Discovery of a Premerger Shock in an Intercluster Filament in Abell 98

Clusters of galaxies are primarily assembled and grow via accretion, gravitational infall, and mergers of smaller substructures and groups. In such merging events, a significant fraction of kinetic energy dissipates (on a Gyr timescale) in the intracluster medium (ICM) via shocks and turbulence (Markevitch et al. 1999). Such shocks are the major heating sources for the X-ray emitting ICM plasma (Markevitch & Vikhlinin 2007). Shock fronts provide an essential observational tool in probing the physics of transport processes in the ICM, including electron–ion equilibration and thermal conduction, magnetic fields, and turbulence (e.g., Markevitch 2006; Markevitch & Vikhlinin 2007; Botteon et al. 2016, 2018).

Despite the intrinsic interest and significance of merger shocks, X-ray observations of merger shocks with a sharp density edge and an unambiguous jump in temperature are relatively rare. Currently, only a handful of merger shock fronts have been identified by Chandra, such as 1E 0657-56 (Markevitch et al. 2002), A520 (Markevitch et al. 2005), A2146 (Russell et al. 2010, 2012), A2744 (Owers et al. 2011), A754 (Macario et al. 2011), A2034 (Owers et al. 2014), and A665 (Dasadia et al. 2016).

Cosmic filaments are thought to connect the large-scale structures of our universe (e.g., Dolag et al. 2006; Werner et al. 2008; Alvarez et al. 2018; Reiprich et al. 2021). Several independent searches for baryonic mass have confirmed discrepancies in baryonic content between the high- and low-redshift universe (e.g., Fukugita et al. 1998; Fukugita & Peebles 2004), with fewer baryons being detected in the local universe. They concluded that a significant fraction of these missing baryons may be "hidden" in the WHIM, in cosmic filaments that connect clusters and groups. The WHIM has a temperature in the 10⁵–10⁷ K (or, kT ∼ 0.01–1 keV) regime, and relatively low surface brightness (e.g., Davé et al. 1999; Cen & Ostriker 1999; Davé et al. 2001; Smith et al. 2011).

Abell 98 (hereafter A98) is a richness class III early-stage merger with three subclusters: central (A98S; z ≈ 0.1063), northern (A98N; z ≈ 0.1042), and southern (A98SS; z ≈ 0.1218). The northern and southern subclusters are at projected distances of ∼1.1 Mpc and 1.4 Mpc from the central subcluster, respectively (e.g., Abell et al. 1989; Burns et al. 1994; Jones & Forman 1999; Paterno-Mahler et al. 2014). The central subcluster is undergoing a separate late-stage merger, with two distinct X-ray cores. Previous observations using Chandra and showed that A98N is a cool core cluster with a marginal detection of a warm gas arc, consistent with the presence of a leading bow shock, but that the exposure time was insufficient to confirm this feature (Paterno-Mahler et al. 2014).

To investigate further, we analyzed deep (∼227 ks) Chandra observations of A98N and A98S. In this Letter, we report on the detection of an intercluster filament connecting A98N and A98S, and of a leading bow shock in the region of the filament, associated with the early-stage merger between A98N and A98S. We adopted a cosmology of H₀ = 70 km s⁻¹ Mpc⁻¹, Ω_Λ = 0.7, and Ω_m = 0.3, which gives a scale of 1'' = 1.913 kpc at the redshift z = 0.1042 of A98. Unless otherwise stated, all reported error bars are at 90% confidence level.

A98 was observed twice with Chandra for a total exposure time of ∼227 ks. The observation logs are listed in Table 1. We discuss the detailed data reduction processes in Appendix A.

2.1. Imaging Analysis

The image showing the both A98N and A98S in the 0.5–2 keV energy band are shown in Figure 1. We derived a Gaussian gradient magnitude (GGM) filtered image of A98, zooming in the northern subcluster, as shown in Figure 2. The GGM-filtered image provides a powerful tool to reveal substructures and any associated sharp features in the cluster core, as well as at larger cluster radii (Walker et al. 2016). The intensity of the GGM images indicates the slope of the local surface brightness gradient, with steeper gradients showing up as brighter regions. The GGM image we present here is filtered on a length scale of 32 pixels. Each pixel is 0.492'' wide. We observe a rapid change in the magnitude of the surface brightness gradient at ∼400 kpc to the south of the A98N center, as seen in Figure 2.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

GGM images often show artifacts from the filtering process, particularly in low surface brightness regions. Therefore, we next test for the presence of the edge feature indicated in Figure 2 by extracting a surface brightness profile across the edge. Figure 2 shows the resulting radial surface brightness profile as a function of distance from the A98N core in the 0.5–2 keV energy band. We observe an edge in the X-ray surface brightness profile at about 420 kpc (0:46:23.14, +20:33:46.32) from the A98N core. The distance of the edge from the A98N core is consistent with the edge observed in the GGM image, which suggests the abrupt change in the gradient corresponds to the surface brightness edge.

