A NEW DISTANCE TO THE ANTENNAE GALAXIES (NGC 4038/39) BASED ON THE TYPE Ia SUPERNOVA 2007sr^*

The Antennae (NGC 4038/39) are the nearest example of a major merger involving two gas-rich disk galaxies of comparable mass. They allow us to study processes of dissipational galaxy assembly close up, thus providing a valuable glimpse of what must have been more frequent events in the early universe. The Antennae have been observed extensively at all wavelengths (e.g., X-rays: Fabbiano et al. 2004; UV: Hibbard et al. 2005; optical: Whitmore et al. 1999; IR: Gilbert & Graham 2007; and 21 cm line: Hibbard et al. 2001) and have also been repeatedly modeled via N-body and hydrodynamical simulations (e.g., Toomre & Toomre 1972; Barnes 1988; Mihos et al. 1993; Hibbard 2003). An accurate distance to this prototypical merger is of obvious importance in assessing its structure and dynamics, as well as for determining the physical properties of its myriad of stars, star clusters, peculiar objects such as ultraluminous X-ray sources (ULXs), and gas clouds.

Traditionally, the distance to NGC 4038/39 has been most often derived from the systemic recession velocity and an adopted Hubble constant H₀, with or without corrections for deviations of the Hubble flow from linearity due to various attractors. A frequently used modern value for the distance is 19.2 Mpc (Whitmore et al. 1999). This value is based on a systemic recession velocity relative to the Local Group of $cz_{{\rm LG}}= 1439$ km s⁻¹ (Whitmore & Schweizer 1995; de Vaucouleurs et al. 1991), a linear Hubble flow, and H₀ = 75 km s⁻¹ Mpc⁻¹. Updated to include the Hubble Space Telescope (HST) Key Project's derived H₀ = 72 ± 8 km s⁻¹ Mpc⁻¹ (Freedman et al. 2001), this often-used distance to the Antennae becomes 20.0^+2.5_−2.0 Mpc.

A significantly shorter distance of 13.3 ± 1.0 Mpc has recently been determined by Saviane et al. (2008) via photometry of the tip of the red giant branch (TRGB) in a region near the tip of the southern tidal tail. This photometry—performed on new, deep images obtained with the HST's Advanced Camera for Surveys (ACS)—seems to support the short distance earlier derived from HST/WFPC2 images of the same region by the same method (Saviane et al. 2004). If the short distance is correct, the Antennae "diminish" in physical size, mass, and luminosity, as do their stars, clusters, and gas clouds. However, their recession velocity then deviates from the best large-scale flow model (Tonry et al. 2000, hereafter TBAD00) by about 500 km s⁻¹ or 2.7σ (Saviane et al. 2008).

Clearly, new measurements of the distance to the Antennae by independent methods are highly desirable. In the present paper we derive a new distance from observations of the Type Ia supernova (SN) 2007sr, which appeared in the midsection of the southern tail in 2007 December. Section 2 presents our observations, data analysis, and new distance. Section 3 discusses problems with the short distance and points out a likely error in the identification of the true TRGB by Saviane et al. (2008). Finally, Section 4 presents our conclusions and recommendation.

SN 2007sr was discovered by the Catalina Sky Survey on 2007 December 18.53 UT (Drake et al. 2007), about 4.2 days after B maximum (Umbriaco et al. 2007; Pojmanski et al. 2008). Since it was of Type Ia (Naito et al. 2007; Umbriaco et al. 2007), it was followed by the Carnegie Supernova Project (CSP) as part of their low-z campaign (Hamuy et al. 2006), with observations beginning on 2007 December 20.33 UT. Figure 1 shows the SN on a stacked V image obtained with the Swope 1 m telescope at Las Campanas Observatory.

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The CSP measured light curves for the SN using the filter set u'g'r'i'BVJH from 6 days until approximately 130 days after B maximum. The appendix gives some details about the photometric system and calibration, while Table 1 lists all measured magnitudes and their uncertainties.

