© The Authors 2024

1 Introduction

Globular clusters (GCs) are very intriguing stellar systems formed by hundreds of thousands of gravitationally bound stars. They have a high spherical symmetry and, in general, a high concentration of stars towards their center. They also host the oldest stars in our galaxy. Therefore, they are similar to fossils and can help us to understand the early formation and evolution of our galaxy, the Milky Way.

In this study, we focused our attention on the GC Terzan 5. According to the Catalog of Parameters for Milky Way Globular Clusters (Harris 1996, 2010 version), Terzan 5 is located at RA(J2000) = 17:48:04.8 and Dec(J2000) = −24:46:45. It has a metallicity of [Fe/H] = −0.23, a reddening of E(B − V) = 2.28 mag, a V magnitude level of the horizontal branch (HB) V_HB = 22.04 mag, a distance modulus of (m − M)_V = 21.27 mag, an absolute visual magnitude of M_V = −7.42 mag, and is found at R_⊙ = 6.9 kpc from the Sun.

Ortolani et al. (1996) produced a VI color–magnitude diagram (CMD) with images taken with the ESO New Technology Telescope (NTT) at ESO La Silla, Chile, with seeing of around 0.34″ − 0.50″, and derived a reddening of E(B − V) = 2.49 and a distance from the Sun of R_⊙ = 5.6 kpc.

Origlia et al. (2011) carried out a spectroscopic study where 33 red giant members of Terzan 5 were analyzed. The spectra were taken using the NIRSPEC instrument at the Keck II telescope at W. M. Keck Observatory, Hawaii. The resulting spectra have a resolution of R = 25 000. Inspection of the iron abundance distribution showed that the cluster has two stellar populations, the first with an average metallicity of about [Fe/H] = −0.25 ± 0.07 rms and the second with about [Fe/H] = +0.27 ± 0.04 rms. In the Catalog of Variable Stars in Galactic Globular Clusters (Clement et al. 2001, August 2019 update), and in the literature available so far, there are 13 variable stars known in the field of Terzan 5.

The first variables reported were two Mira variables (V1-V2) discovered by Spinrad et al. (1974) using observations taken with photographic plates (~20 epochs) with telescopes at Lick, Cerro Tololo, and Palomar observatories. Later, Edmonds et al. (2001) discovered two more variables using data taken with the Hubble Space Telescope (HST). One (V3) corresponds to the first RR Lyrae RR0 type discovered in Terzan 5 with a period of 0.60 days, and the second (V4) is a blue faint sinusoidal variable with a period of about 7 hr. The authors consider that this star is a possible eclipsing blue straggler or (less likely) the infrared counterpart to the low-mass X-ray binary discovered by Makishima et al. (1981) and also analyzed by Johnston et al. (1995) and Verbunt et al. (1995). Sloan et al. (2010) discovered five Mira variables (V5-V9) using the SIRIUS near-infrared camera at the 1.4 m Infrared Survey Facility telescope at the South African Astronomical Observatory, which produced simultaneous photometry in the J, H, and K_s bands. Finally, Origlia et al. (2019) discovered four more variables, one Mira type (V 10) and three RR Lyrae RR0 type (V 11, V 12, and V 13). In this latter work, the authors used 24 images taken with the HST Wide Field Planetary Camera 2, 12 images in F606W, and 12 in the F814W passbands.

There are also, as of the time of this study, 42 millisecond pulsars¹ (MSPs) known in the field of Terzan 5 (see e.g., Ransom et al. 2005, 2018; Cadelano et al. 2018; Bahramian et al. 2022, and references therein). It is well established that MSPs are neutron stars rotating at incredibly fast and precise periods, typically in the range of milliseconds. The strength of their magnetic fields is believed to significantly influence their rotation rates. In the context of GCs, MSPs are known to form binary systems where they possibly accrete matter from their companions, leading to changes in their magnetic fields and rotation speeds (see e.g., Bhattacharyya et al. 2022, and references therein). Globular clusters host a large population of MSPs, with approximately 300 known in 38 clusters. Notably, Terzan 5 stands out with over 20 more detections than the well-studied cluster 47 Tucanae¹, making it an ideal target for investigating these phenomena further. Additionally, there have been observational indications of electromagnetic signals from MSP companions in the visual range, which offers the potential to quantify these variations and gain insights into their physical origins, such as interactions with companions or the ejection of accreted material. Visual detections not only provide independent confirmation of variations in these systems but also facilitate precise positional measurements for the observed targets (see e.g., Breton et al. 2013; Pallanca & Cosmic-Lab Team 2016).

Furthermore, GCs encompass a wide array of stars in various stages of evolution. Among them, numerous types of variable stars have been identified, including Miras, type II Cepheids, RR Lyrae, SX Phoenicis, and eclipsing binaries (e.g., Clement et al. 2001; Clement 2017; Belloni & Rivera 2021; Lugger et al. 2023, and references therein). Some clusters exhibit a higher abundance of these variables than others. The comprehensive census, detection, and characterization of the variable stars within these stellar systems present an excellent opportunity to deepen our understanding of stellar evolution theories and the formation and evolution of GCs. Pulsating variable stars, such as RR Lyrae, have proven invaluable as independent estimators of physical properties within GCs, including metallicities, distances, and the Oosterhoof dichotomy. Moreover, given the evidence of multiple stellar populations within GCs, the study of variable stars can contribute to their detection and characterization. Worthy of note is the fact that GCs harbor the oldest stars in our galaxy, making an accurate census and characterization of these stars crucial for advancing our knowledge of early galaxy formation and evolution (see e.g., Catelan & Smith 2015; Figuera Jaimes 2018, and references therein).

Terzan 5, located in the Galactic bulge, poses unique challenges for observations due to its complex nature. The presence of background stars greatly affects observations of this cluster. Furthermore, Terzan 5 is known for its strong differential reddening, adding another layer of complexity. Additionally, the target itself is faint due to strong obscuration from heavy extinction, with a V magnitude level of approximately 22.04 mag on the HB. With a central luminosity density of 5.14, it stands as one of the densest known GCs (Harris 1996, 2010 version).

