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# Astrophysics/Why Hubble Diagrams are lineal?

Question
Dear Dr Stahl:

When Hubble diagrams plot redshift vs distance, why relationship is lineal all the way through, even when light from older events (farhter away to the right part of the graph) come from stages of the universe expansion when redshift should be smaller?

Shouldnt you expect a curved graph with a shape like the one Perlmutter (1999) plots for effective mB vs redshift Z?

Regards,

Hello, Rony,

Actually, no. As I earlier noted these are two different varieties of measurement. The Perlmutter measurements use type Ia supernovae (which actually discloses accelerated expansion from dark energy) while the Hubble expansion uses the redshifts measured from distant galaxy clusters, quasars.

Because Perlmutter proposes *dark energy* as the primary agency for the ongoing increased rate of accelerated expansion, then one would not expect a linear relationship. A good example is when considering kinematics and looking at different graphs, say for d (distance) vs. t in the case of accelerated vs. non-accelerated motion.  In the latter case we see a linear relationship, while in the former it's a curved line.

The Hubble diagram, then, depicts a linear relationship because it is based on a conventionally accepted constant of proportionality (H) which is taken not to vary over that time period for which the observations are made. Thus:

v = HD

where H is known as the 'Hubble constant'.

Think of H analogous to the value of the slope, m, for the standard straight line relationship, i.e.

y = mx + c

Since the value of m will not change, i.e. the rise over the run is constant, then the graph produced display constant slope or gradient, hence be linear - not curved.

Currently, we estimate H   = 70 km/ sec/Mpc.

In order to obtain a Hubble graph of the type associated with Perlmutter's,  one would have to see or observe variable H over defined (increasing) time scales, i.e. maybe H   = 70 km/ sec/Mpc for the first 1 billion Ly, H   = 80 km/ sec/Mpc, for the next, H   = 90 km/ sec/Mpc for the next and so forth.

This we do not observe, so when discussing the two types of graph we must take care to ensure we are talking of the same things. The key point once more is that Perlmutter's results are based on dark energy, such that we have an equation of state, w = (p/ rho) = -1

leading to gravity that repels. This is what we suspect is responsible for the accelerating expansion.

In the Hubble case, we have a simple extrapolation of the Doppler effect principle to the apparent recessional velocities of distant galaxy clusters etc. We do not interject Perlmutter's results into these because thus far there is no basis to do so. (There is still controversy over the nature of dark energy, for example)

I hope this helps, also that you have had a chance to read Lawrence Krauss's book (previously recommended)

Astrophysics

Volunteer

#### Philip A. Stahl

##### Expertise

I specialize in stellar and solar astrophysics. Can answer questions pertaining to these areas, including: stellar structure and evolution, HR diagrams, binary systems, collapsars (black holes, neutron stars) stellar atmospheres and the spectroscopic analysis of stars – as well as the magnetohydrodynamics of sunspots and solar flares. Sorry – No homework problems done or research projects! I will provide hints on solutions. No nonsense questions accepted, i.e. pertaining to astrology, or 'UFOs' or overly speculative questions: 'traveling through or near black holes, worm holes, time travel etc. Absolutely NO questions based on the twaddle at this Canadian site: http://members.shaw.ca/warmbeach/FAQ.htm purporting to show a "new physics". Do not waste my time or yours by wasting bandwidith with reference to such bunkum.

##### Experience

Have constructed computerized stellar models; MHD research. Gave workshops in astrophysics (stellar spectroscopy, analysis) at Harry Bayley Observatory, Barbados. More than twenty years spent in solar physics research, including discovery of SID flares. Developed first ever consistent magnetic arcade model for solar flares incorporating energy dissipation and accumulation. Developed first ever loop-based solar flare model using double layers and incorporating cavity resonators. (Paper presented at Joint AGU/AAS Meeting in Baltimore, MD, May 1994)

Organizations
American Astronomical Society (Solar physics and Dynamical astronomy divisions), American Geophysical Union, American Mathematical Society, Intertel.

Publications
Papers appearing in Solar Physics, Journal of the Royal Astronomical Society of Canada, Journal of the Barbados Astronomical Society, Meudon Solar Flare Proceedings (Meudon, France). Books: 'Fundamentals of Solar Physics', 'Selected Analyses in Solar Flare Plasma Dynamics', 'Physics Notes for Advanced Level', 'Astronomy & Astrophysics: Notes, Problems and Solutions', 'Modern Physics: Notes, Problems and Solutions'

Education/Credentials
B.A. degree in Astronomy; M.Phil. degree in Physics - specializing in solar physics.

Awards and Honors
Postgraduate research award- Barbados government; Studentship Award in Solar Physics - American Astronomical Society. Barbados Astronomical Society award for service (1977-91) as Journal editor.

Past/Present Clients
Caribbean Examinations Council (as advisor, examiner), Barbados Astronomical Society (as Journal Editor 1977-91), Trinidad & Tobago Astronomical Society (as consultant on courses, methods of instruction, and guest speaker).