1 INTRODUCTION

The globular clusters are spherically symmetric stellar systems which may be found in all galaxies. They are very rich stellar systems that may be found in our Galaxy in remote regions of the galactic halo and also close to the galactic centre. They contain hundreds of thousands of stars within a radius 20 - 50 pc, having typical central densities between 10² and 10⁴ stars/pc³. Globular clusters are dynamically very stable and may live for a long time. They represent a remnant of a primordial stellar formation epoch and may be considered as proper galactic subsystems ^{Ruelas-Mayorga et-al.(2010)}.

Many Milky Way globular clusters have been known for a long time (see the Messier (1771) catalogue). Presently we think there are approximately 150-200 in our Galaxy, although this figure does not include those clusters close to the galactic plane or very low surface brightness objects, (see ^{Monella(1985)}] and ^Harris(1996)).

Because globular clusters are very luminous systems they may be observed at very large distances. This fact makes them fundamental in the study of galactic structure.

Some characteristics of globular clusters are:

Studies of globular clusters are important because they serve a variety of astronomical purposes, such as: determination of the galactic centre position, as indicators of the galactic gravitational potential (i.e. ^{Ishchenko et al., 2023} and references therein), studies of the evolution of low mass and low metallicity stars, and also of chemical evolution of galactic systems. Globular clusters can also provide restrictions on galaxy formation (i.e. ^{Strader et-al.(2005)} ], ^{Harris et-al.(2013)}], ^{Beasley(2020)}], and ^Palma(2023)).

NGC 5893 is a low concentration cluster (c=log  rt/r  c=1.19) ^{Webbink(1985)}. There are in the literature several published colour-magnitude diagrams for this cluster (^{Sandage Katem(1968)}, ^{Sarajedini(1992)}, ^{Ferraro et-al.(1992)} and ^{Stetson(2019)}). Sandage Katem(1968) obtained B and V photometry down to V≈17 which was just able to include the horizontal branch (HB) of this cluster. They found that V(HB)=16.20, E(B-V)=0.11±0.02 and (B-V)0,g=0.78±0.03 (the dereddened colour of the giant branch (GB) at the level of the HB), this allowed them to determine the metallicity of NGC 5893 to be between that of M3 and M92. The HB of this cluster is made mainly of blue stars. ^Wehlau(1990)] found the average of the V magnitude of the RR Lyrae star in this cluster to be V(RR)=16.30. Sarajedini(1992) obtained CCD B and V photometry of this cluster down to V≈22. In this paper he reached the following conclusions:

This paper is organised as follows: in § 2 we present the observations and describe the reduction of the standard stars, in § 3 the reduction of the photometry of the cluster stars is described, as well as the procedure for aligning and matching the different sections of the cluster which we observed. § 4 deals with the derivation of the fiducial lines and the introduction of the colour-magnitude diagrams, the following section (§5) presents the different colour-magnitude diagrams which we derived. § 6 talks about the calculation of the metallicity and the reddening using the Sarajedini & Layden method (see [ ^{Sarajedini(1994)}] and ^{Sarajedini Layden(1997)}). § 7 derives the distance modulus to NGC 5897, and finally, in § 8 we present our conclusions.

2 The Observations

The globular cluster NGC 5897 is located on the constellation of Libra (AR(2000: 15 ^h 17 ^m 24.5 ^s , DEC(2000:-21°00’37.0´´), it contains several hundred thousands stars (see Figure 1). Its most important properties are listed in Table 1 [^Harris(1996)].

Figure 1: The globular cluster NGC 5897. The image is 12.6 vertically (Taken from: http://astrim.free.fr/ngc5897.htm/). 

We obtained the observations at the Observatorio Astronómico Nacional in San Pedro Mártir (OAN-SPM), Baja California during 2006, March 20-23 and 2007, March 14.

We utilised two different CCD cameras attached to the 1.5 m telescope. The characteristics of these detectors are presented in Table 2.