Given these factors, studying the densely populated central region of Terzan 5 poses significant difficulties, including issues related to crowding, blending, and saturation of stars. Blending and saturation can result in the loss of variability information for some of the variables. To address these challenges and achieve a comprehensive census of the variable stars in the central region, the utilization of an EMCCD camera, high frame-rate imaging, and difference image analysis (DIA) becomes crucial. This study marks the first time-series observational program specifically designed to accurately detect and capture the complete phase variation of variable stars within the densely crowded central region of Terzan 5.

In Sect. 2, we present the instruments used, the observations obtained, and the pipelines and techniques employed to produce the photometry. In Sect. 3, the techniques employed to search for and detect variable stars are explained. The CMD of Terzan 5 is given in Sect. 5. Known variables in the field observed are presented in Sect. 6. In Sect. 7, new variables and candidates discovered in this study are shown. Stars flagged as variables in the Gaia survey are discussed in Sect. 8. In Sect. 7.4, we present the cases of two stars that show significant displacement. Finally, conclusions are given in Sect. 10.

2 Instruments and observations

2.1 Telescope

The Danish 1.54 m telescope² was employed to carry out observations. This telescope is located at an altitude of 2375 m in ESO’s La Silla Observatory, Chile at 70º44′07″.662W 29° 15′ 14″.235S.

2.2 Detector

The telescope is equipped with an Andor Technology iXon+897 EMCCD camera (Lesser 2015; Howell 2006), which has a 512 × 512 array of 16 µm pixels, a pixel scale of 0″.09 per pixel, and a total field of view of ~45 × 45 arcsec². For the purpose of this research, the camera was configured to work at a frame rate of 10 Hz (this is ten images per second) and an EM gain of 300 e⁻ /photon. The camera is placed behind a dichroic mirror, which works as a long-pass filter. Considering the mirror and the sensitivity of the camera, it is possible to cover a wavelength range of between 650 nm and 1050 nm (Skottfelt et al. 2015b), corresponding roughly to a combination of SDSS i′ + z′ filters (Bessell 2005).

2.3 Observations

The MINDSTEp consortium program was designed to explore the Milky Way bulge for exoplanet detection and characterization, with observations occurring annually from April to September. However, in cases where observations of the Galactic bulge were not possible, GCs were targeted as alternatives. Terzan 5 was one of the chosen GCs for these observations. A histogram in Fig. 1 displays the distribution of science images obtained between 2014 and 2021, showing that a total of 242 science images were obtained within the field of Terzan 5.

2.4 Exposure times

The target exposure time for each of the mentioned images was 10 minutes (600 seconds). To achieve this, the camera was continuously taking images (at the rate of 10 images per second) for the total exposure time of 10 minutes and then all the images obtained during the 10 minutes were stacked to produce a single observation (see Figuera Jaimes et al. 2016b; Skottfelt et al. 2015a, for a detailed explanation of the technique employed to perform the stacking). In other words, a ten-minute exposure time observation is the result of stacking 6000 images that were continuously taken. We produced 161 images with a total exposure time of 600 s, 71 images in the range of 550-559 s, 7 images in the range of 500–549 s, 2 images in the range of 450-499 s, and 1 image in the interval of 400–449 s.

Science images with 600 s mean that all frames were used, while science images with different exposure times mean that some frames were not included. This might be due to different reasons, such as poor seeing, telescope tracking issues, or limitations. The reference frame with a 0″.41 FWHM (see Sect. 2.5) was intentionally obtained by discarding images with poor seeing and selecting only those with the best possible seeing to create the best reference frame possible for use in subsequent steps.

Fig. 1 Histogram of observations obtained after the stacking in the field of the GC Terzan 5. The colors represent the images obtained for each year: black (group 1) is 2014, blue (group 2) is 2015, green (group 3) is 2016, olive (group 4) is 2017, purple (group 5) is 2019, and pink (group 6) is 2021.

2.5 Photometry

Once the stacked images were produced, the next step was to analyze the images for scientific purposes. To this end, we extracted the photometry in each of the images obtained. Nowadays, there are several methods and techniques used to achieve this goal (see e.g., Catelan 2023, and references therein). In our case, we employed the DanDIA³ pipeline (Bramich 2008; Bramich et al. 2013), which is based on difference image analysis (DIA; Alard & Lupton 1998; Alard 2000).

The reference frame used to perform the difference image analysis was built by stacking a total of 3000 images, which is equivalent to a science image with a 300 s exposure time. The resulting mean FWHM measured in the stars in the reference frame was about 0″.41.

The instrumental magnitudes m_ins for each star in the light curves obtained are represented by $$m_{\text{ins\hspace{0.17em}}}(t)=17.5-2.5\log \left(f_{\text{tot}}(t)\right),$$(1)

where f_tot(t) is the total flux in analog-to-digital units per second (ADU/s), defined as $$f_{\text{tot}}(t)=f_{\text{ref}}+\frac{f_{\text{diff}}(t)}{p(t)},$$(2)

where f_ref (ADU/s) corresponds to the reference fluxes of each star detected in the reference frame, f_diff(t) (ADU/s) is the difference fluxes measured in the difference images at the position of each star detected in the reference frame, and p(t) is the photometric scale factor used to scale the reference frame to each image (Bramich et al. 2011). For a comprehensive explanation of how the pipeline works, we direct the reader to Figuera Jaimes et al. (2016b) and Bramich (2008). The light curve information, photometric measurements, and fluxes of all variable stars studied in this work are available from the CDS⁴ database in the format given in Table 1.

2.6 Photometric calibration

The resulting instrumental magnitudes were transformed to the standard Johnson-Kron-Cousins photometric system (Landolt 1992) by taking advantage of the I magnitudes electronically available in Ortolani et al. (1996). The linear transformation found between both magnitudes is $$I=m_{inst}+(8.7053\pm 0.0543),$$(3)

where m_inst corresponds to the instrumental magnitudes and I the resulting standard magnitude. Figure 2 shows the data used (black points) and the best fit obtained (red line). A total of 339 stars were used in the fit and the obtained correlation coefficient is 0.999.

