DETECTION OF A HOT GASEOUS HALO AROUND THE GIANT SPIRAL GALAXY NGC 1961

Our original intent was to use images taken a degree off-axis from the galaxy as background images that could be subtracted pixel-by-pixel from the halo images, accomplishing both flat fielding and background subtraction at once. We took two background pointings for this purpose. The former (ObsID 10532) was pointed at blank sky 173 away from the galaxy for 10.14 ks and was taken 29 days before the science pointings. The latter (ObsID 10533) was pointed at blank sky 09 away from the galaxy for 10.02 ks, 7.5 days before the science pointings began.

Unfortunately these background images proved unsuitable for background subtraction because the count rate across the image was different than the count rates in the source images. After processing and point-source subtraction, the mean 0.6–2 keV count rate in the background images is 0.31 counts s⁻¹ compared to 0.36 counts s⁻¹ in the source images. This 17% discrepancy is comparable to the total signal from hot halo emission integrated out to 500 kpc (see Section 6), and probably stems from variations either in the unresolved X-ray background of the images or in variations in the solar X-ray flux between the background observations and the source observations. In either case, the discrepancy was large enough that we were unable to use the background images for background subtraction. Similarly, the standard background images are even more spatially and temporally separate from our source images and could not be used either.

We therefore decided to use in-field background subtraction instead. In-field subtraction is not ideal for our project, since we are trying to measure diffuse emission that, in principle, could fill the entire field of view. However, the diffuse emission is only detectable out to a few arcminutes from the galaxy, and even over most of that range the background is larger than the signal. Thus, it is possible to compute the background in-field and use this for background subtraction.

We first attempted to model the background. We assumed that the 0.6–2.0 keV background consisted of two components: a vignetted component from the diffuse X-ray background (which we assumed would be proportional to the effective throughput at each pixel, computed using the exposure map), and an unvignetted component from particles in the solar wind. In each observation, we sampled the background at various points across the detector (away from the direction of the galaxy) and fit the background to a linear combination of these two components.

This procedure worked adequately for two of the four observations (10528 and 10530), but the other two had large-scale variations in the background across the image or other unmodeled effects and therefore did not yield reasonable fits to the two background components.

We found more success with in-field conjugate subtraction. The idea is to assume that the vignetted background is azimuthally symmetric over large scales around the aimpoint of the image (located on the ACIS-I3 chip at approximately (x, y) = (974, 969) in detector coordinates²). We selected "conjugate" background regions in the image of the same shape and size as the source, but at the opposite position angle from the aimpoint of the image. We then subtracted each conjugate region from the corresponding source region (see Figure 2).

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As shown in Figure 2, we faced different geometrical combinations of source, conjugate, and aimpoint for each observation. For observation 10528, the galaxy is just off the edge of the boundary between the I0 and I1 chips, the aimpoint is on the opposite side of the center of the ACIS-I array, and so the conjugate point is 170'' beyond the edge of the I3/I4 chips. We therefore had to choose annuli at the same distance from the aimpoint, but at angles of 120° and 240° instead of 180° to find conjugate regions on the detector for the source photons from the inner 170'' (45 kpc) around the galaxy in this observation. For observation 10529, the galaxy is just off the edge of the I0/I2 chips, the aimpoint is again on the opposite side of the center of the array, and the conjugate point is 130'' beyond the edge of the I3/I1 chips. We therefore had to choose annuli at the same distance from the aimpoint, but at angles of 120° and 240° instead of 180° to find conjugate regions on the detector for the source photons from the inner 130'' (35 kpc) around the galaxy in this observation. For observation 10530, the galaxy is 200'' off the edge of the I1/I3 chips, but the aimpoint is now on the same side of the center of the array, so the conjugate point is close to the edge of the I0/I2 chips. But since the galaxy is off the detector, we do not have a measurement of the source for the inner 200'' (50 kpc) around the galaxy in this observation. For observation 10531, the galaxy is on the I3 chip, near the I2 chip, 270'' from the aimpoint. The conjugate point is also on the detector, on the boundary between the I0/I1 chips. So for this observation, we have measurements of the source and background emission out to 270'' (75 kpc); beyond this radius the background and source annuli begin to overlap. We excluded the data beyond this radius for observation 10531 for the rest of the analysis but also repeated the analysis with these points included and found that they have no effect on the results since the halo emission has disappeared by 50 or 60 kpc.

