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A loss of photons along the line-of-sight can explain the Hubble diagram for quasars

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In order to explain the Hubble diagram for quasars, an alternative to ΛCDM is proposed, namely, a simple Newtonian cosmological model where the loss of photons along the line-of-sight mimics the cosmic distance-duality relation, up to z ≈ 0.2. According to this model, after ≈ 3 Gyr of travel, half of the photons emitted by a galaxy have been lost.
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A loss of photons along the line-of-sight
can explain the Hubble diagram for quasars
Yves-Henri Sanejouand∗
Facult´e des Sciences et des Techniques, Nantes, France.
July 18th, 2019
Abstract
In order to explain the Hubble diagram for quasars,
an alternative to ΛCDM is proposed, namely, a sim-
ple Newtonian cosmological model where the loss of
photons along the line-of-sight mimics the cosmic
distance-duality relation, up to z≈0.2. According
to this model, after ≈3 Gyr of travel, half of the
photons emitted by a galaxy have been lost.
Keywords: distance modulus, distance duality.
Introduction
According to ΛCDM, the nowadays standard cos-
mological model, the dimming of supernovae of
type Ia is due to an accelerated expansion of the
space-time metric [1, 2]. However, the redshift of
the farthest observed type Ia supernova is ≈1.4 [3]
and it has recently been shown that, at higher red-
shifts, the Hubble diagram for quasars can not be
handled by ΛCDM, with a statistical significance
of 4σ[4]. Of course, these latter data can be ac-
commodated by extended versions of the model,
through the adjustment of additional free parame-
ters, like the equation of state parameter w[4].
Hereafter, it is shown that the loss of photons
along the line-of-sight is a possible alternative for
explaining the Hubble diagram for quasars, at least
in the context of a pair of Newtonian cosmological
models. It is then shown that the cosmic distance
duality relation [5] can be used to single out one of
them.
∗yves-henri.sanejouand@univ-nantes.fr
Cosmological model
Let us assume that τ(z), the age of the Universe at
redshift z, is approximately given by:
τ(z) = 1
H0(1 + z)(1)
where H0is the Hubble constant. Eqn 1, which
is for instance a consequence of the linear-coasting
cosmological model [6, 7, 8], has noteworthy proved
able to cope with the age of objects that, according
to ΛCDM, seem significantly older than the Uni-
verse itself [9, 10, 11].
Let us also assume that, during its travel, a pho-
ton ages as the Universe does, namely:
∆t=τ(0) −τ(z) (2)
where ∆tis the time taken by the photon to fly
from a source at redshift zto an observer on Earth.
Since the speed of light, c0, is constant, with eqn 1
and 2, Dc, the light-travel distance, is so that [12]:
Dc=c0
H0
z
1 + z(3)
Moreover, let us assume that DL, the luminosity
distance, has the following, rather general form:
DL=Dc(1 + z)ne
1
2
∆t
τp(4)
where nis a half-integer, τpbeing the photon life-
time along the line-of-sight.
In the context of Newtonian cosmological mod-
els, as a consequence of the energy loss of photons
during their travel, n=1
2. However, if, as pre-
dicted by metric theories of gravity like ΛCDM,
1
time-dilation of remote events is a general phe-
nomenon [13, 14, 15], then n= 1. Both cases are
considered hereafter.
Observables
Distance modulus
With eqn 2, 3 and 4, µ, the distance modulus:
µ= 5 log10(DL) + 25
becomes:
µ= 5 log10 z(1 + z)n−1+αTH
τp
z
1 + z+µ0(5)
where TH=H−1
0is the Hubble time, with µ0=
5 log10(c0TH) + 25 and α= 2.5 log10 e.
Distance duality
If there is no photon loss along the path between
a source at redshift zand an observer on Earth,
metric theories of gravity predict that [5, 16]:
DL=DA(1 + z)2
where DAis the angular distance. Deviations from
this so-called cosmic distance duality relation can
be quantified using the following quantity [17]:
η(z) = DL
DA(1 + z)2(6)
In practice, such deviations have been measured
using single-parameter functional forms [16, 17]
like, as considered herein:
η(z) = 1 + η0z(7)
In the context of Newtonian cosmological mod-
els, DA=Dc. Thus, with eqn 1, 2 and 4, eqn 6
becomes:
η(z) = (1 + z)n−2e
1
2
TH
τp
z
1+z(8)
Datasets
Quasars
A homogeneous sample of 1598 quasars [4] with
luminosity-distances determined using their rest-
frame X-ray and UV fluxes [18, 19] was considered.
Since such luminosity-distances are rather noisy,
the dataset was sorted by increasing values of the
redshift and 16 subsamples of 101 quasars1were an-
alyzed, using the median redshift and luminosity-
distance of each subsample.
