THE CHANDRA LOCAL VOLUME SURVEY: THE X-RAY POINT-SOURCE POPULATION OF NGC 404

NGC 404 was observed during Chandra X-Ray Observatory Cycle 12 on 2010 October 21–22 for 97 ks using the ACIS-S array (Obs. ID 12339), with the nucleus nearly centered on the nominal aim point of the S3 chip. We additionally utilize archival observations: NGC 404 was observed on 1999 December 19 (Obs. ID 870) for ∼24 ks and on 2000 August 30 (Obs. ID 384) for ∼2 ks, both using the ACIS-S array. Table 1 summarizes the Chandra observations used in this work.

Table 1. Summary of Chandra Observations

Obs. ID	Date	Exposure (ks)	R.A. (J2000)	Decl. (J2000)
(1)	(2)	(3)	(4)	(5)
384	1999 Aug 30	1.8	01h09m2690	+35d43m0300
870	2000 Dec 19	24	01h09m2690	+35d43m0340
12239	2010 Oct 21–22	97	01h09m2700	+35d43m0400

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Data reduction was performed using CIAO v4.3 and CALDB v4.4.2 using standard reduction procedures. All observations were reprocessed from evt1 level files using the CIAO routine acis_process_events with default parameters. The data were corrected for bad pixels/columns, charge transfer inefficiency, and time-dependent gain variations, and we removed the pixel randomization. The event list was then filtered for grades = 0, 2, 3, 4, 6, status = 0, and the pipeline-provided good time intervals. We checked for background flares by creating a background light curve and the source-free event lists on the S3 chip in each observation, and applied a sigma-clipping algorithm to remove time intervals with count rates more than 3σ from the mean. Exposure maps and exposure-corrected images were made using fluximage and observations were then merged using reproject_image. Spectral weights used for the instrument maps were generated assuming a power-law spectrum with Γ = 1.9 (appropriate for both XRBs and background AGNs), and the average foreground column density N_H = 5.13 × 10²⁰ cm⁻² (Kalberla et al. 2005) was used.

We created images in the following energy bands (keV): 0.35–8.0, 0.35–1.0, 1.0–2.0, 2.0–8.0 with bin sizes of 1, 2, 3, and 4. A composite X-ray image of NGC 404 is shown in Figure 1; soft X-rays (0.35–1.0 keV) are displayed in red, medium-hard X-ray emission (1–2 keV) is shown in green, and hard X-rays (2–8 keV) are shown in blue. The optical extent of the galaxy is superimposed in white. The combined exposure map for all three NGC 404 observations is shown in Figure 2.

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Three HST fields were used to search for optical counterparts for each of our X-ray sources. One field (labeled "DEEP") was taken as part of the Advanced Camera for Surveys (ACS) Nearby Galaxy Survey Treasury (ANGST, GO-10915; Dalcanton et al. 2009), while the other two shallowered fields (labeled "NE" and "SW") were obtained as part of GO-11986. Details of the HST data acquisition and data reduction are provided in Williams et al. (2010). Figure 3 shows the locations of our HST fields and Chandra X-ray point sources superimposed on a Galaxy Evolution Explorer (GALEX) image of NGC 404.

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To identify candidate optical counterparts to our Chandra X-ray sources, we place both the Chandra and HST fields onto the International Celestial Reference System (ICRS) by finding matches (within ∼5'') between stars or background galaxies in the Two Micron All Sky Survey (2MASS) Point Source Catalog (Skrutskie et al. 2006). We were able to identify 3–4 bright 2MASS sources per field which matched either a Chandra X-ray source or optical foreground star or background galaxy. The plate solutions were computed using the IRAF task ccmap, with rms residuals typically less than a few hundredths of an arcsecond in both right ascension and declination. The total alignment error applied to each X-ray source within a given field were computed by summing the Chandra and HST rms errors in quadrature. The results of our astrometry are summarized in Table 2.

Table 2. Alignment of Chandra and HST Observations to 2MASS

Observatory	Field	No. of Sources Used	R.A. rmsa	Decl. rmsa	No. of X-Ray Sources
		for Alignment
(1)	(2)	(3)	(4)	(5)	(6)
Chandra	merged	3	0049	0087	74
HST	DEEP (Obs. ID 10915)	3	0066 (0082)	0030 (0042)	3
HST	NE (Obs. ID 11986)	4	0041 (0064)	0017 (0034)	5
HST	SW (Obs. ID 11986)	4	0088 (0100)	0001 (0087)	3

Note. ^aThe rms values listed are for each individual HST field. In parentheses we list the combined rms value for each field, obtained by adding the Chandra and HST rms values in quadrature.

