Talk:Hayashi track

slogging through this

Could this article just start out:

The Hayashi track refers to the path on the Hertzsprung-Russell diagram taken by an interstellar cloud which is evolving into a star. The gas contracts and heats by gravitational collapse into a dense core and glows as a black body without any nuclear reactions. At around 4000 K hydrostatic equilibrium is reached and the temperature remains constant. Heat lost by black body radiation is replenished by gravity as collapse continues at a slower pace—this appears as an upwards vertical line on the Hertzsprung-Russell diagram. The Hayashi track ends and the ... track begins when nuclear fusion is ignited by the rising pressure.

As a layman and lazyman, I can't be sure of this or verify it, but it would seem to summarize how I interpret the article. Astronomers have a habit of stating ideas very precisely without connecting to related ideas and fusion doesn't even merit a mention here for some reason... Potatoswatter 05:09, 3 April 2007 (UTC)

Well, what's wrong with your text is:

• `protostar' is the accepted term for `an interstellar cloud which is evolving into a star' -- so it would be confusing not to use it.
• It's true that the heating is by conversion of gravitational into internal energy, and it's true that an optically thick object appears as a black body -- but neither of these is at all a particular feature of the Hayashi track. They're also true of clouds before they reach the track and of pre-main-sequence stars after they leave it.
• Clouds are in approximate hydrostatic eqm before they reach the Hayashi track.
• The track of a particular protostar is a downwards vertical line on the H-R diagram.
• The track doesn't end when fusion is ignited (except for very low-mass stars) but, as the article says, when the core becomes hot enough that radiative energy transport is important. Then you get the Henyey track which takes you to fusion and the main sequence. Fusion isn't mentioned because it isn't relevant at either end of the track. It would help if it were mentioned explicitly in the Henyey track article...

Hope this makes things clearer. Mhardcastle 07:26, 3 April 2007 (UTC)

Haha... so that's the academic answer. Let me try again then.

The Hayashi track refers to a linear path on the Hertzsprung-Russell diagram taken by a protostar, an interstellar cloud of gas evolving into a star. The gas contracts and heats by gravitational collapse into a dense core and glows as a black body without any nuclear reactions. Hydrostatic forces give the cloud its shape and size, as gas pressure due to heat balances gravity. The Hayashi track begins when the temperature reaches approximately 4000 K and remains constant. Across a wide range of stellar masses, this is the final equilibrium temperature when collapse due to gravity is complete. However, the protostar continues to shrink due to heat lost to space through black body radiation. This causes decreasing surface area and decreasing brightness. As it remains at hydrostatic equilibrium, the temperature remains a constant 4000 K. These trends form a downwards vertical line on the Hertzsprung-Russell diagram. Eventually the protostar becomes small enough that the temperature gradient becomes significant. Pressure at the center is greater, causing correspondingly higher temperature. On the Hayashi track convection or "churning" keeps the protostar near a consistent 4000 K throughout. The Hayashi track ends and the Henyey track begins when the fluid is too dense for convection to maintain constant temperature. On the Henyey track, the temperature rises with very slowly increasing density until fusion begins.

I feel like I understand now :v) ... this needs a few paragraph breaks but let me know if it's alright... Potatoswatter 10:47, 28 April 2007 (UTC)

The following quote is incorrect, "The Hayashi track ends and the [Henyey] track begins when nuclear fusion is ignited by the rising pressure". No — the Henyey track begins, when the whole star becomes so thoroughly heated, that even the outer surface layers heat up above 4000K. That is the temperature of Hydrogen recombination, cp. Recombination in cosmology. Once even surface layers are too hot to "dump heat" via recombination, the superficially "pseudo-isothermal" Hayashi track is left, and the collapsing protostar "veers left" onto the Henyey track, along which radiative cooling is important. But nuclear fusion does not begin, until the protostar settles down, onto the Main sequence, becoming a full-fledged star. Nuclear fusion begins on the MS, not Henyey track. 66.235.38.214 (talk) 13:55, 2 November 2012 (UTC)

Visual aids needed

As a layman, I've been finding it hard to understand what an example of Hayashi and Henyey tracks would look like; I've been cobbling together an understanding from WP, from discussion pages and from other web sources, but I haven't found a great and complete explanation yet.

I found this picture: http://en.wikipedia.org/wiki/File:Stellar_evolutionary_tracks-en.svg on the Asymptotic giant branch page, but it's describing the end-of-life; I've seen useful things on other sites such as [1] which has an excellent visual aid, but that site also claims that the path the AGB takes is essentially a backwards Hayashi track. I'm not sure if they mean to say that it follows a Hayashi track on the way to Main Sequence, and then looks kind of similar on the way back out, or if they mean it actually follows a Hayashi track again on the way back out. That external image (around 1 solar mass) certainly LOOKS like the graphic on AGB (at 2 solar masses).

Could someone enlighten, and maybe even endeavor to create an image demonstrating these tracks--however simplistic? While I've been looking stuff up to make this post, I've mostly figured out what is going on...but it's been half an hour of research on other sites, when it could probably be made a lot clearer with one diagram here and on Henyey track.

(Is there any reason not to merge Henyey track and Hayashi track, by the way? They both deal with protostars turning into stars, and stars > 0.5 solar masses even switch from Hayashi to Henyey.) --Sowelu (talk) 09:42, 21 October 2009 (UTC)

Hayashi Limit?

Hayashi Limit redirects here, but this article never explains what the "Hayashi Limit" is, nor even mentions it. Could someone please add info on the Hayashi Limit? TIA. 65.216.138.253 (talk) 14:05, 11 November 2015 (UTC)

Derivation Math

I'm trying to follow along with the math in the derivation and can't quite make sense of it. Specifically this part:

"

$P_{0}=\int _{R}^{\infty }g\rho dr$

$={\frac {GM}{R^{2}}}\int _{R}^{\infty }\rho dr$

$={\frac {GM\tau }{kR^{2}}}$

The optical depth at the photosphere turns out to be $\tau =2/3$. By definition, the temperature of the photosphere is $T=T_{eff}$ where effective temperature is given by $L=4\pi R^{2}T_{eff}^{4}$. Therefore, the pressure is:

$P_{0}={\frac {GM}{R^{2}}}{\frac {2\tau }{3k}}$

"

I believe the author was trying to substitute $\tau$ with 2/3, however the $\tau$ is still there, so that $P_{0}$ is now 2/3 of what it used to be. I think the $\tau$ in the last line above should be removed. Am I missing something?

150.135.210.48 (talk) 06:08, 26 January 2017 (UTC)

Yes, you are absolutely right. I've fixed the error. --Bowlhover (talk) 01:31, 12 May 2017 (UTC)