Heon-Young Chang

Titius-Bode's Relation and Distribution of Exoplanets

The distance distribution in our planetary system has been a controversial matter. Two kinds of important issues on Titius-Bode’s relation have been discussed up to now: one is if there is a simple mathematical relation between distances of natural bodies orbiting a central body, and the other is if there is any physical basis for such a relation. We have examined, by applying it to exo-planetary systems, whether Titius-Bode’s relation is exclusively applicable to our solar system. We study, with the ´ 2 test, the distribution of period ratios of two planets in multiple planet systems by comparing it with that derived from not only Titius-Bode’s relation but also other forms of it. The ´ 2 value between the distribution of the orbital period derived from Titius-Bode’s relation and that observed in our Solar system is 12.28 (dof = 18) with high probability, i.e., 83.3 %. The value of ´ 2 and probability resulted from Titius-Bode’s relation and observed exo-planetary systems are 21.38 (dof = 26) and 72.2 %, respectively. Modified forms we adopted seem also to agree with the planetary system as favorably as Titius-Bode’s relation does. As a result, one cannot rule out the possibility that the distribution of the ratio of orbiting periods in multiple planet systems is consistent with that derived from Titius-Bode’s relation. Having speculated Titius-Bode’s relation could be valid in exo-planetary systems, we tentatively conclude it is unlikely that Titius-Bode’s relation explains the distance distribution in our planetary system due to chance. Finally, we point out implications of our finding.

Detection probability of a low-mass planet for triple lens events: implication of properties of binary-lens superposition

In view of the assumption that any planetary system is likely to be composed of more than one planet, and that a multiple planet system with a large-mass planet has a greater chance of detailed follow-up observations, the multiple planet system may be an efficient way to search for sub-Jovian planets. We study the central region of the magnification pattern for the triple lens system composed of a star, a Jovian mass planet and a low-mass planet to answer the question of if the low-mass planet can be detected in high-magnification events. We compare the magnification pattern of the triple lens system with that of a best-fitted binary system composed of a star and a Jovian mass planet, and check the probability of detecting the low-mass secondary planet whose signature will be superposed on that of the primary Jovian mass planet. Detection probabilities of the low-mass planet in the triple lens system are quite similar to the probability of detecting such a low-mass planet in a binary system with a star and only a low-mass planet, which shows that the signature of a low-mass planet can be effectively detected even when it is concurrent with the signature of the more massive planet, implying that the binary superposition approximation works over a relatively broad range of planet mass ratio and separations, and the inaccuracies thereof do not significantly affect the detection probability of the lower-mass secondary planet. Since the signature of the Jovian mass planet will be larger and lasting longer, thereby warranting more intensive follow-up observations, the actual detection rate of the low-mass planet in a triple system with a Jovian mass can be significantly higher than that in a binary system with a low-mass planet only. We conclude that it may be worthwhile to develop an efficient algorithm to search for ‘super-Earth’ planets in the paradigm of the triple lens model for high-magnification microlensing events.

Bimodal distribution of area-weighted latitude of sunspots and solar North–South asymmetry

Abstract We study the latitudinal distribution of sunspots observed from 1874 to 2009 using the center-of-latitude (COL). We calculate COL by taking the area-weighted mean latitude of sunspots for each calendar month. We then form the latitudinal distribution of COL for the sunspots appearing in the northern and southern hemispheres separately, and in both hemispheres with unsigned and signed latitudes, respectively. We repeat the analysis with subsets which are divided based on the criterion of which hemisphere is dominant for a given solar cycle. Our primary findings are as follows: (1) COL is not monotonically decreasing with time in each cycle. Small humps can be seen (or short plateaus) around every solar maxima. (2) The distribution of COL resulting from each hemisphere is bimodal, which can well be represented by the double Gaussian function. (3) As far as the primary component of the double Gaussian function is concerned, for a given data subset, the distributions due to the sunspots appearing in two different hemispheres are alike. Regardless of which hemisphere is magnetically dominant, the primary component of the double Gaussian function seems relatively unchanged. (4) When the northern (southern) hemisphere is dominant the width of the secondary component of the double Gaussian function in the northern (southern) hemisphere case is about twice as wide as that in the southern (northern) hemisphere. (5) For the distribution of the COL averaged with signed latitude, whose distribution is basically described by a single Gaussian function, it is shifted to the positive (negative) side when the northern (southern) hemisphere is dominant. Finally, we conclude by briefly discussing the implications of these findings on the variations in the solar activity.