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We employed the same iterative source detection strategy as in Paper I (see also Tüllmann et al. 2011). We present a summary of the approach here; the reader is referred to Paper I and Tüllmann et al. (2011) for details.

The CIAO task wavdetect (Freeman et al. 2002) was first used to create a list of potential source candidates to be used as input to ACIS-Extract (AE; Broos et al. 2010). AE is a source extraction and characterization tool which was used to determine various source properties (source and background count rates, detection significances, fluxes, etc.) and to generate light curves and spectra (with appropriate response matrices). We use the Poisson probability of not being a source (prob_no_source, hereafter pns) provided by AE as our threshold criteria when constructing the NGC 404 point-source catalog.

For each input source, AE creates background regions by first removing all sources from the data and then searching for the smallest circular region around each source that encompasses at least the minimum number of background counts specified by the user. We require each background area to contain at least 50 counts (Tüllmann et al. 2011 found that changing the number of background counts required from 50 to 100 does not significantly affect source properties). These circular background regions are additionally the regions used to extract background spectra. To extract the X-ray spectrum for each source, AE constructs a polygonal region that approximates the 90% contour of the Chandra-ACIS point-spread function at the location of the source. The CIAO tools mkacisrmf and mkarf are used to create appropriate response and ancillary response matrices for each source.

The initial source list generated by wavdetect was deliberately made to include many more sources (762) than we anticipated being statistically significant. We then applied the iterative procedure described in Paper I and Tüllmann et al. (2011) to remove false sources. Our final iteration required that a candidate X-ray source have pns <4 × 10⁻⁶ (see also Nandra et al. 2005; Georgakakis et al. 2008; Tüllmann et al. 2011) in any of the following energy bands: 0.5–8, 0.5–2, 2–8, 0.5–1, 1–2, 2–4, 4–8, 0.35–1, or 0.35–8 keV.

The final CLVS source catalog for NGC 404 contains 74 sources.⁶ Their positions and properties, such as detection significance (pns value), net counts, and photon fluxes (in eight different energy bands) are listed in Tables 3–6. Both Georgakakis et al. (2008) and Tüllmann et al. (2011) have found that using a pns threshold of 4 × 10⁻⁶ results in ∼0.5 false sources per megapixel. Given the survey size of our NGC 404 observations, we expect there to be ∼1.6 false sources included in our final source catalog.

Subsequent analyses in this work require sensitivity maps, which provide the energy flux level at which a source could be detected for each point in our survey area. AE provides an estimate of the photon flux for each source (flux2), which is based on the net source counts, exposure time, and the mean of the auxiliary response file (ARF) in each energy band. We convert these photon fluxes to energy fluxes assuming a power law with Γ = 1.9 that is absorbed by the Galactic column (N_H = 5.13 × 10²⁰ cm⁻²). Hereafter, we refer to this as the "standard model." Roughly 80% of our X-ray sources had their spectra automatically fit with AE (see Section 3.4), and most were consistent with a power-law model (Γ ∼ 1.7–1.9) with no absorption beyond the Galactic column, as would be expected for a population dominated by XRBs and background AGNs. We do not expect the standard model to systematically bias the log N–log S distribution toward higher or lower fluxes.

To create sensitivity maps, we calculated the number of source counts that would be required to meet our pns criteria (<4 × 10⁻⁶) for each point in the survey area. This method for generating sensitivity maps has been tested using simulated Chandra observations by Georgakakis et al. (2008). The 90% complete limiting flux in the 0.35–8 keV, 0.5–2 keV, and 2–8 keV energy bands are 6.2 × 10⁻¹⁶ erg s⁻¹ cm⁻², 1.3 × 10⁻¹⁶ erg s⁻¹ cm⁻², and 8.7 × 10⁻¹⁶ erg s⁻¹ cm⁻², respectively. At the distance of NGC 404, these fluxes correspond to luminosities of 6.3 × 10³⁵ erg s⁻¹, 1.6 × 10³⁵ erg s⁻¹, and 1.0 × 10³⁶ erg s⁻¹, respectively. Table 7 summarizes the limiting fluxes for the 70%, 90%, and 95% completeness levels for our total energy range, the soft band, and the hard band. For comparison, we additionally constructed sensitivity maps using the CIAO task lim_sens, and found the predicted limiting fluxes to be ∼30% higher than found using our pns analysis.