This yielded similar backgrounds to the results of the modeling for 10528 and 10530, but the results were much better for 10529 and 10531, so we adopted this approach for the rest of the analysis. To help verify the reliability of this technique, we also tested the conjugate technique 90° on either side of the source and obtained zero signal.

It is critically important to be sure we are measuring the hot diffuse emission and not a collection of X-ray binaries in and around the galaxy, whose surface density also falls off with radius like the halo gas. The first step to ensuring a clean measurement is the automated point-source removal using WAVDETECT, described above, which removed six point sources within the inner 50'', with the faintest point source having a luminosity of L_{0.6–2 keV} ∼ 3 × 10³⁸ erg s⁻¹ if at the assumed distance of 56 Mpc. One of these point sources falls on the galactic nucleus, which is reported to host a low-luminosity active galactic nucleus (AGN; Roberts & Warwick 2000). For the central point source, within the WAVDETECT ellipse (which is about the size of the 90% encircled energy region at this radius) we have 114 counts in the 0.6–2 keV band and 176 counts in the 0.6–6.0 keV range. Using a power-law×PHABS spectral model, we are unable to get an acceptable fit to the 0.6–6.0 keV spectrum, but if we add in an APEC component with Galactic absorption based on our later results (see Section 5) we do get an acceptable fit and find the AGN power-law component has Γ = 1.4^+0.5_{− 0.4} and a 0.6–2.0 keV luminosity of 5⁺²_{− 1} × 10³⁹ erg s⁻¹.

To estimate the contribution of unresolved point-source emission to the surface brightness profile, we extracted and reduced an image of the 2–6 keV emission, using the identical procedure as we used for the 0.6–2 keV images. We expect no contribution from the <1 keV gas in this higher energy band, so all the emission should come from point sources in the galaxy or the background. Using the in-field conjugate subtraction technique, we subtracted the background emission and derived radial surface brightness profiles for the 2–6 keV galactic emission. We attributed all this emission to unresolved point sources.

Irwin et al. (2003) found that the integrated emission from low-mass X-ray binaries (which dominate the point-source emission over most of the region in our analysis) has a universal spectrum that can be fit with a power-law distribution with a slope Γ = 1.56. Using this slope and accounting for absorption, we find that each unit of 2–6 keV emission corresponds to 1.7 units of 0.6–2 keV emission. We scaled the 2–6 keV galactic emission by a factor of 1.7 and subtracted this from the 0.6–2 keV emission to remove the point-source contribution. We stopped the unresolved point-source removal after reaching the average background 2–6 keV surface brightness for each observation; this occurred at 32 kpc for observation 10528, 30 kpc for observation 10529, and 25 kpc for observation 10531 (observation 10530 has the galaxy 50 kpc off the edge of the detector, so there is no contribution from galactic point sources). The total amount of emission due to unresolved point sources was ≈1.5 × 10⁴⁰ erg s⁻¹, about 10%–20% of the total emission.

