Testing eROSITA Hot Halo Stacking with Individual Edge-on Spirals

[TODO: to be written after Section 2 is settled]

A Milky Way class spiral galaxy with its gaseous disk comprises only about a quarter of the total baryon content for its halo mass. These missing baryons are thought to be much more extended, possibly extending beyond the virial radius, R_vir. This is known as the circumgalactic medium (CGM) and is probably a combination of a hot gaseous phase near the virial temperature as well as cooler material. Most of the hot phase is initially produced at large radii by accretion shocks for halo masses above M_halo ≳ 10^11.5 M_⊙ (Birnboim & Dekel 2003; Dekel & Birnboim 2006) and near the virial temperature, T_vir ≃ 2 × 10⁶ (V_c/250 km s⁻¹)² K. Beyond ≲ 70 kpc, the radiative cooling time exceeds the age of the universe so that gas is not very active.

The hot CGM virializes from the outside-in, with the inner CGM (∼ 0.1 R_vir) being the last region to reach a steady thermal-pressure-supported state (Stern et al. 2021). It is this inner region where feedback is active, with simulations showing that supernovae supplies metals and sets the density normalization but does not greatly change the temperature (Faucher-Giguère & Oh 2023). Detecting the galactic fountain component has been successful (references), but this is typically within 10 kpc of the galaxy and only a small fraction of the CGM. Studying the CGM beyond the galactic fountain has been much more challenging but is also of great importance in understanding galaxy structure and formation.

Stacking of the eROSITA All-Sky Survey has produced a measurement of the extended hot circumgalactic medium (CGM) emission around thousands of Milky Way-mass galaxies. Zhang et al. (2024) stacked eRASS:4 data around central galaxies and found that the soft X-ray luminosity follows log L_X ≃ 2.4 log M_∗ + 14.6. Star-forming and quiescent galaxies host equally luminous hot halos at fixed mass (Zhang et al. 2025), and the stacked profiles now set the hot baryon budget of Milky Way-mass galaxies (Zhang et al. 2026).

In potential conflict are the deep pointed observations of individual edge-on spirals. Those observations argue for fainter X-ray extended halos. The observational situation is summarized in Figure 1, which compares the stacked eROSITA profile with upper limits at 10–30 kpc for five edge-on galaxies observed with XMM-Newton for 160–1300 ks (Hodges-Kluck 2024) [TODO: more citations?]. Four of the five limits lie below the stacked mean at the same radius. NGC 891 (500 ks) lies a factor of three below the mean, and NGC 5907 (1300 ks) lies a factor of five below it and outside the shaded band. [TODO: state whether the band is the error on the stacked mean or the intrinsic scatter]

Models find that there can be significant variation in the halo masses within the R₅₀₀ of L* galaxies, by perhaps a factor of 2 to 3 [Davies et al. 2019; other references]. That raises the possibility that a small sample of L* galaxies may, by chance, have fainter halos than the eROSITA stack and that no such discrepancy exists. We propose XMM-Newton observations to improve the single galaxy sample both in number and quality of the limiting luminosities and surface brightnesses.

Four spiral galaxies have X-ray observations sufficiently sensitive to challenge the eRosita mean emission profile. The chance of all four lying below the mean profile is only 1.5 sigma, so it is not significant. However, increasing the number to seven brings us to the 99% confidence level if all lie below the mean profile. This a simple argument conveys the need for a larger sample and in practice, the comparison will be more sophisticated, including the dispersion of the eRosita band and the distance from the mean line.

We speculate that this could lead to further examination of the eROSITA result, which might have some unanticipated issues, despite extensive analysis. Resolving the apparent difference between eROSITA and single galaxies would be a big step to obtaining a clearer understanding of the hot gas properties of the extended CGM.

A sample of seven galaxies, analyzed uniformly, will determine whether individual galaxies differ from the eROSITA mean, and by how much. Five of the seven will reach half of their mass-scaled eROSITA prediction, and the other two will reach about the prediction itself (§2B). We adopt a lognormal scatter about the stacked mean. A single galaxy then has a probability of 0.26 of lying below half of the mean for a scatter of 0.3 dex, and 0.49 for a scatter of 0.5 dex. If all five deep galaxies lie below half of their predictions, the joint probability is 1 × 10⁻³ for 0.3 dex and 0.03 for 0.5 dex. If the two shallower galaxies also lie below their predictions, the probabilities fall to 4 × 10⁻⁴ and 0.01 [TODO: adopt a scatter from simulations or the eROSITA bootstrap]. Such an outcome would place the stacked mean in doubt for this mass range. If instead the new galaxies are detected near their mass-scaled predictions, the tension in Figure 1 reflects scatter, and the stack stands.