2.7 Astrometry

To carry out the astrometry correction to our reference frame, we used an HST image available in the HST archive (file name: hst_12933_01_acs_wfc_f814wjc3801iu_drc.fits). We matched stars in the field of our reference frame with those in the field of the HST image using the GAIA software (Graphical Astronomy and Image Analysis Tool; Draper 2000). A total of 260 stars were matched over the entire field of view. The root-mean-square (RMS) scatter obtained was approximately 0″.03 (~0.3 pixels). The HST astrometry was also corroborated with Gaia astrometry and with the STScI⁵ documentation. The final reference frame with the resulting astrometric solution was employed to produce the finding chart shown in Fig. 3, which contains the position and identification of all variable stars studied in this work. Table A.1 provides the equatorial J2000 celestial coordinates for all variables in this study.

Fig. 2 Standard I magnitude available in Ortolani et al. (1996) as a function of the instrumental magnitude. The red line is the fit that best matches the data and is given in the title of this plot and equation (3). The correlation coefficient is 0.999.

3 Variable star detection

We explored several techniques in order to find a semi-automated way of searching for variable stars in the field covered by our reference image. Our final selection, which is displayed in Fig. 4, is based on a judicious combination of different criteria, as well as careful inspection of the difference images, as discussed in the following subsections.

3.1 Root-mean-square diagram

We started using the RMS calculated for all stars detected versus their mean I magnitude obtained with the final photometry. However, on this occasion, we fitted a polynomial model to the data to define where most of the stars are located. Thereafter, we defined a threshold that was shifted by a factor of 3 over the model. Any star placed over the threshold was selected as a candidate variable, subject to further scrutiny of its light curve and examination in the difference images.

Fig. 3 Finding chart for GC Terzan 5. Black labels are variable stars studied in this work. Circled labels correspond to new discoveries and previously known variable stars, while labels in squares are the candidate variables. Blue labels are the 33 red giant stars studied in Origlia et al. (2011). The average FWHM obtained for the stars in the reference frame was about 0″.41. The big black square is the region explored in our study for new variable star detection and characterization, which corresponds to a field of view of about 38″ × 40″. Labeled stars lying outside the black box correspond to stars previously studied in the literature.

3.2 𝒮_ℬ statistic

Another approach used was the 𝒮_ℬ statistic defined in Figuera Jaimes et al. (2013) for semi-automatic detection of variable star candidates. The 𝒮_ℬ statistic is defined as $${\mathcal{S}}_{ℬ}=\left(\frac{1}{NM}\right){\displaystyle \sum _{i=1}^M{\left(\frac{r_{i,1}}{{\sigma }_{i,1}}+\frac{r_{i,2}}{{\sigma }_{i,2}}+\dots +\frac{r_{i,k_i}}{{\sigma }_{i,k_i}}\right)}^2},$$(4)

where N is the number of data points for a given light curve, and M is the number of groups formed from time-consecutive residuals of the same sign from a constant-brightness light-curve model (e.g., mean or median). The residuals r_i,1 to $r_{i,k_i}$ correspond to the ith group of k_i time-consecutive residuals of the same sign with corresponding uncertainties σ_i,1 to ${\sigma }_{i,k_i}$. The 𝒮_ℬ statistic is larger in value for light curves with long runs of consecutive data points above or below the mean, which is the case for variable stars with periods longer than the typical photometric cadence.

In Fig. 4, the 𝒮_ℬ is plotted against the mean I magnitude for all stars detected in our analysis. Candidates for variability were selected based on their position above the threshold, set at ten times the model 𝒮_ℬ values. These candidates, along with those obtained in Sect. 3.1 were further scrutinized in the difference images, as described in Sect. 3.3. Figure 4 presents the final selection of variable stars determined through the combined analysis discussed in Sects. 3.1 and 3.3.

A comparison between the RMS and the SB is shown in Fig. 4. All newly discovered variables exhibited high RMS and 𝒮_ℬ values well exceeding the thresholds. Gaia stars (G1-G9) flagged as variables, for which we found a period and classified as semi-regular, also exceeded the thresholds, except for G7, G8, and G9. In the case of G9, is due to the fact that it was not automatically detected in the reference frame. The remaining fraction of stars with RMS and 𝒮_ℬ values that resembled nonva-riable stars correspond to Gaia-identified long-period variables (LPVs), mainly stars with low amplitudes listed in Table A.1 (G11-G34). These are depicted as blue squares in Fig. 4, potentially indicating that they are at the threshold of uncertainties. Further exploration of variables at RMS and 𝒮_ℬ values below the thresholds described above may require methods to detrend our data.

Fig. 4 RMS and 𝒮ℬ index versus the mean I magnitude in the GC Terzan 5. The green-circled point is the previously known RR Lyrae V3, dark-yellow triangle points are the semiregular variables, orange five-pointed star symbols are the stars selected as candidate variables, blue squares are stars flagged as LPVs in Gaia Data Release 3 (DR3), and the light-yellow five-pointed star symbol is an eclipsing binary candidate. The lower red lines correspond to the fits applied to the data, while the upper red lines are the shifts applied to define the thresholds for variable candidate detection.

3.3 Analysis of difference images

Difference image analysis is a powerful technique used for photometry in crowded fields (Alard & Lupton 1998). The technique involves subtracting a sequence of aligned images of the same field from a reference frame. The result of this subtraction is a set of difference images that capture the flux variation due to the changes in brightness of variable stars. When these difference images are stacked, the flux variation of these stars can be accumulated into a single image. Consequently, this procedure can be used as a method to potentially detect variable stars in observed fields. Stacked images can be represented as: $$S_{ij}={\displaystyle \sum _k\frac{\left|D_{k,ij}\right|}{{\sigma }_{k,ij}}},$$(5)

where S_ij is the sum of all the difference images, D_k,ij is the kth difference image, σ_k,ij· is the pixel uncertainty for each image k, and i and j denote pixel positions.

