THE NOVA RATE IN NGC 2403

Nova candidates were selected based on their observed brightness and the nature of their variability. Novae are transient variables with a rapid rise to peak luminosity (−10 ≲ M_V ≲ −6) followed by a slower return to quiescence with a timescale that varies significantly from nova to nova. It is often challenging to differentiate low-luminosity novae from long-period variables (LPVs), such as Mira variables, which have similar luminosities. Unlike novae, however, LPVs are sources with a limited magnitude range that can be detected multiple times in a survey having a sufficiently deep limiting magnitude and sufficiently long time coverage. Thus, to qualify as a nova, a variable source had to appear suddenly (i.e., not be detected in prior epochs) and then fade (or disappear completely) in subsequent epochs. The fields of all nova candidates were scrutinized to make sure that the nova candidates were undetectable in all epochs observed more than a year from the date of discovery. For eliminating the possibility that some of our faint nova candidates could be in fact red LPVs, we also used V-, R-, and I-band images of NGC 2403 taken with the Suprime-Cam mounted on the 8.2 m Subaru Telescope and obtained from the SMOKA (Baba et al. 2002). Using these images we rejected a few faint nova candidates, due to their presence on images obtained well before or after the Hα detection and their apparently red color, which suggests that they are red LPVs around maximum light.

For the images obtained with the BT, identification of the candidates in the crowded and complex background of NGC 2403 was expedited using the ISIS package (Alard & Lupton 1998), which aligns the images over all epochs and differences them. The resulting images are subsequently blinked by eye to reveal variable sources. Of the several transient sources discovered, two passed our criteria for inclusion as novae: N2403 2005-10a and 2005-12a. NGC 2403 is host to a number of H ii regions, which are bright in Hα and are difficult to cleanly difference with ISIS. In the attempt to recover possible candidates in these regions, as well as the nucleus of the galaxy, the IRAF median routine was performed using a variety of box sizes, with a 9 × 9 pixel box producing the cleanest images. With the bright background light of NGC 2403, blinking the median-subtracted images further enhanced the completeness of our survey. This process, however, did not produce any additional nova candidates.

The nova candidates from the INT images were identified through a visual comparison of a given image with a high-quality master image after the images had been flattened by median filtering. Master images, which were created from images separated by at least three years from the epoch being searched, were obtained under very good seeing conditions that resulted in deeper limiting magnitudes compared with the searched image. For comparison with the deepest images, we used a master image created from the combination of more than one epoch. Once transient sources were identified, their transient nature was confirmed through a comparison with all other INT images and the Subaru images. Finally, the confirmed transients found in the INT images were cross-checked against our BT images to assure that they were not visible at other epochs. A similar cross-check was performed for the BT candidates using the INT images. Although our nova search method might seem overly simplistic, we have found that it does a better job in detecting transient sources in a galaxy such as NGC 2403 where the complex structures of Hα regions render more sophisticated and automated detection methods less effective in the discovery of transient point sources.

Astrometry of novae discovered in the INT data was conducted in APHOT using positions of field stars from the UCAC2 (Zacharias et al. 2004). Derived positions of novae have uncertainties in order of tenths of an arcsecond. Astrometry of the two BT novae, as well as photometry of all novae in our survey, was carried out with the aid of the IRAF phot routine in the APPHOT package. Magnitudes for the novae were then determined through a differential comparison with respect to three secondary Hα standard stars. The secondary standard stars, N2403-S1 ($\alpha _\mathrm{J2000} = 07^{{\rm h}}36^{{\rm m}}04\mbox{$.\!\!^{\mathrm s}$}67, \delta _\mathrm{J2000} = +65\mbox{$^\circ $}34\mbox{$^\prime $}39\farcs 66$), N2403-S2 ($\alpha _\mathrm{J2000} = 07^{{\rm h}}36^{{\rm m}}11\mbox{$.\!\!^{\mathrm s}$}78, \delta _\mathrm{J2000} = +65\mbox{$^\circ $}35\mbox{$^\prime $}55\farcs 41$), N2403-S3 ($\alpha _\mathrm{J2000} = 07^{{\rm h}}37^{{\rm m}}31\mbox{$.\!\!^{\mathrm s}$}98, \delta _\mathrm{J2000} = +65\mbox{$^\circ $}38\mbox{$^\prime $}47\farcs 09$), were calibrated with respect to the photometric standard Feige 34 (Stone 1977), and found to have m_Hα = 15.18, m_Hα = 16.00, and m_Hα = 16.46, respectively. As in our previous surveys (Shafter & Irby 2001; Williams & Shafter 2004; Coelho et al. 2008; Güth et al. 2010), we have assumed a 100% filling factor for the Hα filter. This assumption allows consistency between surveys, with the recognition that the bandpass will not always be filled by a particular nova's Hα emission. For computing of offsets of particular novae from the NGC 2403 center we used $\alpha _\mathrm{J2000} = 7^{{\rm h}}36^{{\rm m}}51\mbox{$.\!\!^{\mathrm s}$}40, \delta _\mathrm{J2000} = +65\mbox{$^\circ $}36\mbox{$^\prime $}09\farcs 2$ as the reference position for the center of NGC 2403.

