Variability of the proton-to-electron mass ratio on cosmological …adlibitum.oats.inaf.it/seminari/wendt.pdf · 2007. 11. 28. · Theory of shilly-shally constants Kaluza-Klein theories

Variability of the proton-to-electronmass ratio on cosmological scales

Quasar absorption line spectroscopy

Martin Wendt – Hamburger Sternwarte

Osservatorio Astronomico di Trieste, November 28th

Variability of the proton-to-electron mass ratio on cosmological scales – p.

Overview

• Short introduction of theory behind variation• How is variation reflected in observations?• Molecular Hydrogen H2

• Methods involved• Analysis• Summary and Outlook


Theory of shilly-shally constants



Kaluza-Klein theories• Theodor Kaluza: generalisation of Einstein’s

GTR and the Maxwell equations in fivedimensions in 1921





• Oscar Klein: fifth dimension possibly curledup






• fundamental constants only constant in e.g.five-dimensional space







• observed constants a mere projection







• observed constants a mere projection• another byproduct: scalar field as possible

source for accelerationVariability of the proton-to-electron mass ratio on cosmological scales – p.

How to measure variation?

• possible variation of the finestructureconstant α = e2/4π~c ≈ 1/137.Results under heavy debate.



• possible variation of the finestructureconstant α = e2/4π~c ≈ 1/137.Results under heavy debate.

• variation of the gravitational constant GN .Recent paper last week:GN/GN . 10−17yr−1.





• possible variation of the proton-to-electronmass ratio µ =

mp

me.

µ0 = 1836.15267261(85) (Mohr & Taylor 2000)




mp

me.

µ0 = 1836.15267261(85) (Mohr & Taylor 2000)

• laboratory experiments not yet very accurate(5 years)




mp

me.

µ0 = 1836.15267261(85) (Mohr & Taylor 2000)

• laboratory experiments not yet very accurate(5 years)

• measure possible variation on cosmologicalscales



molecular hydrogen H2 - energy levels

• Etotal = Eelectronic + Evibration + Erotation (BOA)





• vibrational: Ev =(

v + 12

)

ωosc






v + 12

)

ωosc

• with ωosc = 12πc

·√

kµ






v + 12

)

ωosc

• with ωosc = 12πc

·√

kµ

• the classical oscillation frequency dependenton the reduced mass as µ− 1

2 .




• rotational: I = m1m2

m1+m2

r20 = µr2

o





m1+m2

r20 = µr2

o

• EJ = BJ(J + 1); J = 0, 1, 2, 3, . . .





m1+m2

r20 = µr2

o

• EJ = BJ(J + 1); J = 0, 1, 2, 3, . . .

• B = h8π2Ic





m1+m2

r20 = µr2

o

• EJ = BJ(J + 1); J = 0, 1, 2, 3, . . .

• B = h8π2Ic

• rotational transitions are proportional to µ−1



• homonuclear molecule - no detectable merevibrational or rotational spectrum




• only observable in combinations withelectronic transitions (UV-Band)





• UV radiation is a very efficient dissociator ofH2, so any H2 that survived would presumablybe located inside very dense interstellarclouds.





• UV radiation is a very efficient dissociator ofH2, so any H2 that survived would presumablybe located inside very dense interstellarclouds.

• So far observations have borne out thissupposition.



molecular hydrogen H2

Variability of the proton-to-electron mass ratio on cosmological scales – p. 10



• electron-vibro-rotational transitions dependon reduced mass of molecule

• different dependence for different transitions





• different dependence for different transitions• distinguish cosmological redshift of a line from

the shift caused by possible variation of µ







• λobs = λrest × (1 + zabs)(1 + Ki∆µµ

)








)








)

(Varshalovich & Levshakov 1993)


How to measure variation?sensitivity coefficient Ki = d ln λ0

i

d ln µ


How to measure variation?sensitivity coefficient Ki = d ln λ0

i

d ln µ

−0.01

0.00

0.01

0.02

0.03

0.04

0.05

950 1000 1050 1100

sens

itivi

ty c

oeffi

cien

t Ki

restframe wavelength [Å]

Lyman

Werner

(Reinhold et al. 2006)


extragalactic H2

• local observations with UV-satelliteCOPERNICUS


extragalactic H2


• the most abundant molecule in space


extragalactic H2


• the most abundant molecule in space• formation on dust grains


extragalactic H2


• the most abundant molecule in space• formation on dust grains• shielding from UVB vs. dust obscuration


extragalactic H2


• the most abundant molecule in space• formation on dust grains• shielding from UVB vs. dust obscuration• transitions in UV (restframe) – redshiftet into

visual band


extragalactic H2

• highly inhomogeneous, clumpy distribution [1]

