STAR FORMATION EFFICIENCY IN THE BARRED SPIRAL GALAXY NGC 4303

The single-dish NRO45 observations were carried out in 2008 March at NMA. The 25 beam array, BEARS (Sunada et al. 2000), consists of double-sideband (DSB) superconductor-insulator-superconductor (SIS) receivers on a 5 × 5 grid with a separation of ≈411 at 115 GHz. We used the digital auto-correlator for the NRO45 (Sorai et al. 2000) with a bandwidth of 512 MHz (∼1340 km s⁻¹) and 500 kHz resolution (1.3 km s⁻¹ at 115 GHz).

The chopper wheel method was used for atmospheric and antenna ohmic loss corrections and to calibrate the antenna temperature in the double-sideband (DSB) T*_A(DSB). A typical system temperature T_sys was 300–400 K in the DSB during our observations. T*_A(DSB) was converted to the single-sideband (SSB) temperature T*_A(SSB) by applying scale factors (hereafter, we use T*_A to refer to T*_A(SSB)). The scale factors were measured by comparing images of the Orion IRc2 region in the CO (J = 1 − 0) line obtained using BEARS and the single-beam SSB receiver S100. The main beam efficiency of NRO45 was η_MB = 0.30 at 115 GHz. The main beam temperature is calculated as T_MB = T*_A/η_MB.

The telescope pointing was checked roughly every 30 minutes by observing the nearby SiO maser source R-Crv with another SIS receiver, S40 near 40 GHz. The standard deviation of the pointing offset between the optical axes of S40 and BEARS was 087, which is measured by the observatory. The pointing error was less than 6'' during our observations. We mapped the 8' × 8' region centered on NGC 4303 with the OTF-observing mode (Sawada et al. 2008), which corresponds to a 37 kpc × 37 kpc area at the distance of NGC 4303. This area covers the optical extent of the galaxy. We alternated between continuous scans in R.A. and decl., as systematic noise appears dominantly along the direction perpendicular to the scan, which causes it to cancel out when the scans are combined. The 25 beams draw a regular 5'' stripe in a single scan, which is finer than the Nyquist spacing of the 15'' NRO45 beam—no spatial information is missed, which is critical in producing good u–v coverage and in combining with CARMA data. We construct data cubes only for the 5' × 5' area covered by all 25 beams (Figure 1).

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We used the data reduction package Nobeyama OTF Software Tools for Analysis and Reduction (NOSTAR) developed at NRO (Sawada et al. 2008). After the DSB to SSB conversion, we subtracted spectral baselines with a first-order polynomial fit and flagged bad integrations. The R.A. and decl. scans provide data points roughly along a 5'' lattice. We used a spheroidal function to regrid them onto a regular grid to produce an integrated data cube. The spheroidal function has low sidelobes in the Fourier domain and is advantageous in deconvolving the map to produce u − v data. The convolution smears out the resolution of the map produced by the 15'' NRO45 beam to 221. We produced separate data cubes for the scans taken in the R.A. and decl. directions and combine them using the basket-weave method in NOSTAR. Lower weights were applied to the data at small wave-numbers in the scan directions in the Fourier domain, which significantly reduces the systematic noise in the combined map.

The final data cube has a spatial resolution of 221 and a pixel scale of 75, which is the half-size of 15'' NRO45 beam. The rms noise is 75 mK at the velocity resolution of ΔV = 2.6 km s⁻¹.

We observed the central 23 region of NGC 4303 with CARMA in the C-configuration (2007 October and November) and in the D-configuration (2008 June). CARMA is a 15-element array, which consists of nine 6.1 m antennas (formerly BIMA) and six 10.4 m antennas (formerly OVRO). The angular resolution and baseline coverage of C-configuration (D-configuration) are 2'' (5'') and 26–370 m (11–148 m). The spatial resolution corresponding to the minimum baseline (11 m) is 49''. We adopted a 19-point hexagonal mosaic pattern with 30'' spacing (i.e., the Nyquist spacing of a 10.4 m primary beam; Figure 1). We used a 3 mm SIS receivers, and digital correlators with three bands, each of which has 62 MHz of bandwidth in an SSB with 977 kHz resolution (2.5 km s⁻¹ at 115 GHz).

