Determining H₀ using a model-independent method

Abstract

By using type Ia supernovae (SNIa) to provide the luminosity distance (LD) directly, which depends on the value of the Hubble constant H₀ = 100h km·s⁻¹·Mpc⁻¹, and the angular diameter distance from galaxy clusters or baryon acoustic oscillations (BAOs) to give the derived LD according to the distance duality relation, we propose a model-independent method to determine h from the fact that different observations should give the same LD at a given redshift. Combining the Sloan Digital Sky Survey II (SDSS-II) SNIa from the MLCS2k2 light curve fit and galaxy cluster data, we find that at the 1σ confidence level (CL), h=0.5867±0.0303 for the sample of the elliptical β model for galaxy clusters, and h=0.6199±0.0293 for that of the sphericall β model. The former is smaller than the values from other observations, whereas the latter is consistent with the Planck result at the 2σ CL and agrees very well with the value reconstructed directly from the H(z) data. With the SDSS-II SNIa and BAO measurements, a tighter constraint, h = 0.6683±0.0221, is obtained. For comparison, we also consider the Union 2.1 SNIa from the SALT2 light curve fitting. The results from the Union 2.1 SNIa are slightly larger than those from the SDSS-II SNIa, and the Union 2.1 SNIa+ BAOs give the tightest value. We find that the values from SNIa+ BAOs are quite consistent with those from the Planck and the BAOs, as well as the local measurement from Cepheids and very-low-redshift SNIa.

Keywords

Hubble constant / luminosity distance / angular diameter distance

References

[1] W. L. Freedman, B. F. Madore, B. K. Gibson, L. Ferrarese, D. D. Kelson, S. Sakai, J. R. Mould, R. C. JrKennicutt, H. C. Ford, J. A. Graham, J. P. Huchra, S. M. G. Hughes, G. D. Illingworth, L. M. Macri, and P. B. Stetson, Final results from the Hubble Space Telescope key project to measure the Hubble constant, Astrophys. J. 553(1), 47 (2001)

[2] A. Riess, L. Macri, S. Casertano, H. Lampeitl, H. C. Ferguson, A. V. Filippenko, S. W. Jha, W. Li, and R. Chornock, A 3% solution: Determination of the Hubble constant with the Hubble Space Telescope and Wide Field Camera 3, Astrophys. J. 730(2), 119 (2011)

[3] C. L. Bennett, D. Larson, J. L. Weiland, N. Jarosik, G. Hinshaw, , Nine-Year Wilkinson Microwave Anisotropy Probe (WMAP) observations: Final maps and results, Astrophys. J. Suppl. 208(2), 20 (2013)

[4] G. Hinshaw, D. Larson, E. Komatsu, D. N. Spergel, C. L. Bennett, , Nine-Year Wilkinson Microwave Anisotropy Probe (WMAP) observations: Cosmological parameter results, Astrophys. J. Suppl. 208(2), 19 (2013)

[5] C. L. Bennett, D. Larson, J. L. Weiland, and G. Hinshaw, The 1% concordance Hubble constant, Astrophys. J. 794(2), 135 (2014)

[6] E. Calabrese, M. Archidiacono, A. Melchiorri, and B. Ratra, Impact of H0 prior on the evidence for dark radiation, Phys. Rev. D 86(4), 043520 (2012)

[7] G. Chen and B. Ratra, Median statistics and the Hubble constant, Publ. Astron. Soc. Pac. 123(907), 1127 (2011)

[8] P. A. R. Ade, . (Planck Collaboration), Planck 2013 results. XVI. Cosmological parameters, Astron. Astrophys. 571, A16 (2014)

[9] P. A. R. Ade, . (Planck Collaboration), Planck 2015 results. XIII. Cosmological parameters, arXiv: 1502.01589

[10] É. Aubourg, . (BOSS Collaboration), Cosmological implications of baryon acoustic oscillation measurements, Phys. Rev. D 92(12), 123516 (2015)

[11] L. Anderson, E. Aubourg, S. Bailey, F. Beutler, V. Bhardwaj,, The clustering of galaxies in the SDSSIII Baryon Oscillation Spectroscopic Survey: Baryon Acoustic Oscillations in the Data Release 10 and 11 galaxy samples, Mon. Not. R. Astron. Soc. 441(1), 24 (2014)

[12] M. Betoule, R. Kessler, J. Guy, J. Mosher, D. Hardin, , Improved cosmological constraints from a joint analysis of the SDSS-II and SNLS supernova samples, Astron. Astrophys. 568, A22 (2014)

[13] V. Marra, L. Amendola, I. Sawicki, and W. Valkenburg, Cosmic variance and the measurement of the local Hubble parameter, Phys. Rev. Lett. 110(24), 241305 (2013)

[14] S. N. Zhang and Y. Z. Ma, Direct measurement of evolving dark energy density and super-accelerating expansion of the universe, arXiv: 1303.6124

[15] G. Efstathiou, H0 revisited, Mon. Not. R. Astron. Soc. 440(2), 1138 (2014)