It is now well known that SNe of Type Ia (SNe Ia) can serve as excellent standard candles and have been used to both discover the presence (Riess et al. 1998; Perlmutter et al. 1999) and constrain the nature of dark energy (Knop et al. 2003; Astier et al. 2006; Clocchiatti et al. 2006; Wood-Vasey et al. 2007). Once corrected for the extinction and the well-known correlation between the intrinsic luminosity and decline rate of the light curve (Phillips 1993; Hamuy et al. 1996; Riess et al. 1996), SNe Ia have an intrinsic dispersion of approximately ±0.15 mag. We can therefore use SN 2007sr to constrain the distance to NGC 4038/39 to this level.

Because SN 2007sr was discovered after B maximum, it is necessary to use SN Ia light-curve templates to estimate the peak magnitude in each passband as well as the decline-rate parameter Δm₁₅—defined as the change in B magnitude between maximum and 15 days later in the rest frame of the SN. This parameter will allow us to correct for the intrinsic luminosity of the SN and also to predict its intrinsic colors, from which we can derive the host galaxy extinction. More formally, we model the light curve in each passband X with the following formula:

$$\begin{eqnarray} m_{X}&=&T_{X}(t-t_{\rm max},{\Delta m_{15}})+M_{X}^{0}+ b_{X}({\Delta m_{15}}-1.1)\nonumber\\ &&+ R_{X}^{\rm MW}E(B-V)_{\rm MW}+R_{X}^{\rm host}E(B-V)_{\rm host}+ K_{X}+\mu _0\,,\nonumber\\ \end{eqnarray} \tag{ 1 }$$

where T_X is the light-curve template for passband X, t_max is the time of maximum for the B light curve, M⁰_X is the absolute magnitude in passband X of a SN Ia with Δm₁₅ = 1.1 mag, b_X is the slope of the luminosity–Δm₁₅ relationship, K_X is the K-correction in passband X, and μ₀ is the true distance modulus. The extinctions from the Milky Way and host galaxy are R^MW_XE(B − V)_MW and R^host_XE(B − V)_host, respectively. The color excess due to the Milky Way foreground extinction is taken from Schlegel et al. (1998), which, for the position of SN 2007sr, corresponds to E(B − V)_MW = 0.046 ± 0.005 mag.

The values of the parameters M⁰_X and b_X are determined from the set of SNe Ia observed by the CSP in the first-year campaign by assuming a fixed cosmological model (H₀ = 72 km s⁻¹ Mpc⁻¹, Ω_m = 0.28, and Ω_Λ = 0.72; Spergel et al. 2007), computing distance moduli from the observed redshifts of the host galaxies, correcting for Milky Way and host-galaxy extinction, and fitting the resulting absolute peak magnitudes in each passband to the formula

$$\begin{equation} M_{X}=M_{X}^{0}+b_{X}({\Delta m_{15}}-1.1). \end{equation} \tag{ 2 }$$

The details of this procedure are given in G. Folatelli et al. (2008, in preparation).

In performing this calibration, it has become apparent that, for whatever reason, a standard reddening law with the typical Milky Way value of R^MW_V = 3.1 does not provide a good fit to this sample of SNe Ia. Instead, we obtain a value R^host_V = 1.6 ± 0.1 (G. Folatelli et al. 2008, in preparation). Other groups have also found surprisingly low values of R^host_V (Astier et al. 2006; Wang et al. 2006). This may be due to either the SNe Ia being embedded in an environment that differs significantly from a typical interstellar medium (ISM), or, perhaps, another intrinsic color–magnitude effect at play that has been inadvertently combined with E(B − V). Whatever the reason, we are interested in determining the distance and therefore appeal to the empirical result R^host_V = 1.6. However, we note that changing R^host_V in Equation (1) not only affects the extinction term, but also changes the values of M⁰_X because the calibrating sample has non-zero average extinction. Indeed, only an SN with extinction equal to the average extinction of the calibrating sample would be insensitive to changes in R^host_V. In the case of SN 2007sr the extinction is slightly larger than that of the calibrating sample, so an increase in R^host_V would slightly decrease the distance modulus. Specifically, changing R^host_V from 1.6 to 3.1 would change the estimated true distance modulus of this SN by −0.06 mag.

