Draft version October 17, 2013Preprint typeset using LATEX style emulateapj v. 12/16/11

AGE AND METALLICITY OF M13

Nathan Harmon, Wesley Peters and Steven Roy

Draft version October 17, 2013

ABSTRACT

We analyze photometry from SDSS g-band and r-band images. The age and metallicity of M13are calculated via fitting a Padua isochrone to a G − R color-magnitude diagram. We determinedZ = 0.0004 and a distance of about 6900 kpc. These values, excluding age, are matched by previousstudies, and our color-magnitude diagram follows Johnson (1997). We find that M13 has a bluerthan normal horizontal branch, consistent with the literature. We determined an age of 10.25 Gyr bymaximizing the age allowed for the isochrone. We conclude that more accurate age determination ispossible through an older isochrone.

1. INTRODUCTION

Determining the age of globular clusters is an impor-tant tool in stellar astronomy. Globular clusters are alarge group of stars that were all born at or aroundthe same time. Because they were all born at roughlythe same time in roughly the same place, they all havethe same metallicity (Chaboyer (2001)). The fact thatthey all have the same age, metallicity, and distance fromEarth makes it easy for us to determine these parametersby fitting an isochrone to a color magnitude diagram ofthe cluster.

An isochcrone is a line consisting of stars of the sameage, which can have different masses and temperatures.The shape of the isochrone is affected by both the ageand metallicity of the stars, while its magnitude is de-pendent upon its distance. By adjusting these three pa-rameters, it is possible to determine the age and metal-licity of the globular cluster. Globular clusters’ old agesallows determining of a lower limit to the age of the uni-verse (VandenBerg (1988); VandenBerg et al. (1990)) aswell as ivestigating the evolution of the structure of theGalactic Disk (Carraro (1994b)). Due to its close prox-imity and brightness, M13 is considered one of the mostimportant clusters for such a calculation and is a primecandidate to study Population II stars (Paltrinieri et al.(1998)).

M13 is of special interest due to its unusually blue hori-zontal branch (Sandquist et al. (2010)). The stars in thisbranch are mostly Population I stars, which is contraryto what is expected. This blue horizontal branch (HB)is a good contrast to cluster M3, even though they areof similar metallicity (Mezaros et al. (2009)). This bluecolor implies a metal poor cluster (Lee et al. (1994)).

Section 2 deals with acquiring the photometry, includ-ing the cuts made to the data. Our color-magnitude ofM13 and its general features are presented in section 3.The age and metallicity of M13 are determined in section4. Section 5 compares our color-magnitude diagram withJohnson (1997), an almost identical study to our own, aswell as with the general literature.

2. METHODS

To calculate the photometry, we first had to identifystars and find their coordinates. First we examined a se-ries of stars and blank points in the sky in the g-band im-age, determining a FWHM of 2.7 pixels and a sky back-

ground of 1060. We located our stars using DAOFIND inIRAF on the g-band image implementing generic sharp-ness cuts of 0.4 to 0.8 and roundness cuts of -1 to 1, again noise of 4.0 and a read noise of 1.96 in the g-band.

After picking out our stars, we calculated their WorldCoordinates System (WCS) positions and used those toidentify the same stars in the r-band image. Additionally,we had to calculate the airmass for each frame, which wedid by approximating the airmass as the secant of thezenith angle

Xair = sec(90 −Alt) (1)

The airmass is 1.004 in the g-band and 1.005 in r-band.Now that we had the locations of each star in both

images and the airmasses, we proceeded to calculate thephotometry using IRAFs qphot. We set annulus, dannu-lus, and aperture all to five, used appropriate vales forthe gain (4.0 for the g-band and 4.76 for the r-band),andthrew out stars that qphot could not measure a flux for.

