THE AGES OF HIGH-MASS X-RAY BINARIES IN NGC 2403 AND NGC 300

All photometry and artificial star tests were measured and performed as described by the ANGST project paper (Dalcanton et al. 2009). Briefly, all photometry was performed using DOLPHOT, an updated version of HSTphot optimized for ACS photometry. Photometry was culled based on signal-to-noise ratio and the quality parameters of sharpness and crowding, as described in Dalcanton et al. (2009). We selected only the photometry from a circular region with a radius of 50 pc around the positions of the HMXBs (51 and 32 in NGC 300 and NGC 2403, respectively). The color–magnitude diagrams (CMDs) of these regions are shown in Figures 2 and 3. Fake star tests were taken from larger regions (25'' and 15'') in order to gain a large number of tests to improve statistics of the photometric uncertainties and completeness as a function of color and brightness. The HST images of one source in each galaxy are given in Figure 1, showing that the stellar density and extinction does not vary strongly within these relatively small spatial scales.

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We fit the CMDs for each of the fields in our study using the software package MATCH (Dolphin 2002). The overall technique for our fitting, as it has been applied for all ANGST papers, is described in detail in Williams et al. (2009); however, there have been some changes in the method for uncertainty estimation. Output star formation rates are renormalized to a Kroupa (2001) initial mass function. Furthermore, we find the best-fitting mean extinction to each location with the distance fixed to 2.0 Mpc and 3.2 Mpc for NGC 300 and NGC 2403, respectively (Dalcanton et al. 2009). We found the best fitting extinction to be consistent with the foreground value from Schlegel et al. (1998). In addition, we attempted to improve the model fits by including differential reddening in the model Hess diagrams by spreading the model photometry along the reddening line using the MATCH dAv flag; however, we found no improvement and therefore no evidence for significant differential reddening in these locations, suggesting these are not extremely young active regions associated with O-type stars. With these distance and extinction values applied, we then run a series of 100 Monte Carlo (MC) tests.

To assess the full combination of systematic errors due to model deficiencies as well as random errors due to the depth and size of the sample, realizations of the best-fitting model solution are fitted with the models shifted in bolometric magnitude and effective temperature (Dolphin 2012). These shifts account for the uncertainties due to any potential systematic offsets between the data and models.

However, when searching for differences between the stellar populations of multiple locations, systematic uncertainties due to offsets between the models and the data are not of concern, since these systematics will affect all fields. To estimate the relative uncertainty for differences between two locations analyzed using the same models, we need only to assess the random errors due to the depth and size of the sample. Therefore, for the other locations, our MC error analysis did not include shifts between the models and data.

One interesting test case is NGC 2403 source 42, which is a well-studied ULX that is thought to have a black hole primary (Fabbiano & Trinchieri 1987; Swartz et al. 2004; Feng & Kaaret 2005; Isobe et al. 2009). The black hole mass is estimated from Suzaku X-ray spectra to be 10–15 M_☉, assuming radiation near the Eddington limit (Isobe et al. 2009). There is no confirmed optical counterpart; however, a promising candidate that is UV-bright has been identified by Roberts et al. (2008). This candidate is included in Figure 1. Our analysis suggests that it resides in a region with no stars younger than 50 Myr, but with a significant population of stars with ages 60 ± 5 Myr. Since the progenitor of the black hole likely had a main sequence lifetime of ≲10 Myr, our result suggests that this ULX either has had a very long X-ray lifetime compared to the lifetime of the primary, or the ULX is so bright now because it has a secondary that is in a state of rapid mass-loss, as in the model of King et al. (2001). Spitzer imaging from the SINGS (Kennicutt et al. 2003) program shows no obvious counterpart in the near or mid infrared, so it does not appear to be an IR-bright asymptotic giant branch star, shedding its envelope. In any case, if the ULX is associated with this 60 Myr population, then the secondary likely has a zero-age main-sequence mass of ≲7 M_☉.