The full NGC 404 catalog was systematically searched for sources showing both significant short-term (i.e., variability that occurs on timescales less than the exposure time, ∼27 hr) and long-term variability in the 0.35–8 keV band. While rapid X-ray variability is routinely observed in both AGN and XRB systems (Vaughan et al. 2003), it is typically not observed in other sources of X-ray emission (i.e., SNRs). We used a Kolmogorov-Smirnov (K-S) test to compare the cumulative photon arrival time distribution for each X-ray source to a uniform count rate model. The K-S test returns the probability (denoted by ξ) that both distributions were drawn from the same parent distribution. We searched for rapid variability only in Obs ID 12239, due to its significantly longer exposure time than the archival observations. We used the three separate Chandra observations to search for significant changes in the long-term X-ray flux of each source.

Only two sources, 1 and 72, have K-S probabilities of 0.06% and 0.09%, respectively, which may be indicative of potential short-term variability. To investigate the long-term variability of each of the NGC 404 sources, we utilize the variability threshold η (as in Tüllmann et al. 2011), defined as η = (flux_max − flux_min)/Δflux, where flux_max and flux_min are the maximum and minimum observed fluxes of the source, respectively, and the flux error Δflux is calculated using the Gehrels approximation (appropriate for low-count data; Gehrels 1986). We consider any sources with η ⩾ 3 potentially variable. One source (16) in NGC 404 has η ⩾ 5 and is highly likely to exhibit long-term variability.

We also consider the possibility that the NGC 404 catalog may contain transient sources. We found 18 X-ray sources that were detected in at least one exposure, but were not detected in another exposure (despite the source's position being within the field of view). We use these non-detections to place an upper limit on the source flux at the time of the exposure; some of these sources are faint, and so may have been just below the detection limit of the shallower exposure without requiring a significant change in flux. However, seven X-ray sources exhibited a change in X-ray flux of at least an order of magnitude and had η ⩾ 3—we refer to these sources as candidate X-ray transients (XRTs). Both LMXBs and HMXBs are known to experience X-ray outbursts of this magnitude (Bozzo et al. 2008; Fragos et al. 2008; Paul & Naik 2011; Revnivtsev et al. 2011), and may have implications for the slope of the XLF (see Section 5).

Table 8 lists the variability properties for all sources in the NGC 404 catalog that exhibit some form of temporal variability. We include three potentially variable sources (sources 27, 49, and 57, noted with italics) which fall short of our definition of an XRT candidate by less than 10%. That is, if any of these three sources were to change either their lowest or highest observed fluxes by less than 10%, the fractional change in flux would be more than an order of magnitude (the typical flux error for an NGC 404 source is ∼20%–25%).

While direct, multi-wavelength detection of X-ray source counterparts provides an excellent means of discriminating between sources associated with NGC 404 and background or foreground contaminants, this approach is likely to fail when classifying faint sources. As a result, the physical nature of many faint X-ray sources in our catalog will remain ambiguous. We therefore adopt an additional, statistical approach to constrain the number of sources in NGC 404.

We construct an X-ray galactocentric profile of NGC 404 by summing number of sources detected as a function of galactocentric radius. We assign an inclination-corrected galactocentric distance to each X-ray source assuming the galaxy center is located at α₀ = 17362500, δ₀ = +35718056 (Evans et al. 2010), and i = 11° (del Río et al. 2004). The maximum radius we find for an X-ray source in our Chandra field is r = 6.1 kpc. We divide the X-ray sources into radial bins (spaced 0.7 kpc apart) based on their distance from the center of the galaxy. We use the cumulative log N–log S distribution of Cappelluti et al. (2009), corrected for the decreasing Chandra sensitivity with increasing off-axis angle, to estimate the expected contamination by background AGNs. This was done by finding the number of AGNs predicted (for the flux sensitivity of our survey) for the area spanned by each radial bin. In Figure 4, we show both a histogram of our derived galactocentric distances and the number of X-ray sources per square kiloparsec.

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The majority of the NGC 404 X-ray sources have r ≲ 2.5 kpc, and the number of X-ray sources per kpc² beyond 2.5 kpc is roughly equal to the number predicted by the AGN log N–log S distribution. We therefore expect the 29 X-ray sources with r > 2.5 kpc to be predominantly contaminating background AGNs or foreground stars, while the X-ray sources with r < 2.5 kpc are expected to be a mix of contaminants and X-ray sources associated with NGC 404. This interpretation is consistent with the observed bulge effective radius (r_e = 0.9 ± 0.4 kpc) and disk scale length (∼1.9 kpc) derived by both Baggett et al. (1998) and Williams et al. (2010).