As stated above, the observations were collected during two observing runs, during which, we observed in a standard way obtaining bias and flat field frames in each filter, plus obtaining multiple observations of standard star regions. In Tables 3 and 4 we present the logs for both observation seasons regarding the globular cluster NGC 5897.

2.1 Reduction of Standard Stars

In order to express the magnitude of the stars in the globular cluster in a standard system, we performed aperture photometry of stars in some of the Landolt Standard Regions [ ^{Landolt(1992)}] listed in Tables 3 and 4. The photometric observations of the standard stars was carried out using the APT (Aperture Photometry Tool) ^{Laher et-al.(2012)}, (see also https://www.aperturephotometry.org/about/).

The APT programme is a software that permits aperture photometry measurements of stellar images on a frame. The programme accepts images in the fits format, so no transformation of our images to other formats was necessary. The standard regions which were measured had already been processed by removal of hot and cosmic ray pixels, and were bias and flat-field corrected.

We propose a set of transformation equations from the observed to the intrinsic photometric system that looks as follows:

Bint-Bobs=AB*X+KB*(B-V)obs+CB, (1)

Vint-Vobs=AV*X+KV*(B-V)obs+CV, (2)

Rint-Robs=AR*X+KR*(R-I)obs+CR, (3)

​​​​​​Iint-Iobs=AI*X+KI*(R-I)obs+CI, (4)

where the suffixes int and obs stand for intrinsic and observed, and A, K and C correspond to the negative of the atmospheric absorption coefficient, the colour term and the zero point term. These are the terms that we intend to calculate using the intrinsic values for the magnitudes given in [^{Landolt(1992)}], and the observed values measured with APT. The equations are solved using the least squares procedure and the coefficients obtained are shown in Tables 5, 6, 7 and 8.

Table 5 

Standard System	AB	KB	CB
21-22 March 2006	-0.36496	0.19409	26.83682
22-23 March 2006	-1.23555	0.17829	26.39759
23-24 March 2006	-0.41733	0.42103	26.78603
12-13 March 2007	1.16919	0.10874	25.34031
13-14 March 2007	-0.30223	0.10583	27.47228
14-15 March 2007	-0.37970	0.13717	27.53140

Table 6 

Standard System	AV	KV	CV
21-22 March 2006	0.94214	0.05596	25.03835
22-23 March 2006	-1.67073	0.00563	28.07604
23-24 March 2006	-0.46776	0.30053	27.38143
12-13 March 2007	0.12127	-0.02352	27.58167
13-14 March 2007	-0.25039	-0.03984	27.76332
14-15 March 2007	-0.32799	-0.02824	27.86426

Table 7 

Standard System	AR	KR	CR
21-22 March 2006	-	-	-
22-23 March 2006	-1.83264	0.13357	28.60749
23-24 March 2006	-0.59665	0.50853	27.63788
12-13 March 2007	0.37819	-0.02996	27.22330
13-14 March 2007	-0.13806	-0.04880	27.22305
14-15 March 2007	-0.23895	-0.05205	27.75572

Table 8 

Standard System	AI	KI	CI
21-22 March 2006	-	-	-
22-23 March 2006	-2.25859	0.14873	29.11512
23-24 March 2006	-0.56102	0.78455	27.07607
12-13 March 2007	1.14735	0.06524	25.31618
13-14 March 2007	-0.02309	0.00138	26.50840
14-15 March 2007	0.11989	-0.02645	26.57065

In Figure 2 we plot, for magnitudes B, V, R and I, on the vertical axis the difference between the intrinsic magnitude of the standard stars and their calculated values using the transformation equations (equations 1, 2, 3 and 4) given above, and on the horizontal axis we plot the corresponding observed value for the magnitude. It is clear from these graphs that the calculated values minus the intrinsic values of the magnitudes for the standard stars are, in its majority, distributed around the zero value. However, there are two groups of stars that differ significantly from zero and appear displaced above and below the rest of the stars. These anomalous stars belong in general to the regions PG0942, Rubin 152, PG 1323 and Area 98. We have checked that the stars in these regions are well identified with our observation frames. However, we have been unable to find the cause of this discrepancy; therefore, these anomalous stars were eliminated from the rest of the analysis.

