2 Distances to 12 globular clusters

 

 

Table 1: Parameters per globular cluster needed for evaluating their distances, d. References: [1] Harris (1996), [2] Pritzl et al. (2001), [3] Heasley et al. (2000), [4] Chaboyer et al. (2000), [5] Paltrinieri et al. (2001), [6] Idiart et al. (2002), [7] Cohn et al. (2002), [8] Davidge (2000), [9] Origlia et al. (2002).

Cluster	EB-V	$V_{\rm HB}$	[Fe/H]	ref	(m-M)0	d (kpc)
NGC 1851	0.02 $\pm$ 0.01	16.09 $\pm$ 0.05	-1.22 $\pm$ 0.1	[1]	15.41 $\pm$ 0.06	12.1 $\pm$ 0.3
NGC 6440	1.07 $\pm$ 0.10	18.70 $\pm$ 0.20	-0.34 $\pm$ 0.2	[1]	14.63 $\pm$ 0.36	8.4 +1.5-1.3
NGC 6441	0.51 $\pm$ 0.05	17.51 $\pm$ 0.05	-0.53 $\pm$ 0.2	[1],[2]	15.21 $\pm$ 0.17	11.0 +0.9-0.8
NGC 6624	0.32 $\pm$ 0.03	16.10 $\pm$ 0.05	-0.63 $\pm$ 0.1	[3]	14.40 $\pm$ 0.11	7.6 $\pm$ 0.4
NGC 6652	0.12 $\pm$ 0.02	15.96 $\pm$ 0.05	-0.90 $\pm$ 0.1	[1],[4]	14.92 $\pm$ 0.08	9.6 $\pm$ 0.4
NGC 6712	0.33 $\pm$ 0.05	16.25 $\pm$ 0.05	-0.90 $\pm$ 0.1	[1],[5]	14.56 $\pm$ 0.16	8.2 $\pm$ 0.6
NGC 7078	0.10 $\pm$ 0.02	15.83 $\pm$ 0.05	-2.25 $\pm$ 0.05	[1]	15.06 $\pm$ 0.08	10.3 $\pm$ 0.4
Terzan 1	2.00 $\pm$ 0.30	19.95 $\pm$ 0.20	-1.3 $\pm$ 0.2	[1],[6]	13.14 $\pm$ 0.95	4.3 +2.3-1.5
Terzan 2	1.57 $\pm$ 0.15	20.30 $\pm$ 0.20	-0.40 $\pm$ 0.2	[1]	14.88 $\pm$ 0.51	9.5 +2.5-2.0
Terzan 5	2.18 $\pm$ 0.20	22.26 $\pm$ 0.30	0.00 $\pm$ 0.2	[1],[7]	14.70 $\pm$ 0.69	8.7 +3.3-2.4
Terzan 6	2.14 $\pm$ 0.20	22.25 $\pm$ 0.20	-0.50 $\pm$ 0.2	[1]	14.89 $\pm$ 0.65	9.5 +3.3-2.5
Liller 1	3.13 $\pm$ 0.20	25.20 $\pm$ 0.30	-0.20 $\pm$ 0.2	[8],[9]	14.73 $\pm$ 0.69	8.8 +3.3-2.4

The distances to the twelve globular clusters have been re-evaluated for the purposes of this paper, to ensure that they are on an internally homogeneous system. We adopt the luminosity level of the horizontal branch (or equivalently the RR Lyrae stars) in the cluster as the fiducial distance indicator, following Harris (1996).

The three key observational quantities needed to deduce the distance are then the apparent magnitude of the horizontal branch, $V_{\rm HB}$, the foreground reddening, E_B-V, and the metallicity, [Fe/H]. The best recent estimates for these are listed in Table 1, either from the catalog of Harris (1996) or from the more recent literature as listed individually in the table.

The absolute calibration of distance follow the prescription adopted by Harris (1996), namely

$$(m-M)_0 = V_{\rm HB} - M_V({\rm HB}) - 3.1~E_{B-V}$$ (1)

where the absolute magnitude is a function of metallicity,

$$M_V({\rm HB}) = 0.15 {\rm [Fe/H]} + 0.80 .$$ (2)

We note that $V_{\rm HB}$ and $M_V({\rm HB})$ refer to the observed mean level of the horizontal branch stars, and not the (slightly fainter) level of the zero-age horizontal branch, $M_V({\rm ZAHB})$. The uncertainties in $V_{\rm HB}$, M_V, and E_B-V have been added in quadrature to get the final uncertainty in the distance modulus, (m-M)₀. The dominant source of uncertainty is either the $V_{\rm HB}$ estimate or, for highly-reddened globular clusters, the uncertainty in the reddening. In some cases the errors are rather large; the last five clusters in Table 1 have formal distance uncertainties that are on the order of 30%.

In some other recent papers, a slightly steeper slope for the relation between $M_V({\rm HB})$ and metallicity [Fe/H] is used (see, e.g., Chaboyer et al. 1998, where $M_V({\rm HB}) = 0.23 [$Fe/H] + 0.83). These relations are negligibly different from Eq. (2) for the range [Fe/H] > -1 which covers most of our clusters, and at worst gives a difference of $\simeq$0.1 mag in the distance modulus for the most metal-poor cluster in the list, a level which is within the current uncertainties in the absolute distance scale for globular clusters.