The X-ray spectrum of a source can provide a key diagnostic for separating different populations. For example, LMXBs and AGNs are well described by power laws with photon indices ranging from Γ ∼ 1–2, and may show high levels of intrinsic absorption (i.e., in the case of obscured AGNs). Super-soft sources (SSSs) and contaminating foreground stars will exhibit significantly softer, thermal X-ray emission with plasma temperatures of a few keV or less. However, when studying XRBs at distances of a few magaparsec it is nearly impossible to constrain spectral parameters to any degree of accuracy, especially for those sources with ≲ 50 counts. The majority of NGC 404 X-ray sources fall within this low-count regime, as shown in Figure 5.

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Instead of directly measuring the X-ray spectral shape, we define hardness ratios (HRs; also called X-ray colors) to separate different populations. HRs measure the fraction of photons emitted by a source in three energy ranges: soft (S, 0.35–1.1 keV), medium (M, 1.1–2.6 keV), and hard (H, 2.6–8 keV). We evaluate two HRs for each source using the approach developed in Tüllmann et al. (2011; see also Prestwich et al. 2009). Source and background counts were determined by AE in each band, and we define a "soft" color,

$$\begin{equation} {\it HR}1 = \frac{M-S}{H+M+S}, \end{equation} \tag{ 1 }$$

and a "hard" color,

$$\begin{equation} {\it HR}2 = \frac{H-M}{H+M+S}. \end{equation} \tag{ 2 }$$

We use the Bayesian Estimation of Hardness Ratios⁷ (BEHR; Park et al. 2006) in a manner similar to that described by Tüllmann et al. (2011) and Prestwich et al. (2009) to determine the hardness ratios of the NGC 404 X-ray sources. For low-count sources (which make up the majority of the NGC 404 point-source catalog), the net counts can be negative due to fluctuations in the source and background estimates, resulting in unphysical HRs when calculated using a traditional approach. The BEHR code accounts for the fact that source and background counts are non-negative, ensuring that our approach produces physically allowable values of the HRs. In the high-count regime, the results of the Bayesian approach become equivalent to traditionally computed HRs.

For each source, the inputs are source counts, background counts, the AE "backscale" parameter (which accounts for the ratio of the source and background extraction areas and efficiencies), and a factor converting from counts to photon flux (i.e., the exposure time multiplied by the mean ARF over the extraction region in the respective energy band). The "softeff" and "hardeff" parameters take into account the variations in effective area and exposure times between the different observations, especially important considering the strong differences in ACIS filter contamination between the observations utilized in this work; we set these parameters to the exposure time multiplied by the mean ARF values computed by AE in the appropriate energy band for each observation in which the source was observed.

The BEHR code is then run twice (once for S and M, and again for S and H). For each energy band, we set the BEHR "burnin" parameter to 50,000 and the "total draws" parameter to 100,000. This provides 50,000 samples from the probability distribution for each energy band. Combining the results from the two BEHR runs, we obtain 50,000 samples from the probability distribution for the S, M, and H counts. Using these distributions, we compute 50,000 values for HR1 and HR2 for each source. Because the difference of two Poisson distributions does not follow Poisson statistics, we do not use the error estimates directly provided by these BEHR runs. Instead, the HR value is defined as the mean of the distribution, and the credible interval is evaluated based on the 68.2% equal-tail estimates (i.e., 0.682/2 of the samples have values below the lower limit, and 0.682/2 of the samples have values above the upper limit).

To aid in the interpretation of our HR calculations, we use the same X-ray color–color classification scheme developed in Paper I. We define six categories of X-ray sources: "XRB" (which is likely contaminated with background AGNs, given their X-ray similarities to LMXBs), "BKG" for likely background sources with an indeterminate spectral shape, "ABS" for heavily absorbed sources, "SNR" (although, given the morphology and SFH of NGC 404, these sources are likely to be foreground stars or SSSs, and not true supernova remnants), and indeterminate "HARD" and "SOFT" sources. Our X-ray color–color classification scheme, along with the number of sources belonging to each category, is given in Table 9. The HRs and corresponding source classification is given in Table 10, and a plot of our HR values is shown in Figure 6. Figure 6 additionally shows the agreement between the HRs and spectral fitting (see Section 3.4)—HRs provide a useful technique for identifying highly absorbed sources, sources with thermal emission, and sources with power law-like spectra. However, HRs cannot be used to separate power laws with different photon indices.

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We find ∼61% of the NGC 404 X-ray sources fall within the "XRB"-like category, and ∼20% of sources show evidence for high levels of intrinsic absorption. Only four sources (5%) are designated as "SNR"-like—one of these sources (source 65) is coincident with a foreground star (see Section 3.4). Given the latitude of NGC 404 and the small area subtended by the galaxy, these are likely foreground objects not associated with NGC 404. The remaining X-ray sources are categorized as "HARD" or "SOFT" and are likely not associated with NGC 404.

