8 replies to this topic

[rekokich]

The only primary evidence available to an astronomer about a very remote object consists of photometric measurements, a spectrogram, and an image which is in many cases no more than a pinpoint of light. In this article we present basic cosmological concepts and simplified mathematical methods which allow an amateur to derive from this meager data a surprising number of physical properties of distant extragalactic objects with a precision of several percent within professional results.

Click here to view the article

[rekokich]

I received several questions regarding the difference between the Relativistic Recession Velocity and the Proper Recession Velocity.

 

Relativistic Recession Velocity, Vr, is an objective value obtained from the target's redshift. It describes the recession velocity a distant light source had in the remote past, when the photons we are presently observing were emitted.

 

Proper Recession Velocity, Vp, represents an estimated recession velocity of an object in the present cosmological epoch, calculated from its redshift and the currently accepted expansion rate of the universe. If Vp is greater than the speed of light, the object has already crossed the event horizon.

[rekokich]

Extragalactic Cosmological Calculator, CosmiCalc.exe, is finally finished. It derives a number of physical properties of remote galaxies and quasars based on objective data, such as redshift, apparent magnitude, and apparent diameter. Such data is readily available for all named objects at:
the SIMBAD Astronomical Database, [ http://simbad.u-strasbg.fr/simbad/ ]
and at the NASA/IPAC Extragalactic Database (NED), [ http://ned.ipac.caltech.edu/ ]
 
The program is based on equations in the CloudyNights.com series of articles titled Basic Extragalactic Astronomy. These equations are accurate within several percent of professional results for extragalactic objects which recede primarily by Hubble flow, or by the expansion of the universe. They will not be accurate for very nearby galaxies, like M31, whose motion relative to us is mostly due to the "peculiar velocity" through space.

The program is free and compatible with all Windows versions. It is self-contained, with no need for INI files or registry entries. It is "portable", which means it can be run from any location in the file system, including the Desktop, or from an external USB drive.

 

The program can be downloaded from Google Drive at

https://drive.google...iew?usp=sharing

 

The source code BAS file can be opened with Notepad, and is available at

https://drive.google...iew?usp=sharing

 

The first screenshot is for quasar 3c 273.
https://www.cloudyni...2694_118274.jpg

The second screenshot is for the distant quasar APM 8279 which is used as an example in the articles.
https://www.cloudyni...2694_216952.jpg

Suggestions on improving the program will be appreciated.

Edited by rekokich, 29 February 2020 - 12:07 AM.

[rekokich]

Extragalactic Cosmological Calculator v 2.0 information and download links:

https://www.cloudyni...download-links/

[GeoNole94]

Thank you, I learned some new things and reinforced some that I already knew. This series represents a lot of work, tip-o-the-cap to all of you. Steve

[Rupert]

This is a nice article, but unfortunately it promotes some widely-held misconceptions, most notably (1) that the distance at which recession velocity is c (the Hubble sphere) is an event horizon beyond which we can't detect light, and (2) that special relativity (SR), as in formulae 6 and 7, can be used to interpret cosmological redshifts.

 

We, as comoving observers, do see galaxies that are and always have been receding faster than c, because the distance to the Hubble sphere also increases due to the metric expansion of the universe: a photon emitted towards us in a superluminal region recedes from us at Vr-c, where Vr>c is the superluminal recession velocity, but if the rate at which the radius of the Hubble sphere increases exceeds Vr-c the photon will eventually enter the subluminally receding region, and will reach us.

 

In lambda-CDM cosmology galaxies with redshifts z>~1.5 are receding from us superluminally now, and for galaxies with z>~2, dz/dt<0 (i.e., z decreases with time). Therefore, a galaxy with z>~2 such as APM 8279 (z=3.911) was receding superluminally at the time of emission of the radiation we see now (its redshift was >3.911 then because dz/dt<0), and in fact it always has been receding superluminally.

 

The interpretation of cosmological redshifts requires general relativity (GR), not SR. The latter applies to kinematic motion (motion through space in an inertial frame, but not to the metric expansion of space (it is a good approximation to the GR velocity-redshift relation only for small redshifts, z<~0.3 or so). According to GR with the lambda-CDM cosmology, the present-day recession velocity of APM 8279 is about ~1.7c.

