CMB component separation intution and GreenPol

Transcription

1 CMB component separation intution and GreenPol Hans Kristian Eriksen University of Oslo Nordita, Stockholm July 2017 in collaboration with Unni Fuskeland, Ari Kaplan, Ingunn Wehus, Hao Liu, Phil Lubin, Peter Meinhold, Pavel Naselsky and Andrea Zonca

2 The Challenge 40' FWHM

3 The Challenge 40' FWHM

4 The Challenge 1 degree FWHM

5 The Challenge 1 degree FWHM

6 The Challenge

7 The Challenge Du s t

8 The Challenge Du s Sync hrotr on t

9 The Challenge Du s Sync hrotr on Noise floor t

10 Rules of thumb: The Challenge Du s Sync hrotr on Noise floor t

11 Rules of thumb: Afg < 1µK The Challenge at fsky ~ 0.1 Du s Sync hrotr on Noise floor t

12 Rules of thumb: Afg < 1µK Afg < 10µK The Challenge at fsky ~ 0.1 at fsky ~ 0.7 Du s Sync hrotr on Noise floor t

13 Rules of thumb: The Challenge Afg < 1µK at fsky ~ 0.1 Afg < 10µK at fsky ~ 0.7 Afg < 100µK at fsky ~ 0.99 Du s for ν0synch = 30 GHz ν0dust = 353 Ghz Sync hrotr on Noise floor t

14 Rules of thumb: The Challenge Afg < 1µK at fsky ~ 0.1 Afg < 10µK at fsky ~ 0.7 Afg < 100µK at fsky ~ 0.99 Du s for ν0synch = 30 GHz ν0dust = 353 Ghz For comparison, the RMS of a pure B-mode signal (l= at 1 deg FWHM) with a given value of r is ~35 nk for r = 10-2 ~3.5 nk for r = 10-4 Sync hrotr on Noise floor t

15 Tensor-to-scalar ratio foreground floor Question: What bias would one expect if neglecting foregrounds completely?

16 Tensor-to-scalar ratio foreground floor Question: What bias would one expect if neglecting foregrounds completely?

17 Tensor-to-scalar ratio foreground floor Question: What bias would one expect if neglecting foregrounds completely? NB! Only intended to provide a rough order-of-magnitude estimate! Precise values depend of course sensitively on sky location and angular scales

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20 What is the ideal frequency coverage for a typical CMB + synchrotron + thermal dust model space?

21 Method: Posterior mapping Assume following typical model for a single pixel on the sky: where g(ν) is the conversion factor between RJ and thermodynamic temperature units

22 Method: Posterior mapping Assume following typical model for a single pixel on the sky: where g(ν) is the conversion factor between RJ and thermodynamic temperature units Six free parameters: Acmb: CMB amplitude

23 Method: Posterior mapping Assume following typical model for a single pixel on the sky: where g(ν) is the conversion factor between RJ and thermodynamic temperature units Six free parameters: Acmb: CMB amplitude As: Synchrotron amplitude at 30 GHz

24 Method: Posterior mapping Assume following typical model for a single pixel on the sky: where g(ν) is the conversion factor between RJ and thermodynamic temperature units Six free parameters: Acmb: CMB amplitude As: Synchrotron amplitude at 30 GHz Ad: Thermal dust amplitude at 353 GHz

25 Method: Posterior mapping Assume following typical model for a single pixel on the sky: where g(ν) is the conversion factor between RJ and thermodynamic temperature units Six free parameters: Acmb: CMB amplitude As: Synchrotron amplitude at 30 GHz Ad: Thermal dust amplitude at 353 GHz βs: Synchrotron spectral index

26 Method: Posterior mapping Assume following typical model for a single pixel on the sky: where g(ν) is the conversion factor between RJ and thermodynamic temperature units Six free parameters: Acmb: CMB amplitude As: Synchrotron amplitude at 30 GHz Ad: Thermal dust amplitude at 353 GHz βs: Synchrotron spectral index βd: Thermal dust spectral index

27 Method: Posterior mapping Assume following typical model for a single pixel on the sky: where g(ν) is the conversion factor between RJ and thermodynamic temperature units Six free parameters: Acmb: CMB amplitude As: Synchrotron amplitude at 30 GHz Ad: Thermal dust amplitude at 353 GHz βs: Synchrotron spectral index βd: Thermal dust spectral index Td: Effective thermal dust temperature

