Metallicity, or What the Hex is a Dex

[BDanielMayfield]

The news re the newly discovered Proxima b exoplanet has rekindled my interest, and so I'd like to have some questions answered por favor.

The star Proxima's metallicity is reported as 0.21 dex. I know that since the dex value is positive Proxima has a higher metal content than our Sol, but how much higher, in % please. I'd love to have a formula to convert dex values into percents, which would be easier to explain to people in general.

Also, if a star system's metallicity is significantly higher than ours is, wouldn't it follow that the system's planets on average should be more rocky than ours?

Bruce

[neufer]

<<The overall stellar metallicity is often defined using the total iron-content of the star "[Fe/H]": though iron is not the most abundant heavy element (oxygen is), it is among the easiest to measure with spectral data in the visible spectrum. The abundance ratio is defined as the logarithm of the ratio of a star's iron abundance compared to that of the Sun and is expressed thus:

• 

  ---

where N_Fe and N_H are the number of iron and hydrogen atoms per unit of volume respectively. The unit often used for metallicity is the "dex" which is a (now-deprecated) contraction of 'decimal exponent'. By this formulation, stars with a higher metallicity than the Sun have a positive logarithmic value, whereas those with a lower metallicity than the Sun have a negative value. The logarithm is based on powers of 10; stars with a value of +1 have ten times the metallicity of the Sun (10¹). Conversely, those with a value of −1 have one-tenth (10⁻¹), while those with a value of −2 have a hundredth (10⁻²), and so on. Young Population I stars have significantly higher iron-to-hydrogen ratios than older Population II stars. Primordial Population III stars are estimated to have a metallicity of less than −6.0, that is, less than a millionth of the abundance of iron in the Sun.>>

[Chris Peterson]

Also, if a star system's metallicity is significantly higher than ours is, wouldn't it follow that the system's planets on average should be more rocky than ours?

Probably not. Rocky is rocky- as opposed to gaseous or icy. If the metallicity is higher we might expect more rocky planets, but given the current evidence suggesting that most of the planets that form in a system (or some systems) are ejected very early, even that may be a poor assumption.

[BDanielMayfield]

<<The overall stellar metallicity is often defined using the total iron-content of the star "[Fe/H]": though iron is not the most abundant heavy element (oxygen is), it is among the easiest to measure with spectral data in the visible spectrum. The abundance ratio is defined as the logarithm of the ratio of a star's iron abundance compared to that of the Sun and is expressed thus:

• 

  ---

where N_Fe and N_H are the number of iron and hydrogen atoms per unit of volume respectively. The unit often used for metallicity is the "dex" which is a (now-deprecated) contraction of 'decimal exponent'. By this formulation, stars with a higher metallicity than the Sun have a positive logarithmic value, whereas those with a lower metallicity than the Sun have a negative value. The logarithm is based on powers of 10; stars with a value of +1 have ten times the metallicity of the Sun (10¹). Conversely, those with a value of −1 have one-tenth (10⁻¹), while those with a value of −2 have a hundredth (10⁻²), and so on. Young Population I stars have significantly higher iron-to-hydrogen ratios than older Population II stars. Primordial Population III stars are estimated to have a metallicity of less than −6.0, that is, less than a millionth of the abundance of iron in the Sun.>>

Thanks, but I'd read that before posting my questions...

Could it be that the dex to percent conversion I'm seeking is as simple as:

%Diff of star from sun = 10^{Dex of star} ?

If true then Proxima would have 10^0.21 or 1.62 times more metals by percent of mass as our sun, 62% more "metallic", so to speak?

[BDanielMayfield]

Also, if a star system's metallicity is significantly higher than ours is, wouldn't it follow that the system's planets on average should be more rocky than ours?

Probably not. Rocky is rocky- as opposed to gaseous or icy. If the metallicity is higher we might expect more rocky planets, but given the current evidence suggesting that most of the planets that form in a system (or some systems) are ejected very early, even that may be a poor assumption.

Ok, but how about the content of such a system's rocky worlds? Higher percentages of the heavier elements than here perhaps?

[Chris Peterson]

Also, if a star system's metallicity is significantly higher than ours is, wouldn't it follow that the system's planets on average should be more rocky than ours?

Probably not. Rocky is rocky- as opposed to gaseous or icy. If the metallicity is higher we might expect more rocky planets, but given the current evidence suggesting that most of the planets that form in a system (or some systems) are ejected very early, even that may be a poor assumption.

Ok, but how about the content of such a system's rocky worlds? Higher percentages of the heavier elements than here perhaps?

Yeah, but not so you would notice, I think, without very careful analysis. The geochemistry is going to be similar, the process of gravimetric differentiation is going to be similar.

[neufer]

Could it be that the dex to percent conversion I'm seeking is as simple as:

%Diff of star from sun = 10^{Dex of star} ?

If true then Proxima would have 10^0.21 or 1.62 times more metals by percent of mass as our sun, 62% more "metallic", so to speak?

Could be