The shape of the extracted surface brightness profile across the edge is consistent with what is expected from a projection of a 3D density discontinuity (Markevitch et al. 2000). To quantify the surface brightness edge, we fit the surface brightness profile by projecting a 3D discontinuous double power-law model along the line of sight, defined as

$$\begin{eqnarray}{n}_{e}(r)\propto \left\{\begin{array}{ll}{\left(\displaystyle \frac{r}{{r}_{\mathrm{edge}}}\right)}^{-{\alpha }_{1}}, & \mathrm{if}\ r\lt {r}_{\mathrm{edge}}\\ \displaystyle \frac{1}{\mathrm{jump}}{\left(\displaystyle \frac{r}{{r}_{\mathrm{edge}}}\right)}^{-{\alpha }_{2}}, & \mathrm{if}\ r\geqslant {r}_{\mathrm{edge}}\end{array}\right.,\end{eqnarray} \tag{ 1 }$$

where n_e (r) is the 3D electron density at a radius r, r_edge is the radius of the putative edge, jump is the density jump factor, and α₁ and α₂ are the slopes before and after the edge, respectively. A constant term was also added to the model to account for any residual background, after blank-sky subtraction. The best-fit value of this term was consistent with zero, suggesting we successfully eliminated sky and particle background. We project the estimated emission measure profile onto the sky plane and fit the observed surface brightness profile by using least-squares fitting technique with α₁, α₂, r_edge, and jump as free parameters. Figure 2 shows the best-fit model and the 3D density profile (inset). The best-fit power-law indices across the edge are α₁ = 0.76 ± 0.01 and α₂ = 0.83 ± 0.02, respectively (χ²/dof = 57/21). The density jumps, across the edge, by a factor of ρ₂/ρ₁ = 2.5 ± 0.3, where suffixes 2 and 1 represent the regions inside and outside of the front. Assuming that the edge is a shock front, this density jump corresponds to a Mach number of ${ \mathcal M }$ = 2.3 ± 0.3, estimated from the Rankine–Hugoniot jump condition, defined as

$$\begin{eqnarray}&&{ \mathcal M }={\left[\displaystyle \frac{2r}{\gamma +1-r\left(\gamma -1\right)}\right]}^{\tfrac{1}{2}},\end{eqnarray} \tag{ 2 }$$

where r = ρ₂/ρ₁ and for a monoatomic gas γ = 5/3. The edge radius, obtained from the fit, is 420 ± 25 kpc. We estimated the uncertainties by allowing all the other model parameters to vary freely. The best-fit edge radius is consistent with the distance of the GGM peak from the A98N center.

2.2. Spectral Analysis

Early-stage, major mergers between two roughly equal mass subclusters are expected to typically have their merger axis aligned with the filaments of the cosmic web (see Alvarez et al. 2018 for further discussion). To search for faint X-ray emission associated with the filament between A98N and A98S, we extracted a surface brightness profile from nine box regions across the bridge between A98N and A98S in the 0.5–2 keV energy band (see Figure 1). Figure 3 shows the surface brightness profile of the bridge. This surface brightness profile includes the emission from the extended ICM of both subclusters, and from the filament. To account for only the extended ICM emission from both subclusters, we extracted surface brightness profiles from similar regions placed in the opposite directions of the filament, using Suzaku observations of A98 (Alvarez et al. 2022), assuming in each that the contribution from the neighboring subcluster is negligible. We used Suzaku observations because the existing Chandra observations do not cover the part of the sky needed for such analysis. These two diffuse surface brightness profiles are then subtracted from the surface brightness profile of the bridge, yielding the surface brightness profile of the filament. We use WebPIMMS ⁹ to convert Suzaku and Chandra count rates to physical units (erg cm⁻² s⁻¹ arcsec⁻²) in the 0.5–2 keV energy band. We assumed a thermal APEC model with absorption fixed to N_H = 3.06 × 10²⁰ cm⁻², abundance Z = 0.2Z_⊙, and temperature kT = 2.6 keV (as discussed later in the current Section).