We examined every edge-on disk galaxy within about 30 Mpc to find those that can test the eROSITA stack [TODO: state distance limit and inclination cut]. For each galaxy we scaled the stacked profile to its halo mass, using L_X ∝ M₅₀₀^1.32 (Zhang et al. 2024) and M₅₀₀ ∝ V_c³, so that the predicted surface brightness scales as V_c⁴. The exposure needed to reach a fixed fraction of that prediction grows as D² but falls as V_c⁻⁸. Massive galaxies are therefore efficient targets even at larger distances.

We request about 250 ks for NGC 4565 and NGC 2613, the two massive edge-on spirals whose existing data are too shallow for this test. NGC 4565 (D = 11.87 Mpc, V_c = 245 km s⁻¹) has a single 14 ks XMM observation. NGC 2613 (D = 22.8 Mpc, V_c = 304 km s⁻¹) has 19–24 ks of usable data after background flaring (Li et al. 2006). It is twice as distant as NGC 4565, but its predicted surface brightness is 2.4 times higher, so it needs less time to reach the same fraction of its prediction. The goal for both galaxies is a limiting surface brightness of half the mass-scaled prediction at 10–20 kpc from the disk plane. This requires about 120 ks of additional clean time for NGC 4565 and 60 ks for NGC 2613, or 250 ks after the background inflation recommended by the SOC (§3). NGC 2613 also tests an earlier result, since Li et al. (2006) found its extraplanar emission to be a factor of ten below the prediction of accretion models.

The two new galaxies join five with archival XMM data. NGC 891, 5746 and 5907 already lie below half of their predictions. NGC 3079 lies at about 0.8 times its prediction. NGC 3628 has 70 ks of archival data, which should reach about its prediction once reanalyzed, so it requires no new time [TODO: confirm clean exposure and EDD distance for NGC 3628]. These seven galaxies form the test sample. Several well-known edge-on galaxies are not in it. NGC 3044, 4013, 4631 and 5775 are less massive (V_c = 140–190 km s⁻¹), so their predicted halos are three to ten times fainter than that of NGC 4565. Reaching even their predictions would take 0.6–4.7 Ms each. Their archival limits lie above their predictions and do not constrain the stack, so we report them for completeness but exclude them from the statistical test.

The program has three objectives. First, we will measure the surface brightness, or its upper limit, in two height bins (10–20 and 20–30 kpc) for all seven test galaxies. Each value is compared with the eROSITA profile scaled to that galaxy's halo mass. Second, we will combine the seven test galaxies into a sample mean and median and compare them directly with the stack. Third, we will measure the temperature of the extraplanar gas within 10 kpc of the disk of NGC 4565, which forms stars at only 0.7 to 1 M_⊙ yr⁻¹ (Vargas et al. 2019). With little current feedback, this gas should lie near the virial temperature of 0.17 keV for V_c = 245 km s⁻¹. A temperature well above this value would show that feedback heats the inner halo even in a quiescent spiral. Above 10 kpc we expect upper limits on the temperature, and we do not propose to measure the metallicity.

NGC 3628 is the one test galaxy in an interacting system, the Leo Triplet. The eROSITA stack is built from central galaxies, which are not selected against interactions, so it belongs in the comparison. We will mask its tidal features and report the sample mean both with and without NGC 3628, since an interaction could raise the halo luminosity.

To be improved. All seven test galaxies will be reduced with a single pipeline, so that new and archival data share the same screening, masking and background model. We will filter soft-proton flares with the XMM-Newton Extended Source Analysis Software and mask point sources at the 90% encircled-energy radius. Surface brightness profiles will be extracted in rectangular regions parallel to the disk, in height bins of 10–20 and 20–30 kpc, with spiral arms and tidal features excluded. The sky background comprises the Local Hot Bubble, the Milky Way halo and the cosmic X-ray background. We will fit it jointly with ROSAT All-Sky Survey spectra from an annulus outside the galaxy, and check for solar-wind charge exchange by comparing the oxygen line strengths between observations. For the nearest galaxies, the background region will be placed beyond 40 kpc, and we will quote the halo emission that the stacked profile predicts at that radius as a systematic error.