The bright quasar, 3C273, was observed for bandpass and gain calibrations. We observed it roughly every 20 minutes to calibrate for atmospheric and instrumental gain variations. We corrected the telescope pointing by observing 3C273 with the 3 mm receiver. We frequently monitored and corrected the pointing during tracks, using the optical pointing method developed by Corder (2008), which involves observing bright optical stars close to 3C273 every gain calibration cycle (around 20 minutes). The pointing offset vector between the radio and optical pointings was measured at the beginning of the observations.

We used the data reduction package MIRIAD (Sault et al. 1995) for calibration and data analysis. The rms noise level of the CARMA data is 43 mJy beam⁻¹ in a channel of ΔV = 2.6 km s⁻¹. The synthesized beam size is 31 × 25.

We combined CARMA and NRO45 data in the Fourier domain as done in Koda et al. (2009) and Kurono et al. (2009). The NRO45 provided the short-spacing data which filled the central hole in the CARMA u–v coverage. The combined image achieved higher angular resolution than the NRO45 map and recovered the flux missing in the CARMA map.

By utilizing MIRIAD ⁵ and new routines that we developed, we combined NRO45 and CARMA data in the following way.

• 1.  
  Deconvolution of single-dish map with single-dish beam. The point-spread function (PSF) of the NRO45 map is a convolution of the NRO45 beam pattern and the spheroidal function that we applied to regrid the data points and create the final data cube. The map should be deconvolved by the PSF before being Fourier transformed to the u–v plane. The NRO45 beam size is Gaussian with an effective beam size of 221.
• 2.  
  Multiplying dummy 2' Gaussian primary beam. This step produced the same data structure for the single-dish data as is used by the interferometer data in order for the files to be read into MIRIAD. We used a 19 point hexagonal mosaic technique in our CARMA observations, so the NRO45 map was divided into 19 smaller maps corresponding to CARMA's mosaic points. The pseudo-primary beams were multiplied by each of the 19 maps to mimic CARMA observations. CARMA has three types of primary beam pattern with an FWHM of 64'' for 10.4 m–10.4 m, 85'' for 6.1 m–10.1 m, and 115'' for 6.1 m–6.1 m at 115 GHz. To mimic this behavior, we applied a Gaussian primary beam with an FWHM of 2' to the deconvolved NRO45 map at each of the 19 pointings and produced 19 maps. The Fourier transformations of these maps are the u–v data we need (see step 4).
• 3.  
  Determining weightings. The relative weighting of NRO45 and CARMA data changes the synthesized beam pattern. By changing the weighting, we can control the sidelobes of the synthesized beam and the noise level. This is similar to the conventional weighting schemes (e.g., natural and uniform weighting or robust parameter). We decided to use the weighting that minimized the sidelobes.
• 4.  
  Constructing visibility data from NRO45 data. All of the visibility data of NRO45 are built after applying the relative weight balance between the visibility data of NRO45 and CARMA (Kurono et al. 2009). We made 57 visibility data sets, i.e., for 19 pointings × 3 primary beams. All 57 NRO45 visibility data sets are concatenated to produce the final NRO45 u–v data.
• 5.  
  Imaging. We obtain the combined data cube by adding together the visibility data sets from NRO45 and CARMA, and by Fourier transforming the result, we created a combined image. The total flux of the combined image is similar to that of the NRO45 image. The rms noise of the combined cube is 34 mJy beam⁻¹ with ΔV = 2.6 km s⁻¹. The synthesized beam is 32 × 32.