The light-curve templates T_X are constructed in a manner similar to that used by Prieto et al. (2006) and further described in C. R. Burns et al. (2008, in preparation). Essentially, the highest-quality optical light curves from the CSP, which have clearly observed maxima, are fit with a cubic spline, from which Δm₁₅, t_max, and the peak magnitude are extracted. These light curves then define a sparsely sampled 2D surface in Δm₁₅–t–m_X space. A template of any given Δm₁₅ can then be generated by 2D interpolation of this surface. At present, there are an insufficient number of near-infrared (NIR) light curves with which to construct templates in this way. Fortunately, the decline-rate parameter for SN 2007sr (Δm₁₅ = 0.97 mag) is nearly identical to that of SN 2006X (Δm₁₅ = 0.98 mag), for which the CSP has obtained high-quality NIR photometry well before and after B maximum. We therefore use spline fits of the J and H light curves of SN 2006X as templates for fitting the J and H data of SN 2007sr.

The u'Bg'Vr'i'JH light curves of SN 2007sr are shown in Figure 2 along with the best-fit models for the optical data given by Equation (1). The extracted light-curve parameters of interest are the true distance modulus of SN 2007sr, μ₀ = 31.74 ± 0.07 mag, the color excess due to the host galaxy, E(B − V)_host = 0.13 ±  0.01 mag, and the decline-rate parameter, Δm₁₅ = 0.97 ± 0.02 mag. The value of this parameter is a typical value for SNe Ia, and the color excess is reasonably low, as one would expect for a source far from the host center. The uncertainties are derived from the covariance matrix of the fit to the light curves, scaled so that χ²_ν = 1. To be conservative, we add to the uncertainty in μ₀ the following systematic errors: (1) $\sigma _{M_X}=0.15$ mag for the intrinsic dispersion in SN Ia luminosities; (2) uncertainties in the calibration parameters of δR_V = 0.1, δM⁰_X = 0.04 mag, and δb_X = 0.1; and (3) an uncertainty in the Hubble constant of δH₀ = 8 km s⁻¹ Mpc⁻¹. With this error budget, we arrive at a final distance estimate to SN 2007sr of D_SN Ia = 22.3 ± 2.8 Mpc (μ_SN Ia = 31.74 ± 0.27 mag) using the optical data.

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As a check on this distance, we also fitted the J- and H-band data with templates generated from SN 2006X in order to estimate the peak magnitudes: m_J = 13.31 ± 0.06 and m_H = 13.47 ± 0.02. We then used the calibration by Krisciunas et al. (2004), M_J = −18.57 ± 0.14 mag and M_H = −18.24 ± 0.18 mag, to compute an average distance modulus of μ₀ = 31.80 ± 0.11 mag. This modulus, based on NIR data and an independent calibration, is nearly insensitive to assumptions about the reddening law of the dust in the host galaxy and agrees with the formal modulus of 31.74 ± 0.07 mag from the optical data to within the combined errors, thus supporting the derived distance of D_SN Ia = 22.3 ± 2.8 Mpc.

As we demonstrate below, the new SN Ia distance to NGC 4038/39 agrees well with the distance inferred from the system's recession velocity and the large-scale flow model by TBAD00. If the short distance of 13.3 ± 1.0 Mpc measured by Saviane et al. (2008) were to be correct, it would create at least three serious problems: (1) NGC 4038/39 would have an exceptionally large peculiar recession velocity of about +522 km s⁻¹; (2) SN 2007sr would have had a peak luminosity differing by ∼1.1 mag (about 7 $\sigma _{M_X}\!$) from the mean peak luminosity of SNe Ia; and (3) the Antennae would lose their membership in Tully's (1988) Group 22–1 of 13 galaxies. We now discuss these three problems in turn and then point out a likely error in the derivation of the short distance by Saviane et al. (2008).