All the variable star candidates obtained using the RMS diagrams or the 𝒮_ℬ statistic explained in Sects. 3.1 and 3.2 were inspected visually in the stacked images to confirm or refute their variability. Additionally, any other candidate detected in the stacked images that might have been initially overlooked (e.g., if it fell below the defined thresholds in the SB and RMS diagrams) was included in the inspection process. Difference images were also blinked to finally corroborate the variation of the stars selected. Difference fluxes for all variable stars studied in this work were significantly higher than the background level measured in the stacked image defined in Eq. (5), that is, by at least 6σ. Only two of the LPVs previously reported in Gaia DR3 were slightly below the 6σ level.

4 Period search

To corroborate or improve the period of previously known variable stars and to find possible periods for newly discovered variables, several very well-known techniques were implemented, such as the string length, fast χ², and least squares methods (see, e.g., Lafler & Kinman 1965; Palmer 2009; Lenz & Breger 2014, respectively). From our previous experience, we note that the string length is very useful in searching for short periods; however, because the technique has to test a significant number of periods and measure the dispersion in the resulting phased light curves for each period, we only searched for periods with this method in the range of 0.01–0.9 days.

To search for periods in other intervals, for example, from zero to the Nyquist frequency, we used the fast χ² method, which is optimized for the detection of periods in irregularly sampled data with nonuniform errors. Finally, we also implemented the least squares technique to detect the strongest frequency that dominates the frequency spectrum in each light curve. In the cases where a discrepancy was evident between the frequencies found, we compared both frequencies by plotting the phased light curves and chose the one that visually better phased the data. In the cases where differences between the frequencies were very small, and the phased light curves did not show any significant improvement from one to the next, we chose the strongest frequency found in the periodogram using the least squares method. The adopted periods in our analysis are given in Table A.1.

5 Color-magnitude diagram

To build the CMD of Terzan 5, we employed the data already available in Table 2 in Ortolani et al. (1996). The aim here is to highlight all variable stars in the CMD that were detected in the field of our reference image. However, we noticed that the mentioned table did not have celestial coordinates available to compare with our reference frame, but instead the x and y physical coordinates of the image they used in their Fig. 1. For this reason, we obtained the mentioned frame from the ESO archive⁶ (file name: ONTT.1994-05-16T06:36:38.000.fits), for which we calculated the equatorial coordinates, which is similar to what is done in Sect. 2.7. Table 2 includes the magnitudes and colors obtained by Ortolani et al. (1996), but in the present case, the celestial coordinates have been included; the CMD is shown in Fig. 5.

In Fig. 5, it is possible to see that most of the variables and candidates are located at the top of the red giant branch (RGB), and some are more toward the middle level of the RGB. The dispersion is due to the known intense differential reddening associated with this cluster (see e.g., Origlia et al. 2019; Ortolani et al. 1996, and references therein). The reddening effect can also be seen in the diagonally extended HB, which is located at I ~ 18.24 mag (Ortolani et al. 1996). Also, the RR Lyrae V3 can be seen to be located below the level of the HB by ~0.31 mag.

Fig. 5 CMD obtained for the GC Terzan 5. The vertical axis corresponds to the I magnitude and the horizontal axis is the V–I color. The green-circled point is the previously known RR Lyrae V3, dark-yellow-triangle points are the semiregular variables, orange five-pointed star symbols are the stars selected as candidate variables, blue squares are stars flagged as LPVs in Gaia DR3, and the light-yellow five-pointed star symbol is an eclipsing binary candidate.

6 Previously known variables

As mentioned earlier, so far there are 13 known variable stars in the field of Terzan 5. The authors used their own nomenclature to label their discoveries and for practical reasons Clement et al. (2001) adopted a new nomenclature in her catalog, as shown in Table 3; we adopt this latter nomenclature in the present article.

6.1 RR Lyrаe V3

V3 is one of the two known variables whose coordinates fall inside the field of view covered by our observations. The light curve for this star is presented in Fig. 6. The top plot is the light curve in magnitude against the heliocentric Julian date (HJD) version, while the bottom plot shows the phased version. To produce the very clear phased light curve shown, we detected that this star is pulsating in the fundamental mode typical for RR Lyrae RR0 type with a period of about 0.590887 ± 0.000013 days. The peak-to-peak amplitude of our light curve is 0.57 mag.

This star is highlighted as a green filled circle in the RMS and 𝒮_ℬ index given in Fig. 4. In the CMD shown in Fig. 5, the star appears at an I-band magnitude of about 18.55 mag and a color of 4.05 mag. The equivalent V magnitude given in Ortolani et al. (1996) is about 22.60 mag. The position of this star (green point) is shown in more detail in Fig. 7. However, the blue square is the position of the star using the mean I magnitude obtained in the present work. As the light curve obtained in this analysis covers the star’s variation very well, the median I magnitude represents an improvement in its CMD position, which brings it closer to the HB at 18.37 ± 0.04 mag, a difference of about 0.18 mag compared to the measurement in Ortolani et al. (1996). The size of the blue square represents the vertical uncertainty.

To obtain an estimate of the uncertainty in the color, we proceeded as follows. Ortolani’s V and I data were taken almost simultaneously, and therefore their V and I magnitudes were captured at roughly the same phase. As there is no reliable mean V measurement, we adopted the V difference of 0.18 mag mentioned above as a lower limit to the uncertainty in the color, adding to this twice the uncertainty associated with our mean I value. Taking into account the dispersion due to differential reddening, the inclination of the HB, and the new position of V3 in the CMD, it is likely that this star is a cluster member.

If V3 is a cluster member, the period and amplitude can be used to infer the Oosterhoff type of Terzan 5. Figure 8 shows the period–amplitude diagram for RR Lyrae stars. Solid lines represent the Oosterhoff type I (Ool) locus as obtained with equations (1) and (2) of Kunder et al. (2013). The dashed lines represent the Oosterhoff type II (OoII) ridge line, as defined by equations (3) and (4), which consider I amplitudes and periods. Previous research (Figuera Jaimes et al. 2016b) shows that A_i′+z′ amplitudes obtained in this project align well with the analysis obtained with equations in Kunder et al. (2013), facilitating the proper classification of clusters with known Oosterhoff types. In Figure 8, the position of RR0 V3 is indicated with a blue circle. We measured the distance from the point to each of the reference loci, noting that V3 is 0.08 mag away from the OoI locus, but is approximately 0.16 mag away from the OoII reference line. However, as this analysis was conducted with only one RR Lyrae star, we consider this tentative classification as our initial attempt to determine its Oosterhoff type.