Bright CO emission is detected throughout the disk of NGC 4303, even in the inter-arm region in NRO45 map (Figure 2(a)). On the other hand, the CARMA map shows emission only from a compact component in the nuclear region and the spiral arms (Figure 2(b)). The combined data map clearly shows strong CO emission in the nucleus, the bar, and the disk region along the two arms (Figure 2(c)). A comparison of the total flux in the NRO45, CARMA, and combined images clearly shows that the missing flux has been completely recovered (Table 3).

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Table 3. NRO45, CARMA, and Combined Data Results

Parameters	NRO45	CARMA	Combined Data
Velocity resolution ΔV	2.6 km s−1	2.6 km s−1	2.6 km s−1
The rms noise in a channel	73 mK	43 mJy beam−1	34 mJy beam−1
The rms noise in an intensity map	1.5 K km s−1	810 mJy beam−1 km s−1	710 mJy beam−1 km s−1
Beam/Synthesized beam size	221	31 × 25	32 × 32
Total flux	2.8 × 103 Jy km s−1	9.8 × 102 Jy km s−1	2.9 × 103 Jy km s−1

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We obtained archival Hα (Knapen et al. 2004) and K-band (Möllenhoff & Heidt 2001) images from the NASA Extragalactic Database (NED⁶) and a 24 μm image (P.I.: Kotak) from the Spitzer Space Telescope data archive using the Leopard software. The retrieved 24 μm image suffered from residual sky background emission, which we subtracted using the Image Reduction and Analysis Facility (IRAF ⁷) package.

UV photons from recently formed, young, massive stars primarily ionize the surrounding gas (H ii regions) or heat dust grains (thermal radiation). Thus, the combination of Hα and 24 μm dust continuum emissions traces the SFR fairly accurately (Calzetti et al. 2007; Kennicutt et al. 2007). The SFR is calculated using the formulae from Kennicutt et al. (2007) and Calzetti et al. (2007), namely

$$\begin{eqnarray} \mbox{SFR} \mbox{($M_{\odot }$ yr$^{-1}$)} &=& 7.9 \times 10^{-42} L(\mbox{H$\alpha $})_{\rm corr} \mbox{(erg s$^{-1}$)}\nonumber \\ &=& 7.9 \times 10^{-42}(L(\mbox{H$\alpha $})_{\rm obs}\nonumber\\ &&+ (0.031 \pm 0.006) L(24\, \mu \rm m)) \mbox{(erg s$^{-1}$)}, \quad\ \ \ \end{eqnarray} \tag{ 1 }$$

where L(Hα) and L(24 μm) are the Hα and 24 μm luminosities. From the Hα and 24 μm images, we found that Hα emission defined the sites of star-forming regions very well, although it does not quantitatively trace the SFR. Since the Hα image has a much higher resolution (15) than the 24 μm image, we use the Hα image in discussing the offsets between star-forming regions and parental gas qualitatively. For quantitative measurements, we convolve the Hα data and smooth the Hα and CO images to match the spatial resolution of the 24 μm image (6'' ∼ 500 pc). We clip the SFR and CO data at the 2σ rms noise level. The SFR map is shown in Figure 3 (left).

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Molecular gas distributions in barred spiral galaxies have been studied by many authors, from high resolution observations of central bars (e.g., Kenney et al. 1993; Ishizuki 1999; Sakamoto et al. 1999a, 1999b) to lower resolution observations of larger disks (Sheth et al. 2000). The gas distribution in NGC 4303 is typical among barred spiral galaxies; it shows two narrow ridges (namely, offset ridges) at the leading side of the bar, and spiral arms in the outer part, and coincides with dust lanes in optical images. Figure 2(d) shows an overlay of CO contours on an archival HST F450 band image (P.I.: Smartt).