Table 2 contains the dates, positions, and m_Hα of all nine candidates found in our survey. Each candidate was detected in at least one subsequent epoch. Two of the candidates, N2403 2001-02a and N2403 2010-02a, were found to have very slow fade rates of greater than 6 months, indicating that these are particularly slow novae.

An estimate of the nova rate in NGC 2403 requires a knowledge of the completeness of the survey as a function of magnitude. Unlike our previous surveys (e.g., Coelho et al. 2008; Güth et al. 2010), the present study has been conducted using different telescopes, instruments, and observing conditions. As a result, the limiting magnitude of our observations varies significantly over each epoch of observation. To account for this variability the completeness of each epoch should be assessed separately. In our earlier studies, we have determined the survey completeness by performing artificial star tests using the IRAF routine addstar. Rather than conduct artificial star tests on each of the 48 nights individually (which would be impractical), we have chosen to perform the artificial star tests on a single "fiducial" image and then shift this completeness function by an amount Δm_i appropriate for images obtained in each of the remaining epochs. The value of Δm_i (=m_{lim, 0} − m_{lim, i}) is simply the difference in magnitude between the faintest star that can be reliably detected in our fiducial epoch and that in the ith epoch.

We began the completeness tests by creating artificial novae with magnitudes ranging between m_Hα = 18.0 and m_Hα = 24.0, which were then divided into 12 equally spaced 0.5 mag bins. Next, following the spatial distribution of the K-band light (from the data of Pierini et al. 1997), 100 artificial novae in each magnitude bin were randomly distributed throughout the fiducial image, which we take to be the BT image from 2005 December 28. We searched for these artificial "novae" following the same procedures as the ones employed to discover the actual novae. In practice, however, our detection criteria were somewhat different. In conducting our artificial star tests, the completeness at a given magnitude was simply taken to be the fraction of artificial novae recovered. On the other hand, for a transient source to qualify as an actual nova candidate, we required that it be ∼0.5 mag brighter than that required for a mere detection. To compensate for this difference in detection criteria, we have applied a corresponding 0.5 mag correction to each magnitude bin of the completeness function. This correction renders the effective limiting magnitude of the fiducial epoch 0.5 mag brighter than it would be if based directly on the artificial star tests. The resulting completeness function for the fiducial image, C(m), is shown in Figure 1. For this epoch, the recovered nova fraction starts to decline steeply at a magnitude of m_Hα ≃ 21.5. The completeness function for the ith epochs can then be simply estimated as C(m + Δm_i).

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We have estimated the nova rate in NGC 2403 by employing a Monte Carlo simulation similar to that we applied previously for M101 and M94 (Coelho et al. 2008; Güth et al. 2010). As just described, a difference in our approach here is that we have explicitly taken into account differences in completeness at various epochs. In the current analysis, we compare the number of novae discovered in our survey (n_obs = 9) with an estimate of the number of novae we would expect to see, N_obs, which is a function of our survey depth, temporal sampling, and of course, R, the intrinsic nova rate in NGC 2403. We begin by computing, for a wide range of possible R, a set of model Hα light curves based on randomly selected peak magnitudes and decay rates for M31 and M81 novae (Shafter & Irby 2001; Neill & Shara 2004). Then, based on the dates of our survey (see Table 1) and our adopted distance to NGC 2403 (μ₀ = 27.48 ± 0.10; Freedman et al. 2001), we computed an observed nova luminosity function for each epoch, n_i(m, R), over the complete range of possible intrinsic nova rates, R. Finally, the resulting luminosity function was convolved with the completeness function, C(m + Δm_i), appropriate for the ith epoch, and then summed over all epochs to determine the expected number of novae in NGC 2403:

$$\begin{equation} N_{{\rm obs}}(R) = \sum _{i}\sum _{m}{C(m+\Delta m_i) n_i(m,R)}, \end{equation} \tag{ 1 }$$

where Δm_i = m_{lim, 0} − m_{lim, i}. As part of a Monte Carlo process, we repeated the above procedure 10⁵ times over the range 1 < R(yr⁻¹) < 10 in steps of 0.1 yr⁻¹, and recorded the number of times that N_obs(R) matched n_obs = 9, the actual number of novae identified in this survey. After normalizing the number of matches as a function of R, we obtained the probability distribution function shown in Figure 2. The most probable nova rate is represented by the peak in the distribution at 2.0^+0.5_{− 0.3} yr⁻¹, where the error range encompasses 50% of the integrated probability distribution.

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As a consistency check, we have also analyzed the BT and INT data sets independently. Despite the small number of novae detected in the BT survey, as shown in Figure 3, the two runs yielded consistent results with the BT and INT surveys giving nova rates of 2.0^+0.8_{− 0.4} and 1.8^+0.6_{− 0.2} novae per year, respectively.