Zoom In Zoom Out Reset image size

Figure 3 shows the resulting surface brightness profile of the filament in the 0.5–2 keV energy band. We detected excess X-ray surface brightness in the region of the bridge with a ∼3.2σ significance level. Similar excess emission along the bridge with somewhat lower significance (∼2.2σ) was also found by Alvarez et al. (2022) using only Suzaku data. Being very nearby to both subcluster cores, where emission is dominated by the respective subcluster, we could not detect any significant filament emission from the first two and last two regions. This excess X-ray emission suggests the presence of a filament along the bridge connecting A98N and A98S.

To measure the temperature across the bridge region, we adopted similar regions used for the surface brightness profile of the bridge. The spectra were then fitted to a single-temperature APEC model (1-T), keeping the metallicity fixed to 0.2 Z_⊙. Figure 3 shows the projected temperature profile. The temperatures across the bridge are consistent within their ∼2.7σ (90%) uncertainty, except for third region where we detected a shock. We next measured the global properties of the bridge using a 0.6 Mpc × 0.7 Mpc box region (632 kpc from the A98N and 505 kpc from the A98S; shown with cyan in Figure 1). Using a single-temperature emission model for the bridge region, we obtained a temperature of ${1.8}_{-0.4}^{+0.7}$ keV and an abundance of ${0.22}_{-0.16}^{+0.12}$ Z_⊙. Our measured temperature of the bridge is consistent with the temperatures obtained by Paterno-Mahler et al. (2014) using XMM-Newton and relatively short exposure Chandra observations. We next estimated the electron density of the bridge using

$$\begin{eqnarray}\begin{array}{rcl}{n}_{e} & = & \left[1.73\times {10}^{-10}\times N\ \sin \left(i\right)\times {\left(1+z\right)}^{2}\right.\\ & & \times {\left.{\left(\displaystyle \frac{{D}_{A}}{\mathrm{Mpc}}\right)}^{2}{\left(\displaystyle \frac{r}{\mathrm{Mpc}}\right)}^{-2}{\left(\displaystyle \frac{{l}_{\mathrm{obs}}}{\mathrm{Mpc}}\right)}^{-1}\right]}^{1/2}\ {\mathrm{cm}}^{-3},\end{array}\end{eqnarray} \tag{ 3 }$$

where N is APEC normalization, D_A is the angular diameter distance, r and l_obs are the radius and the projected length of the filament, respectively. We obtained an electron density of n_e = 4.2${}_{-0.8}^{+0.9}$ × 10⁻⁴ cm⁻³, assuming the filament is in the plane of the sky (i = 90°) and has cylindrical symmetry, since for i ≪ 90° we would not expect to detect a clear leading merger shock edge. Our measured temperature and electron density are higher than the expected temperature (≲1 keV) and electron density (∼10⁻⁴ cm⁻³) for the WHIM (e.g., Bregman 2007; Werner et al. 2008; Eckert et al. 2015; Alvarez et al. 2018; Hincks et al. 2022).

The surface brightness profiles seen in Figure 3 show that the emission from the filament itself is much fainter than the diffuse, extended cluster emission. A low-density gas emission is expected together with the ICM emission at the bridge region. We, therefore, adopted a two-temperature emission model for the bridge and obtained a temperature of kT_hot = 2.60${}_{-0.62}^{+0.93}$ keV for the hotter component and kT_cool = 1.07 ± 0.29 keV for the cooler component. The higher temperature gas is probably mostly the overlapping extended ICM of the subclusters seen in projection. The two-temperature model was a marginal improvement over the one-temperature model with an F-test probability of 0.08. The emission measure of the cooler component corresponds to an electron density of n_e = 1.30${}_{-0.31}^{+0.28}$ × 10⁻⁴ cm⁻³, assuming the filament is in the plane of the sky. From the temperature and electron density of the cooler component, we obtain an entropy of ∼416 keV cm². Our measured temperature, density, and entropy of the cooler component are consistent with what one expects for the hot, dense part of the WHIM (e.g., Eckert et al. 2015; Bulbul et al. 2016; Alvarez et al. 2018; Reiprich et al. 2021). Suzaku observations also show similar emission to the north of A98N, beyond the virial radius, in the region of the putative large-scale cosmic filament (Alvarez et al. 2022). We also check for any systematic uncertainties in measuring the filament temperature, abundance, and density by varying the scaling parameter of blank-sky background spectra by ±5%. We find no significant changes.