 

It's not correct to say that "relativistic recession velocity" (as in SR formulae 6 and 7) describes the recession velocity a distant light source had in the remote past, when the photons we are presently observing were emitted. The calculation of recession velocity at the present (proper) time, Vobs, and at the (proper) time the detected photons were emitted, Vem, must be done (1) within GR, and (2) for an assumed cosmological model. As an example, for the Einstein-de Sitter cosmology (it's analytically simple compared with lambda-CDM, and is a reasonable representation of the universe in the redshift range ~2-300) we have in terms of observed redshift, z

 

Vobs = 2c[1-1/sqrt(1+z)]  (~1.1c for APM 8279)
Vem  = 2c[sqrt(1+z)-1]    (~2.4c for APM 8279)

 

Finally, note that the redshift of the cosmic microwave background we detect now is ~1100, and in lambda-CDM cosmology this corresponds to a present-day recession velocity of Vobs~3.2c, and Vem~50c at the time of emission! Clearly a recession velocity of c isn't an event horizon.

Edited by Rupert, 25 August 2022 - 04:38 AM.

[rekokich]

Hello Rupert,

I am sorry for a delayed reply. I just noticed your comment yesterday

I believe you may have misunderstood the article on several levels:

1) The article never states that "the distance at which recession velocity is c (the Hubble sphere) is an event horizon beyond which we can't detect light..."  Please reread section 3 carefully, paying attention to galaxies C and D, which at time T2 accelerated beyond the event horizon. The article specifically states that "at time T2, galaxies C and D will REMAIN VISIBLE TO THE OBSERVER FOR BILLIONS OF YEARS because the photons they had emitted before crossing the event horizon will take billions of years to reach the observer, albeit with an ever increasing redshift and decreasing apparent magnitude". Thus, we can clearly see galaxies which are PRESENTLY beyond the event horizon because we are detecting photons which had been emitted BEFORE the galaxy crossed the event horizon.

2) Equations 6 and 7 are correct general relativistic equations for relating measured redshift to recession velocity, AT THE TIME THE PHOTONS WERE EMITTED.
http://astronomyonli...ticRedshift.asp
For APM 8279, RELATIVISTIC recession velocity is 0.920376 C, AT THE TIME THE PHOTONS WERE EMITTED. In the PRESENT EPOCH, the quasar's PROPER recession velocity is 1.714383 C, and these photons no one will ever see.

3) It is possible you misunderstand the term "comoving". Please read carefully section 8 in this article:
https://www.cloudyni...parameter-r3214

Thus, while we see, and will continue to see forever at increasing redshift, objects which emitted light while they were WITHIN the event horizon, we have never seen, and will never see, objects which were originally created BEYOND the event horizon. While the event horizon radius does increase with the expansion of the Universe, it does NOT catch up to objects originally created outside of it because they recede at a faster speed.

4) The photons we are PRESENTLY observing are precisely the photons emitted at the LOOKBACK = LIGHT TRAVEL TIME/DISTANCE. Which other photons would they be? The photons an object is PRESENTLY emitting will only reach us in billions of years providing its COMOVING = PROPER DISTANCE is within the cosmic event horizon.

5) The reason we can detect cosmic microwave background radiation (CMBR) with a redshift of ~1100 is very simple - the future location of our Galaxy was situated WITHIN an event horizon (one of an infinite number of event horizons) WITHIN the Big Bang. As our event horizon increases in size, we continue to see CMBR photons (originally emitted WITHIN our event horizon) FOREVER at increasing redshift, increasing wavelength, decreasing temperature, and decreasing luminosity.

Thanks to your comment, I plan to expand and clarify these subjects in the ebook version of this article series.

Clear Skies

[Rupert]

Hello again , I just saw your response. I would hope I do understand "comoving observer" - this field is my day job 😀

Can I refer you to the following article, which gives a very clear exposition of these issues:

astro-ph/0310808

Good luck with your forthcoming book

Rupert

[SpitzA3P]

Thank you for your article.

 

I would like to know if there is a formula for determining the percentage of recessional velocity due to redshift versus radial velocity ie  expansion of space versus doppler affect.

 

I saw 3c273 a few years ago and became enchanted with its distance.