It is worth noting that the results for the distances in Table 1 (d-values in the last column) are consistent with the view that all these clusters, except for NGC 1851, NGC 6441 and NGC 7078, are within the Galactic bulge: they lie roughly in the direction of the Galactic center, and have distances in the approximate range $8 \pm 2$ kpc which place them in the extended bulge region. Thus the very rough assumption that $d \sim 8$ kpc for all the clusters in our list, independent of other observational information about their individual distances, would not give a calibration of their X-ray burst luminosities that was grossly in error.

Figure 1: Interstellar absorption as derived from the known relation between optical extinction and dust (and hydrogen) column densities (Predehl & Schmitt 1995) versus the interstellar absorption as derived from X-ray spectral fits, see text. We have indicated the different globular clusters as follows, e.g.: N1851 = NGC 1851, T1 = Terzan 1, and L1 = Liller 1.

A strong correlation exists between the visual extinction, A_V, and the dust (and hydrogen) column densities, if there is no additional absorption within the binary itself: $N_{\rm H}$ [cm^-2]/ $A_V=1.79 \times 10 ^{21}$ (Predehl & Schmitt 1995). In Fig. 1 we show $N_{\rm H}$ as derived from the optical extinction towards the globular clusters in Table 1 ( A_V = 3.1 E_B-V) using the above relation, versus $N_{\rm H}$ as derived from the X-ray spectral fits to the globular cluster source spectra, see Table 2 (see also Sidoli et al. 2001). Most lie close to the correlation, except A1850-08/NGC 6712, XB 1733-30/Terzan 1, and XB 1745-25/Terzan 5. For these latter sources the discrepancy may be partly due to the X-ray continuum model used (XB 1733-30; see also Sidoli et al. 2001, Table A.1), energy range used in the X-ray spectral fitting (XB 1745-25), or to intrinsic absorption near or in the binaries themselves.

 

 

Table 2: Parameters for the twelve X-ray bursters in globular clusters ordered along right ascension. Given are the X-ray burst source name, the globular cluster to which it belongs, the interstellar absorption column towards the source ($N_{\rm H}$), the orbital period, $P_{\rm orb}$, if known, its bolometric black-body peak flux for radius expansion bursts, $\overline {F_{\rm bb,peak}}$, or the maximum bolometric black-body peak flux for normal X-ray bursts, $F_{\rm bb,max}$ (see Appendix B for details), and whether it exhibited photospheric radius expansion (RE) X-ray bursts or not. References are given between brackets: [1] Sidoli et al. (2001), [2] Masetti et al. (2000), [3] Parmar et al. (1989), [4] this paper (see Appendix A), [5] Parmar et al. (2001), [6] White & Angelini (2001), [7] Deutsch et al. (2000), [8] Homer et al. (2001), [9] Sansom et al. (1993) and references therein, [10] in 't Zand et al. (2000), [11] Stella et al. (1987), [12] Chou & Grindlay (2001) and references therein, [13] Heinke et al. (2001), [14] Homer et al. (1996).

X-ray burster	globular	$N_{\rm H}$	ref	$P_{\rm orb}$	ref	$\overline {F_{\rm bb,peak}}$ or $F_{\rm bb,max}$	RE?
	cluster	(1022 cm-2)		(hr)		(10-8 erg s-1)
MX 0513-40	NGC 1851	0.026 +0.030-0.005	[1]	<1?	[7], [8]	2.00 $\pm$ 0.18	yes
4U 1722-30	Terzan 2	0.78 $\pm$0.05	[1]			6.15 $\pm$ 0.09	yes
MXB 1730-335a	Liller 1	1.5 $\pm$ 0.3	[2]			1.66 $\pm$ 0.08	no
XB 1733-30	Terzan 1	1.63 $\pm$ 0.12	[3]			7.4 $\pm$ 1.0	no
XB 1745-25	Terzan 5	3.8 +0.9-0.7	[4]			4.75 $\pm$ 0.12	yes
MX 1746-20	NGC 6440	0.47 $\pm$ 0.07	[1]			1.77 $\pm$ 0.14	no
4U 1746-37	NGC 6441	0.26 $\pm$ 0.02	[1]	5.7	[9]	0.95 $\pm$ 0.07	yes
GRS 1747-312	Terzan 6	1.39 $\pm$ 0.08	[1]	12.4	[10]	1.71 $\pm$ 0.06	yes
4U 1820-30	NGC 6624	0.16 $\pm$ 0.003	[1]	0.19	[11], [12]	5.27 $\pm$ 0.72	yes
H1825-331	NGC 6652	0.046 +0.023-0.012	[5]	0.92 or 2.2 hr?	[13]	2.87 $\pm$ 0.07	no
A1850-08	NGC 6712	0.39 +0.01-0.03	[1]	0.34	[14]	5.2 $\pm$ 0.5	yes
4U 2129+12b	NGC 7078	<0.034	[6]			3.94 $\pm$ 0.29	yes

^a More popularly known as the Rapid Burster.

^b NGC 7078 X-2 is the likely source of the X-ray bursts (White & Angelini 2001).