We attempted to verify this result by assuming the six point sources detected with WAVDETECT represent a complete sample down to 3 × 10³⁸ erg s⁻¹. Using the Chandra point-source number counts of Kim et al. (2007), we expect 0.6 background point sources above our flux limit in the (50'' radius) aperture, so one of these six sources is likely actually an unrelated background object (and one is the central low-luminosity AGN). We applied the luminosity function of Grimm et al. (2002), which was calibrated using Galactic low-mass X-ray binaries (LMXBs) and high-mass X-ray binaries (HMXBs), to the five non-nuclear point sources. We adopted a power-law function for N(> L) with a slope of α = −0.3. The ratio of the total luminosity (with a lower luminosity cutoff at 10³⁶ erg s⁻¹) to the luminosity above 3 × 10³⁸ erg s⁻¹ is 5.0, and the total 0.6–2 keV luminosity of our five point sources is 7.0 × 10³⁹ erg s⁻¹, so we expect a point-source luminosity of 3.5 × 10⁴⁰ erg s⁻¹. This figure is about twice as high as the point-source luminosity we infer from the 2–6 keV flux, although the likely presence of a background point source is probably causing us to overestimate the background using this method.

If we assume that all five detected non-nuclear point sources within 50'' (13 kpc) are associated with the galaxy, then our method of scaling from the high-energy emission corresponds to a flat power-law slope of α = −0.15 for N(> L). This slope is 1.4σ away from the best-fit slope to the LMXB luminosity function in Grimm et al. (2002). It does seem more likely for NGC 1961 to have a different point-source luminosity function than the Milky Way instead of a different X-ray spectrum for its point sources. Supporting this result, a flattening of the point-source luminosity function below a few × 10³⁷ erg s⁻¹ is also observed in Centaurus A (Voss et al. 2009).

We also included a correction for X-ray emission from stars at a level fainter than 10³⁶ erg s⁻¹. This emission seems to scale with total stellar mass (inferred from the K-band luminosity), at least for old stellar populations (Revnivtsev et al. 2008). While NGC 1961 is a late-type spiral and therefore not likely to be dominated by an old stellar population, the Revnivtsev et al. scaling is the best available at present for accounting for this emission. We took the K-band radial surface brightness profile for NGC 1961 from 2MASS (Jarrett et al. 2003), rebinned it to match our X-ray annuli, and assumed a K-band mass-to-light ratio of 0.6 to convert into stellar mass (Bell & de Jong 2001). We then applied the Revnivtsev et al. conversion between stellar mass and 0.5–2.0 keV X-ray luminosity to estimate the stellar X-ray emission. Finally, we multiplied the predicted X-ray emission by 73% to account for absorption by the Galactic hydrogen column in the direction of NGC 1961. We find that the stellar emission is never a significant fraction of the total X-ray emission, even at very small radii; the total 0.5–2.0 keV emission from stars is 2.6 × 10³⁹ erg s⁻¹, or about 5% of the total luminosity in the central region. The K-band half-light radius is 35'' (9.6 kpc), and the K-band surface brightness reaches the 2MASS 1σ background at about 78'' (21 kpc)—a much more concentrated profile than the X-ray emission.

Our assumed parametric form for the surface brightness profile is the class of models knows as β-models. These models parameterize the surface brightness as

$$S(r) = S_0 \left[ 1 +\left(\frac{r}{r_0}\right)^2 \right]^{0.5\hbox{--}3\beta }$$

which, if the gas is isothermal and has a constant metallicity, corresponds to a density distribution of the form

$$n(r) = n_0 \left[1 + \left(\frac{r}{r_0}\right)^2\right]^{-1.5\beta }.$$

These models provide good fits to hot gas around elliptical galaxies (Forman et al. 1985) as well as the hot gas in galaxy groups and clusters (Sarazin 1986). We quantified fits to the β-models using χ² minimization and we binned the data to have at least 20 photons per radial bin. Using the radial surface brightness profiles, we attempt to exclude specific choices of β-model, and the best-fit models are the profiles which can be excluded at the lowest confidence. We want to be able to exclude at less than 95% confidence for the model to be considered statistically acceptable.