3.1. Peculiar Recession Velocity

A careful assessment of the many radial velocities measured for NGC 4038/39 and compiled in the NASA/IPAC Extragalactic Database (NED) yields a systemic heliocentric velocity of cz_sys,hel = 1640 ±  10 km s⁻¹. Figure 3 compares this systemic velocity with recession velocities predicted by the large-scale flow model, which is based on surface-brightness fluctuation distances to 300 early-type galaxies (TBAD00). The Antennae are plotted at both the short distance and the new SN Ia distance, while the solid curve represents the predicted large-scale flow velocity in their direction. The undulation in the model curve reflects the gravitational influences of the Virgo Cluster, whose center lies 32.2° away from the Antennae, and of the Great Attractor. As the figure illustrates, with the new SN Ia distance the Antennae fall within +15(±188) km s⁻¹ or +0.1 σ_th of the predicted flow velocity, where σ_th = 187 km s⁻¹ is the best-fit "thermal" (or random) radial-velocity dispersion of the model. If instead we choose the short distance, the peculiar velocity becomes +522 (± 50) km s⁻¹ or +2.8 σ_th, clearly an exceptionally high value. We conclude that the newly measured SN Ia distance is in significantly better agreement with the best available large-scale flow model than the short distance.

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3.2. Peak Luminosity of SN 2007sr

Our determination of a distance of 22.3 ± 2.8 Mpc to SN 2007sr has been based on the assumption that this SN reached the mean absolute magnitude M⁰_X typical for its decline rate. The quoted distance error includes a term reflecting the intrinsic dispersion of the corrected peak absolute magnitudes M_X of SNe Ia around the mean value M⁰_X, which is $\sigma _{M_X} \approx 0.15$ mag for CSP observations of similar quality (Section 2).

If the short distance of 13.3 Mpc were to be correct, SN 2007sr would have reached a peak absolute magnitude that differed by Δ(m − M)₀ = 5log(22.3/13.3) = 1.12 mag, or about $7 \sigma _{M_X}$, from the mean value for SNe Ia. This seems quite unlikely, given the spectral normality of SN 2007sr (Naito et al. 2007; Umbriaco et al. 2007). To illustrate this normality, Figure 4 shows an optical spectrum obtained by the CSP on 2007 December 27.33 UT with the Baade 6.5 m telescope and the Inamori-Magellan Areal Camera and Spectrograph (IMACS), corresponding to an epoch of 13 days after B maximum. For comparison, we include the SN Ia template spectrum by Hsiao et al. (2007) at +13 days. Although there are small differences between the two spectra, the overall resemblance is extremely close, demonstrating that SN 2007sr was both photometrically and spectroscopically a completely normal SN Ia. Hence, the fact that such an extraordinarily low peak luminosity (by 7 $\sigma _{M_X}!$) would result from taking a distance of 13.3 Mpc is a second good reason for distrusting the short distance.

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3.3. Group Membership

3.4. A Likely Misidentification of the TRGB

Why is the TRGB distance of 13.3 ± 1.0 Mpc determined by Saviane et al. (2008) so discrepant? The answer seems to lie in a misidentification of what constitutes the true TRGB of the mixed-age stellar populations near the tip of the southern tidal tail. The area imaged by Saviane et al. with HST/ACS contains several H ii regions (Schweizer 1978; Mirabel et al. 1992) and a very blue, dwarf-like feature dubbed the "S78 Region," which is now recognized to be the bent H i-rich tip of the southern tail (Hibbard et al. 2001).

In their Figure 3, Saviane et al. (2008) displayed two luminosity functions (LFs) for the RGB, one derived for the S78 Region and the other for a "NE Region" that is free of H i and also, supposedly, of relatively young stars. The LF of the S78 Region shows a relatively sharp rise at F814 W₀ = 26.57 mag (where F814W is an instrumental magnitude close to the Kron–Cousin I magnitude), which Saviane et al. (2008) identified as the TRGB but which—given the H i and blue stellar content of the S78 Region—seems equally likely to be caused by relatively young AGB stars. In contrast, the LF of the gas-free NE Region shows only a minor sharp rise there, but features a more significant "discontinuity at F814W₀ ≈ 27.5 mag" (Saviane et al. 2008) that falls within ≲0.2 mag of the TRGB expected for a distance of 22 Mpc. While Saviane et al. (2008) dismissed this discontinuity as possibly "due to the RGB of a younger, ∼200 Myr population," we suggest that its stars—being fainter than the claimed TRGB—actually mark the true location of the TRGB.