Figure 2: Calculated minus intrinsic magnitude versus observed magnitude. 

The reduction of the data was done in a standard way, that is, removing dead and hot pixels produced by cosmic rays, and performing bias subtraction, and flat field correction. This reduction process was achieved using the general purpose software: Image Reduction and Analysis Facility (IRAF). Once the fields have been bias and flat field corrected we proceed to utilise the routine DAOPHOT to obtain the photometry of the many starts present in the field using the Point Spread Function (PSF) technique [^{Stetson(1992)}]. As an example of an image on which we apply the DAOPHOT technique see Figure 3.

Figure 3: Image of the central zone of the globular cluster NGC 5897 in the R filter after the process of preparation. 

Figure 4 show graphs of the measurement errors as function of the value of the observed magnitude for B, V, R and I,. It is clear that for brighter magnitudes the measurement errors are very small and begin to increase as we move to fainter magnitudes, becoming of the order of several tenths of magnitude by a magnitude value of ≈20.

Fig. 4 Measurement error ∆Mag vs Mag _Obs for B, V, R and I. 

3 Photometry of the Cluster Stars

The calculation of the different observed magnitudes of the stars in the cluster NGC 5897 was obtained by a standard application of the DAOPHOT subroutine present in IRAF to all the observed frames in each filter, after having the frames bias-subtracted and flat fielded.

The magnitude catalogues produced by the subroutine ALLSTAR for the observations were combined to obtained the observed colours for the stars in the globular cluster, so that the application of equations 1, 2, 3 and 4 with the appropriate transformation coefficients was straightforward.

4 Photometry of the stars in NGC 5897, Colour Catalogues and Fiducial Lines

The standard magnitudes for the stars in the cluster NGC 5897 were obtained by comparison with the published photometry results for this cluster published by [^{Stetson(2019)}]. A number of stars were identified in our and Stetson’s observations, and a linear transformation between one set of observations and the other was proposed as follows:

where α represents right ascension, C ₁ is the longitudinal stretching coefficient, X _pos represents the X coordinate value in our files and C ₂ is the longitudinal coefficient of translation.

Analogously,

where δ represents the declination, C ₃ is the transversal stretching coefficient, Y _pos represents the Y coordinate in our files and C ₄ is the transversal coefficient of translation.

The values we obtained for the transformation coefficients between our positions and those of Stetson’s are as follows:

The magnitude transformation results simply on an additional displacement for the four filters. This procedure is applied to our four mosaics in filters B, V, R and I, producing a final set of NGC 5897 stars in four filters on a standard system of position and magnitude.

4.2 Fiducial Lines (FL) and Colour-Magnitude Diagrams (CMD)

In this section we shall present the colour magnitude diagrams which we obtained from the photometry performed on the stars of the globular cluster NGC 5897. Each colour-magnitude diagram will be presented as a plot of magnitude versus colour, on which we have superimposed a series of lines which correspond to the fiducial line for the giant branch and part of the main sequence. The fiducial line was obtained with the following procedure:

• • We calculate the maximum and minimum value of the magnitude interval.

• • We divide this interval in a number of magnitude bins.

• • Along each magnitude bin we find the number of stars in a number of colour bins. This allows us to find a distribution of the number of stars along a magnitude bin in bins of colour. We obtain a distribution histogram for the number of stars in each magnitude bin.

• • Each one of these histograms is fitted by a Gaussian function and we obtain for this function its maximum height (A), its central value (x0) and its standard deviation (σ).

• • The fiducial line is formed from the points with coordinates (x0,m0) where m0 is the average magnitude in each magnitude bin.

Table 9 presents the FL derived by [^{Sarajedini(1992)}] (Columns 1 and 2), that derived by us in this paper (Columns 3, 4 and 5), an eyeball fit to our FL (Columns 6 and 7) and an eyeball fit to the [^{Sarajedini(1992)}] CMD made by us (Columns 8 and 9). Tables 10 and 11 give the colours, magnitudes and colour dispersion for the fiducial lines, calculated with the procedure described above, for the B vs (B - V) and V vs (V - I) colour magnitude diagrams.