[16] M. Rigault, G. Aldering, M. Kowalski, Y. Copin, P. Antilogus, , Confirmation of a star formation bias in Type Ia supernova distances and its effect on the measurement of the Hubble constant, Astrophys. J. 802, 20 (2015)

[17] A. E. Romano and S. A. Vallejo, Directional dependence of the local estimation of H0 and the nonperturbative effects of primordial curvature perturbations, Europhys. Lett. 109(3), 39002 (2015)

[18] A. E. Romano and S. A. Vallejo, Low red-shift effects of local structure on the Hubble parameter in presence of a cosmological constant, Eur. Phys. J. C 76(4), 216 (2016)

[19] D. Spergel, R. Flauger, and R. Hlozek, Planck data reconsidered, Phys. Rev. D 91(2), 023518 (2015)

[20] E. M. L. Humphreys, M. J. Reid, J. M. Moran, L. J. Greenhill, and A. L. Argon, Toward a new geometric distance to the active galaxy NGC 4258. III. Final results and the Hubble constant, Astrophys. J. 775(1), 13 (2013)

[21] F. Beutler, C. Blake, M. Colless, D. H. Jones, L. Staveley- Smith, L. Campbell, Q. Parker, W. Saunders, and F. Watson, The 6dF galaxy survey: Baryon acoustic oscillations and the local Hubble constant, Mon. Not. R. Astron. Soc. 416(4), 3017 (2011)

[22] E. A. Kazin, J. Koda, C. Blake, N. Padmanabhan, S. Brough, , The WiggleZ Dark Energy Survey: Improved distance measurements to z= 1 with reconstruction of the baryonic acoustic feature, Mon. Not. R. Astron. Soc. 441(4), 3524 (2014)

[23] T. Delubac, J. E. Bautista, N. G. Busca, J. Rich, D. Kirkby, , Baryon acoustic oscillations in the Lyα forest of BOSS DR11 quasars, Astron. Astrophys. 574, A59 (2015)

[24] C. H. Chuang, F. Prada, A. J. Cuesta, , The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: Single-probe measurements and the strong power of $f(z)nsigma_8(z)$ on constraining dark energy, Mon. Not. R. Astron. Soc. 433, 3559 (2013)

[25] M. D. P. Hemantha, Y. Wang, and C. H. Chuang, Measurement of H(z) and DA(z) from the two-dimensional power spectrum of Sloan Digital Sky Survey luminous red galaxies, Mon. Not. R. Astron. Soc. 445(4), 3737 (2014)

[26] C. Cheng and Q. G. Huang, An accurate determination of the Hubble constant from Baryon Acoustic Oscillation datasets, Sci. China: Phys. Mech. Astron. 58(9), 599801 (2015)

[27] V. C. Busti, C. Clarkson, and M. Seikel, Evidence for a lower value for H0 from cosmic chronometers data? Mon. Not. R. Astron. Soc. 441(1), L11 (2014)

[28] M. Bonamente, M. K. Joy, S. J. LaRoque, J. E. Carlstrom, E. D. Reese, and K. S. Dawson, Determination of the cosmic distance scale from Sunyaev-Zel’dovich effect and Chandra X-ray measurements of high redshift galaxy clusters, Astrophys. J. 647(1), 25 (2006)

[29] I. Ferreras, A. Pasquali, S. Malhotra, J. Rhoads, S. Cohen, R. Windhorst, N. Pirzkal, N. Grogin, A. M. Koekemoer, T. Lisker, N. Panagia, E. Daddi, and N. P. Hathi, Early-type galaxies in the PEARS survey: Probing the stellar populations at moderate redshift, Astrophys. J. 706(1), 158 (2009)

[30] M. Longhetti, P. Saracco, P. Severgnini, R. D. Ceca, F. Mannucci, R. Bender, N. Drory, G. Feulner, and U. Hopp, The Kormendy relation of massive elliptical galaxies at z’ 1:5. Evidence for size evolution? Mon. Not. R. Astron. Soc. 374(2), 614 (2007)

[31] E. Gaztañaga, A. Cabré, and L. Hui, Clustering of Luminous Red Galaxies IV: Baryon acoustic peak in the line-of-sight direction and a direct measurement of H(z), Mon. Not. R. Astron. Soc. 399(3), 1663 (2009)

[32] J. Simon, L. Verde, and R. Jimenez, Constraints on the redshift dependence of the dark energy potential, Phys. Rev. D 71(12), 123001 (2005)

[33] D. Stern, R. Jimenez, L. Verde, M. Kamionkowski, and S. A. Stanford, Cosmic Chronometers: Constraining the equation of state of dark energy (I): H(z) measurements, J. Cosmol. Astropart. Phys. 2(02), 8 (2010)

[34] D. J. Eisenstein, I. Zehavi, D. W. Hogg, R. S coccimarro, M. R. Blanton, , Detection of the baryon acoustic peak in the large-scale correlation function of SDSS luminous red galaxies, Astrophys. J. 633(2), 560 (2005)

[35] J. A. S. Lima and J. V. Cunha, A 3% determination of H0 at intermediate redshifts, Astrophys. J. 781(2), L38 (2014)