Fig. 6 Variable star V3. The top plot shows the light curve in I magnitude versus HJD while the bottom plot shows the I magnitude versus the phase obtained with a period of 0.590887 d. The colors of the plots match those in Fig. 1.

Fig. 7 Zoom onto the HB given in Fig. 5. The green circle corresponds to the I value given in Ortolani et al. (1996). The blue square is the median I magnitude obtained in our light curve.

6.2 Variable V4

This is the second previously reported star that falls inside the field of view of our observations. It was reported as a possible eclipsing blue straggler with faint sinusoidal variability with a period of about 7 h. Edmonds et al. (2001) consider − in a much less likely scenario − that the star is the infrared counterpart to the low-mass X-ray binary. No optical information is provided in this latter work. We did not find any variable source at the given coordinates or in surrounding areas. We checked the position in the finding chart supplied by Edmonds et al. (2001) in their Fig. 3, and still no detection was found. Perhaps this star is so faint that it was outside the limits of detection of our detector and the methodology employed in our observations. V4 was not detected either in Ortolani et al. (1996).

Fig. 8 Period–amplitude diagram for RR Lyrae stars. The blue circle is star V3. The continuous line corresponds to Oosterhoff type I (Ool) and the dotted line is Oosterhoff type II (OoII) according to the models in Kunder et al. (2013).

6.3 EXO 1745-248/CXOGIb J174805.2-244647/CX 3

This is another object detected during inspection of the difference images, located at the celestial coordinates RA(J2000) =17:48:05.213 and Dec(J2000) =−24:46:47.57. This target was initially identified as an X-ray burst in a study by Makishima et al. (1981) using data from the Hakucho satellite, which observed 14 outbursts between August 5 and 21, 1980. Heinke et al. (2003, and references therein) also examined this target using Chandra X-ray observations and noted irregular activity since its discovery. Designated CX 3, it is classified as a low-mass X-ray binary (LMXB).

In 2000, Heinke et al. (2003) conducted observations using the Chandra X-Ray Observatory and detected an outburst at its position. These authors attempted to identify an infrared counterpart for this LMXB using HST images, identifying two possible star candidates. However, they did not observe any variability, leading to uncertainty in their identification. The authors suggested that CX 3 may be an ultracompact LMXB based on comparison with other sources in GCs. Subsequent observations were carried out by Wijnands et al. (2005) in 2003 using the Chandra Observatory, which found CX 3 in a quiescent state, as well as a hard spectral component. These findings were consistent with a study by Heinke et al. (2006). Finally, Ferraro et al. (2015) conducted an observational program with HST during a CX 3 outburst and made a visual detection at its position with data acquired on April 20, 2015. In their observations, CX 3 increased in brightness by approximately 3 mag. The authors were able to detect the target in their CMD and concluded that it is a subgiant-branch (SGB) star in a quiescent state, transitioning to the RGB. They proposed that CX 3 could be a peculiar object in the process of forming a radio MSP. These observations align with our own visual counterpart detection shown in Fig. 9 during the year 2015. We recorded a signal increase on May 1 (HJD 2457143.871736619), reaching its maximum on May 4 (HJD 2457146.899496661), and then decreasing until returning to its baseline around June 9 (HJD 2457182.670915530).

Fig. 9 Variability detection at the position of CX 3. The colors of the plots match those in Fig. 1.

Fig. 10 Zoom onto the signal found at the position of the visual detection N1. The top boxes show the last image taken before the detection (left), the image containing the detection (middle), and the image taken after the registered detection (right), while the bottom boxes correspond to the difference images obtained by subtracting the reference frame from each of the science images shown at the top. Each box is about 6″ × 6″ in size, and the color scale is logarithmic.

7 New discoveries

In this section, we present new variable sources detected and discovered in the field of Terzan 5 covered by our observations and the methodology employed.

7.1 The unexpected outburst (N1)

Inspection of the difference images (see Fig. 10) revealed an outburst (Fig. 11) that took place on HJD 2457177.682793049, located at position RA(J2000) = 17:48:04.914 and Dec(J2000) = −24:46:53.15. However, upon exploration of the reference frame at the given coordinates, no stars were found. In an effort to better understand the origin of this signal, a review of the literature revealed that the closest reported object (separated by 0″.65) corresponds to target J1748-2446N, also known as Ter5 N and Ter5-VLA27. This nearby source, J1748-2446N, which could be associated with our visual detection, is an MSP that has been detected and analyzed in several radio observations.

Urquhart et al. (2020) reported this target at position RA(J2000) = 17:48:04.914 (±0″.05) and Dec(J2000) = −24:46:53.75 (±0″.05), using the Karl G. Jansky Very Large Array (resolution 0″.2 − 0″.04⁷) in the USA, with observations conducted in the frequency interval of 2–8 GHz. Prager et al. (2017) reported coordinates of RA(J2000) = 17:48:04.919 and Dec(J2000) = −24:46:53.78 using the Green Bank Telescope. Martsen et al. (2022) also detected this target using the same facility.

This MSP also has an X-ray counterpart detection (Bogdanov et al. 2021; Zhao & Heinke 2022) at reported coordinates RA(J2000) = 17:48:04.906 and Dec(J2000) = −24:46:54.00 with an astrometric offset between the radio MSP position and the nearest X-ray source of ∆α = 0″.20 and ∆δ = 0″.18, respectively. This pulsar was discovered by Ransom et al. (2005) based on observations with the Green Bank Telescope. These authors reported a period of 8.66690 ms for this target, as well as an orbital period of 0.3855 d, and an eccentricity of 0.000045.

The slight difference between the coordinates reported in radio and the X-ray position is noteworthy. One might attribute this discrepancy to the pointing accuracy of the instruments. However, as noted in Bogdanov et al. (2021), the uncertainties are often related to the X-ray sources, while the radio MSP positions are determined with very high accuracy (i.e., to better than 0″.1).

