Tuesday 21 May 2024

Apparent Hubble Parameter Value

In Mathematics for Taking Another Look at the Universe, I presented this chart:

Then, right at the end, I wrote: “I do acknowledge that the ‘Apparent’ values of H in the recent past/near vicinity are very high.  This is worthy of further investigation.”

The notion here is that, for closer events (in time and also space), the equation H=Δx'/Δt/x gives higher values of H.  For clarity, Δx' is the difference in proper distance over the period Δt for a location at an effective distance from an observer given by x=ct (where t is how long ago a photon would have had to have been emitted to be observed at the equivalent of t=0 [ie now]).

Note that this equation blends two variants of distance, so its use would be problematic.  Using the equation H=Δx/Δt/x results in the invariant H=70.855km/s/Mpc for all values of x=ct (the flat blue line).

I downloaded the NASA/IPAC Extragalactic Database list of galaxies to get an idea of what values of H were recorded to galaxies at various distances (and also redshift values).

Unfortunately, it appears that the value of H recorded appears to depend more on the paper from which it is extracted rather than the distance of the relevant galaxy.  H values range from as low as 42 to as high as 103, per the table below.


H

Year

Method

Ref Code

Galaxies (N)

103

1984

1985

1986

Tully-Fisher

1984A&AS...56..381B

1985A&AS...59...43B

1986A&A...156..157B

2073

887

398

100

1981

1992

2013

Tully-Fisher

1981ApJ...248..408D

1992ApJ...395..347B

2013ApJ...771...88L

303

35

568

100

1992

D-Sigma

1992ApJ...384...43G

35

100

1998

Magnitude

1998A&A...337...31R

72

100

2009

2010

GRB

2009EPJC...63..139W

2010JCAP...08..020W

32

19

95

1980

Tully-Fisher

1980ApJ...239...12A

40

95

1984

Faber-Jackson

Tertiary

1984ApJS...56...91D

1104

278

92

1993

Tully-Fisher

1993AJ....105...97S

16

91

1984

Tully-Fisher

1984ApJ...278..475B

20

90

1985

Tully-Fisher

1985A&A...153..125G

257

88

1989

Faber-Jackson

FP

1989ApJ...344L..57P

20

20

85

1995

Tully-Fisher

1995A&A...294L...9W

1

85

1992

Tully-Fisher

1992ApJS...81..413M

2711

85

1988

Tully-Fisher

1988ApJ...330..579P

40

85

1984

Sosies

1984ApJ...282..382P

17

84

1986

Tully-Fisher

1986AJ.....91.1286S

22

82

1997

1987

Tully-Fisher

SNIa

1997ApJS..108..417Y

1987PASP...99..592P

207

1

80

1983

Tully-Fisher

1983ApJ...265....1A

44

77

2000

1994

Tully-Fisher

1994AJ....107.1962B

2000ApJ...533..744T

2

21

75

2016

2014

2013

2012

2012

2008

2006

2005

2002

2001

1994

1990

1986

Tully-Fisher

2016AJ....152...50T

2014MNRAS.444..527S

2013ApJ...765...94S

2012ApJ...749...78T

2012ApJ...749..174C

2008Ap.....51..336K

2006Ap.....49..450K

2005Ap&SS.298..577R

2002ApJ...565..681R

2001PhDT.......242M

1994A&A...283...21S

1990ApJ...351L...5W

1986A&A...164...17G

2306

3470

22

18

98

406

2724

2

1

23

64

2

2

75

1997

Tully-Fisher

IRAS

D-Sigma

1997ApJS..109..333W

8839

2946

1086

75

1988

Tully-Fisher

Tully est

1988NBGC.C....0000T

942

1434

75

1997

FP

1997MNRAS.291..488H

22

75

1995

GRB

1995ApJ...453..583W

8

75

1991

1982

SNIa

1991AJ....102..208H

1982ApJ...254....1A

1

2

75

1982

CMD

1982AJ.....87..462G

2

75

1982

SZ effect

1982ApJ...257..473B

2

75

2010

GC radius

2010ApJ...715.1419M

1

74.4

2014

Tully-Fisher

2014ApJ...792..129N

110

74.4

2013

Tully-Fisher

FP

SBF

Statistical

TRGB

SNIa

