arXiv:astro-ph/9907345v3 7 Sep 1999 l,S 94 a aeld“nmlu”b ihode al. et Richmond exam- by For “anomalous” . labelled host was the 1994D of SN r distance ple, a the without of fo i.e. knowledge arguments, claim able indirect the on that relies finds often one anomaly literature, etc. bright/faint/red the too checking are However, which 4527, 4526, NGC NGC in fit in 1991T 1994D SN SN not prominent 4347, and NGC the do in al.; 1991bg apparently SN et being which Hamuy cases observed of Cal´an/Tololo sample been the have with SNe few a 1 B N19Di G 56 omlybih yeI supernova Ia type Drenkhahn bright Georg normally a 4526: NGC in 1994D SN in n osueetedseso vnbelow correc- even introduce dispersion to the used squeeze be to can and a sam- phase rate tions a maximum decline for Moreover, at quality. is, colour remarkably observational Ia high how SNe of showed among ple dispersion (1996) in brightness candles al. the standard et small best Hamuy the are universe. Ia the type of (SNe) Supernovae Introduction 1. 2 aiu-ieiodfi eun paettr-vrmagni- turn-over of apparent dat pub- tudes returns archive been HST fit of maximum-likelihood yet globular basis A the of not on method has functions the luminosity cluster, by cluster distance the the determined We of lished. 4526 that NGC galaxy, than host brightn its other and of colour, distance rate, individual an decline However, between relation the into Abstract. 1999 July 19 Accepted / 1999 March 17 Received I cl.Teaslt antds(o orce o eln r decline for are colour) corrected and (not dista absolute magnitudes the absolute of The estimation scale. our reflects error the where − antdsare magnitudes N19D–glxe:idvda:NC42 lblrclus- globular scale – distance 4526 – NGC general individual: ters: : – 1994D SN words: Key therefore is It decline-rate–colo errors. uniform relation. a the brightness against within counter-example a fits not 1994D SN distances, − 3(81.4 81. N19D 10. G 56 00.;1 10.07.2; 4526; NGC 11.09.1 1994D; SN 08.19.5 (08.19.04; 03 are: codes thesaurus Your later) hand by inserted be (will no. manuscript A&A h orsodn itnemdlsis modulus distance corresponding The . 18 18 , trwredrUiesta on u e ¨gl7,511B 53121 H¨ugel 71, dem Auf Universit¨at Bonn, der Sternwarte a-lnkIsiu ¨rAtohsk otah12,857 1523, Postfach f¨ur Astrophysik, Max-Planck-Institut V oprdwt te uenvewt eibydetermined reliably with supernovae other with Compared . . 40 44 and , ± ± 23 0 0 N19Do yeI a enssetdntt fit to not suspected been has Ia type of 1994D SN . I 30 . . 31 16 Tip19;Rcte rnhh 99.But 1999). Drenkhahn & Richtler 1998; (Tripp uenve eea uenve individual: supernovae: – general supernovae: a for mag mag. − − ± 18 18 0 1 , . . . 2 16 69 67 n o Richtler Tom and B a in mag ± ± , V 0 0 and , . . 31 30 mag, mag, V I epciey h corrected The respectively. , and − − 18 18 21 1 . . 62 69 . 96 30 ± ± ± . 0 0 4 . . 0 31 30 0 ± . . 09 15 a,and mag, a,and mag, 0Grhn e ¨nhn emn ([email protected] M¨unchen, Germany bei Garching 40 0 a in mag a in mag . 3 mag, n,Gray([email protected]) Germany onn, ess. nce eli- ur– ate nd a. r , Jcb ta.19) nteohrhn,tedsac mod- distance the as hand, adopted other was the 1316 NGC On of 1992). ulus al. et (Jacoby N18Ni G 36 hc aeS 94 pertoo appear and 1994D SN M66 made in by which 1989B SN bright 1316, NGC with in comparison 1980N a SN on based (1995), na ro nteaslt antd fteorder the of magnitude absolute the re in relation, error Tully-Fisher the an in in dispersion Mor which the extinction, with galaxies. uncertain individual gether from for resi suffers exist method large this relation that over, mean known the is to it uals which for distance, Tully-Fisher rmswr ae ihtesm onigadtephotometry the and pointing (1996). same the al. with et taken Biretta were rece frames to most (Ru- according the 1994 with parameters 8th, done calibration May was was calibration observation Pipe-line the 1994). bin of date w The associated filters data. and the a times exposure facility the Coordinating lists European 1 Table taken the ESO. been of have archive HST and the images from HST-WFPC2 of consist data Our Data 2.1. reduction and Data 2. 1994D SN SNe. of Fornax brightness the the to well that reasonably demonstrate fits 1997) globular to Whitmore want of (e.g. we method and (GCLFs) the functions by derived luminosity 4526, cluster NGC for distance a aoee l 98 esne l 98 o ge navleof value a on agree now 1998) al. ∼ et Jensen 1998, 199 al. al. et et fluctuati Valle Madore Della 1996, brightness al. et surface (Kohle measurements and (SBF) Cepheids, (GCs), clusters 19)adPtt(96 sa nulse B itnemodu- distance SBF of unpublished Richmond lus an by is used (1996) 4526 Patat value NGC and distance for (1995) The published. distance been individual yet has no However, not valid. relation erally discrepa decline-rate–luminosity the the any increase rendering marginal, would hence be rate on a decline may comparison the is difference their for 4526 the correction NGC based While that and SNe. Virgo fact cluster Virgo other the the used of They member mag. 0.25 by (1999). bright al. et Richtler in F found the be of can discussion distance Cluster up-to-date nax An distance. cluster 13 NGC the to with distance the identify we compactness cluster’s the 2.04.3) 31 adg amn 19)as on N19Dtoo 1994D SN found also (1995) Tammann & Sandage . 35 30 . a o h onxCutrdsac ouu.Deto Due modulus. distance Cluster Fornax the for mag 68 0 . ± 5 a.Adsdatgsi htM6ol a a has only M66 that is disadvantages A mag. 0 . 13 a rmTny nti ae,w hl give shall we paper, this In Tonry. from mag ASTROPHYSICS ASTRONOMY 31 . 02 a hl globular while mag AND g.de) 0 . 25 sults gen- mag to- , ncy, All or- ith on 16 d- e- nt 8, t , 2 Georg Drenkhahn & Tom Richtler: SN 1994D in NGC 4526: a normally bright type Ia supernova