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In addition to our Monte Carlo calculation, we have also made an estimate of the nova rate using a mean nova lifetime method, which is similar to the method first employed by Zwicky (1942) to determine extragalactic supernova rates. This method, which has been described in several previous efforts to determine extragalactic nova rates (e.g., Shafter 2008, and references therein), suffers from the major drawback that it requires the adoption of a specific limiting magnitude for the survey. The method implicitly assumes that all novae brighter than the limiting magnitude are discovered, while all novae fainter than the limiting magnitude are missed. This is clearly not the case as demonstrated by our artificial star tests (see Figure 2). In addition, the method implicitly assumes that there is no variation in the limiting magnitude from epoch to epoch.

In order to correct these limitations, we have modified the traditional mean nova lifetime calculation as follows. In the case of multi-epoch surveys where the limiting magnitude varies with epoch, the nova rate, R, in the surveyed region can be expressed as

$$\begin{equation} R = 2.0 \times \frac{\sum _i n_i (M < M_{c,i})}{T_{e}}, \end{equation} \tag{ 2 }$$

where n_i(M < M_{c, i}) is the total number of novae observed in the ith epoch that are brighter than the absolute magnitude M_{c, i} where 50% of the novae are expected to be recovered, and T_e is the "effective survey time." The effective survey time depends both on the mean nova lifetime, τ_{c, i}, which is defined as the length of time a typical nova remains brighter than the limiting absolute magnitude of the ith epoch, and the frequency of sampling in the survey. We have

$$\begin{equation} T_{e} = \tau _{c,1} + \sum _{i=2}^{n}\min (t_{i} - t_{i - 1},\tau _{c,i}), \end{equation} \tag{ 3 }$$

where t_i is the time of the ith observation. Based on observations from the bulge of M31, Shafter et al. (2000) have provided a simple calibrated relationship between τ_{c, i} and M_{c, i}, which we implement here:

$$\begin{equation} \log \tau _{c,i}({\rm day}) \simeq (6.1 \pm 0.4) + (0.56 \pm 0.05)\,M_{c,i}. \end{equation} \tag{ 4 }$$

Values of M_{c, i} corresponding to 50% completeness at a given epoch have been determined using the completeness functions described in Section 3.1, taking μ₀ = 27.48 ± 0.10 (Freedman et al. 2001), and assuming a foreground Galactic extinction of A_B  =   ∼0.17 mag (Schlegel et al. 1998). The effective survey time was then calculated using the survey dates provided in Table 1, coupled with Equations (3) and (4). We find T_e = 3466 ± 36 days. Noting that eight of the nine novae discovered satisfy the condition that M < M_{c, i} at the time of discovery, Equation (2) then yields a nova rate of 1.7 ± 0.6 yr⁻¹. Given the uncertainties inherent in this method, the nova rate agrees reasonably well with the value determined in the more sophisticated Monte Carlo calculation.

To compare nova rates between different galaxies, it is necessary to normalize the rates by the luminosity of the galaxy. Typically, the rates are normalized by the integrated infrared K-band luminosity, which provides a better tracer of the mass in stars than does visual light. The resulting K-band LSNR, ν_K, is usually parameterized as the number of novae per year per 10¹⁰ L_{☉, K}.

The K-band luminosity of NGC 2403 has been determined using the integrated K-band magnitude of 6.19 ± 0.04 measured in the Two Micron All Sky Survey's (2MASS) Large Galaxy Atlas (Jarrett et al. 2003). At the distance of N2403, a nova rate of 2.0^+0.5_{− 0.3} yr⁻¹ yields ν_K = (2.5 ± 0.7) × 10⁻¹⁰ L_{☉, K} yr⁻¹. The LSNR of NGC 2403 is typical of those of other galaxies with measured nova rates (e.g., see Güth et al. 2010), and is consistent with that of the similar Hubble type galaxy, M33, where ν_K = (2.17 ± 0.89) × 10⁻¹⁰ L_{☉, K} yr⁻¹ (Williams & Shafter 2004).

In Figure 4, we have plotted the positions of all nine nova candidates discovered in our overall survey over an image of the galaxy from the BT observations. To further explore the spatial distribution of the novae, we have used the K-band photometry of Pierini et al. (1997) to compute the radii of the isophotes that pass through the nova positions. The cumulative distribution of the nova isophotal radii is compared with the cumulative distribution of the galaxy's K-band light in Figure 5. The integrated K-band light falls off somewhat more rapidly than the observed nova distribution. A Kolmogorov–Smirnov (K-S) test shows that there is a 25% chance that the distribution would differ by as much as observed if they were drawn from the same parent distribution (i.e., if the nova frequency was proportional to the surface brightness of the galaxy). Thus, it is possible that the nova distribution is incomplete in the inner regions of the galaxy where the background is particularly bright and inhomogeneous.

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