The Paper-and-Pencil Cosmological Calculator

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The Paper-and-Pencil Cosmological Calculator

Post by bystander » Wed Apr 03, 2013 5:55 am

The Paper-and-Pencil Cosmological Calculator
MIT Technology Review | The Physics arXiv Blog | 2013 Apr 03

Ever struggled with the problem of converting redshift into parsecs, your worries are over thanks to a new cosmological distance chart based on the very latest data.

Examine the light from a distant galaxy and you’ll notice that it is significantly different to light from nearby stars: its wavelength will be increased or shifted towards the red part of spectrum. This so-called redshift is the result of an object’s movement away from us–you can hear the same effect in the pitch of police car sirens when they move past us at speed.

Redshift plays a hugely significant role in astronomy. Early in the last century, the astronomer Edwin Hubble noticed that the amount of redshift was proportional to an object’s distance. So more distant objects have a bigger redshift. That’s an extraordinary discovery because it clearly implies that the universe must be expanding. It also means that objects with bigger redshifts must be older.

Today, astronomers often do away with traditional distance measurements entirely, never mentioning kilometres or even light years. Instead, they talk only in terms of redshift. For example, the most distant galaxy, known as UDFy-38135539, has a redshift of 8.6 and dates from some 600 million years after the Big Bang. The cosmic microwave background radiation, which is made of light emitted 379,000 years after the Big Bang, has a redshift of 1089. And the yet-to-be-observed cosmic neutrino background, emitted just 2 seconds after the Big Bang, should have a redshift of 1010.

But how far way are these objects in kilometres or light years? If you’ve ever tried to convert redshift into kilometres, parsecs or light years, you’ll know the task is fraught with difficulty. For a start, the calculation depends on the model of the universe you use, whether flat or expanding for example. Then there are the actual parameters of the model that need to be measured from the universe itself, such as the value of Hubble constant.

Not even Google does this kind of distance conversion.

Today, all that changes thanks to the work of Sergey Pilipenko of the Astrospace Center of the Lebedev Physical Institute in Moscow. Pilipenko has taken the necessary parameters from the latest Planck telescope results, unveiled last week, and has plugged them into a standard model of the universe called Lambda-CDM, which includes the effects of dark energy and cold dark matter.

The result is a series of simple charts showing the relationship between redshift, parsecs, age and a few other parameters. (He’s even made public the code that performs the calculation.) The chart above shows the relationship for redshifts less than 20.

Paper-and-pencil cosmological calculator - Sergey V. Pilipenko
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Re: The Paper-and-Pencil Cosmological Calculator

Post by Ann » Wed Apr 03, 2013 9:22 am

The result is a series of simple charts showing the relationship between redshift, parsecs, age and a few other parameters.
I get what parsecs are, or even megaparsecs. I get what kiloparsecs are, and I understand that 1 kpc is one kiloparsec. But I don't understand "angle 1kpc", and I don't understand how z=0 can correspond to 10.00 angle 1kpc. Above all, I don't understand what distance this is.

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Re: The Paper-and-Pencil Cosmological Calculator

Post by Chris Peterson » Wed Apr 03, 2013 9:21 pm

Ann wrote:I get what parsecs are, or even megaparsecs. I get what kiloparsecs are, and I understand that 1 kpc is one kiloparsec. But I don't understand "angle 1kpc", and I don't understand how z=0 can correspond to 10.00 angle 1kpc. Above all, I don't understand what distance this is.
I believe that value gives the angle subtended by a 1 kpc wide body at the calculated distance. If you look closely, I don't think the value is actually 10 arcsec at z=0, but at a value of z greater than zero. The actual value must become infinite at z=0, so that column of the nomogram doesn't quite get to zero.

Personally, I think the nomogram is a bit difficult to use (and I'm certainly not going to recompile a Fortran program when the parameters change!) Much simpler is this nifty cosmology calculator, my favorite from the large crop of them out on the Internet.
Chris

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Re: The Paper-and-Pencil Cosmological Calculator

Post by MargaritaMc » Wed Apr 03, 2013 9:38 pm

In his paper, Pilipenko notes that he envisages his nomogram being of use when neither the Internet nor a PC is available.
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Re: The Paper-and-Pencil Cosmological Calculator

Post by neufer » Wed Apr 03, 2013 9:45 pm

Image
Chris Peterson wrote:
Personally, I think the nomogram is a bit difficult to use (and I'm certainly not going to recompile a Fortran program when the parameters change!) Much simpler is this nifty cosmology calculator, my favorite from the large crop of them out on the Internet.
  • More of a slide rule than a nomogram, I think.
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Re: The Paper-and-Pencil Cosmological Calculator

Post by Chris Peterson » Wed Apr 03, 2013 11:24 pm

neufer wrote:More of a slide rule than a nomogram, I think.
I agree. The author called it a nomogram, and it superficially looks like one, but the fact that all the values line up horizontally makes "slide" sound like a better term. Every true nomogram I've seen involves connecting a pair of values along two columns in order to read a result on a third.
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Re: The Paper-and-Pencil Cosmological Calculator

Post by Ann » Thu Apr 04, 2013 4:59 am

Chris Peterson wrote:
Ann wrote:I get what parsecs are, or even megaparsecs. I get what kiloparsecs are, and I understand that 1 kpc is one kiloparsec. But I don't understand "angle 1kpc", and I don't understand how z=0 can correspond to 10.00 angle 1kpc. Above all, I don't understand what distance this is.
I believe that value gives the angle subtended by a 1 kpc wide body at the calculated distance. If you look closely, I don't think the value is actually 10 arcsec at z=0, but at a value of z greater than zero. The actual value must become infinite at z=0, so that column of the nomogram doesn't quite get to zero.

Personally, I think the nomogram is a bit difficult to use (and I'm certainly not going to recompile a Fortran program when the parameters change!) Much simpler is this nifty cosmology calculator, my favorite from the large crop of them out on the Internet.
Please, Chris, I still don't understand how to use or read this calculator. Bystander recently posted this link about a nearby starburst galaxy. I wanted to know exactly how distant it was since its proximity was of importance. But the only distance indication given was the redshift of the galaxy pair, z=0.047.

Could you tell me how to enter z=0.047 into your calculator and receive the correct answer in lightyears or parsecs?

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Re: The Paper-and-Pencil Cosmological Calculator

Post by rstevenson » Thu Apr 04, 2013 1:18 pm

For z=0.047 the paper-and-pencil calculator gives a co-moving distance of about 200 Mpc and a lookback time of about 0.6 Gyr. It'll be interesting to see how this compares to the calculator Chris mentioned. ... ...

Not too bad. When I enter that z value into that calculator, and choose a Flat universe, I get 196.5 Mpc and 0.626 Gyr.

All I did was enter 0.047 into the z field near the top-left corner of that screen, then click the Flat button just below it. I didn't change anything else. Click the Open button to see the values change for an open universe model. (I don't know enough about those choices to know which is "better".)

Rob

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Re: The Paper-and-Pencil Cosmological Calculator

Post by Ann » Thu Apr 04, 2013 4:36 pm

Thanks, Rob! :D :D :D

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