To check on this suggestion, we downloaded the ACS/WFC (Wide Field Camera) frames obtained under proposal GO-10580 (P.I.: Ivo Saviane) from the HST Archive, reprocessed them, and extracted a calibrated color–magnitude diagram (CMD) for the entire tidal-tail tip region. Our search and photometry algorithms, which use DOLPHOT (for technical details, see Mager et al. 2008), detected about 30,000 stellar objects brighter than I ≈ 28.0 mag. Figure 5 (left panel) shows the CMD in a new form proposed by Madore et al. (2008), in which the traditional I (or extinction-corrected I₀) magnitude is replaced by the magnitude T_RGB for the RGB. This magnitude is a color-corrected I-band magnitude specifically designed to be insensitive to varying metallicity and is defined by

$$\begin{equation} T_{\rm RGB}\equiv I_0 - \beta [(V-I)_0 - \gamma ], \end{equation} \tag{ 3 }$$

where the color slope β = 0.20 ± 0.05 is chosen to track the known, metallicity-induced run of the I₀ magnitude of the TRGB as a function of (V − I)₀, and γ = 1.50 mag is the fiducial color of reference (Madore et al. 2008). By construction, in any T_RGB–(V − I)₀ diagram of an old stellar population with a range of metallicities, the TRGB lies at some constant value of T_RGB.

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To locate the TRGB objectively, we selected all stars in the color range 1.6 ⩽ (V − I)₀ ⩽ 2.6 and used a Sobel edge-detection kernel (Lee et al. 1993) to filter their numbers (in 0.03 mag bins) as a function of T_RGB. The resulting filter output, expressed as a ratio of the filter response to local Poisson noise, is shown in the right panel of Figure 5. In this panel, a peak at a normalized filter response of 2.0 indicates an edge detection at a 2σ level of significance. Figure 5 shows a very clear, 5.4σ detection of the TRGB at  T_RGB = 27.46 ±  0.12 mag (marked "TRGB") or about 0.9 mag fainter than the TRGB position of I^TRGB₀ = 26.65 mag as claimed by Saviane et al. (2008). The latter position (at T_RGB ≈ 26.55 mag) approximately corresponds to the broad ∼ 3.5σ "hump" seen centered on T_RGB ≈ 26.5 mag in the normalized filter response of Figure 5. We conclude that Saviane et al. (2008) probably misidentified youngish AGB stars for the true TRGB, in the process overestimating its brightness by about −0.9 mag. This, then, is the likely source of their discrepant 13.3 ± 1.0 Mpc distance.

Our newly determined T_RGB = 27.46 ± 0.12 mag yields a true distance modulus to the Antennae of approximately  μ_TRGB ≡ T_RGB − M^TRGB_I = 31.51 ±  0.17 mag, where M^TRGB_I = −4.05 ± 0.12 mag is the absolute I magnitude for the TRGB of ω Cen (Bellazzini et al. 2004) and holds at the fiducial color of reference (Madore et al. 2008). This distance modulus, which is corrected for Milky Way foreground extinction via T_RGB (Equation (3)), but not for (varying) extinction within the tidal-tail tip region, corresponds to a linear distance of D_TRGB = 20.0 ± 1.6 Mpc. We postpone a more elaborate determination of μ_TRGB, including a careful assessment of local extinction and any possible small biases due to the presence of young stellar populations, to a future paper dedicated to that subject. However, note that D_TRGB = 20.0 ± 1.6 Mpc agrees with both D_SN Ia = 22.3 ± 2.8 Mpc (Section 2) and D_flow = 22.5 ± 2.8 Mpc (Section 4) to within the combined errors, while it strongly disagrees with the short distance of 13.3 ± 1.0 Mpc derived by Saviane et al. (2008). Thus, D_TRGB also supports the new SN Ia distance.