Turning now to the broader sample, in Figures 4 and 5, we show the recent star formation histories (SFHs) for the regions surrounding all 18 HMXB candidates. For reference, we highlight the age range between 30 and 60 Myr. All but three (N300-95, N2403-39, and N2403-85) show a significant peak in between 20 and 70 Myr. One of these (NGC 2403-85) shows a population of 10–20 Myr, and therefore is still a potential HMXB. HMXBs are expected to appear in populations even younger than 10–20 Myr. The population synthesis models of Van Bever & Vanbeveren (2000) show that substantial numbers of HMXBs appear 4–5 Myr after the beginning of star formation. A possible evolutionary scenario for the formation of such an HMXB on a time scale of 5–6 Myr is described in Belczynski & Taam (2008; assuming that the binary survives the first supernova). Observationally, a case in point is provided by the Galactic cluster Westerlund 1, which has an age of ∼4 Myr. This cluster has several Wolf–Rayet binaries (potential progenitors of HMXBs), one candidate HMXB, and a magnetar, indicating that a number of compact objects have already formed from supernovae (SNe; see Muno et al. 2006; Clark et al. 2008).

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N300-95 has a 100 Myr population, pushing the old-age limits for an HMXB, and N2403-39, while showing no significant population younger than 100 Myr, has upper limits that allow the possibility of some young stars in the region. The X-ray sources in regions with very little recent star formation could also be low-mass X-ray binaries (LMXBs), since all of these regions also contain significant old populations. However, if for example, N2403-39 is an LMXB, then the counterpart is not the blue star that falls in the Chandra error circle.

When we combine the results from all of the candidates in our sample, as shown in Figure 6, we find a prominent enhancement in the age distribution at 40–55 Myr. This result provides more evidence that 40–55 Myr is a common age for HMXB systems, and therefore may represent the post star-formation epoch with the largest number of HMXBs per unit stellar mass formed. Furthermore, this epoch would presumably also be the interval of maximum feedback from HMXB jets, outflows, and high-energy radiation.

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To quantify the likelihood of such a peak in a summed age distribution appearing by chance, we fit photometry from a control sample. This control sample consisted of photometry drawn from 18 regions within 05 of randomly drawn bright blue stars in the HST fields. We required the same number of regions per field as the HMXB sample. We ran these random locations through our fitting technique and summed the results, finding no clear peak in the age distribution (Figure 6). We then ran this test 1000 times to see if we ever randomly recovered a peak similar to that seen in the age distribution of the HMXB sample. We found that 1.5% of our trials resulted in a peak of at least a factor of 2.35 in two adjacent bins between the ages of 20 and 140 Myr (as seen in the HMXB sample). A smaller number (0.4%) of our trials had such peaks as old as the 40–55 Myr peak seen in the HMXB distribution. Thus, a peak like that seen in the HMXB sample is a 3σ outlier in our trials, roughly consistent with the uncertainty estimates shown in Figure 6.

The standard model of massive binary evolution suggests that in a massive binary (e.g., B and O stars or A and O stars), the more massive star evolves first and transfers mass to the less massive companion when it overflows its Roche lobe. The core of the massive star subsequently collapses, forming a neutron star or black hole. If the binary remains bound after the core-collapse SN, it may become an HMXB (e.g., van den Heuvel & De Loore 1973; van den Heuvel 1976).

After mass accretion, the less massive star is spun up due to the addition of high angular momentum material (Pols et al. 1991; van Bever & Vanbeveren 1997), and subsequent evolution occurs at higher temperatures (e.g., van Bever & Vanbeveren 1998). The rapid rotation pushes the wind of this hot star into the equatorial plane and leads to the formation of an equatorial outflow disk (Bjorkman & Cassinelli 1993), which makes this an active B-star (Be star). As this mass is transferred back to, and accreted by, the compact object, X-ray emission is produced and the binary becomes a Be-HMXB (Van Bever & Vanbeveren 2000).

Because the B-star is rapidly rotating, the mass outflow is localized in the equatorial plane. This "outflow disk" increases the mass transfer efficiency. The resulting X-ray luminosity is low a large fraction of the time (<10³⁵ erg s⁻¹). However, these systems can sometimes reach luminosities of 10³⁷ erg s⁻¹ because the outflow disk is unstable and can have episodes of enhanced outflow (e.g., Reig et al. 2007), which lead to an increase in the accretion rate (and X-ray luminosity) of the compact object.

Given this model of HMXB formation, one might expect a correspondence between HMXB ages and B-star evolution. Observations suggest that the fraction of active B stars (Be stars) peaks at 25–80 Myr (McSwain & Gies 2005). Our measurements suggest that the fraction of HMXBs appears to peak at 40–55 Myr, in good agreement. Thus, the activity cycle of B-stars appears to be involved in the observed peak in the age distribution.