We then proceeded to make our first data cut basedon sharpness and roundness parameters. In using ourgeneric sharpness and roundness cuts, we incorporatedunwanted objects such as galxies, interlopers, detectoranomalies, etc. To make our cut, we plotted up our val-ues of sharpness and roundness and chose cuts to sur-round the area of highest density , found in Figure 1.The cuts we chose were 0.46 to 0.65 in sharpness and -0.8 to 0.3 in roundness. Using these new parameters, weran daofind and qphot again to get new photometry.

Our photometry data was in instrumental magnitudes,so we converted it to apparent magnitudes to constructour color-magnitude diagram. We did that using theformula

m = minst − zpiraf − zpSDSS − k ∗ sec(z) (2)

where sec(z) is the airmass, zpiraf is IRAFs zero pointof 25 and k and zpSDSS are Sloan values that depend onthe filter.

For the g filter the zero point is -24.39982 and theairmass coefficient, k, is 0.246473. For the r filter the zeropoint is -23.96686 and the airmass coefficient is 0.16686.Finally we subtracted the reddening caused by galacticdust. Looking up M13 reddening values for Sloan filterson NASA Extragalactic Database (NED) gave reddeningvalues of 0.055 for the g filter and 0.038 for the r filter.

2 Harmon, Peters, Roy

Figure 1 shows the quality of magnitudes in positionspace. It is clear that good and bad points are every-where without any clear pattern. The data was brokenup into different bins, with σ < 0.05 being the cutoffpoint. Everything higher was eliminated. Looking atthe plot of error as a function of magnitude, it becomesclear that the highest errors come from the dimest ob-jects, even after the error cut.

Finally, we applied a position cut in order to removethe worst data points near the cluster center. This wasdone by applying a defined radius, by eye, to the centerof the globular cluster and excluding everything that fellinside. This radius was determined to be 700 pixels, asit greatly improved the quality of the color-magnitudediagram. Figure 1 also shows the sample before and afterthe position cuts, with the quality of error as color.

3. COLOR-MAGNITUDE DIAGRAM

With this photometry, a G, G − R diagram is shownin Figure 2. Our diagram extends to about 21 magni-tudes on the faint end and to bout 15 on the bright side.After all the sample cuts, the diagram clearly shows themain sequence (MS) from 21 < G < 18, main sequenceturn off (MSTO) at G ≈ 17.5, and finally the horizontalbranch (HB) at G ≈ 16. M13’s HB is quite blue andextends almost to the level of the MSTO, G ≈ 17, whichis expected (Rey et al. (2001); Paltrinieri et al. (1998);Sandquist et al. (2010); Ferraro et al. (1998)) We believethe gaps around the HB and MSTO to be the G1 andG3 from Ferraro et al. (1998). A key difference betweenour diagram and those listed is the flat branch connect-ing the MSTO and HB. This could be due to either oursample cuts or to our color choice of G − R instead ofB − V .

It is noticeable that there are still numerous stray starseven after the cuts are made. This is inevitable, as nocut will eliminate all bad data. It is very possible thatthese are interlopers, not actually stars in this cluster.However, these stars make up a very small percentage ofthe stars in our field, so we can ignore them.

4. AGE AND METALLICITY

With this color-magnitude diagram, it is possible tofit an isochrone, stars of the same age, to determinethe age, metallicity and distance of M13. Here thePadua isochrones for Sloan data were used (Girardi etal. (2002)). The only correction needed was to convertthe absolute magnitudes to apparent:

m−M = 5log(d) − 5 (3)

where m is apparent magnitude, M is absolute and d isthe distance in parsecs, which is varied for fitting theisocrhone.

Isochrones allow for better understanding of the pho-tometric data. They are dependant on stellar models inwhich the luminosity and effective temperature (teff ) areconverted into useable measures, magnitudes and colorfor example (Girardi et al. (2002); Reid (1997)). This isdone by means of conversions through bolometric correc-tions and teff—color relations.