We fit the surface brightness profiles to the β-profiles and solved for S₀, r₀, and β using χ² minimization. We include annuli extending out to 370'' in our fit, since this radius appears to enclose all the excess emission visible in the surface brightness profile (see Figure 3). However, varying this radius does not affect the result much. We also require a core radius of at least 1 kpc. It would be better if we did not have to constrain the core radius at all, but the core radius is not well constrained due to the presence (and masking) of the X-ray nucleus, so an observational constraint is difficult. A 1 kpc core radius is very small for a hot gaseous halo around a galaxy of this size, so our constraint is at least still somewhat conservative.

We fit all four profiles simultaneously and find a single set of parameters that worked for all four observations. The best-fit parameters were S₀ = 9.77 × 10⁻⁸ counts s⁻¹ cm⁻² arcsec⁻², r₀ = 1.00 kpc, and β = 0.47, and the full range of acceptable fits is narrowly clustered around these values (see Figure 3).

While we had at least 20 source photons in each radial bin, in the inner annuli where the galaxy is brighter than the background there are fewer than 20 background photons per bin. Additionally, from the size of the radial background variations at large radii, we can infer that there are small-scale spatial variations in the background (probably due to unresolved point sources). We attempted to correct for these two effects by fitting a second-order polynomial to the surface brightness profile of the background. Quadratics were the lowest-order polynomials with acceptable fits to the background surface brightness profile (reduced χ² = 1.42, 1.70, 1.08, and 1.02, respectively, for 33, 33, 26, and 47 degrees of freedom). Observation 10529 has the least well-behaved background at small radii, and this is partially responsible for the lower values at small radii for this observation.

As noted above, our main conclusion—that there is extended coronal emission around NGC 1961 out to at least 40 kpc—does not depend on this smoothing technique, and we can still get an acceptable fit to the data without any smoothing. Smoothing the background allows us to remove a principal source of error in our analysis, however, yielding a wider and more reliable range of acceptable fits. The data with smoothed background, as well as the acceptable fits, are shown in Figure 4. We take the fits to the smoothed data (unacceptable at less than 95% confidence) as the fiducial range for the rest of the paper. Note that this range encompasses the entire range of acceptable fits to the unsmoothed data.

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We present the smoothed surface brightness profile in log–log space in Figure 5. In this figure, we have subtracted out the estimated contribution from X-ray binaries and from stars, as discussed in Section 3.4. For ease of visualization in log–log space, for this figure we have not subtracted out the smoothed background; rather, we indicate the level of the smoothed background for comparison. Again, we clearly detect emission above the background out to 40–50 kpc, in multiple quadrants, and this emission is more extended than the emission from stars and X-ray binaries.

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The parameters for the joint fit with the highest enclosed mass are (S₀ = 3.85 × 10⁻⁸ counts s⁻¹ cm⁻² arcsec⁻², β = 0.41, and r₀ = 1.00 kpc), and the parameters for the fit with the lowest enclosed mass are (S₀ = 1.38 × 10⁻⁸ counts s⁻¹ cm⁻² arcsec⁻², β = 0.54, and r₀ = 4.04 kpc).

We can also now reexamine the assumption we made at the beginning of this section that the emission is spherically symmetric. This assumption is plausible since we detect emission in multiple quadrants and are able to get an acceptable fit, but there is also some evidence of asymmetry in Figures 3–5. In particular, the data in observation 10529 are clearly below the other data, and observation 10531 is clearly above the other data at a radius of 25–35 kpc. There is also a large diffuse H i tail in the quadrant examined by observation 10529 (Haan et al. 2008). While too thin to absorb much X-ray emission, this tail does show that the cold gas is not spherically symmetric in detail. Further observations will be necessary to understand the distribution and kinematics of the gas around this galaxy.

