al. 2008). The connection of these concepts with the so called second-parameter problem is addressed in detail by Catelan (2009). Thus, it is significant that of the clusters we have revised, in all Oo II the modes are well segregated around the red edge of the first overtone instability strip (black vertical line in Fig. 7), while this is observed only in some Oo I. It would be of interest to revise the RR Lyrae distributions in those clusters in the Oosterhoff gap and that have been associated to dwarf galaxy satellites of the Milky Way (see Table 3 of Catelan 2009).

For the case of M14, we refer to the CMD of Fig 4. in the paper by Contreras Peña et al. (2018), where it is clear that the inter-mode region is populated by both RRab and RRc stars. In passing let us point out that NGC 4590 is the Oo II type cluster with the reddest HB, still, its RRab and RRc stars are well separated.

9 NGC 4147 in the -[Fe/H] relation

The dependence of the HB luminosity on the metallicity of a globular clusters is now a well known fact from theoretical and empirical investigations made over 1990’s, (e.g. Lee, Demarque & Zinn 1990, Walker 1992, Carney et al. 1992, Sandage 1993, Chaboyer 1999). In a recent paper (Arellano Ferro, Bramich & Giridhar 2017) we have studied the -[Fe/H] relation for families of Oo I and Oo II groups in a homogeneous way, from the results of the Fourier decomposition of the RR Lyrae light curves. We found that the slope of the relationship obtained from RRab stars is significantly different from that of the RRc stars. In Fig. 10 we reproduce the -[Fe/H] relation for the RRc stars and place NGC 4147 using our present results for the average and [Fe/H]. These values are consistent with the family of Oo I clusters and do follow the general trend defined by the results from the RRc stars. Note the higher slope of the relationship when calculated from RRab star (red line in Fig 10) determined by Arellano Ferro, Bramich & Giridhar (2017).

Figure 10: The -[Fe/H] relation calculated via the Fourier decomposition of RRc star light curves. NGC 4147 does follow the general trend (thick black line) and it stands out as the most metal deficient of all Oo I globular clusters. Note the different slope obtained by a similar analysis for RRab stars (red line) found by Arellano Ferro, Bramich & Giridhar 2017.

10 Summary of results

New differential CCD photometry of NGC 4147 in the VI-bands allowed us to revise the light curves of the RR Lyrae stars in the cluster, to discuss certain peculiarities of individual stars and calculate the mean distance and metallicity of the cluster. The Blazhko nature of V6 and its period of about 67.46d are confirmed. Erratic phasing in the RRc type stars V13 and V16, previously noticed by AF04 and SCS05, is also seen in the present data. It is suggested that it may be due to the presence of a secondary not-yet-identified frequency similar to case of V37 in NGC 6362 (Smolec et al. 2017; Arellano Ferro et al. 2018). The controversy surrounding the variable status of V18 has been resolved now with the star clearly classified as SR variable with period about 24.8d. The star, near the TRGB, can be used to estimate the distance to the cluster.

From the Fourier decomposition of RRc stars we calculate the averages of the metallicity and distance of the parental cluster as [Fe/H] and 19.050.46 kpc. It was argued that none of the RRab stars in the cluster is suitable for the calculation of physical quantities via the Fourier decomposition since their light curves present strong amplitude modulations. With the estimated metallicity, and its HB structure parameter , NGC 4147 marginally falls in the Oosterhoff gap which may support its classification as Oo-Int and its possible extragalactic origin.

The CMD displays some peculiarities. The isochrone for [Fe/H], distance and reddening estimated in this work falls to the red of the RGB by as much as 0.05 mag, suggesting perhaps a lower metallicity. The blue tail of the HB is found to be too red by about 0.1 mag relative to theoretical predictions. While we do not really have an explanation for these empirical results, we stress that the red edge of the first-overtone instability strip falls where it is expected according to the results from similar analysis of other clusters. We found that the RRab and RRc stars are separated by this locus as it seems to be the case in all Oo II but only in some Oo I clusters.


AAF acknowledges the support from DGAPA-UNAM grant through project IN104917. FCRG is indebted to the Instituto de Astronomía, UNAM, for warm hospitality. We have made an extensive use of the SIMBAD and ADS services, for which we are thankful.

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