We have presented u'Bg'Vr'i'JH light curves of SN 2007sr, which were obtained during four months by the CSP, beginning six days after B maximum. Analysis of these light curves in conjunction with SNe Ia data from the first-year campaign by the project yields a formal true distance modulus of μ₀ = 31.74 ± 0.07 mag. With all known systematic errors and uncertainties included, this distance modulus becomes μ_SN Ia = 31.74 ± 0.27 mag, corresponding to a distance of D_SN Ia = 22.3 ± 2.8 Mpc to NGC 4038/39. Differential depth effects between SN 2007sr and the center of mass of the galaxies are negligible.

This new SN Ia distance agrees well with the distance D_flow = 22.5 ± 2.8 Mpc estimated from the systemic recession velocity of the Antennae and the large-scale flow model by TBAD00, where the quoted error reflects the cosmic random radial velocity (σ_th = 187 km s⁻¹) of the model. On the other hand, D_SN Ia strongly disagrees with the short distance of D = 13.3 ± 1.0 Mpc estimated by Saviane et al. (2008) from the assumed TRGB. We have discussed three serious problems with such a short distance, and have pointed out the likely misidentification of the TRGB by these authors as the cause of the short distance.

Reprocessing their HST/ACS frames and using an improved method of TRGB detection, we have located what we believe to be the true TRGB at I₀ ≈ T_RGB = 27.46 ± 0.12 mag, fully 0.9 mag below (i.e., fainter than) the TRGB claimed by Saviane et al. Analyzing photometry of this new, fainter TRGB, we have derived a preliminary distance of D_TRGB = 20.0 ± 1.6 Mpc.

Clearly, additional distance estimates to the Antennae (e.g., from Cepheids, planetary nebulae, etc.) will be very valuable. However, for the moment we see no reason for adopting any distance shorter than 20 Mpc. Given the concordant new D_SN Ia = 22.3 ± 2.8 Mpc and recession-velocity-based D_flow = 22.5 ± 2.8 Mpc, both supported by our new, preliminary D_TRGB = 20.0 ± 1.6 Mpc, we recommend using a conservative, rounded value of D = 22 ±  3 Mpc as the best currently available distance to the Antennae.

We thank David Murphy for his efforts in building instruments for the CSP, John Tonry for his flow-model software and advice, and Claudia Maraston for helpful discussions. This research has made use of the NASA/IPAC Extragalactic Database, which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with NASA. M.H. and G.F. acknowledge support from the Millennium Center for Supernova Science through grant P06-045-F funded by "Programa Bicentenario de Ciencia y Tecnología de CONICYT" and "Programa Iniciativa Científica Milenio de MIDEPLAN." M.H. acknowledges additional support from Centro de Astrofísica FONDAP 15010003 and Fondecyt through grant 1060808. Observations made under the Carnegie Supernova Project were supported in part by the NSF through grants AST 03-06969 and AST 06-07438.

The magnitudes for SN 2007sr presented in this paper are in the CSP natural system. Details of the data reduction, calibration, and filter functions and color terms defining this natural system can be found in Hamuy et al. (2006) and C. Contreras et al. (2008, in preparation), as well as on the CSP Web site: http://csp1.lco.cl/cspuser1. In this appendix, we briefly outline the natural system and present a table of the photometry for SN 2007sr.

The u'g'r'i' magnitudes are calibrated via the Smith et al. (2002) standard stars. A color sequence of these stars is used to establish color terms that transform our instrumental magnitudes to the standard system of Smith et al. However, since SNe Ia have spectra that are very different from those of normal stars and evolve with age, these color terms cannot be used to transform the SN magnitudes to the standard system. Instead, we use the color terms in reverse to transform the standard magnitudes to our natural system, and then calibrate our SN observations using these natural magnitudes. It is in this system that we present the photometry of SN 2007sr and perform our entire analysis.

The BV magnitudes are treated in a similar way, though using the system of Landolt (1992) standard stars. The JH magnitudes are calibrated using the Persson et al. (1998) standards, for which the instrument and filters used were nearly identical to those employed by the CSP and, therefore, were equivalent to our natural system.

Table 1 presents the photometry for SN 2007sr in the CSP natural system. The uncertainties listed include the usual photon statistics, as well as errors in the zero points.