We also examined joint and individual fits with two-component β-models. One component is the β ∼ 0.5 profile described above, and another is a much flatter profile (β ∼ 0.35) with a much larger core radius (r₀ ∼ 100 kpc). This joint profile is motivated by theoretical work that suggests hot halos might have higher entropy than expected, which would flatten the profiles and allow them to contain more material (Crain et al. 2010a; Kaufmann et al. 2009; Guedes et al. 2011). In a previous paper (Anderson & Bregman 2010) we used a fiducial slope of β = 0.35 for flattened profiles, so we constrain the flattened profile to have that slope in our fit. We also fix the core radius at 50 kpc to reduce the parameter space, but our conclusion is not very sensitive to this parameter. We choose logarithmically spaced values for the normalization of the flattened component, and for each normalization, we search for values of β, r₀, and S₀ corresponding to the non-flattened (β ∼ 0.5) profile, such that we minimize the total χ² of the fit to the data of the sum of the flattened and non-flattened profiles. We fit the data out to radii of 500'' so as to incorporate constraints from beyond the region of visible emission.

The resulting minimum χ² is a function of the normalization of the flattened profile component, and the strongest constraint (ruled out at 95%) is a maximum normalization of S₀ = 1.5 × 10⁻¹⁰ counts s⁻¹ cm⁻² arcsec⁻². This corresponds to a total count rate out to 500 kpc of 6.5 × 10⁻² counts s⁻¹, or an unabsorbed flux of 5.2 × 10⁻¹³ erg s⁻¹ cm⁻², or a 0.6–2 keV luminosity of 2.0 × 10⁴¹ erg s⁻¹. The normalization is 1.1 × 10⁻³, corresponding to a hot halo mass in the flattened component of 7.4 × 10¹¹ M_☉.

Given the historical observational difficulties in detecting diffuse emission at large radii around spiral galaxies, and our own experience and difficulties with this observation, we point out a few lessons learned that may be of use for future observers in this field. First, it is inadvisable to place the galaxy too close to the aimpoint of the telescope. There are numerous instrumental effects (vignetting, point-source detectability, decreasing throughput, etc.) that all vary with distance from the aimpoint; while corrections can be applied for each, it is very difficult to disentangle instrumental effects from diffuse emission at or below the surface brightness of the background. Second, it is also inadvisable to place the galaxy at the very edge of the detector (as we did for observations 10528 and 10529). While this configuration allows for conjugate subtraction to circumvent many of the radially varying instrumental effects, the throughput and vignetting effects are so large at the edge of the detector that it becomes difficult to see the galaxy. The optimal configuration is probably similar to our observation 10531, where the galaxy is placed a few arcminutes from the edge of the detector. This allows for conjugate subtraction while still retaining enough throughput to detect faint emission. The primary shortcoming of this configuration is that the conjugate annuli begin to overlap sooner than they would if the galaxy is at the edge of the detector. For observation 10531, we can only probe the inner 45 of the halo, but the halo falls below the background at a radius of about 3' so we can still see all the useful emission.

As described in Section 4.1, we also found that a quadratic fit to the soft X-ray background as a function of radius is generally statistically acceptable. Using quadratic fits to the background for conjugate subtraction, our technique is able to detect emission down to about 20% of the background for very faint and diffuse emission (see Figure 4).

As mentioned in Section 1, it has been known that hot halos around spiral galaxies are underluminous in comparison to hot halos around ellipticals, but now that we have a detection of one we can finally quantify this. Benson et al. (2000) examine a sample of three large spirals, of which the largest (NGC 4594, the Sombrero galaxy) is similar in mass but much more bulge-dominated than NGC 1961. They predict a bolometric hot halo luminosity within the inner 76 kpc of 6.9  ±  0.5 × 10⁴¹ erg s⁻¹ for a metal abundance of 0.3 Z_☉ (which would be 50% higher for our assumed abundance of 0.5 Z_☉). This is not observed, but they do establish an observational upper limit of 4.4  ±  2.8 × 10⁴⁰ erg s⁻¹ for the emission at radii between 16 and 30 kpc. Our detection falls below this limit. We find an absorbed 0.6–2 keV luminosity (which is about half the bolometric luminosity for 0.6 keV gas) within the 16–30 kpc annulus of 5.2–6.5 × 10³⁹ erg s⁻¹, which is 75% below their upper limit and only 2% as luminous as the theoretical prediction. The hypothetical flattened component would be even fainter within this annulus, with a luminosity of only 2.3 × 10³⁹ erg s⁻¹.