For sufficiently bright sources (≳ 50 counts), the X-ray spectrum of a source can be used to constrain the physical nature of the X-ray emission. Both XRBs and AGNs are typically described by power laws, with photon indices ranging from Γ ∼ 1 to 2. If the source is a likely XRB, the photon index can sometimes be used to constrain the nature of the compact object: NS primaries typically exhibit harder X-ray emission, with Γ ∼ 1–1.5, while BHs (which lack a solid surface) often produce Γ ∼ 2–2.5. Foreground stars will show significantly softer X-ray emission, and typically have their spectra fit with a thermal plasma.

Spectra were extracted by AE using the CIAO tool dmextract. Response products were created by AE using the CIAO tools mkacisrmf and mkarf. Due to the low number of counts found for most of the sources in our catalogs, we fit spectral models to the unbinned spectra and use C-statistics in lieu of traditional χ² statistics (see, e.g., Cash 1979; Humphrey et al. 2009). Three sources were found have more than 200 net counts in the 0.35–8 keV band; these sources are discussed in more detail below. Detailed spectral fitting was performed for the NGC 404 central engine in Binder et al. (2011).

The ungrouped spectra for 60 out of 74 sources in NGC 404 were automatically fit in AE with one of four models: a power-law model, an APEC model (Smith et al. 2001), or either a power-law or thermal model with additional absorption. The Galactic absorption was modeled with the tbabs model (Wilms et al. 2000) by freezing the Galactic N_H at 5.13 × 10²⁰ cm⁻² (Kalberla et al. 2005). In order to determine the best-fit model, models that predicted unreasonably high photon indices (Γ > 4) or plasma temperatures (kT > 6.0 keV) were rejected.

Because the C-statistic cannot be directly interpreted as a goodness-of-fit, we use a different approach to select the preferred spectral model for each source. First, we used XSPEC's goodness command to perform 5000 Monte Carlo simulations for each spectral model (power-law and thermal models, both with and without additional absorption). The goodness command simulates spectra based on the model parameters and finds the number of simulations with a fit statistic less than that found for the data. If the observed spectrum was produced by that model, the "goodness" should be ∼50%. For some sources, the choice of preferred spectral model was obvious: three of the spectral models yielded a goodness of less than ∼2%, while one model produced a goodness in the range of ∼40%–60%. In the remaining cases, no obviously preferred model was found—for these sources, we chose the simple, unabsorbed power law unless the spectrum showed indications for emission features (in which case, the unabsorbed thermal model was selected). The best-fit model and parameters for sources with greater than 50 net counts are listed in Table 11. All errors represent the 90% uncertainties.

The spectra of bright sources often require multiple component models. Three X-ray sources (1, 7, and 65, excluding the NGC 404 nucleus) have more than 450 net counts; however, none of these sources is likely to be associated with NGC 404. Sources 1 and 7 are likely background AGNs whose spectra do not require more complex models than what is presented in Table 11.

3.4.1. Source 65

Although source 65 (a likely foreground star) does not require a more complex spectral model to adequately describe its X-ray spectrum, it is interesting enough to warrant a brief discussion. Source 65 was detected in two of the observations considered here (Obs IDs 12239 and 384). The X-ray source was detected on the back-illuminated S3 chip in Obs ID 12239, while it was detected on the front-illuminated S4 detector in Obs ID 384. The differences in front and back-illuminated responses make merging the source 65 spectrum problematic; we therefore use only the spectrum extracted from the 97 ks Obs ID 12239 observation (which is much higher quality than the 1.8 ks snapshot taken in Obs ID 384). Source 65 has a large off-axis angle from the nominal aim point of Obs ID 12239, ∼68.

Source 65 (010959.34+354206.3) is the brightest X-ray source in our total NGC 404 X-ray point-source catalog, excluding the NGC 404 central engine. It was detected with 708 net counts in the 0.35–8 keV band during Obs ID 12239, however, the X-ray source is very soft—97% of the counts were detected at energies below 2 keV. We therefore refine our spectral modeling by considering only the 0.35–8 keV portion of the spectrum. The best fit model is a thermal plasma APEC model, with kT = 0.57^+0.03_−0.04 keV (C/dof = 106/98), predicting a 0.35–8 keV flux of 3.6 × 10⁻¹⁴ erg s⁻¹ cm⁻². A smoothed image of source 65 from Obs ID 12239 and the 0.35–2 keV spectrum is shown in Figure 7.