The CO emission is concentrated in the central 40'' (∼3.2 kpc), which includes the offset ridges and circumnuclear disk. In particular, the circumnuclear disk shows a circular structure (r = 44 ∼ 350 pc), extending from 1541.3 km s⁻¹ southeast of the nucleus to 1611.5 km s⁻¹ to the northwest in the velocity channel maps (Figures 4 and 5). This structure is called a ring or part of the offset ridges (i.e., inner spiral arms; Schinnerer et al. 2002; Koda & Sofue 2006). The circumnuclear disk hosts a spiral arm in the UV continuum image (Colina et al. 1997), and the CO ring/spiral arm structure is offset from the UV spiral arm.

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Low-level CO emission is also present in the space outside of the offset ridges (namely, inter-offset ridge regions). Strong concentrations of gas exist at the outer ends of the offset ridges (Figure 2(c)). Molecular spiral arms extend from those end points toward the outer regions. The map resolves the widths of the offset ridges of the bar and the outer spiral arms at high resolution. The surface densities of the gas in the offset ridges and outer spiral arms are not similar at the high resolution, differing by factor of ∼2.

We derive the inclination and position angle of the galaxy using the task GAL in the AIPS data reduction package. The results are shown in Table 1. We use these values for the rest of our analysis.

We estimate the gas mass from the CO-integrated intensity S_CO (see Figure 2(c)), using the Galactic I(CO)-to-N(H₂) conversion factor X_CO. We adopt the standard value X_CO = 2.0 × 10²⁰ cm⁻² (K km s⁻¹)⁻¹ (Strong 1987). The gas mass is then

$$\begin{eqnarray} M_{{\rm H}_2} &=& 1.0 \times 10^4 \left(\frac{S_{\rm CO}}{\mbox{Jy km s$^{-1}$}} \right) \left(\frac{D}{\mbox{Mpc}} \right)^2\nonumber\\ &&\times\left[ \frac{X_{\rm CO}}{3.0 \times 10^{20}\, \mbox{cm$^{-2}$ (K km s$^{-1}$)$^{-1}$}} \right] M_{\odot }, \end{eqnarray} \tag{ 2 }$$

where D is the distance to the galaxy, which assumed to be 16.1 Mpc (Ferrarese et al. 1996). The total gas mass of the galaxy is calculated from the NRO45 map to be 5.3 × 10⁹ M_☉. The CARMA mosaic covered the circular area with a radius of 80''. The enclosed mass is 3.4 × 10⁹ M_☉. The average gas surface density in the central 160'' of the molecular disk is 36 M_☉ pc⁻².

Both CO and Hα emission appear clearly along stellar spiral arms, and the Hα arms are offset toward the leading side of the CO arms. Similar offsets are evident between CO and 24 μm emission. The 24 μm emission is at the leading side of the CO emission. These offsets are due to the delay of star formation from the accumulation of gas in the spiral arms (Egusa et al. 2004); approximately, an offset would be (Ω − Ω_p)t_SF, where Ω and Ω_p are the angular speed of the gas and pattern speed of spiral arms, respectively, and t_SF is the timescale of star formation. The sites of star formation are resolved in our observations. The analysis of local SFR and efficiency should take this into account, since the parental gas and star-forming regions would not be correlated at the high spatial resolution. This means that the KS law breaks down at this resolution. We need to smooth the data before characterizing the spatial variation of the SFE in Section 4.2.

Figures 6(a) and (b) show a close-up of the offset between CO (black contours) and Hα emissions (gray scale). In the upper panels, the arrows indicate the direction of gas flow, assuming pure azimuthal rotation and a time lag between star formation and gas accumulation in spiral arms. Figure 6(c) shows the phase diagrams of CO (contours) and Hα (gray scale). Again, the Hα emission is found predominantly at the leading side of the CO spiral arms over the entire range of radii (over 40'', ∼3.1 kpc).

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The offsets between the CO and Hα arms range from 0 to 1 kpc, with an average of ∼500 pc at radius, r ⩾ 40'' (∼3.1 kpc; i.e., the area we define as outer spiral arms in Section 4.4). Thus, we will smooth the data to the spatial resolution of ∼500 pc for later discussions; it also especially affects the analysis of SFE. We will discuss this further in Section 4.4.