28 Method: Posterior mapping Given a set of observed frequencies with associated instrumental noise RMS's, the posterior distribution for this model reads P ( θ ) L ( θ ) P ( θ ) =e 1 2 ( d s 2 ν ν σ ν ) P ( β,β,t ) s d d

29 Method: Posterior mapping Given a set of observed frequencies with associated instrumental noise RMS's, the posterior distribution for this model reads P ( θ ) L ( θ ) P ( θ ) =e 1 2 ( d s 2 ν ν σ ν ) P ( β,β,t ) s d d Computationally very cheap, and mapping out the full posterior distribution by Metropolis-Hastings MCMC (producing ~few millions samples) takes a few seconds on a single CPU core

30 Method: Posterior mapping Given a set of observed frequencies with associated instrumental noise RMS's, the posterior distribution for this model reads P ( θ ) L ( θ ) P ( θ ) =e 1 2 ( d s 2 ν ν σ ν ) P ( β,β,t ) s d d Computationally very cheap, and mapping out the full posterior distribution by Metropolis-Hastings MCMC (producing ~few millions samples) takes a few seconds on a single CPU core Note: This is essentially a special case of the Planck 2015 analysis, reducing Commander to a single pixel, and including only CMB, synchrotron and thermal dust in the model

31 Experiment setup To parametrize different experiment setups, we introduce three experiment parameters:

32 Experiment setup To parametrize different experiment setups, we introduce three experiment parameters: Nband: Number of frequency bands between νmin and νmax

33 Experiment setup To parametrize different experiment setups, we introduce three experiment parameters: Nband: Number of frequency bands between νmin and νmax νmin: Lowest frequency

34 Experiment setup To parametrize different experiment setups, we introduce three experiment parameters: Nband: Number of frequency bands between νmin and νmax νmin: Lowest frequency fν: Ratio between two neighboring frequencies (ie., logarithmic spacing)

35 Experiment setup To parametrize different experiment setups, we introduce three experiment parameters: Nband: Number of frequency bands between νmin and νmax νmin: Lowest frequency fν: Ratio between two neighboring frequencies (ie., logarithmic spacing) For modelling per-detector noise as a function of frequency, we adopt the radiometer equation ( T cmb +T inst +T sidelobe + ) +T atmos σ 0 +σ atm ( ν ) σ= = Δν Δν ν T sys

36 Experiment setup To parametrize different experiment setups, we introduce three experiment parameters: Nband: Number of frequency bands between νmin and νmax νmin: Lowest frequency fν: Ratio between two neighboring frequencies (ie., logarithmic spacing) For modelling per-detector noise as a function of frequency, we adopt the radiometer equation ( T cmb +T inst +T sidelobe + ) +T atmos σ 0 +σ atm ( ν ) σ= = Δν Δν ν T sys In addition, since most experiments are limited by focal plane area, and the size of a diffraction limited detector scales inverse proportionally to its wavelength, the effective noise (including focal plane penalty) scales as σ sat ( ν ) σ0 ν 3/ 2 σ ground ( ν ) σ 0 +σ atm ( ν ) ν 3/ 2

37 Experiment setup To parametrize different experiment setups, we introduce three experiment parameters: Nband: Number of frequency bands between νmin and νmax νmin: Lowest frequency fν: Ratio between two neighboring frequencies (ie., logarithmic spacing) For modelling per-detector noise as a function of frequency, we adopt the radiometer equation ( T cmb +T inst +T sidelobe + ) +T atmos σ 0 +σ atm ( ν ) σ= = Δν Δν ν T sys In addition, since most experiments are limited by focal plane area, and the size of a diffraction limited detector scales inverse proportionally to its wavelength, the effective noise (including focal plane penalty) scales as σ sat ( ν ) σ0 ν 3/ 2 σ ground ( ν ) σ 0 +σ atm ( ν ) ν 3/ 2 (Lots of other effects as well, of course, but we only care about order-of-magnitude estimates here)

38 Experiment setup To parametrize different experiment setups, we introduce three experiment parameters: Nband: Number of frequency bands between νmin and νmax νmin: Lowest frequency fν: Ratio between two neighboring frequencies (ie., logarithmic spacing) For modelling per-detector noise as a function of frequency, we adopt the radiometer equation ( T cmb +T inst +T sidelobe + ) +T atmos σ 0 +σ atm ( ν ) σ= = Δν Δν ν T sys In addition, since most experiments are limited by focal plane area, and the size of a diffraction limited detector scales inverse proportionally to its wavelength, the effective noise (including focal plane penalty) scales as σ sat ( ν ) σ0 ν 3/ 2 σ ground ( ν ) σ 0 +σ atm ( ν ) ν 3/ 2 (Lots of other effects as well, of course, but we only care about order-of-magnitude estimates here) Distribute channels according to total signal-to-noise in the following cases