Tabla 9 Fiducial lines for V vs (B-V) 

(B−V)ₛₐ	Vₛₐ	(B−V)ₒ	Vₒ	σₒ	Eye (B−V)ₒ	Eye Vₒ	Eye (B−V)ₛₐ	Eye Vₛₐ
1.019	15.1	1.45	13.33	0.06	1.59	13	1.2	14
0.987	15.3	1.2	13.61	0.01	1.25	13.5	1.1	14.5
0.958	15.5	1.04	14.25	0.05	1.11	14	1.05	15
0.93	15.7	0.97	14.66	0.04	0.98	14.5	0.95	15.5
0.906	15.9	0.9	15.18	0.07	0.95	15	0.87	16
0.884	16.1	0.84	15.65	0.11	0.89	15.5	0.85	16.5
0.862	16.3	0.84	16.25	0.08	0.84	16	0.8	17
0.84	16.5	0.82	17.19	0.07	0.84	16.5	0.75	17.5
0.822	16.7	0.82	17.72	0.09	0.79	17	0.72	18
0.804	16.9	0.78	18.06	0.09	0.79	17.5	0.7	18.5
0.791	17.1	0.79	18.03	0.08	0.73	18	0.67	19
0.777	17.3	0.76	18.52	0.09	0.75	18.5	0.6	19.25
0.767	17.5	0.71	18.97	0.14	0.64	19	0.5	19.5
0.757	17.7	0.64	19.4	0.14	0.61	19.5	0.48	19.75
0.749	17.9	0.62	19.89	0.13	0.5	20	0.47	20
0.741	18.1	0.58	20.33	0.17			0.5	20.25
0.733	18.3	0.53	20.87	0.25			0.52	20.5
0.724	18.5	0.48	21.33	0.02			0.56	20.75
0.712	18.7						0.65	21
0.695	18.9
0.664	19.1
0.638	19.2
0.602	19.3
0.552	19.4
0.528	19.5
0.515	19.6
0.506	19.7
0.502	19.8
0.5	19.9
0.5	20
0.501	20.1
0.503	20.2
0.506	20.3
0.51	20.4
0.516	20.5
0.524	20.6
0.544	20.8
0.569	21
0.598	21.2
0.629	21.4
0.661	21.6

TABLE 10 FIDUCIAL LINE FOR B VS (B−V) 

B - V	B	σ
1.365	14.683	0.106
1.05	15.238	0.068
0.968	15.608	0.085
0.895	16.078	0.098
0.864	16.444	0.113
0.838	16.969	0.081
0.747	17.382	0.019
0.814	17.925	0.073
0.773	18.639	0.102
0.737	18.888	0.055
0.731	19.248	0.12
0.718	19.592	0.253
0.656	19.682	0.151
0.611	19.993	0.143
0.456	20.441	0.138

TABLE 11 FIDUCIAL LINE FOR V VS (V − I) 

V - I	V	σ
1.544	13.325	0.092
1.616	14.177	0.211
1.314	14.254	0.179
1.107	15.169	0.088
1.062	15.576	0.114
1.057	15.641	0.093
1.062	16.109	0.058
0.992	16.574	0.078
0.971	17.08	0.08
0.926	17.542	0.082
0.894	18.026	0.08
0.811	18.516	0.204
0.775	18.977	0.179
0.76	19.417	0.165
0.806	19.883	0.167
1.007	20.324	0.33
1.355	20.858	0.026
1.422	21.332	0.269

Figure 5 presents the FL derived by [^{Sarajedini(1992)}] (blue) from an eyeball fitting to the points on his CMD and the FL we derived in this paper (red) following the procedure described above. We have also included in this figure an eyeball fit to our FL (pink), as well as an eyeball fit made to the CM diagram of Sarajedini’s made by us (green). The FL we derived using the Gaussian technique has errors in the (B - V) colour that bring it in close agreement with the [^{Sarajedini(1992)}] fiducial line. However, in the magnitude range 14.0≤V≤16.0 our fiducial line appears ≈0.1 units bluer than that of Sarajedini’s. Even if we consider the estimated error for the (B - V) colour of our observations (≈0.03) this cannot explain a shift of this magnitude. Fainter than V≈16.0 and down to V≈19.0 our FL and that of Sarajedini’s coincide within the errors. Further down than V≈19.0 there is again a discrepancy which, in this case, is simply due to the paucity of our data at these faint magnitudes.