Egusa et al. (2004) introduced a new method to estimate the timescale of star formation using these offsets, measuring the offset/time lag between gas accumulation and star formation. Tamburro et al. (2008) applied this method to H i and 24 μm data. Their offsets ⩽250 pc (calculated from their paper) are translated to the timescale of ∼1 myr. On the other hand, Egusa et al. (2009) used CO and Hα data for NGC 4303 and derived the offsets of 700–1000 pc and the timescale of ∼10 myr, an order of magnitude longer than the Tamburro et al. (2008) results. Our offsets are closer to those in Egusa et al. (2009). To understand this discrepancy, we compared 24 μm and Hα images and found no significant offsets between the two. Thus, Hα traces the locations of star-forming regions as well as 24 μm. The discrepancy may come from the difference of CO and H i. If the H i emission traces the gas dissociated by star formation, and not the natal gas for star formation, it explains the small offsets between H i and 24 μm emissions. Our simple analysis with CO and Hα/24 μm favors the longer star formation timescale of Egusa et al. (2009) in the case of NGC 4303. These results should be confirmed with a larger sample of galaxies.

We compare the SFR and SFE between the bar and outer spiral arms, as well as within other components (i.e., circumnuclear disk, inter-arm regions), at the spatial resolution of ∼500 pc. The SFE is the ratio of the SFR to the gas mass within an aperture, namely

$$\begin{equation} \mbox{SFE} (\mbox{yr$^{-1}$}) = \frac{\mbox{SFR} ({M}_{\odot }\, \mbox{yr$^{-1}$})}{M_{{\rm H}_2} ({M}_{\odot })}, \end{equation} \tag{ 3 }$$

where $M_{{\rm H}_2}$ is the molecular hydrogen gas mass. We calculate the SFR and gas mass within an aperture and use the averaged parameters to derive the SFE. We smooth our CO and Hα images to the same resolution as the 24 μm image (6'' resolution) in order to correlate the parental gas and star-forming regions. This resolution corresponds to a linear size of ∼500 pc, similar to the linear resolution at which Kennicutt et al. (2007) find the correlation between gas surface density and associated SFR.

A SFR map is shown in Figure 3(a). High SFRs are apparent in intense star-forming regions which are sparsely distributed along the spiral arms, as well as in the circumnuclear disk. However, SFRs are lower in the bar, even though the gas surface densities along the bar offset ridges are as high as those in the spiral arms. The low SFR in the bar has been suggested qualitatively by previous studies (most systematically by Sheth et al. 2002), and we discuss this quantitatively in the following sections.

Figure 3(b) shows a map of the SFE. Low SFEs are seen in the bar (especially around the offset ridges) and in the inter-arm regions. Exceptionally high SFEs appear at the leading side of the CO arms. This indicates that the offsets between Hα and CO emission are not fully smoothed out even at the resolution of ∼500 pc (see Section 3.2), even though the parental gas shows a fair correlation with SFR (Kennicutt et al. 2007).

We first compare the gas surface density ($\Sigma _{{\rm H}_2}$), area-averaged SFR (Σ_SFR), and SFE between the bar and spiral arms on the basis of azimuthal averages (Figure 7). The average values are derived in 1 kpc (128) width annuli, which is enough to average out the spatial offsets (see Section 3.2). The 1 kpc resolution can still separate the bar, spiral arms, and nucleus without significant contamination from each other. Figure 8(a) shows the definitions of nucleus, bar, and outer spiral arms. The nucleus might include a portion of the bar region; however, we are mainly interested in the differences between the bar and spiral arms, so it does not affect our analysis. We will comment on the properties of the circumnuclear star formation in Section 4.4.