Similar offsets to that seen in our study have also been documented in other targets in the literature. Bogdanov et al. (2021) reported a position offset (0″.55) between the timing position and the X-ray position in Ter5 A, suggesting that Ter5 A is an eclipsing redback with timing difficulties. These authors also found similar issues with the position of other redback targets associated with timing, such as NGC 6397 A and M281, with offsets of 0″.811 and 2", respectively. Given that Ter 5 N has not exhibited eclipses, it does not appear to be a redback. Additionally, considering the precise astrometry results obtained in our analysis, the visual detection shown in Fig. 11 is very unlikely to be associated with the MPS. To the best of our knowledge, the detection of a visual counterpart to this object has not been previously reported in the literature.

Fig. 11 Light curve of source N1, located in the vicinity of PSR J1748-2446N and possibly associated with it (see Sect. 7.1). The colors of the plots match those in Fig. 1.

7.2 Semiregulаr variables

(V14-V17): Several of the brightest stars have high RMS values and are also highlighted by the 𝒮_ℬ index. This, combined with the difference images, helped us to confirm that these four stars indeed varied during the observations analyzed here. The resulting light curve for each of the stars was analyzed to explore periodicity in their variation. The periods found range from about 46 to 193 days, with amplitudes from about 0.14 to 0.28 mag. These stars are located along the RGB in Fig. 5, and we therefore classify them as long-period semiregular variables. Their light curves are presented in Fig. A.1 and the period estimates are listed in Table A.1. A comparison between the frequencies found by least squares and fast χ² methods is provided in Table 4, which are also highlighted in Fig. A.3.

7.3 Other candidate variables

(C1a-C4): Although some stars appear to exhibit actual variation in their light-curve shapes, they were found to be very close to (either above or below) the RMS or 𝒮_ℬ index thresholds defined in Sect. 3. Stars whose photometry was affected by any systematic issue in the difference images or other errors were classified as candidate variables to aid in future research and analysis. These candidate variables are highlighted by orange star-shaped symbols in Figs. 4 and 5, and are the black square labels in the finding chart presented in Fig. 3. Their light curves are plotted in Fig. 12, and their ephemerides can be found in Table A.1.

Of note among these candidates, C4 corresponds to star 1 listed in Origlia et al. (2011) as a red giant star in Terzan 5. Due to lack of availability of V and I data, it was not possible to plot C1a on the cluster CMD presented in Fig. 5. Additionally, C1a is one of the stars discussed in more detail in Sect. 7.4.

7.4 The C1a and C1b cases

By comparing the positions of the stars in our reference frame (EMCCD) with their positions in the images used in Sects. 2.7 (HST) and 5 (NTT), we note that there is a very strong displacement at the positions of two sources, which we label C1a and C1b in the finding chart given in Fig. 3.

In Fig. 13, it is possible to visually compare how their positions changed from the image (taken in 1994) used in Ortolani et al. (1996), to the HST image in 2013, and then to the first image used in our reference frame (taken in 2014). Upon visual inspection, it is possible to see that both sources seem to be moving in the same direction and with approximately the same displacement, giving the impression that they might be physically associated.

In Table 5, we register their positions in the three images in which we noticed this displacement: the EMCCD image (2014), the HST (2013), and the NTT (1994). Considering the position of the center of Terzan 5 (RA(J200) = 17:48:04.80 and Dec(J2000) = −24:46:45) taken from Harris (1996, 2010 version), we calculated the angular distance of C1a and C1b from the cluster center, noting that in 1994 they were about 18″.33 and 18″.23 away, respectively, while in 2014 they were about 18″.45 and 18″.46 away, respectively, from the cluster center. The displacements registered in the positions of C1a and C1b in the EMCCD image with respect to their position in the NTT image are ~0″.62 and 0″.59, respectively.

Finally, the total proper motion calculated for C1a was about 22.9 mas/yr between NTT and HST images, and 28.4 mas/yr between NTT and EMCCD images. Similarly, in the case of C1b, the total proper motion was about 23.4 mas/yr using the NTT and HST images, while it was 27.5 mas/yr using the NTT and the EMCCD images. This gives us mean values of 25.7 mas/yr and 25.5 mas/yr for C1a and C1b, respectively, strongly indicating that these two stars are not cluster members.

Fig. 12 Light curves in I magnitude as a function of HJD for candidate variables C1a-C4 . The colors of the plots match those in Fig. 1.

Fig. 13 Comparison of the positions of C1a and C1b in a section of the NTT image from 1994 (on the left) with the positions in the HST image taken in 2013 (in the middle), and the EMCCD image taken in 2014 (on the right). The crosses represent the star’s positions measured in the NTT image. The stars labeled R1 and R2 are for comparison. The size of the images is about 7″. The color scale is not exactly the same in the three plots. North is up and east is left.

8 Gaia variables

An exploration of the Gaia DR3 survey (Eyer et al. 2023) pointed out that some stars were flagged as variables. Matching the position of these stars in our reference frame helped us to identify 34 stars in the field covered by our observations. These stars are labeled G1-G34 in Fig. 3 and their ephemerides are also given in Table A.1. A comparison between the ID used in this work and the unique ID assigned in Gaia is shown in Table 6. All these stars appear classified in Gaia as LPV stars of types: omicron Ceti (Mira), OGLE small-amplitude red giants, and semiregular. Their subtypes, amplitudes, and periods are not reported.

(G1-G9): Several of these variables were also detected in our analysis for variable star detection and it was possible to classify them as semiregular variables, similar to what is done in Sect. 7.2. Amplitudes range from about 0.1 to 0.46 mag, and periods from about 20 to 266 d. G9 was not automatically detected by the pipeline in the reference frame, and so its variation was detected directly in the difference images. Its peak-to-peak amplitude is about 21 250 ADU/s and the period found is about 48 d.

(G10): This star, rather than showing a long period, seems to exhibit a variation similar to those found in short-period variables. The least squares method found a period of 0.497880 days (close to half a sidereal day) with a signal-to-noise ratio of about 3.2. However, the light curve appears better phased with a period of 0.301770 days, as found using the string length method. This period leads to a more defined light-curve shape, resembling that found in eclipsing binaries of the W Ursae Majoris type. The amplitude is approximately 0.11 mag. The period found is tentative, and a proper classification of this star is still missing. Further analysis is encouraged. The phased light curve for this star is shown in Fig. 14.

