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Check my math, distance from redshift

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#1 Inkswitch

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Posted 16 July 2019 - 09:08 PM

I recently viewed the galaxy UGC10151 and I got to thinking about distance.  People always ask me and I always say I don't know because I never really cared before.  I'm a voracious reader.  I found the following formula on a website called teachastronomy dot com. d=zc/h.  In this equation d is distance, z is the observed redshift, c is the speed of light, h is the Hubble constant.  This is not truly d equals, it is an approximation which is more than good enough for me.

 

For UGC 10151, according the Simbad site, the spectroscopic redshift is z=.03249, the same teachastronomy article has the Hubble constant at h=70.8 km/second/MegaParsec (This value for h is approximate).  Since h is km/second then I must use km/second for c, therefore c=300,000 (it is slightly less than this but it's all an approximation anyway).  All this junk leads to:  d=0.03249 * 300,000 / 70.8 or d=137.669492.  This number is in MegaParsecs, since the Parsec (per Wikipedia) is 3.26 lightyears we have to take 137.669492 and multiply it by 3.26 Million which yields d=448,802,542 light years.

 

Does this sound right?

 

Sources:

http://simbad.u-stra...t=SIMBAD search

 

https://www.teachast...t-and-Distance/

 

https://en.wikipedia...ec#cite_note-14

 

 


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#2 GamesForOne

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Posted 16 July 2019 - 09:56 PM

Sounds pretty good to me. A handy site for double-checking is of course here.

 

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#3 ShaulaB

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Posted 16 July 2019 - 10:11 PM

Yes, it sounds ok, but round it off to the proper number of significant digits. When I teach chemistry, it takes half a semester for some students to get with sig figs. Since your Hubble constant is 70.8, then the distance is 449 million light years.

Consider that M31 is 2.5 million light years away, and it is our neighbor. A galaxy with a UGC, not an NGC, listing logically would be much further away. Good work!
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#4 GamesForOne

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Posted 16 July 2019 - 10:25 PM

My fellow club members recently took an exposure with a 65mm APO of M13 in a wide field. The faintest smudges were remote galaxies on the order of 2 billion ly distant (specific example: SDSS J163936.36+370501.4). Amazing.

 

It is hard to find published redshifts for galaxies out that far (z > 0.15) as even the SDSS does not have values for many.

 

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#5 NMCN

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Posted 17 July 2019 - 05:37 AM

My fellow club members recently took an exposure with a 65mm APO of M13 in a wide field. The faintest smudges were remote galaxies on the order of 2 billion ly distant (specific example: SDSS J163936.36+370501.4). Amazing.

 

It is hard to find published redshifts for galaxies out that far (z > 0.15) as even the SDSS does not have values for many.

 

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Michael Mc

I think "amazing" is an understatement.



#6 Starman1

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Posted 17 July 2019 - 12:30 PM

Y'all might like this thread:

https://www.cloudyni... and clusters


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#7 quazy4quasars

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Posted 17 July 2019 - 03:22 PM

  Couple of things:

 

  At "local distances" the redshift z (the offset of observed absorbtion or emission lines) approximates distance (light travel time) as an "equal" proportion of the age of the Universe:  As an example, IC1101 (z~.07) is 13.7(billion years age of universe) times .07 (z) equals .931 (billion years light travel time).  However, that Galaxy is about a  Billion light years away right now-  it has receded another 65 million light years during that time:  931mly x z(.07) -so its co-moving (current) distance is ~.997 Billion ly. (NED)   disclaimer:  these numbers are from memory - you get the gist.

 

  The value of z does not increase linearly with distance:  z increases logarithmically as distance increases linearly: Example: a z of 1 indicates an observed doubling of an emitted wavelength( a halving of its frequency) and as such, a recession velocity V well below the speed of light,  I believe the formula is V=1/(z+1)^2  (Please feel free to check me).  At z=1, the observed distance (light travel time) is about .6 the age of the universe, at z=3 it is about .9 the age of the universe,  at z=7 it's about .97....

 

  There are some current issues as to the value of the Hubble constant, and there are in fact major differences based on cosmology (flat, curved, open, hyperbolic)  that affect such distance estimates materially.  

 

  Remember also that the observed recession velocity reflects the sum of the Hubble flow(not nailed down to one provably correct value yet- may not be possible) plus the source's local radial velocity( to be cosidered (near) zero for only the very largest Masscons (mass concentrations- i.e. Brightest Cluster Central elliptical Galaxies as markers of massive Galaxy clusters and super-clusters' gravicenters- love that word!).

 

  In a nutshell, the accepted light travel time is probably nearly correct, given the above fudge factors.  Use that to determine (estimate!) the co-moving distance:  NED lays out the basic relationships for any Galaxy you may search on that database, fairly well.