The baryon fraction of this galaxy is dominated by the stars: the 2MASS K_S-band total magnitude of 7.73 corresponds to an absolute K_S magnitude of −26.0. Assuming a mass-to-light ratio of 0.6 (Bell & de Jong 2001), we infer a stellar mass of 3.1 × 10¹¹ M_☉. The cold gas component can be approximated by the H i mass, which is 4.7 × 10¹⁰ M_☉ (Haan et al. 2008). We find a hot halo mass of 1.4–2.6 × 10¹¹ M_☉. So the baryon budget of this galaxy is approximately 6:1:3–5 stars:cold gas:hot gas (with the flattened profile the ratio is 6:1:14). Within 50 kpc, the baryon budget is approximately 60:10:1 stars:cold gas:hot gas. So, out to 50 kpc, most of the gas in NGC 1961 is cold, but if we are justified in integrating to the virial radius, the majority of the gas in the galaxy is in the hot phase, as predicted by theory for large galaxies.

It is important to highlight the uncertainties in our measurement of the hot halo mass. Our β-model fitting has a 95% confidence uncertainty of a factor of three in the halo mass. A 10% uncertainty in the distance to the galaxy would introduce a roughly 20% additional uncertainty in the estimated mass, and our choice of 500 kpc for an outer radius of integration probably introduces another 10% error relative to the true (unknown) virial radius. The assumptions of isothermality and azimuthal symmetry may not be true at larger radii as well. By far the biggest source of uncertainty, however, is the metallicity of the gas. At the virial temperature of this galaxy, X-ray emissivity is inversely proportional to the square root of the gas metallicity, so if the gas is actually enriched to 1 Z_☉ instead of our assumed value of 0.5 Z_☉, the true halo mass is 30% below the value we infer, and if the gas is actually 0.25 Z_☉, the true halo mass is 40% higher than the value we infer. A metallicity gradient in the hot halo would make an accurate mass estimate even more difficult. Obtaining a measurement of the metallicity of the hot halo gas around a spiral galaxy is critically important for accurately measuring the mass (as well as constraining the formation history of the halo).

For our value of Z = 0.5 Z_☉, we can convert the baryon budget into a baryon fraction with an estimate of the total dark halo mass. The most recent measurement of the circular velocity finds an inclination-corrected H i velocity at 34 kpc of 402 km s⁻¹ (Haan et al. 2008), which is comparable to older measurements for this galaxy (e.g., Rubin et al. 1979). If this measurement is correct and the dark matter follows a Navarro–Frenk–White (NFW) profile, the expected virial mass is M₂₀₀ = 2.3 × 10⁵v³_fh⁻¹ M_☉ (Navarro 1998). So NGC 1961 would have an inferred mass of 2.1 × 10¹³ M_☉—the mass of a medium-sized galaxy group. Even if the halo is not precisely NFW, the total mass seems unlikely to differ by more than 50% or so.

Since NGC 1961 is at the center of a poor group, the other galaxies in its group should also be added to the baryon budget. We added the H i masses for the six other candidate group members (Haan et al. 2008) and found a total H i mass of 7.5 × 10⁹ M_☉, which is less than a sixth of the H i mass of NGC 1961. We estimated the stellar mass of the six group members using their H-band absolute magnitudes from the NASA/IPAC Extragalactic Database (NED) and a mass-to-light ratio of 0.6; this yields a total stellar mass for the group members of 3 × 10¹⁰ M_☉, less than a tenth of the stellar mass of NGC 1961. NGC 1961 is therefore by far the dominant reservoir of baryons in its group, but we do include the small baryonic contributions from the other galaxies when we compute the baryon budget.

