Astro-H observations of galaxy clusters have the potential to measure gas motions from turbulence and sloshing. Simulations show that while Astro-H may not be able to distinguish between different turbulence dissipation scales or spectral indices, it could distinguish between different injection scales with certain pointing configurations. Observations of sloshing gas may measure line shifts and widths, but distinguishing between broadening from sloshing versus turbulence will be difficult, limiting constraints on viscosity. Accounting for photon scattering from the cluster center is also important to avoid biases in line shift measurements. Overall, better spatial resolution provided by future missions will be needed to fully characterize gas motions in clusters.

1. GALAXY CLUSTER GAS MOTIONS
AND ASTRO-H: PREDICTIONS AND
CHALLENGES FROM SIMULATIONS
John ZuHone, MIT Kavli Institute
with
Aurora Simionescu (ISAS/JAXA), Eric Miller (MIT), Mark Bautz (MIT),
Maxim Markevitch (NASA/GSFC), and Irina Zhuravleva (Stanford)

2. ASTRO-H MISSION
• To be launched early next year
• Soft X-ray Spectrometer
(SXS):
• 3’x3’ FOV
• ~5 eV spectral resolution
• ~1’ spatial PSF

3. VELOCITY BROADENING
6.4 6.5 6.6
0.1110
normalizedcountss−1keV−1
Energy (keV)
data and folded model
sekiya 6−Jun−2011 12:36
vturb = 0 km/s
vturb = 100 km/s
vturb = 300 km/s
vturb = 1000 km/s
6.7
w
xyz
j
k
e
po
Perseus simulated spectrum (wabs＊bapec)
Astro-H cluster white paper, arXiv:1412.1176
He-like Fe line at
E0 ≈ 6.7 keV

4. Coma
200 kpc
Turbulence
A2319
200 kpc
Sloshing
Astro-H cluster white paper, arXiv:1412.1176

5. Inertial Range
Dissipation
Scale
Injection
Scale
P(k) ~ k-α
k
P(k)
Homogeneous, isotropic turbulence

6. (Zhuravleva et al 2012)
second-order structure function
velocity autocorrelation power spectrum
proportionality of 2D and 3D power spectra

7. VARYING DISSIPATION SCALES

8. VARYING INJECTION SCALES

9. MODEL FOR COMA
THERMAL PROPERTIES
Isothermal β-model:
•β = 2/3
•nc = 3×10-3 cm-3
•rc = 300 kpc
•T = 8 keV
1. Generate density, velocity fields
2. Project along z-axis for SB, line shift, width
3. Reblock images to 1.5’ resolution (SXS is 3’x3’)
KINEMATIC PROPERTIES
•Gaussian random field:
•homogeneous, isotropic
•power-law spectrum
with upper and lower
cutoffs

13. ERRORS
• “cosmic variance errors”
• Natural variations in the velocity field
• 100 realizations of the velocity field taken from the
power spectrum
• Decrease with more baselines (more pointings
spaced out at distance scales we want to resolve)

14. “strip” “big cross” “small cross”
“fill” “checkerboard”

15. COSMIC
VARIANCE

16. ERRORS
• “measurement errors”
• Statistical errors on line shift and width from Poisson statistics
(increase with increasing line width, decrease with increasing
exposure)
• Systematic errors on the line shift from gain uncertainty
• For most configurations, we assume ~100 ks per pointing, except
“checkerboard”, for which we assume ~55 ks per pointing
• Assume errors are normally distributed and add them to the map

17. BIAS CORRECTION

18. VARYING
DISSIPATION
SCALES
Curves are essentially
indistinguishable

19. VARYING
INJECTION
SCALES

20. VARYING
SPECTRAL
INDEX
Curves are essentially
indistinguishable
Kraichnan (MHD)
Kolmogorov
Burgers (shocks)

21. VARYING MACH NUMBERS

22. 1-σ confidence
limits on
power
spectrum
normalization
and injection
scale
fits to structure
function and
average line
width

23. WHAT SHOULD WE DO?
“big cross” “checkerboard”
~500 ks total exposure
(~100 ks per pointing)
~500 ks total exposure
(~55 ks per pointing)

24. SLOSHING CORES
FLASH simulations from ZuHone, Markevitch, & Johnson 2010
Gas motions of M ~ 0.3-0.5, several hundred km/s

25. • Can we detect these sloshing motions with
Astro-H?
• If so, what effect will these motions have on
the shift and shape of spectral lines?
• Can we use this spectral analysis to tell us
something about microphysics?