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Source 65 is spatially coincident within ∼06 of a high proper motion F5 star (HD 6892, Høg et al. 2000), with M_V ∼ 8.5 (located at a distance of d ∼ 110 pc). This optical magnitude implies an X-ray-to-optical flux ratio log (f_X/f_V) of −2.9, typical of the X-ray-to-optical flux ratios reported for F stars by Agüeros et al. (2009). A UV counterpart has also been detected by GALEX, with an FUV magnitude of 17.60 ± 0.07 (see Section 4.2). Our observations support the classification of this object as a foreground star not previously detected in X-rays.

We searched for optical counterpart candidates for each of the 11 X-ray sources that was contained within one or more of the overlapping HST fields. The typical Chandra error circle for these sources was ∼06. We kept only those optical sources that met the quality cuts described in Williams et al. (2010; i.e., sources with sufficient signal-to-noise, not flagged as unusable, meeting predetermined crowding and sharpness thresholds, etc.). The HST exposures reach a typical limiting magnitude of 26 in F814W and 27 in F606W, equivalent to M₈₁₄ = −1.4 and M₆₀₆ = −0.4 (i.e., late B or early A-type main-sequence stars).

Figure 8 shows F606W 5'' × 5'' finding charts for the 11 X-ray sources with overlapping HST fields. Only two X-ray sources (27 and 29) were found to have optical counterpart candidates, shown in Figure 8 with arrows. The source 27 optical counterpart has F606W = 25.33 ± 0.02 and F606W − F814W = 1.08 ± 0.02, while the optical counterpart to source 29 has F606W = 21.68 ± 0.01 and F606W − F814W = 2.47 ± 0.03. The optical colors of both sources are consistent with a red giant branch (RGB) star or a background AGN. We estimate the X-ray-to-optical flux ratio log (f_X/f_V) (where f_X is the 2–8 keV flux and f_V is the F606W flux). For source 27, we find log (f_X/f_V) = 0.74, while source 29 has log (f_X/f_V) = −2.14. These X-ray-to-optical flux ratios are consistent with an AGN or LMXB origin. The low number of optical counterparts, and the lack of any blue optical counterpart candidates, suggests that there are few HMXBs in NGC 404.

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We have attempted to place additional constraints on the nature of the NGC 404 X-ray sources by examining archival multi-wavelength data. We searched for counterparts in the following point-source catalogs: the GALEX GR6 data release (NUV, FUV), USNO-B1.0 (B, R), 2MASS All Sky (J, H, K), and NVSS (1.4 GHz).

UV emission can be a good tracer of young stars and background AGNs; however, since the stellar populations of NGC 404 are primarily old, we expect the majority of UV detected sources to be background AGNs. It is possible that some LMXBs in NGC 404 will exhibit detectable levels of UV emission, although their optical colors are expected to be significantly redder than that of an AGN. The optical USNO-B1.0 catalog is sensitive to Milky Way stars, compact clusters, and AGNs. The infrared data are also sensitive to Milky Way stars, red giants, associations of older stars located in NGC 404, and background galaxies, while radio emission is indicative of radio-loud background AGNs.

Table 12 summarizes the multi-wavelength observations available for each of the 31 X-ray sources with at least one multi-wavelength detection. Ten of these sources have counterpart detections in multiple wavelengths.

We combine all of the X-ray and multi-wavelength data available for each source to determine a likely source classification. The first indicator we consider is the source's galactocentric radius; as discussed in Section 3.2, we expect sources with d > 2.5 kpc to be dominated by contaminants (background AGNs and foreground stars), while sources with d < 2.5 kpc will represent a mix of sources associated with NGC 404 and those that are not. We next take into account the shape of a source's X-ray spectrum using our derived hardness ratios (for faint sources) and X-ray spectral fitting (for sufficiently bright sources). In cases where the spectral fits and hardness ratios are in conflict, we only consider the spectral fit. This occurred for only three sources (20, 32, and 45), and in all cases the sources could be described, within the uncertainties, by multiple HR classifications (i.e., source 20 is classified as "SOFT" but the HR uncertainties may also place it within the "XRB" category). Finally, we consider the detection of a multi-wavelength counterpart.

Sources with d > 2.5 kpc and hardness ratios "XRB," "HARD," "BKG," "ABS," or with an X-ray spectrum best fit by a power law are classified as AGNs. Those sources with additional UV or radio detections are highly likely to be background AGNs. X-ray sources with d > 2.5 kpc and "SOFT," "SNR," or thermal spectra are classified as foreground stars (FSs), while softer/thermal sources with d < 2.5 kpc are potentially SSSs and may be associated with NGC 404. We feel especially confident that softer sources with an IR detection in 2MASS are indeed FSs. Sources with d < 2.5 kpc with "XRB" hardness ratios or a power-law spectrum are classified as XRBs.