4.1. Nature of the Shock Front

4.2. Electron–Ion Equilibrium

The electron heating mechanism behind a shock front is still up for debate. The collisional equilibrium model predicts that a shock front propagating through a collisional plasma heats the heavier ions dissipatively. Electrons are then compressed adiabatically, and subsequently come to thermal equilibrium with the ions via Coulomb collisions after a timescale defined in Equation (B1) (Spitzer 1962; Sarazin 1988; Ettori & Fabian 1998; Markevitch & Vikhlinin 2007). By contrast, the instant equilibrium model predicts that electrons are strongly heated at the shock front, and their temperature rapidly rises to the postshock gas temperature, similar to the ions (Markevitch 2006; Russell et al. 2012). The electron and ion temperature jumps at the shock front are determined by the Rankine–Hugonoit jump conditions. Markevitch (2006) showed that the observed temperature profile across the shock front of the Bullet cluster supports the instant equilibrium model. Russell et al. (2012) found that the temperature profile across one shock front of A2146 supports the collisional model while another shock supports the instant model. However, in all cases the measurement errors prevented a conclusive determination. Later, Russell et al. (2022) with deeper Chandra observations found both shocks in A2146 favor the collisional model.

Here, we compare the observed temperature profile across the shock front of A98 with the predicted temperature profiles from collisional and instant equilibrium models. We estimate the model electron temperatures and project them along the line of sight, as described in Appendix B. The resulting temperature profiles are shown in Figure 4. The observed postshock electron temperature appears to be higher than the temperature predicted by the collisional equilibrium model and favors the instant equilibrium model, although we cannot rule out the collisional equilibration model due to the large uncertainty in the postshock electron temperature.

Zoom In Zoom Out Reset image size

4.3. Filament Emission

We are grateful to the anonymous referee for insightful comments that greatly helped to improve the Letter. This work is based on observations obtained with Chandra observatory, a NASA mission and Suzaku, a joint JAXA and NASA mission. A.S. and S.R. are supported by the grant from NASA's Chandra X-ray Observatory, grant number GO9-20112X.

A98 was observed twice with Chandra ACIS-I in VFAINT mode, in 2009 September for 37 ks split into two observations and later in 2018 September–2019 February for 190 ks divided into eight observations. The combined exposure time is ∼227 ks (detailed observation logs are listed in Table 1). The Chandra data reduction was performed using CIAO version 4.12 and CALDB version 4.9.4 provided by the Chandra X-ray Center (CXC). We have followed a standard data analysis thread. ¹⁰

All level 1 event files were reprocessed using the chandra_repro task, employing the latest gain and charge transfer inefficiency corrections, and standard grade filtering. VFAINT mode was applied to improve the background screening. The light curves were extracted and filtered using the lc_clean script to identify and remove periods affected by flares. The filtered exposure times are listed in Table 1. We used the reproject_obs task to reproject all observations to a common tangent position and combine them. The exposure maps in the 0.5–2.0 keV energy bands were created using the flux_obs script by providing a weight spectrum. The weight spectrum was generated using the make_instmap_weights task with an absorbed APEC plasma emission model and a plasma temperature of 3 keV. To remove low signal-to-noise areas near chip edges and chip gaps, we set the pixel value to zero for those pixels with an exposure of less than 15% of the combined exposure time.

Point sources were identified using wavdetect with a range of wavelet radii between 1 and 16 pixels to maximize the number of detected point sources. We set the detection threshold to ∼10⁻⁶, for which we expect ≲1 spurious source detection per CCD. We used blank-sky observations provided by the CXC to model the non-X-ray background and emission from the foreground structures (e.g., Galactic Halo and Local Hot Bubble) along the observed direction. The blank-sky background was generated using the blanksky task and then reprojected to match the coordinates of the observations. The resulting blank-sky background was normalized so that the hard-band (9.5–12 keV) count rate matched the observations.