Galaxy clusters
η0(eqn 7) has been determined by several groups,
using various datasets [20]. The following two mea-
sures are considered hereafter:
•η0=−0.15 ±0.07 [21]. This measure was ob-
tained with a cosmological model-independent
approach, using the gas mass fraction, from
the Sunyaev-Zeldovich effect, and X-ray sur-
face brightness observations of 38 massive
galaxy clusters spanning redshifts between
0.14 and 0.89.
•η0=−0.08 ±0.10 [22]. This measure was ob-
tained using the gas mass fraction, from the
Sunyaev-Zeldovich effect, of 91 massive galaxy
clusters spanning redshifts between 0.1 and
1.4, luminosity distances coming from super-
novae of the Union 2.1 compilation [3] with
similar redshifts.
Results
Quasars
With eqn 5, when n=1
2, a least-square fit of the
median distance modulus of the 16 subsamples of
quasars yields:
TH
τp
= 3.2±0.4
with µ0= 18.0±0.2.
On the other hand, when n= 1, TH
τp= 1.0±
0.4, µ0= 18.4±0.2. As illustrated in Figure 1,
in both cases, the fit matches the data nicely, with
a root-mean-square of the residuals of 0.2. Note
that several other simple cosmological models have
already proven able to pass this test [23].
2
Figure 1: The distance modulus of quasars, as a
function of redshift. Each point (filled circle) is
the median of 101 values, the error bars showing
the corresponding interquartiles. Plain line: least-
square fit of these 16 median values, when n=1
2.
Dashed line: when n= 1.
Distance duality
With the TH
τpvalues determined above, eqn 8 can
be plotted as a function of redshift. As shown in
Figure 2, n= 1 is not found consistent with ob-
servational data, since it yields values more than
2σaway from both measurements, on the whole
redshift range considered.
On the other hand, n=1
2matches the data
comfortably. Interestingly, while ΛCDM predicts
η(z)≥1 [5], it has been noticed that mea-
surements of η(z) tend to yield values below one
[17, 20, 21, 24], like when n=1
2.
Discussion
How are photons lost ?
TH
τp= 3.2 means that half of the photons are lost
after ≈3 Gyr of travel (assuming TH= 13.3 Gyr
[25]). As briefly detailed below, their loss along the
line-of-sight can for instance be due to absorption.
It could also have a less mundane origin.
Absorbers
Photons can be absorbed along the line-of-sight.
Indeed, it has been suggested that gray intergalac-
1With only 83 quasars in the highest-redshift subsample.
Figure 2: Compatibility with the cosmic distance
duality relation, as a function of redshift. Grey and
hatched sectors: measurements obtained using the
gas mass fraction of 38 or 91 globular clusters, re-
spectively, the lower and upper limits of each sector
being 2σaway from the average value. Horizon-
tal dotted line: minimum value expected within
the frame of metric theories of gravity like ΛCDM.
Plain and dashed lines: values expected if pho-
tons are lost along the line-of-sight, when n=1
2
or n= 1, respectively.
tic dust could account for the dimming of type Ia
supernovae [26]. However, in particular because the
luminosity-distances of quasars considered herein
have been determined by comparing their X-ray
and UV fluxes [4], to be relevant, such absorption
would have to exhibit little dependence upon pho-
ton frequency.
Photon decay
It has also been suggested that photons could have
a finite lifetime [27, 28], e.g. by decaying into
lighter particles like massive neutrinos [29], thus
reducing their flux along the line-of-sight.
Is time-dilation universal ?
In the context of the Newtonian cosmological mod-
els considered herein, the fact that observations
support n=1
2likely means that X-ray and UV
fluxes from quasars have not experienced time-
3
dilation. As a matter of fact, while it has been
found that light-curves of type Ia supernovae are
dilated by a (1+ z) factor [30, 31, 32], no such time-
dilation was observed in the light curves of quasars
[33, 34].
Conclusion
As shown in Figure 2, when a loss of photons along
the line-of-sight is taken into account, η(z)≈1 is
also expected within the frame of a simple Newto-
nian cosmological model (n=1
2), up to z≈0.2.
However, above this value, η(z) is predicted to be
significantly lower than one, while metric theories
of gravity like ΛCDM predict η(z)≥1 [5].
In any case, the present study shows that the
combination of the Hubble diagram for quasars
with the cosmic distance duality relation is a pow-
erful test for cosmological models.
Nevertheless, as Figure 2 suggests, more accu-
rate data, over a wider range of redshifts, would
be welcome. They could for instance be obtained
using the Sunyaev-Zeldovich effect for galaxy clus-
ters and luminosity-distances of samples of quasars
with similar redshifts.
Acknowledgements
I thank Guido Risaliti, for providing the latest
dataset of QSO luminosity-distances, and Georges
Paturel, for fruitful discussions.