The 40–55 Myr timescale is also associated with a possible peak in the neutron star production rate. Current theory and observations suggest that stars with zero age main-sequence masses of 7–8 M_☉ are the lowest mass stars to undergo core-collapse to form neutron stars (e.g., Jennings et al. 2012). According to the initial mass function (Kroupa 2001), for a given star forming episode, there are always more lower mass stars than higher mass ones. Therefore the highest rate of core-collapse likely occurs when the lifetime of 7–8 M_☉ stars has been reached. This lifetime is 40–55 Myr according to, for example, the Padova stellar evolution models (Marigo et al. 2008). Therefore, the production rate of neutron stars is likely involved in the observed peak in the age distribution as well. Thus, both the mass-loss by B stars and the number of potential HMXB systems are at a maximum at ∼50 Myr after star formation, conspiring to form the peak that we see in the HMXB age distribution.

Recent attempts to include baryonic physics in galaxy formation models and simulations have found that the treatment of feedback, energy injection into the interstellar gas, plays an important role in shaping not only the mass function (e.g., Benson et al. 2003) and SFHs of galaxies (e.g., Stinson et al. 2007; Quillen & Bland-Hawthorn 2008), but also their dark matter halo density profiles (Governato et al. 2010). The necessary timescale and energetics of the feedback required to reproduce observed galaxy properties are complex, and as a result, the origin of the feedback remains controversial. At least part of the necessary feedback appears to be related to star formation, especially in low mass galaxies where no active nucleus is present.

We note that the peak we observe in HMXB activity ∼50 Myr after star formation is generally consistent with HMXBs contributing significantly to the feedback resulting from star formation. For example, Justham & Schawinski (2012) suggest that the cumulative energy input from HMXBs can be similar to that from SNe, and they point out that HMXB feedback may have the appropriate delay time required to produce episodic SFHs of low mass galaxies. Our results suggest that feedback from HMXBs is maximized ∼50 Myr after star formation, roughly consistent with the delay time required by some models (e.g., Quillen & Bland-Hawthorn 2008). However, the delay between star formation and the transfer of SNe energy into the interstellar medium (ISM) is a similar length at low SN-rates (Dib et al. 2006), therefore both processes should be considered potentially important to the feedback budget.

Furthermore, Stilp et al. (2013) recently discovered a correlation between the energetics of the neutral ISM and the star formation rate 30–40 Myr earlier. This result suggests that the energy associated with star formation is transferred to the neutral ISM with roughly this delay time. The consistency of this timescale with the delay time of HMXB feedback provides further evidence that feedback from both HMXBs and SNe are potentially important for regulating star formation in low-mass galaxies.

While the observed delay time between star formation and HMXB activity makes HMXB feedback potentially important in low-mass galaxies, the relatively low energies associated with HMXBs, makes them only minor contributors to feedback in more massive systems. Massive galaxies contain supermassive black holes. Central black holes have masses of M_BH  ∼  1.4  ×  10⁻³M_gal (Fabian 2012). Assuming the energy released in producing the central black hole is E_BH  =  0.1 M_BHc², putting E_BH in units of erg and M_BH in units of solar masses yields E_BH  =  2.5  ×  10⁵⁰ M_gal/M_☉. We can also determine E_HMXB as a function of M_gal by assuming that E_HMXB/t, where t has units of seconds, is equivalent to the X-ray luminosity (L_X), and setting SFR_s × t < M_gal, where SFR_s is the star formation rate in units of M_☉ s⁻¹. We can now apply the relation between L_X and SFR from Grimm et al. (2003), which is L_X = 6.7 × 10³⁹SFR, where L_X is in units of erg s⁻¹ and SFR is in units of M_☉ yr⁻¹. Substituting SFR_s for SFR yields L_X = 2.1 × 10⁴⁷SFR_s; then applying M_gal/t  >  SFR_s and E_HMXB/t  =  L_X gives E_HMXB  <  2.1  ×  10⁴⁷ M_gal/M_☉. Thus, E_BH/E_HMXB  ≳  10³, making E_HMXB a very minor contributor to the global evolution of massive galaxies. If we apply an updated relation between L_X and SFR, such as that from Mineo et al. (2012) which includes a much larger range of data and has a flatter slope, the relative importance of E_HMXB is further reduced.