Again, "SOFT" and "SNR" sources are classified as FSs, and sources with harder spectra are classified as AGNs. Table 13 lists our final source classifications.

We find 21 candidate XRBs, 46 likely background AGNs, 4 candidates SSSs, and 2 likely FSs (plus the NGC 404 central engine). Six sources have been tentatively labeled as "AGN?," but have at least one source property (for example, d  <  2.5 kpc) that makes them a potential XRB candidate. Given the Cappelluti et al. (2009) AGN log N–log S distribution, we expect ∼37–40 X-ray sources to be background AGNs; it is therefore likely that at least some of these six AGN candidates are in fact associated with NGC 404. We find no obvious HMXB candidates in our X-ray source catalog.

While HMXBs are expected to trace the star formation rate (SFR), LMXBs have been shown to correlate with the stellar mass of the host galaxy. We estimate the number ratio of LMXBs to HMXBs in NGC 404 (Gilfanov 2004) assuming a stellar mass of NGC 404 of 6.9 × 10⁸ M_☉ (Thilker et al. 2010); LMXBs are expected to outnumber HMXBs by a factor of 4/10/18 at luminosities greater than 10³⁵/10³⁶/10³⁷ erg s⁻¹. It is therefore possible that 1–2 of the X-ray sources in our catalog are HMXBs associated with NGC 404. Although we do not observe a high-mass optical counterpart to an X-ray source, we note that less than 15% of the X-ray sources detected by Chandra have overlapping HST coverage.

The number of X-ray sources normalized by stellar mass was investigated by Gilfanov (2004) for both early- and late-type galaxies. The galaxies included in the Gilfanov (2004) sample all have stellar masses greater than a few 10¹⁰ M_☉—more than two orders of magnitude greater than NGC 404. We therefore test whether NGC 404 follows the same scaling relations between the number of LMXBs and stellar mass as its more massive counterparts. We note that the Gilfanov (2004) work relied on X-ray source catalogs compiled from the literature; the original publications used different (broad) energy bands, assumed different spectral models for converting between count rates to energy fluxes, and employed different source detection strategies. However, it was anticipated that such differences contributed uncertainties of only ∼20%–30%. We assume the 0.35–8 keV energy flux and our standard model for all following analysis.

The Gilfanov (2004) work evaluated the number of luminous X-ray sources per unit stellar mass of the host galaxy (N_X/M_*) found in late-type galaxies to the populations of early-type galaxies (see their Table 5), although no significant difference was found between earlier- and later-type galaxies. The average number of X-ray sources more luminous than 10³⁷ erg s⁻¹ per 10¹¹ M_☉ stellar mass of the host galaxy was found to be 166.3 ± 20.5. We do not find any of the NGC 404 XRB candidates to have a 0.35–8 keV luminosity above 10³⁷ erg s⁻¹. To find an upper limit on the number of XRBs in NGC 404, we employ a similar strategy as described in Section 5 for our XLF fitting. We randomly add 10 sources from our list of background AGNs and find the number of sources above 10³⁷ erg s⁻¹, as well as their collective luminosity. This was done 500 times. On average, 2.2 ± 1.3 sources have a luminosity above 10³⁷ erg s⁻¹ with a collective luminosity of ∼2.6 × 10³⁷ erg s⁻¹. We therefore estimate the number of XRBs more luminous than 10³⁷ erg s⁻¹ in NGC 404 to be <3.5.

Assuming NGC 404 hosts <3.5 X-ray sources above 10³⁷ erg s⁻¹, and using the same units as Gilfanov (2004), we find N_X/M_* for NGC 404 is <51 sources per 10¹⁰ M_☉, more than 5σ below the average found for more massive galaxies. Similarly, we compare the collective luminosity of sources above 10³⁷ erg s⁻¹ per unit stellar mass of the host galaxy (L_X/M_*) of NGC 404 to the more massive galaxies considered in Gilfanov (2004). The sample average from Gilfanov (2004) was 0.83 ± 0.08, where L_X is in units of 10⁴⁰ erg s⁻¹ and M_* is in units of 10¹¹ M_☉. In these units, we find an upper limit on L_X/M_* for NGC 404 of 0.38. Although this result is again more than 5σ below the average for all galaxies, the L_X/M_* values show considerably more scatter for Gilfanov (2004) sample. Figure 9 shows both N_X/M_* and L_X/M_* as a function of stellar mass for the Gilfanov (2004) sample and NGC 404.