Finally, we did not find coherent periods for the remaining stars flagged as variables in Gaia survey (G11-G34) and these objects are left classified as LPVs. Light curves for these stars are shown in Fig. A.2.

Fig. 14 Light curve of variable star G10. The top panel shows the light curve in I magnitude versus HJD while the bottom panel shows the phased light curve with the periods and epochs given in Table A.1. Colours are the same as in Fig. 1.

Fig. 15 Period-luminosity diagram for the semiregular variables studied in this work (dark-yellow triangles). The black points correspond to the semiregular variables listed in the Clement et al. (2001, August 2019 update) catalog for the GC NGC 6715. The red line represents the best-fit line for both datasets.

9 Period-luminosity relation for semiregular variables

All stars classified as semiregular variables in Table A.1 were plotted on a period–luminosity (P–L) diagram. For comparison, we include all semiregular variables (discovered by Rosino 1952; Rosino & Nobili 1958; Layden & Sarajedini 2000; Sollima et al. 2010; Figuera Jaimes et al. 2016a; Hamanowicz et al. 2016) available in the catalog of Clement et al. (2001, August 2019 update) for NGC 6715 (M54). A clear linear relation between the two groups of semiregulars is observed. To adjust the zero points, we transformed the apparent magnitudes to absolute magnitudes using the distances to the GCs of 26 280 ± 330 pc and 6620 ± 150 pc for NGC 6715 and Terzan 5, respectively (Baumgardt & Vasiliev 2021). Similarly, an extinction of A_I = 0.23 (Schlafly & Finkbeiner 2011) mag was adopted for NGC 6715. However, as previously mentioned, Terzan 5 is a cluster that is affected by a large but uncertain amount of foreground extinction. Using, for instance, the reddening reported by Harris (1996), and assuming a standard extinction law, we find A_I = 3.42 mag. Similarly, the reddening map provided by Massari et al. (2012) gives an average extinction towards the cluster of A_I ≈ 3.78 mag. The maps of Schlafly & Finkbeiner (2011) on the other hand report A_I = 5.91 mag. None of these extinction values lead to an alignment of the NGC 6715 and Terzan 5 relations. Accordingly, in our analysis, we assume that both clusters share the same P–L relation, and let the fit determine the best extinction value for Terzan 5 while fitting both datasets simultaneously. This leads to an extinction value for Terzan 5 of A_I = 4.76 ± 0.09 mag, which is intermediate between the values quoted above. The final P–L relation, as shown in Fig. 15, is $$M_{\text{I}}=-2.505(\pm 0.274)-0.722(\pm 0.155)\log (P),$$(6)

where P is the period of the star and M_I is the absolute magnitude. The fit did not include the outlier stars (e.g., V16 and G4). These outliers might follow a different P–L relation, as is known to happen in these types of stars (Soszyński & Wood 2013; Trabucchi et al. 2021).

10 Conclusions

1. Our analysis of the very crowded central region in Terzan 5 with the very high angular resolution obtained in this work drove us to several interesting discoveries;

2. The use of EMCCD and proper manipulation of the obtained images have shown to be a very efficient alternative way to mitigate the effect of atmospheric turbulence;

3. We were able to produce high-angular resolution images with ground-based telescopes;

4. It was possible to avoid saturation of the brightest stars presented in the field observed;

5. The employment of very sophisticated pipelines to process the images and produce the photometry − such as difference image analysis − and the implementation of our techniques for variable star detection helped us automatically or semi-automatically analyze around 1670 stars in the very crowded central region of Terzan 5;

6. As a result of the analysis employed in this work and the 242 observations obtained after the stacking, it was possible to produce a very good coverage of the light curve variation of the only RR Lyrae previously known in the field covered by our reference frame in Terzan 5, which we confidently classify as RR0 type. It was also possible to calculate an accurate period for this star;

7. We present the discovery of four semiregular variable stars, and the classification of stars flagged as variables in the Gaia survey;

8. We observed an outburst in the visual, and its position appears to coincide with MSP J1748-2446N. We also obtained a visual light curve of the detected 2015 outburst in the LMXB, known as CX 3.

In conclusion, this study provides a new variability study of stars in the massive, metal-rich GC Terzan 5. Located in the Galactic bulge, Ter 5 has been suggested to be the remnant of a much more massive parent system, which may have contributed to the build-up of the bulge (Ferraro et al. 2016; Taylor et al. 2022). Our study, which is the first one based on time-series observations carried out with electron-multiplying CCDs, contributes to the literature on this fascinating object by providing a comprehensive reassessment of the known variable stars, along with several new discoveries. It is our hope that our paper will provide a useful reference for future studies of this most interesting GC.

Data availavility

Full Tables 1 and 2 are available at the CDS via anonymous ftp to cdsarc.cds.unistra.fr (130.79.128.5) or via https://cdsarc.cds.unistra.fr/viz-bin/cat/J/A+A/689/A108

Acknowledgements

Support for this project is provided by ANID’s Millennium Science Initiative through grant ICN12_009, awarded to the Millennium Institute of Astrophysics (MAS), and by ANID’s Basal project FB210003. M.C. acknowledges additional support from FONDECYT Regular grant #1171273. This research has received funding from the Europlanet 2024 Research Infrastructure (RI) programme. The Europlanet 2024 RI provides free access to the world’s largest collection of planetary simulation and analysis facilities, data services and tools, a ground-based observational network and programme of community support activities. Europlanet 2024 RI has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No. 871149. N.P. acknowledge financial support by FCT-Fundação para a Ciência e a Tecnologia through Portuguese national funds and by FEDER through COMPETE2020-Programa Operacional Competitividade e Internacionalização by the grants UIDB/04434/2020 and UIDP/04434/2020. ChatGPT (powered by OpenAI’s language model, GPT-4; http://openai.com was used to generate code to produce the fit described in Sect. 9.