It is necessary to assume a value of metallicity, Z, inorder to fit the isochrone. We used a Z range between0.0001 to 0.004 as our starting point. A Z of 0.004

was not able to match M13 regardless of distance andage. While a Z of 0.0001 came close, we found thatthe isochrone of Z = 0.0004 gave the best fit. Whenconstraining the distance, the MSTO was the feature ofinterest. By running through different distances, it waseasy to find the general best distance, which we deter-mined to be 6900 parsecs.

In order to check this metallicity, we found [Fe/H] val-ues of -1.66 and -1.51 (Rey et al. (2001); Behr et al.(1999)). We converted these to Z value using the for-mula

logZ = 1.03[Fe/H] − 1.698 (4)

from Carraro & Chiosi (1994a). Doing a rough calcula-tion yields a Z of about 0.0005, which matches the metal-licity predicted by the isochrone.

5. DISUCSSION

In this section we compare our data to what is found inthe literature. Emphasis is placed on Johnson (1997) dueto the identical SDSS image used. Different photometrywas used for the two samples.

5.1. Johnson (1997)

Figure 1 shows the comparison with Johnson (1997),the red points. This work is almost identical to thework that was done here, except for the IRAF packagesused, i.e. DAOPHOT ALLFRAME and DAOGROW,which performed multiple-aperture photometry. John-son’s study had a range of 7—35 different measurements,with the giants and main sequence stars having the leastnumber of observations. Overall, there are no systematicdifferences between the two samples. The MS, MSTOand HB all fall along the same magnitude range.

Immediately clear is the difference in magnituderange between the two samples. Johnson (1997) goesmuch fainter, down to about 24 magnitudes, and muchbrighter, higher than 13 magnitudes. This large differ-ence is likely due to the difference in IRAF packagesused since both samples use the SDSS G, R image. Theamount of scatter, i.e. the width of the main sequence, inboth samples is comparable, although there appears to bemore in Johnson (1997) which is likely due to the highernumber of points. The branch connecting the MSTO andHB is present in both samples, which makes it more likelythat it is a feature present in G−R, rather than a relic ofphotometry. Overall, our sample is less populated, bestseen in the main sequence.

The best fit isochrone, as expected, also fits Johnson(1997) very well. However, it fails above the MSTOand before the HB on both samples. This is fine sinceisochrones generally fail here.

5.2. M13 in the Literature

As previously discussed, our color-magnitude diagramis consistent with what is found in the literature. Theisochrone fit to this diagram gives a metllacitiy and dis-tance that is also consistent, although the age deter-mined posses a problem. Logt = 10.25 implies an ageyounger than found in the literature (Reid (1997); Reyet al. (2001); Chaboyer et al. (1998); Yi et al. (2001)).

The most likely cause of this discrepency is the upperlimit on logt found in the isochrones. This upper limit

3

Fig. 1.— Top left plot shows roundness as a function of sharpness. The red box gives the sharpness and roundness cut of 0.45 < s < 0.65and −0.8 < r < 0.3. This range was chosen by eye to give a tighter selection on the grouping seen. Bottom left plot gives the positionsof our data. Points are color-coded based on quality of error. Green points have errors σ < 0.02, blue have 0.02 < σ < 0.05 and red haveerrors σ > 0.05. Bottom right shows our sample after position cuts. Magnitude error is also shown as a function of magnitude. There is aclear trend for worse errors as the magnitude gets fainter. Red is r-band and blue is g-band.

is exactly 10.25, the age we determined for M13. It isreasonable to assume that if the ischrones extended intologt ≈ 12 then it would be possible to more accuratleydetermine the age. As it stands, the isochrone is tellingus that M13 has a maximum age of 10.25 Gyr.

The blue HB branch is a distinctive feature of M13(Rey et al. (2001); Paltrinieri et al. (1998); Sandquistet al. (2010); Ferraro et al. (1998)). The HB stars areone of the causes of debate over cluster ages (Catelan(2009a)), specifically why M13 is bluer. Catelan (2009b)found that age differences between clusters can explainthe difference in HB color, where M13 must be older thanM3.