Upper limits will be computed at a common confidence level for all seven galaxies [TODO: match the confidence level used in Figure 1]. The sample mean and scatter will be estimated with survival analysis for censored data, using the Kaplan–Meier estimator (Feigelson & Nelson 1985 [TODO: verify on ADS]), and compared with the mass-scaled eROSITA prediction. For NGC 4565 we will fit an absorbed APEC model to the extraplanar spectrum within 10 kpc, jointly for the three EPIC detectors. The abundance will be fixed at 0.14 Z_⊙, the value measured for NGC 891 (Hodges-Kluck, Bregman & Li 2018). The required exposure for each target is derived in §3.

We request 250 ks: 165 ks on NGC 4565 and 85 ks on NGC 2613. These exposures yield about 118 ks and 61 ks of clean time after the 40% background inflation recommended by the SOC. Combined with the existing 14 ks on NGC 4565 and 19–24 ks on NGC 2613 (Li et al. 2006), the clean totals are 132 ks and about 85 ks. Each galaxy then reaches a limiting surface brightness at 10–20 kpc of half its mass-scaled eROSITA prediction: 2.1 × 10³⁵ and 4.9 × 10³⁵ erg s⁻¹ kpc⁻² in the 0.5–2 keV band. NGC 4565 will be observed in two pointings of about 83 ks, within the AO-26 limit for a single observation [TODO: confirm the per-observation limit; if there is a preference to give full orbit exposures, of 110 ks, then the program goes to 330 ks, a large proposal, which isn't bad].

The exposures are scaled from the 500 ks observation of NGC 891, which reached 0.9 × 10³⁵ erg s⁻¹ kpc⁻² at 10–20 kpc (Figure 1). For a region of fixed physical size, the source and background counts both fall as D⁻². The signal-to-noise ratio then depends only on the product t/D², and the limit on surface brightness Σ improves as t^−1/2. The required time therefore scales as t ∝ D² Σ⁻². This scaling is empirical in one respect: it carries over whatever background systematics limited the NGC 891 data. We also note that NGC 3628 needs no new time. Its 70 ks of archival data should already reach about its prediction [TODO: confirm the clean exposure].

A direct count-rate estimate supports these exposures. For a 0.2 keV thermal plasma, the target surface brightness of NGC 4565 corresponds to 1.5 × 10⁻¹⁶ erg cm⁻² s⁻¹ arcmin⁻², or 7 × 10⁻⁵ counts s⁻¹ arcmin⁻² in the EPIC pn camera. The extraction region covers 10–20 kpc on both sides of the disk and 30 kpc along it, which is 45 arcmin² after masking point sources. In 132 ks the pn camera collects about 440 source counts against 6000 background counts, a statistical significance of 5.7σ. For NGC 2613 the region is 12 arcmin², and 85 ks gives 190 source counts against 1100 background counts, also 5.7σ. The two MOS cameras add about 60% to these counts. [TODO: verify the conversion and background rates with PIMMS and the ESAS quiescent background]

The same calculation for NGC 891 gives 5.7σ at its published limit. If that limit is at 3σ, it is about twice as high as statistics alone would allow [TODO: confirm the confidence level of the NGC 891 limit]. We attribute this factor to systematic errors in the background model, which matter most when the source is a small fraction of the background. The source-to-background ratio is 0.03 for NGC 891 but 0.07 for NGC 4565 and 0.17 for NGC 2613. Background systematics are therefore less important for our targets, and the scaled exposures are conservative.

The temperature measurement for NGC 4565 uses the region 2–10 kpc from the disk plane. If the surface brightness there is about 5 × 10³⁵ erg s⁻¹ kpc⁻², as the stacked profile predicts at these radii, the pn camera collects about 850 source counts against 4800 background counts. With the MOS data, the spectrum contains about 1400 source counts. This is enough to distinguish the virial temperature of 0.17 keV from gas at 0.3 keV or hotter [TODO: confirm with a simulated XSPEC spectrum].

Two practical issues affect the observations. First, background flaring removed more than half of the earlier NGC 2613 exposure. Flaring depends on the orbit and the solar cycle rather than on the target, so we adopt the SOC inflation factor for both galaxies. Second, point sources must be masked down to a common luminosity. For NGC 4565, the 60 ks of archival Chandra data provide source positions below the XMM detection limit, but the soft response of Chandra ACIS is now too low to measure the diffuse emission itself [TODO: check the Chandra ObsIDs and depth]. Both targets are observed with EPIC pn and MOS in Full Frame mode with the medium filter. Neither target has a known scheduling constraint in AO-26 [TODO: confirm with the XMM-Newton Visibility Checker].

XMM-Newton is the only observatory that can make this measurement. eROSITA has not observed since 2022, and its survey depth and point spread function cannot isolate the halo of a single nearby galaxy. The XRISM field of view is too small to cover the region 10–20 kpc above the disk.