39 The atmosphere

40 The atmosphere

41 Case 1: Low foreground, high-latitude sky Nband = 9 Afg = 1 µk

42 Case 1: Low foreground, high-latitude sky Nband = 9 Afg = 1 µk 1) For low-foreground regions, the optimal solution is ~ Ghz (ie., COrE+ - like)

43 Case 1: Low foreground, high-latitude sky Nband = 9 Afg = 1 µk 1) For low-foreground regions, the optimal solution is ~ Ghz (ie., COrE+ - like) 2) However, extending to lower frequencies carries a very low cost in sensitivity, even when accounting for focal plane area. Critical point: S ~ ν-3, while N ~ ν-3/2.

44 Case 2: Intermediate latitude sky Nband = 9 Afg = 10 µk

45 Case 2: Intermediate latitude sky Nband = 9 Afg = 10 µk O pt im al so lu t io n

46 Case 2: Intermediate latitude sky Nband = 9 Afg = 10 µk O pt im al so lu t io n 1) As foregrounds become brighter, the optimal solution moves to lower frequencies.

47 Case 2b: Intermediate latitude sky, no focal plane penalty Nband = 9 Afg = 10 µk Assume all detectors require the same amount of focal plane area

48 Case 2b: Intermediate latitude sky, no focal plane penalty Nband = 9 Afg = 10 µk Assume all detectors require the same amount of focal plane area GHz

49 Case 2b: Intermediate latitude sky, no focal plane penalty Nband = 9 Afg = 10 µk Assume all detectors require the same amount of focal plane area GHz GHz

50 Case 2b: Intermediate latitude sky, no focal plane penalty Nband = 9 Afg = 10 µk Assume all detectors require the same amount of focal plane area GHz GHz Without the focal plane penalty, a pure low-frequency experiment would perform better than a pure high-frequency experiment

51 Case 2b: Intermediate latitude sky, no focal plane penalty Nband = 9 Afg = 10 µk Assume all detectors require the same amount of focal plane area GHz GHz Without the focal plane penalty, a pure low-frequency experiment would perform better than a pure high-frequency experiment This is because the CMB is more orthogonal to synchrotron (S ~ ν-3) than to thermal dust (T ~ ν1.5) over relevant frequencies

52 Case 2b: Intermediate latitude sky, no focal plane penalty Nband = 9 Afg = 10 µk Assume all detectors require the same amount of focal plane area GHz GHz Without the focal plane penalty, a pure low-frequency experiment would perform better than a pure high-frequency experiment This is because the CMB is more orthogonal to synchrotron (S ~ ν-3) than to thermal dust (T ~ ν1.5) over relevant frequencies

53 Case 2b: Intermediate latitude sky, no focal plane penalty Nband = 9 Afg = 10 µk Assume all detectors require the same amount of focal plane area GHz GHz Without the focal plane penalty, a pure low-frequency experiment would perform better than a pure high-frequency experiment This is because the CMB is more orthogonal to synchrotron (S ~ ν-3) than to thermal dust (T ~ ν1.5) over relevant frequencies

54 Case 3: Galactic plane Nband = 9 Afg = 100 µk

55 Case 3: Galactic plane Nband = 9 Afg = 100 µk General conclusions: 1) If foregrounds are negligible, minimum CMB RMS is obtained by focussing all detectors around the foreground minimum, covering ~ GHz

56 Case 3: Galactic plane Nband = 9 Afg = 100 µk General conclusions: 1) If foregrounds are negligible, minimum CMB RMS is obtained by focussing all detectors around the foreground minimum, covering ~ GHz 2) But if foregrounds are non-negligible, extend the frequency range as much as possible until the model breaks down, even when accounting for focal plane area!

57 Spectral index constraining power Nband = 9 Afg = 10 µk

58 Spectral index constraining power Nband = 9 Afg = 10 µk

59 Spectral index constraining power Nband = 9 Afg = 10 µk

60 Spectral index constraining power Nband = 9 Afg = 10 µk ) While a lowest frequency of ~40-60 GHz is good for optimizing CMB RMS in the low foreground case, such experiments have essentially no handle on βs.