Cepheids

2013AJ....146...86T

5851

1366

274

249

243

216

3

74.3

2015

L(Hβ)-δ

2015MNRAS.451.3001T

25

74.3

1983

Tully-Fisher

1983ApJ...275..430V

54

74.2

2011

2010

SNIa

2011A&A...526A..81B

2010ApJ...716..712A

26

687

74

2017

GRB

2017A&A...598A.112D

158

74

2012

2003

SNIa

2012ApJ...744...38F

2003AJ....125..166K

1

2

74

1996

Tully-Fisher

1996ApJ...463...60B

3

73.8

2017

2014

SNIa

2017JCAP...03..056C

2014ApJ...795...44R

19

335

73

2016

2011

SNII optical

2016AcA....66..219H

2011MNRAS.417.1417F

1

2

73

2015

Maser

2015ApJ...800...26K

1

73

2013

2012

SNIa

2013ApJ...777...40M

2012A&A...546A..12V

1

3

73

2011

Tully-Fisher

2011A&A...532A.104N

688

73

2010

GRB

2010JCAP...08..020W

2006astro.ph..9262M

12

24

73

2009

Cepheids

2009RoAJ...19...35A

93

72

2017

G Lens

2017ApJ...835L..25M

1

72

2015

FP

2015MNRAS.451.2723S

8

72

2015

2014

2013

2012

2011

2011

2010

2010

2010

2009

2009

2009

2009

2008

2008

2008

2007

2007

2006

2006

2006

2004

SNIa

2015ApJ...798...39M

2014ApJ...784..105W

2013ApJ...773...53F

2012ApJ...754...19M

2011ApJ...731..120M

2011AJ....141...19B

2010ApJ...721.1608B

2010AJ....140.2036S

2010AJ....139..120F

2009ApJ...704.1036F

2009ApJ...704..629M

2009ApJ...697..380W

2009A&A...505..265L

2008MNRAS.384..107E

2008ApJ...689..377W

2008AJ....136.1482S

2007AJ....133...58K

2007A&A...469..645S

2006ApJ...647..501P

2006ApJ...645..488W

2006AJ....131.1639K

2004ApJ...602..571B

1

108

79

20

110

33

17

15

28

56

39

3

1

1

44

3

1

1

90

98

3

58

72

2014

Tully-Fisher

2014Ap.....57..457K

145

72

2011

GeV TeV ratio

2011arXiv1111.0913P

2010MNRAS.405L..76P

18

17

72

2011

2010

2008

GRB

2011ApJ...736....7C

2010JCAP...08..020W

2008JCAP...07..004M

1

8

69

72

2002

D-Sigma

2002AJ....123.2159B

46

71.6

2014

2013

SNIa

2014ApJ...786....9P

2013ApJ...768..166J

10

1

71

2014

BL Lac Luminosity

2014A&A...565A..12P

3

71

2013

2011

2011

GRB

2013MNRAS.431.3550G

2011MNRAS.413.2173G

2011A&A...526A.153K

1

2

5

71

2010

SGRB

2010ApJ...709..664R

12

71

2005

HII LF

2005MNRAS.356.1117S

15

71

2001

1982

Tully-Fisher

2001ApJ...553...47F

1982PASAu...4..419V

36

11

70.8

2015

2008

SNIa

2015ApJS..219...13W

2008MNRAS.389.1577T

31

107

70

2018

SNIa

SNIa SDSS

2018PASP..130f4002S

2795

3027

70

2018

2017

2016

2016

2015

2014

2014

2014

2013

2013

SNIa

2018ApJ...859..101S

2017MNRAS.464.4476C

2016JBAA..126..364F

2016ApJ...821..115W

2015ApJ...811...70R

2014MNRAS.438.1391P

2014AJ....148....1Z

2014A&A...568A..22B

2013MNRAS.434.1443X

2013MNRAS.433.2240G

2013ApJ...763...88C

2013ApJ...763...35R

2012MNRAS.426.2359M

2012ApJ...748..127F

2012ApJ...746...85S

2011ApJS..192....1C

2011ApJ...740...92G

2011ApJ...738..162S

2008ApJ...686..749K

2006A&A...447...31A

2000ApJ...539..658K

1992ApJ...400..127R

1987ApJ...315L.129F

847

4

1

345

4

60

1

740

48

583

1504

1

28

75

15

472

206

860

398

117

5

1

1

70

2017

2017

SNII optical

2017MNRAS.472.4233D

2017ApJ...835..166D

61

133

70

2017

2015

2015

2015

2014

2014

2013

2013

2013

2013

2012

2011

2009

2006

BL Lac Luminosity

2017ApJ...834...41K

2015arXiv150203012A

2015ApJ...799....7A

2015AJ....150..181L

2014ApJ...784..151S

2014A&A...570A.126L

2013ApJ...768L..31F

2013ApJ...766...35F

2013ApJ...764..135S

2013ApJ...764...57D

2012A&A...547A...1N

2011A&A...529A..49H

2009MNRAS.397L..55B