Within 500 kpc, the baryon fraction f_b ≡ M_b/M_total is therefore 0.024–0.029 (or 0.051 with a flattened halo profile)—far less than the cosmological mean value f_b = 0.171 ± 0.006 (Dunkley et al. 2009). This corresponds to a baryon fraction within R₅₀₀ of 0.023–0.033 for the single-component fit and a maximum baryon fraction within R₅₀₀ of 0.043 for the two-component flattened β-model. Thus, within the virial radius NGC 1961 is missing over 75% of its baryons, which is surprising since the missing baryon fraction is nearly always smaller in structures of this size (McGaugh et al. 2010).

The baryonic Tully–Fisher relation (BTF; Stark et al. 2009) predicts that this galaxy should have a baryonic mass of 1.1 × 10¹² M_☉ (corresponding to a baryon fraction f_b = 0.052), so NGC 1961 is slightly below the BTF, but still potentially within the typical scatter about the relation. Including a flattened profile would definitely place this galaxy on the BTF, as would changing the gas metallicity to 0.1 Z_☉. Additionally, using the higher inclination angle of Combes et al. (2009; discussed in Section 2) would also bring NGC 1961 onto the BTF due to the steep dependence of this relation on v_circ.

We can estimate the cooling radius of this hot halo and the implied accretion rate onto the galaxy, which has implications for setting and regulating the star formation rate in the galaxy. We define the cooling radius as the radius for which the cooling time is 10 Gyr, using the expression for cooling time from Fukugita & Peebles (2006):

$$\begin{equation} \tau (r) = \frac{1.5 nkT}{\Lambda n_e \left(n-n_e\right)} \approx \frac{1.5kT\times 1.92}{\Lambda n_e \times 0.92}, \end{equation} \tag{ 1 }$$

where the latter expression assumes primeval helium abundance so that the total particle density n = 1.92n_e. For T = 10^6.85 K and Z = 0.5 Z_☉, Λ = 10^−22.85 erg cm³ s⁻¹ (Sutherland & Dopita 1993). Thus, the cooling radius occurs at n_e = 6.8 × 10⁻⁴ cm⁻³. For the range of best-fit β-model profiles listed above, this corresponds to a cooling radius between 17.8 and 18.2 kpc, and an interior hot halo mass of 8.9–10.2 × 10⁸ M_☉. It is difficult to estimate the accretion rate onto the disk from this hot halo, since the heating rate is unconstrained, but we can make an order-of-magnitude estimate by dividing the hot gas thermal energy within the 10 Gyr cooling radius by the luminosity within that radius; this yields a cooling time of 2.0–2.4 Gyr for material within the cooling radius, or an effective cooling rate of 0.4 M_☉ yr⁻¹. In contrast, we can estimate the star formation rate in NGC 1961 from the total Hα luminosity (7.6  ±  0.9 × 10⁴¹ erg s⁻¹) using the relation in Kennicutt (1998): star formation rate SFR = 7.9 × 10⁻⁴² L(Hα) = 6.0 ± 0.7 M_☉ yr⁻¹. The halo accretion rate is therefore insufficient to produce the star formation rate of the galaxy. More relevant for galaxy formation, the halo accretion rate is two orders of magnitude too low to assemble the stellar mass of this galaxy within a Hubble time. If we preserve β and r₀ for the halo, but increase S₀ to add the present-day stellar mass of 3.1 × 10¹¹ M_☉ to the halo, the cooling rate becomes 1.2–1.8 M_☉ yr⁻¹, which is still insufficient to assemble the stellar mass by a factor of 20.