Figure 5: The blue dots show the fiducial line derived by [^{Sarajedini(1992)}] from an eyeball fit to his CMD. The red dots show the FL derived in this paper following the procedure described herein (see text); error bars for these points are also shown. The pink dots show an eyeball fit to our FL and finally, the green dots show an eyeball fit to the Sarajedini CMD made by us. The colour figure can be viewed online. 

The difference we observe between our FL and that of Sarajedini’s at brighter magnitudes baffles us and we cannot find, at this point, a reasonable explanation for it. Our observations are quite incomplete at levels deeper than V≈19; that is why our FL shows neither the turn-off point nor the beginning of the main sequence.

5 Colour-Magnitude Diagrams

Figure 6 shows the colour-magnitude diagrams B vs B - V, V vs B - V, B - V vs V - I and I vs V - I. The lines show the fiducial Line (FL) obtained following the procedure described above and the FL displaced one and two standard deviations. We can say that those stars that lie outside the 2σ limit and do not belong to the horizontal branch of the cluster have a very low probability (≈5%) of belonging to the globular cluster.

Figure 6 Colour-magnitude diagrams for B vs B - V, V vs B - V, B - V vs V - I and I vs V - I. The central red line is the fiducial line (FL) (see text) and the other red lines indicate a 1σ and 2σ separation from the FL. The estimated errors are ≈0.02 for the magnitudes and ≈0.03 for the colours, smaller than the dots representing the stars. The colour figure can be viewed online. 

Figure 7 presents the colour-magnitude diagrams corresponding to the following combinations of magnitude and colour: V vs (V - R), R vs (V - R), R vs (R - I) and I vs (R - I). On these diagrams we have not drawn the fiducial lines, but they can be easily obtained following the procedure described above.

Figure 7 Colour-magnitude diagrams for V vs V - R, R vs V - R, R vs R - I and I vs R - I. The estimated errors are ≈0.02 for the magnitudes and ≈0.03 for the colours, smaller than the dots representing the stars. 

On all the colour-magnitude diagrams presented here we can clearly appreciate the presence of the giant branch (GB) which, on the V vs B - V diagram extends from V≈13.5 to V≈20 where the main sequence (MS) appears to begin. Our observations are not sufficiently deep to allow us a clear detection of the MS of this cluster. However, on the V vs V - R diagram we see stars that extend down to magnitude V≈22, where the turn-off point (TO) and the beginning of the MS are more clearly shown on this diagram. It is also clear that there is a number of stars that most probably do not belong to the globular cluster and that most certainly are foreground and to a lesser extent background stars. As mentioned above, the FLs obtained for three of the colour-magnitude diagrams permit us to eliminate with a high degree of certainty those stars which are located far away from the calculated fiducial line for the cluster. Below the HB and to the left (bluer colours) of the GB there is a large number of stars that could possibly be blue stragglers belonging to this cluster.

The giant branch (GB) of this cluster is very well delineated on the R vs R - I and I vs R - I diagrams and it extends from ≈12 to ≈18 magnitudes.

The presence of horizontal branch (HB) stars is obvious in all the diagrams. In those diagrams that include the R and I magnitudes, it is clear that the HB stars become fainter very quickly as we move towards bluer colours. In all our photometric catalogues we separated from the bulk of our observations the HB stars, and on each one of the colour-magnitude diagrams we explicitly state the number of HB stars belonging to this diagram.