2006AJ....132....1S

5

2

1

1

11

2

1

1

1

1

1

1

1

4

70

2016

2015

2015

2015

2015

2014

2014

GeV TeV ratio

2016MNRAS.459.3271A

2015MNRAS.449.1018Y

2015MNRAS.447.2810Y

2015MNRAS.446..217A

2015ApJ...802...65A

2014PASJ...66...12Z

2014A&A...567A.135A

1

1

1

1

1

2

1

70

2016

2013

2013

2013

2010

2007

2004

GRB

2016MNRAS.458.3821U

2013A&A...551A.133P

2013ApJ...763..125M

2013A&A...552L...5P

2010JCAP...08..020W

2007ApJ...660...16S

2004AIPC..727...37A

19

1

1

2

2

69

42

70

2016

2014

2001

FP

2016A&A...596A..14S

2014MNRAS.445.2677S

2001MNRAS.321..277C

119078

8884

396

70

2015

2013

2012

SGBR

2015ApJ...808..190R

2013ApJ...766...41S

2012A&A...545A..77R

1

1

20

70

2014

G Lens

Magnitude

2014ApJ...797...98L

20

22

70

2014

GeV TeV ratio

BL Lac Luminosity

2014A&A...572A.121A

1

1

70

2012

G Lens

2012MNRAS.426..868S

1

70

2011

1999

1992

Tully-Fisher

2011A&A...531A..87I

1999AJ....118.1489D

1992ApJ...396..453H

42

111

33

70

1997

SZ effect

1997ApJ...481...35H

5

70

1988

D-Sigma

1988MNRAS.235.1177L

18

69.7

2010

2009

GRB

2010JCAP...08..020W

2009MNRAS.400..775C

18

152

69

1997

Tully-Fisher

1997MNRAS.290L..77S

3

69

1991

D-Sigma

1991BAAS...23..956G

5

68

1996

SNIa

1996ApJ...465L..83R

7

67

1996

SNIa

1996ApJ...457..500H

26

66

1994

SNIa

1994A&A...281...51M

13

65.2

1997

Tully-Fisher

1997A&A...326..915T

21

65

2010

2010

2009

2009

2007

2007

2007

2006

2006

2005

2004

2003

2003

2002

2001

2001

2001

2000

1998

1998

1998

1998

1996

1996

1996

1995

SNIa

2010arXiv1006.2112L

2010ApJ...708.1748F

2009ApJS..185...32K

2009ApJ...700.1097H

2007ApJ...666..694W

2007ApJ...659..122J

2007ApJ...659...98R

2006MNRAS.366..682S

2006ApJ...642....1C

2005AJ....130.2453K

2004ApJ...607..665R

2003ApJ...594....1T

2003ApJ...589..693B

2002ApJ...577L...1B

2001ApJ...560...49R

2001AJ....122.1616K

2001AJ....121.3127V

2000A&A...361...63T

1998ApJ...507...46S

1998ApJ...504..935R

1998ApJ...493L..53G

1998AJ....116.1009R

1996ApJ...473..588R

1996ApJ...473...88R

1996AJ....112.2398H

1995ApJ...445L..91R

249

2

576

1486

414

131

41

1

9

21

186

35

6

1

1

8

1

1

2

10

8

80

20

23

8

13

65

1999

GRB

1999ApJ...511L..79S

52

65

1980

Tully-Fisher

Statistical

1980ApJ...238..458M

23

1

62.3

2008

SNIa

2008A&ARv..15..289T

20

60

2000

SNIa

BCG

2000ApJ...540..634P

239

288

58

1997

Grav Stab Gas Disk

1997ApJ...485..439B

2

56

1992

SBF

SNIa

1992ARA&A..30..359B

1

5

55

1984

Faber-Jackson

1984ApJS...56...91D

383

54

1997

Tully-Fisher

1997A&A...326..915T

21

53.9

1984

Tully-Fisher

1984A&A...132..253R

19

50

1996

FP

SNII optical

1996MNRAS.280..167J

52

26

50

1994

SNII optical

1994ApJ...433...19S

2

50

1989

D-Sigma

1989ApJS...69..763F

798

50

1983

Tully-Fisher

1983A&A...125..187R

1

44

2007

AGN time lag

2007MNRAS.380..669C

14

42

1999

AGN time lag

1999MNRAS.302L..24C

1


Of all the papers listed (the Ref Code refers to papers), there are two that have more than one value of H for the galaxies surveyed.

1984ApJS...56...91D refers to A comparison of distance scales for early-type galaxies by de Vaucouleurs and Olson.  Looking through the paper, it does not appear that the Hubble parameter value was calculated.  Looking through the table above, two values are presented, H=95 and H=55 (km/s/Mpc).  Looking at the spreadsheet (NASA/IPAC Extragalactic Database (NED) list of galaxies) it can be seen that 284 entries have H=55 marked against them and 1382 entries have H=95.  However, there are not 1666 unique galaxies, only 425.  For every instance of H=55, there is at least one entry with H=95 recorded.  It’s extremely strange.

