Measuring the Temperature of Extremely Hot Shock-Heated Gas in the Major Merger MACS~J0717.5+3745 With Relativistic Corrections to the Sunyaev-Zel'dovich Effect

TL;DR

This study tackles measuring extreme ICM temperatures in a major merger by exploiting relativistic corrections to the Sunyaev–Zel'dovich effect (rSZe). It combines space-based SPIRE-FTS spectroscopy with ground-based Bolocam data and X-ray temperatures from Chandra and XMM-Newton to constrain $T_{ m rSZe}$ in MACS J0717.5+3745, finding $T_{ m rSZe} = 15.1^{+3.8}_{-3.3}$ keV with intrinsic scatter $σ_{ m rSZe} = 5.4^{+5.1}_{-3.4}$ keV, consistent with X-ray values of $T_{ m Chandra} = 18.0^{+1.1}_{-1.1}$ keV and $T_{ m XMM} = 13.9^{+0.9}_{-0.9}$ keV. The work demonstrates the feasibility of using rSZe with moderate spectral resolution sub-mm data to probe superheated ICM gas and highlights crucial steps—CIB correction, instrumental systematics control, and joint multi-wavelength modeling—for reliable rSZe thermometry. It also discusses the limitations imposed by X-ray calibrations and the potential of future spectrophotometric SZ instruments to map non-isothermal, high-temperature gas in high-redshift clusters.

Abstract

The conversion of gravitational potential to kinetic energy results in an intracluster medium (ICM) gas with a characteristic temperature near 10 keV in the most massive galaxy clusters. X-ray observations, primarily from Chandra and XMM-Newton, have revealed a wealth of information about the thermodynamics of this gas. However, two regimes remain difficult to study with current instruments: superheated gas well above 10~keV generated by shocks from major mergers, and distant systems strongly impacted by cosmological dimming. Relativistic corrections to the Sunyaev-Zel'dovich effect (rSZe) produce a fractional spectral distortion in the cosmic microwave background at sub-millimeter and millimeter wavelengths that could offer a complimentary probe of both high temperature and high redshift ICM gas. Here we describe multi-band measurements of the rSZe, including observations from the Fourier Transform Spectrometer on the Herschel-SPIRE instrument, that constrain the ICM thermodynamics of the major merger MACSJ0717.5+3745. Within the seven observed lines of sight, we find an average temperature of $T_{\mathrm{rSZe}}=15.1^{+3.8}_{-3.3}$ keV, which is consistent with the values obtained from X-ray measurements of the same regions, with $T_{\mathrm{Chandra}}=18.0^{+1.1}_{-1.1}$ keV and $T_{\mathrm{XMM}}=13.9^{+0.9}_{-0.9}$ keV. This work demonstrates that the rSZe signal can be detected with moderate spectral resolution sub-millimeter data, while also establishing the utility of such measurements for probing superheated regions of the ICM.

Figures (11)

• Figure 1: The spectrum of each component of the SZe for a range of $T_{\rm rSZe}$ calculated from SZPackSZpack1SZpack2 assuming a Comptonization $y = 2.4 \times 10^{-4}$ and a peculiar velocity of $800$ km s$^{-1}$. Dark grey regions denote the observing bands of Bolocam bolo_instrument and red points indicate the band centers of the SPIRE-FTS, both of which are utilized to fit the SZe spectrum in our analysis. Also shown as light grey regions are the observing bands of the Herschel-SPIRE photometer observer_manual, which are used to estimate the contaminating signal from thermal dust emission.
• Figure 2: Datasets used in this analysis. The markers (labeled at the top) and circles show the average pointing location and effective beam size for each SPIRE-FTS SLW detector considered in this work. Top left: false color image of MACS J0717.5$+$3745 from the Herschel-SPIRE photometer where red represents $600$ GHz emission, green $856$ GHz, and blue $1200$ GHz. Top right: velocity map from cluster-member redshifts. Middle row: Bolocam measurements of the SZe intensity at $270$ and $140$ GHz. Bottom row: electron temperature measured by Chandra and XMM- Newton.
• Figure 3: The Dark Sky observation described in Table \ref{['tab:obs']} as processed through HIPE following the procedure outlined in §\ref{['sec:hipe']} including the standard LR correction. The widths of the lines represent the per-datum error estimate from HIPE. A systematic pattern associated with beam vignetting is evident in the outer ring of detectors; for example, the average standard deviation of the intensity of these outer ring detectors is $6.3$ MJy sr$^{-1}$ compared to $1.9$ MJy sr$^{-1}$ for the inner detectors. There remains a low frequency increase up to $\sim 6$ MJy sr$^{-1}$ that is consistent with a $4.5$ K blackbody, as we would expect from the beam intercepting cold optics with slowly varying temperatures.
• Figure 4: The signal after HIPE processing for each of the seven inner SLW bolometers. The black points denote the SPIRE-FTS spectrum that we retrieve from HIPE, the red points indicate the same for the Dark Sky observations, and the green points indicate the cleaned spectrum obtained from subtracting a scaled version of the Dark Sky data. We estimate the noise covariance of these cleaned data from Equation \ref{['eq:cov']}, and the square root of the diagonal elements are shown as error bars.
• Figure 5: The constraining power on $T_{\rm rSZe}$ estimated by the inverse square of equation \ref{['eq:sze_sensivity']}. The solid black vertical lines highlight where the low and high frequency cuts from §\ref{['sec:hipe']} are applied, and outside of which the constraining power is small. While the SZe distortion is spectrally smooth (see Fig. \ref{['fig:sze_theo']}), the relativistic corrections exhibit $\sim 100$ GHz-wide spectral deviations whose relative amplitudes change over the falling edge of the SZ spectrum. These differential effects provide a lever arm to distinguish gas at different temperatures independently of X-ray information. Hence, the constraining power peaks at $640$ and $800$ GHz. This is informative for cutting the low and high frequency ends of the FTS bandpass, as the regions with very low constraining power, e.g. $\nu < 550$, will contribute disproportionately more noise to the measurement.