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Figure 7 shows the radial distributions of the area-averaged SFR Σ_SFR (a), gas surface density $\Sigma _{\rm H_2}$ (b), and SFE (c). The definitions of the nucleus, bar, and spiral arms are indicated with arrows in Figure 7(a). SFE drops abruptly from the circumnuclear disk to the bar and increases toward the spiral arms (Figure 7(c)). Quantitatively, the average SFE is about twice as high in the spiral arms as in the bar.

The SFE (Equation (3)) is a correlation between star-forming regions and their parental gas. We have resolved the scale where the star-forming regions and gas are spatially separated; therefore, we have to smooth the data to derive an SFE with physical importance. Kennicutt et al. (2007) found a good correlation between the surface densities of SFR and gas mass at the 500 pc scale. This is similar to the typical separation of Hα and CO emission that we see in NGC 4303 (Section 4.1). We smooth Hα and our CO images to the scale of the Spitzer 24 μm image (6''; ∼500 pc) and compare local SFR and SFE between the bar and spiral arms at this scale.

Four regions (i.e., bar, spiral arms, inter-arms regions, and circumnuclear region) are defined as in Figure 8(b). The circumnuclear region is a 6'' diameter circle (∼500 pc), based on a near-infrared (NIR) image of Pérez-Ramírez et al. (2000). We define the bar as an ellipse with the deprojected major and minor axis diameters of 40'' × 26'' (3.1 × 2.0 kpc), based on a K-band image. This definition yields an ellipticity similar to the one derived by Laine et al. (2002) based on a near-infrared H-band image and a major axis diameter consistent with the determination of Schinnerer et al. (2002). The spiral arms and inter-arm regions are separated by eye using the K-band image. Figure 8(b) shows our definitions overlaid on the K-band image.

Figure 9 shows the histograms of $\Sigma _{{\rm H}_2}$ (left), Σ_SFR (center), and SFE (right) for the spiral arms and bar (top and bottom). High gas surface density regions are present only in the bar, but not in the spiral arms. However, high SFR and SFE regions appear only in the spiral arms and are absent in the bar. Therefore, high SFR and SFE are evident in the spiral arms in the local average, as well as in the azimuthal average.

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We calculate the excesses of SFR and SFE in each region with respect to the averages over the entire disk excluding the nucleus (Table 4). The SFR and SFE in the bar are 10% and 30% smaller than the disk averages, respectively. Star formation activity in the bar is low compared to the entire disk. On the contrary, the SFR and SFE in the spiral arms are about 10% and 40% higher than those over the disk, respectively. Active star formation preferentially occurs in the spiral arms. SFR and SFE are about 30% and twice as high in the spiral arms as in the bar. The results confirm quantitatively the notion that star formation in bar is less than in spiral arms.

The effect of the spatial offsets between Hα and CO emissions is significantly reduced by the smoothing to estimate local SFE (∼500 pc resolution). However, it still shows some residual effects in SFEs, since the average of this offset is also ∼500 pc. If the offset is below 500 pc, parent GMCs and star-forming regions exist within our resolution for SFE discussions. If the offset is above 500 pc, we cannot recognize both parent GMCs and star-forming regions within the resolution. SFEs obtained in such a region will not fairly represent the local SFE. This produces SFEs above 10^−7.8 yr⁻¹ are the artifacts (Figure 3).

The SFR and SFE are the highest in the nuclear region. The azimuthal averages of Σ_SFR and SFE (Figures 7(a) and (c)) clearly show this tendency, being about 5 times and twice higher than the disk averages, respectively. The locally averaged SFE in the nucleus is also high. The locally averaged SFR and SFE are higher by a factor of 6.9 and 1.3, respectively than those of the entire disk region.