Table 1. The names of the respective HST data set, the filter, comparable to cluster candidates in NGC4526, normally have and the exposure time in seconds. quite red colours. Remaining candidates are foreground stars and faint background galaxies, where the balances an Name Filter texp intrinsic blue colour. Our strategy, described in more detail be- u2dt0501t F555W 60 low, is the following: we first select our sample with respect to u2dt0502t F555W 230 the elongationas given by the SEXTRACTOR program, then the u2dt0503t F555W 230 angular size measured as the difference between two apertures, u2dt0504t F814W 60 u2dt0505t F814W 230 and finally the colour. u2dt0506t F814W 230 3.1.1. Elongation was performed on averaged frames with an effective exposure time of 520s each. The elongation is taken as the ratio E = A/B, where A and B Hot pixels were removed with the IRAF task WARMPIX. are the major and the minor axes as given by SEXTRACTOR. However, the undersampling can cause a spurious elongation if The limited Charge Transfer Efficiency was corrected for with the prescriptions given by Whitmore & Heyer (1997). Cosmics a given object is centred between 2 pixels. We therefore chose were identified with the IRAF task CRREJ and eventually the E < 1.9 in both filters to exclude only the definitely elongated objects. frames were combined with a weighted average. We modelledthe galaxy light with the IRAF task IMSUR- FIT and achieved a very satisfying subtraction of the galaxy 3.1.2. Size light with no visible residuals. After this, the photometric ef- fects of the image distortion were corrected for by a multipli- The SEXTRACTOR stellarity index is not very suitable for cation with a correcting image (Holtzman et al. 1995). undersampled images because the neural network of SEX- TRACTOR is trained with normally sampled objects (Bertin & Arnouts 1996). We use the magnitude difference in two aper- 2.2. Object search and photometry tures as a size measure (Holtzman et al. 1996). These aper- Due to the Poisson noise of the galaxy light, one finds a tures should be compatible with the expected size of a GC in noise gradient towards the centre of the galaxy. The normally NGC4526. A typicalhalf-lightradius of a GC is of the order of used finding routine DAOFIND from the DAOPHOT pack- a few pc. Thus the larger clusters are marginally resolvable, as- age (Stetson 1987) does not account for a position-dependent suming a distance of 13Mpc to NGC4526, which corresponds background noise. Using DAOFIND with a mean noise level to 6pc per pixel. The parameter m12 := m1 m2 (m1 m2)∗ results in many spurious detections near the galaxy centre and is defined as the magnitude difference between− − one and− two missed objects in regions with lower noise background. There- pixel apertures m m minus the appropriate value for a star- 1 − 2 fore we used the finding routine of the SEXTRACTOR program like object (m1 m2)∗. The latter subtraction accounts for the (Bertin & Arnouts 1996). The lower threshold was adjusted in position-dependent− PSF of the WFPC2. order to include also the strongest noise peaks with a number To find a reasonable size limit, we simulated cluster can- of connected pixels of 3 and a threshold of 1.4 σ. Our ini- didates by projecting the data for Galactic GCs at a distance · tial object list consists of 304 found and matched objects in the of 13Mpc, based on the McMaster catalogue of Galactic glob- three wide-field frames of the F555W and F814W images. The ular clusters (Harris 1996). We generated oversampled King- planetary camera data were not used because they showed only profiles (King 1962) with the geometric parameters from this very few -like objects. catalogue and convolved them with an oversampled PSF of the For these objects aperture photometry (with DAOPHOT) WFPC2. The resulting images were rebinned at four differ- ′′ has been obtained throughan aperture of 0. 5. These instrumen- ent subpixel positions giving WFPC2 images of the Galactic tal magnitudes were finally corrected for total flux and trans- globular cluster system (GCS) as it would be observed from a formed into standard Johnson magnitudes with the formulae distance of 13Mpc. Fig. 1 shows the measured m12 values as given by Holtzman et al. (1995). functions of the core radii rc. It turns out that m12 is a suffi- ciently good quantity to measure rc. Applying a selection cri- 3. The luminosity function terion of m12 < 0.45 in both filters excludes extended GCs with rc > 5 pc. This reduces the size of the GC sample but 3.1. The selection of globular cluster candidates by does not introduce a bias because rc and MV are not corre- elongation, size and colour lated. The m12 magnitude is not suitable to place a lower size The selection of cluster candidates in HST images benefits limit because the smaller GCs are unresolved and cannot be greatly from the enhanced resolution. While in ground-based distinguished from a stellar-like image. imaging, cluster candidates often cannot be distinguished from Fig. 2 compares the distribution of m12 of the sample of background galaxies, this problem is less severe in HST im- our detected sources with that of the simulated clusters for both ages. Galaxies that are so distant that their is filters. The dotted histogram represents the backgroundsources Georg Drenkhahn & Tom Richtler: SN 1994D in NGC 4526: a normally bright type Ia supernova 3