61 Spectral index constraining power Nband = 9 Afg = 10 µk ) While a lowest frequency of ~40-60 GHz is good for optimizing CMB RMS in the low foreground case, such experiments have essentially no handle on βs. 2) If at all possible, one should strive to include frequencies below 30 GHz in order to measure synchrotron properly (as opposed to gambling on being lucky)

62 Case 4: Ground-based, intermediate latitudes Nband = 5 Afg = 10 µk

63 Case 4: Ground-based, intermediate latitudes Nband = 5 Afg = 10 µk 1) Best 5-band ground-based solution is GHz (maximum leverage)

64 Case 4: Ground-based, intermediate latitudes Nband = 5 Afg = 10 µk 1) Best 5-band ground-based solution is GHz (maximum leverage) 2) Two nearly equally sensitive solutions exist for GHz and GHz.

65 What do we know at this stage?

66 What do we know at this stage? There are no «lucky» foreground holes in which we can see Bmodes below r ~ 0.01 without component separation

67 What do we know at this stage? There are no «lucky» foreground holes in which we can see Bmodes below r ~ 0.01 without component separation There is no realistic frequency range in which either synchrotron or dust may be neglected for r < 0.01

68 What do we know at this stage? There are no «lucky» foreground holes in which we can see Bmodes below r ~ 0.01 without component separation There is no realistic frequency range in which either synchrotron or dust may be neglected for r < 0.01

69 What do we know at this stage? There are no «lucky» foreground holes in which we can see Bmodes below r ~ 0.01 without component separation There is no realistic frequency range in which either synchrotron or dust may be neglected for r < 0.01 In order to go deep (r < 0.01), we need to measure both low and and high frequencies to high precision!

70 «GreenPol» -- low frequencies from Greenland

71 «GreenPol» -- low frequencies from Greenland

72 «GreenPol» -- low frequencies from Greenland Possibly one of the cleanest spots in the entire sky!

73 «GreenPol» -- low frequencies from Greenland Possibly one of the cleanest spots in the entire sky! re e h sp i em h ere n r h sp he i t r em No h rn e h ut o S

74 «GreenPol» -- low frequencies from Greenland Possibly one of the cleanest spots in the entire sky! re e h sp i em h ere n r h sp he i t r em No h rn e h ut o S Long: W El: masl Lat: N Danish Com for Sci Res NSF-OPP

75 Global water vapor distribution

76 Global water vapor distribution

77 Global water vapor distribution

78 Global water vapor distribution

79 Global water vapor distribution

80 72 N supports unique cross-linking

81 Sensitivity per focalplane Frequency [GHz] FWHM [Arcmin] Bandwidth [GHz] NET [µk* sec] Pixels/Telescop Aggregate NET e [µk* sec] * GHz receivers assume currently available HEMT amplifiers cooled to 20K 45 GHz receiver assumes an achievable bolometric detector array. The above assumptions are for one telescope each frequency. We expect a real experiment will incorporate more than one telescope per frequency.

82 Commander simulations Fuskeland et al. 2017, in prepration

83 Commander simulations Fuskeland et al. 2017, in preparation

84 Conclusions

85 Conclusions Strict noise optimization was a good strategy for the CMB field as a whole as long as CMB experiments were noise dominated

86 Conclusions Strict noise optimization was a good strategy for the CMB field as a whole as long as CMB experiments were noise dominated That strategy ended abruptly with Planck and BICEP2

87 Conclusions Strict noise optimization was a good strategy for the CMB field as a whole as long as CMB experiments were noise dominated That strategy ended abruptly with Planck and BICEP2 From now on, the name of the game is component separation, not noise reduction

88 Conclusions Strict noise optimization was a good strategy for the CMB field as a whole as long as CMB experiments were noise dominated That strategy ended abruptly with Planck and BICEP2 From now on, the name of the game is component separation, not noise reduction In this landscape, frequency leverage is the key factor

89 Conclusions Strict noise optimization was a good strategy for the CMB field as a whole as long as CMB experiments were noise dominated That strategy ended abruptly with Planck and BICEP2 From now on, the name of the game is component separation, not noise reduction In this landscape, frequency leverage is the key factor Low-frequency observations should be an integral part of any ambitious next-generation project, both for sensitivity and robustness