26. Z-PROJECTION
Inviscid Viscous
SB T
σμ
SB T
σμ

27. X-PROJECTION
Inviscid Viscous
SB T
σμ
SB T
σμ

28. Y-PROJECTION
Inviscid Viscous
SB T
σμ
SB T
σμ

29. ASTRO-H POINTINGS AND
REGIONS

30. INVISCID: X-PROJECTION

31. INVISCID:Y-PROJECTION

32. INVISCID: Z-PROJECTION

33. INVISCID: Z-PROJECTION

34. VISCOUS: X-PROJECTION

35. VISCOUS:Y-PROJECTION

36. VISCOUS: Z-PROJECTION

37. VISCOUS: Z-PROJECTION

38. DIFFERENTVISCOSITY, SAME
SHAPE

39. DIFFERENT MOTIONS, SAME SHAPE
(SOMETIMES)

40. SYNTHETIC OBSERVATIONS
ZuHone et al 2014, arXiv:1407.1783
SIMX
http://www.youtube.com/watch?v=fUMq6rmNshc
http://yt-project.org
http://hea-www.harvard.edu/simx/
+ PHOX
http://www.mpa-garching.mpg.de/~kdolag/Phox/
(Biffi et al 2012, 2013, MNRAS)
event lists: RA, Dec, E
Astro-H
event files

41. 0.01
0.1
1
countssu−1d
2 4 6 8
−0.2
0
0.2
residuals
Energy (keV)
0 2 8 17 30 48 68 93 122 154 190
SXI SXS

42. FITTING SPECTRA:Y-AXIS
Model 1:
Single-T APEC
model,
w/ thermal
broadening
only
exposure time = 200 ks
0.01
0.1
0.02
0.05
0.2
countss!1
6.2 6.3 6.4 6.5 6.6 6.7
!0.1
0
0.1
residuals
Energy (keV)
Model 1μ = 291 +9 -12 km/skeV-1

43. FITTING SPECTRA:Y-AXIS
Model 2:
Single-T APEC
model,
w/ thermal
and velocity
broadening
exposure time = 200 ks
0.01
0.1
0.02
0.05
0.2
countss!1
6.2 6.3 6.4 6.5 6.6 6.7
!0.1
0
0.1
residuals
Energy (keV)
Model 2
μ = 224 +15 -18 km/s
σ = 276 +14 -15 km/skeV-1

44. FITTING SPECTRA:Y-AXIS
Two single-T
APEC
models,
w/ thermal
broadening
only
exposure time = 200 ks
0.01
0.1
0.02
0.05
0.2
countss!1
6.2 6.3 6.4 6.5 6.6 6.7
!0.1
0
0.1
residuals
Energy (keV)
Model 3μ1 = 377 +13 -10 km/s
μ2 = -51 +16 -20 km/skeV-1

45. ✓ ✓✖ (ish)
What’s wrong with the line shifts?

46. REASON 1: NEED A BETTER
MODEL

47. REASON 2: PSF SCATTERING

48. ✓ ✓
Correct for PSF Scattering

49. A2319
200 kpc
A3667
200 kpc

50. SUMMARY
• What motions will Astro-H measure in galaxy clusters?
• Turbulence in Coma:
• Can’t distinguish between dissipation scales, spectral indices (for sane turbulence models)
• Can distinguish between injection scales, but only for certain spatial configurations of pointings
(“big cross” or “checkerboard”)
• Gas sloshing:
• Will be able to measure line shifts and widths from sloshing motions
• It will be difficult to distinguished line broadening from sloshing motions vs. turbulent motions—
constraints on viscosity are probably limited
• Need to worry about contamination of photons from cluster center—can bias line shifts significantly
• What do we need? Better spatial resolution! (Athena, SMART-X, etc.)