Redshift periodicity and its significance for Recent observation

H.Arp (Refs. \onlineciteArp1994,Arp2001) observed that a cluster of high redshift quasars appears to be physically connected with a lower redshift galaxy . He claimed that their redshifts do not indicate distance and furthermore, redshifts of those clusters are quantized and obey a simple formula:

where $Z_{k}$ is the redshift of a quasar and $Z_{k+1}$ is the next higher redshift. Karlsson (Refs. \onlineciteKarlsson1977) observed that the peaks of the histogram of the redshifts, form a mathematical series $Z=0.061,0.3,0.6,0.96$. Hawkins (Refs. \onlineciteHawkins2002) found non existence of periodicity, but their methodology was challenged by Napier (Refs. \onlineciteNapier2003). Next, Tang (Refs. \onlineciteTang2005, Tang2008) claimed the non- existence of periodicity with a dataset that was 15 times larger than the previous one. Duari (Refs. \onlineciteDuari1992, Duari1997) found redshift periodicity statistically. Fulton (Refs. \onlineciteFulton2018) explains redshift periodicity using ejection velocity computations. Mal (Refs. \onlineciteMal2020) have already shown the existence of periodicity of redshift for quasar as well as for galaxy; here we have analysed the data for quasar-galaxy pair datasets and try to understand the physics behind the quantization of redshift in such datasets.

We examine the existence of redshift periodicity in quasar-galaxy pair data following the procedure outlined here. After the initial selection of data in accordance with the flag values provided, selection of the bin width for formation of the histogram is optimized as in (Refs. \onlineciteShimazaki2007, Shimazaki2009) minimizing the cost function for the overall data set of Solan Digital Sky Survey’ sample (SDSS DR-7). Next, an SVD- based method (Refs. \onlineciteKanjilal1995) has been adapted for estimating the fundamental periodicity present in the histogram of the red shift data. (Refs. \onlineciteMal2020) have established the superiority of the SVD based approach of periodicity detection over the periodogram-based approach. The periodogram is not a suitable tool for data of a quasi-periodic nature or a dataset containing multiple periodic components and a large number of overtones or a somewhat irregular periodic part. Hence, periodicity detection for the quasar-galaxy pair data examined in this article has been performed using the SVD based method.

The SDSS DR7 database contains information pertaining to galaxies with low redshift -quasar pair, where the quasars are projected within 100 Kpc of the galaxy. A total of 97489 galaxy/ quasar pairs are reported from a sample of 105783 spectroscopic quasars and 798948 spectroscopic galaxies. This database contains spectroscopically observed galaxy/quasar projections that can be used to study quasar absorption-line systems arising from known galaxies with redshifts between $0<Z<0.6$ and quasar redshifts $0<Z<3.5$.

The quasar and galaxy redshift data was collected from SDSS DR-7 (Refs. \onlineciteCherinka2011 )and redshifts corresponding to Ca-II and Na-I flags showing warning were rejected. Narlikar (Refs. \onlineciteNarlikar1993) explain that if quasars are physically connected with a parent galaxy, the redshift of each quasar must be transformed to reference frame of the putative parent as :

where $Z_{0}$ is the transformed quasar redshift, $Z_{c}$ is the observed companion quasar redshift and $Z_{p}$ is the observed redshift of the object. The data was transformed to rest frame as proposed by (Refs. \onlineciteNarlikar1980) according to equation (3). The transformed quasar redshift data $Z_{0}$ with values greater than 0.8 were selected for further processing, in order to avoid the possibility of mistakenly including galaxy redshift data.

As proposed by Mal (Refs. \onlineciteMal2020), the two main stages of the approach consist of the formation of an appropriate histogram after determining the optimal bin width and application of SVD for periodicity determination. For the convenience, the procedure is briefly outlined here.

Determination of optimal bin width and histogram formation: The optimal bin width is obtained by minimizing the mean integrated square error (Refs. \onlineciteShimazaki2007, Shimazaki2009) for the entire data set. optimum binwidth is 0.0029 for the Analysis of transformed quasar redshift data.

Matrix formulation & application of SVD: In order to examine the existence of a periodic component, candidate period lengths are selected and the input matrix for application of SVD, formed accordingly. For a candidate period length of say, $L$, the corresponding data matrix $A$ is formed by partitioning the data into contiguous segments of length each and placing each segment (aligned in phase) as a row of $A$. This matrix is used for singular value decomposition. We follow two approaches outlined below: Our first method (SVR1) is defined as the ratio of the first two singular values. A plot of this ratio versus row length is called the SVR1 plot which shows the presence of multiple peaks at integer multiples of the value of the fundamental red shift. The second method (SVR2) for measuring periodicity is defined as the ratio of residual energy to the energy content of the aperiodic signal. The plot of this quantity versus row length is called the SVR2 plot which shows repeated peaks at integral multiples of the value of the fundamental red shift.

Physical interpretation of redshift periodicity confirm the objects which have same redshift are physical members of same clusters, or evolution of quasar is concentrated about epochs spaced in this way, i.e it must have some sort of ”periodic ”structure / ” crystalline” structure or It can be interpreted that non cosmological origin is more stronger than other components of redshift as discussed in equation 1.

There are two conventional alternatives to account for the discretization of redshift or anomalous redshift of QSO, one is Doppler shift and another one is gravitational redshift, but they cannot explain physical association of low redshift galaxy with multiple QSOs and evolution process.

