[Paper Review] RW Tri - its Negative Superhumps and System Parameters

J. Smak|arXiv (Cornell University)|Feb 20, 2019

Geophysics and Gravity Measurements4 citations

TL;DR

This paper reports the detection of negative superhumps in RW Tri with a period of 0.2203 d, using photometric data from September 1994 and confirming earlier observations from 1957. By combining $K_2$, $V_{2, ext{rot}}\sin i$, and the negative superhump period to constrain the mass ratio, it revises the system parameters to $M_1 = 0.60 \pm 0.20 M_\odot$, $M_2 = 0.48 \pm 0.15 M_\odot$, $i = 72.5 \pm 2.5^\circ$, and $A = 1.13 \pm 0.09 \times 10^{11}$ cm, resolving inconsistencies in prior mass estimates due to irradiation corrections.

ABSTRACT

Negative superhumps are detected in the light curves of RW Tri collected in September 1994 (Smak 1995) and November/December 1957 (Walker 1963). New system parameters, obtained using $K_2$ and $V_{2,rot}\sin i$ (from Poole et al. 2003) and $q$ (estimated from $P_{nSH}$), are $M_1=0.60\pm 0.20M\odot$, $M_2=0.48\pm 0.15M\odot$, $A=1.13\pm 0.09 imes 10^{11}$cm and $i=72.5\pm 2.5$.

Motivation & Objective

• To confirm the presence of negative superhumps in RW Tri using archival photometric data from 1994 and 1957.
• To resolve inconsistencies in prior mass estimates by correcting $K_2$ for irradiation effects using a consistent mass ratio.
• To derive improved system parameters by combining $K_2$, $V_{2,\text{rot}}\sin i$, and the negative superhump period $P_{nSH}$.
• To validate the precessing, tilted disk model for negative superhumps in cataclysmic variables.

Proposed method

• Periodogram analysis of BV light curves from September 1994, with prewhitening to isolate $P_{nSH} = 0.2203$ d and $P_{\text{prec}} = 4.40$ d.
• Use of the precessing, tilted disk model to relate $P_{nSH}$, $P_{\text{orb}}$, and $P_{\text{prec}}$ via $1/P_{\text{prec}} = 1/P_{nSH} - 1/P_{\text{orb}}$.
• Application of the negative superhump amplitude $\epsilon_{nSH} = 0.050 \pm 0.006$ to derive the mass ratio $q = 0.85 \pm 0.25$ using the formula $37q(1+q)^{1/2} r_d^{3/2} = \epsilon_{nSH}/(1 + \epsilon_{nSH})$.
• Use of the $i = i(M_1)$ relation from Smak (1995) to link orbital inclination to primary mass.
• Simultaneous fitting of three constraints: $K_{2,\text{corr}}$, $V_{2,\text{rot}}\sin i$, and $\epsilon_{nSH}$, to determine $M_1$ and $M_2$ via iterative solution of mass equations.
• Re-evaluation of irradiation correction to $K_2$ using the correct $q$, yielding $\Delta K_2 = 24$ km/s, smaller than Poole et al.'s estimate.

Experimental results

Research questions

• RQ1 Does RW Tri exhibit negative superhumps, and what is their period and amplitude?
• RQ2 How do the observed $K_2$ and $V_{2,\text{rot}}\sin i$ values constrain the system's mass ratio and component masses?
• RQ3 What is the correct irradiation correction to $K_2$, and how does it affect mass estimates?
• RQ4 Can the precessing, tilted disk model explain the observed $P_{nSH}$ and $P_{\text{prec}}$?
• RQ5 What are the revised system parameters, including orbital inclination and disk radius, based on multi-constraint fitting?

Key findings

• Negative superhumps in RW Tri were confirmed with $P_{nSH} = 0.2203 \pm 0.0014$ d and $\epsilon_{nSH} = 0.050 \pm 0.006$, consistent with the precessing, tilted disk model.
• The precession period was determined as $P_{\text{prec}} = 4.40$ d, matching the observed low-frequency peak after prewhitening.
• The mass ratio was derived from $\epsilon_{nSH}$ as $q = 0.85 \pm 0.25$, providing a robust third constraint on system parameters.
• The revised system parameters are $M_1 = 0.60 \pm 0.20 M_\odot$, $M_2 = 0.48 \pm 0.15 M_\odot$, $i = 72.5 \pm 2.5^\circ$, and $A = 1.13 \pm 0.09 \times 10^{11}$ cm.
• The irradiation correction to $K_2$ was recalculated as $\Delta K_2 = 24$ km/s, significantly smaller than Poole et al.'s estimate, resolving prior inconsistencies.
• The secondary radius is $R_2 = 0.59 \pm 0.09 R_\odot$, consistent with main-sequence expectations for its mass.