Appendix A Additional material

Fig. A.1 Light curves of newly discovered variables V14-V17 in the GC Terzan 5, as well as variables classified as semiregular. The top plot shows the I-band light curves with time in units of HJD, while the bottom plot displays the phased light curves with periods and epochs listed in Table A.1. The colors of the plots match those in Fig. 1.

Fig. A.2 Light curves in I magnitude as a function of HJD for stars flagged as LPVs in Gaia. The colors of the plots match those in Fig. 1.

Fig. A.3 Periodograms for all stars classified as semiregular in this study, including the newly discovered variables (V14-V17) and earlier stars flagged as variables in Gaia (G1-G9). The vertical solid purple line represents the strongest frequency found in the periodogram using the least square technique, while the dashed orange line represents the frequency found using the fast χ2 method.

References

All Tables

All Figures

	Fig. 1 Histogram of observations obtained after the stacking in the field of the GC Terzan 5. The colors represent the images obtained for each year: black (group 1) is 2014, blue (group 2) is 2015, green (group 3) is 2016, olive (group 4) is 2017, purple (group 5) is 2019, and pink (group 6) is 2021.
In the text

	Fig. 2 Standard I magnitude available in Ortolani et al. (1996) as a function of the instrumental magnitude. The red line is the fit that best matches the data and is given in the title of this plot and equation (3). The correlation coefficient is 0.999.
In the text

Fig. 3 Finding chart for GC Terzan 5. Black labels are variable stars studied in this work. Circled labels correspond to new discoveries and previously known variable stars, while labels in squares are the candidate variables. Blue labels are the 33 red giant stars studied in Origlia et al. (2011). The average FWHM obtained for the stars in the reference frame was about 0″.41. The big black square is the region explored in our study for new variable star detection and characterization, which corresponds to a field of view of about 38″ × 40″. Labeled stars lying outside the black box correspond to stars previously studied in the literature.

In the text

Fig. 4 RMS and 𝒮ℬ index versus the mean I magnitude in the GC Terzan 5. The green-circled point is the previously known RR Lyrae V3, dark-yellow triangle points are the semiregular variables, orange five-pointed star symbols are the stars selected as candidate variables, blue squares are stars flagged as LPVs in Gaia Data Release 3 (DR3), and the light-yellow five-pointed star symbol is an eclipsing binary candidate. The lower red lines correspond to the fits applied to the data, while the upper red lines are the shifts applied to define the thresholds for variable candidate detection.

In the text

Fig. 5 CMD obtained for the GC Terzan 5. The vertical axis corresponds to the I magnitude and the horizontal axis is the V–I color. The green-circled point is the previously known RR Lyrae V3, dark-yellow-triangle points are the semiregular variables, orange five-pointed star symbols are the stars selected as candidate variables, blue squares are stars flagged as LPVs in Gaia DR3, and the light-yellow five-pointed star symbol is an eclipsing binary candidate.

In the text

	Fig. 6 Variable star V3. The top plot shows the light curve in I magnitude versus HJD while the bottom plot shows the I magnitude versus the phase obtained with a period of 0.590887 d. The colors of the plots match those in Fig. 1.
In the text

	Fig. 7 Zoom onto the HB given in Fig. 5. The green circle corresponds to the I value given in Ortolani et al. (1996). The blue square is the median I magnitude obtained in our light curve.
In the text

	Fig. 8 Period–amplitude diagram for RR Lyrae stars. The blue circle is star V3. The continuous line corresponds to Oosterhoff type I (Ool) and the dotted line is Oosterhoff type II (OoII) according to the models in Kunder et al. (2013).
In the text

	Fig. 9 Variability detection at the position of CX 3. The colors of the plots match those in Fig. 1.
In the text

Fig. 10 Zoom onto the signal found at the position of the visual detection N1. The top boxes show the last image taken before the detection (left), the image containing the detection (middle), and the image taken after the registered detection (right), while the bottom boxes correspond to the difference images obtained by subtracting the reference frame from each of the science images shown at the top. Each box is about 6″ × 6″ in size, and the color scale is logarithmic.

In the text

	Fig. 11 Light curve of source N1, located in the vicinity of PSR J1748-2446N and possibly associated with it (see Sect. 7.1). The colors of the plots match those in Fig. 1.
In the text

	Fig. 12 Light curves in I magnitude as a function of HJD for candidate variables C1a-C4 . The colors of the plots match those in Fig. 1.
In the text

Fig. 13 Comparison of the positions of C1a and C1b in a section of the NTT image from 1994 (on the left) with the positions in the HST image taken in 2013 (in the middle), and the EMCCD image taken in 2014 (on the right). The crosses represent the star’s positions measured in the NTT image. The stars labeled R1 and R2 are for comparison. The size of the images is about 7″. The color scale is not exactly the same in the three plots. North is up and east is left.

In the text

	Fig. 14 Light curve of variable star G10. The top panel shows the light curve in I magnitude versus HJD while the bottom panel shows the phased light curve with the periods and epochs given in Table A.1. Colours are the same as in Fig. 1.
In the text

	Fig. 15 Period-luminosity diagram for the semiregular variables studied in this work (dark-yellow triangles). The black points correspond to the semiregular variables listed in the Clement et al. (2001, August 2019 update) catalog for the GC NGC 6715. The red line represents the best-fit line for both datasets.
In the text

	Fig. A.1 Light curves of newly discovered variables V14-V17 in the GC Terzan 5, as well as variables classified as semiregular. The top plot shows the I-band light curves with time in units of HJD, while the bottom plot displays the phased light curves with periods and epochs listed in Table A.1. The colors of the plots match those in Fig. 1.
In the text

	Fig. A.2 Light curves in I magnitude as a function of HJD for stars flagged as LPVs in Gaia. The colors of the plots match those in Fig. 1.
In the text

	Fig. A.3 Periodograms for all stars classified as semiregular in this study, including the newly discovered variables (V14-V17) and earlier stars flagged as variables in Gaia (G1-G9). The vertical solid purple line represents the strongest frequency found in the periodogram using the least square technique, while the dashed orange line represents the frequency found using the fast χ2 method.
In the text