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Although there is a large amount of scatter among the galaxies considered in Gilfanov (2004), the upper limits on the number of XRBs and the collective luminosity of XRBs per stellar mass found for NGC 404 is low. No obvious trends in these quantities with stellar mass are observed in Figure 9, so it is unclear whether the lower stellar mass of NGC 404 is responsible for this difference. Instead, the relatively recent increase in SFR experienced by NGC 404 may have produced a population of low-luminosity LMXBs powered by MS donor stars which is currently dominating the X-ray emission from XRBs. Future work will be required to understand whether this difference in collective XRB luminosity is common for dwarf galaxies, or if NGC 404 is an outlier.

The shape of the hard XLF is consistent with observations of LMXB populations (over similar energy ranges) in external galaxies (Primini et al. 1993; Gilfanov 2004; Voss & Gilfanov 2006, 2007; Voss et al. 2009) and the Milky Way (Grimm et al. 2002; Gilfanov 2004). We additionally note that nearly all elliptical galaxies used to construct XLFs in the literature have a larger stellar mass, by an order of magnitude or more, than the dwarf galaxy NGC 404; e.g., Cen A (Wernli et al. 2002), NGC 1407 (Kim & Fabbiano 2004; Trentham et al. 2006), NGC 4372 (Napolitano et al. 2011). No obvious correlation between XLF slope and stellar mass of the host galaxy is observed.

Several explanations for the ∼10³⁷ erg s⁻¹ break in the XLF of LMXBs have been proposed. One particularly attractive explanation involves the nature of the donor companion star: for a persistent, sub-Eddington LMXB, the accretion luminosity L_X is directly proportional to the mass transfer rate $\dot{m}$ from the secondary star—thus, mass transfer in an LMXB can be driven by either the loss of orbital angular momentum (Paczynski & Sienkiewicz 1981; Verbunt & Zwaan 1981) or the increasing radius of the donor due to nuclear evolution (Taam 1983; Ritter 1999). Recently, Revnivtsev et al. (2011) showed that LMXB systems with X-ray luminosities below ∼2 × 10³⁷ erg s⁻¹ have unevolved, main-sequence (MS) secondary companions, while systems exhibiting higher X-ray luminosities possess predominantly giant donors. Mass transfer from a giant companion greatly shortens the lifetime of the binary, thus steepening the XLF at the high-luminosity end. The boundary between MS and giant companions has also been found in numerical simulations of LMXB populations by Fragos et al. (2008) and Kim et al. (2009).

Unlike its more massive counterparts, NGC 404 experienced a period of enhanced star formation ∼0.5 Gyr ago (Williams et al. 2010). Although massive stars would have expired after ∼100 Myr, F- and G-type stars formed during this epoch would still be on the MS. This scenario additionally explains the lack of optical counterparts observed with the overlapping HST exposures—at a distance of 3.05 Mpc, A-type stars and later would fall below our optical detection limits. Further FUV observations performed by GALEX suggest that NGC 404 may host a small number of stars as young as ∼160 Myr old. Stellar population studies have shown that dwarf ellipticals exhibit, on average, younger stellar ages compared to their massive counterparts (Michielsen et al. 2008)—the same may be true for the X-ray populations of dwarf ellipticals. It is therefore plausible that NGC 404 hosts a population of LMXBs powered by MS donors, not typically found in more massive ellipticals.

The recent (<400 Myr) SFR density of NGC 404 was estimated using HST observations to be ∼2 × 10⁻⁴ M_☉ yr⁻¹ kpc⁻² (Williams et al. 2010). No radial trends in the SFR out to ∼5 kpc were observed, implying a typical SFR of ∼0.005 M_☉ yr⁻¹. Thilker et al. (2010) additionally estimated the SFR in the H i ring at 1.6–6.4 kpc to be 0.0025 M_☉ yr⁻¹. X-ray emission from HMXBs has been shown to trace recent star formation of the host galaxy (Grimm et al. 2003), and the HMXBs identified in Paper I were successfully used to confirm the SFR of NGC 300. However, the recent SFR of NGC 404 is a factor of ∼70 lower than is observed in NGC 300. Using the estimated 2–10 keV luminosity of all of our XRB candidates, we place an upper limit on the NGC 404 SFR of 0.01 M_☉ yr⁻¹, a factor of ∼2–4 larger than the observed rate. This represents one of the first attempts to use X-ray emission to constrain the SFR of an early-type dwarf galaxy.