[36] R. F. L. Holanda, V. C. Busti, and G. P. da Silva, Robustness of H0 determination at intermediate redshifts, Mon. Not. R. Astron. Soc. 443(1), L74 (2014)

[37] E. De Filippis, M. Sereno, M. W. Bautz, and G. Longo, Measuring the three-dimensional structure of galaxy clusters. 1. Application to a sample of 25 clusters, Astrophys. J. 625(1), 108 (2005)

[38] R. Kessler, A. Becker, D. Cinabro, J. Vanderplas, J. A. Frieman, , First-year Sloan Digital Sky Survey-II (SDSS-II) supernova results: Hubble diagram and cosmological parameters, Astrophys. J. Suppl. 185(1), 32 (2009)

[39] R. Amanullah, C. Lidman, D. Rubin, G. Aldering, P. Astier, , Spectra and light curves of six type Ia supernovae at 0:511<z<1 : 12 and the Union2 compilation, Astrophys. J. 716, 712 (2010)

[40] S. Jha, A. G. Riess, and R. P. Kirshner, Improved distances to type Ia supernovae with multicolor light curve shapes: MLCS2k2, Astrophys. J. 659(1), 122 (2007)

[41] J. Guy, P. Astier, S. Baumont, D. Hardin, R. Pain, , SALT2: Using distant supernovae to improve the use of Type Ia supernovae as distance indicators, Astron. Astrophys. 466(1), 11 (2007)

[42] N. Suzuki, D. Rubin, C. Lidman, G. Aldering, R. Amanullah, , The Hubble space telescope cluster supernova survey: V. improving the dark energy constraints above z>1 and building an early-type-hosted supernova sample, Astrophys. J. 746(1), 85 (2012)

[43] B. A. Bassett and M. Kunz, Cosmic distance-duality as probe of exotic physics and acceleration, Phys. Rev. D 69(10), 101305 (2004)

[44] B. A. Bassett and M. Kunz, Cosmic acceleration vs. axion-photon mixing, Astrophys. J. 607(2), 661 (2004)

[45] M. Kunz and B. A. Bassett, A Tale of Two Distances, arXiv: astro-ph/0406013

[46] R. Nair, S. Jhingan, and D. Jain, Cosmic distance duality and cosmic transparency, J. Cosmol. Astropart. Phys. 1212, 028 (2012)

[47] H. Lampeitl, R. C. Nichol, H. J. Seo, T. Giannantonio, C. Shapiro, , First-year Sloan Digital Sky Survey-II (SDSS-II) supernova results: consistency and constraints with other intermediate-redshift datasets, Mon. Not. R. Astron. Soc. 401(4), 2331 (2009)

[48] Z. Li, P. Wu, and H. Yu, Cosmological-modelindependent tests for the distance-duality relation from Galaxy Clusters and Type Ia Supernova, Astrophys. J. 729(1), L14 (2011)

[49] R. F. L. Holanda, J. A. S. Lima, and M. B. Ribeiro, Testing the distance-duality relation with galaxy clusters and type Ia supernovae, Astrophys. J. 722(2), L233 (2010)

[50] P. Wu, Z. Li, X. Liu, and H. Yu, Cosmic distance-duality relation test using type Ia supernovae and the baryon acoustic oscillation, Phys. Rev. D 92(2), 023520 (2015)

[51] P. R. Bevington and D. K. Robinson, Data reduction and error analysis for the physical sciences, 3rd Ed., edited by P. R. Bevington and K. D. Robinson, MA: McGraw-Hill, 2003

[52] E. D. Reese, J. E. Carlstrom, M. Joy, J. J. Mohr, L. Grego, and W. L. Holzapfel, Determining the cosmic distance scale from interferometric measurements of the Sunyaev-Zel’dovich effect, Astrophys. J. 581(1), 53 (2002)

[53] B. S. Mason, S. T. Myers, and A. C. S. Readhead, A Measurement of H0 from the Sunyaev-Zel’dovich Effect, Astrophys. J. 555, L11 (2001)

[54] B. A. Bassett and R. Hlozek, Baryon acoustic oscillations, arXiv: 0910.5224

[55] C. Blake, S. Brough, M. Colless, C. Contreras, W. Couch, , The WiggleZ Dark Energy Survey: Joint measurements of the expansion and growth history at z<1, Mon. Not. R. Astron. Soc. 425(1), 405 (2012)

[56] X. Xu, A. J. Cuesta, N. Padmanabhan, D. J. Eisenstein, and C. K. McBride, Measuring DA and H at z= 0 : 35 from the SDSS DR7 LRGs using baryon acoustic oscillations, Mon. Not. R. Astron. Soc. 431(3), 2834 (2013)

[57] L. Samushia, B. A. Reid, M. White, W. J. Percival, A. J. Cuesta, , The clustering of galaxies in the SDSSIII Baryon Oscillation Spectroscopic Survey: Measuring growth rate and geometry with anisotropic clustering, Mon. Not. R. Astron. Soc. 439(4), 3504 (2014)

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