 

  A final point:  SDSS and other surveys have collected millions of spectra of galaxies- most within the local Universe - not even close to how many remain only photometrically observed and catalogued -even among targets identifiable in amateur images. It's... humbling... and... sorry about the word salad. 

 

 

 


Edited by quazy4quasars, 17 July 2019 - 04:10 PM.

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#8 GamesForOne

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Posted 17 July 2019 - 04:16 PM

...

 

  A final point:  SDSS and other surveys have collected millions of spectra of galaxies- most within the local Universe - not even close to how many remain only photometrically observed and catalogued -even among targets identifiable in amateur images. It's... humbling... and... sorry about the word salad. 

 

 

Are most (all?) of the 3D renderings I've seen of galactic distribution generated from the SDSS data and limited to about 1 billion ly?

 

There is a lot of Universe out there still to investigate.  tongue2.gif   I wonder what the 3D renderings of galactic distribution would tell us out to say 5 or 6 billion ly?

 

EDIT: Actually it looks like SDSS-III is working toward that exact goal.

 

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Edited by GamesForOne, 17 July 2019 - 04:19 PM.


#9 quazy4quasars

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Posted 17 July 2019 - 05:09 PM

  I think you are referring more specifically to SDSS III - BOSS (Baryonic Oscilliation Sky Survey) which is one of many SDSS goals: My understanding is that it involves mapping the distribution of neutral hydrogen density variation across the large-scale universe:  While galaxies are found in greater numbers where the densities are high, beyond the local universe they are mostly too faint to get accurate estimates of their true numbers and distances(that would quantify the density variations accurately):  for that reason, the BOSS surveyed QSOs whose brightness allowed high quality spectra -that carry the imprint (absorbtion lines) of neutral hydrogen along their lines of sight, and allowing the density variations along said lines- to be estimated -and mapped- with high precision. (to a 3 (or was it 5?) sigma confidence level) based on the strength and redshift of those absorbtion lines:  An ambitious undertaking. requiring more Teraflops and Petabytes -than a whole housefull of Playstation 5s. shocked.gif

 

  The main reason this is important is to determine the largest scale (if any) at which the anisotropy (variation in neutral hydrogen density across distance ) can be shown to be real.  For a long time, the Universe was assumed to be uniform on large (and now- only the largest) scale: this places constraints on theoretical cosmology;  We need to determine if that really is- or is not- the case - to know which models must (read may) be discarded -or altered.  So it's not so much mapping the distribution of Galaxies as it is the distribution of hydrogen (and helium, and dark matter...?) from which they formed... confused1.gif

 

  Interesting stuff!  Good day to you.


Edited by quazy4quasars, 17 July 2019 - 05:38 PM.


#10 Stephen Kennedy

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Posted 17 July 2019 - 05:23 PM

137 Mpc places it well beyond the Virgo Cluster (15 Mpc) and even the Coma Supercluster which is about 100 Mpc from us.



#11 Inkswitch

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Posted 18 July 2019 - 07:04 PM

Perhaps I should rephrase laugh.gif.  Is a rounded to significant digits approximation, namely 449MLy, good enough that I can feel like I am not lying to someone when I tell them I saw an object this far away?

 

I find the conversation fascinating.  But while I find the difference due to the expansion of space between here and there very interesting, most of the folks I talk to about this will not.

 

 

  There are some current issues as to the value of the Hubble constant, and there are in fact major differences based on cosmology (flat, curved, open, hyperbolic)  that affect such distance estimates materially.  

 

I noted the various +- error bars for the Hubble constant depending on the shape of space.  In the article they were all +- 70.8 so I just used that figure. 



#12 quazy4quasars

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Posted 18 July 2019 - 07:55 PM

  You could consider that uncertainty an opportunity to talk about the factors that affect distance estimates...observational limitations (spectral resolution)... attractors (mascons);   local motion;   the difficulties in constraining the value of the Hubble constant- (or is it constant?)  and how all distant galaxies (beyond Virgo) have receded further than their observed light-travel time distance... not in great detail but just as factors that are not all nailed down,  An equation with uncertainties in it -must contain uncertainties in its solution.   All the figures given in NED etc  are accompanied by  +/- : estimated uncertainty.  The 70.8 figure is used because it is most likely to be close to correct: it is within the overlap of the "error bars" of several differing estimates from very different methods. 

 

  If you want to relate numbers, you might say "just about 450 million light years"  " or, "an estimated  448 million light years"... "at least 440 million"... They will all be decent descriptors of the unknown "exact" distance, (which is increasing by about... 10,000km every second, give or take a hundred or so.) and point out the difference between the time the light took to get here and the present distance.