1 45

0.9 40 0.8 35 0.7 30 0.6 0.5 25

0.4 20

in F555W [mag] 0.3 12 15 m 0.2 Objects around NGC 4526 10 0.1 0 5 -0.1 0 0 5 10 15 20 25 30 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 rc [pc] m12 in F555W 400 Fig. 1. The measured m12 values of the simulated Galactic GCs as a function of the core radius rc. Every GC is represented 350 by 12 crosses according to the 3 WF cameras and 4 different 300 subpixel positions. 250

200 (see Sec. 3.3). The objects with m12 > 0.45 can be almost entirely explained as resolved background objects. 150

Number of simulated GCs 100

3.1.3. Colours 50

The range of existing colours among Galactic GCs is not a 0 very good guide in our case: large error bars and a possibly -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 m12 in F555W different metallicity distribution may cause a different shape of the colour histogram. However, as Fig. 3 shows, a selection Fig. 2. These histograms show the distribution of m12 for with regard to shape and size selects also according to colours, the detected sources (upper panel) and the simulated clusters i.e. the redder objects, which are presumably redshifted back- (lower panel). The dotted histogram shows the expected back- ground galaxies, can be effectively removed. groundobjects (=galaxies)derived from the Medium Deep Sur- The colour histogram of the remaining objects shows some vey frames. Objects with values m12 > 0.45 are resolved and similarity to other GCSs with regard to the apparent “bimodal- mostly background objects. The distribution for F814W is es- ity”, for example in M87 (Whitmore et al. 1995). One may sus- sentially the same. pect that there is a dichotomy in the population of GCs in the sense that the blue (=metal poor) objects belong to a halo pop- ulation and the red ones to the bulge. Unfortunately, the num- We evaluated the completeness in our V , I sample by in- ber of objects found does not allow a deeper investigation. The serting artificial objects in the V -frame and we used the same mean colour is V I =1.1. coordinates for inserting objects in the I-frame, after having h − i fixed the colour for all objects to the value of V I = 1.1. We also exclude very faint objects with large photomet- − ric errors ∆m > 0.3 in at least one of the two filters. They In total we used 19000 artificial “stars” in the magnitude range hardly contribute to the determination of the turn-over magni- 23

35 Table 2. The exposures from the Medium Sky Survey which have been used for the background evaluation. Given are the 30 data set names, total exposuretimes in seconds, and the number of individual frames, which entered the averaging process. 25

texp [s] texp [s] # # 20 Name in F606W in F814W in F606W in F814W u30h3 1200 1266 6 8 Number 15 uy400 866 1000 6 6 uy401 600 700 4 8 10 uyx10 800 700 3 3 5 uzx01 696 1550 5 4

0 -0.5 0 0.5 1 1.5 2 2.5 3 V-I

Fig. 3. This colour histogram shows the shape- and size- 3.3. Foreground and background sources selected sample of objects. The dotted line denotes the distribu- The field of our HST images is too small for a proper analy- tion of the complete sample. It can be seen that the shape and sis of the contaminating background sources that survived all size distribution can already discriminate against red objects selection processes. which are presumably distant galaxies. For the final sample, we chose the colour interval 0.8 < V I < 1.4. Therefore, we used the WFPC2 Medium Deep Survey − (MDS) (Ratnatunga et al. 1999) to obtain an estimation of the 1 background. Suitable fields should be possibly nearby, in par- ticular regarding the Galactic latitude, and should be deep with several single exposures. We found the exposures which are 0.8 listed in Table 2 together with some information. The frames are deepenough(in F606W and F814W) that the source finding 0.6 is complete in the relevant magnitude interval. V and I magni- tudes are calculated according to the prescriptions of Holtzman et al. (1995). 0.4 The selection criteria discussed above are applied in exactly the same way as in the case of the NGC4526 frames. It turns 0.2 out that most background objects are selected out. The Poisson scatter of background objects from frame to frame is in the ex- 0 pected statistical range. Thus any clustering in the background 23 23.5 24 24.5 25 25.5 V galaxy number density does not influence the background LF. So we can assume that the background LF derived from the 1 MDS frames gives also a good estimate for the background LF near NGC4526. 0.8 As can be assessed also from Fig. 2, the fraction of back- ground objects in the selected samples is only 7%. The result- 0.6 ing luminosity function b(m) enters the maximum-likelihood fitting process as described in Sec. 3.4.1.

