Stellar temperature

What always gets me is reporting the Teff of these cool stars as
their 'temperature'. Since stars don't have a surface, they
should be reported as the temperature of their photosphere,
which is roughly the _maximum_ brightness temperature in the
optical spectrum. The difference is small for the Sun - 6500 K
vs. 5830 K roughly - but very large for T dwarfs and in fact is
about 1000 K vs. 400 K when water clouds begin to form.

Andrew Usher

On 3/24/11 1:39 AM, Andrew Usher wrote:
What always gets me is reporting the Teff of these cool stars as
their 'temperature'. Since stars don't have a surface, they
should be reported as the temperature of their photosphere,
which is roughly the _maximum_ brightness temperature in the
optical spectrum. The difference is small for the Sun - 6500 K
vs. 5830 K roughly - but very large for T dwarfs and in fact is
about 1000 K vs. 400 K when water clouds begin to form.

Andrew Usher



Mo

The surface (photosphere) temperature determines the spectral
class of the star. Wien's displacement law
http://en.wikipedia.org/wiki/Wien%27s_displacement_law
relates the peak wavelength to the "blackbody" temperature.

Andrew Usher wrote:
What always gets me is reporting the Teff of these cool stars as
their 'temperature'. Since stars don't have a surface, they
should be reported as the temperature of their photosphere,
which is roughly the _maximum_ brightness temperature in the
optical spectrum. The difference is small for the Sun - 6500 K
vs. 5830 K roughly - but very large for T dwarfs and in fact is
about 1000 K vs. 400 K when water clouds begin to form.

Andrew Usher

The effective temperature Teff is the T in the equation L(total) = 4piR^2
sigma T^4 (for a spherical star). It is directly related to the total
energy radiated by the star (or planet, or anything else).

Because these very cool stars have lots of opacity in molecular lines and
bands, the emitted spectrum is very much chopped up when you observe it.

If you want some sort of "physical" temperature, you might try using the
temperature of the gas and electrons at Rosseland mean optical depth 2/3
(approximately). This will allow for the fact that radiation can escape
only in between the lines and bands.

The effective temperature has one virtue--we know exactly what we are
discussing (total integrated flux of radiation over all wavelengths) when we
use it.

--
Mike Dworetsky

(Remove pants sp*mbl*ck to reply)

[Newsgroups snipped: 'sci.math'?!]

In article ,
Andrew Usher writes:
What always gets me is reporting the Teff of these cool stars as
their 'temperature'. Since stars don't have a surface, they
should be reported as the temperature of their photosphere,

The problem is that the height and therefore temperature of the
"photosphere" depend on what wavelength one observes. For cool stars
in particular, the opacity and hence photosphere height and
temperature can vary dramatically across a fairly small wavelength
interval. No single temperature can describe such atmospheres, but
if you have to have just one number, the effective temperature is
probably as good as any. The OP's suggestion of the maximum
brightness temperature at any visible wavelength seems arbitrary: why
limit to visible wavelengths? Also, he probably meant the brightness
temperature at the wavelength (in some range) of minimum opacity,
which isn't quite the same thing. The real point is that there are
several definitions that might be used, and it isn't obvious why
effective temperature is so bad.

From later comments, it seems the OP is criticizing press releases,
not usage in the professional literature. It seems to me that an
unfamiliar definition of "temperature" is hardly the worst feature a
press release can have.

--
Help keep our newsgroup healthy; please don't feed the trolls.
Steve Willner Phone 617-495-7123
Cambridge, MA 02138 USA