 

 Better yet, you can do both.  Hope that helps?

 

Edit:  Your desire to state solid figures without exaggeration is really commendable.  My thinking is that stating a legitimate estimate as such- in good faith- is never lying- as in lying- stating a falsehood, intending to mislead... Anyway-  Good on ye!


Edited by quazy4quasars, 18 July 2019 - 09:07 PM.

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#13 Inkswitch

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Posted 30 July 2019 - 10:50 AM

I did the math on the other UGC I have observed, UGC 9897.  My distance record has increased to 483MLy.

 

Of interest to this thread.  Simbad has a distance measurement for UGC 10151 that is a few MLy longer than mine.  I suspected my number to be on the conservative side so this isn't surprising.  Hence I can confidently say 483MLy while knowing that it is likely more.  Simbad does not list a distance measurement to UGC 9897.



#14 Starman1

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Posted 30 July 2019 - 04:02 PM

SIMBAD shows:  z(~) 0.03498  for UGC 9897

NED shows:

Luminosity Distance        : 150 Mpc      
Angular-Size Distance      : 139 Mpc      
Co-Moving Radial Distance  : 144 Mpc     
Co-Moving Tangential Dist. : 144 Mpc      

1 Mpc = 3.26mly, so it's in the range of 453mly to 489mly.

 

I suggest you check NED for these "close" galaxies.


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#15 quazy4quasars

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Posted 30 July 2019 - 10:48 PM

SIMBAD shows:  z(~) 0.03498  for UGC 9897

NED shows:

Luminosity Distance        : 150 Mpc      
Angular-Size Distance      : 139 Mpc      
Co-Moving Radial Distance  : 144 Mpc     
Co-Moving Tangential Dist. : 144 Mpc      

1 Mpc = 3.26mly, so it's in the range of 453mly to 489mly.

 

I suggest you check NED for these "close" galaxies.

 

 Of those four parameters,  two are key in how we describe physical extra-galactic source distances:

 

The Angular Size Distance is that which the light- the visible object image - traveled to get to your eye, here, now, over time.

The co-moving radial distance is the distance to the object right now- it having receded further during that time interval.

 

Remember that these distances as measured by spectra are affected by local velocity of the observer as well as the source, and are computed using some slightly "fuzzy" numbers-  like H nought.  They are very close to, but not to be regarded as, exact, thus we see slightly differing z values across NED, SIMBAD, LEDA, etc, for almost all extra-galactic sources.  (except when derived from a single source; i.e.SDSSIII) 

 

EDIT: And for other computed values as well!  I'm still wondering why NED gives the Age of the Universe at 13.299 Billion years- when most modern estimates are around 13.7 to 13.8 Billion years!   (That pesky H nought again...)


Edited by quazy4quasars, 30 July 2019 - 11:02 PM.

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#16 russell23

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Posted 01 August 2019 - 09:13 AM

Yes, it sounds ok, but round it off to the proper number of significant digits. When I teach chemistry, it takes half a semester for some students to get with sig figs. Since your Hubble constant is 70.8, then the distance is 449 million light years.

Consider that M31 is 2.5 million light years away, and it is our neighbor. A galaxy with a UGC, not an NGC, listing logically would be much further away. Good work!


We can also add that the uncertainty in the Hubble distances to individual galaxies is quite large so you could say “about 400-500 million light years” for this galaxy and possibly still be offering its distance with too much accuracy.

Edited by russell23, 01 August 2019 - 09:14 AM.


#17 GamesForOne

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Posted 01 August 2019 - 09:56 AM

...

 

EDIT: And for other computed values as well!  I'm still wondering why NED gives the Age of the Universe at 13.299 Billion years- when most modern estimates are around 13.7 to 13.8 Billion years!   (That pesky H nought again...)

Perhaps because the NED equations do not include variations in the expansion rate that are part of the more complex ΛCDM theory of the evolution of the Universe.

 

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#18 quazy4quasars

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Posted 01 August 2019 - 10:52 AM

We can also add that the uncertainty in the Hubble distances to individual galaxies is quite large so you could say “about 400-500 million light years” for this galaxy and possibly still be offering its distance with too much accuracy.

We have a number of other measures that fill in the first few steps of the cosmological "Distance ladder" which include Cepheids and Type II supernovae, etc,  that are derived from fairly solid astrophysics.  NED gives good descriptions of the many independent means of estimating distances on extra-galactic scales.

 

Yes, your point is valid in principle, and the FAR greater likelihood is that the true value does fall within the generous 20% uncertainty your estimate offers:  I see no reason to posit that such an estimate might be "too accurate". For one thing, it implies that we know what we don't know (the hypothetical large "true" error in the estimate),  and for another,  the uncertainties in the various methods are constrained by their results'good correlations with each other (to within a small amount).  It is reassuring that the Hubble Constant estimates all fall within about 68-74 km/s/mpc because they are derived by widely differing methods.  That's a <10% variation; part of it due to observational limitations, no doubt.  