6 Metallicity and Reddening

The metallicity and the reddening of a globular cluster may be determined simultaneously by the Sarajedini method (^{Sarajedini, 1994} and ^{Sarajedini & Layden, 1997}), which takes into consideration the shape of the red giant branch (RGB), the observed magnitude (VHB) of the horizontal branch (HB), the intrinsic (B - V) colour of the RGB at the level of the HB; this value will be denoted herein as: (B-V)0,g, and the difference in observed V magnitude between the HB and the RGB at (B-V)int=1.2 denoted by ΔV1.2=VHB  Obs-VRGB  Obs  at  1.2  int, where VRGB  Obs  at  1.2  int means the observed V magnitude of the RGB at an intrinsic (B - V) colour equal to 1.2. Defined this way, ΔV1.2 results in an intrinsically positive quantity.

We applied the Sarajedini method for the stars in the V vs (B - V) and the V vs (V - I) colour-magnitude diagrams and obtained values for the metallicity [Fe/H] and colour excesses E(B - V) and E(V - I). Unfortunately, these values were completely absurd, resulting in very high metallicities and negative colour excesses. We conducted a few numerical experiments and saw that the values of the metallicity and the colour excess are very sensitive to variations of the values of the fit coefficients. The coefficients we obtained for the FLs in the V vs (B - V) and V vs (V - I) diagrams had errors of the order 30 % which might explain the troublesome results we obtained. We therefore decided to adopt the values given in the Harris catalogue (^{Harris, 1996}) Fe/H=-1.90 and E(B - V) = 0.09.

The parameters discussed in this section could also be determined by means of isochrone fitting. There are in the literature several sets of isochrones which could be used ([^{Girardi et-al.(2002)}, ^{Spada et-al.(2013)}, http://www.astro.yale.edu/demarque/yyiso.html, and references therein, http://stev.oapd.inaf.it/cgi-bin/cmd and references therein. We shall report on this elsewhere.

7 Distance Modulus

Using the assumption that the average absolute magnitude of the HB is equal to the absolute magnitude of the RR-Lyrae stars in the cluster, we calculate the distance to the cluster we study here (for a justification of this assumption see, for example, ^{Christy, 1966}; ^{Demarque & McClure, 1977} and ^{Saio, 1977}).

For the RR-Lyrae stars, a linear relation between absolute magnitude and metallicity of the form M=a+bFe/H is proposed in the astronomical literature. Determination of the constants a and b is achieved using the following methods: (i) statistical parallaxes, (ii) the BBW moving atmosphere method, and (iii) main sequence fitting ([^{Sandage Tammann(2006)}]).

In the following paragraphs we shall use different absolute magnitude-metallicity relations from the literature for RR-Lyraes, which combined with the metallicity and the apparent magnitude for the HB of NGC 5897, will permit us to determine the value of its distance modulus.

A compilation of statistical parallaxes of field RR-Lyrae stars has been presented by ^{Wan et-al.(1980)} in a Catalogue of the Shanghai Observatory. This compilation is summarised in Table 3 of [^Reid(1999)]. There is a value for 〈MV〉RR=0.83±0.23 for 〈Fe/H〉 values around -0.75 and another 〈MV〉RR=0.85±0.15 for 〈Fe/H〉 values around -1.56. A linear extrapolation to the metallicity of NGC 5897 (Fe/H=-1.90) produces a value for

The extrapolation process poses a problem for this determination.

Using a combination of the infrared flux and the Baade-Wesselink analysis methods ^{Fernley et-al.(1989)}, ^{Fernley et-al.(1990)}, ^{Fernley et-al.(1990)}, ^{Skillen et-al.(1989)}, and ^{Skillen et-al.(1993)} study 21 RR-Lyrae variable stars and obtain a mean relation for their absolute magnitude expressed as follows:

which for the metallicity value of our globular cluster produces a result of

[^{Fernley(1993)}] uses his near-IR Sandage period-shift effect (SPSE) and a theoretical pulsation relation to derive the following relation:

which applied to our cluster gives

[^{McNamara(1997)}] has reanalysed these same 29 stars making use of more recent Kurucz model atmospheres and derives a steeper, more luminous calibration given as follows:

The RR-Lyraes studied in the McNamara paper belong to a metallicity interval from approximately -2.2 to 0.0. The metallicity value for our globular cluster (-1.90) lies within this interval, making it reasonable to apply this relation to this cluster. The value we obtain from this relation is:

^{Tsujimoto et-al.(1998)} have analysed data for 125 Hipparcos RR Lyraes in the metallicity range -2.49 < [Fe/H] < 0.07 using the maximum likelihood technique proposed by Smith (1988). This technique allows simultaneous correction of the Malmquist and Lutz-Keller biases, allowing a full use of negative and low-accuracy parallaxes. They derive the following relation:

Given that Fe/HNGC  5897=-1.90 is contained within the studied metallicity interval, applying this relation to the cluster studied in this paper produces

^{Arellano Ferro et-al.(2008)} using the technique of Fourier decomposition for the light curves of RR-Lyraes in several globular clusters derive the following relation:

This relation was obtained for a set of globular clusters contained within the metallicity interval -2.2<Fe/H<-1.2 making it appropriate for the metallicity value (-1.90) we have for NGC 5897.

Applying this relation to our cluster we find

There are many different empirical and theoretical determinations of the 〈MV〉-Fe/H relation for RR-Lyrae stars, for ample discussions see [^{Chaboyer(1999)}], [^{Cacciari & Clementini(2003)}] and [^{Sandage Tammann(2006)}]. Determining which one is the most appropriate for NGC 5897 is beyond the scope of this paper, so we have decided to consider all of them for the calculation of the distance modulus of the globular cluster studied in this paper.

From the data presented in this paper we determine an apparent V magnitude for the HB of NGC 5897 of 16.60±0.46, which combined with the values for the absolute magnitudes of the RR-Lyrae stars and the assumption that the HB and the RR-Lyraes have the same absolute magnitude yields the distance modulus values presented in Table 7.

A weighted average (by the inverse square of the errors) of these values results in an average distance modulus for NGC 5897 of 15.96±0.64 (15500-3900+5200 pc). The errors we encounter represent a ≈±34% error in distance. For the most part the error in the distance modulus comes from the errors in the absolute magnitude versus metallicity relations (see Table 13, Column 2), and not from the errors in our photometry.

^{Benedict et-al.(2002)}, using the HST parallax for the prototype RR-Lyrae star, determine an absolute magnitude for this star of Mv=0.61±0.10. If we assume that the HB of NGC 5897 has this value for its absolute magnitude, then we obtain a distance modulus of:

which agrees, within the errors, with previous determinations. This value of the distance modulus produces a distance of 13800-4600+6800 pc to NGC 5897 with an error of ≈±49%.

We adopt as our best determination for the NGC 5897 distance modulus the average of the values obtained with the [^{Fernley(1993)}] (16.04±0.10), and the ^{Arellano Ferro et-al.(2008)} (16.01±0.10) calibrations due to the fact that these calibrations present the smallest errors. This average results in 16.02±0.14.

8 Conclusions

In this paper we present B, V, R and I CCD photometry for the globular cluster NGC 5897. We obtained aperture photometry for a number of standard stars in the [^{Landolt(1992)}] regions, and then compared our observed stars with the magnitudes published by [^{Stetson(1992)}]. After aligning and matching the different sections of the globular cluster, we were able to produce magnitude catalogues for all the filters (a sample of these catalogues is presented in Appendix A). We formed eight colour magnitude (CM) diagrams (see Figures 6 and 7). In all these CM diagrams we can clearly see the red giant branch (RGB), the horizontal branch (HB) and the beginning of the main sequence (MS). Towards bluer colours from the MS turn-off point, we see a somewhat large number of stars that we identify as blue stragglers in this cluster. We tried to calculate the metallicity and the reddening of this cluster making use of the Sarajedini-Layden method (see [ ^{Sarajedini(1994)}] and [^{Sarajedini &Layden(1997)}]), but we were unable to do so. We calculated the distance modulus to this cluster, and it resulted in 16.02±0.14 which corresponds to a distance of 16.0±1.0 kpc.