These results are also evidence against the emission around this galaxy being dominated by a galactic fountain or other internal processes related to star formation. One of the brightest known galactic fountains, in NGC 891, has a bolometric luminosity of 4 × 10³⁹ erg s⁻¹ (Bregman & Houck 1997) and a star formation rate of about 4 M_☉ yr⁻¹ (Strickland et al. 2004b). For the NGC 1961 star formation rate of 6 M_☉ yr⁻¹, the highest expected luminosity of a fountain is therefore ∼6 × 10³⁹ erg s⁻¹, whereas we measure an (absorbed) luminosity within 50 kpc of 2.6–3.0 × 10⁴⁰ erg s⁻¹. Moreover, the cooling time for the gas we observe beyond 18 kpc is greater than 10 Gyr, so even if the material has an internal origin it should be treated as quasi-static instead of as a fountain.

Within the context of galaxy formation models, the physical explanation for the missing baryons from NGC 1961 is unclear. The amount of missing matter in this galaxy and the depth of the potential well make it difficult for supernova-driven winds to expel the missing baryons. The escape velocity for material originating in the galactic disk (at an assumed radius of 10 kpc) in an NFW halo of mass 2.1 × 10¹³ M_☉ is about 1300 km s⁻¹. The missing baryonic mass is 3.2 × 10¹² M_☉, so the energy needed to unbind the missing baryons from the gravitational potential of the galaxy is ∼5 × 10⁶¹ erg. A supernova with perfect coupling to the interstellar medium can inject up to ∼10⁵¹ erg of kinetic energy, so expelling the missing baryons from this galaxy requires ∼5 × 10¹⁰ supernovae. Based on the present-day stellar mass of the galaxy and the average supernova rates per stellar mass per century from Mannucci et al. (2005), the expected total amount of supernovae (Type I + II) over 13 Gyr is 4 × 10⁹, so NGC 1961 would need to have 13 times more stellar mass to supply enough energy from supernovae to unbind its missing baryons. Performing this calculation in more detail (e.g., accounting for smaller stellar mass at earlier times, allowing for cooling of supernova-heated gas) in general exacerbates the discrepancy.

We also considered the possibility of AGN feedback for ejecting the missing baryons. However, NGC 1961 is a late-type spiral galaxy, so it has a relatively small bulge and presumably a correspondingly small central black hole, which makes an AGN-driven superwind less plausible. For example, if we assume the bulge contains one-sixth of the stellar mass for this galaxy, and use the bulge-mass–black-hole-mass relation (Marconi & Hunt 2003), we estimate a central black hole of mass 1 × 10⁸ M_☉. Assuming accretion converts 10% of the infalling mass into energy, over its lifetime this black hole could have produced 2 × 10⁶¹ erg, of which it is generally assumed only about 2% can couple to the interstellar medium (Shankar et al. 2006; Bower et al. 2008) for a total available AGN feedback energy of only 4 × 10⁵⁹ erg. The most likely explanation for the missing baryons from this galaxy is probably some form of very early preheating which prevents the baryons from falling deeply into the potential well in the first place.

We also note that other giant spirals show similar baryon deficits. For example, UGC 12591, at a distance of 134 Mpc (NED average) has a peak (inclination-corrected) H i rotation velocity of 476  ±  23 km s⁻¹ (Giovanelli & Haynes 1985), which yields a virial mass of 3.5 × 10¹³ M_☉ according to the NFW relation cited above. The H i mass is 4.3 × 10⁹ M_☉ (Ho 2007), and, using the 2MASS K_S-band total magnitude (8.9) as above, we estimate a total stellar mass of 5.9 × 10¹¹ M_☉ for a baryon fraction of 0.017 before including the hot halo. We also obtained XMM-Newton observations of the hot halo around this galaxy (X. Dai et al. 2011, in preparation), which point to a similarly underluminous halo, to be discussed further in an upcoming paper.

In future work we hope to increase the sample of hot halos detected around giant spirals and further quantify the halo properties such as metallicity. If the trend of underluminous halos is common for the giant spirals, it would signal a break in the BTF somewhere between Milky Way mass galaxies and the giant spirals.