Distance and Red Shift of stars

PhiJ

Are there any tables for the distance against red shift of stars. I've heard that for stars close enough so you can measure the distance by triangulation it is correlated but not as strongly as the "almost perfect correlation" that I have been taught.

Garth

Hi PhilJ,
Welcome to these Forums and keep asking questions.

The "tables for the distance against red shift of stars" is in fact the Hubble parameter H, which for nearby galaxies is H = v.d .

A modern evaluation of H is 71 km/sec/Megaparsec.

The stars concerned are in other galaxies because those in our own galaxy have their own velocities as they orbit around the galactic centre and it is generally thought that our galaxy does not expand with the universe.

Galaxies also have their own peculiar motions and so there is a variation around the value of H which becomes less significant at greater distances.

The Hubble relationship is one of the last rungs in what is known as the Distance Ladder, which you can find more about here.

Garth

matt.o

Just a slight typo there Garth. The Hubble parameter is H=v/d.

Garth

Dooh!
Homer

matt.o

Homer puts on smart glasses;
Homer: “The sum of the square roots of any two sides of an isosceles triangle is equal to the square root of the remaining side.”
Man in bathroom stall: “That's a right triangle, you idiot!”
Homer: “D'oh!”
gotta love the Simpsons!

PhiJ

Thanks!

Chronos

Triangulating the motion of stars outside our own galaxy is an enormous challenge. You can appreciate this by considering stars in our next door neighbor, the Andromeda galaxy, are no less than about 2 million light years distant. Earth orbit, by comparison, is about 15 light minutes across. Achieving precision under these circumstances is... difficult. Standard candles are considered more accurate yardsticks. Cepheid variables are best, followed by SNe Ia supernova for this purpose. Even this is a complicated process. Intervening gas and dust can severely affect the results.

SpaceTiger

Just wanted to give some updates on the stuff Chronos just mentioned. Trigonometric parallax has, so far, only given us distances to objects within ~100 parsecs (~300 light years). Beyond that, the parallax angle becomes too small for our instruments to resolve. However, the upcoming Space Interferometry Mission (SIM) is going to be able to do microarcsecond astrometry, which means that it could, in principle, measure the distance to anything in the galaxy (within its limiting magnitude, of course).

Beyond the distances that can be measured by parallax, we must use "secondary" methods. This includes the standard candles that Chronos mentioned. The reason they should be thought of as secondary (or, in some cases, tertiary or higher) is that they must be calibrated by some other distance-finding method. That is, we don't know the intrinsic brightness of a standard candle unless we can measure the distance and flux to one nearby. This means, unfortunately, that higher-order distance-finding methods carry with them the systematic errors of the lower-order ones.

The standard candle that can take us furthest (so far) is the Type Ia supernova. In principle, this can be used to measure the Hubble constant and normalize the distance-redshift relationship that is the subject of this thread. However, it turns out that Cepheids are actually better for this job. Why? Well, the basic reason is that we can get better statistics with Cepheids -- there aren't enough supernovae occurring nearby. However, supernovae are much brighter than Cepheids, so they can take us to much larger distance and are much better for measuring the higher-order changes in the distance-redshift relationship. This is why we were able to detect the acceleration of the universe with them.

Nereid

To expand upon SpaceTiger's excellent post ...

The best trigonometric parallaxes, to date, have been determined by the HIPPARCOS mission, whose primary catalogue says the "Median precision of parallaxes (Hp < 9 mag)" is 0.97mas.

In addition to SIM, GAIA will provide a substantially increased 'parallax' view of most of the Milky Way galaxy, at least for stars which are bright enough for it to 'see' (which will be an awful lot, down to Vmag ~20!)

There are a number of means by which distance can be measured, circumventing the 'distance ladder', with all its attendant cascading of standards (and uncertainties). For example, gravitational lensing. Unfortunately, these methods all have their own challenges (and errors), limitations, etc. To date, the ladder built on standard candles remains pretty much the most accurate.

wolram

What is a standered candle ? a candle can burn with brightness according to its
chemical makeup, which do we know first ?

SpaceTiger

A standard candle is an object whose luminosity can be inferred from other observables (such as its spectrum or pulsation period). Once the luminosity is inferred, we need only measure its flux (or apparent magnitude) to determine the distance.


Chemical makeup is only one example of a parameter that might be used to infer an object's luminosity. The way that standard candles are calibrated is by observations of nearby objects for which distances can be obtained by other means. For example, if I measure the parallaxes of a bunch of stars near the sun and find their luminosities, I can look for trends between luminosity and other properties -- say, pulsation period and spectral type. If I then observe a much more distant object (for which there is no parallax), I can infer that object's luminosity by simply measuring the pulsation period and spectral type. Once I've inferred the luminosity, it's only a matter of plugging into the equation:

[tex]d=\sqrt{\frac{L}{4\pi F}}[/tex]

where d is the distance, L is the luminosity, and F is the flux. Since F is measurable, this gives me the distance.

Note: For extremely large distances, cosmological corrections become important and the above expression gives only the "luminosity distance", not the proper distance. You can check out Ned Wright's tutorial for more information on this distinction:

Many Distances

Chronos

The big plus, when it comes to Cepheids, is some of them are near enough to triangulate their distance. That takes a lot of the guess work out making them extremely reliable distance indicators. The supernova distance ladder was built from the Cepheid distance ladder, which was built from parallax measurements. It [Cepheids] is one of the most important areas of study in modern cosmology because so much rides on getting accurate distances. If you wonder why scientists are so excited about SIM or GAIA, that is reason enough.

PhiJ

Cool, Thanks for the help! :)