0.4 3.4. The turn-over magnitude

0.2 3.4.1. Remarks on the maximum-likelihood fit and the TOM of NGC4526 0 22 22.5 23 23.5 24 24.5 For the representation of the GCLF, we choose the t5-function, I which has been shown to be the best analytical representation of the Galactic GCLF and that of M31 (Secker 1992). It reads Fig. 4. The completeness for V and I for three different noise intervals, which are characterised by the mean values ρ = − 1.75 DN, 2.05 DN and 3.35 DN (from right to left) in the V 0 2 3 0 8 (m m ) filter. t5(m; m , σt)= 1+ − 2 . (1) 3√5πσt  5σt  Georg Drenkhahn & Tom Richtler: SN 1994D in NGC 4526: a normally bright type Ia supernova 5

The maximum-likelihood fitting method evaluates the most Table 3. The fitted turn-over magnitudes and t5 dispersions for probable parameters for a given distribution φ by maximising the globular cluster system of NGC4526. the likelihood Filter m0 σt 0 0 L(m , σt)= φ(mi; m , σt). (2) V 23.16 ± 0.16 1.01 ± 0.12 Yi I 21.96 ± 0.09 0.94 ± 0.09 For the theoretical background of this method see Bevington & Robinson (1992), Caso et al. (1998). Secker (1992) and Secker itself is not used in the fitting it shows that the fitted distribution & Harris (1993) already applied it to the fitting of GCLFs. models the data reasonably well. From simply looking at the What is to be fitted is the t5-function modified by the differ- histogram one could conclude that the TOM lies at a slightly ent influencing factors, i.e. the completeness, the background, fainter magnitude. But one has to keep in mind the large statis- and the photometric errors. We used an extended version of tical scatter within the single bins and that this picture changes the distribution of Secker (1992) that accounts for a position- with different bin positions and widths. Note also the differ- dependent background noise. ences between the maxima of the functions φ(m;1.75 DN), 0 φ(m; ρ,m , σt)= φ(m;2.00 DN), and φ(m;3.25 DN) in V caused by the dif- 0 (3) K κ(m; ρ,m , σt)+(1 K) β(m; ρ) ferent completeness limits. The completeness function in our · − · data decreases at the same magnitude value as the declining with κ being the normalised distribution of the GCs part of the intrinsic LF. It is therefore crucial to determine the 0 completeness function most precisely and any error in this part κ(m; ρ,m , σt)= ′ 0 ′ ′ (4) of the calculation introduces a significant systematic error in I(m; ρ) t (m ; m , σt) ε(m; m ,ρ) dm · 5 · the TOM. This problem is only resolved if the observation is R  and β being the normalised distribution of the background ob- complete down to at least one magnitude beyond the TOM. jects Fig. 6 shows the likelihood contours for the fitted param- eters and Table 3 gives the resulting values. The width σt is β(m; ρ)= I(m; ρ) b(m). (5) · 0.09 mag larger than σt for the Galactic system (Table 4) but Special care must be taken when κ and β are normalised and still small compared to other early-type galaxies (Whitmore 1997 use σt =0.78 σ to convert the Gaussian widths). mixed through the mixing value K, because this depends on · g the completeness and therefore on ρ. ε is a Gaussian distribution accounting for the photometric 3.4.2. The TOM of the Galactic system error Although the Galactic TOM has been discussed by many au- ′ 2 ′ 1 (m m ) thors, it is not a parameter that can be simply looked up in the ε(m; m ,ρ)= ′ exp − ′ (6) √2π σ(m ,ρ) · 2 σ(m ,ρ) literature. The exact value depends on the method of fitting, on · · with a magnitude- and noise-dependent width the selection of GCs that enter the fitting process, on the dis- tance scale of GCs, and on the exact application of a reddening σ(m,ρ)= 100.4·(m−a) + ρ2 100.8·(m−b) (7) law. Even if our values do not differ much from previous eval- p · uations, we discuss them for numerical consistency. as used by DAOPHOT (Stetson 1987). a and b depend on the We take the LMC distance as the fundamental distance for photometry parameters but are more easily determined by just calibrating the zero-point in the relation between metallicity fitting the photometry data to (7). and horizontal branch/RRLyrae brightness. The third funda- The necessity for this more complicated approach is most mental distance determination beside trigonometric parallaxes clearly seen in the noise-dependent completeness functions in and stellar stream parallaxes is the method of Baade-Wesselink Fig. 4. One could also perform the analysis for objects in a parallaxes. It has been applied to the LMC in its modified form small range of background noise but this would further reduce known as the Barnes-Evans method. So far, it has been applied our already small GC sample. to Cepheids in NGC1866 (Gieren et al. 1994), and the most Fig. 5 shows two-dimensional slices through the three- accurate LMC distance determination to date stems from the dimensionally fitted luminosity function at a noise level of period-luminosity relation of LMC Cepheids by Gieren et al. ρ = 1.75, 2.00, and 3.25 DN, respectively, in both filters. The (1998). We adopt the distance modulus from the latter work, background noise of ρ = 2.00 DN corresponds approximately which is 18.46 0.06 mag, and which is in very good agree- to the mode of the background noise distribution and is there- ment with most± other work (e.g. Tanvir 1996). fore most representative. The figure also displays the low back- If we adopt the apparent magnitudeof RRLyrae stars in the ground contribution and a down-scaled completeness function LMC from Walker (1992), 18.94 0.1 mag for a metallicity for ρ = 2.00 DN. The histogram includes all objects indepen- of [Fe/H] = 1.9 dex, and the metallicity± dependence from dent of their ρ-values. It therefore does not correspond to a sin- Carretta et al. (1999),− we find gle fitted function but is rather a superposition of many func- tions belonging to a variety of ρ-values. Though the histogram MV (RR)=(0.18 0.09)([Fe/H]+1.6)+0.53 0.12. (8) ± ± 6 Georg Drenkhahn & Tom Richtler: SN 1994D in NGC 4526: a normally bright type Ia supernova