Microlensing by a wide-separation planet: detectability and boundness

We explore the detection condition of a wide-separation planet through the perturbation induced by the planetary caustic for various microlensing parameters, especially for the size of the source stars. By constructing the fractional deviation maps at various positions in the space of microlensing parameters, we find that the pattern of the fractional deviation depends on the ratio of the source radius to the caustic size, and the ratio satisfying the observational threshold varies with the star-planet separation. We have also obtained the upper limits of the source size that allows the detection of the signature of the host star as a function of the separation for given observational threshold. It is shown that this relation further leads one to a simple analytic condition for the star-planet separation to detect the boundness of wide-separation planets as a function of the mass ratio and the source radius. For example, when 5% of the detection threshold is assumed, for a source star with the radius of ~1 R_sun, an Earth-mass planet and a Jupiter-mass planet can be recognized of its boundness when it is within the separation range of ~10 AU and ~30 AU, respectively. We also compare the separation ranges of detection by the planetary caustic with those by the central caustic. It is found that when the microlensing light curve caused by the planetary caustic happens to be analyzed, one may afford to support the boundness of the wide-separation planet farther than when that caused by the central caustic is analyzed. Finally, we conclude by briefly discussing the implication of our findings on the next-generation microlensing experiments.

Dependence of GCRs influx on the Solar North-South Asymmetry

Abstract We investigate the dependence of the amount of the observed galactic cosmic ray (GCR) influx on the solar North–South asymmetry using the neutron count rates obtained from four stations and sunspot data in archives spanning five solar cycles from 1953 to 2008. We find that the observed GCR influxes at Moscow, Kiel, Climax and Huancayo stations are more suppressed when the solar activity in the southern hemisphere is dominant compared with when the solar activity in the northern hemisphere is dominant. Its reduction rates at four stations are all larger than those of the suppression due to other factors including the solar polarity effect on the GCR influx. We perform the students t -test to see how significant these suppressions are. It is found that suppressions due to the solar North–South asymmetry as well as the solar polarity are significant and yet the suppressions associated with the former are larger and more significant.

Correlation Between Collimation-Corrected Peak Luminosity and Spectral Lag of Gamma-ray Bursts in the Source Frame

We revisit the relation between the peak luminosity Liso and the spectral time lag in the source frame. Since gamma-ray bursts (GRBs) are generally thought to be beamed, it is natural to expect that the collimation-corrected peak luminosity may well correlate with the spectral time lag in the source frame if the lag-luminosity relation in the GRB source frame exists. With 12 long GRBs detected by the Swift satellite, whose redshift and spectral lags in the source frame are known, we computed L0,H and L0,W using bulk Lorentz factors Γ0,H and Γ0,W archived in the published literature, where the subscripts H and W represent homogeneous and wind-like circumburst environments, respectively. We have confirmed that the isotropic peak luminosity correlates with the spectral time lag in the source frame. We have also confirmed that there is an anti-correlation between the source-frame spectral lag and the peak energy, Epeak (1 + z) in the source frame. We have found that the collimation-corrected luminosity correlates in a similar way with the spectral lag, except that the correlations are somewhat less tight. The correlation in the wind density profile seems to agree with the isotropic peak luminosity case better than in the homogeneous case. Finally we conclude by briefly discussing its implications.