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  • Mar 2016
  • ASTROPHYS J
The observed relation between the soft X-ray and the optical-ultraviolet emission in active galactic nuclei (AGNs) is nonlinear and it is usually parametrized as a dependence between the logarithm of the monochromatic luminosity at 2500 Å and at 2 keV. Previous investigations have found that the dispersion of this relation is rather high (~0.35–0.4 in log units), which may be caused by measurement uncertainties, variability, and intrinsic dispersion due to differences in the AGN physical properties (e.g., different accretion modes). We show that, once optically selected quasars with homogeneous SED and X-ray detection are selected, and dust reddened and/or gas obscured objects are not included, the measured dispersion drops to significantly lower values (i.e., ~0.21–0.24 dex). We show that the residual dispersion is due to some extent to variability, and to remaining measurement uncertainties. Therefore, the real physical intrinsic dispersion should be dex. Such a tight relation, valid over four decades in luminosity, must be the manifestation of an intrinsic (and universal) physical relation between the disk, emitting the primary radiation, and the hot electron corona emitting X-rays.
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A Hubble Diagram for Quasars
Article
  • May 2015
  • ASTROPHYS J
We present a new method to test the cosmological model, and to estimate the cosmological parameters, based on the non-linear relation between ultraviolet and X-ray luminosity of quasars. We built a data set of ~1,250 quasars by merging several literature samples with X-ray measurements at 2 keV and SDSS photometry, which was used to estimate the extinction-corrected 2500~\AA\ flux. We obtained three main results: (1) we checked the non-linear relation between X-ray and UV luminosities in small redshift bins up to z~6, confirming that it holds at all redshifts with the same slope; (2) we built a Hubble diagram for quasars up to z~6, which is well matched to that of supernovae in the common z=0-1.4 redshift interval, and extends the test of the cosmological model up to z~6; (3) we showed that this non-linear relation is a powerful tool to estimate cosmological parameters. With present data, assuming a Λ\LambdaCDM model, we obtain ΩM\Omega_M=0.21−0.10+0.08^{+0.08}_{-0.10} and ΩΛ\Omega_\Lambda=0.95−0.20+0.30^{+0.30}_{-0.20} (ΩM\Omega_M=0.28±\pm0.04 and ΩΛ\Omega_\Lambda=0.74±0.08\pm0.08 from a joint quasar-SNe fit). However, much more precise measurements will be achieved in the future. A few thousands SDSS quasars already have serendipitous X-ray observations with Chandra or XMM-Newton, and at least 100,000 quasars with UV and X-ray data will be available from the eROSITA all-sky survey in a few years. Euclid, LSST, and Athena surveys will further increase the sample size to at least several hundred thousands. Our simulations show that these samples will provide tight constraints on the cosmological parameters, and will allow to test possible deviations from the standard model with higher precisions than available today.
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Probing photon decay with the Sunyaev-Zel'dovich effect
Article
  • Dec 2013
The fundamental properties of the photon have deep impact on the astrophysical processes that involve it, like the inverse Compton scattering of CMB photon by energetic electrons residing within galaxy cluster atmospheres, usually referred to as the Sunyaev-Zel'dovich effect (SZE). We calculate the combined constraints on the photon decay time and mass by studying the impact of the modified CMB spectrum, as recently calculated (Heeck 2013), on the SZE of galaxy clusters. We analyze the modifications of the SZE as produced by photon decay effects. We study in details the frequency regimes where these modifications are large and where the constraints derived from the SZE can be stronger with respect to those already obtained from the CMB spectrum. We show that the SZE can set limits on the photon decay time and mass, or on E∗=t0τγmγc2E^* = \frac{t_0}{\tau_\gamma}m_\gamma c^2, that are stronger than those obtained from the CMB: the main constraints come from the low frequency range ν≈10−50\nu \approx 10-50 GHz where the modified SZE ΔImod\Delta I_{mod} is larger than the standard one ΔI\Delta I, with the difference ∣(ΔImod−ΔI)∣|(\Delta I_{mod} - \Delta I)| increasing with the frequency for increasing values of E∗E^*; additional constraints can be set in the range 120−180120 - 180 GHz where there is an increase of the frequency position of the minimum of ΔImod\Delta I_{mod} with respect to the standard one with increasing values of E∗E^*. We demonstrated that the effect of photon decay can be measured or constrained by the Square Kilometer Array in the optimal range ≈10−30\approx 10-30 GHz setting limits of E∗≤1.4×10−9E^* \leq 1.4 \times 10^{-9} eV and 5×10−105 \times 10^{-10} eV for 30 and 260 hour integration for A2163, respectively. These limits are stronger than those obtained with the COBE-FIRAS spectral measurements of the CMB.
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