0.6 1.6 1.5

0.5 1.4

1.3

0.4 1.2 [mag] t 1.1 σ

0.3 1 x

0.9 0.2 σ 0.8 =1.0 2.0 3.0 0.7 0.1 22.8 23 23.2 23.4 23.6 23.8 V0 [mag]

1.4 0 19 20 21 22 23 24 25 26 1.3 V 1.2 0.6 1.1

1 [mag]

0.5 t

σ x 0.9

0.4 0.8

0.7 σ=1.0 2.0 0.3 3.0 0.6 21.6 21.8 22 22.2 22.4 I0 [mag] 0.2

0 0.1 Fig. 6. 1, 2, and 3σ contours for the fitted parameters m and σt in V and I. 0 18 19 20 21 22 23 24 25 I Table 4. Fitted TOMs and σt-values for the Galactic GC sys- tem. The I values are biased due to selection effects as dis- Fig. 5. The result of the maximum-likelihood fit for the cussed in the text. V and I filter (solid line). Histogram: all selected objects Filter M 0 σ # of GCs independent of their ρ values. Solid lines: fitted GCLFs t V −7.61 ± 0.08 0.92 ± 0.07 120 φ(m;1.75 DN), φ(m;2.00 DN), and φ(m;3.25 DN). Dotted- I −8.60 ± 0.07 0.85 ± 0.06 93 dashed line: down-scaled completeness 0.6 I(m;2 DN). Dashed line: background contribution β(m;2 DN· ). The ordi- nate is the dimensionless probability per magnitude for φ, β Fig. 7 shows the scaled histograms (V and I) for the sample and the histogram while for I it just denotes the probability. As of Galactic globular clusters. The solid line is the t5-function required by any probability density function the area under the resulting from the maximum-likelihood fit. It is not the fit to the fitted distribution function φ(m; ρ) and the histogram is unity histograms, which are shown just for visualisation purposes. for all values of ρ. It is apparent from Fig. 7 that the symmetry in the V distri- bution breaks down for clusters at the faint end of the distribu- tion. It is reasonableto include in the fit onlythe symmetric part This zero-point is in excellent agreement with the value of up to a certain limiting magnitude. To determine an appropriate 0.58 0.12 mag derived from HB-brightnesses of old LMC cut-off magnitude m we carry out the maximum-likelihood fit ± c globular clusters from Suntzeff et al. (1992), if the above metal- for various mc and look at how the fitted parameters evolve. 0 licity dependence is used. It also agrees within a one-σ limit Fig. 8 shows that the V -TOM MV and the width σt clearly de- with 0.56 0.12 mag (Chaboyer 1999) and 0.57 0.04 mag pend on m . The inclusion of the asymmetric part shifts M 0 ± ± c V (Carretta et al. 1999). systematically to greater values. This trend stops at our adopted We calculate the absolute magnitudesof Galactic GCs from value mc = 5.8 mag and lowering mc further just results in a − 0 the McMaster catalogue (Harris 1996), using AV /E(B V )= random scatter of MV . 3.1 (Rieke & Lebofsky 1985) and E(V I)/E(B V )=1− .53 There is no asymmetric part in the histogram of the I band (Ardeberg & Virdefors 1982) as a compromise− between− the ex- data in Fig. 7. The reason for this is a selection effect in the treme values 1.6 mag (Rieke & Lebofsky 1985) and 1.35 mag I photometry. Looking at the McMaster catalogue data reveals (Drukier et al. 1993). We exclude clusters with E(B V ) > 1 missing I data in approximately 22% of the listed GCs. All so that the sample embraces 120 clusters in V and 93− in I. of these clusters with missing data belong to the fainter end Georg Drenkhahn & Tom Richtler: SN 1994D in NGC 4526: a normally bright type Ia supernova 7