[1] H.Hirashita, A.Ferrara, K.Wada, P.Richter,P.2003, MNRAS, 341, L18


extragalactic H2

• highly inhomogeneous, clumpy distribution [1]

• observable only in dense systems

[1] H.Hirashita, A.Ferrara, K.Wada, P.Richter,P.2003, MNRAS, 341, L18


Quasar absorption linespectroscopy



torus of coolergas and dust

hot, denseaccretion diskblack hole

rotating massive

accelerated jetsof relativistic particles

to large−scale

emission lineclouds

small dense

radio lobes





• cosmological redshift z due to expansion ofspace.




λobs = λrest × (1 + zabs)





• Quasars as bright distant backgroundsources against which intervening gas can beobserved.





• Quasars as bright distant backgroundsources against which intervening gas can beobserved.

e.g., the Lyα transition at λrest = 1215.67 Å



(Springel et. al 2006)


Quasar absorption line spectra -probing the universe

0

100

200

300

400

3700 3800 3900 4000 4100 4200 4300 4400 4500

a.u.

observed wavelength [Å]

Q 0347−383



0

100

200

300

400

3700 3800 3900 4000 4100 4200 4300 4400 4500

a.u.


Q 0347−383

0

100

200

3807 3808 3809 3810 3811 3812 3813 3814 3815 3816

a.u.


L14R1

W3Q1

0

100

200

4120 4122 4124 4126 4128 4130 4132 4134

a.u.


L6R2

HI Ly−β





• H2 lines in DLA systems



• H2 lines in DLA systems• contaminated continuum




0

100

200

300

4173 4174 4175 4176 4177 4178 4179 4180

a.u.


L5R1

L5P1




0

100

200

300

4173 4174 4175 4176 4177 4178 4179 4180

a.u.


L5R1

L5P1

(Ivanchik et al. 2005)



simulated fits to estimate accuracy




0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

−3.0 −2.0 −1.0 0.0 1.0 2.0 3.0

tru

e p

ositio

nin

g e

rro

r [Å

]

relative lineposition [Å]

fit of synthesized line

synthesized H2 line

synthesized HI line+ continuum

resulting error




0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

−3.0 −2.0 −1.0 0.0 1.0 2.0 3.0

tru

e p

ositio

nin

g e

rro

r [Å

]


fit of synthesized line

synthesized H2 line

synthesized HI line+ continuum

resulting error

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

−3.0 −2.0 −1.0 0.0 1.0 2.0

tru

e p

ositio

nin

g e

rro

r [Å

]


1 component fit line with S/N = 90

0.00

0.01

0.02

0.03

0.04

0.05

−1.0 −0.5



0.00

0.05

0.10

0.15

0.20

−2.0 −1.5 −1.0 −0.5 0.0 0.5 1.0 1.5 2.0

mea

n er

ror o

f pos

ition

[Å]

relative line position [Å]

output from fit

mean true error

0.00

0.05

0.10

0.15

0.20

−2.0 −1.5 −1.0 −0.5 0.0 0.5 1.0 1.5 2.0

mea

n er

ror o

f pos

ition

[Å]


mean true error


0.00

0.05

0.10

0.15

0.20

−2.0 −1.5 −1.0 −0.5 0.0 0.5 1.0 1.5 2.0

mea

n er

ror o

f pos

ition

[Å]


output from fit

mean true error

0.00

0.05

0.10

0.15

0.20

−2.0 −1.5 −1.0 −0.5 0.0 0.5 1.0 1.5 2.0

mea

n er

ror o

f pos

ition

[Å]


mean true error

−0.15

−0.10

−0.05

0.00

0.05

0.10

0.15

0.20

−2.0 −1.5 −1.0 −0.5 0.0 0.5 1.0 1.5 2.0

net s

hift

in p

ositi

on [Å

]


−0.15

−0.10

−0.05

0.00

0.05

0.10

0.15

0.20

−2.0 −1.5 −1.0 −0.5 0.0 0.5 1.0 1.5 2.0

net s

hift

in p

ositi

on [Å

]



b = (1 + zabs) ×∆µµ


b = (1 + zabs) ×∆µµ

−2.0

−1.5

−1.0

−0.5

0.0

0.5

1.0

1.5

2.0

2.5

−0.01 0.00 0.01 0.02 0.03 0.04 0.05

rela

tive

reds

hift

z i ×

106

sensitivity coefficient Ki

J=1J=2J=3

corresponding to ∆µ

µ= 2.1 ± 1.4 × 10−5

(Reinhold et al. 2006: ∆µ

µ= 2.0 ± 0.6 × 10−5)