We, however, note that NGC 4303 is suggested to harbor an active galactic nucleus (AGN) in addition to a starburst (e.g., Kennicutt et al. 1989; Colina et al. 1997; Tschöke et al. 2000), and our analysis could suffer from AGN contamination. We checked the spectral energy distribution of the nucleus in 1–24 μm, using the archival data (Catalog of Infrared Observations;⁸ Gezari et al. 1993, 2000). We found a flat spectrum from 10 to 24 μm, similar to AGN spectra (Alonso-Herrero et al. 2003). Thus, 24 μm emission from the nucleus is dominated by the AGN. This indicates that the much higher values of SFR in the nucleus are overestimated.

We adopt the standard conversion factor X_CO. However, there are some arguments supporting a metallicity-dependent X_CO (e.g., Arimoto et al. 1996; Boselli et al. 2002). NGC 4303 has a relatively large radial metallicity gradient (Skillman et al. 1996), which may affect the result that SFE is low in the bar (inner disk) and high in spiral arms (outer disk). We confirmed as follows that this does not change the results (except for the nucleus, where metallicity is exceptionally high).

The average metallicities (12 + log [O/H]) in the nucleus, bar, and spiral arms (the definition is same as in Figure 8(b)) are 9.5, 9.3, and 9.2 from Skillman et al. (1996). If we adopt the X_CO–metallicity relation of Boselli et al. (2002), the gas surface densities decrease, and the average SFEs increase (by a factor of 4.2, 2.3, and 1.8), respectively. The difference in SFE between the bar and spiral arms is reduced only by 30%. This is too small to change the trend that the SFE is roughly a factor of two higher in spiral arms than in bar. A significant effect appears only in the nucleus, where a much higher metallicity results in a significantly higher SFE (a factor of two to four higher than that from the standard X_CO).

Figure 10(a) compares our result with those from previous studies. The solid black line is the result of Kennicutt (1998); N = 1.4 ± 0.15. They calculated gas surface densities with CO data (gas density), and H i and CO data (total gas density). The gray region indicates the scatter in Kennicutt (1998, their Figure 9). Dashed lines are the fit in Kennicutt et al. (2007); the large and small dashes are the fits for H i and CO (N = 1.56 ± 0.04) and for CO-only (N = 1.37 ± 0.03), respectively. The dotted line is from Bigiel et al. (2008) and is for N = 0.96 ± 0.07. Our result, N = 0.67, is closer to Bigiel et al. (2008), than to Kennicutt (1998), though it is smaller than the linear correlation N = 1.

Our data lie roughly in the range of Kennicutt (1998; gray region), although some data points deviate from the exact range. The deviations occur on the spiral arms, where the offsets between the gas and star-forming regions are large (Section 4.4). At the 500 pc resolution, the KS law is present, but suffers slightly from the offset effect. Two types of scatter appear in Figures 10(a) and (b). One is the scatter of NGC 4303 itself, i.e., its deviation from the average of galaxies, and the other is within the disk of NGC 4303. The distribution of our points is concentrated in a small region, and the scatter within the galaxy is smaller than that of Kennicutt (1998). Therefore, the scatter among galaxies seems dominant. Overall, NGC 4303 fits on the plot of Kennicutt (1998), but has slightly higher SFE than the average.

Both $\Sigma _{{\rm H}_2}$ and Σ_SFR show one order of magnitude scatters in Figure 10(b), which is consistent with the results of Bigiel et al. (2008, their Figure 4). Therefore, an order of magnitude scatter of star formation activity is common at a sub-kpc scale. Leroy et al. (2008) showed that SFE varies strongly with local conditions. Since the KS law breaks down at the scale of a few 100 pc, we could attribute the variation of SFE to local environments at the scale of a few 100 pc. One of the key environmental factors might be galactic dynamics (e.g., spiral arms).

We verify a scatter of NGC 4303 itself among nearby galaxies, i.e., a scatter from the KS law. Rough estimation of scatter shows that our results are a factor of ∼5 higher than that of Kennicutt (1998). However, the KS plot has a ± 1 order of magnitude scatter, as we discussed in Section 5.1. Even though our data are the fit by Kennicutt (1998), they are still within the scatter (gray region).