0.5 of the luminosity function in V . This is shown by plotting the 0.45 subset of GCs without I magnitudes onto the MV histogram in Fig. 7. This incompleteness shifts the fitted I TOM to brighter 0.4 magnitudes. Thus, a comparison between the difference of the 0.35 fitted TOMs and the mean colour of the Galactic GCs gives 0.3 0.87 0.09 = V I

0.1 0 0 MI = MV V I MW = 8.48 0.10 (10) 0.05 − h − i − ± as an absolute TOM in the I band. Alternatively, we intro- 0 -10 -8 -6 -4 -2 duce a cut-off magnitude in the I band data and fit only the Mv more complete luminous part of the distribution like we did in 0.6 the V band. As expected, the fitted I TOM becomes smaller with decreasing cut-off magnitude. If the cut-off magnitude 0.5 approaches the TOM the fitted TOM values begin to scatter greatly around approximately 8.52 mag because the sample − 0.4 size decreases and the fit results are less well determined. We therefore do not rely on this approach but rather regard it as a 0.3 confirmation of the validity of (10).

0.2 3.5. Metallicity correction and distance

0.1 The luminosity of a GC depends not only on its mass but also on its metallicity. Any difference between the metallicities of 0 the GCS of NGC4526 and the Galactic GCS must be corrected -12 -10 -8 -6 -4 -2 to avoid a systematic bias. Mi The amount of this correction has been studied by Ashman Fig. 7. This graph shows the normalised distribution of ab- et al. (1995) and we adopt their values. The only metallicity solute magnitudes in V and I for Galactic globular clusters. indicator that is available for us is the mean V I colour of the − Overplotted as solid lines are the t5-functions resulting from a GCS, for which we adopt the relation given by Couture et al. maximum-likelihood fit. The bold histogram in the left panel (1990): shows the GCs with missing I-band photometry. The dotted V I =0.2 [Fe/H]+1.2. (11) vertical line denotes the cut-off magnitude at mc = 5.8. − · − A mean colour of V I = 1.1 indicates [Fe/H]NGC4526 = -7.2 1.6 h − i 0 0.5 0.3 and we find a metallicity correction of ∆MV = − ± 0 -7.3 1.5 0.28 0.19 and ∆MI = 0.11 0.05. The large error of 0.3±dex for the metallicity arises± from the fact that V I -7.4 1.4 depends± only weakly on the metallicity. This value canh be− esti-i mated from looking at the scatter in the – plot -7.5 1.3 [Fe/H] (V I) of the Galactic GCS. − t 0 V

-7.6 1.2 σ M Hence the distance moduli in V and I are

-7.7 1.1 µV = 30.49 0.26 and µI = 30.33 0.14. (12) ± ± -7.8 1 If the universality of the TOM of 0.2 mag (Whitmore 1997) ≈ -7.9 0.9 and the uncertainty in the horizontal branch calibration of 0.1 mag is included as external errors we obtain ≈ -8 0.8 -7.5 -7 -6.5 -6 -5.5 -5 -4.5 -4 -3.5 -3 m µ = 30.4 0.3 mag (13) c NGC4526 ± 0 ✕ and Fig. 8. Dependence of the fitted MV (symbol ) and σt (sym- bol +) on the cut-off magnitude mc for the Galactic GCS. The DNGC4526 = 12.0 1.6 Mpc (14) chosen mc = 5.8 is indicated by the dashed line. ± − as our final value for the distance modulus and distance. 8 Georg Drenkhahn & Tom Richtler: SN 1994D in NGC 4526: a normally bright type Ia supernova

Table 5. The table lists the coefficients according to (15) for -1.5 the relation between brightness, decline rate, and colour for the ± ± (1.52 0.62) ´ (Bmax-Vmax) - (3.31 0.07) Cal´an/Tololo sample. -2 - 1.1)

Band Z b R 15 m

B −3.306 ± 0.063 −0.48 ± 0.23 −1.51 ± 0.62 ∆ -2.5 V −3.320 ± 0.058 −0.52 ± 0.19 −0.83 ± 0.57 I −3.041 ± 0.060 −0.40 ± 0.22 −0.81 ± 0.59 -3 - 5 log cz + b(