The global temperature anomaly and solar North-South asymmetry

We investigate whether the global temperature anomaly is associated with the solar North-South asymmetry using data archived approximately for five solar cycles. We are motivated by both the accumulating evidence for the connection of Galactic cosmic-rays (GCRs) to the cloud coverage and recent finding of the association of GCR influx and the solar North-South asymmetry. We have analyzed the data of the observed sunspot, the GCR influx observed at the Moscow station, and the global temperature anomaly. We have found that the mean global temperature anomaly is systematically smaller (∼0.56 in the unit of its standard deviation) during the period when the solar northern hemisphere is more active than the solar southern hemisphere. The difference in the mean value of the global temperature anomaly for the two data sets sub-sampled according to the solar North-South asymmetry is large and statistically significant. We suggest the solar North-South asymmetry is related to the global temperature anomaly through modulating the amount of GCR influx. Finally, we conclude by discussing its implications on a climate model and a direction of future work.

Statistical properties of effective drought index (EDI) for Seoul, Busan, Daegu, Mokpo in South Korea

Time series of drought indices has been considered mostly in view of temporal and spatial distributions of a drought index so far. Here we investigate the statistical properties of a daily Effective Drought Index (EDI) itself for Seoul, Busan, Daegu, Mokpo for the period of 100 years from 1913 to 2012. We have found that both in dry and wet seasons the distribution of EDI as a function of EDI follows the Gaussian function. In dry season the shape of the Gaussian function is characteristically broader than that in wet seasons. The total number of drought days during the period we have analyzed is related both to the mean value and more importantly to the standard deviation. We have also found that according to the distribution of the number of occasions where the EDI values of several consecutive days are all less than a threshold, the distribution follows the exponential distribution. The slope of the best fit becomes steeper not only as the critical EDI value becomes more negative but also as the number of consecutive days increases. The slope of the exponential distribution becomes steeper as the number of the city in which EDI is simultaneously less than a critical EDI in a row increases. Finally, we conclude by pointing out implications of our findings.

On the Relation Between the Sun and Climate Change with the Solar North-South Asymmetry

We report the relation between the solar activity and terrestrial climate change with the solar north-south asymmetry. For this purpose, we calculate sliding correlation coefficients between sunspot numbers and earth`s mean annual temperature anomalies. Then, we compare the epoch that the sign of correlation changes with the epoch that the sign of the solar north-south asymmetry changes. We obtain that corresponding times are 1907 and 1985, respectively. Further more, these two epoches are well consistent with those of signs of the solar north-south asymmetry changes. We also obtain that the plot between sunspot numbers and temperature anomalies could be classified by 1907 and 1985. We conclude that temperature anomalies are shown to be negatively correlated with sunspot numbers when the southern solar hemisphere is more active: and vice versa.

Microlensing Optical Depth Revisited with Recent Star Counts

More reliable constraints on the microlensing optical depth can come from a better understanding of the Galactic model. Based on well-constrained Galactic bulge and disk models constructed from survey observations, such as those from HST, 2MASS, and SDSS, we calculate the microlensing optical depths toward Galactic bulge fields and compare them with recent results from microlensing surveys. We test the χ2 statistics of the microlensing optical depths expected from these models, as well as from previously proposed models, using two types of data: optical depth maps in (l, b) and averaged optical depth over Galactic longitude l as a function of latitude b. From this analysis, we find that the Galactic bulge models from 2MASS and Han & Gould, and model G2 of Stanek et al., show good agreement with the microlensing optical depth profiles for all the microlensing observations, compared with model E2 of Stanek et al. On the other hand, we find that models involving an SDSS disk model produce relatively higher χ2 values. It should be noted that modeled microlensing optical depths diverge at low Galactic latitudes, |b| 2°. Therefore, we suggest microlensing observations toward regions much closer to the center of the Galaxy to further test the proposed Galactic models, if technically feasible, rather than waiting for a larger data set of microlensing events.