When a shock front propagates through a plasma, it heats the ions dissipatively in a layer that has a width of few ion–ion collisional mean free paths. On the other hand, having very high thermal velocity compared to the shock, the electron temperature does not jump by the same high factor as the ion temperature. The electrons are compressed adiabatically at first in merger shocks and subsequently equilibrate with the ions via Coulomb scattering after a timescale (Spitzer 1962; Sarazin 1988) given by

$$\begin{eqnarray}&&{t}_{\mathrm{eq}}(e,p)\approx 6.2\times {10}^{8}\mathrm{yr}{\left(\displaystyle \frac{{T}_{e}}{{10}^{8}{\rm{K}}}\right)}^{3/2}{\left(\displaystyle \frac{{n}_{e}}{{10}^{-3}{\mathrm{cm}}^{-3}}\right)}^{-1},\end{eqnarray} \tag{ B1 }$$

where T_e and n_e are the electron temperature and density, respectively.

Alternatively, the instant collisionless shock model predicts that the electrons and ions reach thermal equilibrium on a timescale much shorter than t_eq after passing the shock front, where the postshock electron temperature is determined by the preshock electron temperature and the Rankine–Hugonoit jump conditions (Markevitch & Vikhlinin 2007). We use the best-fit density profile shown in Figure 2 to project this model electron temperature along the line of sight analytically (Russell et al. 2012).

In the collisional equilibration model, the electron temperature rises at the shock front through adiabatic compression,

$$\begin{eqnarray}&&{T}_{e,2}={T}_{e,1}{\left(\displaystyle \frac{{\rho }_{2}}{{\rho }_{1}}\right)}^{\gamma -1},\end{eqnarray} \tag{ B2 }$$

where ρ₁ and ρ₂ are the gas density in the preshock and postshock regions, and γ = 5/3. Electron and ion temperatures then subsequently equilibrate via Coulomb collision at a rate given by

$$\begin{eqnarray}&&\displaystyle \frac{{{dT}}_{e}}{{dt}}=\displaystyle \frac{{T}_{i}-{T}_{e}}{{t}_{\mathrm{eq}}},\end{eqnarray} \tag{ B3 }$$

where T_i is the ion temperature. Since the total kinetic energy density is conserved, the local mean gas temperature, T_gas, is constant with time, where T_gas is given by

$$\begin{eqnarray}&&{T}_{\mathrm{gas}}=\displaystyle \frac{{n}_{e}{T}_{e}+{n}_{i}{T}_{i}}{{n}_{i}+{n}_{e}}=\displaystyle \frac{1.1{T}_{e}+{T}_{i}}{2.1},\end{eqnarray} \tag{ B4 }$$

where n_i is the ion density.

We integrate Equation (B3) by using Equations (B1) and (B4) to obtain the model electron temperature analytically. Finally, we project the model electron temperature profile along the line of sight (Ettori & Fabian 1998) by

$$\begin{eqnarray}&&\langle T\rangle ={\int }_{{b}^{2}}^{\infty }\displaystyle \frac{\epsilon (r){T}_{e}(r){{dr}}^{2}}{\sqrt{{r}^{2}-{b}^{2}}}/{\int }_{{b}^{2}}^{\infty }\displaystyle \frac{\epsilon (r){{dr}}^{2}}{\sqrt{{r}^{2}-{b}^{2}}},\end{eqnarray} \tag{ B5 }$$

where (r) is the emissivity at physical radius r and b is the distance from the shock front.

The emissivity-weighted electron temperature should be close to what one observes with a perfect instrument with a flat energy response across the relevant energy range. Since this is not the case, we convolve the instant and collisional model electron temperatures with the response of the telescope to predict what we expect to measure (Russell et al. 2012). We first estimate the emissivity-weighted electron temperature using the above models and corresponding emission measure using the best-fit density discontinuity model (Equation (3)) in a small volume dV. We then sum the emission measures with similar temperatures for each annulus using a temperature binning of 0.1 keV. We simulate spectra in XSPEC using a multitemperature absorbed apec model. We fix the temperature of each component with the median temperature of each bin and calculate the normalization based on the summed emission measure in that temperature bin. We also fix the abundance to 0.4 Z_⊙, N_H to galactic value, and redshift to 0.1043. To estimate the expected projected temperature in this annulus, we finally fit this simulated spectra with a single-temperature absorbed apec model with abundance, N_H, and redshift fixed as above.

We adopt the Monte Carlo technique with 1000 realizations to measure uncertainty in model electron temperatures. Assuming a Gaussian distribution of the preshock temperature, which is the largest source of uncertainty, we repeated the model and projected temperature calculations 1000 times with a new value of preshock temperature each time. The resulting instant and collisional model temperature profiles with 1σ uncertainty are shown in Figure 4.