max -3.5

Thus, NGC4526 is located in the foreground of the Virgo B cluster and a comparison with apparent magnitudes of other SNe in the is misleading. This result is consis- -4 tent within with Tonry’s unpublished SBF distance modulus -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1σ Bmax-Vmax 30.68 0.13 mag, which was used by Richmond et al. (1995). ± Fig. 9. This plot shows the relation between Bmax Vmax rate and the apparent maximum brightness in B corrected− for the 4. Comparison with other supernovae decline rate. A clear dependence is visible. We point out that 4.1. The dependence on decline rate and colour only blue SNe with Bmax Vmax < 0.2 have been included in the fit. The fact that the redder− SNe are well represented by this The publication of the Cal´an/Tololo-sample of Ia SNe (Hamuy relation is a point in favour of the validity of this relation even et al. 1996) confirmed in a compelling way what has been sug- over a larger colour range. gested earlier, namely that the luminosity of Ia’s depends on the decline rate and also on the colour of the SN at maximum phase. Here we report convenient expressions which relate in the its 3 Ia SNe SN1980N, SN1981D (both in NGC1316), and sample of Hamuy et al. the decline rate ∆m15 and the fore- SN1992A(in NGC1380).The light curves of the first two SNe ground extinction-corrected colour Bmax Vmax with the ap- have been presented by Hamuy et al. (1991), while SN1992A − parent maximum magnitude (the recently published sample by (one of the best observed SNe) is described by Suntzeff (1996). Riess et al. (1998) does not change significantly the numerical All these SNe are relatively fast decliners, and thus fol- values). These linear relations read low the trend already visible in the Cal´an/Tololo SN sample (Hamuy et al. 1996) that spiral galaxies host all kinds of SNe, m + b (∆m 1.1)+ R (B V ) max,i 15 max max (15) while early-typegalaxies tend to host only fast decliners(which =5 log cz· + Z − · − · are intrinsically fainter). where i B,V,I denotes the different bands. Table 5 lists The Fornax cluster is well suited to serve as a distance stan- the coefficients,∈ { which} have been obtained by a maximum- dard. It is compact with hardly any substructure and consists in likelihood fit, together with their errors. Only SNe with B its core region almost entirely of ellipticals and S0 galaxies, max − Vmax < 0.2 have been used for the fit. Fig. 9 shows the relation the characteristics of a well relaxed galaxy cluster. The dis- between Bmax Vmax and the apparent maximum brightness tance based on GCLFs has been determined through the work corrected for decline− rate. The fact that the red SNe are also of Kohle et al. (1996) and Kissler-Patig et al. (1997a), who well fitted by this relation indicates the validity of this relation analysed the GCSs for several early-type galaxies. In addition, for a larger colour range. The coefficients of the colour term Kissler-Patig et al. (1997b) and Della Valle et al. (1998) deter- also deviate strongly from the Galactic reddening law so that mined the luminosity function for the GCS of NGC1380, host one may conclude that the red colours are indeed intrinsic and of SN1992A. Kohle et al. (1996) derived mean apparent TOMs not significantly affected by reddening. for their sample of 5 Fornax galaxies of V 0 = 23.67 0.06. The corrected magnitudes can now be compared with those This is in perfect agreement with the TOM of NGC1380± given of other SNe. by Della Valle et al. (1998), which is V 0 = 23.67 0.11. The difference in distance moduli between Kohle et al.± (1996) and Della Valle et al. (1998) stems from a revised absolute TOM 4.2. Comparison with other SNe of the Galactic GCS. If this is based on the Gratton et al. A meaningful comparison of SN1994D with other SNe re- (1997) relation, which is similar to our eq. (8), the distance quires the distances of the comparison objects to be derived modulus is µFornax = 31.35 0.15 mag. It is very satisfac- with the same method of GCLFs, because then the comparison tory that several other independent± methods confirm our dis- is valid without the need for an absolute calibration of GCLFs. tance estimate (Richtler et al. 1999). For example, Madore et al. Moreover, these SNe should be well observed. These two con- (1998) recently published a Cepheid distance to NGC1365 ditions are fulfilled only in the Fornax galaxy cluster with and quoted 31.35 0.2 mag. Moreover, the method of sur- ± Georg Drenkhahn & Tom Richtler: SN 1994D in NGC 4526: a normally bright type Ia supernova 9

Table 6. The observational data and distance moduli of the SNe. The first three rows show the extinction-corrected apparent magnitudes computed with AB /E(B V )=4.09, AV /E(B V )=3.09 and AI /E(B V )=1.49 (Rieke & Lebofsky 1985). Photometric data, colour excesses− and decline rates are taken− from Richmond et al. (1995)− for SN1994D, from Hamuy et al. (1996) for SN1992A and SN1980N, and from Hamuy et al. (1991) for SN1981D. The absolute magnitudes are corrected for decline rate and colour by (15).