For example, for NGC 3619, there are two entries, one with H=55 and one with H=95.  However, the entry with H=55 has a distance of 44.7 Mpc and the entry with H=95 has a distance of 23.3 Mpc.  Similarly with NGC 3203 (D=20.3 and 37.8), NGC 3193 (various values of D from 14.7 through to 25.6 for H=95 and D=38.5 for H=55) and so on.

Given the age of the survey, 40 years ago now, and these peculiarities I’d suggest that we ignore it.

2010JCAP...08..020W refers to Observational constraints on cosmological models with the updated long gamma-ray bursts by Wei.  Again, the paper doesn’t specifically calculate the value of the Hubble parameter.  The NED list has 109 entries against this paper, covering 97 distinct galaxies of which only 46 have Hubble parameter values entered against them.  There does not seem to be any relationship between Hubble parameter and distance (despite Wei writing about “the discovery of current accelerated expansion of our universe”).  

The H values attributed to this paper vary between 100 and 69.7 km/s/Mpc.  At the upper range there are GRB 071020 (D=12,700 Mpc) and GRB 050904 (D=15,300 Mpc), with H=100 and H=69.7 respectively and towards the lower range there are GRB 010921 (D=1,620 Mpc) and XRF 040912 (D=1,760 Mpc), with H=73 and H=100 respectively.

So, while this paper is newer, at 14 years ago, it doesn’t seem to be aiming at establishing Hubble parameter values (but rather establishing the validity of the Gamma Ray Burst method, and filling in a gap in the data, referred to as a ‘desert’), and probably could be safely ignored.

That leaves all the other papers for which there is one value for the Hubble parameter, and one value only.

Interestingly, if we consider only the papers over certain period, the values for the Hubble constant calculated in the “wisdom of the crowd sort of way” (average of all values) are: past 40 years (1985-2024) – H=71.3, past 30 years (1995-2024) – H=70.87, past 20 years (2005-2024) – H=70.57 and past 10 years (2015-2024) – H=70.1.  I wouldn’t get too excited about the value zeroing in 70 since the spreadsheet generally seems to have a low level of specificity.  I think that 100 just means the value is considered to be somewhere between 50 and 150 (or even higher).  Similarly, 70 probably means something between 65 and 75.  There are more accurate values provided, for example 70.8, recorded against 2015ApJS..219...13W – First Results from the La Silla-QUEST Supernova Survey – and 2008MNRAS.389.1577T – Light-curve studies of nearby Type Ia supernovae with a Multiband Stretch method, but note that the authors in both instances set the value of H0, they don’t calculate it.  This raises the question of whether, in the documents referred to the NED list, is H always an assumed value?  If so, then the list is of no use for what I am trying to establish.

As a consequence, there does not appear to be any supporting evidence, so I cannot say with any huge confidence that the apparent acceleration of the universe (using recent measurements of nearer galaxies) is due to an artefact of measurement related to blending values of x=ct and x'.  All there is is a potential mechanism.

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