 

Let's not assume catastrophic uncertainty where there is good evidence of its absence.  This is science.  We're on it.


Edited by quazy4quasars, 01 August 2019 - 11:19 AM.

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#19 russell23

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Posted 01 August 2019 - 11:06 AM

I've published research using the Tully-Fisher relation so I have a pretty good grasp of the pitfalls of different methods and the Hubble relation is not particularly reliable for individual galaxies. There can be very large errors.

#20 quazy4quasars

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Posted 01 August 2019 - 03:27 PM

I've published research using the Tully-Fisher relation so I have a pretty good grasp of the pitfalls of different methods and the Hubble relation is not particularly reliable for individual galaxies. There can be very large errors.

Perhaps there is some misunderstanding.  The spectra of those Galaxies give their relative distance based on features like the 400 nm discontinuity at red-shifted position.  There can be errors due to local motion and attractor infall velocity estimates, and others, as well as H nought;  if we know they are in error, then that knowledge is based on the other methods' results.  What would you define as a "large" error?  And to what sigma confidence level would you place your "about 400-500 mly" uncertainty range NOT containing the true distance(the null hypothesis)? Feel free, even obligated, to clarify your summations.

 

I'm not published;  It's a lifelong interest -with gaps in my education: I'm here to learn more -and to share what I think I've learned. smile.gif   Genius and Passion -are all I have to show (Jeez, I let myself say that? [*redacted*]).

 

My Apologies for the combative tone; I'd be honored to read any of your work you'd care to share.


Edited by quazy4quasars, 01 August 2019 - 04:29 PM.


#21 Inkswitch

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Posted 02 August 2019 - 01:41 PM

This is a hobby for me but being accurate is also important to me.  I would like to see this discussion come to resolution.  How much faith can I put in d=zc/h?  I know there are uncertainties in the Hubble Constant (some constant eh?) but I figure if I am with a few MLy, less than 20, then I am good enough.  There won't be any published work done from my distance estimates therefore no chance of any errors creeping into common knowledge.

 

EDIT:  Forgot to add, for the purpose of the conversation, the number I am really interested in is the distance traveled by the photons I am observing.  That will give me a number that I can say "I am seeing this as it was xxxMY ago".  While the current distance to the object is of lesser interest.


Edited by Inkswitch, 02 August 2019 - 01:45 PM.

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#22 russell23

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Posted 02 August 2019 - 02:56 PM

I will get back to you guys on this topic when I can find time - maybe later today but definitely over the next few days.  The problem is there is a lot to say and - while I am swamped right now with some work around the house and family stuff - I'm giving some thought to which things I should bring into the discussion and which things I should leave out.  However, a few months back I explained some of what I did with the Tully-Fisher relation on this thread post #26:

 

https://www.cloudyni...galaxies/page-2

 

I'll get to the Hubble stuff in a later post when I get some time and have my thoughts organized.   It will be a long post like the post linked to above.


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#23 Inkswitch

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Posted 02 August 2019 - 04:40 PM

I will get back to you guys on this topic when I can find time

 

Your time will not go unappreciated.



#24 quazy4quasars

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Posted 05 August 2019 - 12:38 PM

Your time will not go unappreciated.

 

   Put in your own time and you'll appreciate it even more.  Perhaps a course in Observational Astronomy at your local JC will give you a better sense of the issues;  and you may get to share views through your telescope too.  

 

  I really love to share the universe with people who never even looked through a telescope before.  Many have never seen the night sky outside of a city...I'm blessed to have had many opportunities to share it. There is nothing like it, and It's OK to say "we're not exactly sure"....The mysteries are part of the magic, the mystique...

 

  When somebody who never looked through an eyepiece before sees a Galaxy Cluster or a Quasar for the first time;  or the Veil Nebula or Jupiter or M5 or a slim evening moon lit by Earth-light,  perhaps it may inspire them to learn; to ask questions that don't have, may never have; exact answers:   I helped the Universe ignite the fire of wonder in their minds.

 

  Here's to mysteries that endure, wonders still to discover, questions not yet even asked, let alone answered! 


Edited by quazy4quasars, 05 August 2019 - 01:07 PM.


#25 Inkswitch

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Posted 05 August 2019 - 09:46 PM

However, a few months back I explained some of what I did with the Tully-Fisher relation on this thread post #26:

 

https://www.cloudyni...galaxies/page-2

 

I read the entire thread.  I begin, through a glass darkly, to see the issues with these distance relationships.




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