The extremely active field of gravitational lensing has also made rapid strides in locating and imaging of a variety of lensed quasars at various wavelengths. High resolution radio imaging was used by Kratzer (Refs. \onlineciteKratzer2011) to resolve a large separation lensed quasar at $Z=2.197$. Zimmer (Refs. \onlineciteZimmer2010) used archival Chandra data to construct an x-ray light curve of all four images of the quadruply lensed quasar at Z=1.695. High energy gamma rays were used for gravitational lensing for the first time by Barnacka (Refs. \onlineciteBarnacka2011). Corredoira (Refs. \onlineciteCorredoira2006) propose weak gravitational lensing by dark matter as the cause of the statistical correlation between low and high redshift object. However,Scranton (Refs. \onlineciteScranton2005) have contradicted them and claimed that the correlation found was an ad-hoc fit of the halo distribution function to an angular cross correlation with very small amplitude of the galaxy selected photometrically. Even to this day, standard cosmology is unable to provide an explanation for the correlation of galaxies and QSOs. Gravitational lensing explains the association of a high redshift galaxy with a single quasar using the standard cosmological model but fails to explain multiple gravitational lensing within the galaxy.

The generally accepted idea is that a galaxy is surrounded by background QSOs. However the question of statistical analysis of the background /foreground object probability in a small area distributed according to its position and average density in any line of sight, raises much controversy in the astrophysical community. The main approach here is to demonstrate that two extragalactic objects with very different redshifts may be physically neighbors in reality. The physical association of quasar and galaxy is an example of the two cosmological objects being neighbors of each other.

Physical association of quasar and galaxy also explain using super massive black hole(SMBH) and Active galactic Nuclei(AGN). SMBH can grow in size up to billions of solar masses from “seed”, the grow process depend on feeding mechanism from surrounding gas, Astronomer think that every galaxy have extremely bright centre region called Active galactic Nuclei(AGN) and think that they are powered by SMBH in their centre. The most luminous of all the AGN are quasars. Recent discovery of J0313-1806 discovery leads to a question of formation of it. J0313-1806 is thought to sit inside a galaxy with a very active region, the host galaxy produces 200 solar masses worth of star per year. The SMBH that powers this quasar formed just 670 million year after Big-Bang, which ask question on how “seed” grew from to form and how this black hole stellar !. Next researchers propose alternative mechanism called ‘direct collapse’, but truth is unknown.

One of the outstanding mysteries in astronomy today is: How did supermassive black holes, weighing millions to billions of times the mass of the Sun, get to be so huge so fast at the edge of universe.

Recent observations of extra-galactic objects that do not appear to be consistent with the cosmological hypothesis that their redshifts arise from the expansion of the universe.

Our statistical analysis of redshift data clearly establishes the existence of discrete redshift using quasar galaxy/ pair red shift dataset. In the view of the above difficulties with the conventional model, we look for alternative models which can explain the periodicity of redshifts. One such model is proposed as by Hoyle-Narlikar (Refs. \onlineciteNarlikar1980,Hoyle1964,Hoyle1966) which tries to explain the periodicity of redshifts based on Variable Mass Hypothesis(VMH). According to this, the inertia of matter arises due to interaction of other matter in the universe, the matter created from zero mass surface based on quantum principle. The excess redshift does not Aries from high speed of ejection but from the low mass of the newly created matter. Narlikar (Refs. \onlineciteNarlikar1980)explain that the ejected QSO can be bound to the parent galaxy with typical separation of the order of  100-200kpc.Hoyle (Refs. \onlineciteHoyle2000) explain redshift periodicity using variable mass hypotheses. Redshift periodicity is a direct confirmation of the fact that quantization in redshift implies quantization in mass.VMH theory predict that the age of an object usually measured from zero mass epoch on its world line hence higher the redshift of quasar younger it is, this is well matched with recent observation of extragalactic objects: HD1,HD2,GNz7Q,GNZ11.

Another model proposed and elaborated upon by Roy et al. (Refs. \onlineciteRoy2007,Roy2000) based on Wolf mechanism is known as Dynamic Multiple Scattering (DMS) theory. It is shown in a recent paper that DMS can explain the redshift for Galaxy-Quasar association. This depends on the property of the environments around galaxies as well as that of quasars. This mechanism mimics Doppler shift even in the absence of relative motion of the observer and the source.

Wolf(Refs. \onlineciteWolf1986) explains correlation induced spectral shift as well as the broadening and shifts of the spectral line. Roy et al.(Refs. \onlineciteRoy2007,Roy2000) analyzed statistically the Veron-Cetty (V-C) quasar catalogue (2006) and SDSS DR3 data set and concluded that the Hubble law is linear up to small redshifts less than 0.3($z<0.3$) but nonlinear for higher redshift, which adds fuel to the cosmological debate. Roy et al (Refs. \onlineciteRoy2000) explain the broadening of the spectral line using dynamic multiple scattering. They also found a critical source frequency below which no spectrum can be observed for a particular medium. The broadening due to multiple scattering is more than the shift due to cosmological effect. In our future works we will discuss the possible explanation of periodicity of redshifts within DMS framework.

There are two fundamental objection against the ejection hypotheses. First, in the ejection model, ejection is always away from us means redshifted. second, The apparent velocity difference is a large fraction of the speed of light.Many researchers has explained the 1st problem using different selection mechanism, also this is well explained using wolf effect based method . The spectral shift of quasar depend on the surrounding scattering medium of quasar and ejection angle. Peter.M(Refs. \onlinecitepeterM2006) explain apparent redshift components of quasar-galaxy association using parametric model in the wolf framework. The second problem does not exist in the relativistic slingshot process by Saslaw(Refs. \onlinecitesaslaw1974)of ejecting black-hole.