Query on Cosmic Dark Energyby

Error Analyses of Type Ia Supernova

Qiu-he Peng

(Depart. of Astronomy, Nanjing University)

§I

Question of “Cosmic Dark Energy”

Origin of the Question of “Cosmic Dark Energy”

“Cosmic Dark Energy” ← “Acceleration of the Universe” ← Observation of remote SNIa with z > 0.5 + Taking SNIa as a Standard Candle Power (Assumption)

← Standard Picture of SNIa Explosion : SNIa Explode when

Mass of Accreting White Dwarf (in binary system) reaches at Chandrashkar critical mass

Sun

Sune

ch

M

MY

MM

38.1

)5.0

(46.1 2

Ye : fraction of electrons

Supernova Light Curves

SNIa as A Standard Candle

Light Curves and spectrums are similar for almost all SNIa

Mmax (- 18m) – ( -20m) ; Mmax = -2.5 log10 L It seems is very close. It may be take as a standard candle at the maximum luminosity of SNIa

M = m + 5 – 5log D(pc) – A + K A: interstellar extinction ; K: correct by redshift of galaxiesThe distance of SNIa may be determined by measuring its apparent luminance (m) when M is given

m – M +A – K = …… “distance modulus ” ( = 5log D(pc) – 5)

Phillips relation Reducing SNIa as a standard candle

Phillips (1993) suggests a semi-experience relation by observation

Δm15 : decrease in apparent luminance during 15 days after the maximum luminance First, For some given SNIa with low redshift which their distances are given by another way of distance determination(e.g. by observation of cepheid variables ), we may get their Mmax by observations of their apparent luminance (m) at the moment of maximum brightness. We may get the two parameters (a, b) through statistics by Mmax and observations of Δm15 . Then, We may caculate Mmax by measuring Δm15 for the remote SNIaFrom the formula above. But, This is only an assumption no any reason on theory.i.e. No physics.

Advanced Phillips WayAdvanced Phillips Way (1996 – 2007) : They are based on two assumptions: a) luminosity is related with the width of the light curve of SNIa;b) luminosity is related with the color index (B-V) in the course of explosion SNIa It is a very complicated statistical relation. SALT2 (Guy, J. et al., 2007) Software to deal with observational data of SNIa

continue

The spectral energy distribution of light curve for SNIa:

F(SN, p, λ) = x0 [M0(p, λ) + x1M1(p, λ) + ...] exp{cCL(λ)}P: time(day) from the maximum moment in B wave band at the rest reference system.: wavelength at the reference system of SNIa. M0(p,): a function of spectral evolution with time in average for SNIa

Mk(p,): (k>0) Describing variance of other factors

X1: describing the width of the light curve for SNIa

CL(λ): corresponding to a color correction function in averagec = (B -V )MAX - < B -V > : variance of color index

Mk(p,) and CL(λ) describing the global behavior of SNIa

c , xi : parameters of each SNIa

continueDistance modulus of the SNIa

2 check test

Nobel Price for Physics in 2011

Riess et al. (1998), Perlmutter et al. (1999) , Guy, J., et al. (2007, SALT2)Amanullah, R., et al. (2010, UNION2)By observation of SNIa with high redshiftAccelerating expansion of the Universe Cosmic Dark Energy

Perlmutter, Smith and Riess have got the Nobel Price for Physics in 2011

§IIStandard Candle of SNIa

is rejected by Recent progress of researches on SNIa

Recent progress of researches on SNIa

1. The Progenitor of SN Ia Tych(1572) has not been found up to now.

2. The total mass of the remnant of SNIa Tych(1572) mSNR >1.8 mSun rather than mSNR <1.4 mSun (Chandrashkar critical mass )→ “Standard Picture of SNIa Explosion” is rejected. → The physical basis of both Philips relation and advanced Philips way are lost. The Standard candle of SNIa is only an assumption on theory

without physical basis . i.e. No physics.

Asymmetry explosion of SNIaIt is shown that material distribution in some remnant of SNIa are obviously asymmetry in space direction by observation. (Kasen D., 2010, Nature, 466,37-38). It is also confirmed by simulation: (Maeda K. et al., 2010, Nature, 466, 82-85)

It is shown that the visual brightness of SNIa depends on the direction of observer. Then the Phillips’ (and advanced Phillips’) mathord is unphysical.

§IIIQuery on

Accelerating expansion of the Universe

byError analyses

Query on the error analyzingboth Philips relation and advanced Philips way are

Assumptions or they are mathematic models without physical basis only.

The Set of SNIa after deal with by SALT2(software)

is just a set of “modeling SNIa” ,

rather than real set of SNIa.

There are some serious flaws in the error statistics for all previous researches:

Some flaws in the error analysis of SNIa observation

However, the based assumption of standard candle power of SNIa has been negated by progress of researches on SNIa recent years.Besides, Some serious flaws are in the error analysis of those papers:1.Error of absolute magnitude at maximum luminance (for SNIa ) caused by the advanced Phillips’ way has not been included. 2 The set of modeling SNIa in their papers (Amanullah, R., et al.(2010) (including 685 SNIa) is really no Gaussian distribution .it is incorrect to find the intrinsic error of SNIa by 2 check test method.

1. No Gaussian distribution for the set of modeling SNIa

2. Errors of the absolute magnitude for SNIa

The Statistic distribution of the absolute magnitude at maximum luminosity for SNIa

Complete date （ interval per 0.2mag）

-20 -19 -18 -17 -16 -15 -14-20

0

20

40

60

80

100

120

140

160

180

count of S

NIa

absolute magnitude

count of SNIa

)( 1515)(

max mbmbaM ph

Averaged total observational error of the distance modulus

Redo the statistics

Varies of (average) The observational error of the distance modulus with redshift of SNIa (our methord)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.2

0.25

0.3

0.35

0.4

0.45

0.5

0.55

Redshift

err

or(

mag) mean dispersion

The residual error for the distance modulus of SNIa.

10-1

100

-1.5

-1

-0.5

0

0.5

1

1.5

redshift

resid

ual dis

tance m

odulu

s

complete dataset with outlier

OmegaM=0.295

Conclusion

Conclusion

Problem on Period-luminosity relation of Cepheid variables

Thanks