SN 1994D SN 1992A SN 1980N SN 1981D Bmax 11.73 ± 0.02 12.57 ± 0.03 12.49 ± 0.03 12.59 Vmax 11.78 ± 0.02 12.55 ± 0.03 12.44 ± 0.03 12.40 Imax 12.00 ± 0.05 12.80 ± 0.03 12.70 ± 0.04 — ∆m15(B) 1.31 ± 0.08 1.47 ± 0.05 1.28 ± 0.04 — Bmax − Vmax −0.05 ± 0.04 0.02 ± 0.04 0.05 ± 0.04 0.19 E(B − V ) 0.04 ± 0.03 0 0 0 (?) µ 30.40 ± 0.30 31.35 ± 0.15 31.35 ± 0.15 31.35 ± 0.15 MB,cor −18.69 ± 0.31 −18.99 ± 0.16 −19.02 ± 0.16 — MV,cor −18.69 ± 0.31 −19.01 ± 0.16 −19.04 ± 0.16 — MI,cor −18.44 ± 0.31 −18.69 ± 0.16 −18.74 ± 0.16 — face brightness fluctuations gives a Fornax distance modulus example against the general validity of the decline-rate–colour– of 31.32 0.24 mag (Jensen et al. 1998). luminosity relation. ± For the other host galaxy in Fornax, NGC1316, no pub- lished GCLF distance exists. Grillmair et al. (1999), using HST 4.3. The Hubble constant data, found no turn-over but an exponential shape of the GCLF. They explained this with a population of open clusters mixed Once the absolute brightness of a supernovais known,the Hub- in, presumably dating from the past merger event. Preliminary ble diagram of SNe Ia (Hamuy et al. 1996) allows the deriva- results from ongoing work (G´omez et al., in preparation), how- tion of the Hubble constant with an accuracy which is largely ever, place the TOM of the entire system at the expected mag- determined only by the error in the supernova brightness. The nitude, but indicate a radial dependence in the sense that the fact that the Fornax SNe are well observed in combination with TOM becomes fainter at larger radii. At this moment, we have a reliable distance makes these objects probably the best SNe no good explanation.Perhaps, the different findings correspond for this purpose. The relation between the Hubble constant, the to the different regions in NGC 1316 investigated. This issue is absolute corrected magnitude M and the zero-point Z in (15) not yet settled. reads An individual distance value for NGC1316 based on plan- H etary nebulae seems to indicate a shorter distance to this log 0 =0.2 (M Z)+5. (16) kms−1 Mpc−1 · − galaxy than to the Fornax cluster. McMillan et al. (1993) find µPN,NGC 1316 = 31.13 mag, but this value is based on a Taking the data from SN1994D, SN1992A, and SN1980N M31 distance modulus of 24.26 mag. Adopting the now widely presented in Table 6 and the zero-points from Table 5 yields a accepted M31 Cepheid distance modulus of 24.47 mag (e.g. Hubble constant of Stanek & Garnavich 1998, Kochanek 1997), the NGC1316 −1 −1 modulus increases to 31.34 mag, perfectly consistent with the H0 = 75 6 6kms Mpc . (17) global Fornax distance. We therefore adopt the Fornax distance ± ± modulus of µFornax = 31.35 0.15 mag for SN1992A and The systematic error originates from the horizontal branch SN 1980N. ± magnitude, the universality of the TOM, the adopted Fornax Table 6 lists the absolute magnitudes of SN1994D together distance and the error in Z. The statistical error is just the with two Fornax cluster SNe (SN1981D was badly observed), scatter from the three corrected SNe absolute magnitudes. This corrected for decline-rate and colour. All values can be derived Hubble constant value is dominated by the data from the For- from the photometric data and distances shown in table 6 to- nax SNe because of the small statistical weight of SN1994D. gether with our correction equation (15). One notes that SN1994D seems to be 0.3mag too faint in 5. Summary all three photometric bands. However, the error bars overlap with those of the other SNe. Thus, there is no reason to claim We determined the GCLF distance of NGC4526 to be 12.0 that this SN is peculiarly dim. On the other hand, if one takes 3.9 Mpc, placing this galaxy in front of the Virgo cluster. Al-± Tonry’s unpublished SBF distance modulus, which is 0.28mag though this distance is not precise enough to give a good ab- greater than ours, all three SNe brightnesses would agree solute magnitude it is sufficient to show that SN 1994D is not within 0.05 mag. At any rate, it is apparent that SN1994D is an overluminous type Ia SN but rather a normally bright event definitely± not overluminous and cannot be taken for a counter- compared to the two Fornax SNe SN1992A and SN1980N. 10 Georg Drenkhahn & Tom Richtler: SN 1994D in NGC 4526: a normally bright type Ia supernova

All GCLF distances depend on the absolute luminosities Holtzman J.A., Burrows C.J., Casertano S., et al., 1995, PASP 107, of the Galactic GCs. It is therefore vital to calibrate the ab- 1065 solute TOM properly to minimise systematic errors. The most Holtzman J.A., Watson A.M., Mould J.R., 1996, AJ 112, 416 important calibration parameter is the absolute magnitude of Jacoby G.H., Branch D., Clardullo R. , 1992, PASP 104, 599 the horizontal branch which directly enters our distance scale. Jensen J.B., Tonry J.L., Luppino G.A., 1998, ApJ 505, 111 The treatment of the Galactic GC sample shows that the asym- King I., 1962, AJ 67, 471 Kissler-Patig M., Kohle S., Hilker M., et al., 1997a, A&A, 319, 470 metric distribution in and incompleteness effects in the V I Kissler-Patig M., Richtler T., Storm J., Della Valle M., 1997b, A&A, band can introduce a bias in the TOM of over 0.1 mag. 327, 503 With the distances and the apparent decline-rates and Kochanek C.S., 1997, ApJ 491, 13 colour-corrected magnitudes of the three SNe SN1994D, Kohle S., Kissler-Patig M., Hilker M., et al., 1996, A&A 309, L39 SN1982A, and SN1980N one obtains an absolute corrected Madore B.F., Freedman W.L., Silbermann N., et al., 1998, ApJ 515, peak magnitude of type Ia SNe. The Cal´an/Tololo SN sample 29 gives us the zero-point of the Hubble diagram, the second in- McMillan R., Ciardullo R., Jacoby G.H., 1993, ApJ 416, 62 gredient in calculating the Hubble constant from type Ia SNe. 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