b = (1 + zabs) ×∆µµ

3.02488

3.02489

3.02490

3.02491

3.02492

−0.01 0.00 0.01 0.02 0.03 0.04 0.05

reds

hift

z i

Ki

J=1−3

−0.01 0.00 0.01 0.02 0.03 0.04 0.05Ki

J=3


b = (1 + zabs) ×∆µµ

3.02488

3.02489

3.02490

3.02491

3.02492

−0.01 0.00 0.01 0.02 0.03 0.04 0.05

reds

hift

z i

Ki

J=1−3

−0.01 0.00 0.01 0.02 0.03 0.04 0.05Ki

J=2


b = (1 + zabs) ×∆µµ

3.02488

3.02489

3.02490

3.02491

3.02492

−0.01 0.00 0.01 0.02 0.03 0.04 0.05

reds

hift

z i

Ki

J=1−3

−0.01 0.00 0.01 0.02 0.03 0.04 0.05Ki

J=1


b = (1 + zabs) ×∆µµ

3.02488

3.02489

3.02490

3.02491

3.02492

−0.01 0.00 0.01 0.02 0.03 0.04 0.05

reds

hift

z i

Ki

J=1−3

−0.01 0.00 0.01 0.02 0.03 0.04 0.05Ki

J=1

Merely transitions with high vibrational quantum numbersin the first rotational level contribute to a positive result


News or noise?

3.02488

3.02489

3.02490

3.02491

3.02492

−0.01 0.00 0.01 0.02 0.03 0.04 0.05

reds

hift

z i

Ki


News or noise?

3.02488

3.02489

3.02490

3.02491

3.02492

−0.01 0.00 0.01 0.02 0.03 0.04 0.05

reds

hift

z i

Ki

no detectable correlation in a 85% subset


News or noise?

3.02488

3.02489

3.02490

3.02491

3.02492

−0.01 0.00 0.01 0.02 0.03 0.04 0.05

reds

hift

z i

Ki

no detectable correlation in a 85% subset

|∆µ/µ| ≤ 4.9 × 10−5 over the period of ≈ 11.5 Gyr


Outlook


Outlook

• line lists of required accuracy just available⇒ increased need for high resolution


Outlook


• in general attach more importance to datareduction


Outlook



• search for more quasar spectra with DLA andH2 signatures


Outlook




• further simulations of detectability of variation


Outlook




• further simulations of detectability of variation• better understanding of the nature of DLAs



150

300

450

a.u.

of f

lux

A1 A2 A3

150

300

450

a.u.

of f

lux

B1 B2 B3

150

300

450

4396 4398 4400

a.u.

of f

lux


C1

4396 4398 4400


C2

4396 4398 4400


C3

4396 4398 4400


COADDED

Nine separately observed spectra with errorbarsand exemplary fit of L1R1.


1.6

2.0

2.4

2.8

3.2

3.6

4.0

L1P12.0

2.4

2.8

3.2

3.6

4.0

L1R11.6

2.0

2.4

2.8

3.2

3.6

4.0

L2R10.4

0.8

1.2

1.6

2.0

2.4

2.8

3.2

L3R1

2.0

2.4

2.8

3.2

L3P10.8

1.2

1.6

2.0

2.4

2.8

3.2

L4R1-0.40.00.40.81.21.62.02.42.83.2

L4P10.8

1.2

1.6

2.0

2.4

2.8

L5P1

0.4

0.8

1.2

1.6

2.0

2.4

2.8

L5R10.8

1.2

1.6

2.0

2.4

L7R1

A

0.8

1.2

1.6

2.0

2.4

L8R1

A

0.8

1.2

1.6

2.0

2.4

L9P1

A

0.0

0.4

0.8

1.2

1.6

2.0

L9R1

A

0.8

1.2

1.6

2.0

2.4

L10P1

A

0.0

0.4

0.8

1.2

1.6

2.0

-50.0 0.0 50.0

radial velocity [km/s]

W2Q10.4

0.8

1.2

1.6

2.0

2.4

-50.0 0.0 50.0


W3Q1

0.8

1.2

1.6

2.0

-50.0 0.0 50.0


L13R1

A

-0.4

0.0

0.4

0.8

1.2

1.6

2.0

-50.0 0.0 50.0


L14R1

A


Documents

Variability of the proton-to-electron mass ratio on cosmological …adlibitum.oats.inaf.it/seminari/wendt.pdf · 2007. 11. 28. · Theory of shilly-shally constants Kaluza-Klein theories