Another explanation of this blue HB is that variationsin the helium percentage (Y) can move the Hb’s posi-tion (D’Antona & Caloi (2008); Sandquist et al. (2010)).From Sandage (1969) we know that M13 must have a

Y of 0.3, consistent with helium enriched models fromD’Antona & Caloi (2008). However, all of M13’s starsmust have greater Y’s than M3 due to a low populatedinstability strip.

6. CONCLUSION

Our color-magnitude diagram of M13 shows its char-acteristic features, including its blue HB. The source ofthis is still up for debate, but possible explanations rangefrom its age to its helium abundance. In fitting theisochrone to the SDSS data, we determined a metallicityZ = 0.0004 and age of 10.25 Gyr at a distance of 6900parsecs.

This age is required based on the upper limit of theisochrones provided. It is most likely that the age ofM13 is older (Reid (1997); Rey et al. (2001); Chaboyeret al. (1998); Yi et al. (2001)), which would have beenobserved given a wider range of aged isochrones.

4 Harmon, Peters, Roy

Fig. 2.— Color-Magnitude diagram of M13. Black points are our data, red is data from Johnson (1997) and the green line is the bestfit isochrone of z = 0.004. The main sequence (G ≈ 20), main-sequence turn off (G ≈ 18) and horizontal branch (G ≈ 16) are quite clear.The scatter is comparable in both studies, with Johnson (1997) having many more points.

Work was divided up the following way: Nathan Har-mon acquired the photometry and wrote the majority ofmethods, including sharpness-roundness cuts and mag-nitude conversion, as well as portion of section 4; Wesley

Peters made the plots, which includes writing of section3, fit the isochrone, and wrote sections 5 and 6; StevenRoy contributed to the introduction, general literaturesearch and was responsible for editing.

REFERENCES

Behr, B. et al. 1999, ApJ, 517, L135Carraro, G. & Chiosi, C. 1994, A&A, 287, 761Carraro, G. 1994, MMSAI, 65, 685Catelan, M. 2009, IAUS, 258, 209CCatelan, M. 2009, Ap&SS, 320, 261Chaboyer, B., Demarque, P., Kernan, P.J. & Krauss, L.M. 1998,

ApJ, 494, 96Chaboyer, B. 2001, ASP, 245, 162D’Antona, F. & Caloi, V. 2008, MNRAS, 390, 693Ferraro, F.R., Paltrinieri, B., Pecci, F.F., Rood, R.T. & Dorman,

B. 1998, ApJ, 500, 311Girardi, L., Bertelli, G., Bressan, A., Chiosi, C., Groenewegen,

M.A.T., Marigo, P., Salasnich, B. & Weiss, A. 2002, A&A, 391,195

Johnson, J.A. & Bolte, M. 1997, AJ, 115, 693

Lee, Y-W., Demarque, P. & Zinn, R. 1994, ApJ, 423, 248Mezaros, Sz., Dupree, A.K. & Szalai, T. 2009, AJ, 137, 4282Paltrinieri, B., Ferraro, R., Pecci, F.F. & Carretta, E. 1998,

MNRAS, 293, 434Reid, N. 1997, AJ, 114, 161Rey, S., Yoon, S., Lee, Y., Chaboyer, B. & Sarajedini, A. 2001,

AJ, 122, 3219Sandage, A. 1969, ApJ, 153, 515Sandquist, E.L., Gordon, M., Levine, D. & Bolte, M. 2010, AJ,

139, 2374Vandenberg, D.A. 1998, IAUS, 126, 107VandenBerg, D.A., Bolte, M. & Stetson, P.B. 1990, AJ, 100, 445Yi, S., Demarque, P., Yong-Cheol, K., Young-Wook, L., Chang

H., R., Thibault, L. & Barnes, S. 2001, ApJS, 136, 417